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https://kk.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/finding-square-root-of-decimal	If you're seeing this message, it means we're having trouble loading external resources on our website. Егер веб фильтрлерін қолдансаң, .kastatic.org мен .kasandbox.org домендері бұғатталмағанын тексер. Негізгі бет # Ондық бөлшектің квадрат түбірі ## Видео транскрипті - Let's see if we can solve the equation P squared is equal to 0.81. So how could we think about this? Well one thing we could do is we could say, look if P squared is equal to 0.81, another way of expressing this is, that well, that means that P is going to be equal to the positive or negative square root of 0.81. Remember if we just wrote the square root symbol here, that means the principal root, or just the positive square root. But here P could be positive or negative, because if you square it, if you square even a negative number, you're still going to get a positive value. So we could write that P is equal to the plus or minus square root of 0.81, which kind of helps us, it's another way of expressing the same, the same, equation. But still, what could P be? In your brain, you might immediately say, well okay, you know if this was P squared is equal to 81, I kinda know what's going on. Because I know that nine times nine is equal to 81. Or we could write that nine squared is equal to 81, or we could write that nine is equal to the principal root of 81. These are all, I guess, saying the same truth about the universe, but what about 0.81? Well 0.81 has two digits behind, to the right of the decimal and so if I were to multiply something that has one digit to the right of the decimal times itself, I'm gonna have something with two digits to the right of the decimal. And so what happens if I take, instead of nine squared, what happens if I take 0.9 squared? Let me try that out. Zero, I'm gonna use a different color. So let's say I took 0.9 squared. 0.9 squared, well that's going to be 0.9 times 0.9, which is going to be equal to? Well nine times nine is 81, and I have one, two, numbers to the right of the decimal, so I'm gonna have two numbers to the right of the decimal in the product. So one, two. So that indeed is equal to 0.81. In fact we could write 0.81 as 0.9 squared. So we could write this, we could write that P is equal to the plus or minus, the square root of, instead of writing 0.81, I could write that as 0.9 squared. In fact I could also write that as negative 0.9 squared. Cause if you put a negative here and a negative here, it's still not going to change the value. A negative times a negative is going to be a positive. I could, actually I would have put a negative there, which would have implied a negative here and a negative there. So either of those are going to be true. But it's going to work out for us because we are taking the positive and negative square root. So this is going to be, P is going to be equal to plus or minus 0.9. Plus or minus 0.9, or we could write it that P is equal to 0.9, or P could be equal to negative 0.9. And you can verify that, you would square either of these things, you get 0.81.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8719004392623901, "perplexity": 260.55695709388186}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662564830.55/warc/CC-MAIN-20220524045003-20220524075003-00320.warc.gz"}
https://www.helpteaching.com/questions/CCSS.Math.Content.3.OA.A.2	Tweet Common Core Standard 3.OA.A.2 Questions Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. You can create printable tests and worksheets from these questions on Common Core standard 3.OA.A.2! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page. Which story could be solved with $64 -:8$? 1. Tim used all but 8 of the 64 nails. How many nails were used? 2. Mrs. Pemberton bought 64 bags of hotdog buns for the picnic. Each bag had 8 buns. How many buns did she buy? 3. Alex made 64 placemats. If he makes 8 more, how many placemats will he have made? 4. Jeff has 64 ounces of juice. Each glass holds 8 ounces. How many glasses can he have? 1. $24 -: 4 = 6$ 2. $24 -: 4 = 8$ 3. $24 -: 6 = 6$ 4. $24 -: 6 = 4$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3375127613544464, "perplexity": 2954.120108788763}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221212910.25/warc/CC-MAIN-20180817202237-20180817222237-00090.warc.gz"}
https://www.tyrrell4innovation.ca/tag/cosine-distance/	## MiWORD of the Day Is…Cosine Distance! Today we will talk about a way to measure distance, but not about how far away two objects are. Instead, cosine distance, or cosine similarity, is a measure of how similar two non-zero vectors are in terms of orientation, or to put it simply, the direction to which they point. Mathematically, the cosine similarity between two 2-D vectors is equal to the cosine of the angle between them, which can also be calculated using their dot product and magnitudes, as shown on the right. Two vectors pointing in the same direction will have a cosine similarity of 1; two vectors perpendicular to each other will have a similarity of 0; two vectors pointing in opposite direction will have a similarity of -1. Cosine distance is equal to (1 – cosine similarity). In this case, two vectors will have a cosine distance between 0 to 2: 0 when they are pointing in the same direction, and 2 when they are pointing in opposite direction. Cosine similarity and distance essentially measure the same thing, but the distance will convert any negative values to positive. Cosine distance and similarity also apply to higher dimensions, which makes them useful in analyzing images, texts, and other forms of data. In machine learning, we can use an algorithm to process a dataset of information and store each object as an array of multidimensional vectors, where each vector represents a feature. Then, we can use cosine similarity to compare how similar each pair of vectors are between the two objects and come up with an overall similarity score. In this case, two identical objects will have a similarity score of 1. In higher dimensions, we can rely on the computer to do the calculations for us. For example, we have the distance.cosine function in the SciPy package in Python will compute the cosine distance between two vector arrays in one go. Here are two examples of how you can use cosine distance in a conversation: Serious: “I copied an entire essay for my assignment and this online plagiarizing checker says my similarity score is only 1! Time to hand it in.” “It says a COSINE similarity of 1. Please go back and write it yourself…” Less serious: during a police car chase “Check how far are we from the suspect’s car!” “Well, assuming that he doesn’t turn, the distance between us will always be zero. Remember from your math class? Two vectors pointing in the same direction will always have a cosine distance of zero…” … I’ll see you in the blogosphere. Jenny Du	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.883958101272583, "perplexity": 333.46227094086987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710829.5/warc/CC-MAIN-20221201153700-20221201183700-00030.warc.gz"}
http://math.stackexchange.com/questions/115900/could-this-algorithm-detect-shortest-cycle-in-a-direct-graph	# Could this algorithm detect shortest cycle in a direct graph? Suppose I want to detect the shortest cycle in a directed graph with positive or negative weights. My idea is to run dfs on every vertex to find cycles by remembering the back edge, then storing all cycles discovered on to a stack. After that I check the cycle with the shortest length in the stack and output it. Does this algorithm work? - The first hits under "shortest cycle" are this question: stackoverflow.com/questions/3911626/… and this article: en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm. Also note that storing the cycles on a stack is wasteful if you just want to find the shortest one in the end; you only have to keep the shortest one you've found so far to do that. – joriki Mar 3 '12 at 7:23 Listing's answer assumes that by "cycle" you mean "simple cycle", i.e. a cycle without repeated vertices. Perhaps you should clarify whether that was the intended meaning. – joriki Mar 3 '12 at 10:26 Assign every edge weight $-1$. Then the shortest cycle in your digraph is the longest cycle in the unweighted digraph. Therefore computing the answer would yield the result to the np-complete directed hamilton-cycle problem. If $\text{P}\neq\text{NP}$ you can therefore find no polynomial algorithm to compute the shortest cycle. You will therefore not come around finding all cycles in the graph, a discussion on how to do this can be found here. The algorithm you describe is polynomial as far as i can tell (you essential run $n$ times dfs which is linear in time).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6458421945571899, "perplexity": 452.75794170935023}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257825048.60/warc/CC-MAIN-20160723071025-00305-ip-10-185-27-174.ec2.internal.warc.gz"}
http://en.wikipedia.org/wiki/Loop_(algebra)	# Quasigroup (Redirected from Loop (algebra)) In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative. A quasigroup with an identity element is called a loop. ## Definitions There are at least two equivalent formal definitions of quasigroup. One definition casts quasigroups as a set with one binary operation, and the other is a version from universal algebra which describes a quasigroup by using three primitive operations. We begin with the first definition, which is easier to follow. A quasigroup (Q, ) is a set Q with a binary operation (that is, a magma), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that: • a * x = b ; • y * a = b . (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup is a Latin square.) The unique solutions to these equations are written x = a \ b and y = b / a. The operations '\' and '/' are called, respectively, left and right division. The empty set equipped with the empty binary operation satisfies this definition of a quasigroup. Some authors accept the empty quasigroup but others explicitly exclude it.[1][2] ### Universal algebra Given some algebraic structure, an identity is an equation in which all variables are tacitly universally quantified, and in which all operations are among the primitive operations proper to the structure. Algebraic structures axiomatized solely by identities are called varieties. Many standard results in universal algebra hold only for varieties. Quasigroups are varieties if left and right division are taken as primitive. A quasigroup (Q, , \, /) is a type (2,2,2) algebra satisfying the identities: • y = x (x \ y) ; • y = x \ (x * y) ; • y = (y / x) * x ; • y = (y * x) / x . Hence if (Q, ) is a quasigroup according to the first definition, then (Q, , \, /) is the same quasigroup in the sense of universal algebra. ### Loop A loop is a quasigroup with an identity element, that is, an element e such that: • x * e = x and e * x = x for all x in Q. It follows that the identity element e is unique, and that every element of Q has a unique left and right inverse. Since the presence of an identity element is essential, a loop cannot be empty. A Moufang loop is a loop that satisfies the Moufang identity: • (x * y) * (z * x) = x * ((y * z) * x) . ### Total antisymmetry A quasigroup (Q, ∗) is called totally anti-symmetric if for all c, x, yQ, the following implications hold:[3] 1. (cx) ∗ y = (cy) ∗ xx = y 2. xy = yxx = y, and it is called weakly totally anti-symmetric if only the first implication holds.[3] This property is required, for example, in the Damm algorithm. ## Examples • Every group is a loop, because a * x = b if and only if x = a−1 * b, and y * a = b if and only if y = b * a−1. • The integers Z with subtraction (−) form a quasigroup. • The nonzero rationals Q× (or the nonzero reals R×) with division (÷) form a quasigroup. • Any vector space over a field of characteristic not equal to 2 forms an idempotent, commutative quasigroup under the operation x * y = (x + y) / 2. • Every Steiner triple system defines an idempotent, commutative quasigroup: a * b is the third element of the triple containing a and b. These quasigroups also satisfy (x * y) * y = x for all x and y in the quasigroup. These quasigroups are known as Steiner quasigroups.[4] • The set {±1, ±i, ±j, ±k} where ii = jj = kk = +1 and with all other products as in the quaternion group forms a nonassociative loop of order 8. See hyperbolic quaternions for its application. (The hyperbolic quaternions themselves do not form a loop or quasigroup). • The nonzero octonions form a nonassociative loop under multiplication. The octonions are a special type of loop known as a Moufang loop. • An associative quasigroup is either empty or is a group, since if there is at least one element, the existence of inverses and associativity imply the existence of an identity. • The following construction is due to Hans Zassenhaus. On the underlying set of the four-dimensional vector space F4 over the 3-element Galois field F = Z/3Z define (x1, x2, x3, x4) * (y1, y2, y3, y4) = (x1, x2, x3, x4) + (y1, y2, y3, y4) + (0, 0, 0, (x3y3)(x1y2x2y1)). Then, (F4, ) is a commutative Moufang loop that is not a group.[5] • More generally, the set of nonzero elements of any division algebra form a quasigroup. ## Properties In the remainder of the article we shall denote quasigroup multiplication simply by juxtaposition. Quasigroups have the cancellation property: if ab = ac, then b = c. This follows from the uniqueness of left division of ab or ac by a. Similarly, if ba = ca, then b = c. ### Multiplication operators The definition of a quasigroup can be treated as conditions on the left and right multiplication operators L(x), R(y): QQ, defined by \begin{align} L(x)y &= xy \\ R(x)y &= yx \\ \end{align} The definition says that both mappings are bijections from Q to itself. A magma Q is a quasigroup precisely when all these operators, for every x in Q, are bijective. The inverse mappings are left and right division, that is, \begin{align} L(x)^{-1}y &= x\backslash y \\ R(x)^{-1}y &= y/x \end{align} In this notation the identities among the quasigroup's multiplication and division operations (stated in the section on universal algebra) are \begin{align} L(x)L(x)^{-1} &= 1\qquad&\text{corresponding to}\qquad x(x\backslash y) &= y \\ L(x)^{-1}L(x) &= 1\qquad&\text{corresponding to}\qquad x\backslash(xy) &= y \\ R(x)R(x)^{-1} &= 1\qquad&\text{corresponding to}\qquad (y/x)x &= y \\ R(x)^{-1}R(x) &= 1\qquad&\text{corresponding to}\qquad (yx)/x &= y \end{align} where 1 denotes the identity mapping on Q. ### Latin squares The multiplication table of a finite quasigroup is a Latin square: an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column. Conversely, every Latin square can be taken as the multiplication table of a quasigroup in many ways: the border row (containing the column headers) and the border column (containing the row headers) can each be any permutation of the elements. See small Latin squares and quasigroups. ### Inverse properties Every loop element has a unique left and right inverse given by $x^{\lambda} = e/x \qquad x^{\lambda}x = e$ $x^{\rho} = x\backslash e \qquad xx^{\rho} = e$ A loop is said to have (two-sided) inverses if $x^{\lambda} = x^{\rho}$ for all x. In this case the inverse element is usually denoted by $x^{-1}$. There are some stronger notions of inverses in loops which are often useful: • A loop has the left inverse property if $x^{\lambda}(xy) = y$ for all $x$ and $y$. Equivalently, $L(x)^{-1} = L(x^{\lambda})$ or $x\backslash y = x^{\lambda}y$. • A loop has the right inverse property if $(yx)x^{\rho} = y$ for all $x$ and $y$. Equivalently, $R(x)^{-1} = R(x^{\rho})$ or $y/x = yx^{\rho}$. • A loop has the antiautomorphic inverse property if $(xy)^{\lambda} = y^{\lambda}x^{\lambda}$ or, equivalently, if $(xy)^{\rho} = y^{\rho}x^{\rho}$. • A loop has the weak inverse property when $(xy)z = e$ if and only if $x(yz) = e$. This may be stated in terms of inverses via $(xy)^{\lambda}x = y^{\lambda}$ or equivalently $x(yx)^{\rho} = y^{\rho}$. A loop has the inverse property if it has both the left and right inverse properties. Inverse property loops also have the antiautomorphic and weak inverse properties. In fact, any loop which satisfies any two of the above four identities has the inverse property and therefore satisfies all four. Any loop which satisfies the left, right, or antiautomorphic inverse properties automatically has two-sided inverses. ## Morphisms A quasigroup or loop homomorphism is a map f : QP between two quasigroups such that f(xy) = f(x)f(y). Quasigroup homomorphisms necessarily preserve left and right division, as well as identity elements (if they exist). ### Homotopy and isotopy Main article: Isotopy of loops Let Q and P be quasigroups. A quasigroup homotopy from Q to P is a triple (α, β, γ) of maps from Q to P such that $\alpha(x)\beta(y) = \gamma(xy)\,$ for all x, y in Q. A quasigroup homomorphism is just a homotopy for which the three maps are equal. An isotopy is a homotopy for which each of the three maps (α, β, γ) is a bijection. Two quasigroups are isotopic if there is an isotopy between them. In terms of Latin squares, an isotopy (α, β, γ) is given by a permutation of rows α, a permutation of columns β, and a permutation on the underlying element set γ. An autotopy is an isotopy from a quasigroup to itself. The set of all autotopies of a quasigroup form a group with the automorphism group as a subgroup. Each quasigroup is isotopic to a loop. If a loop is isotopic to a group, then it is isomorphic to that group and thus is itself a group. However, a quasigroup which is isotopic to a group need not be a group. For example, the quasigroup on R with multiplication given by (x + y)/2 is isotopic to the additive group (R, +), but is not itself a group. Every medial quasigroup is isotopic to an abelian group by the Bruck–Toyoda theorem. ### Conjugation (parastrophe) Left and right division are examples of forming a quasigroup by permuting the variables in the defining equation. From the original operation (i.e., x * y = z) we can form five new operations: x o y := y * x (the opposite operation), / and \, and their opposites. That makes a total of six quasigroup operations, which are called the conjugates or parastrophes of . Any two of these operations are said to be "conjugate" or "parastrophic" to each other (and to themselves). ### Paratopy If the set Q has two quasigroup operations, and ·, and one of them is isotopic to a conjugate of the other, the operations are said to be paratopic to each other. There are also many other names for this relation of "paratopy", e.g., isostrophe. ## Generalizations An n-ary quasigroup is a set with an n-ary operation, (Q, f) with f: QnQ, such that the equation f(x1,...,xn) = y has a unique solution for any one variable if all the other n variables are specified arbitrarily. Polyadic or multiary means n-ary for some nonnegative integer n. A 0-ary, or nullary, quasigroup is just a constant element of Q. A 1-ary, or unary, quasigroup is a bijection of Q to itself. A binary, or 2-ary, quasigroup is an ordinary quasigroup. An example of a multiary quasigroup is an iterated group operation, y = x1 · x2 · ··· · xn; it is not necessary to use parentheses to specify the order of operations because the group is associative. One can also form a multiary quasigroup by carrying out any sequence of the same or different group or quasigroup operations, if the order of operations is specified. There exist multiary quasigroups that cannot be represented in any of these ways. An n-ary quasigroup is irreducible if its operation cannot be factored into the composition of two operations in the following way: $f(x_1,\dots,x_n) = g(x_1,\dots,x_{i-1},\,h(x_i,\dots,x_j),\,x_{j+1},\dots,x_n),$ where 1 ≤ i < jn and (i, j) ≠ (1, n). Finite irreducible n-ary quasigroups exist for all n > 2; see Akivis and Goldberg (2001) for details. An n-ary quasigroup with an n-ary version of associativity is called an n-ary group. ### Right- and left-quasigroups A right-quasigroup (Q, , /) is a type (2,2) algebra satisfying the identities: • y = (y / x) x; • y = (y * x) / x. Similarly, a left-quasigroup (Q, , \) is a type (2,2) algebra satisfying the identities: • y = x (x \ y); • y = x \ (x * y). ## Number of small quasigroups and loops The number of isomorphism classes of small quasigroups (sequence A057991 in OEIS) and loops (sequence A057771 in OEIS) is given here:[6] Order Number of quasigroups Number of loops 0 1 0 1 1 1 2 1 1 3 5 1 4 35 2 5 1,411 6 6 1,130,531 109 7 12,198,455,835 23,746 8 2,697,818,331,680,661 106,228,849 9 15,224,734,061,438,247,321,497 9,365,022,303,540 10 2,750,892,211,809,150,446,995,735,533,513 20,890,436,195,945,769,617 11 19,464,657,391,668,924,966,791,023,043,937,578,299,025 1,478,157,455,158,044,452,849,321,016 ## Notes 1. ^ Hala O. Pflugfelder (1990). Quasigroups and loops: introduction. Heldermann Verlag. p. 2. 2. ^ Bruck, Richard Hubert (1971), A survey of binary systems, Springer, p. 1, ISBN 0-387-03497-8 3. ^ a b Damm, H. Michael (2007). "Totally anti-symmetric quasigroups for all orders n≠2,6". Discrete Mathematics 307 (6): 715–729. doi:10.1016/j.disc.2006.05.033. ISSN 0012-365X. 4. ^ Colbourn & Dinitz 2007, pg. 497, definition 28.12 5. ^ Smith, Jonathan D. H.; Romanowska, Anna B. (1999), "Example 4.1.3 (Zassenhaus's Commutative Moufang Loop)", Post-modern algebra, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, p. 93, doi:10.1002/9781118032589, ISBN 0-471-12738-8, MR 1673047. 6. ^ McKay, Brendan D.; Meynert, Alison; Myrvold, Wendy (2007). "Small Latin squares, quasigroups, and loops". J. Comb. Des. 15 (2): 98–119. doi:10.1002/jcd.20105. Zbl 1112.05018. ## References • Akivis, M. A., and Vladislav V. Goldberg (2001), "Solution of Belousov's problem," Discussiones Mathematicae. General Algebra and Applications 21: 93–103. • Bruck, R.H. (1958), A Survey of Binary Systems. Springer-Verlag. • Chein, O., H. O. Pflugfelder, and J.D.H. Smith, eds. (1990), Quasigroups and Loops: Theory and Applications. Berlin: Heldermann. ISBN 3-88538-008-0. • Colbourn, Charles J.; Dinitz, Jeffrey H. (2007), Handbook of Combinatorial Designs (2nd Edition ed.), Boca Raton: Chapman & Hall/ CRC, ISBN 1-58488-506-8 • Dudek, W.A., and Glazek, K. (2008), "Around the Hosszu-Gluskin Theorem for n-ary groups," Discrete Math. 308: 4861-4876. • Pflugfelder, H.O. (1990), Quasigroups and Loops: Introduction. Berlin: Heldermann. ISBN 3-88538-007-2. • Smith, J.D.H. (2007), An Introduction to Quasigroups and their Representations. Chapman & Hall/CRC Press. ISBN 1-58488-537-8. • Smith, J.D.H. and Anna B. Romanowska (1999), Post-Modern Algebra. Wiley-Interscience. ISBN 0-471-12738-8.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 25, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9810258746147156, "perplexity": 1207.2132528868322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657141651.17/warc/CC-MAIN-20140914011221-00229-ip-10-234-18-248.ec2.internal.warc.gz"}
https://search.r-project.org/CRAN/refmans/clock/html/calendar-boundary.html	calendar-boundary {clock} R Documentation Boundaries: calendars Description • calendar_start() computes the start of a calendar at a particular precision, such as the "start of the quarter". • calendar_end() computes the end of a calendar at a particular precision, such as the "end of the month". For both calendar_start() and calendar_end(), the precision of x is always retained. Each calendar has its own help page describing the precisions that you can compute a boundary at: Usage calendar_start(x, precision) calendar_end(x, precision) Arguments x ⁠[calendar]⁠ A calendar vector. precision ⁠[character(1)]⁠ A precision. Allowed precisions are dependent on the calendar used. Value x at the same precision, but with some components altered to be at the boundary value. Examples # Hour precision x <- year_month_day(2019, 2:4, 5, 6) x # Compute the start of the month calendar_start(x, "month") # Or the end of the month, notice that the hour value is adjusted as well calendar_end(x, "month") [Package clock version 0.6.1 Index]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8323558568954468, "perplexity": 5916.2770265019235}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499744.74/warc/CC-MAIN-20230129144110-20230129174110-00094.warc.gz"}
http://mathhelpforum.com/calculus/31651-polar-curve-area-print.html	# Polar Curve Area • March 21st 2008, 03:42 PM thegame189 Polar Curve Area Find the area inside both r=5sin(2theta) and r=5cos(2theta). I have NO idea how to do it. My book has no examples and I couldn't find anything online. I ended up trying to do the integral of (5sin(2theta))^2, evaluated from 0 to Pi/8 + the integral of (5cos(2theta))^2 evaluated from 0 to Pi/8 and then multiplying the whole thing by 8 because of symmetry. I don't believe that to be correct. Any explanations would be great! • March 21st 2008, 04:34 PM galactus One point the curves intersect in at Pi/8. If we find the area inside $5sin(2{\theta})$ from 0 to Pi/8 and multiply by 16, we can find the area of all the regions inside the two functions. $8\int_{0}^{\frac{\pi}{8}}\left[5sin(2{\theta})\right]^{2}d{\theta}$ • March 21st 2008, 04:49 PM thegame189 First, I don't understand why you disregard the 5cos(2theta) completely. Why do you only use the sin equation? I also don't understand why you multiply by 16. There are only 8 sections that are in BOTH graphs, so wouldn't you multiply by 8? Edit: Ah, I see you fixed it. I was wondering why it wasn't squared. Thanks for adding a graph, too.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9210138320922852, "perplexity": 645.1436419601646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860124045.24/warc/CC-MAIN-20160428161524-00056-ip-10-239-7-51.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-statistics/157168-probability-random-k-digit-number-contains-least-one-0-1-2-a.html	# Math Help - Probability that a random k-digit number contains at least one 0, 1, and 2 1. ## Probability that a random k-digit number contains at least one 0, 1, and 2 Let $k\geq 3$ be any given integer. What is the probability that a random k-digit number will have at least one 0, at least one 1, and at least one 2? I'm thinking that this could be answered via the principle of inclusion-exclusion, but I could use some clarification (or possible correction). Here's what I've got so far. Assuming that leading zeroes are not allowed, # of k-digits containing no 0’s: $9^k$ # of k-digits containing no 1’s: $8×9^{k-1}$ # of k-digits containing no 2’s: $8×9^{k-1}$ # of k-digits containing no 0’s and no 1’s: $8^k$ # of k-digits containing no 0’s and no 2’s: $8^k$ # of k-digits containing no 1’s and no 2’s: $7×8^{k-1}$ # of k-digits containing no 0’s, 1’s or 2’s: $7^k$ I then applied the following: $\|A\cup B\cup C\|=\|A\|+\|B\|+\|C\|-\|A\cap B\|-\|A\cap C\|-\|B\cap C\|+\|A\cap B\cap C\|$ This would obtain the complement set of what I'm looking for, so this would be subtracted from $9×10^{k-1}$. Am I on the right track? 2. You are. 3. Thanks for confirming that. I currently have the answer written out as follows: $P=(9×10^{k-1} )-[9^k+2(8×9^{k-1})-2(8^k)-(7×8^{k-1})+7^k]$ This probably isn't the cleanest way to show the answer. Is there a more condensed version I could use? 4. There is probably no shorter formula for this case.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6059905290603638, "perplexity": 658.9284939133863}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644065828.38/warc/CC-MAIN-20150827025425-00123-ip-10-171-96-226.ec2.internal.warc.gz"}
https://www.jon.hk/jon/colophon.html	# Colophon # Stack This website is built with Vuepress with various plugins. I wrote most of the content in a soup of Markdown and html tags, mostly for calling components. These tend to be templated in Jade/Pug. • Math $\pi$ and chemistry $\ce{C6H12O6\aq}$ typeset using MathJax with Martin Hensel's mhchem extension. • Flowcharts are described semantically and rendered with mermaid.js • This may be swapped with Vis.js once I wrap my head around the library and the DOT language • Search by Algolia DocSearch • 3D molecules rendered in two ways: • 3Dmol.js is used when fluid generic shape visualizations, or large systems, are needed • Robert Hanson's [JSmol] is used when measurement and scripting is needed on small molecules • biological structures pulled from Protein Data Bank and • (computed) small molecule structures from PubChem • Static hi-res molecule images from VMD • Structures computed through GAMESS, usually B3LYP / 6-311G / gas phase • UI components from Element-UI project • Graphics are penned in Adobe Illustrator / Concepts.app • (micro)interactivity and animations crafted in Haiku.AI • Typography: • Body: Cronos Pro • Color: inherits from the UWC colors # Deployment The repo lives on Github and is deployed to Netlify. # Data sources Dynamic data is ingested from Airtable databases using their (very well documented) API. # Development I primarily work in Visual Studio Code with Adobe Illustrator. The writing and drawing is supplemented on an iPad Pro, where I use Working Copy to pull from the repository, GoCoEdit to edit the files, and Concepts to do vector drawing. Help requests I would love to do MD simulations but don't know where to start. If you have pointers please get in touch with me. Last Updated: 5 months ago	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16647067666053772, "perplexity": 12762.024612580515}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314667.60/warc/CC-MAIN-20190819052133-20190819074133-00269.warc.gz"}
https://forum.bebac.at/forum_entry.php?id=20192	## SAS code for the mixed effects model with sequence mistakenly assigned [Study Assessment] Dear All, We know that the model statement in SAS for the mixed effects model to evaluate bioequivalence is model logpkp =trtseqan aperiod trtan / ..., in which the planned sequence is used. In a 2*2 BE study, if subject A with planned sequence T-R is assigned to R-T and B with planned R-T has the actual sequence of T-R， what code can we use for the model statement with these two subjects included for a sensitivity analysis?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37264615297317505, "perplexity": 5884.6588585197205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585246.50/warc/CC-MAIN-20211019074128-20211019104128-00141.warc.gz"}
https://math.stackexchange.com/questions/1705308/differentiation-and-integration?noredirect=1	# Differentiation and integration Which came first : Differentiation or Integration? If one of them was developed to solve certain types of problems, was the other developed for backward compatibility, or was it an independent development and later discovered that they were inverses? Also, how were they discovered to be linked? It was just something that I was thinking, and I would like to clarify it. (I see that this is related : History of differential and integral calculus, but no answer is present) • Answering questions like this comes down to what you mean exactly by differentiation and integration. As stated in the question you linked (and elsewhere) the ancient Greeks and Romans used techniques like the method of exhaustion. Is this a proto-integration technique? Is it a proto-limits technique? If you are meaning our modern form linked to functions then you'll get a different date/answer. – Ian Miller Mar 20 '16 at 5:58 • Not an answer, but I do know that they developed more or less independently of each other. For a long time, the connection between the two was not obvious, whereas today they are always taught as being intimately related by the fundamental theorem. Integration developed (at least in part) with the very geometric goal of finding areas under curves. – Elliot G Mar 20 '16 at 5:58 • Check out the website below. It seems like the short answer is that integration came first (in the form of areas under curves) and differentiation later (in the form of tangent lines to curves). math.ucdavis.edu/~temple/MAT16A/ArticlesOnCalculus16A/… – Elliot G Mar 20 '16 at 6:01 In a nutshell, the calculus was "discovered" or "invented" during 17th century independently by Leibniz and Newton who merged brilliantly various techniques developed since ancient Greece to solve geometrical problems. Following the development of algebra during the Reanaissance and the pubblication of Descartes' Geometry in 1637, those methods were improved and new ones were discovered: • drawing the normal to a curve: Descartes, Hudde • finding tangents: Roberval, Fermat • finding maxima and minima of curves: Fermat • the method of indivisibles: Cvalieri • arithmetical methods of integration: Wallis. See: The "official" birth of the calculus must be dated with Newton (De analysi of 1669) and Leibniz (various Ms. of 1675) independent developments: Leibniz's differential and integral calculus and Newton's fluxional calculus, though different in many aspects, each involve a clear recognition of what we now call the inverse relationship between differentiation and integration. Moreover, both men worked out a system of notations, symbols and rules through which their methods could be applied in the form of algorithms performed on formulae, rather than in the form of geometrical arguments presented in prose with reference to figures. See into: Ivor Grattan-Guinness, cit., Ch.2 Newton, Leibniz and the Leibnizian Tradition, by H.J.M. Bos, page 49-on This is similar to the chicken-and-the-egg question though relation is not as obvious in the case of integration-and-differentiation. Namely, both types of problems were already studied by Archimedes (areas of figures and volumes of solids), Apollonius (tangents to curves), and others thousands of years ago. However the inverse relationship between the integration and differentiation was not understood until Barrow (some say even earlier by James Gregory), Newton, and Leibniz.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9168841242790222, "perplexity": 1148.4531694563857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027320734.85/warc/CC-MAIN-20190824105853-20190824131853-00514.warc.gz"}
https://puzzling.stackexchange.com/questions/80847/adding-up-numbers-in-portuguese-is-strange	# Adding up numbers in Portuguese is strange My friend from Portugal said that 2 + 2 is 8 in Portuguese. And he could prove it. I did not understand it at first. But then he showed me the following equation: D O I S D O I S + ________ O I T O Ah, now it is clear. Two is "dois" and eight is "oito" in Portuguese. And the equation above makes perfect sense. Could you solve the single one solution that explain this? Rules: D, O, I, S and T are a number between 0 - 9. Each one is unique. Could it be 1246 + 1246 ------ 2492 Then D=1, O=2, I=4, S=6, T=9 • Perfect! Easy one? – Chaotic Mar 20 '19 at 4:50 • Not super easy, but there were a limited number of combinations to try. Good puzzle @Chaotic! – El-Guest Mar 20 '19 at 11:28 From $$S+S=O$$ we know $$O$$ is even. From the $$O+O$$ part, we know $$O\le4$$ because $$2O$$ doesn't carry (otherwise $$O$$ would also have to be odd). Therefore $$I$$ is doubly even ($$I=2O$$), and because $$2I$$ doesn't carry, $$I=4$$ and $$O=2$$. $$D=S\pm5$$ and $$2D$$ doesn't carry, so $$S=6$$ and $$D=1$$. $$T=2I+1=9$$. • You haven't given a value for $T$. – ZanyG Mar 20 '19 at 5:54 Let's start as a basic Brute Force Consider D as 1 Since D and S gives a Unit Place as O So,S is D+5 ;S is 6 So, Here O is 2 Given I = O + O; So,I=4 Since T is I+I with a carry of 1 ;T is 9	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7917072176933289, "perplexity": 1561.239692875355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703644033.96/warc/CC-MAIN-20210125185643-20210125215643-00404.warc.gz"}
https://www.physicsforums.com/threads/relativistic-momentum-definition.119162/	# Relativistic momentum definition 1. Apr 29, 2006 ### bernhard.rothenstein many textbooks start teaching relativistic dynamics by defining the relativistic momentum as p=dx/dtau 2. Apr 29, 2006 ### Meir Achuz It should be p=m dx/dtau. U^i=dx^i/dtau are the three spatial components of a 4-vector. The basic differential space-time 4-vector is dx^mu=(dt;dx,dy,dz) Its invariant length squared (a 4-scalar) is dtau^2=dt^2-dx^2-dy^2-dz^2. To get a 4-vector that behaves like a velocity, the 4-vector is divided by the scalar: U^mu=dx^mu/dtau. Then a 4-vector momentum is just p^mu=mU^mu. It's x,y,z components are seen to behave for small v like the NR momentum. Its time-like component is the energy. 3. Apr 29, 2006 ### bernhard.rothenstein the authors i mention say "Mermin It's about time]and many others ar far from using four vectors as far as I am. Do ou now an other explanation or it is a simple guess work? 4. Apr 29, 2006 ### nrqed The justification for defining a momentum vector is the same as in classical physics, as far as I know. It is a quantity that is conserved in a collision. This is the reason for defining it this way. After all one could define a vector $m {\vec a }$ in Newtonian physics or $m {d^2 x\over d \tau^2 }$ in SR? Of course these could be defined but they would be useless quantities. EDIT I meant ''One could define a vector $m^2 {\vec a }$ in Newtonian physics or $m^2 {d^2 x\over d \tau^2 }$ in SR but this would be useless...'' Last edited: Apr 29, 2006 5. Apr 29, 2006 ### bernhard.rothenstein you think that we should start with the classical defnition of the momentum p=mdx/dt and to search what should we do in order to bring it in accordance with special relativity? but the author I quote start with p=mdx?dtau without to offer an explanation for it. 6. Apr 29, 2006 Staff Emeritus Taylor and Wheeler, in their Spacetime Physics, do specifically derive fourmomentum from collisions under relativistic conditions. 7. Apr 29, 2006 ### nrqed I think that using collisions and looking for a quantity that is conserved is the logical way to introduce the expression for relativistic momentum. If the author just quotes the final result it's because he/she did not want to take the time to justify where it comes from. exactly the same thing happens in Newtonian physics, you know. Why does one introduce this strange vector $m {\vec v}$?? it is because one can show that the total momentum is conserved in a collision. If that was not the case, one would never introduce this quantity in the first place. Regards Patrick 8. Apr 29, 2006 ### nrqed it depends what you mean by ''bringing in accordance with SR''. If you just use the argument ''just replaces dt by dtau'' to get to SR, I would say this is unsatisfactory (my personal opinion) But if the motivation is ''now let's look at a collision in different frames taking into account the Lorentz transformations..then we see that $m {\vec v }$ is not conserved in a collision. Can we figure out a quantity which is conserved? (and that quantity will reduce to the usual expression in the nonrelativistic limit). Yes, and here it is. That's all my personal preference. If I was teaching it, this is the way I would introduce the concept. 9. Apr 29, 2006 ### Staff: Mentor And this is exactly what Mermin takes great pains (and several pages) to do in his nice little book "It's About Time". He certainly doesn't just state the relativistic definition and forget it. To bernhard.rothenstein: What book were you quoting? The only one you mentioned was Mermin's. (True, Mermin doesn't mention 4-vectors, but it's meant as a popular exposition.) 10. Apr 29, 2006 ### bernhard.rothenstein I quote from Jon Ogborn Introducing special relativity Physics Education 40 (3) 213 2005 In Newtonian mechanics momentum p=mdx/dt. The relativistic idea is that the right way to clock the motion of a particle is to use the proper (or "wristwatch time tau. So Einstein replaced dt by dtau and redefined momentum as p=mdx/dtau. The velocity v is still dx/dt so in the new definition p=m(dx/dt)(dt/dtau). We know that t=gamatau so dt/dtau. Thus the newly defined momentum is given by p=gamamv. Is that guesswork or intuition? 11. Apr 29, 2006 ### Staff: Mentor I would say brilliant intuition. But I think most of us here agree that just stating that is not sufficient, certainly not if teaching is your goal. I was just responding to a perceived slight against Mermin's book. (Mermin is an pedagogical master!) 12. Apr 29, 2006 ### bernhard.rothenstein I think in the same way. where could I find your response? 13. Apr 29, 2006 ### robphy In introductory physics, momentum is usually introduced by the impulse-momentum theorem... where it appears in an interesting difference of a quantity characterizing the system before and after the impulse. (Kinetic energy is introduced in a similar way in the work-kineticEnergy theorem.) The discussion of conservation laws comes later. Based on this, it would be great if the relativistic motivation retold this story. Otherwise, I'd suggest that the galilean-newtonian story be rewritten to parallel the relativistic one. From a top-down view, I'd look at the more abstract interpretations of momentum (say, from a Lagrangian or Hamiltonian view), then try to formulate a pedagogical story that could be paralleled in the galilean-newtonian and relativistic cases. 14. May 3, 2006 ### bernhard.rothenstein 15. May 4, 2006 ### robphy The "impulse-momentum theorem" essentially says $$\int_{t_i}^{t_f} dt \vec F_{net}=\vec p_f - \vec p_i$$, where the left-hand side is called the impulse. When introducing momentum for the first time [given Newton's Law in the constant-mass form $$\vec F_{net}=m\frac{d\vec v}{dt}$$ for a point particle], I carry out the integration of the left and define momentum as an interesting quantity associated with the system before and after the impulse. Looking over the relatively new introductory books on my shelf, I see that most books actually state a definition of $$\vec p=m\vec v$$ first, then possibly discuss its conservation, before doing the impulse-momentum theorem. Maybe the approach I used comes from [an old edition of?] Halliday-Resnick? I can't find my [old] copy now. In any case, my motivation is that it parallels the work-[kinetic-]energy theorem, which [I think] is usually introduced before defining kinetic energy and before discussing any notion of energy conservation. Until I can find my reference: http://www.google.com/search?q=+impulse+momentum+theorem	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9156693816184998, "perplexity": 1589.5988758449785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280834.29/warc/CC-MAIN-20170116095120-00013-ip-10-171-10-70.ec2.internal.warc.gz"}
http://www.conserve-energy-future.com/Advantages_NuclearEnergy.php	# Nuclear Energy Energy cannot be created nor be destroyed but it can be converted from one form to another. Nearly all the mass of the atom is concentrated in a tiny nucleus in the center. The nucleus is composed principally of two sorts of particles: the proton which carries the positive charge and the neutron which is electrically neutral and has a mass slightly bigger than that of proton. Nuclear energy is the energy released from the nucleus of an atom. When nuclear reaction occurs weather fission or fusion, it produces large amount of energy. ### How Nuclear Energy is Produced When the heaviest element, uranium was bombarded with neutrons, it was discovered that instead of inducing radioactivity as did other elements, something different happened. This process was named fission. When fission occurred, not only were two lighter elements and a lot of radiation produced, but also more neutrons. It was clear that these neutrons could in turn also cause fission, producing more neutrons and developing a chain reaction which might spread throughout all the uranium present. In the fission of uranium 235 nucleus, the amount of energy released is about 60,000,000 times as much as when a carbon atom burns. Most of the energy from fission appears as kinetic energy as the fission products shoot apart and quickly share their energy with their surroundings, thus producing heat. The first reactors to produce a usable amount of power were built at Calder hall in England. With pure fissionable material, atomic bombs can be made. Of the two bombs dropped on Japan to end the World War 2, one contained plutonium and the other very highly enriched uranium 235. 1. Lower Greenhouse Gas Emissions : As per the reports in 1998, it has been calculated the emission of the greenhouse gas has reduced for nearly half due to the popularity in the use of nuclear power. Nuclear energy by far has the lowest impact on the environment since it does not releases any gases like carbon dioxide, methane which are largely responsible for greenhouse effect. There is no adverse effect on water, land or any habitats due to the use of it. Though some greenhouse gases are released while transporting fuel or extracting energy from uranium. 2. Powerful and Efficient : The other main advantage of using nuclear energy is that it is very powerful and efficient than other alternative energy sources. Advancement in technologies has made it more viable option than others. This is one the reason that many countries are putting huge investments in nuclear power. At present, a small portion of world’s electricity comes through it. 3. Reliable : Unlike traditional sources of energy like solar and wind which require sun or wind to produce electricity, nuclear energy can be produced from nuclear power plants even in the cases of rough weather conditions. They can produce power 24/7 and need to be shut down for maintenance purposes only. 4. Cheap Electricity : The cost of uranium which is used as a fuel in generating electricity is quite low. Also, set up costs of nuclear power plants is relatively high while running cost is low. The average life of nuclear reactor range from 4.-60 years depending upon its usage. These factors when combined make the cost of producing electricity very low. Even if the cost of uranium rises, the increase in cost of electricity will be much lower. 5. Low Fuel Cost : The main reason behind the low fuel cost is that it requires little amount of uranium to produce energy. When a nuclear reaction happens, it releases million times more energy as compared to traditional sources of energy. 6. Supply : There are certain economic advantages in setting up nuclear power plants and using nuclear energy in place of conventional energy. It is one of the major sources of electricity throughout the nation. The best part is that this energy has a continuous supply. It is widely available, has huge reserves and expected to last for another 100 years while coal, oil and natural gas are limited and are expected to vanish soon. 7. Easy Transportation : Production of nuclear energy needs very less amount of raw material. This means that only about 28 gram of uranium releases as much energy as produced from 100 metric tons of coal. Since it’s required in small quantities, transportation of fuel is much easier than fossil fuels. Optimal utilization of natural resources in production of energy is a very thoughtful approach for any nation. It not only enhances the socio-economic condition but also sets example for the other countries. No doubt, nuclear energy has made its way towards the future but like other sources of energy, it also suffers from some serious drawbacks. Let’s take a look at some of its disadvantages. ### Rinkesh Rinkesh is passionate about clean and green energy. He is running this site since 2009 and writes on various environmental and renewable energy related topics. He lives a green lifestyle and is often looking for ways to improve the environment around him.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8580474257469177, "perplexity": 766.234767479289}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783402699.36/warc/CC-MAIN-20160624155002-00017-ip-10-164-35-72.ec2.internal.warc.gz"}
https://www.hepdata.net/record/82145	Precision measurement and interpretation of inclusive $W^+$, $W^-$ and $Z/\gamma^$ production cross sections with the ATLAS detector The collaboration Eur.Phys.J.C 77 (2017) 367, 2017. Abstract (data abstract) CERN-LHC. High-precision measurements by the ATLAS Collaboration are presented of inclusive $W^+\to\ell^+\nu$, $W^-\to\ell^-\bar{\nu}$ and $Z/\gamma^\to\ell\ell$ ($\ell=e,\mu$) Drell--Yan production cross sections at the LHC. The data were collected in proton--proton collisions at $\sqrt{s} = 7$ TeV with an integrated luminosity of 4.6 fb$^{-1}$. Differential $W^+$ and $W^-$ cross sections are measured in a lepton pseudorapidity range $\|\eta_{\ell}\| = 2.5$. Differential $Z/\gamma^*$ cross sections are measured as a function of the absolute dilepton rapidity, for $\|y_{\ell\ell}\| < 3.6$, for three intervals of dilepton mass, $m_{\ell\ell}$, extending from 46 to 150 GeV. The integrated and differential electron- and muon-channel cross sections are combined and compared to theoretical predictions using recent sets of parton distribution functions. The data, together with the final inclusive $e^{\pm}p$ scattering cross-section data from H1 and ZEUS, are interpreted in a next-to-next-to-leading-order QCD analysis, and a new set of parton distribution functions, ATLAS-epWZ16, is obtained. The ratio of strange-to-light sea-quark densities in the proton is determined more accurately than in previous determinations based on collider data only, and is established to be close to unity in the sensitivity range of the data. A new measurement of the CKM matrix element $\|V_{cs}\|$ is also provided. The differential cross sections are provided in two forms, a version with summarised uncertainties as in the paper tables and as "attached resource" files in HerAverager/xFitter format detailing all sources of correlated uncertainties separately. In addition to the experimental results, detailed information on the theoretical predictions are provided as required to reproduce the interpretation.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9804245233535767, "perplexity": 1031.1520460174302}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710218.49/warc/CC-MAIN-20221127073607-20221127103607-00196.warc.gz"}
https://math.stackexchange.com/questions/8337/different-methods-to-compute-sum-limits-k-1-infty-frac1k2-basel-pro/2315350	# Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) As I have heard people did not trust Euler when he first discovered the formula (solution of the Basel problem) $$\zeta(2)=\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}.$$ However, Euler was Euler and he gave other proofs. I believe many of you know some nice proofs of this, can you please share it with us? • @J.M. Thanks. But Euler could very well be a good tag I believe. – AD. Oct 30 '10 at 10:16 • Robin Chapman has a collection of proofs on his homepage: empslocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf – Hans Lundmark Oct 30 '10 at 10:32 • makes no sense to have an Euler tag... maybe Eulerian but that's pushing it. – anon Oct 30 '10 at 10:46 • Probably Robin should answer with a link to his note. I know I've pointed people to it when they ask precisely this, and they've always been more than satisfied! – Mariano Suárez-Álvarez Oct 30 '10 at 14:09 • What I like the most about this thread is that I know most of the proofs that I've seen posted up to this time, it makes me think that perhaps I was given adequate mathematical education after all :) – Asaf Karagila Nov 1 '10 at 12:57 There is a simple way of proving that $\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}$ using the following well-known series identity: $$\left(\sin^{-1}(x)\right)^{2} = \frac{1}{2}\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n^2 \binom{2n}{n}}.$$ From the above equality, we have that $$x^2 = \frac{1}{2}\sum_{n=1}^{\infty}\frac{(2 \sin(x))^{2n}}{n^2 \binom{2n}{n}},$$ and we thus have that: $$\int_{0}^{\pi} x^2 dx = \frac{\pi^3}{12} = \frac{1}{2}\sum_{n=1}^{\infty}\frac{\int_{0}^{\pi} (2 \sin(x))^{2n} dx}{n^2 \binom{2n}{n}}.$$ Since $$\int_{0}^{\pi} \left(\sin(x)\right)^{2n} dx = \frac{\sqrt{\pi} \ \Gamma\left(n + \frac{1}{2}\right)}{\Gamma(n+1)},$$ we thus have that: $$\frac{\pi^3}{12} = \frac{1}{2}\sum_{n=1}^{\infty}\frac{ 4^{n} \frac{\sqrt{\pi} \ \Gamma\left(n + \frac{1}{2}\right)}{\Gamma(n+1)} }{n^2 \binom{2n}{n}}.$$ Simplifying the summand, we have that $$\frac{\pi^3}{12} = \frac{1}{2}\sum_{n=1}^{\infty}\frac{\pi}{n^2},$$ and we thus have that $\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}$ as desired. This is, by no measure, the best nor the simplest approach, but I think the approach is pretty peculiar. We estimate the number $N(x)$ of integer solutions to $a^2+b^2+c^2+d^2\leq x$ as $x\rightarrow\infty$. On one hand, this is the number of lattice points inside the the $4$-ball of radius $\sqrt{x}$, which has volume $\frac{1}{2}\pi^2x^2$, hence $N(x)=\frac{\pi^2}{2}x^2+O(x^{3/2})$. On the other hand, let $r_4(n)$ be the number of solutions to $a^2+b^2+c^2+d^2=n$. Following the derivation in the book by Iwaniec-Kowalski, by Jacobi's four-square identity we can write $$N(x)=\sum_{n\leq x}r_4(n)=8\sum_{m\leq x}(2+(-1)^m)\sum_{dm\leq x,d\text{ odd}} d \\ =8\sum_{m\leq x}(2+(-1)^m)\left(\frac{x^2}{4m^2}+O\left(\frac{x}{m}\right)\right)\\ =2x^2\sum_{m\leq x}(2+(-1)^m)m^{-2}+O(x\log x)\\ =3x^2\zeta(2)+O(x\log x)$$ (I have copied the steps as they were in the book, it's a neat exercise to justify every transition). In particular, we have $$\zeta(2)=\lim\limits_{x\rightarrow\infty}\frac{N(x)}{3x^2}=\frac{\pi^2}{6}.$$ • (+1) I wonder if one can do the same by only exploiting the fact that the average value of $r_2(n)$ is $\pi$ by Gauss circle problem. – Jack D'Aurizio Nov 9 '17 at 4:50 by using Fourier series of $$f(x)=1, x\in[0,1]$$ $$1=\sum_{n=1}^\infty\frac{4}{(2n-1)\pi}\sin (2n-1)\pi x$$ integrate both sides when integration limits are $$x=0 \rightarrow 1$$ $$\int_{0}^{1}1.dx=\int_{0}^{1} \sum_{n=1}^\infty\frac{4}{(2n-1)\pi}\sin (2n-1)\pi x dx$$ $$1=\sum_{n=1}^\infty\frac{8}{(2n-1)^2\pi^2}$$ $$\sum_{n=1}^\infty\frac{1}{(2n-1)^2}=\frac{\pi^2}{8}$$ then we use the equality series $$\sum_{n=1}^\infty\frac{1}{n^2}=\sum_{n=1}^\infty\frac{1}{(2n-1)^2}+\sum_{n=1}^\infty\frac{1}{(2n)^2}$$ simplify it to get $$\sum_{n=1}^\infty\frac{1}{n^2}=\frac{4}{3}\sum_{n=1}^\infty\frac{1}{(2n-1)^2}$$ so, $$\sum_{n=1}^\infty\frac{1}{n^2}=\frac{4}{3}\frac{\pi^2}{8}=\frac{\pi^2}{6}$$ Let $X$ be an independent Laplace random variable with $X\sim L(0,1) = \frac12 \exp{(-\|x\|)}$, then its characteristic function : $$\varphi_X(t)=\mathbb{E}[e^{itX}]=\frac{1}{1+t^2} \newcommand{\var}[1]{\mathrm{var}\left[#1\right]}$$ By symmetry $\mathbb{E}[X]=0$ we write (generally) : $$\varphi_X(t)=\mathbb{E}[e^{itX}]=\mathbb{E}[1+itX-t^2X^2+\cdots\,]=1-\var{X}t^2+O(t^3)\tag{A}$$ since $\var{X}=\mathbb{E}[X^2]-\mathbb{E}[X]^2=\mathbb{E}[X^2]$, for our case : $$\frac{1}{1+t^2}=1-t^2+O(t^3) \rightarrow \var{X}=1$$ Now consider a set of such variables $X_n$, independent of each other, for a construction of a new random variable $Y$ as follows : $$Y=\sum_{n=1}^{\infty}\frac{X_n}{n}$$ Then, taking variance of both sides : $$\var{Y}=\var{\sum_{n=1}^{\infty}\frac{X_n}{n}}=\sum_{n=1}^{\infty}\var{\frac{X_n}{n}}=\sum_{n=1}^{\infty}\frac{\var{X_n}}{n^2}=\var{X}\zeta(2)=\zeta(2)\tag{B}$$ However, for characteristic function instead, using properities of characteristic function : $$\varphi_Y(t)=\varphi_{\sum_{n=1}^{\infty}X_n/n}\left(t\right)=\prod_{n=1}^\infty \varphi_{X}\left(\frac{t}{n}\right) = \prod_{n=1}^\infty \frac{1}{1+\frac{t^2}{n^2}}=\frac{\pi t}{\sinh \pi t} = 1-\frac{\pi^2}{6}t^2+O(t^3)\tag{C}$$ Combining it with $(A)$ and $(B)$ we get : $$\zeta(2)=\var{Y}=\frac{\pi^2}{6}$$ NOTE : As long as the set $\{X_n\}_{n\in\mathbb{N}}$ consist of independent variables with idential pdf. the steps are the same upto $\var{X}=1$. So, there might be distributions for which the product in $C$ is easily evaluable. NOTE2 : by mystake I posted just a fisrst sentence of this answer, so after deleting, this is the second copy I propose a solution... Consider for $n\in\mathbb N^$ : $$(1) : \int_0^\pi \left(\alpha t+\beta t^2\right)\cos(nt)\,\mathrm dt = \dfrac{1}{n^2}$$ Integrate by parts : $$\int_0^\pi t\cos(nt)\,\mathrm dt = \underbrace{\left.\dfrac{t\sin(nt)}{n}\right\vert_0^\pi}_{=\,0} -\int_0^\pi \dfrac{\sin(nt)}{n}\,\mathrm dt = -\underbrace{\int_0^{n\pi}\dfrac{\sin x}{n^2}\,\mathrm dx}_{\mathrm{substitution\;by\;}x=nt} = \dfrac{\cos(n\pi)-1}{n^2}$$ and $$\begin{split}\int_0^\pi t^2\cos(nt)\,\mathrm dt &= \underbrace{\left.\dfrac{t^2\sin(nt)}{n}\right\vert_0^\pi}_{=\,0} - \int_0^\pi \dfrac{2t\sin(nt)}{n}\,\mathrm dt = \left.\dfrac{2t\cos(nt)}{n^2}\right\vert_0^\pi - \int_0^\pi \dfrac{2\cos(nt)}{n^2}\,\mathrm dt \\&= \dfrac{2\pi\cos(n\pi)}{n^2} - \underbrace{\int_0^{n\pi}\dfrac{2\cos x}{n^3}\,\mathrm dx}_{\mathrm{substition\;by\;}x=nt} = \dfrac{2\pi\cos(n\pi)}{n^2}- \underbrace{\left.\dfrac{2\sin x}{n^3}\right\vert_0^{n\pi}}_{=\,0} \\&=\dfrac{2\pi\cos(n\pi)}{n^2} \end{split}$$ Thus $$\int_0^\pi \left(\alpha t+\beta t^2\right)\cos(nt)\,\mathrm dt = \alpha \cdot \dfrac{\cos(n\pi)-1}{n^2} + \beta\cdot\dfrac{2\pi\cos(n\pi)}{n^2}$$ We deduce that $\alpha = -1$ and $\beta = 1/2\pi$ satisfies $(1)$. Since for $x\in\mathbb R\backslash 2\pi\mathbb Z$ : $$\sum_{k=1}^n \cos(kx) =-\dfrac{1}{2} + \dfrac{\sin(nx+x/2)}{2\sin(x/2)}$$ we have $$\begin{split}\sum_{k=1}^n \dfrac{1}{k^2} &= \sum_{k=1}^n \int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\cos(kt)\,\mathrm dt \\&= \int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\sum_{k=1}^n \cos(kt)\,\mathrm dt\\ &= -\dfrac{1}{2}\int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\mathrm dt + \int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\cdot \dfrac{\sin(nt+t/2)}{2\sin(t/2)}\,\mathrm dt \end{split}$$ However $\sin(nt+t/2) = \sin(t/2)\cos(nt)+\sin(nt)\cos(t/2)$. Let $\phi$ and $\psi$ such that $$\phi(t) = \dfrac{t^2}{4\pi}-\dfrac{t}{2} \;\mathrm{and}\; \psi(t) = \left(\dfrac{t^2}{2\pi}-t\right)\cdot\dfrac{\cos(t/2)}{2\sin(t/2)}$$ so that $$\int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\cdot \dfrac{\sin(nt+t/2)}{2\sin(t/2)} = \int_0^\pi \phi(t)\cos(nt)\,\mathrm dt + \int_0^\pi \psi(t)\sin(nt)\,\mathrm dt$$ $\phi$ is continuous on $[0,\pi]$. And $\psi$ can be extended at $t=0$. Indeed as $t\to 0$ $$\psi(t) = \underbrace{\dfrac{t\cos(t/2)}{2\pi}}_{\to\, 0}\cdot\underbrace{\dfrac{t/2}{\sin(t/2)}}_{\to \ 1}- \underbrace{\cos(t/2)}_{\to \, 1}\cdot\underbrace{\dfrac{t/2}{\sin(t/2)}}_{\to\, 1} \xrightarrow[t\to 0]{} -1$$ Therefore, $\psi$ is continuous (by extension) on $[0,\pi]$. There remains to apply Lebesgue-Riemann Lemma, which tells us that : $$\int_0^\pi \phi(t)\cos(nt)\,\mathrm dt \xrightarrow[n\to \infty]{} 0\;\;\mathrm{and}\;\;\int_0^\pi \psi(t)\sin(nt)\,\mathrm dt\xrightarrow[n\to \infty]{} 0$$ Consequently $$\int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\cdot \dfrac{\sin(nt+t/2)}{2\sin(t/2)} \xrightarrow[n\to \infty]{} 0$$ and $$\sum_{k=1}^n \dfrac{1}{k^2} \xrightarrow[n\to \infty]{} -\dfrac{1}{2}\int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\mathrm dt$$ Now, we can evaluate this integral : $$-\dfrac{1}{2}\int_0^\pi \left(\dfrac{t^2}{2\pi}-t\right)\mathrm dt = -\dfrac{1}{2}\left[\dfrac{t^3}{6\pi}-\dfrac{t^2}{2}\right]_0^\pi = -\dfrac{1}{2}\left[\dfrac{\pi^2}{6}-\dfrac{\pi^2}{2}\right] = \dfrac{\pi^2}{6}$$ Then... the desired result : $$\boxed{\sum_{k=1}^\infty \dfrac{1}{k^2} = \dfrac{\pi^2}{6}}$$ This is a similar proof as posted by Hans Lundmark, but I find it to be a little simpler. I ran across this approach in a Dover copy of The USSR Olympiad Problem Book. It is also based on the observation that $$\cot^2x<\frac{1}{x^2}<\csc^2x\,.$$ We first have the trig identity $$\sin(2n+1)\alpha=\sum_{k=0}^n(-1)^k\binom{2n+1}{2k+1}\cos^{2(n-k)}\alpha\sin^{2k+1}\alpha$$ which is arguably the hardest part of this proof. This directly manipulates into $$\sin(2n+1)\alpha=\sin^{2n+1}\alpha\sum_{k=0}^n(-1)^k\binom{2n+1}{2k+1}\cot^{2(n-k)}\alpha\,.$$ This formula reveals that the $n$ distinct quantities below $$\cot^2\frac{\pi}{2n+1},\quad\cot^2\frac{2\pi}{2n+1},\quad\ldots,\quad\cot^2\frac{n\pi}{2n+1}$$ are the roots of the polynomial $$\sum_{k=0}^n(-1)^k\binom{2n+1}{2k+1}x^{n-k}\,.$$ After scaling by the lead coefficient, Viete's Formulas then imply that $$\sum_{k=1}^n \cot^2\frac{k\pi}{2n+1}=\frac{n(2n-1)}{3}$$ By another elementary trig identity, we also get $$\sum_{k=1}^n \csc^2\frac{k\pi}{2n+1}=\frac{2n(n+1)}{3}$$ The inequality above then gives us $$\frac{n(2n-1)}{3}<\frac{(2n+1)^2}{\pi^2}\left(1+\frac{1}{2^2}+\cdots+\frac{1}{n^2}\right)<\frac{2n(n+1)}{3}$$ which gives us the desired conclusion after taking limits. • I later found out that this is one of the three different proofs of the Basel Problem that was presented in "Proofs from the Book". – user123641 May 1 '18 at 15:54 I would like to present you a method I found recently here. Let $A_n=\int_0^{\pi/2}\cos^{2n}x\;\mathrm{d}x$ and $B_n=\int_0^{\pi/2}x^2\cos^{2n}x\;\mathrm{d}x$. The first integral is well known, by per partes we get the recurecnce relation : $$A_{n}=\frac{2n-1}{2n}A_{n-1}\tag{1}$$ By per partes for the second integral: $$A_n=\int_0^{\pi/2}\cos^{2n}x\;\mathrm{d}x=x\cos^{2n}x\bigg{\|}_0^{\pi/2}-\frac{x^2}{2}(\cos^{2n}x)'\bigg{\|}_0^{\pi/2}+\frac{1}{2}\int_0^{\pi/2}x^2(\cos^{2n}x)''\;\mathrm{d}x$$ First two terms vanish, so we are left only with the integral and since $(\cos^{2n}x)''=2n(2n-1)\cos^{2n-2}x-4n^2\cos^{2n}x$ we have : $$A_n=(2n-1)nB_{n-1}-2n^2B_{n}\tag{2}$$ for $n\geq 1$. Rearranging and substituing $(2n-1)=2n\frac{A_n}{A_{n-1}}$ from $(1)$ we get : $$\frac{1}{n^2}=2\frac{B_{n-1}}{A_{n-1}}-2\frac{B_n}{A_n}\tag{3}$$ Summing from $1$ to some $k$ natural we get by telescoping property $$\sum_{n=1}^k\frac{1}{n^2}=2\frac{B_0}{A_0}-2\frac{B_k}{A_k}=\frac{\pi^2}{6}-2\frac{B_k}{A_k}\tag{4}$$ Next, using the inequality $\sin x\geq \frac{2x}{\pi}$ on $(0,\frac{\pi}{2})$ and by $(1)$ : $$\frac{4}{\pi^2}B_{n-1}=\frac{4}{\pi^2}\int_0^{\pi/2}x^2\cos^{2n-2}x\;\mathrm{d}x<\int_0^{\pi/2}\sin^2x\cos^{2n-2}x\;\mathrm{d}x=A_{n-1}-A_n=\frac{A_{n-1}}{2n}$$ so in the limit the last term vanishes by the sqeeze theorem, so we are left with $$\sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6}\tag{4}$$ That concludes the result. • I think you mean $\sin x\geq 2x/\pi$. But this is a clever approach. Another reason to appreciate integration by parts. – user123641 Jun 9 '17 at 0:51 • Thanks for sharing, very easy to follow and totally new to me. Fixed the typo mentioned by @Bryan. – AD. Jun 9 '17 at 10:11 Here is an interesting solution that evaluates three sums, one of which is $\zeta(2).$ $$\tag{1}\label{Double Integral} \int_{0}^{1} \int_{0}^{\sqrt{1-x^2}} \frac{1}{\sqrt{x^2+y^2} \ (1+x^2+y^2)} \ dy \ dx.$$ A quick polar coordinates transformation $x=r \cos(\theta), y= r \sin(\theta)$ transforms \eqref{Double Integral} into $$\int_{0}^{\frac{\pi}{2}}\int_{0}^{1} \frac{1}{1+r^2} \ dr \ d \theta=\frac{\pi^2}{8}.$$ Hence, \eqref{Double Integral} is equal to $\frac{\pi^2}{8}.$ Now integrate \eqref{Double Integral} with respect to $y$ using the fact $$\int \frac{1}{\sqrt{x^2+y^2} (1+x^2+y^2)} \ dy = \frac{\tanh^{-1} \left( \frac{y}{\sqrt{1+x^2}\sqrt{x^2+y^2}} \right)}{\sqrt{1+x^2}}$$ to see that \eqref{Double Integral} becomes $$\tag{2} \label{arctanh} \int_{0}^{1} \frac{\tanh^{-1} \left( \frac{\sqrt{1-x^2}}{\sqrt{1+x^2}} \right)}{\sqrt{1+x^2}} \ dx.$$ Next, observe that \eqref{arctanh} is equal to the double integral $$\tag{3} \label{double integral 2} \int_{0}^{1} \int_{0}^{\sqrt{1-x^2}} \frac{1}{1+x^2-y^2} \ dy \ dx,$$ which can be confirmed by integrating the inner integral of \eqref{double integral 2} with respect to $y.$ Now here comes the interesting part. Use polar coordinates with $x=r\cos(\theta),y=r\sin(\theta)$ on \eqref{double integral 2} and then with $x=r\sin(\theta),y=r\cos(\theta)$ on \eqref{double integral 2} and average the two to see that \eqref{double integral 2} is the same as $$\frac{1}{2}\int_{0}^{\frac{\pi}{2}} \int_{0}^{1} \frac{r}{1+r^2\cos(2\theta)} \ dr \ d \theta + \frac{1}{2}\int_{0}^{\frac{\pi}{2}} \int_{0}^{1} \frac{r}{1-r^2\cos(2\theta)} \ dr \ d \theta \,$$ which simplifies down to \begin{align} \int_{0}^{\frac{\pi}{2}} \frac{\ln(1+\cos(2\theta))}{4\cos(2\theta)}-\frac{\ln(1-\cos(2\theta))}{4\cos(2\theta)} \ d \theta & = \int_{0}^{\frac{\pi}{2}} \frac{\ln \left(\frac{1+\cos(2\theta)}{1-\cos(2\theta)} \right)}{4\cos(2\theta)} \ d \theta\\ & = \int_{0}^{\frac{\pi}{2}} -\frac{\ln(\tan^2(\theta))}{4\cos(2\theta)} \ d \theta \tag{4} \label{double angle} \\ & = \int_{0}^{\infty} \frac{\ln(u)}{2(u^2-1)} \ du \tag{5} \label{pi^2/4} \end{align} with \eqref{double angle} following from simplifying the logarithmic term with the double angle formulas $$\sin^2(\theta)=\frac{1-\cos(2\theta)}{2}, \quad \cos^2(\theta)=\frac{1+\cos(2\theta)}{2},$$ and \eqref{pi^2/4} following from the substitution $u=\tan(\theta).$ Splitting \eqref{pi^2/4} into $$\int_{0}^{1} \frac{\ln(u)}{2(u^2-1)} \ du + \int_{1}^{\infty} \frac{\ln(u)}{2(u^2-1)} \ du,$$ a substitution $u=\frac{1}{t}$ on the second term shows \eqref{pi^2/4} is equal to $$2 \int_{0}^{1} \frac{\ln(u)}{2(u^2-1)} \ du = \int_{0}^{1} \frac{\ln(u)}{u^2-1} \ du.$$ Hence, we have \begin{align} \tag{6} \label{pi^2/8} \int_{0}^{1} \frac{\ln(u)}{u^2-1} \ du = \frac{\pi^2}{8} \end{align} Now following the other users' answers, convert the integrand in the left hand side of \eqref{pi^2/8} into a geometric series, apply the Monotone Convergence Theorem to interchange sum and integral, to see we have $$\sum_{n=0}^{\infty} \frac{1}{(2n+1)^2} = \frac{\pi^2}{8},$$ and observing \begin{align} \zeta(2) & =\sum_{n=1}^{\infty} \frac{1}{(2n)^2}+ \sum_{n=0}^{\infty} \frac{1}{(2n+1)^2} \\ & = \frac{1}{4} \zeta(2) + \frac{\pi^2}{8}, \end{align} we see $$\zeta(2)=\frac{\pi^2}{6}.$$ Those are the first two sums. We refer back to \eqref{arctanh}. Make the substitution $u=\sqrt{\frac{{1-x^2}}{{1+x^2}} }$ and simplify to see \eqref{arctanh} becomes to get: $$\tag{7} \label{complicated sub} \int_{0}^{1} \frac{\sqrt{2} u\tanh^{-1}(u)}{\sqrt{1-u^2}(1+u^2)}\ du.$$ Substituting $u=\tanh(\theta)$ transforms \eqref{complicated sub} into \begin{align} \sqrt{2}\int_{0}^{\infty}\frac{\theta(e^{2\theta}-1)}{e^{4\theta}+1}\ d\theta \end{align} and substituting $z=e^{\theta}$ shows that \eqref{arctanh} is the same as $$\sqrt{2}\int_{1}^{\infty}\frac{(z^2-1)\ln(z)}{z^4+1}\ dz,$$ and splitting the region of integration as with \eqref{pi^2/4} to get \eqref{pi^2/8}, we see \eqref{arctanh} is $$\tag{7} \label {crazy integral} \sqrt{2}\int_{0}^{1}\frac{(t^2-1)\ln(t)}{t^4+1}\ dt.$$ Expanding this integrand into a geometric series and integrating term by term, we see that \begin{align}\frac{\pi^2}{8} & =\sqrt{2}\left(\sum_{n=0}^{\infty}\frac{(-1)^n}{(4n+1)^2}-\frac{(-1)^n}{(4n+3)^2}\right) \\ & =\sqrt{2}\sum_{n=0}^{\infty}\frac{(-1)^n}{(4n+1)^2} +\sqrt{2} \sum_{n=-\infty}^{-1}\frac{(-1)^n}{(4n+1)^2} \\ & = \sqrt{2}\sum_{n=-\infty}^{\infty}\frac{(-1)^n}{(4n+1)^2}. \end{align} Thus, \begin{align} \sum_{n=-\infty}^{\infty}\frac{(-1)^n}{(4n+1)^2}=\frac{\pi^2}{8\sqrt{2}}, \end{align} which is the third sum. Following proof rely on this integral identity : $$\int_{a}^{1}\frac{\arccos x}{\sqrt{x^2-a^2}}\mathrm{d}x=-\frac{\pi}{2}\ln a\qquad ;\,a\in(0,1]$$ We will prove it later on. Now, let's make a power series : $$\zeta(2)=\sum_{n=1}^{\infty}\frac{1}{n^2}=\int_0^1\frac{1}{x}\sum_{n=1}^{\infty}\frac{x^n}{n}\,\mathrm{d}x=-\int_0^1\frac{\ln(1-x)}{x}\,\mathrm{d}x=-\int_0^1\frac{\ln x}{1-x}\,\mathrm{d}x$$ Inserting the formula above we get : $$\zeta(2)=\frac{2}{\pi}\int_0^1\int_{x}^{1}\frac{\arccos y}{(1-x)\sqrt{y^2-x^2}}\,\mathrm{d}y\,\mathrm{d}x$$ Interchanging the order of integration : $$\zeta(2)=\frac{2}{\pi}\int_0^1\int_{0}^{y}\frac{\arccos y}{(1-x)\sqrt{y^2-x^2}}\,\mathrm{d}x\,\mathrm{d}y\tag{A}$$ But, with help of substitution $x=y \cos{\theta}$ and universal $t=\tan\frac{\theta}{2}$ : $$\int_{0}^{y}\frac{\mathrm{d}x}{(1-x)\sqrt{y^2-x^2}}=\int_{0}^{\frac{\pi}{2}}\frac{\mathrm{d}\theta}{1-y \cos{\theta}}=\int_{0}^{1}\frac{\frac{2\mathrm{d}t}{1+t^2}}{1-y\frac{1-t^2}{1+t^2}}=\frac{\pi-\arccos{y}}{\sqrt{1-y^2}}$$ Plugging this to $(A)$ we get : \begin{align}&\zeta(2)=\frac{2}{\pi}\int_{0}^{1}\frac{\pi\arccos{y}-\arccos^2 y}{\sqrt{1-y^2}}\,\mathrm{d}y=\frac{2}{\pi}\left(\frac{\pi}{2}\arccos^2 y- \frac{1}{3}\arccos^3 y\right)\bigg{\|}_{1}^{0}= \\ \\ &\frac{2}{\pi}\left(\frac{\pi}{2}\left(\frac{\pi}{2}\right)^2-\frac{1}{3}\left(\frac{\pi}{2}\right)^3\right) = \frac{2}{\pi}\left(\frac{\pi}{2}\right)^3 \left(1-\frac{1}{3}\right) =\frac{\pi^2}{6} \end{align} ADDENDUM : Proof of the apriori integral : \begin{align}&\int_{a}^{1}\frac{\arccos x}{\sqrt{x^2-a^2}}\mathrm{d}x=\int_{a}^{1}\frac{\arccos\left(\frac{x}{y}\right)}{\sqrt{x^2-a^2}}\bigg{\|}_{y=x}^{y=1}\mathrm{d}x=\int_{a}^{1}\int_{x}^{1}\frac{x}{y}\frac{\mathrm{d}y\,\mathrm{d}x}{\sqrt{x^2-a^2}\sqrt{y^2-x^2}} = \\ \\ & \int_{a}^{1}\int_{a}^{y}\frac{x}{y}\frac{\mathrm{d}x\,\mathrm{d}y}{\sqrt{x^2-a^2}\sqrt{y^2-x^2}} = \frac{\pi}{2}\int_{a}^{1}\frac{\mathrm{d}y}{y} = -\frac{\pi}{2}\ln a \end{align} Where the inner integral was computed via substitution $x^2=a^2\cos^2\theta+y^2\sin^2\theta$ it is clear, taking differential, that $2x\;\mathrm{d}x=2\left(y^2-a^2\right)\sin\theta\cos\theta\;\mathrm{d}\theta$, then : $$(x^2-a^2)(y^2-x^2)=(a^2\cos^2\theta+y^2\sin^2\theta-a^2)(y^2-a^2\cos^2\theta-y^2\sin^2\theta)=(y^2\sin^2\theta-a^2\sin^2\theta)(y^2\cos^2\theta-a^2\cos^2\theta)=(y^2-a^2)^2\sin^2\theta\cos^2\theta$$ Or $$\sqrt{x^2-a^2}\sqrt{y^2-x^2}= \left(y^2-a^2\right)\sin\theta\cos\theta\ = x\,\mathrm{d}x$$ Therefore : $$\int_{a}^{y}\frac{x\,\mathrm{d}x}{\sqrt{x^2-a^2}\sqrt{y^2-x^2}}=\int_{0}^{\frac{\pi}{2}}\frac{x\,\mathrm{d}x}{x\,\mathrm{d}x}=\frac{\pi}{2}$$ \begin{align} \log(2\cos(x)) &=\log\left(e^{ix}+e^{-ix}\right)\tag{1a}\\ &=ix+\log\left(1+e^{-2ix}\right)\tag{1b}\\ &=-ix+\log\left(1+e^{2ix}\right)\tag{1c}\\ &=\cos(2x)-\frac{\cos(4x)}2+\frac{\cos(6x)}3-\cdots\tag{1d} \end{align} Explanation: $$\text{(1a)}$$: $$2\cos(x)=e^{ix}+e^{-ix}$$ $$\text{(1b)}$$: factor out $$e^{ix}$$ $$\text{(1c)}$$: factor out $$e^{-ix}$$ $$\text{(1d)}$$: average $$\text{(1b)}$$ and $$\text{(1c)}$$ using the power series for $$\log(1+x)$$ \begin{align} \sum_{k=1}^\infty\frac1{k^2} &=\frac1{2\pi}\int_0^{2\pi}\sum_{k=1}^\infty\frac{e^{ikx}}k\sum_{k=1}^\infty\frac{e^{-ikx}}k\,\mathrm{d}x\tag{2a}\\ &=\frac1{2\pi}\int_0^{2\pi}\left\|\log(1-e^{ix})\right\|^2\,\mathrm{d}x\tag{2b}\\ &=\frac1{2\pi}\int_{-\pi}^\pi\left\|\log(1+e^{ix})\right\|^2\,\mathrm{d}x\tag{2c}\\ &=\frac1{2\pi}\int_{-\pi}^\pi\left\|\,\log\left(2\cos\left(\frac x2\right)\right)+\frac{ix}2\,\right\|^{\,2}\,\mathrm{d}x\tag{2d}\\ &=\frac1{2\pi}\int_{-\pi}^\pi\left(\log\left(2\cos\left(\frac x2\right)\right)^2+\frac{x^2}4\right)\,\mathrm{d}x\tag{2e}\\ &=\frac{\pi^2}{12}+\frac1{2\pi}\int_{-\pi}^\pi\left(\cos(x)-\frac{\cos(2x)}2+\frac{\cos(3x)}3-\cdots\right)^2\,\mathrm{d}x\tag{2f}\\ &=\frac{\pi^2}{12}+\frac12\sum_{k=1}^\infty\frac1{k^2}\tag{2g}\\ &=\frac{\pi^2}6\tag{2h} \end{align} Explanation: $$\text{(2a)}$$: use the orthogonality of $$e^{ijx}$$ and $$e^{ikx}$$ when $$j\ne k$$ $$\text{(2b)}$$: use the power series for $$\log(1+x)$$ $$\text{(2c)}$$: substitute $$x\mapsto x+\pi$$ $$\text{(2d)}$$: $$1+e^{ix}=2\cos(x/2)e^{ix/2}$$ $$\text{(2e)}$$: $$\left\|\,x+iy\,\right\|^2=x^2+y^2$$ $$\text{(2f)}$$: apply $$(1)$$ $$\text{(2g)}$$: use the orthogonality of $$\cos(jx)$$ and $$\cos(kx)$$ for $$j\ne k$$ $$\text{(2h)}$$: subtract the original from twice $$\text{(2g)}$$ • This is fantastic – Cade Reinberger Jul 9 '19 at 4:28 Using Fourier's expansion of $f(x)=x(1-x)$, we get $$a_{0}=\frac{1}{6}$$ $$a_{n}=\frac{1}{n^2\pi^2}$$ $$b_{n}=0$$ Therefore ,we have $$x(1-x)=\frac{1}{6}-\sum_{n=1}^{\infty}\frac{\cos2xn\pi}{(n\pi)^2}$$ putting $x=0$ we get $$\sum _{k=1}^{\infty} \frac{1}{k^2} = \frac{\pi^2}{6}$$ Define $f$ on $[0;2\pi]$, $\displaystyle f(a)=\int_0^1 \dfrac{\ln(x^2-2x\cos(a)+1)}{x}dx\tag 0$ Theorem: For all $a\in [0;2\pi]$, $f(a)=-\dfrac{1}{2}a^2+\pi a-\dfrac{\pi^2}{3}\tag 1$ For all $a\in [0;2\pi]$, $\displaystyle f\left(\frac{a}{2}\right)+f\left(\pi-\frac{a}{2}\right)=\frac{f(a)}{2}\tag 2$ Proof: \begin{align} f\left(\frac{a}{2}\right)+f\left(\pi-\frac{a}{2}\right)&=\int_0^1 \frac{\ln\left(\left(x^2-2x\cos\left(\frac{a}{2}\right)+1\right)\left(x^2+2x\cos\left(\frac{a}{2}\right)+1\right) \right)}{x}dx\\ &=\int_0^1 \frac{\ln\left(x^4-2x^2\cos(a)+1\right)}{x}dx\\ \end{align} Perform the change of variable $y=x^2$ in the latter integral to obtain (2). According to theorems about functions défined by integrals $f^{\prime\prime}$ exists and it is continuous. Derive twice (2), For all $a\in [0;2\pi]$, $\displaystyle f^{\prime\prime}\left(\frac{a}{2}\right)+f^{\prime\prime}\left(\pi-\frac{a}{2}\right)=2f^{\prime\prime}(a)\tag 3$ $f^{\prime\prime}$ is continuous on $[0;2\pi]$ therefore this fonction has a maximum $M$ and a minimum $m$ that are obtainable. Therefore it exists $a_0\in[0;2\pi]$ such that $f^{\prime\prime}(a_0)=M$. Plug $a_0$ into (3), $\displaystyle f^{\prime\prime}\left(\frac{a_0}{2}\right)+f^{\prime\prime}\left(\pi-\frac{a_0}{2}\right)=2f^{\prime\prime}(a_0)=2M$ But, $f^{\prime\prime}\left(\frac{a_0}{2}\right)\leq M$ et $f^{\prime\prime}\left(\pi-\frac{a_0}{2}\right)\leq M$ according to the définition of $M$. therefore $f^{\prime\prime}\left(\frac{a_0}{2}\right)=f^{\prime\prime}\left(\pi-\frac{a_0}{2}\right)=M$ By recurrence reasoning, for all $n\geq 1$, natural integer, $f^{\prime\prime}\left(\frac{a_0}{2^n}\right)=M\tag 4$ $f^{\prime\prime}$ is continuous in $0$ therefore taking $n$ to infinity in (4) one obtains, $M=f^{\prime\prime}(0)$. Considering $m$ the minimum of $f^{\prime\prime}$ using the same way it can be proved that, $m=f^{\prime\prime}(0)$ Since $m=M$, therefore $f^{\prime\prime}$ is a constant function. therefore, there exist $\alpha,\beta,\gamma$ real such that, For all $a\in[0;2\pi]$, $f(a)=\alpha a^2+\beta a+\gamma\tag 5$ Plug (5) into (3), one obtains: $\alpha\pi+\dfrac{\beta}{2}=0$ and $\alpha \pi^2 +\beta \pi+\dfrac{3}{2}\gamma=0$ On the other hand, for all $a\in [0;2\pi]$, $\displaystyle f^\prime(a)= 2\sin a\int_0^1\dfrac{1}{x^2-2x\cos a+1}dx$ If $a=\dfrac{\pi}{2}$ one obtains, \begin{align} f^\prime\left(\dfrac{\pi}{2}\right)&=2\int_0^1 \dfrac{1}{x^2+1}dx\\ &=2\times \dfrac{\pi}{4}\\ &=\dfrac{\pi}{2} \end{align} Taking derivative of (5), one obtains for all $a\in [0;2\pi]$, $f^\prime(a)=2\alpha a+\beta$ Therefore, $\alpha \pi +\beta=\dfrac{\pi}{2}$ One have obtained a linear system of three equations in $\alpha,\beta,\gamma$. To achieve the proof of the theorem solve it. To get the value of $\zeta(2)$, apply the theorem with $a=0$, one obtains, $\displaystyle \int_0^1 \dfrac{\ln(1-x)}{x}dx=-\dfrac{\pi^2}{6}$ And then, continue in usual way, expand the integrand... From, Euler's integrals, H. Haruki and S. Haruki, The mathematical gazette, 1983. • This one is very simple and straightforward to follow. However, I would like to see the argument for continuity for the second derivative $f''(x)$ to be more explained (or am I so blind to see it?). – Machinato Aug 25 '17 at 12:20 • It uses general theorems about derivation under the integral sign as Lebesgue's dominated convergence theorem (but weaker theorems do exist for the Riemann integral). – FDP Aug 25 '17 at 17:21 I really like this one. Consider $f(x)=x^2-\pi^2$. Compute it's Fourier expansion to obtain $$f(x)=\frac{2}{3}\pi^2-4\sum_{n=1}^\infty\frac{(-1)^n}{n^2}\cos nx.$$ Now let $x=\pi$, then it quickly follows that $$4\zeta(2)=\frac{2}{3}\pi^2\implies \zeta(2)=\frac{\pi^2}{6}.$$ • This is the same as the first part of this one. – AD. Oct 24 '16 at 12:31 I found this proof on YouTube but I did little changes: \begin{align} I&=\int_0^{\pi/2}\ln(2\cos x)\ dx=\int_0^{\pi/2}\ln\left(e^{ix}(1+e^{-2ix})\right)\ dx\\ &=\int_0^{\pi/2}ix\ dx-\sum_{n=1}^\infty \frac{(-1)^n}{n}\int_0^{\pi/2}e^{-2ix}\ dx\\ &=\frac{\pi^2}{8}i-\sum_{n=1}^\infty\frac{(-1)^n}{n}\left(-\frac{(-1)^n-1}{2in}\right)\\ &=\frac{\pi^2}{8}i-\frac12i\left(\zeta(2)-\operatorname{Li}_2(-1)\right)\\ &=\frac{\pi^2}{8}i-\frac12i\left(\zeta(2)+\frac12\zeta(2)\right)\\ &=i\left(\frac{\pi^2}{8}-\frac34\zeta(2)\right) \end{align} By comparing the imaginary parts, we have $$0=\frac{\pi^2}{8}-\frac34\zeta(2)\Longrightarrow\zeta(2)=\frac{\pi^2}{6}$$ Let $$f(x)=\frac 12-x$$ on the interval $$[0, 1)$$, and extend $$f$$ to be periodic on $$\mathbb{R}$$. By definition, \begin{align} \hat f(0)=\int_0^1 f(x)dx=\int_0^1 \left(\frac 12-x\right)dx=0. \end{align} And for $$\kappa\ne 0$$: \begin{align} \hat f(\kappa)&=\int_{0}^{1}f(x)e^{-2\pi i\kappa x }dx=\int_0^1\left( \frac 12 -x \right)e^{-2\pi i\kappa x}dx=-\int_0^1xe^{-2\pi i \kappa x}dx\\ &=\frac{1}{2\pi i\kappa }\int_{0}^{1}xd(e^{-2\pi i\kappa x})=\left.\frac{1}{2\pi i\kappa}xe^{-2\pi i\kappa x}\right\|_0^1+\frac{1}{2\pi i\kappa}\int_0^1 e^{-2\pi i\kappa x}dx\\ &=\frac{1}{2\pi i\kappa}. \end{align} By the Parseval identity \begin{align} \int_{0}^{1}\|f(x)\|^2dx=\sum_{k=-\infty}^{\infty}\|\hat{f}(k)\|^2=\|\hat{f}(0)\|^2+2\sum_{k=1}^{\infty}\|\hat{f}(k)\|^2=2\sum_{k=1}^{\infty}\frac{1}{4\pi^2 k^2}. \end{align} On the other hand, \begin{align} \int_{0}^{1}\|f(x)\|^2dx&=\int_{0}^{1}\left( \frac{1}{2}-x \right)^2 dx=\frac 14-\frac 12+\frac 13=\frac 1{12}. \end{align*} Hence, we have $$\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}.$$ Remark: This is an exercise(Chapter 8.13 on page 254 ) in Folland's book. Here's mine. I'm answering late, I know that, but I am still answering it. We'll use the expansion of $$\tanh^{-1}$$: $$\frac{1}{2}\log\frac{1+y}{1-y}=\sum_{n\geq0}\frac{y^{2n+1}}{2n+1},\quad\|y\|<1$$ We start with this inequality: $$\int_{-1}^{1}\int_{-1}^{1}\frac{1}{1+2xy+y^2}dy\,dx=\int_{-1}^{1}\frac{1}{1+2xy+y^2}dx\,dy$$ The LHS of this equality gives: $$\int_{-1}^{1}\int_{-1}^{1}\frac{1}{1+2xy+y^2}dy\,dx=\int_{-1}^{1}\frac{\arctan \frac{x+y}{\sqrt{1-x^2}}}{\sqrt{1-x^2}}dx\Biggr\|_{y=-1}^{y=1}\\ \quad\,\,\quad\quad\quad\quad\quad\quad\quad\quad\quad=\int_{-1}^{1}\frac{\pi}{2\sqrt{1-x^2}}dx=\frac{\pi^2}{2}$$ The RHS of the former equality yields: \begin{align} \int_{-1}^{1}\int_{-1}^{1}\frac{1}{1+2xy+y^2}dy\,dx&=\int_{-1}^{1}\frac{\log(1+2xy+y^2)}{2y}dy\Biggr\|_{x=-1}^{x=1}\\ &=\int_{-1}^{1}\frac{\log\frac{1+y}{1-y}}{y}dy\\ &=2\int_{-1}^{1}\sum_{n\geq0}\frac{y^{2n}}{2n+1}dy\\ &=4\sum_{n\geq0}\frac{1}{(2n+1)^2} \end{align} Hence, $$\sum_{r\geq0}\frac{1}{(2n+1)^2}=\frac{\pi^2}{8}$$ Now $$\frac{3}{4}\zeta(2)=\zeta(2)-\frac{1}{4}\zeta(2)=\sum_{n\geq 1}\frac{1}{n^2}=\sum_{m\geq1}\frac{1}{(2m)^2}=\sum_{r\geq0}\frac{1}{(2r+1)^2}=\frac{\pi^2}{8}$$ Solving this we get $$\zeta(2)=\frac{\pi^2}{6}$$ as desired. Source:https://www.emis.de/journals/GM/vol16nr4/ivan/ivan.pdf Here are more proofs.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 61, "wp-katex-eq": 0, "align": 12, "equation": 5, "x-ck12": 0, "texerror": 0, "math_score": 0.9971717596054077, "perplexity": 676.5329122045805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141188899.42/warc/CC-MAIN-20201126171830-20201126201830-00716.warc.gz"}
https://www.ademcetinkaya.com/2023/02/ptpi-petros-pharmaceuticals-inc-common.html	Outlook: Petros Pharmaceuticals Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Time series to forecast n: 11 Feb 2023 for (n+6 month) Methodology : Multi-Instance Learning (ML) ## Abstract Petros Pharmaceuticals Inc. Common Stock prediction model is evaluated with Multi-Instance Learning (ML) and Wilcoxon Rank-Sum Test1,2,3,4 and it is concluded that the PTPI stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Buy ## Key Points 1. What is neural prediction? 2. What is a prediction confidence? 3. Fundemental Analysis with Algorithmic Trading ## PTPI Target Price Prediction Modeling Methodology We consider Petros Pharmaceuticals Inc. Common Stock Decision Process with Multi-Instance Learning (ML) where A is the set of discrete actions of PTPI stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4 F(Wilcoxon Rank-Sum Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Multi-Instance Learning (ML)) X S(n):→ (n+6 month) $∑ i = 1 n s i$ n:Time series to forecast p:Price signals of PTPI stock j:Nash equilibria (Neural Network) k:Dominated move a:Best response for target price For further technical information as per how our model work we invite you to visit the article below: How do AC Investment Research machine learning (predictive) algorithms actually work? ## PTPI Stock Forecast (Buy or Sell) for (n+6 month) Sample Set: Neural Network Stock/Index: PTPI Petros Pharmaceuticals Inc. Common Stock Time series to forecast n: 11 Feb 2023 for (n+6 month) According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Buy X axis: Likelihood% (The higher the percentage value, the more likely the event will occur.) Y axis: Potential Impact% (The higher the percentage value, the more likely the price will deviate.) Z axis (Grey to Black): Technical Analysis% ## IFRS Reconciliation Adjustments for Petros Pharmaceuticals Inc. Common Stock 1. An entity's business model refers to how an entity manages its financial assets in order to generate cash flows. That is, the entity's business model determines whether cash flows will result from collecting contractual cash flows, selling financial assets or both. Consequently, this assessment is not performed on the basis of scenarios that the entity does not reasonably expect to occur, such as so-called 'worst case' or 'stress case' scenarios. For example, if an entity expects that it will sell a particular portfolio of financial assets only in a stress case scenario, that scenario would not affect the entity's assessment of the business model for those assets if the entity reasonably expects that such a scenario will not occur. If cash flows are realised in a way that is different from the entity's expectations at the date that the entity assessed the business model (for example, if the entity sells more or fewer financial assets than it expected when it classified the assets), that does not give rise to a prior period error in the entity's financial statements (see IAS 8 Accounting Policies, Changes in Accounting Estimates and Errors) nor does it change the classification of the remaining financial assets held in that business model (ie those assets that the entity recognised in prior periods and still holds) as long as the entity considered all relevant information that was available at the time that it made the business model assessment. 2. Hedging relationships that qualified for hedge accounting in accordance with IAS 39 that also qualify for hedge accounting in accordance with the criteria of this Standard (see paragraph 6.4.1), after taking into account any rebalancing of the hedging relationship on transition (see paragraph 7.2.25(b)), shall be regarded as continuing hedging relationships. 3. For the purpose of applying the requirement in paragraph 6.5.12 in order to determine whether the hedged future cash flows are expected to occur, an entity shall assume that the interest rate benchmark on which the hedged cash flows (contractually or non-contractually specified) are based is not altered as a result of interest rate benchmark reform. 4. If any instrument in the pool does not meet the conditions in either paragraph B4.1.23 or paragraph B4.1.24, the condition in paragraph B4.1.21(b) is not met. In performing this assessment, a detailed instrument-byinstrument analysis of the pool may not be necessary. However, an entity must use judgement and perform sufficient analysis to determine whether the instruments in the pool meet the conditions in paragraphs B4.1.23–B4.1.24. (See also paragraph B4.1.18 for guidance on contractual cash flow characteristics that have only a de minimis effect.) International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS. ## Conclusions Petros Pharmaceuticals Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Petros Pharmaceuticals Inc. Common Stock prediction model is evaluated with Multi-Instance Learning (ML) and Wilcoxon Rank-Sum Test1,2,3,4 and it is concluded that the PTPI stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Buy ### PTPI Petros Pharmaceuticals Inc. Common Stock Financial Analysis* Rating Short-Term Long-Term Senior OutlookBa1Ba1 Income StatementCaa2Caa2 Balance SheetB1B2 Leverage RatiosCB1 Cash FlowCC Rates of Return and ProfitabilityBaa2Caa2 Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents. How does neural network examine financial reports and understand financial state of the company? ### Prediction Confidence Score Trust metric by Neural Network: 93 out of 100 with 841 signals. ## References 1. Künzel S, Sekhon J, Bickel P, Yu B. 2017. Meta-learners for estimating heterogeneous treatment effects using machine learning. arXiv:1706.03461 [math.ST] 2. J. Filar, L. Kallenberg, and H. Lee. Variance-penalized Markov decision processes. Mathematics of Opera- tions Research, 14(1):147–161, 1989 3. G. Konidaris, S. Osentoski, and P. Thomas. Value function approximation in reinforcement learning using the Fourier basis. In AAAI, 2011 4. Athey S, Mobius MM, Pál J. 2017c. The impact of aggregators on internet news consumption. Unpublished manuscript, Grad. School Bus., Stanford Univ., Stanford, CA 5. G. J. Laurent, L. Matignon, and N. L. Fort-Piat. The world of independent learners is not Markovian. Int. J. Know.-Based Intell. Eng. Syst., 15(1):55–64, 2011 6. Doudchenko N, Imbens GW. 2016. Balancing, regression, difference-in-differences and synthetic control methods: a synthesis. NBER Work. Pap. 22791 7. Jiang N, Li L. 2016. Doubly robust off-policy value evaluation for reinforcement learning. In Proceedings of the 33rd International Conference on Machine Learning, pp. 652–61. La Jolla, CA: Int. Mach. Learn. Soc. Frequently Asked QuestionsQ: What is the prediction methodology for PTPI stock? A: PTPI stock prediction methodology: We evaluate the prediction models Multi-Instance Learning (ML) and Wilcoxon Rank-Sum Test Q: Is PTPI stock a buy or sell? A: The dominant strategy among neural network is to Buy PTPI Stock. Q: Is Petros Pharmaceuticals Inc. Common Stock stock a good investment? A: The consensus rating for Petros Pharmaceuticals Inc. Common Stock is Buy and is assigned short-term Ba1 & long-term Ba1 estimated rating. Q: What is the consensus rating of PTPI stock? A: The consensus rating for PTPI is Buy. Q: What is the prediction period for PTPI stock? A: The prediction period for PTPI is (n+6 month)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3954327404499054, "perplexity": 7463.012858208975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00262.warc.gz"}
http://mathhelpforum.com/calculus/23764-basic-complex-analysis-question.html	Math Help - Basic Complex Analysis question 1. Basic Complex Analysis question This question appears really easy, I am just not sure I am undestanding it correctly. I apologize for the large size, ha. Anyways question number 2 is what I am having difficulty with. I realize it is a closed path with poles, but the shape of the path is what is throwing me off. It seems that for the 0 for instance, you would multiply the answer basic Cauchy-Integral answer by -3, but maybe I am not understanding something? 2. Originally Posted by thecow This question appears really easy, I am just not sure I am undestanding it correctly. I apologize for the large size, ha. Anyways question number 2 is what I am having difficulty with. I realize it is a closed path with poles, but the shape of the path is what is throwing me off. It seems that for the 0 for instance, you would multiply the answer basic Cauchy-Integral answer by -3, but maybe I am not understanding something? You need the version of the residue theorem with winding number. RonL 3. We havent yet gone over the residue theorem. We are just supposed to note that there are closed loops around a pole, and then figure out what the result would be. The problem is this graph is very complicated, so I am not entirely sure. The way I see it is that for instance the pole at 0, the integral would just be the integer 3. For the pole at 1, you would get 2e^(ipi) 4. Originally Posted by CaptainBlank You need the version of the residue theorem with winding number. RonL Originally Posted by thecow We havent yet gone over the residue theorem. We are just supposed to note that there are closed loops around a pole, and then figure out what the result would be. The problem is this graph is very complicated, so I am not entirely sure. The way I see it is that for instance the pole at 0, the integral would just be the integer 3. For the pole at 1, you would get 2e^(ipi) You can do what CaptainBlank said and use the residue theorem. But here is a special case, you can rely on the Cauchy integral formula but you still need winding numbers because $\Gamma$ is not a contour (i.e. a simple closed curve). 5. Yea I mean, I get that its a winding number. I am just curious if I am reading it correctly, so for instance the pole at 0 would be a winding number of 3? 6. Originally Posted by thecow Yea I mean, I get that its a winding number. I am just curious if I am reading it correctly, so for instance the pole at 0 would be a winding number of 3? Yes. Just count the number of times it "winds" around the number. 7. Alright thanks. I thought it might be 2 because if you follow the path with your finger you really only go around twice it seems.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9466578364372253, "perplexity": 207.39555784944767}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657125488.38/warc/CC-MAIN-20140914011205-00222-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
http://mathoverflow.net/questions/92865/is-reflexivity-an-open-condition/92880	# Is reflexivity an open condition? Is the condition that a module is reflexive an open condition? That is, if $X$ is a smooth projective complex variety, $T$ a quasi-projective variety, and $F$ a finitely presented module on $X \times T$ that is $T$-flat, then we can form the locus $T' \subset T$ of points $t$ such that the restriction of $F$ to $X \times t$ is reflexive. Is $T' \subset T$ open? If not, is it locally closed? Recall that a coherent sheaf $F$ is said to be reflexive if the natural map $F \to (F^{\vee})^{\vee}$ to the double dual is an isomorphism. - This locus is indeed open. I will explain why using Kollar's "Hulls and Husks" (arXiv:0805.0576). More generally, this article studies in great detail when taking the double dual commutes with base change. First, we may restrict to the open locus of $T$ where $F_t$ is torsion-free (because reflexive sheaves are torsion-free). Then, we choose an ample line bundle $H$ on $X$, and we compute the Hilbert polynomials relatively to $H$. The Hilbert polynomial $P(F_t)$ of $F_t$ is constant by flatness. From the exact sequence $0\to F_t\to F^{\vee\vee}_t\to F^{\vee\vee}_t/F_t\to 0$, we see that $F_t$ is reflexive exactly when $P(F^{\vee\vee}_t)=P(F_t)$, i.e. exactly when $P(F^{\vee\vee}_t)$ takes its minimal value. But the polynomial $P(F^{\vee\vee}_t)$ is constructible and upper semicontinuous by Proposition 28 (3) of Hulls ans Husks. This proves that this locus is open. - @Olivier Benoist: Thanks! – jlk Apr 2 '12 at 21:10 Olivier, how do you know that the polynomial $P(F_t^{\vee\vee})$ is constructible? The problem is that a priori $F_t^{\vee\vee}$ is just a collection of sheaves on the fibers, it is NOT given by restrictions of one coherent sheaf to the fibers... – Sasha Apr 3 '12 at 2:46 @Sasha : It is part of the statement of Kollar's article (arXiv:0805.0576 Proposition 28 (3)), and it is proven there. By noetherian induction, you only need to show that it is constant on an open subset of $T$, hence, you will only have to show that it is "given by restrictions of one coherent sheaf to the fibers" on an open subset of $T$. – Olivier Benoist Apr 3 '12 at 6:54 [EDIT: as Sasha points out, this does not answer the question. Please see it as a comment explaining why $X$ should be proper!] The answer is no in general if $X$ is not proper: take $X=\mathrm{Spec}\,\mathbb{C}[x]$, $T=\mathrm{Spec}\,\mathbb{C}[t]$, and $F=$ the structure sheaf of $Z=\mathrm{Spec}\,(\mathbb{C}[t,x]/(1-tx))$. Then $T'$ is just the origin. Variant: if instead you take $T=\mathrm{Spec}\,\mathbb{C}[t,u]$ and $Z=\mathrm{Spec}\,(\mathbb{C}[t,u,x]/(u,1-tx))$ (i.e. the same $Z$ as before, but embedded in 3-space), then $T'$ is the union of the origin and the complement of the $t$-axis, hence not locally closed (but still constructible). Of course the point here is that $Z$ "goes to infinity" at the origin. I don't have a counterexample where $X$ is proper, but the main problem then is "taking the dual in the fibers", as in Sasha's comment above. - In original question $X$ was proper (even projective). – Sasha Apr 2 '12 at 15:23 @Sasha: oops, sorry! I ha read "quasiprojective" but that was about $T$. – Laurent Moret-Bailly Apr 2 '12 at 17:02 I'll assume you meant to say that $F$ was locally finitely presented or coherent in your second sentence. The locus where $F$ is reflexive is the complement of the union of the supports of the kernel and cokernel of $F\to (F^\vee)^\vee$. This will be open. Postscript As Sasha points out the argument is incomplete because it is not clear that duals commute with restriction to the fibres. PPS Now Laurent has a counter example, so I guess that finishes it. - Donu, the problem is that operation of taking the dual sheaf does not commute with restriction to the fiber over $T$. So, it is not clear why $((F^\vee)^\vee)_{\|X\times\{t\}} \cong ((F_{\|X\times\{t\}})^\vee)^\vee$. – Sasha Apr 2 '12 at 12:00 what happens if you take the derived dual? – Yosemite Sam Apr 2 '12 at 15:28 Well, in the bounded derived category of a smooth variety, everything is reflexive in the sense that $$F\cong RHom(RHom(F, O_X), O_X)$$ – Donu Arapura Apr 2 '12 at 16:08 ah, of course, silly me. it's an open condition then! :) – Yosemite Sam Apr 3 '12 at 23:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9201835989952087, "perplexity": 315.4205510983626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422119446463.10/warc/CC-MAIN-20150124171046-00076-ip-10-180-212-252.ec2.internal.warc.gz"}
https://ndl.iitkgp.ac.in/document/RWhvdjcwams4cU5LZVhWTDNKbXVDMWd4THpJZ1JaKzF4U3dkZStpRnpyY2xVcWt0ZzhzcEtqeDlOQTVsQ1o0Zg	### A study of the Structural Properties of finite $G$-graphs and their CharacterisationA study of the Structural Properties of finite $G$-graphs and their Characterisation Access Restriction Open Author Kavi, Lord Clifford Source arXiv.org Content type Text File Format PDF Language English Learning Resource Type Thesis	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1715405434370041, "perplexity": 6105.339582659241}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362605.52/warc/CC-MAIN-20211203060849-20211203090849-00009.warc.gz"}
https://www.arxiv-vanity.com/papers/1305.7509/	arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org. # On a local mass dimension one Fermi field of spin one-half and the theoretical crevice that allows it Dharam Vir Ahluwalia Institute of Mathematics Statistics and Scientific Computation, Unicamp, 13083-859 Campinas, São Paulo, Brazil, and Department of Physics and Astronomy, Rutherford Building, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand Electronic address: 28 May 2013 ###### Abstract Since the 1928 seminal work of Dirac, and its subsequent development by Weinberg, a view is held that there is a unique Fermi field of spin one-half. It is endowed with mass dimension three-half. Combined, these characteristics profoundly affect the phenomenology of the high energy physics, astrophysics, and cosmology. We here present a counter example by providing a local, mass dimension one, Fermi field of spin one-half. The theory, inter alia, thus allows dimensionless quartic self interaction for the new fermions, and its only other dimensionless coupling is quadratic in the new fermions and in the standard-model scalar field. For these reasons, the immediate application of the new theory resides in the dark-matter sector of physical reality. The lowest-mass associated new particle may leave its unique signature at the Large Hadron Collider. We discuss in detail the theoretical crevice that allows the existence of the new quantum field. ## I Introduction and background To report the existence of a local spin one-half fermion field with mass dimension one is tantamount to claiming an element of incompleteness in our knowledge of quantum fields at a basic level. If true, it would, for example, allow dimensionless couplings of the type ; where and are spin one-half fermionic and spin-zero bosonic fields respectively, and is an appropriate adjoint. That the existence of such a field would have escaped even so careful an analysis as that of Weinberg’s indicates that there is either something non-trivial, or something non-trivially wrong, with such a construct. Tentatively, we assume the former and narrate the circumstances under which the claimed new quantum field came to exist and then proceed to systematically present the construct. Because of the nature of the claim we make an effort to be explicit about every known element that may affect our results. This approach serves the dual purpose of making the presentation pedagogic and to make it more accessible to scrutiny. The rest of this section is presented in the first person singular. This departure from the convention seems necessitated by the subject at hand. During the years 1992-98 I was surrounded by experimental physicists at Los Alamos Meson Physics Facility (LAMPF)111Which since then has undergone several changes in its mission and its name. on the one hand and theoretical colleagues at the Theory Division of the Los Alamos National Laboratory on the other. Initially my interests were what I later called ‘mathematical science fiction’ Ahluwalia (1999) but because of the new results that were emerging from the neutrino experiments my colleagues informally encouraged me to explore Majorana neutrinos. The subject of Majorana field and Majorana spinors was confusing, and somewhat of a mess. And what had one to do with the other, I asked. This realization arose in a conversation with Peter Herczeg. I asked the library to get Majorana’s 1937 paper Majorana (1937) translated into English, and two weeks later a professional translation was in my office. I found that in the standard language Majorana started with the Dirac field and then identified with . An intrinsically neutral field was thus introduced for the first time. There was no mention of any new spinors. My first exposure to Majorana spinors came through two papers McLennan (1957); Case (1957) that appeared some twenty years after Majorana’s original paper on the subject. At the same time I found a very nice group theoretical introduction to these spinors, but in their Grassmannian incarnation, in Ramond’s primer Ramond (1989). My personal exploration of c-number Majorana spinors began with an observation of Ramond on the ‘magic of Pauli matrices’ and how it resulted in the existence of Majorana spinors (Ramond, 1989, Section 1.4). That ‘magic’ confined the Majorana spinors to spin one-half and concealed some of their real content. The realization that Ramond’s argument could be readily generalized to higher spins if the said magic was, instead, associated with the Wigner time reversal operator, led to the writing of two exploratory papers Ahluwalia (1996); Ahluwalia et al. (1994b) and other presentations; see, for example, Ahluwalia et al. (1994a); Ahluwalia (2003). The notion of a complete set of eigenspinors of the spin one-half charge conjugation operator, which was later dubbed Elko in Ahluwalia-Khalilova and Grumiller (2005a, b), originated in those early papers. In the fall of 1998 I left Los Alamos National Laboratory to join the Universidad Autónoma de Zacatecas, México. There, on his way from MIT to Leipzig, Daniel Grumiller came for a short visit and it resulted in an unexpected collaboration. Preprint Ahluwalia (2003) was our starting point, and we now asked: What are the properties of a quantum field constructed with Elko as its expansion coefficients. Had any one of us fully appreciated Weinberg’s work of the sixties Weinberg (1964, 1969), or his later monograph Weinberg (1995), we would have never dared to ask such a question. So with certain element of innocence, and ignorance, we two wrote a paper which opened with the line Ahluwalia-Khalilova and Grumiller (2005a), “we report an unexpected theoretical discovery of a spin one-half matter field with mass dimension one,” soon to be followed by another paper that opened similarly Ahluwalia-Khalilova and Grumiller (2005b), “we provide the first details on the unexpected theoretical discovery of a spin-one-half matter field with mass dimension one.” Our excitement was quite apparent! It was also very clear that the new quantum field provided a very natural dark matter candidate with a quartic self interaction, and it coupled to EB-GHK-H scalar field Englert and Brout (1964); Higgs (1964); Guralnik et al. (1964) but its interactions with other standard-model fields was suppressed. However, when the locality-determining anticommutators were calculated this fermion field of spin one-half exhibited non-locality. In the middle of 2006, I moved to the University of Canterbury in New Zealand. There, with my ever cheerful and hard working students,222Cheng-Yang Lee, Dimitri Schritt, Tom Watson, and later Sebastian Horvath we learned, to our collective surprise, that the Dirac quantum field as presented in many, though not all, textbooks did not transform properly under Poincaré space-time transformations! Not only that, when we identified (in the usual notation), with à la Majorana’s 1937 paper we discovered that the resulting field exhibited nonlocal anticommutators! The fields presented in the monographs of Weinberg and Srednicki, on the other hand, were completely free from such inconsistencies Weinberg (1995); Srednicki (2007). With the insights gained from these monographs we discovered the culprits: there is a freedom of certain global phases associated with each of the expansion coefficients, and this freedom affects various properties of the quantum field; and designation also matter.333That is, what one calls or matters. With a similar remark for Elko. Gradual understanding of these elements led to a much improved locality structure for the Elko-based quantum field Ahluwalia et al. (2010, 2011), but non-locality still remained stubborn and showed up in one additive integral. Then in the 2012-2013 period I reached Instituto de Matemática, Estatística e Computacão Científica (IMECC), Brasil, for a sabbatical year, and the last hurdle evaporated. Under the IMECC expertise, the mischievous integral magically evaluated to zero de Oliveira and Rodrigues (2012). It was also towards the end of my stay at University of Canterbury444The successes at IMECC, and post-earthquake academic turmoil of the University of Canterbury, made my sabbatical end in a transition to Brasil. that a new connection with the Very Special Relativity (VSR) began to emerge Cohen and Glashow (2006b); Ahluwalia and Horvath (2010). Again, the mathematical expertise at IMECC, and other Brazilian institutes, helped me to better understand the symmetry properties of the new field. What follows is a detailed crystallization of these insights. The ‘Abstract’ above, and the opening paragraph of this section, places the mass dimension one Fermi field in the historical context and briefly describes the outcome of this research. The ‘Contents’ serve as a brief summary of the general flow of the paper: in II below resides the necessary background for constructing the local mass dimension one Fermi field of spin one-half in III. ## Ii Coefficient functions for a local mass dimension one Fermi field of spin one-half ### ii.1 Parity, Charge conjugation, and Elko: A review We begin our exposition by setting up the notation. The right- and left-handed Weyl spinors transform under Lorentz boost as ϕR(pμ)=exp(+σ2⋅φ)ϕR(kμ) (1a) ϕL(pμ)=exp(−σ2⋅φ)ϕL(kμ). (1b) The boost parameter is defined so that acting on the standard four momentum555This definition allows us to introduce the helicity basis below. We have verified that the results reported here hold even if we do not work in the helicity basis. These alternate approaches require giving freedom of certain phases to . A freedom that is ultimately constrained by working out the relevant equal-time anticommutators. kμdef=(m,limp→0pp),p=\|p\|. (2) equals the general four momentum pμ=(E,psinθcosϕ,psinθsinϕ,pcosθ). (3) This yields , and . are the matrices for the generators of boosts (in the vector representation).666We shall use the conventions of Ryder, L H (1985) with and set to unity. Equations (1a) and (1b) follow from the fact that are the generators of the boosts for the right-handed Weyl representation space, while are for the left-handed Weyl representation space. For the direct sum of the right- and left-Weyl representation spaces, to be motivated below, the boost generator thus reads κ=(−iσ/200+iσ/2). (4) #### ii.1.1 Parity It is immediately clear from the transformations (1a) and (1b) that parity, which in the vector space corresponds to , interchanges the right- and left-handed Weyl representation spaces. Thus the operation of parity, up to a global phase, for the 4-component spinors ψ(pμ)=(ϕR(pμ)ϕL(pμ))=exp(iκ⋅φ)ψ(kμ) (5) must contain purely off-diagonal identity matrices , and in addition an operation that implements the action of on . Up to a global phase, it is thus defined as (6) Here, is the transformed ; and is a null matrix. Now may be related to as follows ψ(pμ′) =exp(−iκ⋅φ)ψ(kμ) (7) =exp(−iκ⋅φ)exp(−iκ⋅φ)ψ(pμ) =exp(−2iκ⋅φ)ψ(pμ). Substituting (7) in (6), and on using the anti-commutativity of with each of the generators of the boost, , with , (6) becomes Pψ(pμ)=exp(2iκ⋅φ)γ0ψ(pμ). (8) A direct evaluation of the exponential in (8) gives exp(2iκ⋅φ)=m−1γμpμγ0 (9) where are the Dirac matrices in the Weyl representation. Finally, a substitution of the expansion (9) in (8), on combining with the identity (where is an identity matrix in the space of four-component spinors), results in Pψ(pμ)=m−1γμpμψ(pμ). (10) Thus, we have the desired expression for the parity operator777In obtaining this result we have followed a recent work of Speranca Speranca (2013). P=m−1γμpμ. (11) Its eigenvalues are . Each of these has a two fold degeneracy PξS(pμ)=+ξS(pμ),PξA(pμ)=−ξA(pμ). (12) The superscripts refer to self and anti-self conjugacy of under . The Dirac’s and spinors are thus seen as the eigenspinors of the parity operator, , with eigenvalues and , respectively: ξS(pμ)→uσ(pμ),ξA(pμ)→vσ(pμ), (13) where the designation represents the degeneracy index. Seen from this perspective, with the help of (11), (12) translates to (γμpμ−m\openone4)u(pμ)=0,(γμpμ+m\openone4)v(pμ)=0, (14) which are the 1928 Dirac equations in the momentum space. This stage still leaves the global phases associated with each of the Dirac spinors to be still free. They contain important elements of physics affecting locality and transformation properties of the single-particle states associated with the Dirac and the 1937 Majorana quantum fields Majorana (1937).888Both of these fields carry Dirac’s and as their expansion coefficients. These can be read off from Weinberg’s construction of these fields Weinberg (1995). Since the boost operator is not unitary, the Dirac spinors cannot in any sense be considered to represent quantum states. Instead, these enter as expansion coefficients in a quantum field which is specifically built to circumvent this problem. In the configuration space the operator annihilates the Dirac and Majorana quantum fields, generically denoted by the same symbol . But, so does the spinorial Klein-Gordon operator. The question which determines that it is the former, and not the latter, that enters the Dirac/Majorana Lagrangian density is related to the structure of the , where is the usual time ordering operator. So the Lagrangian density is to be seen as a derived object after one has constructed a quantum field.999A reader who may not be familiar with this aspect of quantum field theory may wish to consult III below for an outline of this argument. This view is similar and consistent with the formalism presented in Weinberg (1995). We shall work in this spirit. Incorporating the four-component spinor introduced in (5) is a necessary, but not sufficient, condition for preserving parity symmetry. We end this discussion of parity operator by noting that . There exists an operator that transmutes the self-conjugate eigenspinors of the parity operator to the anti-self conjugates eigenspinors, and vice versa. This operator we discuss next, and arrive at the counterpart of (12) for this operator in (23b) below. We shall discover that eigenspinors of this operator play a central role in constructing the new mass dimension one quantum field of spin one-half. #### ii.1.2 Charge conjugation operator and its eigenspinors (Elko) Introduction of the four-component spinors (5), not necessarily as eigenspinors of the parity operator, doubles the degrees of freedom. In a quantum field theoretic formalism this doubling introduces the notion of antiparticles. The relative charges of the particles and antiparticles are then determined by the type of local gauge symmetries that the underlying kinematic framework supports. The particle-antiparticle symmetry enters via charge conjugation operator. For the four-component spinors, it may be similarly constructed as without first invoking a wave equation or a Lagrangian density. To see this we begin with the observation that the Wigner time reversal operator for spin one-half, , acts on the Pauli matrices as follows101010For any spin, ; with and . For convenience, we abbreviate to . ΘσΘ−1=−σ∗, (15) with Θ=(0−110). (16) It allows the following ‘magic’ to happen (cf. ‘magic of Pauli matrices’ in (Ramond, 1989, Section 1.4)). First complex conjugate (1a) and (1b), then multiply from the left by , and use the above defining feature of the Wigner time reversal operator. This sequence of manipulations gives Θϕ∗R(pμ)=exp(−σ2⋅φ)Θϕ∗R(kμ)) (17a) Θϕ∗L(pμ)=exp(+σ2⋅φ)Θϕ∗L(kμ)). (17b) That is, if transforms as a left-handed Weyl spinor then transforms as a right-handed Weyl spinor, where is an undetermined phase.111111Note: multiplication by a phase does not affect the Lorentz transformation properties of the spinors. Similarly, if transforms as a right-handed Weyl spinor then transforms as a left-handed Weyl spinor, where is an undetermined phase. This crucial observation motivates the introduction of two sets of four-component spinors Ahluwalia (1996) λ(pμ)=(ζλΘϕ∗L(pμ)ϕL(pμ)) (18) and ρ(pμ)=(ϕR(pμ)ζρΘϕ∗R(pμ)). (19) The do not provide an additional independent set of spinors from that in (18) and for that reason we do not consider them further. Generally, this result is introduced as a ‘magic of Pauli matrices’ (Ramond, 1989, Section 1.4) where gets concealed in Pauli’s , which equals . Our argument in terms of the Wigner time reversal operator has the advantage that it immediately generalizes to higher spins. Furthermore, the recognition that there is an element of freedom in the indicated phases, , makes escape their interpretation as Weyl spinors in a four-component disguise. It will become apparent below that we may now have four, rather than two, four-component spinors of the general form carried by . With these observations at hand we are led to entertain the possibility that in addition to the symmetry operator , there may exist a second symmetry operator. Up to a global phase, it has the form Cdef=(0αΘβΘ0)K (20) where complex conjugates to its right. The arguments that leads to (20) are similar to the ones that give (6). Requiring to be an identity operator determines ; giving C=(0iΘ−iΘ0)K=γ2K. (21) There also exists a second solution with . But this does not result is a physically different operator and in any case the additional minus sign can be absorbed in the indicated global phase. This is the same operator that appears in the particle-antiparticle symmetry associated with the 1928 Dirac equation Dirac (1928). We have thus arrived at the charge conjugation operator from the analysis of the symmetries of the -component representation space of spinors. This perspective has the advantage of immediate generalization to any spin: if is taken as a spin Wigner time reversal operator in footnote 10, then the resulting becomes the charge conjugation operator in the dimensional representation space. To construct the eigenspinors of for spin one-half we act it on and re-write the result as Cλ(pμ)=(iζ∗λ)−1(−ζ∗λΘϕ∗L(pμ)ϕL(pμ)). (22) A comparison of the right-hand side of the above expression with the definition (18) shows that become eigenspinors of with eigenvalues if we demand . This requirement translates to, , resulting in . In order that both the right- and left-handed components of remain on the same footing we shall here onwards study the case where we set .121212Departures from may induce violations of discrete symmetries; a subject we do not pursue here. Each of the signs provides a doubly degenerate set of ; and, additionally, these ensure that do not become Weyl spinors in disguise. This discussion adds new insights to the self and anti-self conjugate spinors first introduced in Ahluwalia et al. (1994b); Ahluwalia (1996); Ahluwalia-Khalilova and Grumiller (2005a, b) λ(pμ)={λS(pμ) for ζλ=+iλA(pμ) for ζλ=−i (23a) with CλS(pμ)=+λS(pμ),CλA(pμ)=−λA(pμ). (23b) The physics literature identifies in (23a) with ‘Majorana spinors’ (often, as Grassmann numbers). The seem to have been entirely overlooked. A failure to construct a Lagrangian density using Majorana spinors is noted in (Aitchison and Hey, 2004, Appendix P). We shall see below that this only reflects that the considered Majorana spinors do not satisfy Dirac equation. As Weinberg has emphasized in his monograph on the subject and in his other writings Weinberg (2012), the modern version of Dirac equation in quantum field theory has a much richer physics and is to be separated from its original motivations and interpretations confined to the finite dimensional representation space. It is in this latter sense, as expansion coefficients of a quantum field, that we treat the four-component spinors in this communication. In a quantum field theoretic setting the inevitability of antiparticles is elegantly argued by Feynman in Feynman and Weinberg (1987). In order to avoid confusion with the folklore on Majorana spinors we refer to as Elko (German acronym for Eigenspinoren des Ladungskonjugationsoperators first introduced in Ahluwalia-Khalilova and Grumiller (2005a, b)). ### ii.2 Global phase transformations for Elko In general, a global unitary transformation of the type λ(pμ)→λ′(pμ)=exp(iaϑ)λ(pμ) (24) with, and , does not preserve the self/anti-self conjugacy of under given in (23b) unless the matrix satisfies the condition γ2a∗+aγ2=0 (25) This is due to the presence of the operator in (21). The general form of satisfying these requirements is found to be a =⎛⎜ ⎜ ⎜⎝αβλ0βδ0λλ0−δβ0λβ−α⎞⎟ ⎟ ⎟⎠ (27) =λγ0+i4(α−δ)[γ1,γ2]+i2β[γ2,γ3] −12(α+δ)γ5 with (with no association with the same symbols used elsewhere in this work) and . In II.8 below we will discover that certain symmetries of the spin sums require , and . With the scale factor absorbed in , reduces to . The counterpart of for the Dirac case that preserves the self/anti-self conjugacy under , (12) as opposed to (23b), is simply a identity matrix. ### ii.3 Explicit construction of Elko and on the choice of certain phases To obtain an explicit form of Elko calls for a choice of the ‘rest’ spinors with defined in (2). That done, one then has for an arbitrary λ(pμ)=exp(iκ⋅φ)λ(kμ). (28) In principle, the boosted spinors reside in the boosted frames. But since no frame is a preferred frame they must also exist in all frames (an argument originally due to E. P. Wigner). It is this interpretation that we attach to . With the generator of the boost, , defined in (4), the boost operator in (28) can be readily evaluated using , to the effect that exp(iκ⋅φ)=(e(σ/2)⋅φ00e−(σ/2)⋅φ) =√E+m2m⎛⎝\openone+σ⋅pE+m00\openone−σ⋅pE+m⎞⎠. (29) To provide a concrete example of a mass dimension one quantum field, we confine our attention to the -defining as eigenspinors of σ⋅^pϕ±L(kμ)=±ϕ±L(kμ) (30) with . Furthermore, we adopt the phases given below ϕ+L(kμ) =√m(cos(θ/2)exp(−iϕ/2)sin(θ/2)exp(+iϕ/2)) =ϕ+L(0)∣∣Eq. (A.2) of AG ϕ−L(kμ) =√m(−sin(θ/2)exp(−iϕ/2)cos(θ/2)exp(+iϕ/2)) =−ϕ−L(0)∣∣Eq. (A.3) of AG. The abbreviation AG stands for Ahluwalia-Khalilova and Grumiller (2005a).131313The dictionary of comparison for Ahluwalia (1996) is the same as for AG modulo a minor change of notation: AG’s and . In writing the above ansatz, we have explicitly noted the differences from the most-often used earlier work. There is a second choice of phases, and designations (that is, the indices are assigned), which is invoked when Elko are used as expansion coefficients of a quantum field. This choice we make explicit below in defining the λS+(kμ) =+(iΘ[ϕ+L(kμ)]∗ϕ+L(kμ)) (32a) =λS{−,+}(0)∣∣Of (3.9) of AG λS−(kμ) =+(iΘ[ϕ−L(kμ)]∗ϕ−L(kμ)) (32b) =−[λS{+,−}(0)∣∣Of (3.9) of % AG] and λA+(kμ)=+(−iΘ[ϕ−L(kμ)]∗ϕ−L(kμ)) =−[λA{+,−}(0)andnotλA{−,+}(0)∣∣Of (3.10) of AG] (32c) λA−(kμ)=−(−iΘ[ϕ+L(kμ)]∗ϕ+L(kμ)) =−[λA{−,+}(0)andnotλA{+,−}(0)∣∣Of (3.10) of AG] (32d) If one wishes one can keep the here-chosen phases free and fix them later by demanding locality for the resulting quantum field. It is worth noting that the freedom of global phases associated with each of the four is restricted to as (23b) does not allow a general replacement, , without affecting the self/ant-self conjugacy under .141414This observation was first made by in Schritt, D (circa 2007).. This freedom, and its restriction to , affects the locality properties of the quantum field we shall construct, and its judicious incorporation, in part, lies behind the removal of the non-locality encountered in Ahluwalia-Khalilova and Grumiller (2005a, b). To obtain the explicit form of we need one last piece of information. It is deciphered by complex conjugating (30), then replacing in accord with (15), using , and finally multiplying from the left by . This exercise yields σ⋅^p(Θ[ϕ±L(kμ)]∗)=∓(Θ[ϕ±L(kμ)]∗) (33) and shows that the helicity of is opposite to that of . The interplay of the result (33) with the boost (29) and the chosen form of in (32a) to (32d) gives the following analytically compact forms for λS+(pμ)=√E+m2m(1−pE+m)λS+(kμ) (34a) λS−(pμ)=√E+m2m(1+pE+m)λS−(kμ) (34b) and λA+(pμ)=√E+m2m(1+pE+m)λA+(kμ) (34c) λA−(pμ)=√E+m2m(1−pE+m)λA−(kμ) (34d) These are the expansion coefficients of a quantum field to be introduced below. To construct an adjoint of the field we shall need the spinorial duals of the enumerated in (34a) to (34d). This task is undertaken below in Section II.5 after making a few remarks in II.4 on the Weinberg formalism for the construction of quantum fields and a departure necessitated by a circumstance encountered in constructing a quantum field with Elko as its expansion coefficients. ### ii.4 Misconceptions in Literature and On a departure from the Weinberg formalism The choice for a set of -like objects appears as a trivial task in most textbooks: pick up a wave equation, like that of Dirac, set to , and solve. This straightforward exercise immediately gives the required objects. For the Dirac case, these are and . For the construction of quantum fields, this exercise does not tell which of these coefficients, when appropriately boosted, shall accompany which one of the creation and destruction operators, nor does it tell us about the set of phases to be picked when making this pairing. This is where one of the first errors occurs in many of the modern textbooks on quantum fields. The other important error resides, as already alluded to above, in the lack of appreciation for the phases associated with each of the expansion coefficients. Our 2005 publications Ahluwalia-Khalilova and Grumiller (2005a, b) were not immune to these errors.151515A reader interested in specific examples of these errors in the modern textbooks may correspond with the author in private; or write to any of the former students of mine: Cheng-Yang Lee, Sebastian Horvath, and Dimitri Schritt. Another question that escapes attention in these presentations is as to what tells us, for example, that the spin one-half particles are described by the Dirac fermions, and as to what is the deeper origin of the Dirac operator . The argument that it is the square root of the Klein-Gordon operator is historically correct, but in the modern context it carries with it an element of triviality. The answer to these questions emerges elegantly in the Weinberg formalism Weinberg (1995). It, for example, establishes the uniqueness of the Dirac field assuming Lorentz symmetry along with symmetry under four space-time translations, validity of the cluster decomposition principle, and certain additional assumptions on discrete symmetries. The quantum field is obtained first, and then by calculating the Feynman-Dyson propagator through the evaluation of one arrives at the Dirac operator, and the Lagrangian density. The Dirac spinors appear naturally as expansion coefficients in without any recourse, direct or indirect (except certain symmetries), to Dirac or any other wave equation. The Weinberg formalism however is not designed to furnish a local quantum field if the Lagrangian density is Poincaré covariant and the Feynman-Dyson propagator carries covariance under certain subgroup of Poincaré. This hitherto unknown type of symmetry breaking can arise without violating the null result of Michelson-Morley type experiments Cohen and Glashow (2006b). It allows the charge conjugation symmetry, but incorporating any one of the discrete symmetries of P, T, CP, or CT enlarges the subgroups to the full Poincaré group of Special Relativity (SR). The noted null result, and the existence of massive particles, only requires the breaking of the conformal symmetry to a group containing four space-time translations adjoined to certain - or -parameter subgroups of Lorentz. A theory of relativity based on these subgroups was termed Very Special Relativity (VSR) by its authors. This remarkable result became widely known only in 2006 through the above cited Cohen-Glashow paper. It will become apparent below that it plays a significant role in the interpretational aspects of our work. ### ii.5 Spinorial dual for Elko Under the Dirac dual ¯λ(pμ)def=λ(pμ)†γ0 (35) Elko for massive particles have a null norm Ahluwalia (1996): ¯λS±(pμ)λS±(pμ)=0,¯λS±(pμ)λA±(pμ)=0 ¯λS±(pμ)λA∓(pμ)=0 (36a) ¯λA±(pμ)λA±(pμ)=0,¯λA±(pμ)λS±(pμ)=0 ¯λA±(pμ)λS∓(pμ)=0 (36b) and ¯λS±(pμ)λS∓(pμ)=∓2im ¯λA±(pμ)λA∓(pμ)=±2im. (36c) A lack of full appreciation of this fact in physics literature, in part, leads to the classic problem of constructing a Lagrangian density for c-number Majorana spinors (Aitchison and Hey, 2004, Appendix P). To take an ab initio look at the problem of defining a spinorial dual, let us take a general -component spinor defined for massive particles. Call it . It does not have to be an eigenspinor of , or an eigenspinor of . And ask: What is the dual spinor, denoted by , such that it yields a non-null Lorentz invariant norm, , under boosts as well as rotations. To answer this question we examine a general form of the dual defined as \lx@overaccentset∼ϱα(pμ)def=[Ξϱα(pμ)]†η (37) where is to be so defined that its action on any one of the yields one of the spinors from the same set. It is not necessary that the indices and be the same. We require to define an invertible map, with (possibly, up to a phase). The requirement of a Lorentz invariant norm then translates to the statement that in (37) must anti-commute with the generators of boosts, and commute with the generators of the rotations Ahluwalia et al. (2010, 2011) {κi,η}=0,[ζi,η]=0,i=x,y,z. (38) The three generators of boosts are given by (4). The three generators of rotation are ζ=(σ/200σ/2). (39) A slightly lengthy but a straight forward calculation satisfying the constraints (38) shows to have the form η=(0a\openoneb\openone0),a,b∈R. (40) In order that the right and the left transforming components of a are treated symmetrically, we set .161616The last equality is unimportant. It simply sets a scale of the norms. This is an additional assumption that we explicitly note. The standard Dirac dual corresponds to . Notationally, if represents a Dirac spinor, . For Elko, the results (36a), (36b), and (36c) suggest that we define171717In obtaining this result we have followed a recent e-print of Speranca Speranca (2013). Ξdef=12m( λS+(pμ)¯λS+(pμ)+λS−(pμ)¯λS−(pμ) (41) −λA+(pμ)¯λA+(pμ)−λA−(pμ)¯λA−(pμ)). It is readily seen that and indeed exists and equals itself. We may thus introduce a spinorial dual for Elko in accordance with the general definition (37) and an Elko-specific notation that distinguishes it from the Dirac dual \lx@overaccentset¬λα(pμ)=[Ξλα(pμ)]†η,a=b=1 (42) with given by (41). This definition allows us to rewrite results (36a), (36b), and (36c) into the following orthonormality relations \lx@overaccentset¬λSα(pμ)λSα′(pμ)=2mδαα′ (43a) \lx@overaccentset¬λAα(pμ)λAα′(pμ)=−2mδαα′ (43b) \lx@overaccentset¬λSα(pμ)λAα′(pμ)=0,\lx@overaccentset¬λAα(pμ)λSα′(pμ)=0. (43c) The Elko dual, by construction, does precisely what it is intended to do. It provides a non-null Lorentz invariant norm. Mathematically, as well as physically, it encodes exactly the same information as that contained in (36a), (36b), and (36c). As shall be seen below, in its present incarnation, as opposed to all earlier works since the 2005 publications, it is a much more powerful tool in investigating the symmetry structure that will appear for the mass dimension one quantum fields introduced below. We will discover that this structure is intrinsic to Elko, and to its Majorana cousin. The Elko dual simply makes it manifest through the here-introduced operator . All results that we now obtain can be obtained in a much more cumbersome manner without invoking the Elko dual or the operator . As a consistency check, we find that the Elko dual defined using the operator yields exactly the same dual as in Ahluwalia et al. (2010, 2011). To see this we act (41) from the right by . Use of (36a) and (36b) then gives ΞλS+(pμ)=12mλS−(pμ)¯λS−(pμ)λS+(pμ)=2im=iλS−(pμ) (44) where the last substitution is due to the relevant part of equations (36c). Definition (42) thus yields \lx@overaccentset¬λS+(pμ)=−i[λS−(pμ)]†η. (45a) Repeating similar evaluations with λS−(pμ), λA+(pμ), and λA−(pμ) in succession gives \lx@overaccentset¬λS−(pμ)=i[λS+(pμ)]†η (45b) \lx@overaccentset¬λA+(pμ)=−i[λA−(pμ)]†η (45c) \lx@overaccentset¬λA−(pμ)=i[λA+(pμ)]†η. (45d) A comparison of these results with those given in (Ahluwalia et al., 2010, Eq. 15) and (Ahluwalia et al., 2011, Eq. 22) establishes the equivalence of the Elko dual introduced here and the one introduced in the previous works. This, however, happens with the benefit of providing new insights (see below). The knowledge of the Elko dual will help us define an appropriate adjoint for the quantum fields constructed with Elko as expansion coefficients. The calculation of the Feynman-Dyson propagator associated with these fields would require spin sums for Elko. We, therefore, evaluate these next and study their symmetry properties. The latter lie behind the departure from the Weinberg formalism for the construction of quantum fields noted in Section II.4. ### ii.6 Spin sums and projectors for Elko The spin sums ∑αλSα(pμ)\lx@overaccentset¬λSα(pμ)and∑αλAα(pμ)\lx@overaccentset¬λAα(pμ) (46) can now be readily evaluated using (34a) to (34d) for the and , and (45a) to (45d) for their duals. The first of the two spin sums evaluates to i=1[E+m2m(1−p2(E+m)2)] (47) ×(−λS+(kμ)[λS−(kμ)]†+λS−(kμ)[λS+(kμ)]†)η=−im⎛⎜ ⎜ ⎜ ⎜⎝100−ie−iϕ01ieiϕ00−ie−iϕ10ieiϕ001⎞⎟ ⎟ ⎟ ⎟⎠ which suggests introducing181818Sometimes it may be convenient to use the functional dependence of on , and write it as . G(ϕ)def=⎛⎜ ⎜ ⎜ ⎜⎝cccc000−ie−iϕ00ieiϕ00−ie−iϕ00ieiϕ000⎞⎟ ⎟ ⎟ ⎟⎠. (48) In the spherical polar coordinate system parity is implemented by . The definition (48) thus shows that is an odd function under parity G(ϕ)=−G(ϕ+π). (49) The second of the spin sums can be evaluated in exactly the same manner. The combined result is ∑αλSα(pμ)\lx@overaccentset¬λSα(pμ)=m[G(ϕ)+\openone4] (50a) ∑αλAα(pμ)\lx@overaccentset¬λAα(pμ)=m[G(ϕ)−\openone4]. (50b) These spin sums have the eigenvalues , and , respectively. Since eigenvalues of projectors must be either zero or one (Weinberg, 2012, Section 3.3), we define and confirm that indeed they are projectors and furnish the completeness relation S2=S,A2=A,S+A=\openone4 (52) We have thus arrived at one of the most intriguing and subtle aspects of Elko: Manifestly, through the projectors break Lorentz symmetry. A detailed analysis found in Ahluwalia and Horvath (2010), and reviewed afresh below, shows that respects symmetries of the theory of very special relativity (VSR). For reasons given in the seminal paper on VSR Cohen and Glashow (2006b), the theory thus immediately evades the usual sensitive searches devoted to look for departures from Lorentz invariance (that is, from the symmetries underlying the theory of special relativity (SR)). ### ii.7 The SR→VSR breaking of the Lorentz symmetry It is now necessary to first provide a brief summary of the Cohen-Glashow VSR which asserts, ‘‘invariance under HOM(2),191919HOM(2) is a 3-parameter subgroup of Lorentz to be defined below in II.7.1. rather than (as is often taught) the Lorentz group, is both necessary and sufficient to ensure that the speed of light is the same for all observers, and inter alia, to explain the null result to the Michelson-Morley experiment and its more sensitive successors.” Besides the just mentioned constancy of speed light, VSR also shares with SR the same time dilation, the same law of velocity addition, the same existence of a center-of-mass frame, and the same universal and isotropic maximal attainable velocity. These observations have been explicitly made in the original VSR paper Cohen and Glashow (2006b). #### ii.7.1 Cohen-Glashow VSR: a brief summary The theory of VSR has its origin in the above-quoted observation on necessity and sufficiency of certain subgroups of Lorentz to accommodate the null result of Michelson-Morley experiment and its more sensitive successors. There are four avatars of VSR Cohen and Glashow (2006b); Ahluwalia and Horvath (2010). They are defined through the associated Lie algebras as follows. : Generated by T1def=Kx+Jy,T2def=Ky−Jx (53) where and are generators of rotations and boots, respectively. These provide an Abelian Lie algebra which is isomorphic to the algebra associated with translations in a plane. The two generate the T(2) group transformations exp(iT1ϵ)={\openone4+iT1ϵ−12T21ϵ2for vectors\openone4+iτ1ϵfor spinors (54) where the parameter of transformation is given by ϵ=pxE−pz (55) and and are the four-vector and the spinor representations of , respectively; and similarly exp(iT2ε)={\openone4+iT2ε−12T22ε2for vectors\openone4+iτ2εfor spinors (56) where the parameter of transformation is given by ε=pyE−pz. (57) and and are the four-vector and the spinor representations of , respectively. To obtain the above group transformations the following identities were found helpful T31=T32=04,τ21=τ22=04. (58) 1. yields , an algebra which is isomorphic to the 3-parameter algebra associated with the group of Euclidean motions E(2). 2. yields (2), an algebra which is isomorphic to the 3-parameter algebra associated with the group of orientation preserving similarity transformations, or homotheties, of HOM(2). 3. and simultaneously yields (2), an algebra which is isomorphic to the algebra associated with the four-parameter similitude group, SIM(2). The counterparts of (54) and (56) for rotation about, and boost along, the VSR preferred direction (taken here as the ) are found to be exp(iJzΦ)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩\openone4+iJzsinΦ+J2z(cosΦ−1) for vectors\openone+i2ζzsin(Φ/2)+4ζ2z(cos(Φ/2)−1) for spinors (59)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9272290468215942, "perplexity": 1037.7157397262906}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401600771.78/warc/CC-MAIN-20200928104328-20200928134328-00184.warc.gz"}
https://www.sas1946.com/main/index.php/topic,62908.msg691979.html	• July 02, 2020, 07:07:34 AM • Welcome, Guest Pages: [1] 2 Go Down ### AuthorTopic: Track IR (Read 1437 times) 0 Members and 1 Guest are viewing this topic. #### Flanker27 • member • Offline • Posts: 357 ##### Track IR « on: December 04, 2019, 11:22:58 AM » im thinking about getting a track IR system but they all seem to be well over 100$is there another system other then the one Microsoft sells for cheaper or is it a cornered market thing? Logged #### Gubi • Flying Ass Clown #34 • Modder • member • Offline • Posts: 901 ##### Re: Track IR « Reply #1 on: December 04, 2019, 12:07:28 PM » Nope Logged I am a moron. #### SAS~Storebror • Editor • member • Offline • Posts: 19441 • Failure is not an option. ##### Re: Track IR « Reply #2 on: December 04, 2019, 12:10:03 PM » they all seem to be well over 100$ You get what you pay for. There are other solutions trying to cover the same thing, but TrackIR is the one that comes hassle-free and does a perfect job. Plug&play, no issues, all smooth and dandy. And yes, it's 193 EUR here right now (which is already 17% off) - you will want to have the "pro" set with the active LED clip, trust me. Mike Logged While love lives, while suns set, while snowmoons rise in november skies, while ties bind, while souls cry, while oceans ride in an endless tide, while love grows, while blood flows, while truth is real you need never feel alone. In loving memory of times when I cared. #### sniperton • member • Offline • Posts: 1152 ##### Re: Track IR « Reply #3 on: December 04, 2019, 12:10:43 PM » What you basically need consists of three parts: - a camera (must be bought anyway) - an IR hat or clip (can be either a commercial product or a DIY one for less than 10 bucks) - a software (OpenTrack is a widely used free alternative to Natural Software's TrackIR) Here you have the full range of options: https://www.trackhat.org/shop-cfk4 Logged #### Koi • member • Offline • Posts: 45 ##### Re: Track IR « Reply #4 on: December 04, 2019, 03:19:53 PM » I stumbled across this on Amazon. Its a new tracker similar to the Natural Point Tracker IR so if you don't already have a tracker IR yet take a look at this one on Amazon, look for " S18 OpenTrack Camera plus the clip". It list for $79.28 Canadian If you do have one and need a replace the NP tracker IR clip you have held together with tape then look at this it a "S18 - TrackIR Clip". One can use it with the Track IR 5 or 4. As I already own the Natural Point Tracker IR and IR clip. I just bought the IR clip arm to replace the broken Natural Point one. It only cost me$39.76 Canadian including shipping which is a good deal as the NaturalPoint clip is listed at \$125.00 Canadian. These can be ordered either as a complete set of tracker clip and Camera or each separately. I ordered the clip on Nov 17 and received it yesterday Dec 3. When I Compared it to the Natural Point Tracker IR Headset clip the first thing I noticed was that it is much stronger, being made of solid heavy plastic one quarter of an inch thick. The LEDs are attached to an arm that, unlike the in NP Tracker IR ,dose not move and therefore is more durable and not subject to easy breaking. Like the NP tracker clip it is shaped like a capital letter "Y" but has a flange off the stem. It is this flange that is used to attached it to the headsets. The flange is a sturdy flat plastic plate with two slots running it's length through which two thin Velcro strips are provided for use to attach it to a head set. I found, however that a couple of wire twist ties work better and are less fiddly to use. It is a USB plug n play devise and worked no problem first time. So the up shot is that I think its a winner and a much better deal than the in NP one. Logged #### K5083 • member • Offline • Posts: 67 ##### Re: Track IR « Reply #5 on: December 04, 2019, 05:15:58 PM » Good tip, Koi. I just ordered one. My passive TrackIR reflector clip generally works perfectly, but sometimes gets confused on bright mornings when strong light comes through the window. This should cure that. The power can be furnished by one of those cheap phone chargers rather than have the wire run to your PC and take up another USB port. August Logged #### SAS~Storebror • Editor • member • Offline • Posts: 19441 • Failure is not an option. ##### Re: Track IR « Reply #6 on: December 04, 2019, 11:02:59 PM » a camera (must be bought anyway) ...A camera with removed IR filter to be precise. Not everybody will consider himself capable of removing the IR filter of the camera which he "bought anyway", and definitely not everybody will be happy with the impact on normal webcam operation. https://www.trackhat.org/shop-cfk4 Trackhat is a commercial competitor product to TrackIR and that site only offers products by Trackhat. It's okay to link it, but promoting it as a site that lists "the full range of options" is a bit misleading. As I said: You get what you pay for. If you buy TrackIR 5, you've cut it all. It you buy Trackhat, you've cut most of it. If you buy something from 3rd party source (Amazon, ebay, whatever), you probably cut most of it, but you rely on the quality of someone you don't know. If you decide to try a DIY solution, you save money in exchange for your own contribution - it depends on your abilities then. Mike Logged While love lives, while suns set, while snowmoons rise in november skies, while ties bind, while souls cry, while oceans ride in an endless tide, while love grows, while blood flows, while truth is real you need never feel alone. In loving memory of times when I cared. #### sniperton • member • Offline • Posts: 1152 ##### Re: Track IR « Reply #7 on: December 05, 2019, 01:36:25 AM » Trackhat is a commercial competitor product to TrackIR and that site only offers products by Trackhat. It's okay to link it, but promoting it as a site that lists "the full range of options" is a bit misleading. I linked it only as an example for a site where all needed components can be got either individually or as a complete set. Most alternatives to TrackIR use the PS3 camera as it provides you with a resolution of 640 by 480 @ 60 FPS. For best results, the removal of the IR filter is advised, but if the LEDs are strong enough and the environment is not too bright, a piece of exposed photo film in front of the lense suffices. The most cost-efficent way is to buy a PS3 camera (preferably with the IR filter already removed), and to make a cap or clip yourself. A cap is the easiest to do, but a clip is more handy if you use a headset. Clip with 3D printing (https://www.stlfinder.com/3dmodels/freetrack/): Clip without 3D printing: Logged #### whistler • Modder • member • Offline • Posts: 2179 ##### Re: Track IR « Reply #8 on: December 05, 2019, 02:07:38 AM » I have been using EDTracker Pro Wired for longer than two years now. Stick the little box to your headset or cap and you are good to go. No cameras, no worries about lighting condition. 3 degrees of freedom only by default but you can get pseudo 6 degrees of freedom with some work. TrackIR 5 is probably the best (I never tried it) but when/if my EDTracker Pro fails, I will just buy EDTracker Pro Wireless without a second thought. Logged NG-HUD v3.5H \| NG-MAP v3.1 \| NG-CAM v1.6: https://www.sas1946.com/main/index.php/board,93.0.html #### SAS~Storebror • Editor • member • Offline • Posts: 19441 • Failure is not an option. ##### Re: Track IR « Reply #9 on: December 05, 2019, 02:39:55 AM » Probably one of the biggest caveats in threads like this is the fact that only a very few users can actually compare results with different head tracking solutions. You pick one, you're happy with it, so you stick to it and never worry about any other solution. I can't say anything about EDTracker or Trackhat either. I can say something about FaceTrackNoIR compared to TrackIR 5: They don't compare. FaceTrackNoIR is crap compared to TrackIR 5 and any money and/or time you spend on it is gone to waste. Mike Logged While love lives, while suns set, while snowmoons rise in november skies, while ties bind, while souls cry, while oceans ride in an endless tide, while love grows, while blood flows, while truth is real you need never feel alone. In loving memory of times when I cared. #### whistler • Modder • member • Offline • Posts: 2179 ##### Re: Track IR « Reply #10 on: December 05, 2019, 03:20:22 AM » You can't go wrong with TrackIR 5 and it is option number 1, if you have funds, yes. No doubts. It's the "industry standard" for a reason, I am sure. I was looking for a non-camera based solution and EDTracker just 'does it' for me, as Mike hints. Just like with any hardware, some components and peripheral will take you there just fine while other, often the more expensive the better, will excel at it. My previous DIY solution never truly worked right and I grew tired of it, therefore don't go the DIY route if you are not used to electronics/craftsmanship. Logged NG-HUD v3.5H \| NG-MAP v3.1 \| NG-CAM v1.6: https://www.sas1946.com/main/index.php/board,93.0.html #### Mick • Modder • member • Offline • Posts: 4306 ##### Re: Track IR « Reply #11 on: December 05, 2019, 03:40:30 AM » ... X'Mas is approaching, time to add a TrackIR 5 to your wish list ... 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https://worldbuilding.stackexchange.com/questions/106401/junkyard-planet-trash-distribution	# Junkyard planet trash distribution? So, I've got a planet that's basically a junkyard. It's just one big junkyard. People from various space-faring societies dump all the crap there that they don't want to deal with. Derelict spaceships, obsolete tech, that sort of thing. And because the people doing this are lazy, what they basically do is just haul a big space barge close enough to the planet's gravity well, cut all the garbage loose, push it just over the edge of the well, and let it fall. So my question is, assuming the trash isn't getting permanently trapped in orbit, and assuming both the trajectory and the exact point in space from which the garbage is released are both random, would the places the garbage falls be random too? Would there be an equal distribution over the entire planet's surface, or as the trash collects over thousands of years, would it start to pile up more in some places then others? Would it start to accumulate a whole lot around the equator, but barely any at all near the poles? Would things like mountain ranges or ocean currents influence this at all? Update: Because everyone was asking, the reason there even is a junkyard planet is simply because humans are lazy. Various corporations and space governments figured out that they could just dump a ton of metal on a planet, and after about a hundred years, an eyeblink in space time, desperate folk would move there and begin setting up their own small-scale recycling operations, purifying the metal, lifting it back up out of the gravity well, and selling it to the companies again for a pittance. It takes a while but it's the cheapest and laziest possible way to recycle things on a massive scale. • Sounds like Soldier (1998). Anyway... where the incoming stuff lands depends on the where the space barges comes from. If from a polar direction, then it could land anywhere; if from an equatorial orbit, then somewhere near the equator; etc. Since it's falling from space, mountains and oceans have no impact. – RonJohn Mar 7 '18 at 19:48 • The premise is utterly flawed, though, since metal is 100% recyclable, and the strong, lightweight alloys needed for space travel aren't cheap. Thus, you'd recycle it. And space travel itself is expensive. Much simpler (I mean much simpler) to just drop stuff that's too expensive to recycle stuff into your own star. – RonJohn Mar 7 '18 at 19:52 • #1 free, limitless energy is impossible. #1 e=mc^2 -> m=e/c^2, which means that you need a lot of energy to make mass. LOTS. Recycling your unobtanium is a lot simpler. – RonJohn Mar 7 '18 at 21:17 • Gotta go with RonJon here. Nearly free and nearly limitless energy is nice, but recycling, or simply disposing junk into the nearest star makes more sense in energy and time than going across the galaxy to a junk planet. – Dan Clarke Mar 7 '18 at 21:49 • @Willk Then presumably you can just turn your waste into energy instead of carting it off to some planet. – Samuel Mar 7 '18 at 23:26 The distribution of impact craters on the Moon is random. I believe the same can be said about Mercury, another crater-ridden body in our solar system. They got their craters from asteroids and comets that struck them randomly throughout the ages. If the drop trajectories over your planet are really random, so will be the impact regions. If you still have doubts, a couple hours simulating this on Kerbal Space Program should solve the problem for you in a very practical manner. The initial falling is pretty well covered by the other answers, so this will focus on the other question in the OP. As the trash collects over thousands of years, would it start to pile up more in some places then others? Many of the processes would apply to trash on Junkyard the same way that they apply to dirt on Earth. Precipitation If you wanted there to be a variety in its distribution, you could add weather that would prevent some trash from making it to the surface, or dissolve trash, creating a climate-like distribution of trash. For example, if your planet had acidic oceans, the patterns of accelerated trash decay would form in the same way that patterns of precipitation form on Earth, with less precipitation corresponding to less disintegration, and thus more trash. The oceans themselves would only contain trash that could survive their acidity. For example, if Junkyard had Earth's geography, trash on the Western side of the Rockies would receive a lot more acid rain than trash on the opposite side, analogous to how California receives a lot more rain than Nevada. Geological Activity If the Junkyard planet is geologically active, subduction zones might swallow up a lot of trash, and the areas where new crust is made would be briefly bare. Also, the way trash reacts to lava could cause areas near volcanos to have unusual concentrations of specific types of trash Weathering from Wind Additionally, if certain latitudes have faster wind than others (comparable to the winds around Antarctica here on Earth), that trash would erode faster (on a very slow time scale, but still), and would have a tendency to settle around the belt instead of inside of it. Glaciers I'm sure there are more creative ways to incorporate glacial erosion, but at the very least, if someone dropped a comet onto the planet, its chunks might move like glaciers, carving out valleys behind them. For processes that wouldn't apply to Earth: Tidal Locking If the planet orbits around a star, you might want to make it tidally locked, causing trash on one side to melt, and causing trash on the other side to accumulate. Additionally, dumpers may prefer one side or the other to avoid the heat of the star, or to get its energy, depending on which side you prefer. It sounds like the pattern would indeed be random, if the drop-off process is as haphazard as you suggest. It's just that if the planet is used as often as you suggest, such a random set of flight patterns could get dangerous. You could have ships heading in to make a drop interfering with each other's flight paths. SOME process wold likely emerge, even if it's only getting on the radio and saying "Hey this is the USS Macawber, if we don't hear from anyone in a half hour, we'll be making a drop run around Planet Junkyard". I wouldn't be surprised if some governing body stepped in and set up flight paths, if only to make sure that some of the trash DOESN'T end up in orbit, or missing the planet entirely and causing a flight hazard. Maybe, but I don't think it would be "All over the planet". Most of it would fall along the equator, well assuming normal orbits (equatorial orbits). If you were dropping it in random orbits then it would be random. But if you drop in the plane of the planets rotation (again equatorial) then it would be concentrated at the equator. Obviously if your orbit determines where it will de-orbit, unless you dump it with a good amount of velocity. Anyway now that everyone is done splitting hairs about what I said, and I do stress the OP never defined an "orbit". UPDATE (just an idea) I think a better premise then a Junk planet is a graveyard planet. From an energy standpoint it doesn't make much sense to take the effort of flying garbage to a planet and then slowing down and dumping it, when you can just shoot it into the nearest star. A better idea as I said is a graveyard planet, what I mean by that is something like this: The US military bone yard. For the most part we keep this place pretty clean but a whole planet used for this purpose and it wouldn't be worth the energy to clean it up. The purpose would be for things like military treaties that limit the use or number of certain ships, for example. It could also be used for deprecated/obsolite equipment. Some of this equipment even though obsolete could still be better then some factions have. And then there is always the use as a parts yard, for post production equipment. You know to keep some of the old stuff fit and running you sacrifice some of them for parts. After a few centuries the place would start looking pretty dumpy. And most of this stuff would have been, safe'd by having the engines or fuel removed before being place for long term storage. So it wouldn't be like you could just land there and sneak off with a star destroyer. Besides you could always have the place guarded by some orbital defense satellites and what not. Even if you want to leave the military aspect out of it, I could see a mega corp taking a small, arid and mineral poor planet and using it for this purpose. Basically a giant Scrap/Junk yard. There may be valuable parts that take specialized manufacturing, or dangerous material that needs specialized handling and recycling facilities. So they take the only thing the planet has to offer a somewhat breathable atmosphere and gravity and use that. Being arid its no good for food production, being poor in minerals its no good for mining. The dryness of the place would be good for preventing corrosion etc. Then they import old ships and equipment, cannibalize them and export replacement parts and scrap metals. But in this case, and if you have valuable infrastructure that you don't want destroyed, you probably wont want stuff just falling from orbit randomly over the planet. You might have a corridor that is setup for reviving bulk scrap metals. Stuff that has no salvageable parts as the energy to deorbit it "gently" would not be justified. This could be around the equator (see what I did there). Couple this with prison/slave labor, and I would believe it was possible in some distant future. • #1 There's no such thing as a "normal" orbits. #2 It also assumes that stars exist only in the planet's equatorial plane. – RonJohn Mar 7 '18 at 21:19 • it doesn't matter if there is a sun or not, it matters which way the planet rotates plane of the planets rotation there is a relationship between the orbit, tidal forces, and the planets rotation that can have a small effect on the orbiting bodies. – ArtisticPhoenix Mar 7 '18 at 21:28 • I didn't mention the sun in my comment. All I said was "planet's equatorial plane". – RonJohn Mar 7 '18 at 21:49 • Why would we think that you assume it? Because you wrote, "Most of it would fall along the equator, well assuming normal orbits." – RonJohn Mar 7 '18 at 23:31 • "equatorial orbits, which are more efficient" for ground launches. Not for arriving from another star. – RonJohn Mar 7 '18 at 23:38 Does it rotate? If so, the trash would be more likely to pile up on the plane of rotation, which for an earthlike setup is the Tropics of Cancer to Capricorn. However, I think you need to think through the whole low orbit thing. If people were being at all careless in their dumping, there would quickly be a sheath of debris orbiting this planet such that it'd be difficult to land there, and it'd be constantly bombarded with impacts. This would be a tough place to live. • Trash would pile up in whatever orbit people dumped it in. You might be thinking of the fact that planets are mostly in the orbital plane, but recall that ring systems for planets depend more on the planet's rotation than its orbital plane. Uranus for example has rings that are almost perpendicular to the orbital plane because that's how Uranus rotates. And all that is only that way as a leftover from formation, not because it's a better orbit. – Samuel Mar 7 '18 at 20:56 • You're absolutely right; rotation would trump orbit hands' down. Clarifying my post. – Carduus Mar 7 '18 at 21:07 • Oh, still, the plane of rotation doesn't really come into it unless they're launching from the surface (as it's a cheaper orbit to get to from the surface). Being in orbit at all is assuming people dump their trash at orbital velocities. – Samuel Mar 7 '18 at 21:37 • "If you're orbiting and dropping, the trash is going to come out in a line based on both your trajectory and the planet's rotation" - No, the planet's rotation doesn't enter into it, only the orbital parameters. A ship only needs to enter an orbit if it plans to stay. Would you agree it's feasible for a ship to approach a planet directly, drop its trash, and then make a slight course adjustment to miss the planet entirely? In that case it wouldn't even need to slow down from interplanetary speeds to orbital speeds nor waste the energy slowing its trash down in the same fashion. – Samuel Mar 8 '18 at 17:12 • That's very true. And I suppose with the halo of trash already there, it's best to just throw it and run. – Carduus Mar 8 '18 at 17:17 As @ArtisticPhoenix said, it will likely have a bell curve distribution centering on the equator or some other line near the equator. That is because most planets lie in their star's plane of ecliptic and have a spin that corresponds roughly with the plane of the ecliptic. Most stars are on or near the galaxy's plane of the ecliptic and their spin's correspond generally to the galaxy's plane. This isn't 100% but the majority of the ships dumping stuff should come in with a least cost approach near the equator. Even if ships do not come in on an equatorial plane, since the planet is spinning, their trash has a good chance of crossing the equator and will otherwise be distributed around the planet. If you have ships from different stars coming in at different angles and directions, almost all of their dumps will cross the equator. This will make the distribution higher as you approach the equator. • "The majority of the ships dumping stuff should come in with a least cost approach near the equator. Why? There are a whole lot of stars in the Northern Hemisphere, so what's to stop barges from coming in from a polar direction? – RonJohn Mar 7 '18 at 22:25 • @RonJohn, first, many of the "stars" you see are actually galaxies. Also, get into an area with dark skies and look at the Milkyway or find a picture on the internet (but that's not nearly as good). Even if all of the "stars" you see are actual stars, look at how many more come from near the Milkyway's plane of the ecliptic. Also, in the second part of the question, I address the situation if they aren't in a near equatorial orbit. – ShadoCat Mar 7 '18 at 22:34 • The Milky Way is -- from some point on the Earth at some time of year -- at every angle from almost 0° to 90°. – RonJohn Mar 7 '18 at 22:40 • The premise is "assuming both the trajectory and the exact point in space from which the garbage is released are both random". Are you saying the premise of the question is wrong? – Samuel Mar 7 '18 at 23:23 • A drop of trajectory would only be less costly by bwing close to the equator if the starting trajextory is already within the same plane as the equator. Even in our own solar system that is rarely true, since each planet's orbit around the sun has its own plane. – The Square-Cube Law Mar 8 '18 at 11:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40193337202072144, "perplexity": 1285.500369617311}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389798.91/warc/CC-MAIN-20210309092230-20210309122230-00393.warc.gz"}
https://codeforces.com/blog/entry/52637	### Lewin's blog By Lewin, history, 4 years ago, Hello everyone! I would like to invite you to participate in Hackerearth June Circuits 2017. It's a long contest that will start on June 16, 2017, 21:00 IST (check your timezone). The contest will run for 9 days. The problemset consists of 7 traditional algorithmic tasks and 1 approximate problem. For traditional algorithmic tasks, you will receive points for every test case your solution passes — so you can get some points with partial solutions as well. For the approximation task, your score depends on the best solution in the contest so far. Check contest page for more details about in-contest schedule and rules. I'm the tester of the problemset you'll have to work on — thanks to jtnydv25, saatwik27, harshil, zscoder, Arunnsit for preparing these tasks. As usual, there will be some prizes for the top five competitors: 1. $100 Amazon gift card + HE t-shirt. 2.$75 Amazon gift card + HE t-shirt. 3. \$50 Amazon gift card + HE t-shirt. 4. HE t-shirt. 5. HE t-shirt. Good luck to everyone, and I hope to see you at the contest :) • +60 » 4 years ago, # \| +13 Since no one is replying on the problem's page anymore, I thought about asking here: For the approximation problem (The Grid Organizer) will there be new test cases added after the contest ends? If yes, then please make this information available ASAP. Since the problem is configured to get a score of 0 if any test case fails, it's important to make our solutions more "robust" than usual in case new test cases will be added after the contest (e.g. in order to make sure we avoid any chance of TLE, etc.).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33725684881210327, "perplexity": 2122.005254879309}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00330.warc.gz"}
https://www.physicsforums.com/threads/heisenberg-uncertainty-need-some-clarification-time-sesitive-help.395910/	# Homework Help: Heisenberg Uncertainty, Need Some Clarification. TIME SESITIVE, HELP 1. Apr 16, 2010 ### asl3589 Heisenberg Uncertainty, Need Some Clarification. TIME SESITIVE, HELP!! 1. The problem statement, all variables and given/known data Use the Heisenberg uncertainty principle to calculate Deltax for a ball (mass = 100 g, diameter = 6.65 cm) with Deltav = 0.645 m/s. 2. Relevant equations PX = h/(43.14) 3. The attempt at a solution So, I took the equation and converted the values with my numbers:((h/4π)/(.1kg .645 m/s))/(.0665m) and yielded an 10^-32 m. This answer is wrong and I am not sure why. I only have two hours left to answer this question. I would really appreciate it if someone could guide me on what my mistake is? 2. Apr 16, 2010 ### collinsmark Re: Heisenberg Uncertainty, Need Some Clarification. TIME SESITIVE, HELP!! Hello asl3589, Why did you divide by the diameter of the ball? [Edit: Also, you seem to be using the more formal $$\sigma _x \sigma _p \geq \frac{\hbar}{2}$$ where $$\hbar = \frac{h}{2 \pi}$$. But keep in mind that relationship is not an equality. If you want an approximate value with a $$\approx$$ sign and using $$\Delta x$$ and $$\Delta p$$, there is a slightly different version of the relation.] Last edited: Apr 16, 2010 3. Apr 16, 2010 ### asl3589 Re: Heisenberg Uncertainty, Need Some Clarification. TIME SESITIVE, HELP!! Thanks for looking at it. I just assumed that the diameter factors into somehow. Is that unneccesary. If I take that step out the answer is just 8.174 * 10^-34 m. Is that right? 4. Apr 16, 2010 ### collinsmark Re: Heisenberg Uncertainty, Need Some Clarification. TIME SESITIVE, HELP!! That would give you the minimum possible uncertainty in position. But that's not necessarily the approximate uncertainty. The minimum possible uncertainty in position might be the answer your instructor is looking for, but I'm uncertain about that.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9115045070648193, "perplexity": 978.5407777752707}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376832330.93/warc/CC-MAIN-20181219130756-20181219152756-00537.warc.gz"}
https://msp.org/index/ail.php?jpath=involve&l=P	Paat, Joseph Knot mosaic tabulation Involve, a Journal of Mathematics 11 (2018) 13–26 Pagliari, Giorgia Existence of positive solutions for an approximation of stationary mean-field games Involve, a Journal of Mathematics 10 (2017) 473–493 Paixão, João On the asymptotic behavior of unions of sets of lengths in atomic monoids Involve, a Journal of Mathematics 1 (2008) 101–110 Pal, Nabendu Zero-inflated Poisson (ZIP) distribution: parameter estimation and applications to model data from natural calamities Involve, a Journal of Mathematics 7 (2014) 751–767 Palladino, Frank Difference inequalities, comparison tests, and some consequences Involve, a Journal of Mathematics 1 (2008) 91–100 Palsson, Eyvindur A generalization of Zeckendorf's theorem via circumscribed m-gons Involve, a Journal of Mathematics 10 (2017) 125–150 Characterizing optimal point sets determining one distinct triangle Involve, a Journal of Mathematics 13 (2020) 91–98 Panescu, Priera Symplectic embeddings of 4-dimensional ellipsoids into polydiscs Involve, a Journal of Mathematics 10 (2017) 219–242 Pantano, Alessandra Institutional support for undergraduate research Involve, a Journal of Mathematics 7 (2014) 355–362 Paquette, Elliot The index of a vector field on an orbifold with boundary Involve, a Journal of Mathematics 2 (2009) 161–175 Parisi, Francis A Statistical Study of Extreme Nor'easter Snowstorms Involve, a Journal of Mathematics 2 (2009) 341–350 Parker, Aaron Irreducible Character Restrictions to Maximal Subgroups Of Low-Rank Classical Groups of Type B and C Involve, a Journal of Mathematics 12 (2019) 607–631 Parks, Ryan A Binary Unrelated Question RRT Model Accounting for Untruthful Responding Involve, a Journal of Mathematics 12 (2019) 1163–1173 Parsons, Christopher On the number of pairwise touching simplices Involve, a Journal of Mathematics 8 (2015) 513–520 Pascu, Iuliana The Multi-Dimensional Frobenius Problem Involve, a Journal of Mathematics 4 (2011) 187–197 Pasley, Lillian On commutators of matrices over unital rings Involve, a Journal of Mathematics 7 (2014) 769–772 Passaro, John Average reductions between random tree pairs Involve, a Journal of Mathematics 8 (2015) 63–69 Pathakjee, David Elliptic curves, eta-quotients and hypergeometric functions Involve, a Journal of Mathematics 5 (2012) 1–8 Patrias, Rebecca Coincidences among skew stable and dual stable Grothendieck polynomials Involve, a Journal of Mathematics 11 (2018) 143–167 Patton, Linda Symmetric numerical ranges of four by four matrices Involve, a Journal of Mathematics 11 (2018) 803–826 Paugh, Hannah A generalization of Zeckendorf's theorem via circumscribed m-gons Involve, a Journal of Mathematics 10 (2017) 125–150 Paulhus, Jennifer Jacobian varieties of Hurwitz curves with automorphism group PSL(2,q) Involve, a Journal of Mathematics 9 (2016) 639–655 Pauli, Sebastian On the zeros of $\zeta(s)-c$ Involve, a Journal of Mathematics 6 (2013) 137–146 Paulsen, Chelsey Depths and Stanley depths of path ideals of spines Involve, a Journal of Mathematics 9 (2016) 155–170 Pavlov, Ronald A characterization of the sets of periods within shifts of finite type Involve, a Journal of Mathematics 12 (2019) 203–220 Payne, Catherine Analysis of steady states for classes of reaction-diffusion equations with hump-shaped density dependent dispersal on the boundary Involve, a Journal of Mathematics 13 (2020) 9–19 Pearson, Paul A modified wavelet method for identifying transient features in time signals with applications to bean beetle maturation Involve, a Journal of Mathematics 10 (2017) 21–42 Pechenik, Oliver Zero-divisor ideals and realizable zero-divisor graphs Involve, a Journal of Mathematics 2 (2009) 17–27 Peck, Hailee An exploration of ideal-divisor graphs Involve, a Journal of Mathematics 8 (2015) 87–98 Pedroza, Dianne Matrix Completions for Linear Matrix Equations Involve, a Journal of Mathematics 10 (2017) 781–799 Peifer, Dylan Presentations of Roger and Yang's Kauffman bracket arc algebras Involve, a Journal of Mathematics 9 (2016) 689–698 Peiffer, Amanda Knot mosaic tabulation Involve, a Journal of Mathematics 11 (2018) 13–26 Pelayo, Roberto Co-circular relative equilibria of four vortices Involve, a Journal of Mathematics 9 (2016) 395–410 Pereira, Joel A classification of Klein links as torus links Involve, a Journal of Mathematics 11 (2018) 609–624 Klein links and related torus links Involve, a Journal of Mathematics 9 (2016) 347–359 Perez, Hector Energy Minimizing Unit Vector Fields Involve, a Journal of Mathematics 3 (2010) 435–450 Perez, Stephanie Persistence: a digit problem. 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https://www.physicsforums.com/threads/jumping-physics-problem.362338/	# Jumping physics problem 1. Dec 10, 2009 ### PearlyD 1. The problem statement, all variables and given/known data An exceptional standing jump would raise a person 0.80m off the ground. To do this, what force must a 66 kg person exert against the ground? Assume the person crouches a distance of 0.20 m prior to jumping,and thus the upward force has this distance to act over before he leaves the ground. This question i dont even know how to start can some one explain how to even start it? 2. Dec 10, 2009 ### nickdk Re: Jumping Work = Force * Distance Force = (9.81)(66) Work = (9.81)(66)(.80) Work = 517.968 J Doesn't account for the crouching distance, but it may be irrelevant, someone else will probably cover that. I hope I went in the right direction with this. Similar Discussions: Jumping physics problem	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8522143959999084, "perplexity": 2284.7425798374734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105712.28/warc/CC-MAIN-20170819182059-20170819202059-00536.warc.gz"}
https://worldwidescience.org/topicpages/n/neyman-scott+rectangular+pulses.html	#### Sample records for neyman-scott rectangular pulses 1. An estimating function approach to inference for inhomogeneous Neyman-Scott processes DEFF Research Database (Denmark) Waagepetersen, Rasmus Plenge “This paper is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the “mother” intensity for the Neyman-Scott... 2. An estimating function approach to inference for inhomogeneous Neyman-Scott processes DEFF Research Database (Denmark) Waagepetersen, Rasmus 2007-01-01 This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Sc... 3. Distinguishing different types of inhomogeneity in Neyman-Scott point processes Czech Academy of Sciences Publication Activity Database Mrkvička, Tomáš 2014-01-01 Roč. 16, č. 2 (2014), s. 385-395 ISSN 1387-5841 Institutional support: RVO:60077344 Keywords : clustering * growing clusters * inhomogeneous cluster centers * inhomogeneous point process * location dependent scaling * Neyman-Scott point process Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2014 4. Further developments of the Neyman-Scott clustered point process for modeling rainfall Science.gov (United States) Cowpertwait, Paul S. P. 1991-07-01 This paper provides some useful results for modeling rainfall. It extends work on the Neyman-Scott cluster model for simulating rainfall time series. Several important properties have previously been found for the model, for example, the expectation and variance of the amount of rain captured in an arbitrary time interval (Rodriguez-Iturbe et al., 1987a), In this paper additional properties are derived, such as the probability of an arbitrary interval of any chosen length being dry. In applications this is a desirable property to have, and is often used for fitting stochastic rainfall models to field data. The model is currently being used in rainfall time series research directed toward improving sewage systems in the United Kingdom. To illustrate the model's performance an example is given, where the model is fitted to 10 years of hourly data taken from Blackpool, England. 5. Effect of rising time of rectangular pulse on inactivation of staphylococcus aureus by pulsed electric field Science.gov (United States) Zhang, Ruobing; Liang, Dapeng; Zheng, Nanchen; Xiao, Jianfu; Mo, Mengbin; Li, Jing 2013-03-01 Pulsed electric field (PEF) is a novel non-thermal food processing technology that involves the electric discharge of high voltage short pulses through the food product. In PEF study, rectangular pulses are most commonly used for inactivating microorganisms. However, little information is available on the inactivation effect of rising time of rectangular pulse. In this paper, inactivation effects, electric field strength, treatment time and conductivity on staphylococcus aureus inactivation were investigated when the pulse rising time is reduced from 2.5 μs to 200 ns. Experimental results showed that inactivation effect of PEF increased with electric field strength, solution conductivity and treatment time. Rising time of the rectangular pulse had a significant effect on the inactivation of staphylococcus aureus. Rectangular pulses with a rising time of 200 ns had a better inactivation effect than that with 2 μs. In addition, temperature increase of the solution treated by pulses with 200 ns rising time was lower than that with 2 μs. In order to obtain a given inactivation effect, treatment time required for the rectangular pulse with 200 ns rise time was shorter than that with 2 μs. 6. Effect of rising time of rectangular pulse on inactivation of staphylococcus aureus by pulsed electric field International Nuclear Information System (INIS) Zhang, Ruobing; Liang, Dapeng; Xiao, Jianfu; Mo, Mengbin; Li, Jing; Zheng, Nanchen 2013-01-01 Pulsed electric field (PEF) is a novel non-thermal food processing technology that involves the electric discharge of high voltage short pulses through the food product. In PEF study, rectangular pulses are most commonly used for inactivating microorganisms. However, little information is available on the inactivation effect of rising time of rectangular pulse. In this paper, inactivation effects, electric field strength, treatment time and conductivity on staphylococcus aureus inactivation were investigated when the pulse rising time is reduced from 2.5 μs to 200 ns. Experimental results showed that inactivation effect of PEF increased with electric field strength, solution conductivity and treatment time. Rising time of the rectangular pulse had a significant effect on the inactivation of staphylococcus aureus. Rectangular pulses with a rising time of 200 ns had a better inactivation effect than that with 2 μs. In addition, temperature increase of the solution treated by pulses with 200 ns rising time was lower than that with 2 μs. In order to obtain a given inactivation effect, treatment time required for the rectangular pulse with 200 ns rise time was shorter than that with 2 μs. 7. The nanosecond generator RG-1 with near-rectangular pulse International Nuclear Information System (INIS) Bulan, V.V.; Grabovskij, E.V.; Gribov, A.N.; Luzhnov, V.G. 1996-01-01 The 300 kV, 17 Ohm generator RG-1, which can deliver near-rectangular pulses with a pulse duration of 80 ns FWHM, is described. The polarity of the output pulse can be changed by a simple switch. The fast capacities of the Marx generator are used instead of the pulse forming line. Multi-spark gas switches were developed to decrease the inductance of the discharged circuit. The generator is supplied by a built-in high voltage source and its operation is controlled by a minicomputer. It is used the power supply-line 220 V. The RG-1 can be used in different modes of operation: gas discharge, particle beam formation, etc. (author). 4 figs., 3 refs 8. The nanosecond generator RG-1 with near-rectangular pulse Energy Technology Data Exchange (ETDEWEB) Bulan, V V; Grabovskij, E V; Gribov, A N; Luzhnov, V G [TRINITI, Troitsk (Russian Federation) 1997-12-31 The 300 kV, 17 Ohm generator RG-1, which can deliver near-rectangular pulses with a pulse duration of 80 ns FWHM, is described. The polarity of the output pulse can be changed by a simple switch. The fast capacities of the Marx generator are used instead of the pulse forming line. Multi-spark gas switches were developed to decrease the inductance of the discharged circuit. The generator is supplied by a built-in high voltage source and its operation is controlled by a minicomputer. It is used the power supply-line 220 V. The RG-1 can be used in different modes of operation: gas discharge, particle beam formation, etc. (author). 4 figs., 3 refs. 9. A Novel Transcranial Magnetic Stimulator Inducing Near Rectangular Pulses with Controllable Pulse Width (cTMS) Science.gov (United States) Jalinous, Reza; Lisanby, Sarah H. 2013-01-01 A novel transcranial magnetic stimulation (TMS) device with controllable pulse width (PW) and near rectangular pulse shape (cTMS) is described. The cTMS device uses an insulated gate bipolar transistor (IGBT) with appropriate snubbers to switch coil currents up to 7 kA, enabling PW control from 5 μs to over 100 μs. The near-rectangular induced electric field pulses use 22–34% less energy and generate 67–72% less coil heating compared to matched conventional cosine pulses. CTMS is used to stimulate rhesus monkey motor cortex in vivo with PWs of 20 to 100 μs, demonstrating the expected decrease of threshold pulse amplitude with increasing PW. The technological solutions used in the cTMS prototype can expand functionality, and reduce power consumption and coil heating in TMS, enhancing its research and therapeutic applications. PMID:18232369 10. High-voltage nanosecond Marx generator with quasi-rectangular pulses International Nuclear Information System (INIS) Bulan, V.V.; Grabovskij, E.V.; Gribov, A.N.; Luzhnov, V.G. 1999-01-01 The automated high-voltage nanosecond generator, forming single pulses of any polarity on the load of 17 Ohm with polarity voltage from 100 up to 300 kV at the semiheight of 80 ns and the front of 7 ns is described. The generator is assembled on the basis of low-inductive capacitors, which by discharge form the pulse, close by form to rectangular one [ru 11. Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model OpenAIRE Dongkyun Kim; Francisco Olivera; Huidae Cho; Scott A. Socolofsky 2013-01-01 Parameters of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) stochastic rainfall simulation model were regionalized across the contiguous United States. Three thousand four hundred forty-four National Climate Data Center (NCDC) rain gauges were used to obtain spatial and seasonal patterns of the model parameters. The MBLRP model was calibrated to minimize the discrepancy between the precipitation depth statistics between the observed and MBLRP-generated precipitation time series. These... 12. A novel compact low impedance Marx generator with quasi-rectangular pulse output Science.gov (United States) Liu, Hongwei; Jiang, Ping; Yuan, Jianqiang; Wang, Lingyun; Ma, Xun; Xie, Weiping 2018-04-01 In this paper, a novel low impedance compact Marx generator with near-square pulse output based on the Fourier theory is developed. Compared with the traditional Marx generator, capacitors with different capacity have been used. It can generate a high-voltage quasi-rectangular pulse with a width of 100 ns at low impedance load, and it also has high energy density and power density. The generator consists of 16 modules. Each module comprises an integrative single-ended plastic case capacitor with a nominal value of 54 nF, four ceramic capacitors with a nominal value of 1.5 nF, a gas switch, a charging inductor, a grounding inductor, and insulators which provide mechanical support for all elements. In the module, different discharge periods from different capacitors add to the main circuit to form a quasi-rectangular pulse. The design process of the generator is analyzed, and the test results are provided here. The generator achieved pulse output with a rise time of 32 ns, pulse width of 120 ns, flat-topped width (95%-95%) of 50 ns, voltage of 550 kV, and power of 20 GW. 13. Numerical simulation of microwave pulse coupling into the rectangular cavity with aperture arrays International Nuclear Information System (INIS) Li Rui; Yang Yiming; Qian Baoliang 2008-01-01 In this paper, the finite-difference time-domain (FDTD) algorithm is employed to simulate microwave pulse coupling into the rectangular cavity with aperture arrays. In the case in which the long-side of the slot in aperture arrays is perpendicular to the incident electrical field, and the electrical distribution of each center of slot in the aperture arrays in the process of microwave pulse coupling into the rectangular cavity with aperture arrays is analyzed in detail. We find that the effect of field enhancement of the slot in the middle of all the slots which distribute in the direction parallel to the incident electrical field is minimum and increases in turn from the middle to both sides symmetrically. We also find that the effect of field enhancement of the slot in the middle of all the slots which distribute in the direction perpendicular to the incident electrical field is maximum and decreases in turn from the middle to both sides symmetrically. In the same time, we investigate the factors that influence the effect of field enhancement of the center of each slot and the coupling electrical distribution in the cavity, including the number of slots and the spacing between slots. (authors) 14. Damage Evaluation of Critical Components of Tilted Support Spring Nonlinear System under a Rectangular Pulse Directory of Open Access Journals (Sweden) Ningning Duan 2015-01-01 Full Text Available Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system. 15. Surface Crack Detection for Carbon Fiber Reinforced Plastic Materials Using Pulsed Eddy Current Based on Rectangular Differential Probe Directory of Open Access Journals (Sweden) Jialong Wu 2014-01-01 Full Text Available Aiming at the surface defect inspection of carbon fiber reinforced composite, the differential and the direct measurement finite element simulation models of pulsed eddy current flaw detection were built. The principle of differential pulsed eddy current detection was analyzed and the sensitivity of defect detection was compared through two kinds of measurements. The validity of simulation results was demonstrated by experiments. The simulation and experimental results show that the pulsed eddy current detection method based on rectangular differential probe can effectively improve the sensitivity of surface defect detection of carbon fiber reinforced composite material. 16. Pulsed neutron intensity from rectangular shaped light water moderator with fast-neutron reflector International Nuclear Information System (INIS) Kiyanagi, Yoshiaki; Iwasa, Hirokatsu 1982-01-01 With a view to enhancing the thermal-neutron intensity obtained from a pulsed neutron source, an experimental study has been made to determine the optimum size of a rectangular shaped light water moderator provided with fast neutron reflector of beryllium oxide or graphite, and decoupled thermal-neutronically by means of Cd sheet. The optimum dimensions for the moderator are derived for the neutron emission surface and the thickn ess, for the cases in which the neutron-producing target is placed beneath the moderator (''wing geometry'') or immediately behind the moderator (''slab geometry''). The major conclusions drawn from the experimental results are as follows. The presence of the Cd decoupler inserted between the moderator and reflector prevent the enhancement of thermal-neutron emission time gained by the provision of reflector. With a graphite reflector about 14 cm thick, (a) the optimum area of emission surface would be 25 x 25 cm 2 for wing geometry and still larger for slab geometry, and (b) the optimum moderator thickness would be 5.5 cm for slab geometry and 8.5 cm for wing geometry. It is thus concluded that a higher neutron emission intensity can be obtained with slab than with wing geometry provided that a large emission surface can be adopted for the moderator. (author) 17. Analysis of Dietz's single, rectangular pulse theory for the generation of radiation via photoelectrons International Nuclear Information System (INIS) Dipp, T.M. 1993-12-01 The generation of radiation via photoelectrons induced off of a conducting surface has been analytically modeled and computationally simulated by several researchers. This paper analyzes and compares Dietz's theory predictions with my research to form a unified foundation of consistent, inter-supporting results that should provide confidence in the independently performed basic research and resulting scaling laws and predictions. In doing so, this paper concentrated on Dietz's small-spot, single, rectangular, ''weak'' pulse theory and equations, which involve nonrelativistic, monoenergetic photoelectrons emitted normal to a conducting surface in vacuum. In this paper I: (1) analytically compare Dietz's theory equations with my theory equations, (2) compare Dietz's theoretical scaling laws with my Particle-In-Cell (PIC) code simulation results, and (3) make Dietz's equations easier to use in predicting and optimizing photoelectron-generated radiation. As a result, it is shown that Dietz's equations match my theory's equations in their predicted scaling laws, differing only slightly in their coefficients and unique model parameters. Also, Dietz's equations generally agree with the PIC code results. Finally, optimization analysis showed that theoretical conversion efficiencies for typical real metals can meet and exceed values of 10 -5 if optimal photon energies of 15 to 20 eV are used. Even better efficiencies should be possible if the small-spot constraint is violated as well 18. Stochastic Modeling of Rainfall in Peninsular Malaysia Using Bartlett Lewis Rectangular Pulses Models Directory of Open Access Journals (Sweden) Ibrahim Suliman Hanaish 2011-01-01 Full Text Available Three versions of Bartlett Lewis rectangular pulse rainfall models, namely, the Original Bartlett Lewis (OBL, Modified Bartlett Lewis (MBL, and 2N-cell-type Bartlett Lewis model (BL2n, are considered. These models are fitted to the hourly rainfall data from 1970 to 2008 obtained from Petaling Jaya rain gauge station, located in Peninsular Malaysia. The generalized method of moments is used to estimate the model parameters. Under this method, minimization of two different objective functions which involve different weight functions, one weight is inversely proportional to the variance and another one is inversely proportional to the mean squared, is carried out using Nelder-Mead optimization technique. For the purpose of comparison of the performance of the three different models, the results found for the months of July and November are used for illustration. This performance is assessed based on the goodness of fit of the models. In addition, the sensitivity of the parameter estimates to the choice of the objective function is also investigated. It is found that BL2n slightly outperforms OBL. However, the best model is the Modified Bartlett Lewis MBL, particularly when the objective function considered involves weight which is inversely proportional to the variance. 19. Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model Directory of Open Access Journals (Sweden) Dongkyun Kim 2013-01-01 Full Text Available Parameters of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP stochastic rainfall simulation model were regionalized across the contiguous United States. Three thousand four hundred forty-four National Climate Data Center (NCDC rain gauges were used to obtain spatial and seasonal patterns of the model parameters. The MBLRP model was calibrated to minimize the discrepancy between the precipitation depth statistics between the observed and MBLRP-generated precipitation time series. These statistics included the mean, variance, probability of zero rainfall and autocorrelation at 1-, 3-, 12- and 24-hour accumulation intervals. The Ordinary Kriging interpolation technique was used to generate maps of the six MBLRP model parameters for each of the 12 months of the year. All parameters had clear to discernible regional tendencies; except for one related to rain cell duration distribution. Parameter seasonality was not obvious and it was more apparent in some locations than in others, depending on the seasonality of the rainfall statistics. Cross-validation was used to assess the validity of the parameter maps. The results indicate that the suggested maps reproduce well the observed rainfall statistics for different accumulation intervals, except for the lag-1 autocorrelation coefficient. The boundaries of the expected residual, with 95% confidence, between the observed rainfall statistics and the simulated rainfall statistics based on the map parameters were approximately ±0.064 mm hr-1, ±1.63 mm2 hr-2, ±0.16, and ±0.030 for the mean, variance, lag-1 autocorrelation and probability of zero rainfall at hourly accumulation levels, respectively. The estimated parameter values were also used to estimate the storm and rain cell characteristics. 20. Coupling Poisson rectangular pulse and multiplicative microcanonical random cascade models to generate sub-daily precipitation timeseries Science.gov (United States) Pohle, Ina; Niebisch, Michael; Müller, Hannes; Schümberg, Sabine; Zha, Tingting; Maurer, Thomas; Hinz, Christoph 2018-07-01 To simulate the impacts of within-storm rainfall variabilities on fast hydrological processes, long precipitation time series with high temporal resolution are required. Due to limited availability of observed data such time series are typically obtained from stochastic models. However, most existing rainfall models are limited in their ability to conserve rainfall event statistics which are relevant for hydrological processes. Poisson rectangular pulse models are widely applied to generate long time series of alternating precipitation events durations and mean intensities as well as interstorm period durations. Multiplicative microcanonical random cascade (MRC) models are used to disaggregate precipitation time series from coarse to fine temporal resolution. To overcome the inconsistencies between the temporal structure of the Poisson rectangular pulse model and the MRC model, we developed a new coupling approach by introducing two modifications to the MRC model. These modifications comprise (a) a modified cascade model ("constrained cascade") which preserves the event durations generated by the Poisson rectangular model by constraining the first and last interval of a precipitation event to contain precipitation and (b) continuous sigmoid functions of the multiplicative weights to consider the scale-dependency in the disaggregation of precipitation events of different durations. The constrained cascade model was evaluated in its ability to disaggregate observed precipitation events in comparison to existing MRC models. For that, we used a 20-year record of hourly precipitation at six stations across Germany. The constrained cascade model showed a pronounced better agreement with the observed data in terms of both the temporal pattern of the precipitation time series (e.g. the dry and wet spell durations and autocorrelations) and event characteristics (e.g. intra-event intermittency and intensity fluctuation within events). The constrained cascade model also 1. Electrostatic deposition of a micro solder particle using a single probe by applying a single rectangular pulse International Nuclear Information System (INIS) Nakabayashi, Daizo; Sawai, Kenji; Saito, Shigeki; Takahashi, Kunio 2012-01-01 Recently, micromanipulation techniques have been in high demand. A technique to deposit a metal microparticle onto a metal substrate by using a single metal probe has been proposed as one of the techniques. A solder particle with a diameter of 20–30 µm, initially adhering to the probe tip, is detached and deposited onto a substrate. The success rate of the particle deposition was 44% in the previous research, and is insufficient for industrial applications. In this paper, a technique of particle deposition by applying a single rectangular pulse is proposed, and the mechanism of the deposition is described. In the mechanism, an electric discharge between the probe and the particle when the particle reaches the substrate plays an important role in the particle deposition. Moreover, the mechanism of the proposed technique is verified by experiments of particle deposition, which are observed using a high-speed camera, a scanning electron microscope (SEM) and an oscilloscope. The success rate of the particle deposition has increased to 93% by the proposed technique. Furthermore, the damage to the particle by the electric discharge is evaluated using an RC circuit model, and the applicability of the proposed technique is discussed. (paper) 2. Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers Czech Academy of Sciences Publication Activity Database Mrkvička, T.; Muška, Milan; Kubečka, Jan 2014-01-01 Roč. 24, č. 1 (2014), s. 91-100 ISSN 0960-3174 R&D Projects: GA ČR(CZ) GA206/07/1392 Institutional support: RVO:60077344 Keywords : bayesian method * clustering * inhomogeneous point process Subject RIV: EH - Ecology, Behaviour Impact factor: 1.623, year: 2014 3. Study on the cutting quality by rectangular pulse wave of the CO sub 2 laser. CO sub 2 laser no kukei pulse hakei ni yoru setsudan hinshitsu no kenkyu Energy Technology Data Exchange (ETDEWEB) Kanaoka, M. (Mitsubishi Electric Corporation, Tokyo (Japan)) 1992-05-20 The paper studies effects of laser power parameters on processing quality in cutting metal by the use of rectangular pulse waveform formed by the triaxial cross flow resonator. As a result, the heat affected zone appearing around the kerf expands from the upper part to the lower part, and by increasing pulse peak power the width of the heat affected zone from the central part of board thickness to the lower part lessens. Further, by lowering pulse frequency, the width of the heat affected zone appearing around the kerf from the central part of board thickness to the lower part lessens. Also, by lowering frequency, an energy absortion rate of the workpiece to be processed decreases. Cutting surface roughness is affected by pulse peak power, and the high the peak value is, the better the surface roughness is improved. In addition, the surface roughmess is affected by pulse frequency, and the higher the frequency is, the better the surface roughness is improved. 6 refs., 15 figs. 4. Evaluation of high resolution spatio-temporal precipitation extremes from a stochastic weather generator DEFF Research Database (Denmark) Sørup, Hjalte Jomo Danielsen; Christensen, O. B.; Arnbjerg-Nielsen, Karsten 2017-01-01 Spatio-temporal rainfall is modelled for the North-Eastern part of Zealand (Denmark) using the Spatio-Temporal Neyman-Scott Rectangular Pulses model as implemented in the RainSim software. Hourly precipitation series for fitting the model are obtained from a dense network of tipping bucket rain...... gauges in the model area. The spatiotemporal performance of the model with respect to precipitation extremes is evaluated in the points of a 2x2 km regular grid covering the full model area. The model satisfactorily reproduces the extreme behaviour of the observed precipitation with respect to event...... intensity levels and unconditional spatial correlation when evaluated using an event based ranking approach at point scale and an advanced spatiotemporal coupling of extreme events. Prospectively the model can be used as a tool to evaluate the impact of climate change without relying on precipitation output... 5. Evaluation of high resolution spatio-temporal precipitation extremes from a stochastic weather generator DEFF Research Database (Denmark) Sørup, Hjalte Jomo Danielsen; Christensen, O. B.; Arnbjerg-Nielsen, Karsten gauges in the model area. The spatio-temporal performance of the model with respect to precipitation extremes is evaluated in the points of a 2x2 km regular grid covering the full model area. The model satisfactorily reproduces the extreme behaviour of the observed precipitation with respect to event...... intensity levels and unconditional spatial correlation when evaluated using an event based ranking approach at point scale and an advanced spatio-temporal coupling of extreme events. Prospectively the model can be used as a tool to evaluate the impact of climate change without relying onprecipitation output......Spatio-temporal rainfall is modelled for the North-Eastern part of Zealand (Denmark) using the Spatio-Temporal Neyman-Scott Rectangular Pulses model as implemented in the RainSim software. Hourly precipitation series for fitting the model are obtained from a dense network of tipping bucket rain... 6. Rectangular cartograms: the game NARCIS (Netherlands) Berg, de M.T.; Nijnatten, van F.S.B.; Speckmann, B.; Verbeek, K.A.B. 2009-01-01 Raisz [3] introduced rectangular cartograms in 1934 as a way of visualizing spatial information, such as population or economic strength, of a set of regions like countries or states. Rectangular cartograms represent geographic regions by rectangles; the positioning and adjacencies of the rectangles 7. A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process Science.gov (United States) Abas, Norzaida; Daud, Zalina M.; Yusof, Fadhilah 2014-11-01 A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial-Temporal Neyman-Scott Rectangular Pulse model was used. The model, which is governed by the Neyman-Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region. 8. Best connected rectangular arrangements Directory of Open Access Journals (Sweden) Krishnendra Shekhawat 2016-03-01 Full Text Available It can be found quite often in the literature that many well-known architects have employed either the golden rectangle or the Fibonacci rectangle in their works. On contrary, it is rare to find any specific reason for using them so often. Recently, Shekhawat (2015 proved that the golden rectangle and the Fibonacci rectangle are one of the best connected rectangular arrangements and this may be one of the reasons for their high presence in architectural designs. In this work we present an algorithm that generates n-4 best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs. 9. Cooling of rectangular bars International Nuclear Information System (INIS) Frainer, V.J. 1979-01-01 A solution of the time-transient Heat Transfer Differential Equation in rectangular coordinates is presented, leading to a model which describes the temperature drop with time in rectangular bars. It is similar to an other model for cilindrical bars which has been previously developed in the Laboratory of Mechanical Metallurgy of UFRGS. Following these models, a generalization has been made, which permits cooling time evaluation for all profiles. These results are compared with experimental laboratory data in the 1200 to 800 0 C range. Some other existing models were also studied which have the purpose of studing the same phenomenon. Their mathematical forms and their evaluated values are analyzed and compared with experimental ones. (Author) [pt 10. Experiences with rectangular waveguide International Nuclear Information System (INIS) Beltran, J.; Sepulveda, J. J.; Navarro, E. A. 2000-01-01 A simple and didactic experimental arrangement is presented to show wave propagation along a structure with translational symmetry, particularly the rectangular waveguide. Parameters of this waveguide as cutoff frequency, guide wavelength and field distribution of fundamental mode can be measured. For this purpose a large paralelepipedical waveguide structure is designed and built, its dimensions can be varied in order to change its parameters. (Author) 9 refs 11. Rectangular spectral collocation KAUST Repository Driscoll, Tobin A. 2015-02-06 Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems. 12. A Characterization of Rectangular Distributions OpenAIRE Terrell, George R. 1983-01-01 It is well known that the smaller and the larger of a random sample of size two are positively correlated. The coefficient of correlation is at most one-half, and the upper bound is attained only for rectangular distributions. 13. Rectangular waveform linear transformer driver module design International Nuclear Information System (INIS) Zhao Yue; Xie Weiping; Zhou Liangji; Chen Lin 2014-01-01 Linear Transformer Driver is a novel pulsed power technology, its main merits include a parallel LC discharge array and Inductive Voltage Adder. The parallel LC discharge array lowers the whole circuit equivalent inductance and the Inductive Voltage Adder unites the modules in series in order to create a high electric field grads, meanwhile, restricts the high voltage in a small space. The lower inductance in favor of LTD output a fast waveform and IVA confine high voltage in secondary cavity. In recently, some LTD-based pulsed power system has been development yet. The usual LTD architecture provides damped sine shaped output pulses that may not be suitable in flash radiography, high power microwave production, z-pinch drivers, and certain other applications. A more suitable driver output pulse would have a flat or inclined top (slightly rising or falling). In this paper, we present the design of an LTD cavity that generates this type of the output pulse by including within its circular array some number of the harmonic bricks in addition to the standard bricks according to Fourier progression theory. The parallel LC discharge array circuit formula is introduced by Kirchhoff Law, and the sum of harmonic is proofed as an analytic result, meanwhile, rationality of design is proved by simulation. Varying gas spark discharge dynamic resistance with harmonic order and switches jitter are analyzed. The results are as following: The more harmonic order is an approach to the ideal rectangular waveform, but lead to more system complexity. The capacity decreases as harmonic order increase, and gas spark discharge dynamic resistance rises with the capacity. The rising time protracts and flat is decay or even vanishes and the shot to shot reproducibility is degenerate as the switches jitter is high. (authors) 14. On Hubbell's rectangular source integral International Nuclear Information System (INIS) Stalker, John 2001-01-01 The integral H(a,b)=∫ 0 b ∫ 0 a dx dy/(1+x 2 +y 2 ) arises naturally in the study of radiation from a rectangular source and has been studied by many authors. This paper introduces a new series expansion which is rapidly convergent for large a and b 15. Motion of rectangular prismatic bodies International Nuclear Information System (INIS) Poreh, M.; Wray, R.N. 1979-01-01 Rectangular prismatic bodies can assume either a translatory or an auto-rotating mode of motion during free motion in the atmosphere. The translatory mode is stable only when the dimensionless moment of inertia of the bodies is large, however, large perturbations will always start auto-rotation. The characteristics of the auto-rotational mode are shown to depend primarily on the aspect ratio of the bodies which determines the dimensionless rotational speed and the lift coefficient. Both the average drag and lift-coefficients of auto-rotating bodies are estimated, but it is shown that secondary effects make it impossible to determine their exact trajectories in atmospheric flows 16. Partitioning sparse rectangular matrices for parallel processing Energy Technology Data Exchange (ETDEWEB) Kolda, T.G. 1998-05-01 The authors are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. They will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. They will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods -- the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best. 17. Mapping from rectangular to harmonic representation International Nuclear Information System (INIS) Schneider, W.; Bateman, G. 1986-08-01 An algorithm is developed to determine the Fourier harmonics representing the level contours of a scalar function given on a rectangular grid. This method is applied to the problem of computing the flux coordinates and flux surface average needed for 1-1/2-D transport codes and MHD stability codes from an equilibrium flux function given on a rectangular grid 18. Successive Standardization of Rectangular Arrays Directory of Open Access Journals (Sweden) Richard A. Olshen 2012-02-01 Full Text Available In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an iteration begins with operations on columns: first subtract the mean of each column; then divide by its standard deviation. The iteration continues with the same two operations done successively for rows. These four operations applied in sequence completes one iteration. One then iterates again, and again, and again, ... In [1] it was argued that if arrays are made up of real numbers, then the set for which convergence of these successive iterations fails has Lebesgue measure 0. The limiting array has row and column means 0, row and column standard deviations 1. A basic result on convergence given in [1] is true, though the argument in [1] is faulty. The result is stated in the form of a theorem here, and the argument for the theorem is correct. Moreover, many graphics given in [1] suggest that except for a set of entries of any array with Lebesgue measure 0, convergence is very rapid, eventually exponentially fast in the number of iterations. Because we learned this set of rules from Bradley Efron, we call it “Efron’s algorithm”. More importantly, the rapidity of convergence is illustrated by numerical examples. 19. three dimensional photoelastic investigations on thick rectangular African Journals Online (AJOL) user 1983-09-01 Sep 1, 1983 ... Thick rectangular plates are investigated by means of three-dimensional photoelasticity ... a thin plate theory and a higher order thick plate theory. 1. ..... number of fringes lest the accuracy of the results will be considerably. 20. Rectangular-section mirror light pipes Energy Technology Data Exchange (ETDEWEB) Swift, P.D.; Lawlor, R. [School of Physical Sciences, Dublin City University, Dublin 9 (Ireland); Smith, G.B.; Gentle, A. [Department of Applied Physics, University of Technology, Sydney, Broadway, NSW 2007 (Australia) 2008-08-15 Using an integrated-ray approach an expression for the transmission of rectangular section mirror light pipe (MLP) has been derived for the case of collimated light input. The transmittance and the irradiance distribution at the exit aperture of rectangular-section MLPs have been measured experimentally and calculated theoretically for the case of collimated light input. The results presented extend the description of MLPs from the cylindrical case. Measured and calculated transmittances and irradiance distributions are in good agreement. (author) 1. Random Young diagrams in a Rectangular Box DEFF Research Database (Denmark) Beltoft, Dan; Boutillier, Cédric; Enriquez, Nathanaël We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.......We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.... 2. ENDOR with band-selective shaped inversion pulses Science.gov (United States) Tait, Claudia E.; Stoll, Stefan 2017-04-01 Electron Nuclear DOuble Resonance (ENDOR) is based on the measurement of nuclear transition frequencies through detection of changes in the polarization of electron transitions. In Davies ENDOR, the initial polarization is generated by a selective microwave inversion pulse. The rectangular inversion pulses typically used are characterized by a relatively low selectivity, with full inversion achieved only for a limited number of spin packets with small resonance offsets. With the introduction of pulse shaping to EPR, the rectangular inversion pulses can be replaced with shaped pulses with increased selectivity. Band-selective inversion pulses are characterized by almost rectangular inversion profiles, leading to full inversion for spin packets with resonance offsets within the pulse excitation bandwidth and leaving spin packets outside the excitation bandwidth largely unaffected. Here, we explore the consequences of using different band-selective amplitude-modulated pulses designed for NMR as the inversion pulse in ENDOR. We find an increased sensitivity for small hyperfine couplings compared to rectangular pulses of the same bandwidth. In echo-detected Davies-type ENDOR, finite Fourier series inversion pulses combine the advantages of increased absolute ENDOR sensitivity of short rectangular inversion pulses and increased sensitivity for small hyperfine couplings of long rectangular inversion pulses. The use of pulses with an almost rectangular frequency-domain profile also allows for increased control of the hyperfine contrast selectivity. At X-band, acquisition of echo transients as a function of radiofrequency and appropriate selection of integration windows during data processing allows efficient separation of contributions from weakly and strongly coupled nuclei in overlapping ENDOR spectra within a single experiment. 3. Partial rectangular metric spaces and fixed point theorems. Science.gov (United States) Shukla, Satish 2014-01-01 The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results. 4. Using a weather generator to downscale spatio-temporal precipitation at urban scale DEFF Research Database (Denmark) Sørup, Hjalte Jomo Danielsen; Christensen, Ole Bøssing; Arnbjerg-Nielsen, Karsten In recent years, urban flooding has occurred in Denmark due to very local extreme precipitation events with very short lifetime. Several of these floods have been among the most severe ever experienced. The current study demonstrates the applicability of the Spatio-Temporal Neyman-Scott Rectangular...... the observed spatio-temporal differences at very fine scale for all measured parameters. For downscaling, perturbation with a climate change signal, precipitation from four different regional climate model simulations has been analysed. The analysed models are two runs from the ENSEMBLES (RACMO... 5. Dose reduction in pulsed fluoroscopy by modifying the high-voltage pulse shape International Nuclear Information System (INIS) Sabau, M.N.; Phelps, G. 1988-01-01 This paper presents the dose reduction results in pulsed fluoroscopy by modifying the high-voltage pulse shape (HVPS). Since the HVPS in regular pulsed fluoroscopy has a long tail, the radiation pulse shape (RPS) is similar. Using specially designed circuitry in the high-voltage generator to produce a rectangular HVPS, and consequently a rectangular RPS, it was possible to obtain a reduction of up to 25% of patient exposure. This dose reduction obtained by cutting the long tail of RPS does not damage the image quality 6. Solving the rectangular assignment problem and applications NARCIS (Netherlands) Bijsterbosch, J.; Volgenant, A. 2010-01-01 The rectangular assignment problem is a generalization of the linear assignment problem (LAP): one wants to assign a number of persons to a smaller number of jobs, minimizing the total corresponding costs. Applications are, e.g., in the fields of object recognition and scheduling. Further, we show 7. Steady turbulent flow in curved rectangular channels NARCIS (Netherlands) De Vriend, H.J. 1979-01-01 After the study of fully developed and developing steady laminar flow in curved channels of shallow rectangular wet cross-section (see earlier reports in this series), steady turbulent flow in such channels is investigated as a next step towards a mathematical model of the flow in shallow river 8. A solution for the narrow rectangular punch NARCIS (Netherlands) Panek, C.F.; Kalker, J.J. 1977-01-01 This paper considers the problem of a rectangular flat ended punch acting on an elastic half-space. An approximate solution is generated through application of the elastic line integral equations. The results produced by this method are then compared with another approximate solution already 9. g-Weak Contraction in Ordered Cone Rectangular Metric Spaces Directory of Open Access Journals (Sweden) S. K. Malhotra 2013-01-01 Full Text Available We prove some common fixed-point theorems for the ordered g-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results. 10. Interaction of weak shock waves with rectangular meshes in plate Directory of Open Access Journals (Sweden) O.A. Mikulich 2016-09-01 Full Text Available In mechanical engineering, building and other industries a significant part of the process includes the presence of various dynamic loads due to technological and mechanical impacts. Consideration of such load effects allows more accurate assessment of the structural elements strength or machine parts. Aim: The aim is to develop an algorithm for calculating of dynamic stress state of plates with meshes for pulse loading in the form of a weak shock wave. Materials and Methods: An integral and discrete Fourier transform were used to solve the problem. An application of Fourier transform by time allowed reducing the dynamic problem of flat deformation to the solution of a finite number of problems for the established oscillations at fixed cyclic frequency values. In the area of Fourier-images the method of boundary integral equations and the apparatus of a complex variable function theory are used to study the dynamic stress concentration. Results: Based on the developed methodology the distribution change of the dynamic circle stress over time on the edge of a rectangular hole is studied. The time sections of stress distribution fields under the influence of pulse dynamic load is constructed. 11. Metamaterial Embedded Wearable Rectangular Microstrip Patch Antenna Directory of Open Access Journals (Sweden) J. G. Joshi 2012-01-01 Full Text Available This paper presents an indigenous low-cost metamaterial embedded wearable rectangular microstrip patch antenna using polyester substrate for IEEE 802.11a WLAN applications. The proposed antenna resonates at 5.10 GHz with a bandwidth and gain of 97 MHz and 4.92 dBi, respectively. The electrical size of this antenna is 0.254λ×0.5λ. The slots are cut in rectangular patch to reduce the bending effect. This leads to mismatch the impedance at WLAN frequency band; hence, a metamaterial square SRR is embedded inside the slot. A prototype antenna has been fabricated and tested, and the measured results are presented in this paper. The simulated and measured results of the proposed antenna are found to be in good agreement. The bending effect on the performance of this antenna is experimentally verified. 12. Anisotropic rectangular metric for polygonal surface remeshing KAUST Repository Pellenard, Bertrand 2013-06-18 We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, defined at each triangle facet of the input mesh, is derived from both a user-specified normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity. 13. Anisotropic rectangular metric for polygonal surface remeshing KAUST Repository Pellenard, Bertrand; Morvan, Jean-Marie; Alliez, Pierre 2013-01-01 We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, defined at each triangle facet of the input mesh, is derived from both a user-specified normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity. 14. Conformal boundary state for the rectangular geometry Energy Technology Data Exchange (ETDEWEB) Bondesan, R., E-mail: [email protected] [Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Institut Henri Poincare, 11 rue Pierre et Marie Curie, 75231 Paris (France); Dubail, J. [Department of Physics, Yale University, P.O. Box 208120, New Haven, CT 06520-8120 (United States); Jacobsen, J.L. [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Institut Henri Poincare, 11 rue Pierre et Marie Curie, 75231 Paris (France); Universite Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France); Saleur, H. [Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Institut Henri Poincare, 11 rue Pierre et Marie Curie, 75231 Paris (France); Physics Department, USC, Los Angeles, CA 90089-0484 (United States) 2012-09-11 We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a boundary condition changing operator), for which we derive an explicit expression of the associated boundary state, valid for any arbitrary CFT. We check the validity of our solution, comparing it with known results for partition functions, numerical simulations of lattice discretizations, and coherent state expressions for free theories. 15. Numerical study on rectangular microhollow cathode discharge International Nuclear Information System (INIS) He Shoujie; Ouyang Jiting; He Feng; Li Shang 2011-01-01 Rectangular microhollow cathode discharge in argon is investigated by using two-dimensional time-dependent self-consistent fluid model. The electric potential, electric field, particle density, and mean electron energy are calculated. The results show that hollow cathode effect can be onset in the present configuration, with strong electric field and high mean electron energy in the cathode fall while high density and quasineutral plasma in the negative glow. The potential well and electric filed reversal are formed in the negative glow region. It is suggested that the presence of large electron diffusion flux necessitates the field reversal and potential well. 16. Droplet size in a rectangular Venturi scrubber OpenAIRE Costa, M. A. M.; Henrique, P. R.; Gonçalves, J. A. S.; Coury, J.R. 2004-01-01 The Venturi scrubber is a device which uses liquid in the form of droplets to efficiently remove fine particulate matter from gaseous streams. Droplet size is of fundamental importance for the scrubber performance. In the present experimental study, a laser diffraction technique was used in order to measure droplet size in situ in a Venturi scrubber with a rectangular cross section. Droplet size distribution was measured as a function of gas velocity (58.3 to 74.9 m/s), liquid-to-gas ratio (0... 17. Design of open rectangular and trapezoidal channels Science.gov (United States) González, C. P.; Vera, P. E.; Carrillo, G.; García, S. 2018-04-01 In this work, the results of designing open channels in rectangular and trapezoidal form are presented. For the development of the same important aspects were taken as determination of flows by means of formula of the rational method, area of the surface for its implementation, optimal form of the flow to meet the needs of that environment. In the design the parameter of the hydraulic radius expressed in terms of the hydraulic area and wet perimeter was determined, considering that the surface on which the fluid flows is the product of the perimeter of the section and the length of the channel and where shear is generated by the condition of no slippage. 18. Coiled transmission line pulse generators Science.gov (United States) McDonald, Kenneth Fox 2010-11-09 Methods and apparatus are provided for fabricating and constructing solid dielectric "Coiled Transmission Line" pulse generators in radial or axial coiled geometries. The pour and cure fabrication process enables a wide variety of geometries and form factors. The volume between the conductors is filled with liquid blends of monomers, polymers, oligomers, and/or cross-linkers and dielectric powders; and then cured to form high field strength and high dielectric constant solid dielectric transmission lines that intrinsically produce ideal rectangular high voltage pulses when charged and switched into matched impedance loads. Voltage levels may be increased by Marx and/or Blumlein principles incorporating spark gap or, preferentially, solid state switches (such as optically triggered thyristors) which produce reliable, high repetition rate operation. Moreover, these Marxed pulse generators can be DC charged and do not require additional pulse forming circuitry, pulse forming lines, transformers, or an a high voltage spark gap output switch. The apparatus accommodates a wide range of voltages, impedances, pulse durations, pulse repetition rates, and duty cycles. The resulting mobile or flight platform friendly cylindrical geometric configuration is much more compact, light-weight, and robust than conventional linear geometries, or pulse generators constructed from conventional components. Installing additional circuitry may accommodate optional pulse shape improvements. The Coiled Transmission Lines can also be connected in parallel to decrease the impedance, or in series to increase the pulse length. 19. Rectangular source integral and recurrence relations International Nuclear Information System (INIS) Prabha, Hem 2007-01-01 In this paper Hubbell's rectangular source integral H'(a,b), which is a double integral, is expressed as a series of many converging single integrals I n (a,b). Recurrence relations relate these integrals. Once one integral I 1 is computed, recurrence relations are used to compute other integrals. I 1 (a,b) can be computed analytically. H'(a,b) is approximated by considering the first seven terms in the series and the results are found to give good results for various values of a and b. Results are presented for the values of a and b (0.1 to 20 and to 2), respectively. The rate of convergence depends on the values of a and b 20. Droplet size in a rectangular Venturi scrubber Directory of Open Access Journals (Sweden) M. A. M. Costa 2004-06-01 Full Text Available The Venturi scrubber is a device which uses liquid in the form of droplets to efficiently remove fine particulate matter from gaseous streams. Droplet size is of fundamental importance for the scrubber performance. In the present experimental study, a laser diffraction technique was used in order to measure droplet size in situ in a Venturi scrubber with a rectangular cross section. Droplet size distribution was measured as a function of gas velocity (58.3 to 74.9 m/s, liquid-to-gas ratio (0.07 to 0.27 l/m³, and distance from liquid injection point (64 to 173 mm. It was found that all these variables significantly affect droplet size. The results were compared with the predictions from correlations found in the literature. 1. Large - scale Rectangular Ruler Automated Verification Device Science.gov (United States) Chen, Hao; Chang, Luping; Xing, Minjian; Xie, Xie 2018-03-01 This paper introduces a large-scale rectangular ruler automated verification device, which consists of photoelectric autocollimator and self-designed mechanical drive car and data automatic acquisition system. The design of mechanical structure part of the device refer to optical axis design, drive part, fixture device and wheel design. The design of control system of the device refer to hardware design and software design, and the hardware mainly uses singlechip system, and the software design is the process of the photoelectric autocollimator and the automatic data acquisition process. This devices can automated achieve vertical measurement data. The reliability of the device is verified by experimental comparison. The conclusion meets the requirement of the right angle test procedure. 2. The demagnetizing factors for the rectangular samples International Nuclear Information System (INIS) Akishin, P.G.; Gaganov, I.A. 1990-01-01 The influence of the demagnetization effect on the distribution of internal magnetic fields for finite samples is considered. The boundary integral method is used to compute the space distribution of the magnetic field in rectangular samples. On the basis of these calculations we compute the distribution of demagnetization factors in the sample for μSR experimental set-up with the real field geometry. The corresponding mathematical expectation and dispersion of this distribution are estimated. The results of the calculation are used in the analysis of the μSR data obtained for high T c superconductors. It is shown for these compounds that the correction to the penetration depth related to the broadening of the field distribution, is not more than 5%. 8 refs.; 2 figs.; 1 tab 3. Method and structure for cache aware transposition via rectangular subsections Science.gov (United States) Gustavson, Fred Gehrung; Gunnels, John A 2014-02-04 A method and structure for transposing a rectangular matrix A in a computer includes subdividing the rectangular matrix A into one or more square submatrices and executing an in-place transposition for each of the square submatrices A.sub.ij. 4. direct method of analysis of an isotropic rectangular plate direct African Journals Online (AJOL) eobe This work evaluates the static analysis of an isotropic rectangular plate with various the static analysis ... method according to Ritz is used to obtain the total potential energy of the plate by employing the used to ..... for rectangular plates analysis, as the behavior of the ... results obtained by previous research work that used. 5. Towards characterizing graphs with a sliceable rectangular dual NARCIS (Netherlands) Kusters, V.; Speckmann, B.; Di Giacomo, E.; Lubiw, A. 2015-01-01 Let G be a plane triangulated graph. A rectangular dual of G is a partition of a rectangle R into a set R of interior-disjoint rectangles, one for each vertex, such that two regions are adjacent if and only if the corresponding vertices are connected by an edge. A rectangular dual is sliceable if it 6. Obtaining S values for rectangular--solid tumors inside rectangular--solid host organs International Nuclear Information System (INIS) Stinchcomb, T.G.; Durham, J.S.; Fisher, D.R. 1991-01-01 A method is described for obtaining S values between a tumor and its host organ for use with the MIRD formalism. It applies the point-source specific absorbed fractions for an infinite water medium, tabulated by Berger, to a rectangular solid of arbitrary dimensions which contains a rectangular tumor of arbitrary dimensions. Contributions from pairs of source and target volume elements are summed for the S values between the tumor and itself, between the remaining healthy host organ and itself, and between the tumor and the remaining healthy host organ, with the reciprocity theorem assumed for the last. This method labeled MTUMOR, is interfaced with the widely used MIRDOSE program which incorporates the MIRD formalism. An example is calculated 7. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method Directory of Open Access Journals (Sweden) WANG Minhao 2017-08-01 Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application. 8. DIFFUSE DBD IN ATMOSPHERIC AIR AT DIFFERENT APPLIED PULSE WIDTHS Directory of Open Access Journals (Sweden) Ekaterina Alexandrovna Shershunova 2015-02-01 Full Text Available The paper deals with the realization and the diagnostics of the volume diffuse dielectric barrier discharge in 1-mm air gap when applying high voltage rectangular pulses to the electrodes. The effect of the applied pulse width on the discharge dissipated energy was studied in detail. It was found experimentally, the energy stayed nearly constant with the pulse elongation from 600 ns to 1 ms. 9. Flow Characteristics of Rectangular Underexpanded Impinging Jets Institute of Scientific and Technical Information of China (English) Minoru YAGA; Yoshio KINJO; Masumi TAMASHIRO; Kenyu OYAKAWA 2006-01-01 In this paper, the flow fields of underexpanded impinging jet issued from rectangular nozzles of aspect ratio 1,3 and 5 are numerically and experimentally studied. Two dimensional temperature and pressure distributions are measured by using infrared camera and the combination of a pressure scanning device and a stepping motor, respectively. The variation of the stagnation pressure on the impinging plate reveals that a hystcretic phenomenon exists during the increasing and decreasing of the pressure ratio for the aspect ratio of 3.0 and 5.0. It is also found that the nozzle of aspect ratio 1.0 caused the largest total pressure loss pc/p0 = 0.27 at the pressure ratio of p0/pb, = 6.5, where pc is the stagnation center pressure on the wall, p0 the upstream stagnation pressure, pb the ambient pressure. The other two nozzles showed that the pressure loss pc / p0=0.52 and 0.55 were achieved by the nozzles of the aspect ratio 3,0 and 5.0, respectively. The comparison between the calculations and experiments is fairly good, showing the three dimensional streamlines and structures of the shock waves in the jets. However, the hysteresis of the pressure variations observed in the experiments between the pressure ratio of 3.5 and 4.5 cannot be confirmed in the calculations. 10. Physics from angular projection of rectangular grids International Nuclear Information System (INIS) Singh, Ashmeet 2015-01-01 In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple yet interesting, problem has both scholarly value and applications for data extraction techniques to study the physics of various systems. Our work may help undergraduate students to understand subtle points in the angular projection of a grid and describes various quantities of interest in the projection with completeness and sufficient rigour. We show that for certain angular ranges, the projection has non-distinctness, and calculate the details of such angles, and correspondingly, the number of distinct points and the total projected length. We focus on interesting trends obtained for the projected length of the grid elements and present a simple application of the model to determine the geometry of an unknown grid whose spatial extensions are known, using measurement of the grid projection at two angles only. Towards the end, our model is shown to have potential applications in various branches of physical sciences, including crystallography, astrophysics, and bulk properties of materials. (paper) 11. Design and fabrication of circular and rectangular components for electron-cyclotron-resonant heating of tandem mirror experiment-upgrade International Nuclear Information System (INIS) Felker, B.; Calderon, M.O.; Chargin, A.K. 1983-01-01 The electron-cyclotron-resonant heating (ECRH) systems of rectangular waveguides on Tandem Mirror Experiment-Upgrade (TMX-U) operated with a overall efficiency of 50%, each system using a 28-GHz, 200-kW pulsed gyrotron. We designed and built four circular-waveguide systems with greater efficiency and greater power-handling capabilities to replace the rectangular waveguides. Two of these circular systems, at the 5-kG second-harmonic heating locations, have a total transmission efficiency of >90%. The two systems at the 10-kG fundamental heating locations have a total transmission efficiency of 80%. The difference in efficiency is due to the additional components required to launch the microwaves in the desired orientation and polarization with respect to magnetic-field lines at the 10-kG points. These systems handle the total power available from each gyrotron but do not have the arcing limitation problem of the rectangular waveguide. Each system requires several complex components. The overall physical layout and the design considerations for the rectangular and circular waveguide components are described here 12. Design and fabrication of circular and rectangular components for electron-cyclotron-resonant heating of tandem mirror experiment-upgrade Energy Technology Data Exchange (ETDEWEB) Felker, B.; Calderon, M.O.; Chargin, A.K.; Coffield, F.E.; Lang, D.D.; Rubert, R.R.; Pedrotti, L.R.; Stallard, B.W.; Gallagher, N.C. Jr.; Sweeney, D.W. 1983-11-18 The electron-cyclotron-resonant heating (ECRH) systems of rectangular waveguides on Tandem Mirror Experiment-Upgrade (TMX-U) operated with a overall efficiency of 50%, each system using a 28-GHz, 200-kW pulsed gyrotron. We designed and built four circular-waveguide systems with greater efficiency and greater power-handling capabilities to replace the rectangular waveguides. Two of these circular systems, at the 5-kG second-harmonic heating locations, have a total transmission efficiency of >90%. The two systems at the 10-kG fundamental heating locations have a total transmission efficiency of 80%. The difference in efficiency is due to the additional components required to launch the microwaves in the desired orientation and polarization with respect to magnetic-field lines at the 10-kG points. These systems handle the total power available from each gyrotron but do not have the arcing limitation problem of the rectangular waveguide. Each system requires several complex components. The overall physical layout and the design considerations for the rectangular and circular waveguide components are described here. 13. Rectangular maximum-volume submatrices and their applications KAUST Repository Mikhalev, Aleksandr; Oseledets, I.V. 2017-01-01 We introduce a definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices. We generalize results of square maximum-volume submatrices to the rectangular case, show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online. 14. Rectangular maximum-volume submatrices and their applications KAUST Repository Mikhalev, Aleksandr 2017-10-18 We introduce a definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices. We generalize results of square maximum-volume submatrices to the rectangular case, show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online. 15. Rectangular-cladding silicon slot waveguide with improved nonlinear performance Science.gov (United States) Huang, Zengzhi; Huang, Qingzhong; Wang, Yi; Xia, Jinsong 2018-04-01 Silicon slot waveguides have great potential in hybrid silicon integration to realize nonlinear optical applications. We propose a rectangular-cladding hybrid silicon slot waveguide. Simulation result shows that, with a rectangular-cladding, the slot waveguide can be formed by narrower silicon strips, so the two-photon absorption (TPA) loss in silicon is decreased. When the cladding material is a nonlinear polymer, the calculated TPA figure of merit (FOMTPA) is 4.4, close to the value of bulk nonlinear polymer of 5.0. This value confirms the good nonlinear performance of rectangular-cladding silicon slot waveguides. 16. analytical bending solution of all clamped isotropic rectangular plate African Journals Online (AJOL) HP PLATE ON WINKLER'S FOUNDATION USING CHARACTERISTIC. ORTHOGONAL ... foundations, storage tanks, swimming pools, floor system of buildings, highways ..... “Energy Methods in Theory of Rectangular Plates. (use of Polynomial ... 17. Tau method approximation of the Hubbell rectangular source integral International Nuclear Information System (INIS) Kalla, S.L.; Khajah, H.G. 2000-01-01 The Tau method is applied to obtain expansions, in terms of Chebyshev polynomials, which approximate the Hubbell rectangular source integral:I(a,b)=∫ b 0 (1/(√(1+x 2 )) arctan(a/(√(1+x 2 )))) This integral corresponds to the response of an omni-directional radiation detector situated over a corner of a plane isotropic rectangular source. A discussion of the error in the Tau method approximation follows 18. Critical heat flux correlation for thin rectangular channels International Nuclear Information System (INIS) Tanaka, Futoshi; Mishima, Kaichiro; Hibiki, Takashi 2007-01-01 The effect of heated length on Critical heat flux (CHF) in thin rectangular channels was studied based on CHF data obtained under atmospheric pressure. CHF in small channels has been widely studied in the past decades but most of the studies are related to CHF in round tubes. Although basic mechanisms of burnout in thin rectangular channels are similar to tubes, applicability of CHF correlations for tubes to rectangular channels are questionable since CHF in rectangular channels are affected by the existence of non-heated walls and the non-circular geometry of channel circumference. Several studies of CHF in thin rectangular channels have been reported in relation to thermal hydraulic design of research reactors and neutron source targets and CHF correlations have been proposed, but the studies mostly focus on CHFs under geometrical conditions of the application of interest. In his study, existing CHF data obtained in thin rectangular channels were collected and the effect of heated length on CHF was examined. Existing CHF correlations were verified with positive quality flow CHF data but none of the correlations successfully reproduced the CHF for a wide range of heated length. A new CHF correlation for qualify region applicable to a wide range of heated length was developed based on the collected data. (author) 19. Control of the electrode metal transfer by means of the welding current pulse generator Science.gov (United States) Knyaz'kov, A.; Pustovykh, O.; Verevkin, A.; Terekhin, V.; Shachek, A.; Knyaz'kov, S.; Tyasto, A. 2016-04-01 The paper presents a generator of welding current pulses to transfer an electrode metal into the molten pool. A homogeneous artificial line is used to produce near rectangular pulses. The homogeneous artificial line provides the minimum heat input with in the pulse to transfer the electrode metal, and it significantly decreases the impact of disturbances affecting this transfer. The pulse frequency does not exceed 300 Hz, and the duration is 0.6 ÷ 0.9 ms. 20. Experimental and modeling analysis of fast ionization wave discharge propagation in a rectangular geometry International Nuclear Information System (INIS) Takashima, Keisuke; Adamovich, Igor V.; Xiong Zhongmin; Kushner, Mark J.; Starikovskaia, Svetlana; Czarnetzki, Uwe; Luggenhoelscher, Dirk 2011-01-01 Fast ionization wave (FIW), nanosecond pulse discharge propagation in nitrogen and helium in a rectangular geometry channel/waveguide is studied experimentally using calibrated capacitive probe measurements. The repetitive nanosecond pulse discharge in the channel was generated using a custom designed pulsed plasma generator (peak voltage 10-40 kV, pulse duration 30-100 ns, and voltage rise time ∼1 kV/ns), generating a sequence of alternating polarity high-voltage pulses at a pulse repetition rate of 20 Hz. Both negative polarity and positive polarity ionization waves have been studied. Ionization wave speed, as well as time-resolved potential distributions and axial electric field distributions in the propagating discharge are inferred from the capacitive probe data. ICCD images show that at the present conditions the FIW discharge in helium is diffuse and volume-filling, while in nitrogen the discharge propagates along the walls of the channel. FIW discharge propagation has been analyzed numerically using quasi-one-dimensional and two-dimensional kinetic models in a hydrodynamic (drift-diffusion), local ionization approximation. The wave speed and the electric field distribution in the wave front predicted by the model are in good agreement with the experimental results. A self-similar analytic solution of the fast ionization wave propagation equations has also been obtained. The analytic model of the FIW discharge predicts key ionization wave parameters, such as wave speed, peak electric field in the front, potential difference across the wave, and electron density as functions of the waveform on the high voltage electrode, in good agreement with the numerical calculations and the experimental results. 1. Electron acceleration by laser produced wake field: Pulse shape effect Science.gov (United States) Malik, Hitendra K.; Kumar, Sandeep; Nishida, Yasushi 2007-12-01 Analytical expressions are obtained for the longitudinal field (wake field: Ex), density perturbations ( ne') and the potential ( ϕ) behind a laser pulse propagating in a plasma with the pulse duration of the electron plasma period. A feasibility study on the wake field is carried out with Gaussian-like (GL) pulse, rectangular-triangular (RT) pulse and rectangular-Gaussian (RG) pulse considering one-dimensional weakly nonlinear theory ( ne'/n0≪1), and the maximum energy gain acquired by an electron is calculated for all these three types of the laser pulse shapes. A comparative study infers that the RT pulse yields the best results: In its case maximum electron energy gain is 33.5 MeV for a 30 fs pulse duration whereas in case of GL (RG) pulse of the same duration the gain is 28.6 (28.8)MeV at the laser frequency of 1.6 PHz and the intensity of 3.0 × 10 18 W/m 2. The field of the wake and hence the energy gain get enhanced for the higher laser frequency, larger pulse duration and higher laser intensity for all types of the pulses. 2. Pulse Generator Science.gov (United States) Greer, Lawrence (Inventor) 2017-01-01 An apparatus and a computer-implemented method for generating pulses synchronized to a rising edge of a tachometer signal from rotating machinery are disclosed. For example, in one embodiment, a pulse state machine may be configured to generate a plurality of pulses, and a period state machine may be configured to determine a period for each of the plurality of pulses. 3. Stochastic modeling of hourly rainfall times series in Campania (Italy) Science.gov (United States) Giorgio, M.; Greco, R. 2009-04-01 Occurrence of flowslides and floods in small catchments is uneasy to predict, since it is affected by a number of variables, such as mechanical and hydraulic soil properties, slope morphology, vegetation coverage, rainfall spatial and temporal variability. Consequently, landslide risk assessment procedures and early warning systems still rely on simple empirical models based on correlation between recorded rainfall data and observed landslides and/or river discharges. Effectiveness of such systems could be improved by reliable quantitative rainfall prediction, which can allow gaining larger lead-times. Analysis of on-site recorded rainfall height time series represents the most effective approach for a reliable prediction of local temporal evolution of rainfall. Hydrological time series analysis is a widely studied field in hydrology, often carried out by means of autoregressive models, such as AR, ARMA, ARX, ARMAX (e.g. Salas [1992]). Such models gave the best results when applied to the analysis of autocorrelated hydrological time series, like river flow or level time series. Conversely, they are not able to model the behaviour of intermittent time series, like point rainfall height series usually are, especially when recorded with short sampling time intervals. More useful for this issue are the so-called DRIP (Disaggregated Rectangular Intensity Pulse) and NSRP (Neymann-Scott Rectangular Pulse) model [Heneker et al., 2001; Cowpertwait et al., 2002], usually adopted to generate synthetic point rainfall series. In this paper, the DRIP model approach is adopted, in which the sequence of rain storms and dry intervals constituting the structure of rainfall time series is modeled as an alternating renewal process. Final aim of the study is to provide a useful tool to implement an early warning system for hydrogeological risk management. Model calibration has been carried out with hourly rainfall hieght data provided by the rain gauges of Campania Region civil 4. Joining of Aluminium Alloy Sheets by Rectangular Mechanical Clinching International Nuclear Information System (INIS) Abe, Y.; Mori, K.; Kato, T. 2011-01-01 A mechanical clinching has the advantage of low running costs. However, the joint strength is not high. To improve the maximum load of the joined sheets by a mechanical clinching, square and rectangular mechanical clinching were introduced. In the mechanical clinching, the two sheets are mechanically joined by forming an interlock between the lower and upper sheets by the punch and die. The joined length with the interlock was increased by the rectangular punch and die. The deforming behaviours of the sheets in the mechanical clinching were investigated, and then the interlock in the sheets had distribution in the circumference of the projection. Although the interlocks were formed in both projection side and diagonal, the interlock in the diagonal was smaller because of the long contact length between the lower sheet and the die cavity surface. The maximum load of the joined sheets by the rectangular mechanical clinching was two times larger than the load by the round mechanical clinching. 5. A two-component NZRI metamaterial based rectangular cloak Directory of Open Access Journals (Sweden) Sikder Sunbeam Islam 2015-10-01 Full Text Available A new two-component, near zero refractive index (NZRI metamaterial is presented for electromagnetic rectangular cloaking operation in the microwave range. In the basic design a pi-shaped, metamaterial was developed and its characteristics were investigated for the two major axes (x and z-axis wave propagation through the material. For the z-axis wave propagation, it shows more than 2 GHz bandwidth and for the x-axis wave propagation; it exhibits more than 1 GHz bandwidth of NZRI property. The metamaterial was then utilized in designing a rectangular cloak where a metal cylinder was cloaked perfectly in the C-band area of microwave regime. The experimental result was provided for the metamaterial and the cloak and these results were compared with the simulated results. This is a novel and promising design for its two-component NZRI characteristics and rectangular cloaking operation in the electromagnetic paradigm. 6. Errors generated with the use of rectangular collimation International Nuclear Information System (INIS) Parks, E.T. 1991-01-01 This study was designed to determine whether various techniques for achieving rectangular collimation generate different numbers and types of errors and remakes and to determine whether operator skill level influences errors and remakes. Eighteen students exposed full-mouth series of radiographs on manikins with the use of six techniques. The students were grouped according to skill level. The radiographs were evaluated for errors and remakes resulting from errors in the following categories: cone cutting, vertical angulation, and film placement. Significant differences were found among the techniques in cone cutting errors and remakes, vertical angulation errors and remakes, and total errors and remakes. Operator skill did not appear to influence the number or types of errors or remakes generated. Rectangular collimation techniques produced more errors than did the round collimation techniques. However, only one rectangular collimation technique generated significantly more remakes than the other techniques 7. High Power Microwave Emission of Large and Small Orbit Gyrotron Devices in Rectangular Interaction Structures Science.gov (United States) Hochman, J. M.; Gilgenbach, R. M.; Jaynes, R. L.; Rintamaki, J. I.; Luginsland, J. W.; Lau, Y. Y.; Spencer, T. A. 1996-11-01 Experiments utilize large and small orbit e-beam gyrotron devices in a rectangular-cross-section (RCS) gyrotron. This device is being explored to examine polarization control. Other research issues include pulse shortening, and mode competition. MELBA generates electron beams with parameters of: -800kV, 1-10kA diode current, and 0.5-1.0 μ sec pulselengths. The small orbit gyrotron device is converted to a large orbit experiment by running MELBA's annular electron beam through a magnetic cusp. Initial experiments showed an increase in beam alpha (V_perp/V_par) of a factor of ~ 4 between small and large orbit devices. Experimental results from the RCS gyrotron will be compared for large-orbit and small-orbit electron beams. Beam transport data and frequency measurements will be presented. Computer modeling utilizing the MAGIC and E-gun codes will be shown. 8. Arbitrary temporal shape pulsed fiber laser based on SPGD algorithm Science.gov (United States) Jiang, Min; Su, Rongtao; Zhang, Pengfei; Zhou, Pu 2018-06-01 A novel adaptive pulse shaping method for a pulsed master oscillator power amplifier fiber laser to deliver an arbitrary pulse shape is demonstrated. Numerical simulation has been performed to validate the feasibility of the scheme and provide meaningful guidance for the design of the algorithm control parameters. In the proof-of-concept experiment, information on the temporal property of the laser is exchanged and evaluated through a local area network, and the laser adjusted the parameters of the seed laser according to the monitored output of the system automatically. Various pulse shapes, including a rectangular shape, ‘M’ shape, and elliptical shape are achieved through experimental iterations. 9. The spatial thickness distribution of metal films produced by large area pulsed laser deposition DEFF Research Database (Denmark) Pryds, Nini; Schou, Jørgen; Linderoth, Søren 2007-01-01 Thin films of metals have been deposited in the large-area Pulsed Laser Deposition (PLD) Facility at Riso National Laboratory. Thin films of Ag and Ni were deposited with laser pulses from an excimer laser at 248 nm with a rectangular beam spot at a fluence of 10 J/cm(2) on glass substrates of 127... 10. Generation of fast-rise time, repetitive, (sub) nanosecond, high-voltage pulses NARCIS (Netherlands) Huiskamp, T.; Pemen, A.J.M. 2017-01-01 In this contribution we present our fast-rise time nanosecond pulse generator, capable of generating up to 50 kV (positive and negative) rectangular pulses at a repetition rate of up to 1 kHz and with a rise time of less than 200 picoseconds. We focus on the general concepts involved in the design 11. Optimal time-domain technique for pulse width modulation in power electronics Directory of Open Access Journals (Sweden) I. Mayergoyz 2018-05-01 Full Text Available Optimal time-domain technique for pulse width modulation is presented. It is based on exact and explicit analytical solutions for inverter circuits, obtained for any sequence of input voltage rectangular pulses. Two optimal criteria are discussed and illustrated by numerical examples. 12. Natural Vibration Analysis of Clamped Rectangular Orthotropic Plates Science.gov (United States) dalaei, m.; kerr, a. d. The natural vibrations of clamped rectangular orthotropic plates are analyzed using the extended Kantorovich method. The developed iterative scheme converges very rapidly to the final result. The obtained natural frequencies are evaluated for a square plate made of Kevlar 49 Epoxy and the obtained results are compared with those published by Kanazawa and Kawai, and by Leissa. The agreement was found to be very close. As there are no exact analytical solutions for clamped rectangular plates, the generated closed form expression for the natural modes, and the corresponding natural frequencies, are very suitable for use in engineering analyses. 13. Perron-Frobenius Theorem for Rectangular Tensors and Directed Hypergraphs OpenAIRE Lu, Linyuan; Yang, Arthur L. B.; Zhao, James J. Y. 2018-01-01 For any positive integers $r$, $s$, $m$, $n$, an $(r,s)$-order $(n,m)$-dimensional rectangular tensor ${\\cal A}=(a_{i_1\\cdots i_r}^{j_1\\cdots j_s}) \\in ({\\mathbb R}^n)^r\\times ({\\mathbb R}^m)^s$ is called partially symmetric if it is invariant under any permutation on the lower $r$ indexes and any permutation on the upper $s$ indexes. Such partially symmetric rectangular tensor arises naturally in studying directed hypergraphs. Ling and Qi [Front. Math. China, 2013] first studied the $(p,q)$-... 14. A new metamaterial-based wideband rectangular invisibility cloak Science.gov (United States) Islam, S. S.; Hasan, M. M.; Faruque, M. R. I. 2018-02-01 A new metamaterial-based wideband electromagnetic rectangular cloak is being introduced in this study. The metamaterial unit cell shows sharp transmittances in the C- and X-bands and displays wideband negative effective permittivity region there. The metamaterial unit cell was then applied in designing a rectangular-shaped electromagnetic cloak. The scattering reduction technique was adopted for the cloaking operation. The cloak operates in the certain portion of C-and X-bands that covers more than 4 GHz bandwidth region. The experimental results were provided as well for the metamaterial and the cloak. 15. Analysis of High Tc Superconducting Rectangular Microstrip Patches over Ground Planes with Rectangular Apertures in Substrates Containing Anisotropic Materials Directory of Open Access Journals (Sweden) Abderraouf Messai 2013-01-01 Full Text Available A rigorous full-wave analysis of high Tc superconducting rectangular microstrip patch over ground plane with rectangular aperture in the case where the patch is printed on a uniaxially anisotropic substrate material is presented. The dyadic Green’s functions of the considered structure are efficiently determined in the vector Fourier transform domain. The effect of the superconductivity of the patch is taken into account using the concept of the complex resistive boundary condition. The accuracy of the analysis is tested by comparing the computed results with measurements and previously published data for several anisotropic substrate materials. Numerical results showing variation of the resonant frequency and the quality factor of the superconducting antenna with regard to operating temperature are given. Finally, the effects of uniaxial anisotropy in the substrate on the resonant frequencies of different TM modes of the superconducting microstrip antenna with rectangular aperture in the ground plane are presented. 16. Development of multi-channel high power rectangular RF window for LHCD system employing high temperature vacuum brazing technique International Nuclear Information System (INIS) Sharma, P K; Ambulkar, K K; Parmar, P R; Virani, C G; Thakur, A L; Joshi, L M; Nangru, S C 2010-01-01 A 3.7 GHz., 120 kW (pulsed), lower hybrid current drive (LHCD) system is employed to drive non-inductive plasma current in ADITYA tokamak. The rf power is coupled to the plasma through grill antenna and is placed in vacuum environment. A vacuum break between the pressurized transmission line and the grill antenna is achieved with the help of a multi (eight) channel rectangular RF vacuum window. The phasing between adjacent channels of 8-channel window (arranged in two rows) is important for launching lower hybrid waves and each channel should have independent vacuum window so that phase information is retained. The geometrical parameter of the grill antenna, like periodicity (9mm), channel dimensions (cross sectional dimension of 76mm x 7mm), etc. is to be maintained. These design constraint demanded a development of a multi channel rectangular RF vacuum window. To handle rf losses and thermal effects, high temperature vacuum brazing techniques is desired. Based on the above requirements we have successfully developed a multi channel rectangular rf vacuum window employing high temperature vacuum brazing technique. During the development process we could optimize the chemical processing parameters, brazing process parameters, jigs and fixtures for high temperature brazing and leak testing, etc. Finally the window is tested for low power rf performance using VNA. In this paper we would present the development of the said window in detail along with its mechanical, vacuum and rf performances. 17. Development of multi-channel high power rectangular RF window for LHCD system employing high temperature vacuum brazing technique Energy Technology Data Exchange (ETDEWEB) Sharma, P K; Ambulkar, K K; Parmar, P R; Virani, C G; Thakur, A L [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India); Joshi, L M; Nangru, S C, E-mail: [email protected] [Central Electronics Engineering Research Institute, Pilani, Rajasthan 333 031 (India) 2010-02-01 A 3.7 GHz., 120 kW (pulsed), lower hybrid current drive (LHCD) system is employed to drive non-inductive plasma current in ADITYA tokamak. The rf power is coupled to the plasma through grill antenna and is placed in vacuum environment. A vacuum break between the pressurized transmission line and the grill antenna is achieved with the help of a multi (eight) channel rectangular RF vacuum window. The phasing between adjacent channels of 8-channel window (arranged in two rows) is important for launching lower hybrid waves and each channel should have independent vacuum window so that phase information is retained. The geometrical parameter of the grill antenna, like periodicity (9mm), channel dimensions (cross sectional dimension of 76mm x 7mm), etc. is to be maintained. These design constraint demanded a development of a multi channel rectangular RF vacuum window. To handle rf losses and thermal effects, high temperature vacuum brazing techniques is desired. Based on the above requirements we have successfully developed a multi channel rectangular rf vacuum window employing high temperature vacuum brazing technique. During the development process we could optimize the chemical processing parameters, brazing process parameters, jigs and fixtures for high temperature brazing and leak testing, etc. Finally the window is tested for low power rf performance using VNA. In this paper we would present the development of the said window in detail along with its mechanical, vacuum and rf performances. 18. Analysis of Rectangular Microstrip Antennas with Air Substrates ... African Journals Online (AJOL) This paper presents an analysis of rectangular microstrip antennas with air substrates. The effect of the substrate thickness on the bandwidth and the efficiency are examined. An additional thin layer supporting the dielectric material is added to the air substrate in order to make the antenna mechanically rigid and easy to ... 19. Graphene-based tunable terahertz filter with rectangular ring ... A plasmonic band-pass filter based on graphene rectangular ring resonator with double narrow gaps is proposed and numerically investigated by finite-difference time-domain (FDTD) simulations. For the filter with or without gaps, the resonant frequencies can be effectively adjusted by changing the width of the graphene ... 20. Plasma-ﬁlled rippled wall rectangular backward wave oscillator Performance of the backward wave oscillator (BWO) is greatly enhanced with the introduction of plasma. Linear theory of the dispersion relation and the growth rate have been derived and analysed numerically for plasma-ﬁlled rippled wall rectangular waveguide driven by sheet electron beam. To see the effect of plasma ... 1. Internal flow characteristics of a rectangular ramjet air intake NARCIS (Netherlands) Moerel, J.-L.; Veraar, R.G.; Halswijk, W.H.C.; Pimentel, R.; Corriveau, D.; Hamel, N.; Lesage, F.; Vos, J.B. 2009-01-01 Two research institutes TNO Defence, Security and Safety and DRDC-Valcartier have worked together on the improvement of modeling and simulation tools for the functioning of supersonic air intakes for realistic ramjet engines of tactical missiles. The emphasis laid on complex rectangular intake 2. The problem of isotropic rectangular plate with four clamped edges of rectangular plates has been a subject of study in solid mechanics for more than a cen- .... loading is solved first, giving the deflection function for the strip case and .... The authors gratefully acknowledge the advice and encouragement of ... 3. FDTD Analysis of U-Slot Rectangular Patch Antenna Science.gov (United States) Luk, K. M.; Tong, K. F.; Shum, S. M.; Lee, K. F.; Lee, R. Q. 1997-01-01 The U-slot rectangular patch antenna (Figure I) has been found experimentally to provide impedance and gain bandwidths of about 300 without the need of stacked or coplanar parasitic elements [1,2]. In this paper, simulation results of the U-slot patch using FDTD analysis are presented. Comparison with measured results are given. 4. Graphene-based tunable terahertz filter with rectangular ring ... WEI SU 2017-08-16 Aug 16, 2017 ... Abstract. A plasmonic band-pass filter based on graphene rectangular ring resonator with double narrow gaps is proposed and numerically investigated by finite-difference time-domain (FDTD) simulations. For the filter with or without gaps, the resonant frequencies can be effectively adjusted by changing ... 5. Optical vortex propagation in few-mode rectangular polymer waveguides DEFF Research Database (Denmark) 2017-01-01 We demonstrate that rectangular few-mode dielectric waveguides, fabricated with standard lithographic technique, can support on-chip propagation of optical vortices. We show that specific superpositions of waveguide eigenmodes form quasi-degenerate modes carrying light with high purity states... 6. Shielding calculations for changing from circular to a Rectangular ... African Journals Online (AJOL) The Radiation Technology Centre (RTC) of the Ghana Atomic Energy Commission operates a 1.85 PBq Co-60 gamma irradiator for research, food preservation and medical sterilization. It has become necessary to improve the do-se rate delivered by changing the circular arrangement of sources to a rectangular one. 7. Computational Investigations in Rectangular Convergent and Divergent Ribbed Channels Science.gov (United States) Sivakumar, Karthikeyan; Kulasekharan, N.; Natarajan, E. 2018-05-01 Computational investigations on the rib turbulated flow inside a convergent and divergent rectangular channel with square ribs of different rib heights and different Reynolds numbers (Re=20,000, 40,000 and 60,000). The ribs were arranged in a staggered fashion between the upper and lower surfaces of the test section. Computational investigations are carried out using computational fluid dynamic software ANSYS Fluent 14.0. Suitable solver settings like turbulence models were identified from the literature and the boundary conditions for the simulations on a solution of independent grid. Computations were carried out for both convergent and divergent channels with 0 (smooth duct), 1.5, 3, 6, 9 and 12 mm rib heights, to identify the ribbed channel with optimal performance, assessed using a thermo hydraulic performance parameter. The convergent and divergent rectangular channels show higher Nu values than the standard correlation values. 8. Flow Through a Rectangular-to-Semiannular Diffusing Transition Duct Science.gov (United States) Foster, Jeff; Wendt, Bruce J.; Reichert, Bruce A.; Okiishi, Theodore H. 1997-01-01 Rectangular-to-semiannular diffusing transition ducts are critical inlet components on supersonic airplanes having bifucated engine inlets. This paper documents measured details of the flow through a rectangular-to-semiannular transition duct having an expansion area ratio of 1.53. Three-dimensional velocity vectors and total pressures at the exit plane of the diffuser are presented. Surface oil-flow visualization and surface static pressure data are shown. The tests were conducted with an inlet Mach number of 0.786 and a Reynolds number based on the inlet centerline velocity and exit diameter of 3.2 x 10(exp 6). The measured data are compared with previously published computational results. The ability of vortex generators to reduce circumferential total pressure distortion is demonstrated. 9. On the prestressing and deformation of rectangular particle detector frames International Nuclear Information System (INIS) Margulies, S. 1978-01-01 Particle detectors such as spark chambers and multiwire proportional chambers (MWPC) generally contain planar electrodes stretched across rectangular frames. For detectors of reasonable size, this can result in fairly large forces acting on the frames. To maintain the electrode planes under uniform tension and to prevent sagging, the frames must be prestressed. This paper contains a detailed examination of the deformation of rectangular frames under stress. A simple model for this phenomenon is presented. The model consists of treating each side of the frame as an elastic beam subject to the condition that the sides remain perpendicular at the corners. The predictions of the model are in good agreement with measured deflections of a MWPC frame. The model is used to determine the optimum value of a single concentrated prestressing force F to best approximate the total distributed force W of a uniformly tensed electrode plane. For most geometries it is found that F is about 62% of W. (Auth.) 10. Free vibration analysis of rectangular plates with central cutout Directory of Open Access Journals (Sweden) Kanak Kalita 2016-12-01 Full Text Available A nine-node isoparametric plate element in conjunction with first-order shear deformation theory is used for free vibration analysis of rectangular plates with central cutouts. Both thick and thin plate problems are solved for various aspect ratios and boundary conditions. In this article, primary focus is given to the effect of rotary inertia on natural frequencies of perforated rectangular plates. It is found that rotary inertia has significant effect on thick plates, while for thin plates the rotary inertia term can be ignored. It is seen that the numerical convergence is very rapid and based on comparison with experimental and analytical data from literature, it is proposed that the present formulation is capable of yielding highly accurate results. Finally, some new numerical solutions are provided here, which may serve as benchmark for future research on similar problems. 11. Relativistic energy-dispersion relations of 2D rectangular lattices Science.gov (United States) Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi 2017-04-01 An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope. 12. Are Haar-like Rectangular Features for Biometric Recognition Reducible? DEFF Research Database (Denmark) Nasrollahi, Kamal; Moeslund, Thomas B. 2013-01-01 Biometric recognition is still a very difficult task in real-world scenarios wherein unforeseen changes in degradations factors like noise, occlusion, blurriness and illumination can drastically affect the extracted features from the biometric signals. Very recently Haar-like rectangular features...... which have usually been used for object detection were introduced for biometric recognition resulting in systems that are robust against most of the mentioned degradations [9]. The problem with these features is that one can define many different such features for a given biometric signal...... and it is not clear whether all of these features are required for the actual recognition or not. This is exactly what we are dealing with in this paper: How can an initial set of Haar-like rectangular features, that have been used for biometric recognition, be reduced to a set of most influential features... 13. A Novel Dual-Band Circularly Polarized Rectangular Slot Antenna Directory of Open Access Journals (Sweden) Biao Li 2016-01-01 Full Text Available A coplanar waveguide fed dual-band circularly polarized rectangular slot antenna is presented. The proposed antenna consists of a rectangular metal frame acting as a ground and an S-shaped monopole as a radiator. The spatial distribution of the surface current density is employed to demonstrate that the circular polarization is generated by the S-shaped monopole which controls the path of the surface currents. An antenna prototype, having overall dimension 37 × 37 × 1 mm3, has been fabricated on FR4 substrate with dielectric constant 4.4. The proposed antenna achieves 10 dB return loss bandwidths and 3 dB axial ratio (AR in the frequency bands 2.39–2.81 GHz and 5.42–5.92 GHz, respectively. Both these characteristics are suitable for WLAN and WiMAX applications. 14. Postbuckling Analysis Of A Rectangular Plate Loaded In Compression Directory of Open Access Journals (Sweden) Havran Jozef 2015-12-01 Full Text Available The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied. 15. Study of gas-water flow in horizontal rectangular channels Science.gov (United States) Chinnov, E. A.; Ron'shin, F. V.; Kabov, O. A. 2015-09-01 The two-phase flow in the narrow short horizontal rectangular channels 1 millimeter in height was studied experimentally. The features of formation of the two-phase flow were studied in detail. It is shown that with an increase in the channel width, the region of the churn and bubble regimes increases, compressing the area of the jet flow. The areas of the annular and stratified flow patterns vary insignificantly. 16. Two-phase flow patterns in horizontal rectangular minichannel Directory of Open Access Journals (Sweden) Ron’shin Fedor 2016-01-01 Full Text Available The two-phase flow in a short horizontal channel of rectangular cross-section of 1 × 19 mm2 has been studied experimentally. Five conventional two-phase flow patterns have been detected (bubble, churn, stratified, annular and jet and transitions between them have been determined. It is shown that a change in the width of the horizontal channels has a substantial effect on the boundaries between the flow regimes. 17. Bandwidth Study of the Microwave Reflectors with Rectangular Corrugations Science.gov (United States) Zhang, Liang; He, Wenlong; Donaldson, Craig R.; Cross, Adrian W. 2016-09-01 The mode-selective microwave reflector with periodic rectangular corrugations in the inner surface of a circular metallic waveguide is studied in this paper. The relations between the bandwidth and reflection coefficient for different numbers of corrugation sections were studied through a global optimization method. Two types of reflectors were investigated. One does not consider the phase response and the other does. Both types of broadband reflectors operating at W-band were machined and measured to verify the numerical simulations. 18. Thermal stresses in rectangular plates: variational and finite element solutions International Nuclear Information System (INIS) Laura, P.A.A.; Gutierrez, R.H.; Sanchez Sarmiento, G.; Basombrio, F.G. 1978-01-01 This paper deals with the development of an approximate method for the analysis of thermal stresses in rectangular plates (plane stress problem) and an evaluation of the relative accuracy of the finite element method. The stress function is expanded in terms of polynomial coordinate functions which identically satisfy the boundary conditions, and a variational approach is used to determine the expansion coefficients. The results are in good agreement with a finite element approach. (Auth.) 19. Diffusion of heat from a finite, rectangular, plane heat source International Nuclear Information System (INIS) Ferreri, J.C.; Caballero, C.H. 1985-01-01 Non-dimensional results for the temperature field originating in a rectangular, finite, plane heat source with infinitesimal thickness are introduced. The source decays in time, zero decay being a particular case. Results are useful for obtaining an aproximation of the maximum temperature of a system holding an internal heat source. The range selected for the parameters is specially useful in the case of a nuclear waste repository. The application to the case of mass diffussion arises from analogy. (Author) [es 20. Basic study on the rectangular numeric keys for touch screen. Science.gov (United States) Harada, H; Katsuura, T; Kikuchi, Y 1997-06-01 The present study was conducted to examine the optimum inter-key spacing of numeric rectangular keys for touch screens. Six male students (22-25 years old) and three female students (21-24 years old) participated in the experiment. Each subject performed the data entry task using rectangular keys of touch devices. These keys were arranged in both horizontal and vertical layouts. The sizes of the rectangular keys in both layouts were 12 x 21 mm and 15 x 39 mm, and each of the inter-key spacing of each key was 0, 3, 6, 12 and 21 mm. The response time with inter-key spacing of 3 mm was significantly faster than with the inter-key spacing of 0, 12 and 21 mm (p < 0.05). Keys of vertical position produced faster response time than that of horizontal position. The subjective ratings showed that the inter-key spacing of 6 mm was significantly better than the inter-key spacing of 0, 3, 12 and 21 mm (p < 0.05). 1. Azimuthal critical heat flux in narrow rectangular channels Energy Technology Data Exchange (ETDEWEB) Kim, Yong Hoon; Noh, Sang Woo; Kim, Sung Joong; Suh, Kune Y. [Seoul National University, Seoul (Korea, Republic of) 2003-07-01 Tests were conducted to examine the critical heat flux (CHF) on the one-dimensional downward heating rectangular channel having a narrow gap by changing the orientation of the copper test heater assembly in a pool of saturated water under the atmospheric pressure. The test parameters include both the gap sizes of 1, 2, 5 and 10mm, and the surface orientation angles from the downward-facing position (180{sup o}) to the vertical position (90{sup o}), respectively. Also, the CHF experiments were performed for pool boiling with varying heater surface orientations in the unconfined space at the atmospheric pressure using the rectangular test section. It was observed that the CHF generally decreases as the surface inclination angle increases and as the gap size decreases. In consistency with several studies reported in the literature, it was found that there exists a transition angle above which the CHF changes with a rapid slope. An engineering correlation is developed for the CHF during natural convective boiling in the inclined, confined rectangular channels with the aid of dimensional analysis. 2. Rectangular superpolynomials for the figure-eight knot 41 Science.gov (United States) Kononov, Ya. A.; Morozov, A. Yu. 2017-11-01 We rewrite the recently proposed differential expansion formula for HOMFLY polynomials of the knot 41 in an arbitrary rectangular representation R = [rs] as a sum over all Young subdiagrams λ of R with surprisingly simple coefficients of the Z factors. Intriguingly, these coefficients are constructed from the quantum dimensions of symmetric representations of the groups SL(r) and SL(s) and restrict the summation to diagrams with no more than s rows and r columns. Moreover, the β-deformation to Macdonald dimensions yields polynomials with positive integer coefficients, which are plausible candidates for the role of superpolynomials for rectangular representations. Both the polynomiality and the positivity of the coefficients are nonobvious, nevertheless true. This generalizes the previously known formulas for symmetric representations to arbitrary rectangular representations. The differential expansion allows introducing additional gradings. For the trefoil knot 31, to which our results for the knot 41 are immediately extended, we obtain the so-called fourth grading of hyperpolynomials. The property of factorization in roots of unity is preserved even in the five-graded case. 3. Augmented Beta rectangular regression models: A Bayesian perspective. Science.gov (United States) Wang, Jue; Luo, Sheng 2016-01-01 Mixed effects Beta regression models based on Beta distributions have been widely used to analyze longitudinal percentage or proportional data ranging between zero and one. However, Beta distributions are not flexible to extreme outliers or excessive events around tail areas, and they do not account for the presence of the boundary values zeros and ones because these values are not in the support of the Beta distributions. To address these issues, we propose a mixed effects model using Beta rectangular distribution and augment it with the probabilities of zero and one. We conduct extensive simulation studies to assess the performance of mixed effects models based on both the Beta and Beta rectangular distributions under various scenarios. The simulation studies suggest that the regression models based on Beta rectangular distributions improve the accuracy of parameter estimates in the presence of outliers and heavy tails. The proposed models are applied to the motivating Neuroprotection Exploratory Trials in Parkinson's Disease (PD) Long-term Study-1 (LS-1 study, n = 1741), developed by The National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson's Disease (NINDS NET-PD) network. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 4. Research on applications of rectangular beam in micro laser propulsion International Nuclear Information System (INIS) Jiao, L.; Cai, J.; Ma, H.H.; Li, G.X.; Li, L.; Shen, Z.W.; Tang, Z.P. 2014-01-01 Highlights: • Diode laser bar of 808 nm is introduced into the micro laser propulsion field. • Double base propellant (DBP) coating with BOPP substrate was obtained. • The combination of laser power and energy decides the propulsion performance. • The new rectangular beam prefers to produce higher impulse. - Abstract: Micro laser propulsion is a new technology with brilliant future. In order to reduce the thruster mass and volume further, laser bar is introduced into the micro laser propulsion field. A new kind of 220 × 20 μm rectangular beam of 808 nm was obtained by oval lens compressing the light of diode at fast axes and slow axes. The effect of laser power, energy and coating thickness of double base propellant on propulsion performance was studied. Propulsion performance of double base propellant under static and dynamic mode shows some different characters. Compared to round beam, the new beam prefers to produce higher impulse. Ablation efficiency of DBP shows better performance in short laser duration. The combination of power density and energy density decides the laser propulsion performance. The new rectangular beam is appropriate for millisecond micro-laser propulsion 5. A physical model of laser-assisted blocking of blood flow: I. Rectangular radiation pulses CSIR Research Space (South Africa) Zheltov, GI 2007-03-01 Full Text Available as to the investigation of destructive changes in these objects [1–16]. Various models were considered in these studies: a model of skin as a set of plane layers with different optical and physical properties (epider- mis, dermis, blood layer) [1–9], a similar model... conditions of minimal damage to adjacent healthy tissues. The necessity of local block- ing of the blood flow arises, e.g., upon dissection of tis- sues (stanching blood flow), upon treatment of vascular malformations (including those of diabetic origin... 6. Study on the Effect of the Impact Location and the Type of Hammer Tip on the Frequency Response Function (FRF) in Experimental Modal Analysis of Rectangular Plates Science.gov (United States) Mali, K. D.; Singru, P. M. 2018-03-01 In this work effect of the impact location and the type of hammer tip on the frequency response function (FRF) is studied. Experimental modal analysis of rectangular plates is carried out for this purpose by using impact hammer, accelerometer and fast Fourier transform (FFT) analyzer. It is observed that the impulse hammer hit location has, no effect on the eigenfrequency, yet a difference in amplitude of the eigenfrequencies is obtained. The effect of the hammer tip on the pulse and the force spectrum is studied for three types of tips metal, plastic and rubber. A solid rectangular plate was excited by using these tips one by one in three different tests. It is observed that for present experimental set up plastic tip excites the useful frequency range. 7. Visual CRO display of pulse height distribution including discriminator setting for a single channel X-ray analyser International Nuclear Information System (INIS) Shaw, S.E. 1979-01-01 An outline for a simple pulse spectroscope which attaches to a standard laboratory CRO is presented. The peak amplitude voltage of each pulse from the linear amplifier of a single channel X-ray analyser is stored for the duration of one oscilloscope trace. For each amplifier pulse, input from the discriminator is tested and if these is coincidence of pulses the oscilloscope beam is blanked for approximately the first 2 cm of its traverse across the screen. Repetition of pulses forms a pulse height distribution with a rectangular dark area marking the position of the discriminator window. (author) 8. Estimating the uncertainty of the impact of climate change on alluvial aquifers. Case study in central Italy Science.gov (United States) Romano, Emanuele; Camici, Stefania; Brocca, Luca; Moramarco, Tommaso; Pica, Federico; Preziosi, Elisabetta 2014-05-01 There is evidence that the precipitation pattern in Europe is trending towards more humid conditions in the northern region and drier conditions in the southern and central-eastern regions. However, a great deal of uncertainty concerns how the changes in precipitations will have an impact on water resources, particularly on groundwater, and this uncertainty should be evaluated on the basis of that coming from 1) future climate scenarios of Global Circulation Models (GCMs) and 2) modeling chains including the downscaling technique, the infiltration model and the calibration/validation procedure used to develop the groundwater flow model. With the aim of quantifying the uncertainty of these components, the Valle Umbra porous aquifer (Central Italy) has been considered as a case study. This aquifer, that is exploited for human consumption and irrigation, is mainly fed by the effective infiltration from the ground surface and partly by the inflow from the carbonate aquifers bordering the valley. A numerical groundwater flow model has been developed through the finite difference MODFLOW2005 code and it has been calibrated and validated considering the recharge regime computed through a Thornthwaite-Mather infiltration model under the climate conditions observed in the period 1956-2012. Future scenarios (2010-2070) of temperature and precipitation have been obtained from three different GMCs: ECHAM-5 (Max Planck Institute, Germany), PCM (National Centre Atmospheric Research) and CCSM3 (National Centre Atmospheric Research). Each scenario has been downscaled (DSC) to the data of temperature and precipitation collected in the baseline period 1960-1990 at the stations located in the study area through two different statistical techniques (linear rescaling and quantile mapping). Then, stochastic rainfall and temperature time series are generated through the Neyman-Scott Rectangular Pulses model (NSRP) for precipitation and the Fractionally Differenced ARIMA model (FARIMA 9. Investigation of imaging properties for submillimeter rectangular pinholes Energy Technology Data Exchange (ETDEWEB) Xia, Dan, E-mail: [email protected] [The Department of Radiology, The University of Chicago, Chicago, Illinois 60637 (United States); Moore, Stephen C., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected]; Park, Mi-Ae, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected]; Cervo, Morgan, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Brigham and Women’s Hospital and Harvard Medical School, Boston, Massachusetts 02115 (United States); Metzler, Scott D., E-mail: [email protected] [The Department of Radiology, The University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States) 2015-12-15 Purpose: Recently, a multipinhole collimator with inserts that have both rectangular apertures and rectangular fields of view (FOVs) has been proposed for SPECT imaging since it can tile the projection onto the detector efficiently and the FOVs in transverse and axial directions become separable. The purpose of this study is to investigate the image properties of rectangular-aperture pinholes with submillimeter apertures sizes. Methods: In this work, the authors have conducted sensitivity and FOV experiments for 18 replicates of a prototype insert fabricated in platinum/iridium (Pt/Ir) alloy with submillimeter square-apertures. A sin{sup q}θ fit to the experimental sensitivity has been performed for these inserts. For the FOV measurement, the authors have proposed a new formula to calculate the projection intensity of a flood image on the detector, taking into account the penumbra effect. By fitting this formula to the measured projection data, the authors obtained the acceptance angles. Results: The mean (standard deviation) of fitted sensitivity exponents q and effective edge lengths w{sub e} were, respectively, 10.8 (1.8) and 0.38 mm (0.02 mm), which were close to the values, 7.84 and 0.396 mm, obtained from Monte Carlo calculations using the parameters of the designed inserts. For the FOV measurement, the mean (standard deviation) of the transverse and axial acceptances were 35.0° (1.2°) and 30.5° (1.6°), which are in good agreement with the designed values (34.3° and 29.9°). Conclusions: These results showed that the physical properties of the fabricated inserts with submillimeter aperture size matched our design well. 10. Far-field potentials in cylindrical and rectangular volume conductors. Science.gov (United States) Dumitru, D; King, J C; Rogers, W E 1993-07-01 The occurrence of a transient dipole is one method of producing a far-field potential. This investigation qualitatively defines the characteristics of the near-field and far-field electrical potentials produced by a transient dipole in both cylindrical and rectangular volume conductors. Most body segments of electrophysiologic interest such as arms, legs, thorax, and neck are roughly cylindrical in shape. A centrally located dipole generator produces a nonzero equipotential region which is found to occur along the cylindrical wall at a distance from the dipole of approximately 1.4 times the cylinder's radius and 1.9 times the cylinder's radius for the center of the cylinder. This distance to the equi-potential zone along the surface wall expands but remains less than 3.0 times the cylindrical radius when the dipole is eccentrically placed. The magnitude of the equipotential region resulting from an asymmetrically placed dipole remains identical to that when the dipole is centrally located. This behavior is found to be very similar in rectangular shallow conducting volumes that model a longitudinal slice of the cylinder, thus allowing a simple experimental model of the cylinder to be utilized. Amplitudes of the equipotential region are inversely proportional to the cylindrical or rectangular volume's cross-sectional area at the location of dipolar imbalance. This study predicts that referential electrode montages, when placed at 3.0 times the radius or greater from a dipolar axially aligned far-field generator in cylindrical homogeneous volume conductors, will record only equipotential far-field effects. 11. Microwave corrosion detection using open ended rectangular waveguide sensors Energy Technology Data Exchange (ETDEWEB) Qaddoumi, N.; Handjojo, L.; Bigelow, T.; Easter, J.; Bray, A.; Zoughi, R. 2000-02-01 The use of microwave and millimeter wave nondestructive testing methods utilizing open ended rectangular waveguide sensors has shown great potential for detecting minute thickness variations in laminate structures, in particular those backed by a conducting plate. Slight variations in the dielectric properties of materials may also be detected using a set of optimal parameters which include the standoff distance and the frequency of operation. In a recent investigation, on detecting rust under paint, the dielectric properties of rust were assumed to be similar to those of Fe{sub 2}O{sub 3} powder. These values were used in an electromagnetic model that simulates the interaction of fields radiated by a rectangular waveguide aperture with layered structures to obtain optimal parameters. The dielectric properties of Fe{sub 2}O{sub 3} were measured to be very similar to the properties of paint. Nevertheless, the presence of a simulated Fe{sub 2}O{sub 3} layer under a paint layer was detected. In this paper the dielectric properties of several different rust samples from different environments are measured. The measurements indicate that the nature of real rust is quite diverse and is different from Fe{sub 2}O{sub 3} and paint, indicating that the presence of rust under paint can be easily detected. The same electromagnetic model is also used (with the newly measured dielectric properties of real rust) to obtain an optimal standoff distance at a frequency of 24 GHz. The results indicate that variations in the magnitude as well as the phase of the reflection coefficient can be used to obtain information about the presence of rust. An experimental investigation on detecting the presence of very thin rust layers (2.5--5 x 10{sup {minus}2} mm [09--2.0 x 10{sup {minus}3} in.]) using an open ended rectangular waveguide probe is also conducted. Microwave images of rusted specimens, obtained at 24 GHz, are also presented. 12. The demagnetizing field of a non-uniform rectangular prism DEFF Research Database (Denmark) Smith, Anders; Nielsen, Kaspar Kirstein; Christensen, Dennis 2010-01-01 The effect of demagnetization on the magnetic properties of a rectangular ferromagnetic prism under non-uniform conditions is investigated. A numerical model for solving the spatially varying internal magnetic field is developed, validated and applied to relevant cases. The demagnetizing field...... is solved by an analytical calculation and the coupling between applied field, the demagnetization tensor field and spatially varying temperature is solved through iteration. We show that the demagnetizing field is of great importance in many cases and that it is necessary to take into account the non... 13. Nonlinear dynamics and control of a vibrating rectangular plate Science.gov (United States) Shebalin, J. V. 1983-01-01 The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined. 14. Regimes of Two-Phase Flow in Short Rectangular Channel Science.gov (United States) Chinnov, Evgeny A.; Guzanov, Vladimir V.; Cheverda, Vyacheslav; Markovich, Dmitry M.; Kabov, Oleg A. 2009-08-01 Experimental study of two-phase flow in the short rectangular horizontal channel with height 440 μm has been performed. Characteristics of liquid motion inside the channel have been registered and measured by the Laser Induced Fluorescence technique. New information has allowed determining more precisely the characteristics of churn regime and boundaries between different regimes of two-phase flow. It was shown that formation of some two-phase flow regimes and transitions between them are determined by instability of the flow in the lateral parts of the channel. 15. Bubble departure diameter in narrow rectangular channel under rolling condition Energy Technology Data Exchange (ETDEWEB) Xie, T.; Chen, B.; Yan, X.; Xu, J.; Huang, Y.; Xiao, Z. [Nuclear Power Inst. of China, Chengdu, Sichuan (China) 2014-07-01 Forced convective subcooled boiling flow experiments were conducted in a vertical upward narrow rectangular channel under rolling motion. A high-speed digital video camera was used to capture the dynamics of the bubble nucleation process. Bubble departure diameters were obtained from the images. A bubble departure model based on force balance analysis was proposed to predict the bubble departure size under rolling condition by considering the additional centrifugal, tangential and Coriolis force. The proposed model agreed well with the experimental data within the averaged relative deviation of 5%. (author) 16. Experimental study of subsonic microjet escaping from a rectangular nozzle Science.gov (United States) Aniskin, V. M.; Maslov, A. A.; Mukhin, K. A. 2016-10-01 The first experiments on the subsonic laminar microjets escaping from the nozzles of rectangular shape are carried out. The nozzle size is 83.3x3823 microns. Reynolds number calculated by the nozzle height and the average flow velocity at the nozzle exit ranged from 58 to 154. The working gas was air at room temperature. The velocity decay and velocity fluctuations along the center line of the jet are determined. The fundamental difference between the laminar microjets characteristics and subsonic turbulent jets of macro size is shown. Based on measurements of velocity fluctuations it is shown the presence of laminar-turbulent transition in microjets and its location is determined. 17. Finite-size resonance dielectric cylinder in a rectangular waveguide International Nuclear Information System (INIS) Chuprina, V.N.; Khizhnyak, N.A. 1988-01-01 The problem on resonance spread of an electromagnetic wave by a dielectric circular cylinder of finite size in a rectangular waveguide is solved by a numerical-analytical method. The cylinder axes are parallel. The cylinder can be used as a resonance tuning element in accelerating SHF-sections. Problems on cutting off linear algebraic equation systems, to which relations of macroscopic electrodynamics in the integral differential form written for the concrete problem considered here are reduced by analytical transformations, are investigated in the stage of numerical analysis. Theoretical dependences of the insertion of the voltage standing wave coefficient on the generator wave length calculated for different values of problem parameters are constracted 18. Numerical modeling of Harmonic Imaging and Pulse Inversion fields Science.gov (United States) Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis 2003-10-01 Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed. 19. Applicability of electrical resistance tomography to rectangular vessels International Nuclear Information System (INIS) Ichijo, Noriaki; Matsuno, Shinsuke; Tokura, Susumu; Tochigi, Yoshikatsu; Misumi, Ryuta; Nishi, Kazuhiko; Kaminoyama, Meguru 2012-01-01 To ensure a stable operation of Joule-heated glass melters, it is necessary to observe the distribution of platinum group metal particles (noble metals) in molten glass. Electrical resistance tomography (ERT) has a potential to visualize the inside of the melter section because it can be applied at severe conditions such as high temperature and radioactive fields. Due to designing limitations, it is difficult to install electrodes on the wall of the glass melter. In addition, ERT is hardly applied to a rectangular section. To solve these problems, numerical and experimental studies have been implemented. To apply the ERT method, 8 electrodes are inserted from the top of the melter and set near the bottom to visualize the accumulation of noble metals on the bottom area. As a result of the numerical simulation and the experiment, it was clarified that the ERT can be applied to the rectangular vessel by inserting electrodes from the top of the vessel and has a potential to observe the accumulation of noble metals. (author) 20. Mechanical behavior analysis on electrostatically actuated rectangular microplates Science.gov (United States) Li, Zhikang; Zhao, Libo; Jiang, Zhuangde; Ye, Zhiying; Dai, Lu; Zhao, Yulong 2015-03-01 Microplates are widely used in various MEMS devices based on electrostatic actuation such as MEMS switches, micro pumps and capacitive micromachined ultrasonic transducers (CMUTs). Accurate predictions for the mechanical behavior of the microplate under electrostatic force are important not only for the design and optimization of these electrostatic devices but also for their operation. This paper presents a novel reduced-order model for electrostatically actuated rectangular and square microplates with a new method to treat the nonlinear electrostatic force. The model was developed using Galerkin method which turned the partial-differential equation governing the microplates into an ordinary equation system. Using this model and cosine-like deflection functions, explicit expressions were established for the deflection and pull-in voltage of the rectangular and square microplates. The theoretical results were well validated with the finite element method simulations and experimental data of literature. The expressions for the deflection analysis are able to predict the deflection up to the pull-in position with an error less than 5.0%. The expressions for the pull-in voltage analysis can determine the pull-in voltages with errors less than 1.0%. Additionally, the method to calculate the capacitance variation of the electrostatically actuated microplates was proposed. These theoretical analyses are helpful for design and optimization of electrostatically actuated microdevices. 1. Mechanical behavior analysis on electrostatically actuated rectangular microplates International Nuclear Information System (INIS) Li, Zhikang; Zhao, Libo; Jiang, Zhuangde; Ye, Zhiying; Zhao, Yulong; Dai, Lu 2015-01-01 Microplates are widely used in various MEMS devices based on electrostatic actuation such as MEMS switches, micro pumps and capacitive micromachined ultrasonic transducers (CMUTs). Accurate predictions for the mechanical behavior of the microplate under electrostatic force are important not only for the design and optimization of these electrostatic devices but also for their operation. This paper presents a novel reduced-order model for electrostatically actuated rectangular and square microplates with a new method to treat the nonlinear electrostatic force. The model was developed using Galerkin method which turned the partial-differential equation governing the microplates into an ordinary equation system. Using this model and cosine-like deflection functions, explicit expressions were established for the deflection and pull-in voltage of the rectangular and square microplates. The theoretical results were well validated with the finite element method simulations and experimental data of literature. The expressions for the deflection analysis are able to predict the deflection up to the pull-in position with an error less than 5.0%. The expressions for the pull-in voltage analysis can determine the pull-in voltages with errors less than 1.0%. Additionally, the method to calculate the capacitance variation of the electrostatically actuated microplates was proposed. These theoretical analyses are helpful for design and optimization of electrostatically actuated microdevices. (paper) 2. The calculation of dose rates from rectangular sources International Nuclear Information System (INIS) Hartley, B.M. 1998-01-01 A common problem in radiation protection is the calculation of dose rates from extended sources and irregular shapes. Dose rates are proportional to the solid angle subtended by the source at the point of measurement. Simple methods of calculating solid angles would assist in estimating dose rates from large area sources and therefore improve predictive dose estimates when planning work near such sources. The estimation of dose rates is of particular interest to producers of radioactive ores but other users of bulk radioactive materials may have similar interest. The use of spherical trigonometry can assist in determination of solid angles and a simple equation is derived here for the determination of the dose at any distance from a rectangular surface. The solid angle subtended by complex shapes can be determined by modelling the area as a patchwork of rectangular areas and summing the solid angles from each rectangle. The dose rates from bags of thorium bearing ores is of particular interest in Western Australia and measured dose rates from bags and containers of monazite are compared with theoretical estimates based on calculations of solid angle. The agreement is fair but more detailed measurements would be needed to confirm the agreement with theory. (author) 3. Measurement strategy for rectangular electrical capacitance tomography sensor International Nuclear Information System (INIS) Ye, Jiamin; Ge, Ruihuan; Qiu, Guizhi; Wang, Haigang 2014-01-01 To investigate the influence of the measurement strategy for the rectangular electrical capacitance tomography (ECT) sensor, a Finite Element Method (FEM) is utilized to create the model for simulation. The simulation was carried out using COMSOL Multiphysics(trade mark, serif) and Matlab(trade mark, serif). The length-width ratio of the rectangular sensing area is 5. Twelve electrodes are evenly arranged surrounding the pipe. The covering ratio of the electrodes is 90%. The capacitances between different electrode pairs are calculated for a bar distribution. The air of the relative permittivity 1.0 and the material of the permittivity 3.0 are used for the calibration. The relative permittivity of the second phase is 3.0. The noise free and noise data are used for the image reconstruction using the Linear Back Projection (LBP). The measurement strategies with 1-, 2- and 4- electrode excitation are compared using the correlation coefficient. Preliminary results show that the measurement strategy with 2-electrode excitation outperforms other measurement strategies with 1- or 4-electrode excitation 4. A Rectangular Planar Spiral Antenna for GIS Partial Discharge Detection Directory of Open Access Journals (Sweden) Xiaoxing Zhang 2014-01-01 Full Text Available A rectangular planar spiral antenna sensor was designed for detecting the partial discharge in gas insulation substations (GIS. It can expediently receive electromagnetic waves leaked from basin-type insulators and can effectively suppress low frequency electromagnetic interference from the surrounding environment. Certain effective techniques such as rectangular spiral structure, bow-tie loading, and back cavity structure optimization during the antenna design process can miniaturize antenna size and optimize voltage standing wave ratio (VSWR characteristics. Model calculation and experimental data measured in the laboratory show that the antenna possesses a good radiating performance and a multiband property when working in the ultrahigh frequency (UHF band. A comparative study between characteristics of the designed antenna and the existing quasi-TEM horn antenna was made. Based on the GIS defect simulation equipment in the laboratory, partial discharge signals were detected by the designed antenna, the available quasi-TEM horn antenna, and the microstrip patch antenna, and the measurement results were compared. 5. Numerical investigation of flow past a row of rectangular rods Directory of Open Access Journals (Sweden) S.Ul. Islam 2016-09-01 Full Text Available A numerical study of uniform flow past a row of rectangular rods with aspect ratio defined as R = width/height = 0.5 is performed using the Lattice Boltzmann method. For this study the Reynolds number (Re is fixed at 150, while spacings between the rods (g are taken in the range from 1 to 6. Depending on g, the flow is classified into four patterns: flip-flopping, nearly unsteady-inphase, modulated inphase-antiphase non-synchronized and synchronized. Sudden jumps in physical parameters were observed, attaining either maximum or minimum values, with the change in flow patterns. The mean drag coefficient (Cdmean of middle rod is higher than the second and fourth rod for flip-flopping pattern while in case of nearly unsteady-inphase the middle rod attains minimum drag coefficient. It is also found that the Strouhal number (St of first, second and fifth rod decreases as g increases while that of other two have mixed trend. The results further show that there exist secondary interaction frequencies together with primary vortex shedding frequency due to jet in the gap between rods for 1 ⩽ g ⩽ 3. For the average values of Cdmean and St, an empirical relation is also given as a function of gap spacing. This relation shows that the average values of Cdmean and St approach to those of single rectangular rod with increment in g. 6. Measurement on the cavitating vortex shedding behind rectangular obstacles International Nuclear Information System (INIS) Hegedus, F; Hos, C; Pandula, Z; Kullmann, L 2010-01-01 Measurement results on the cavitating vortex shedding behind sharp-edged rectangular bodies are presented, intended to provide benchmark cases for the validation of unsteady cavitation models of CFD codes. Rectangular bodies of increasing aspect ratio (1, 2, 3 and 4) were used with a constant 25mm height (12.5% blockage ratio). The water velocity in the 0.2x0.05m test section of the channel was varied between 1 and 12 m/s resulting in a Reynolds number in the range of (0.4-3.5)x105. Pressure signals were measured at several locations, notably in the wake. Dominant frequencies and Strouhal numbers are reported from cavitation-free flow (classic von Karman vortex shedding) up to supercavitation as a function of the free-stream Reynolds number. The results are in good agreement with the literature in case of the square cylinder. We experienced a slight increase of the dominant Strouhal number with increasing aspect ratio. This result is somewhat inconsistent with the literature, in which a fall of the Strouhal number can be observed at side ratio 2. This may be the consequence of the different ranges of Reynolds numbers. It was also found that between the inception of cavitation and the formation of supercavitation the Strouhal number is not affected by cavitation. 7. Measurement on the cavitating vortex shedding behind rectangular obstacles Energy Technology Data Exchange (ETDEWEB) Hegedus, F; Hos, C; Pandula, Z; Kullmann, L, E-mail: [email protected] [Department of Hydrodynamic Systems, Budapest University of Technology and Economics Muegyetem rkp. 1, Budapest 1111 (Hungary) 2010-08-15 Measurement results on the cavitating vortex shedding behind sharp-edged rectangular bodies are presented, intended to provide benchmark cases for the validation of unsteady cavitation models of CFD codes. Rectangular bodies of increasing aspect ratio (1, 2, 3 and 4) were used with a constant 25mm height (12.5% blockage ratio). The water velocity in the 0.2x0.05m test section of the channel was varied between 1 and 12 m/s resulting in a Reynolds number in the range of (0.4-3.5)x105. Pressure signals were measured at several locations, notably in the wake. Dominant frequencies and Strouhal numbers are reported from cavitation-free flow (classic von Karman vortex shedding) up to supercavitation as a function of the free-stream Reynolds number. The results are in good agreement with the literature in case of the square cylinder. We experienced a slight increase of the dominant Strouhal number with increasing aspect ratio. This result is somewhat inconsistent with the literature, in which a fall of the Strouhal number can be observed at side ratio 2. This may be the consequence of the different ranges of Reynolds numbers. It was also found that between the inception of cavitation and the formation of supercavitation the Strouhal number is not affected by cavitation. 8. On Mathematical Optimization for the Visualization of Frequencies and Adjacencies as Rectangular Maps DEFF Research Database (Denmark) Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero 2018-01-01 individuals as adjacent rectangular portions as possible and adding as few false adjacencies, i.e., adjacencies between rectangular portions corresponding to non-adjacent individuals, as possible. We formulate this visualization problem as a Mixed Integer Linear Programming (MILP) model. We propose......In this paper we address the problem of visualizing a frequency distribution and an adjacency relation attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one... 9. Enhanced Circular Dichroism of Gold Bilayered Slit Arrays Embedded with Rectangular Holes. Science.gov (United States) Zhang, Hao; Wang, Yongkai; Luo, Lina; Wang, Haiqing; Zhang, Zhongyue 2017-01-01 Gold bilayered slit arrays with rectangular holes embedded into the metal surface are designed to enhance the circular dichroism (CD) effect of gold bilayered slit arrays. The rectangular holes in these arrays block electric currents and generate localized surface plasmons around these holes, thereby strengthening the CD effect. The CD enhancement factor depends strongly on the rotational angle and the structural parameters of the rectangular holes; this factor can be enhanced further by drilling two additional rectangular holes into the metal surfaces of the arrays. These results help facilitate the design of chiral structures to produce a strong CD effect and large electric fields. 10. Laser beam welding of titanium nitride coated titanium using pulse-shaping Directory of Open Access Journals (Sweden) Milton Sergio Fernandes de Lima 2005-09-01 Full Text Available A new welding method which allows the assembly of two titanium nitride coated titanium parts is proposed. The welding procedure utilizes the possibility for pulse-shaping in order to change the energy distribution profile during the laser pulse. The pulse-shaping is composed of three elements: a a short high power pulse for partial ablation at the surface; b a long pulse for thermal penetration; and c a quenching slope for enhanced weldability. The combination of these three elements produces crack-free welds. The weld microstructure is changed in comparison to normal welding, i.e. with a rectangular pulse, as the nitrogen and the microhardness are more homogenously distributed in the weld under pulse-shaping conditions. This laser pulse dissolves the TiN layer and allows nitrogen to diffuse into the melt pool, also contributing to an enhanced weldability by providing suitable thermal conditions. 11. Pulse plating CERN Document Server Hansal, Wolfgang E G; Green, Todd; Leisner, Peter; Reichenbach, Andreas 2012-01-01 The electrodeposition of metals using pulsed current has achieved practical importance in recent years. Although it has long been known that changes in potential, with or without polarity reversal, can significantly affect the deposition process, the practical application of this has been slow to be adopted. This can largely be explained in terms of the complex relationship between the current regime and its effect on the electrodeposition process. In order to harness these effects, an understanding of the anodic and cathodic electrochemical processes is necessary, together with the effects of polarity reversal and the rate of such reversals. In this new monograph, the basics of metal electrodeposition from solution are laid out in great detail in seven distinct chapters. With this knowledge, the reader is able to predict how a given pulse train profile can be adopted to achieve a desired outcome. Equally important is the choice of a suitable rectifier and the ancillary control circuits to enable pulse platin... 12. Robust refocusing of 13C magnetization in multidimensional NMR experiments by adiabatic fast passage pulses International Nuclear Information System (INIS) 1999-01-01 We show that adiabatic fast passage (AFP) pulses are robust refocusing elements of transverse 13 C magnetization in multidimensional NMR experiments. A pair of identical AFP pulses can refocus selected parts or a complete 13 C chemical shift range in 13 C spectra. In the constant time 13 C- 1 H HSQC, replacement of attenuated rectangular pulses by selective AFP pulses results in a sensitivity enhancement of up to a factor of 1.8. In the 3D CBCA(CO)NH the signal-to-noise ratio is increased by a factor of up to 1.6 13. Interference Processes During Reradiation of Attosecond Pulses of Electromagnetic Field by Graphene Science.gov (United States) Makarov, D. N.; Matveev, V. I.; Makarova, K. A. 2018-05-01 Interference spectra during reradiation of attosecond pulses of electromagnetic field by graphene sheets are considered. Analytical expressions for calculations of spectral distributions are derived. As an example, the interference spectra of a graphene sheet and a flat rectangular lattice are compared. 14. Evolution of super-Gaussian pulses in a nonlinear optical fiber Science.gov (United States) Bugay, Aleksandr N.; Khalyapin, Vyacheslav A. 2018-04-01 An analytic and numerical study is carried out of the dynamics of parameters of a super-Gaussian pulse whose spectrum can fit both in the region of normal and anomalous dispersion of the group velocity. An analytical solution is found for the parameter characterizing the evolution of the degree of the super-Gaussian momentum. The loss of profile rectangularity is shown to be much faster than the pulse dispersion broadening, and corresponding characteristic length is determined by explicit formula. 15. Rectangular amplitudes, conformal blocks, and applications to loop models Energy Technology Data Exchange (ETDEWEB) Bondesan, Roberto, E-mail: [email protected] [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Jacobsen, Jesper L. [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Universite Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France); Saleur, Hubert [Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Physics Department, USC, Los Angeles, CA 90089-0484 (United States) 2013-02-21 In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan, et al., Nucl. Phys. B 862 (2012) 553-575]. Here we develop a general formalism of rectangle boundary states using conformal field theory, adapted to describe geometries supporting different boundary conditions. We discuss the computation of rectangular amplitudes and their modular properties, presenting explicit results for the case of free theories. In a second part of the paper we focus on applications to loop models, discussing in details lattice discretizations using both numerical and analytical calculations. These results allow to interpret geometrically conformal blocks, and as an application we derive new probability formulas for self-avoiding walks. 16. Calculation of control rods in rectangular reactor, and applications (1960) International Nuclear Information System (INIS) Goshen, S.; Pazy, A. 1960-01-01 The aim of this report is to find a method for estimating the anti-reactivity of control rods perpendicular to the axis in a cylindrical pile. The paper is divided into two parts. In the first is given a method of calculating control rods in a rectangular pile, similar to the Nordheim-Scalettar method for cylindrical piles. As an example the formulas are given for the theories of one and two neutron groups, the generalisation for several groups being evident. In the second part we find by a variation method a formula for estimating the Laplacian of a pile, which may be divided into parallelepipeds for which the Laplacian are given. Finally, this formula is used to calculate the anti-reactivity of rods perpendicular to the axis in a cylindrical pile. (author) [fr 17. Critical current studies of a HTS rectangular coil Energy Technology Data Exchange (ETDEWEB) Zhong, Z. [Department of Engineering, University of Cambridge (United Kingdom); Chudy, M., E-mail: [email protected] [Graduate School of Technology Management, University of Pretoria (South Africa); Institute of Power and Applied Electrical Engineering, Slovak University of Technology in Bratislava (Slovakia); Ruiz, H.S. [Department of Engineering, University of Leicester, Leicester LE1 7RH (United Kingdom); Zhang, X.; Coombs, T. [Department of Engineering, University of Cambridge (United Kingdom) 2017-05-15 Highlights: • Unique square pancake coil was manufactured. • Measurements in relatively high magnetic field were performed. • Different sections of the coil were characterized. • Parts of the coil which are limiting critical current were identified. - Abstract: Nowadays, superconducting high field magnets are used in numerous applications due to their superior properties. High temperature superconductors (HTS) are usually used for production of circular pancake or racetrack coils. However different geometries of HTS coils might be required for some specific applications. In this study, the HTS coil wound on a rectangular frame was fully characterized in homogeneous DC background field. The study contains measurements of critical current angular dependencies. The critical current of the entire coil and two selected strands under different magnitudes and orientations of external magnetic fields are measured. The critical regions of the coil in different angular regimes are determined. This study brings better understanding of the in- field performance of HTS coils wound on frames with right-angles. 18. Stress analysis and evaluation of a rectangular pressure vessel International Nuclear Information System (INIS) Rezvani, M.A.; Ziada, H.H.; Shurrab, M.S. 1992-10-01 This study addresses structural analysis and evaluation of an abnormal rectangular pressure vessel, designed to house equipment for drilling and collecting samples from Hanford radioactive waste storage tanks. It had to be qualified according to ASME boiler and pressure vessel code, Section VIII; however, it had the cover plate bolted along the long face, a configuration not addressed by the code. Finite element method was used to calculate stresses resulting from internal pressure; these stresses were then used to evaluate and qualify the vessel. Fatigue is not a concern; thus, it can be built according to Section VIII, Division I instead of Division 2. Stress analysis was checked against the code. A stayed plate was added to stiffen the long side of the vessel 19. Performance analysis of SOI MOSFET with rectangular recessed channel Science.gov (United States) Singh, M.; Mishra, S.; Mohanty, S. S.; Mishra, G. P. 2016-03-01 In this paper a two dimensional (2D) rectangular recessed channel-silicon on insulator metal oxide semiconductor field effect transistor (RRC-SOI MOSFET), using the concept of groove between source and drain regions, which is one of the channel engineering technique to suppress the short channel effect (SCE). This suppression is mainly due to corner potential barrier of the groove and the simulation is carried out by using ATLAS 2D device simulator. To have further improvement of SCE in RRC-SOI MOSFET, three more devices are designed by using dual material gate (DMG) and gate dielectric technique, which results in formation of devices i.e. DMRRC-SOI,MLSMRRC-SOI, MLDMRRC-SOI MOSFET. The effect of different structures of RRC-SOI on AC and RF parameters are investigated and the importance of these devices over RRC MOSFET regarding short channel effect is analyzed. 20. Experimental study of natural circulation flow instability in rectangular channels Energy Technology Data Exchange (ETDEWEB) Zhou, Tao; Qi, Shi; Song, Mingqiang [North China Electric Power Univ., Beijing (China). School of Nuclear Science and Engineering; Passive Nuclear Safety Technology, Beijing (China). Beijing Key Lab.; Xiao, Zejun [Nuclear, Reactor Thermal Hydraulics Technology, Chengdu (China). CNNC Key Lab. 2017-05-15 Experiments of natural circulation flow instability were conducted in rectangular channels with 5 mm and 10 mm wide gaps. Results for different heating powers were obtained. The results showed that the flow will tend to be instable with the growing of heating power. The oscillation period of pressure D-value and volume flow are the same, but their phase positions are opposite. They both can be described by trigonometric functions. The existence of edge position and secondary flow will strengthen the disturbance of fluid flow in rectangle channels, which contributes to heat transfer. The disturbance of bubble and fluid will be strengthened, especially in the saturated boiling section, which make it possible for the mixing flow. The results also showed that the resistance in 5 mm channel is bigger than that in 10 mm channel, it is less likely to form stable natural circulation in the subcooled region. 1. Specific aspects of turbulent flow in rectangular ducts Directory of Open Access Journals (Sweden) Stanković Branislav D. 2017-01-01 Full Text Available The essential ideas of investigations of turbulent flow in a straight rectangular duct are chronologically presented. Fundamentally significant experimental and theoretical studies for mathematical modeling and numerical computations of this flow configuration are analyzed. An important physical aspect of this type of flow is presence of secondary motion in the plane perpendicular to the streamwise direction, which is of interest from both the engineering and the scientific viewpoints. The key facts for a task of turbulence modeling and optimal choice of the turbulence model are obtained through careful examination of physical mechanisms that generate secondary flows. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no.TR-33018: Increase in Energy and Ecology Efficiency of Processes in Pulverized Coal-Fired Furnace and Optimization of Utility Steam Boiler Air Pre-heater by Using In-House Developed Software Tools 2. Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method Directory of Open Access Journals (Sweden) Seval Pinarbasi 2012-01-01 Full Text Available The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method (HPM. 3. Counter-current flow limited CHF in thin rectangular channels International Nuclear Information System (INIS) Cheng, L.Y. 1990-01-01 An analytical expression for counter-current-flow-limitation (CCFL) was used to predict critical heat flux (CHF) for downward flow in thin vertical rectangular channels which are prototypes of coolant channels in test and research nuclear reactors. Top flooding is the mechanism for counter-current flow limited CHF. The CCFL correlation also was used to determine the circulation and flooding-limited CHF. Good agreements were observed between the period the model predictions and data on the CHF for downflow. The minimum CHF for downflow is lower than the flooding-limited CHF and it is predicted to occur at a liquid flow rate higher than that at the flooding limit. 17 refs., 7 figs 4. Thermoelectric effects in a rectangular Aharonov-Bohm geometry Science.gov (United States) Pye, A. J.; Faux, D. A.; Kearney, M. J. 2016-04-01 The thermoelectric transport properties of a rectangular Aharonov-Bohm ring at low temperature are investigated using a theoretical approach based on Green's functions. The oscillations in the transmission coefficient as the field is varied can be used to tune the thermoelectric response of the ring. Large magnitude thermopowers are obtainable which, in conjunction with low conductance, can result in a high thermoelectric figure of merit. The effects of single site impurities and more general Anderson disorder are considered explicitly in the context of evaluating their effect on the Fano-type resonances in the transmission coefficient. Importantly, it is shown that even for moderate levels of disorder, the thermoelectric figure of merit can remain significant, increasing the appeal of such structures from the perspective of specialist thermoelectric applications. 5. Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses Directory of Open Access Journals (Sweden) Ding Zhou 2012-01-01 Full Text Available A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation. 6. Flow field induced particle accumulation inside droplets in rectangular channels. Science.gov (United States) Hein, Michael; Moskopp, Michael; Seemann, Ralf 2015-07-07 Particle concentration is a basic operation needed to perform washing steps or to improve subsequent analysis in many (bio)-chemical assays. In this article we present field free, hydrodynamic accumulation of particles and cells in droplets flowing within rectangular micro-channels. Depending on droplet velocity, particles either accumulate at the rear of the droplet or are dispersed over the entire droplet cross-section. We show that the observed particle accumulation behavior can be understood by a coupling of particle sedimentation to the internal flow field of the droplet. The changing accumulation patterns are explained by a qualitative change of the internal flow field. The topological change of the internal flow field, however, is explained by the evolution of the droplet shape with increasing droplet velocity altering the friction with the channel walls. In addition, we demonstrate that accumulated particles can be concentrated, removing excess dispersed phase by splitting the droplet at a simple channel junction. 7. Magnethohydrodynamic surface and body waves in rectangular and cylindrical geometries International Nuclear Information System (INIS) Donnelly, I.J. 1982-03-01 Low frequency magnetohydrodynamic (MHD) waves are studied in both rectangular slab and cylindrical geometry cavities containing low β plasmas. The plasma density distribution is modelled by an inner region of constant density surrounded by an outer region of lower density and a conducting boundary. The wave frequencies and fields are obtained as functions of the density distribution and the wavenumber components k(parall) and k(perp). The lowest frequency wave mode is a surface wave in which the wave fields decrease in magnitude with distance from the interface between the two plasma densities. It has the properties of a shear wave when k(perp)/k(parall) is either small or large but is compressive when k(perp) is approximately equal to k(parall). The surface wave does not exist when k(perp) = 0. Higher frequency modes have the properties of fast magnetosonic waves, at least in the inner density region 8. Free Vibration Analysis of Rectangular Orthotropic Membranes in Large Deflection Directory of Open Access Journals (Sweden) Zheng Zhou-Lian 2009-01-01 Full Text Available This paper reviewed the research on the vibration of orthotropic membrane, which commonly applied in the membrane structural engineering. We applied the large deflection theory of membrane to derive the governing vibration equations of orthotropic membrane, solved it, and obtained the power series formula of nonlinear vibration frequency of rectangular membrane with four edges fixed. The paper gave the computational example and compared the two results from the large deflection theory and the small one, respectively. Results obtained from this paper provide some theoretical foundation for the measurement of pretension by frequency method; meanwhile, the results provide some theoretical foundation for the research of nonlinear vibration of membrane structures and the response solving of membrane structures under dynamic loads. 9. Performance analysis of SOI MOSFET with rectangular recessed channel International Nuclear Information System (INIS) Singh, M; Mishra, G P; Mishra, S; Mohanty, S S 2016-01-01 In this paper a two dimensional (2D) rectangular recessed channel–silicon on insulator metal oxide semiconductor field effect transistor (RRC-SOI MOSFET), using the concept of groove between source and drain regions, which is one of the channel engineering technique to suppress the short channel effect (SCE). This suppression is mainly due to corner potential barrier of the groove and the simulation is carried out by using ATLAS 2D device simulator. To have further improvement of SCE in RRC-SOI MOSFET, three more devices are designed by using dual material gate (DMG) and gate dielectric technique, which results in formation of devices i.e. DMRRC-SOI,MLSMRRC-SOI, MLDMRRC-SOI MOSFET. The effect of different structures of RRC-SOI on AC and RF parameters are investigated and the importance of these devices over RRC MOSFET regarding short channel effect is analyzed. (paper) 10. Impedance of curved rectangular spiral coils around a conductive cylinder Science.gov (United States) Burke, S. K.; Ditchburn, R. J.; Theodoulidis, T. P. 2008-07-01 Eddy-current induction due to a thin conformable coil wrapped around a long conductive cylinder is examined using a second-order vector potential formalism. Compact closed-form expressions are derived for the self- and mutual impedances of curved rectangular spiral coils (i) in free space and (ii) when wrapped around the surface of the cylindrical rod. The validity of these expressions was tested against the results of a systematic series of experiments using a cylindrical Al-alloy rod and conformable coils manufactured using flexible printed-circuit-board technology. The theoretical expressions were in very good agreement with the experimental measurements. The significance of the results for eddy-current nondestructive inspection using flexible coils and flexible coil arrays is discussed. 11. Measurement of electron beam bunch phase length by rectangular cavities International Nuclear Information System (INIS) Afanas'ev, V.D.; Rudychev, V.G.; Ushakov, V.I. 1976-01-01 An analysis of a phase length of electron bunches with the help of crossed rectangular resonators with the Hsub(102) oscillation type has been made. It has been shown that the electron coordinates after the duplex resonator are described by an ellipse equation for a non-modulated beam. An influence of the initial energy spread upon the electron motion has been studied. It has been ascertained that energy modulation of the electron beam results in displacement of each electron with respect to the ellipse which is proportional to modulation energy, i.e. an error in determination of the phase length of an electron bunch is proportional to the beam energy spread. Relations have been obtained which enable to find genuine values of phases of the analyzed electrons with an accuracy up to linear multipliers 12. Quantitative study of rectangular waveguide behavior in the THz. Energy Technology Data Exchange (ETDEWEB) Rowen, Adam M.; Nordquist, Christopher Daniel; Wanke, Michael Clement 2009-10-01 This report describes our efforts to quantify the behavior of micro-fabricated THz rectangular waveguides on a configurable, robust semiconductor-based platform. These waveguides are an enabling technology for coupling THz radiation directly from or to lasers, mixers, detectors, antennas, and other devices. Traditional waveguides fabricated on semiconductor platforms such as dielectric guides in the infrared or co-planar waveguides in the microwave regions, suffer high absorption and radiative losses in the THz. The former leads to very short propagation lengths, while the latter will lead to unwanted radiation modes and/or crosstalk in integrated devices. This project exploited the initial developments of THz micro-machined rectangular waveguides developed under the THz Grand Challenge Program, but instead of focusing on THz transceiver integration, this project focused on exploring the propagation loss and far-field radiation patterns of the waveguides. During the 9 month duration of this project we were able to reproduce the waveguide loss per unit of length in the waveguides and started to explore how the loss depended on wavelength. We also explored the far-field beam patterns emitted by H-plane horn antennas attached to the waveguides. In the process we learned that the method of measuring the beam patterns has a significant impact on what is actually measured, and this may have an effect on most of the beam patterns of THz that have been reported to date. The beam pattern measurements improved significantly throughout the project, but more refinements of the measurement are required before a definitive determination of the beam-pattern can be made. 13. Inertial manipulation of bubbles in rectangular microfluidic channels. Science.gov (United States) Hadikhani, Pooria; Hashemi, S Mohammad H; Balestra, Gioele; Zhu, Lailai; Modestino, Miguel A; Gallaire, François; Psaltis, Demetri 2018-03-27 Inertial microfluidics is an active field of research that deals with crossflow positioning of the suspended entities in microflows. Until now, the majority of the studies have focused on the behavior of rigid particles in order to provide guidelines for microfluidic applications such as sorting and filtering. Deformable entities such as bubbles and droplets are considered in fewer studies despite their importance in multiphase microflows. In this paper, we show that the trajectory of bubbles flowing in rectangular and square microchannels can be controlled by tuning the balance of forces acting on them. A T-junction geometry is employed to introduce bubbles into a microchannel and analyze their lateral equilibrium position in a range of Reynolds (1 < Re < 40) and capillary numbers (0.1 < Ca < 1). We find that the Reynolds number (Re), the capillary number (Ca), the diameter of the bubble (D[combining macron]), and the aspect ratio of the channel are the influential parameters in this phenomenon. For instance, at high Re, the flow pushes the bubble towards the wall while large Ca or D[combining macron] moves the bubble towards the center. Moreover, in the shallow channels, having aspect ratios higher than one, the bubble moves towards the narrower sidewalls. One important outcome of this study is that the equilibrium position of bubbles in rectangular channels is different from that of solid particles. The experimental observations are in good agreement with the performed numerical simulations and provide insights into the dynamics of bubbles in laminar flows which can be utilized in the design of flow based multiphase flow reactors. 14. Electrical Machines: Turn-to-Turn Capacitance in Formed Windings with Rectangular Cross-Section Wire NARCIS (Netherlands) Djukic, Nenad; Encica, L.; Paulides, Johan 2015-01-01 Calculation of turn-to-turn capacitance (Ctt) in electrical machines (EMs) with formed windings with rectangular cross-section wire is presented. Three calculation methods are used for the calculation of Ctt in case of rectangular conductors – finite element (FE) method and two previously published 15. 75 FR 82070 - Light-Walled Rectangular Pipe and Tube From China, Korea, and Mexico Science.gov (United States) 2010-12-29 ...-Walled Rectangular Pipe and Tube From China, Korea, and Mexico AGENCY: United States International Trade... from China, Korea, and Mexico that were found to be sold at less than fair value. Nacional de Acero S... panel proceeding in Light-Walled Rectangular Pipe and Tube from Mexico, USA-MEX-1904-04, to file... 16. 77 FR 3497 - Light-Walled Rectangular Pipe and Tube From Taiwan Science.gov (United States) 2012-01-24 ... Rectangular Pipe and Tube From Taiwan Determination On the basis of the record \\1\\ developed in the subject... order on light-walled rectangular pipe and tube from Taiwan would be likely to lead to continuation or recurrence of material injury to an industry in the United States within a reasonably foreseeable time. \\1... 17. Finite element fatigue analysis of rectangular clutch spring of automatic slack adjuster Science.gov (United States) Xu, Chen-jie; Luo, Zai; Hu, Xiao-feng; Jiang, Wen-song 2015-02-01 The failure of rectangular clutch spring of automatic slack adjuster directly affects the work of automatic slack adjuster. We establish the structural mechanics model of automatic slack adjuster rectangular clutch spring based on its working principle and mechanical structure. In addition, we upload such structural mechanics model to ANSYS Workbench FEA system to predict the fatigue life of rectangular clutch spring. FEA results show that the fatigue life of rectangular clutch spring is 2.0403×105 cycle under the effect of braking loads. In the meantime, fatigue tests of 20 automatic slack adjusters are carried out on the fatigue test bench to verify the conclusion of the structural mechanics model. The experimental results show that the mean fatigue life of rectangular clutch spring is 1.9101×105, which meets the results based on the finite element analysis using ANSYS Workbench FEA system. 18. Study on the output factors of asymmetrical rectangular electron beam field International Nuclear Information System (INIS) Chen Yinghai; Yang Yueqin; Ma Yuhong; Zheng Jin; Zou Lijuan 2009-01-01 Objective: To evaluate the variant regularity of the output factors of asymmetrical rectangular electron beam field. Methods: The output factors of three special fields with different applicators and energies were measured by ionization chamber method at different off-axis distances. Then deviations of the output factors between asymmetrical and symmetric rectangular fields were calculated. Results: The changes of output factor with different off-axis distances in asymmetrical rectangular fields were basically consistent with those in standard square fields with the same applicator. It revealed that the output factor of asymmetrical rectangular field was related with the off-axis ratio of standard square field. Applicator and field size did not show obvious influence on the output factor. Conclusions: The output factor changes of asymmetrical rectangular field are mainly correlated with the off-axis ratio of standard square field. The correction of the output factor is determined by the off-axis ratio changes in standard square field. (authors) 19. Analysis of junior high school students' difficulty in resolving rectangular conceptual problems Science.gov (United States) Utami, Aliksia Kristiana Dwi; Mardiyana, Pramudya, Ikrar 2017-08-01 Geometry is one part of the mathematics that must be learned in school and it has important effects on the development of creative thinking skills of learners, but in fact, there are some difficulties experienced by the students. This research focuses on analysis difficulty in resolving rectangular conceptual problems among junior high school students in every creative thinking skills level. This research used a descriptive method aimed to identify the difficulties and cause of the difficulties experienced by five students. The difficulties are associated with rectangular shapes and related problems. Data collection was done based on students' work through test, interview, and observations. The result revealed that student' difficulties in understanding the rectangular concept can be found at every creative thinking skills level. The difficulties are identifying the objects rectangular in the daily life except for a rectangle and square, analyzing the properties of rectangular shapes, and seeing the interrelationships between figures. 20. Repetitive transcranial magnetic stimulator with controllable pulse parameters Science.gov (United States) Peterchev, Angel V.; Murphy, David L.; Lisanby, Sarah H. 2011-06-01 The characteristics of transcranial magnetic stimulation (TMS) pulses influence the physiological effect of TMS. However, available TMS devices allow very limited adjustment of the pulse parameters. We describe a novel TMS device that uses a circuit topology incorporating two energy storage capacitors and two insulated-gate bipolar transistor (IGBT) modules to generate near-rectangular electric field pulses with adjustable number, polarity, duration, and amplitude of the pulse phases. This controllable pulse parameter TMS (cTMS) device can induce electric field pulses with phase widths of 10-310 µs and positive/negative phase amplitude ratio of 1-56. Compared to conventional monophasic and biphasic TMS, cTMS reduces energy dissipation up to 82% and 57% and decreases coil heating up to 33% and 41%, respectively. We demonstrate repetitive TMS trains of 3000 pulses at frequencies up to 50 Hz with electric field pulse amplitude and width variability less than the measurement resolution (1.7% and 1%, respectively). Offering flexible pulse parameter adjustment and reduced power consumption and coil heating, cTMS enhances existing TMS paradigms, enables novel research applications and could lead to clinical applications with potentially enhanced potency. 1. Pulsed power International Nuclear Information System (INIS) Anon. 1977-01-01 The key element of our pulsed power program is concentration of power in time and space by suppression of breakdown in dielectrics and in vacuum. Magnetically insulated vacuum transmission lines and magnetic suppression of insulator flashover have continued as the main reserch directions. Vacuum insulated line studies at Physics International have been expanded and a test bed at Sandia, called MITE (Magnetically Insulated Transmission Experiment), is under development. The choice for the baseline EBFA design will depend on the outcome of these studies and should be made in July 1977. The slow and intermediate speed pulsed power approaches to EBFA will be based on Proto I and Proto II results and several of the projected EBFA subsystems are presently being tested in Proto II. A further stage of power concentration, within the vacuum diode itself, would considerably ease the burden on dielectrics; methods of power multiplication involving magnetically imploded plasmas are being considered and tests have begun using the Ripple III apparatus 2. Three types of pulses delivered from a nanotube-mode-locked fiber laser International Nuclear Information System (INIS) Yao, X K 2015-01-01 Three types of pulses are experimentally investigated in a switchable normal-dispersion nanotube-mode-locked fiber laser by adjusting polarizer controller and pump power. They are a standard dissipative-soliton (DS), conventional soliton (CS)-like pulse, and noiselike pulse, which correspond to three mode-locking states. The standard DS with a rectangular spectrum possesses a Gaussian-shape pulse. The CS-like operation has a Lorenz shape, and the spectrum involves several sidebands similar to the CS case. For the noiselike pulse with a bell-shaped spectrum, a 317 fs peak rides upon the 132.5 ps pedestal in the autocorrelation trace. The spectra of these three pulse operations are centered at three close wavelengths. The generation of three such different types of pulses in one identical normal- dispersion laser cavity may find an important application for the future of mode-locked laser research. (paper) 3. A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space Directory of Open Access Journals (Sweden) Bessem Samet 2011-09-01 Full Text Available Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result. 4. Modelling of ultrasonic nondestructive testing in anisotropic materials - Rectangular crack International Nuclear Information System (INIS) Bostroem, A. 2001-12-01 Nondestructive testing with ultrasound is a standard procedure in the nuclear power industry when searching for defects, in particular cracks. To develop and qualify testing procedures extensive experimental work on test blocks is usually required. This can take a lot of time and therefore be quite costly. A good mathematical model of the testing situation is therefore of great value as it can reduce the experimental work to a great extent. A good model can be very useful for parametric studies and as a pedagogical tool. A further use of a model is as a tool in the qualification of personnel. In anisotropic materials, e.g. austenitic welds, the propagation of ultrasound becomes much more complicated as compared to isotropic materials. Therefore, modelling is even more useful for anisotropic materials, and it in particular has a greater pedagogical value. The present project has been concerned with a further development of the anisotropic capabilities of the computer program UTDefect, which has so far only contained a strip-like crack as the single defect type for anisotropic materials. To be more specific, the scattering by a rectangular crack in an anisotropic component has been studied and the result is adapted to include transmitting and receiving ultrasonic probes. The component under study is assumed to be anisotropic with arbitrary anisotropy. On the other hand, it is assumed to be homogeneous, and this in particular excludes most welds, where it is seldom an adequate approximation to assume homogeneity. The anisotropy may be arbitrarily oriented and the same is true of the rectangular crack. The crack may also be located near a backside of the component. To solve the scattering problem for the crack an integral equation method is used. The probe model has been developed in an earlier project and to compute the signal response in the receiving probe an electromechanical reciprocity argument is employed. As a rectangle is a truly 3D scatterer the sizes of the 5. 78 FR 42546 - Light-Walled Rectangular Pipe and Tube From China, Korea, Mexico, and Turkey: Notice of... Science.gov (United States) 2013-07-16 ...-Walled Rectangular Pipe and Tube From China, Korea, Mexico, and Turkey: Notice of Commission... countervailing duty order on light-walled rectangular pipe and tube from China and the antidumping duty orders on light-walled rectangular pipe and tube from China, Korea, Mexico, and Turkey would be likely to lead to... 6. 78 FR 74161 - Light-Walled Rectangular Pipe and Tube From China, Korea, Mexico, and Turkey; Scheduling of Full... Science.gov (United States) 2013-12-10 ...-Walled Rectangular Pipe and Tube From China, Korea, Mexico, and Turkey; Scheduling of Full Five-Year... the Antidumping Duty Orders on Light-Walled Rectangular Pipe and Tube From China, Korea, Mexico, and... on light- walled rectangular pipe and tube from China, Korea, Mexico, and Turkey would be likely to... 7. Experimental study of falling water limitation under counter-current flow in the vertical rectangular channel International Nuclear Information System (INIS) Usui, Tohru; Kaminaga, Masanori; Sudo, Yukio. 1988-07-01 Quantitative understanding of critical heat flux (CHF) in the narrow vertical rectangular channel is required for the thermo-hydroulic design and the safety analysis of research reactors in which flat-plate-type fuel is adopted. Especially, critical heat flux under low downward velocity has a close relation with falling water limitation under counter-current flow. Accordingly, CCFL (Counter-current Flow Limitation) experiments were carried out for both vertical rectangular channels and vertical circular tubes varried in their size and configuration of their cross sections, to make clear CCFL characteristics in the vertical rectangular channels. In the experiments, l/de of the rectangular channel was changed from 3.5 to 180. As the results, it was clear that different equivalent hydraulic diameter de, namely width or water gap of channel, gave different CCFL characteristics of rectangular channel. But the influence of channel length l on CCFL characteristics was not observed. Besides, a dimensionless correlation to estimate a relation between upward air velocity and downward water velocity was proposed based on the present experimental results. The difference of CCFL characteristics between rectangular channels and circular tubes was also investigated. Especially for the rectangular channels, dry-patches appearing condition was made clear as a flow-map. (author) 8. Effects of rolling on characteristics of single-phase water flow in narrow rectangular ducts International Nuclear Information System (INIS) Xing Dianchuan; Yan Changqi; Sun Licheng; Xu Chao 2012-01-01 Highlights: ► Mass flow rate and friction pressure drop with different pressure head are compared. ► The effect of pressure head on flow fluctuation is considered theoretically. ► Time-mean and real-time friction pressure drop in different rolling motion are studied. ► Rolling motion influences the fluctuation of friction pressure drop in two aspects. ► New correlation for frictional coefficient in rolling motion is achieved. - Abstract: Experimental and theoretical studies of rolling effects on characteristics of single-phase water flow in narrow rectangular ducts are performed under ambient temperature and pressure. Two types of pressure head are supplied by elevate water tank and pump respectively. The results show that the frictional pressure drop under rolling condition fluctuates periodically, with its amplitude decaying as mean Reynolds number increase and the rolling amplitude decrease, while the amplitude is nearly invariable with rolling period. Rolling motion influences the fluctuation amplitude of frictional pressure drop in two aspects, on the one hand, rolling reduced periodical pulsing flow leads to the fluctuation of the frictional pressure drop, on the other hand, additional force acting on fluid near the wall due to the rolling motion makes local frictional resistance oscillate periodically. The mass flow rate oscillates periodically in rolling motion with the pressure head supplied by water tank, while its fluctuation is so weak that could be neglected for the case of the pressure head supplied by pump. An empirical correlation for the frictional coefficient under rolling condition is achieved, and the experimental data is well correlated. A mathematical model is also developed to study the effect of pressure head on mass flow rate fluctuation in rolling motion. The fluctuation amplitude of the mass flow rate decreases rapidly with a higher pressure head. Comparing with the vertical condition, rolling motion nearly has no effects on 9. PULSE COLUMN Science.gov (United States) Grimmett, E.S. 1964-01-01 This patent covers a continuous countercurrent liquidsolids contactor column having a number of contactor states each comprising a perforated plate, a layer of balls, and a downcomer tube; a liquid-pulsing piston; and a solids discharger formed of a conical section at the bottom of the column, and a tubular extension on the lowest downcomer terminating in the conical section. Between the conical section and the downcomer extension is formed a small annular opening, through which solids fall coming through the perforated plate of the lowest contactor stage. This annular opening is small enough that the pressure drop thereacross is greater than the pressure drop upward through the lowest contactor stage. (AEC) International Nuclear Information System (INIS) Greenshields, H.; Seddon, W.A. 1982-03-01 This supplement to two bibliographies published in 1970 and 1972 lists 734 references to the literature of pulse radiolysis, arranged under eight broad subject headings. The references were compiled by searching Biological Abstracts, Chemical Abstracts, Nuclear Science Abstracts and the Weekly List of Papers in Radiation Chemistry issued by the Radiation Chemistry Data Center of Notre Dame University. Full bibliographic data is given for papers published in the period 1971 to 1974. A personal author index listing more than 600 authors and a similar number of co-authors is included 11. Permuting sparse rectangular matrices into block-diagonal form Energy Technology Data Exchange (ETDEWEB) Aykanat, Cevdet; Pinar, Ali; Catalyurek, Umit V. 2002-12-09 This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between different societies, investigate existing techniques for partitioning and propose new ones, and finally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-the-art graph and hypergraph partitioning tools MeTiS and PaT oH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and run time. 12. Modal density of rectangular structures in a wide frequency range Science.gov (United States) Parrinello, A.; Ghiringhelli, G. L. 2018-04-01 A novel approach to investigate the modal density of a rectangular structure in a wide frequency range is presented. First, the modal density is derived, in the whole frequency range of interest, on the basis of sound transmission through the infinite counterpart of the structure; then, it is corrected by means of the low-frequency modal behavior of the structure, taking into account actual size and boundary conditions. A statistical analysis reveals the connection between the modal density of the structure and the transmission of sound through its thickness. A transfer matrix approach is used to compute the required acoustic parameters, making it possible to deal with structures having arbitrary stratifications of different layers. A finite element method is applied on coarse grids to derive the first few eigenfrequencies required to correct the modal density. Both the transfer matrix approach and the coarse grids involved in the finite element analysis grant high efficiency. Comparison with alternative formulations demonstrates the effectiveness of the proposed methodology. 13. Compressibility effects in the shear layer over a rectangular cavity Energy Technology Data Exchange (ETDEWEB) Beresh, Steven J.; Wagner, Justin; Casper, Katya Marie 2016-10-26 we studied the influence of compressibility on the shear layer over a rectangular cavity of variable width in a free stream Mach number range of 0.6–2.5 using particle image velocimetry data in the streamwise centre plane. As the Mach number increases, the vertical component of the turbulence intensity diminishes modestly in the widest cavity, but the two narrower cavities show a more substantial drop in all three components as well as the turbulent shear stress. Furthermore, this contrasts with canonical free shear layers, which show significant reductions in only the vertical component and the turbulent shear stress due to compressibility. The vorticity thickness of the cavity shear layer grows rapidly as it initially develops, then transitions to a slower growth rate once its instability saturates. When normalized by their estimated incompressible values, the growth rates prior to saturation display the classic compressibility effect of suppression as the convective Mach number rises, in excellent agreement with comparable free shear layer data. The specific trend of the reduction in growth rate due to compressibility is modified by the cavity width. 14. Attenuation in Rectangular Waveguides with Finite Conductivity Walls Directory of Open Access Journals (Sweden) K. C. Yeong 2011-06-01 Full Text Available We present a fundamental and accurate approach to compute the attenuation of electromagnetic waves propagating in rectangular waveguides with finite conductivity walls. The wavenumbers kx and ky in the x and y directions respectively, are obtained as roots of a set of transcendental equations derived by matching the tangential component of the electric field (E and the magnetic field (H at the surface of the waveguide walls. The electrical properties of the wall material are determined by the complex permittivity ε, permeability μ, and conductivity σ. We have examined the validity of our model by carrying out measurements on the loss arising from the fundamental TE10 mode near the cutoff frequency. We also found good agreement between our results and those obtained by others including Papadopoulos’ perturbation method across a wide range of frequencies, in particular in the vicinity of cutoff. In the presence of degenerate modes however, our method gives higher losses, which we attribute to the coupling between modes as a result of dispersion. 15. Diversity of acoustic streaming in a rectangular acoustofluidic field. Science.gov (United States) Tang, Qiang; Hu, Junhui 2015-04-01 Diversity of acoustic streaming field in a 2D rectangular chamber with a traveling wave and using water as the acoustic medium is numerically investigated by the finite element method. It is found that the working frequency, the vibration excitation source length, and the distance and phase difference between two separated symmetric vibration excitation sources can cause the diversity in the acoustic streaming pattern. It is also found that a small object in the acoustic field results in an additional eddy, and affects the eddy size in the acoustic streaming field. In addition, the computation results show that with an increase of the acoustic medium's temperature, the speed of the main acoustic streaming decreases first and then increases, and the angular velocity of the corner eddies increases monotonously, which can be clearly explained by the change of the acoustic dissipation factor and shearing viscosity of the acoustic medium with temperature. Commercialized FEM software COMSOL Multiphysics is used to implement the computation tasks, which makes our method very easy to use. And the computation method is partially verified by an established analytical solution. Copyright © 2014 Elsevier B.V. All rights reserved. 16. Propagation of spiral waves pinned to circular and rectangular obstacles. Science.gov (United States) Sutthiopad, Malee; Luengviriya, Jiraporn; Porjai, Porramain; Phantu, Metinee; Kanchanawarin, Jarin; Müller, Stefan C; Luengviriya, Chaiya 2015-05-01 We present an investigation of spiral waves pinned to circular and rectangular obstacles with different circumferences in both thin layers of the Belousov-Zhabotinsky reaction and numerical simulations with the Oregonator model. For circular objects, the area always increases with the circumference. In contrast, we varied the circumference of rectangles with equal areas by adjusting their width w and height h. For both obstacle forms, the propagating parameters (i.e., wavelength, wave period, and velocity of pinned spiral waves) increase with the circumference, regardless of the obstacle area. Despite these common features of the parameters, the forms of pinned spiral waves depend on the obstacle shapes. The structures of spiral waves pinned to circles as well as rectangles with the ratio w/h∼1 are similar to Archimedean spirals. When w/h increases, deformations of the spiral shapes are observed. For extremely thin rectangles with w/h≫1, these shapes can be constructed by employing semicircles with different radii which relate to the obstacle width and the core diameter of free spirals. 17. LEDA 074886: A REMARKABLE RECTANGULAR-LOOKING GALAXY International Nuclear Information System (INIS) Graham, Alister W.; Spitler, Lee R.; Forbes, Duncan A.; Lisker, Thorsten; Janz, Joachim; Moore, Ben 2012-01-01 We report the discovery of an interesting and rare rectangular-shaped galaxy. At a distance of 21 Mpc, the dwarf galaxy LEDA 074886 has an absolute R-band magnitude of –17.3 mag. Adding to this galaxy's intrigue is the presence of an embedded, edge-on stellar disk (of extent 2 R e,disk = 12'' = 1.2 kpc) for which Forbes et al. reported v rot /σ ≈ 1.4. We speculate that this galaxy may be the remnant of two (nearly edge-on) merged disk galaxies in which the initial gas was driven inward and subsequently formed the inner disk, while the stars at larger radii effectively experienced a dissipationless merger event resulting in this 'emerald cut galaxy' having very boxy isophotes with a 4 /a = –0.05 to –0.08 from 3 to 5 kpc. This galaxy suggests that knowledge from simulations of both 'wet' and 'dry' galaxy mergers may need to be combined to properly understand the various paths that galaxy evolution can take, with a particular relevance to blue elliptical galaxies. 18. Preliminary Study of ONB in Narrow-Vertical Rectangular Channel International Nuclear Information System (INIS) Omar, S. AL-Yahia; Jo, Daeseong 2015-01-01 The location where the vapor bubble can first exist at the heated surface is called 'onset of nucleate boiling (ONB). The subcooled boiling is highly efficient to remove the heat owing to the high heat transfer coefficient. The heat transfer is affected by the motion of the bulk liquid as well as the latent heat transport of the liquid microlayer between the bubble and the heated wall. However, with increasing in the wall temperature, the bubble growth will increase and may they aggregate at the heated surface forming a vapor film, which will prevent the heat transport from the wall and that leads to highly rise in wall temperature. This phenomenon called departure from nucleate boiling (DNB). Many experimental and numerical CFD methods were carried out to investigate the subcooled boiling because of its importance in the industrial applications. In the present study, vertical narrow rectangular channel heated from both side was simulated by using CFX-14 to investigate the subcooled wall boiling, and identical simulation is done by using TMAP to compare the ONB location between numerical simulation and empirical correlations that implemented in TMAP. The numerical results using CFX-14 are discussed and compared with the results obtained from TMAP. The coolant temperature increases gradually (linearly) in the downward direction owing to the uniform applied heat flux. 19. Preliminary Study of ONB in Narrow-Vertical Rectangular Channel Energy Technology Data Exchange (ETDEWEB) Omar, S. AL-Yahia; Jo, Daeseong [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of) 2015-10-15 The location where the vapor bubble can first exist at the heated surface is called 'onset of nucleate boiling (ONB). The subcooled boiling is highly efficient to remove the heat owing to the high heat transfer coefficient. The heat transfer is affected by the motion of the bulk liquid as well as the latent heat transport of the liquid microlayer between the bubble and the heated wall. However, with increasing in the wall temperature, the bubble growth will increase and may they aggregate at the heated surface forming a vapor film, which will prevent the heat transport from the wall and that leads to highly rise in wall temperature. This phenomenon called departure from nucleate boiling (DNB). Many experimental and numerical CFD methods were carried out to investigate the subcooled boiling because of its importance in the industrial applications. In the present study, vertical narrow rectangular channel heated from both side was simulated by using CFX-14 to investigate the subcooled wall boiling, and identical simulation is done by using TMAP to compare the ONB location between numerical simulation and empirical correlations that implemented in TMAP. The numerical results using CFX-14 are discussed and compared with the results obtained from TMAP. The coolant temperature increases gradually (linearly) in the downward direction owing to the uniform applied heat flux. 20. Helium-air counter flow in rectangular channels International Nuclear Information System (INIS) Fumizawa, Motoo; Tanaka, Gaku; Zhao, Hong; Hishida, Makoto; Shiina, Yasuaki 2004-01-01 This paper deals with numerical analysis of helium-air counter flow in a rectangular channel with an aspect ratio of 10. The channel has a cross sectional area of 5-50 mm and a length of 200 mm. The inclination angle was varied from 0 to 90 degree. The velocity profiles and concentration profiles were analyzed with a computer program [FLUENT]. Following main features of the counter flow are discussed based on the calculated results. (1) Time required for establishing a quasi-steady state counter flow. (2) The relationship between the inclination angle and the flow patterns of the counter flow. (3) The developing process of velocity profiles and concentration profiles. (4) The relationship between the inclination angle of the channel and the velocity profiles of upward flow and the downward flow. (5) The relationship between the concentration profile and the inclination angle. (6) The relationship between the net in-flow rate and the inclination angle. We compared the computed velocity profile and the net in-flow rate with experimental data. A good agreement was obtained between the calculation results and the experimental results. (author) 1. Computation of rectangular source integral by rational parameter polynomial method International Nuclear Information System (INIS) Prabha, Hem 2001-01-01 Hubbell et al. (J. Res. Nat Bureau Standards 64C, (1960) 121) have obtained a series expansion for the calculation of the radiation field generated by a plane isotropic rectangular source (plaque), in which leading term is the integral H(a,b). In this paper another integral I(a,b), which is related with the integral H(a,b) has been solved by the rational parameter polynomial method. From I(a,b), we compute H(a,b). Using this method the integral I(a,b) is expressed in the form of a polynomial of a rational parameter. Generally, a function f (x) is expressed in terms of x. In this method this is expressed in terms of x/(1+x). In this way, the accuracy of the expression is good over a wide range of x as compared to the earlier approach. The results for I(a,b) and H(a,b) are given for a sixth degree polynomial and are found to be in good agreement with the results obtained by numerically integrating the integral. Accuracy could be increased either by increasing the degree of the polynomial or by dividing the range of integration. The results of H(a,b) and I(a,b) are given for values of b and a up to 2.0 and 20.0, respectively 2. A Multi-Objective Approach to Visualize Proportions and Similarities Between Individuals by Rectangular Maps DEFF Research Database (Denmark) Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero In this paper we address the problem of visualizing the proportions and the similarities attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one individual...... area and adjacency requirements, this visualization problem is formulated as a three-objective Mixed Integer Nonlinear Problem. The first objective seeks to maximize the number of true adjacencies that the rectangular map is able to reproduce, the second one is to minimize the number of false... 3. Pulse pile-up. I: Short pulses International Nuclear Information System (INIS) Wilkinson, D.H. 1990-07-01 The search for rare large pulses against an intense background of smaller ones involves consideration of pulse pile-up. Approximate methods are presented, based on ruin theory, by which the probability of such pile-up may be estimated for pulses of arbitrary form and of arbitrary pulse-height distribution. These methods are checked against cases for which exact solutions are available. The present paper is concerned chiefly with short pulses of finite total duration. (Author) (5 refs., 24 figs.) 4. Experimental investigations of pulse shape control in passively mode-locked fiber lasers with net-normal dispersion International Nuclear Information System (INIS) Wang, L R; Han, D D 2013-01-01 Pulse shape control in passively mode-locked fiber lasers with net-normal dispersion is investigated experimentally. Three kinds of pulses with different spectral and temporal shapes are observed, and their pulse-shaping mechanisms are discussed. After a polarization-resolved system external to the cavity, the maximum intensity differences of the two polarization components for the rectangular-spectrum (RS), Gaussian-spectrum (GS), and super-broadband (SB) pulses are measured as ∼20 dB, ∼15 dB, and ∼1 dB, respectively. It is suggested that the equivalent saturable absorption effect plays an increasingly important role from the RS to GS and then to SB pulses in the pulse-shaping processes, while the spectral filtering effect declines. This work could help in systematically understanding pulse formation and proposing guidelines for the realization of pulses with better performance in fiber lasers. (paper) 5. Investigation of process induced warpage for pultrusion of a rectangular hollow profile DEFF Research Database (Denmark) Baran, Ismet; Hattel, Jesper Henri; Akkerman, Remko 2015-01-01 A novel thermo-chemical–mechanical analysis of the pultrusion process is presented. A process simulation is performed for an industrially pultruded rectangular hollow profile containing both unidirectional (UD) roving and continuous filament mat (CFM) layers. The reinforcements are impregnated... 6. Heat transfer augmentation in rectangular micro channel covered with vertically aligned carbon nanotubes NARCIS (Netherlands) Taha, T.J.; Lefferts, Leonardus; van der Meer, Theodorus H. 2016-01-01 An experimental heat transfer investigation was carried out to examine the influence of carbon nanotubes (CNTs) layer deposits on the convective heat transfer performance inside rectangular microchannels. Successful synthesis of vertically aligned CNTs was achieved using a catalytic vapor deposition 7. Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation KAUST Repository Saghir, Shahid 2016-12-01 The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear static and dynamic behavior of rectangular microplates under small and large actuating forces. In the first part, we present and compare various approaches to develop reduced order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. In the second part, we present an investigation of the static and dynamic behavior of a fully clamped microplate. We investigate the effect of different non-dimensional design parameters on the static response. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of midplane stretching. However, the behavior switches to softening as the DC load is increased. Next, near-square plates are studied to understand the effect of geometric imperfections of microplates. In the final part of the dissertation, we investigate the mechanical behavior of 8. Compression and heating of a cladding target by a partially profiled laser pulse International Nuclear Information System (INIS) Andreev, A.A.; Samsonov, A.G.; Solov'ev, N.A. 1990-01-01 The CLADDING-T semiempirical model and numerical calculations in accordance with the SPHERE program have been employed to show that the action of a partially profiled pulse on a simple cladding target raises the fuel compession degree and reduces the fuel temperature as compared to the action of a rectangular pulse (or a polynomial-shaped pulse) with the same energy. From the standpoint of the flash criterion the system composed of the profiled pulse and the simple (cladding) target is shown to be equivalent to that composed of a simple pulse and a dual-cascade (profiled) target. An analysis of the system composed of the laser and the simple target shows that the use of the partially profiled pulse and the simple target makes it possible to reduce requirements to the energy of laser systems 9. Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies Science.gov (United States) Suh, Peter M.; Conyers, Howard Jason; Mavris, Dimitri N. 2015-01-01 This report introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this report is on tool presentation, verification, and validation. These processes are carried out in stages throughout the report. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust. 10. Experimental study of critical heat flux in inclined rectangular gap International Nuclear Information System (INIS) Kim, S.J.; Kim, Y.H.; Noh, S.W.; Suh, K.Y.; Rempe, J.L.; Cheung, F.B.; Kim, S.B. 2003-01-01 In the TMI-2 accident, the lower part of the reactor pressure vessel was overheated and then rather rapidly cooled down, as was later found out in a vessel investigation project. This accounted for the possibility of gap cooling feasibility. For this reason, a great deal of investigations was performed to determine the critical heat flux (CHF) from the standpoint of in-vessel retention (IVR). As part of a joint Korean-U.S. International Nuclear Energy Research Initiative (INERI) project, Tests were conducted to examine the critical heat flux (CHF) on the one-dimensional downward heating rectangular channel having a narrow gap by changing the orientation of the copper test heater assembly in a pool of saturated water under the atmospheric pressure. The test parameters include both the gap sizes of 1, 2, 5 and 10 mm, and the surface orientation angles from the downward-facing position (180deg) to the vertical position (90deg), respectively. It was observed that the CHF generally decreases as the surface inclination angle increases and as the gap size decreases. However, in downward-facing position (180deg), somewhat differing results were detected relative to previous reports. For a certain gap size having a similar dimension with vapor layer thickness, more efficient heat transfer was detected and this may be interpreted by characteristic property such as the vapor layer thickness of water. In consistency with several studies reported in the literature, it was found that there exists a transition angle above that the CHF changes with a rapid slope. (author) 11. Turbulent subcooled boiling flow visualization experiments through a rectangular channel International Nuclear Information System (INIS) Estrada-Perez, Carlos E.; Dominguez-Ontiveros, Elvis E.; Hassan, Yassin A. 2008-01-01 Full text of publication follows: Proper characterization of subcooled boiling flow is of importance in many applications. It is of exceptional significance in the development of empirical models for the design of nuclear reactors, steam generators, and refrigeration systems. Most of these models are based on experimental studies that share the characteristics of utilizing point measurement probes with high temporal resolution, e.g. Hot Film Anemometry (HFA), Laser Doppler Velocimetry (LDV), and Fiber Optic Probes (FOP). However there appears to be a scarcity of experimental studies that can capture instantaneous whole-field measurements with a fast time response. Particle Tracking Velocimetry (PTV) may be used to overcome the limitations associated with point measurement techniques. PTV is a whole-flow-field technique providing instantaneous velocity vectors capable of high spatial and temporal resolution. PTV is also an exceptional tool for the analysis of boiling flow due to its ability to differentiate between the gas and liquid phases and subsequently deliver independent velocity fields associated with each phase. In this work, using PTV, liquid velocity fields of a turbulent subcooled boiling flow in a rectangular channel were successfully obtained. The present results agree with similar studies that used point measurement probes. However, the present study provides additional information; not only averaged profiles of the velocity components were obtained, instantaneous 2-D velocity fields were also readily available with a high temporal and spatial resolution. Analysis of fluctuating velocities, Reynolds stresses, and higher order statistics of the flow are presented. This work is an attempt to enrich the database already collected on turbulent subcooled boiling flow, with the hope that it will be useful in turbulence modeling efforts. (authors) 12. Psyplot: Visualizing rectangular and triangular Climate Model Data with Python Science.gov (United States) Sommer, Philipp 2016-04-01 The development and use of climate models often requires the visualization of geo-referenced data. Creating visualizations should be fast, attractive, flexible, easily applicable and easily reproducible. There is a wide range of software tools available for visualizing raster data, but they often are inaccessible to many users (e.g. because they are difficult to use in a script or have low flexibility). In order to facilitate easy visualization of geo-referenced data, we developed a new framework called "psyplot," which can aid earth system scientists with their daily work. It is purely written in the programming language Python and primarily built upon the python packages matplotlib, cartopy and xray. The package can visualize data stored on the hard disk (e.g. NetCDF, GeoTIFF, any other file format supported by the xray package), or directly from the memory or Climate Data Operators (CDOs). Furthermore, data can be visualized on a rectangular grid (following or not following the CF Conventions) and on a triangular grid (following the CF or UGRID Conventions). Psyplot visualizes 2D scalar and vector fields, enabling the user to easily manage and format multiple plots at the same time, and to export the plots into all common picture formats and movies covered by the matplotlib package. The package can currently be used in an interactive python session or in python scripts, and will soon be developed for use with a graphical user interface (GUI). Finally, the psyplot framework enables flexible configuration, allows easy integration into other scripts that uses matplotlib, and provides a flexible foundation for further development. 13. Modeling on bubbly to churn flow pattern transition in narrow rectangular channel International Nuclear Information System (INIS) Wang Yanlin; Chen Bingde; Huang Yanping; Wang Junfeng 2012-01-01 A theoretical model based on some reasonable concepts was developed to predict the bubbly flow to churn flow pattern transition in vertical narrow rectangular channel under flow boiling condition. The maximum size of ideal bubble in narrow rectangular channel was calculated based on previous literature. The thermal hydraulics boundary condition of bubbly to churn flow pattern transition was exported from Helmholtz and maximum size of ideal bubble. The theoretical model was validated by existent experimental data. (authors) 14. Thermal vibration of a rectangular single-layered graphene sheet with quantum effects International Nuclear Information System (INIS) Wang, Lifeng; Hu, Haiyan 2014-01-01 The thermal vibration of a rectangular single-layered graphene sheet is investigated by using a rectangular nonlocal elastic plate model with quantum effects taken into account when the law of energy equipartition is unreliable. The relation between the temperature and the Root of Mean Squared (RMS) amplitude of vibration at any point of the rectangular single-layered graphene sheet in simply supported case is derived first from the rectangular nonlocal elastic plate model with the strain gradient of the second order taken into consideration so as to characterize the effect of microstructure of the graphene sheet. Then, the RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet simply supported on an elastic foundation is derived. The study shows that the RMS amplitude of the rectangular single-layered graphene sheet predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The maximal relative difference of RMS amplitude of thermal vibration appears at the sheet corners. The microstructure of the graphene sheet has a little effect on the thermal vibrations of lower modes, but exhibits an obvious effect on the thermal vibrations of higher modes. The quantum effect is more important for the thermal vibration of higher modes in the case of smaller sides and lower temperature. The relative difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet decreases monotonically with an increase of temperature. The absolute difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet increases slowly with the rising of Winkler foundation modulus. 15. Recovery of the Dirac system from the rectangular Weyl matrix function International Nuclear Information System (INIS) Fritzsche, B; Kirstein, B; Roitberg, I Ya; Sakhnovich, A L 2012-01-01 Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are studied for such Weyl functions, and some results are new even for the square Weyl functions. High-energy asymptotics of Weyl functions and Borg–Marchenko-type uniqueness results are derived too. (paper) 16. The time of simultaneous tunneling of identical particles through the rectangular quantum barrier International Nuclear Information System (INIS) Martsenyuk, L.S.; Omelchenko, S.A. 2010-01-01 Work is devoted to studying the influence of exchange processes on a time of simultaneous crossing by identical particles of a rectangular quantum barrier. It is shown, that such processes essentially influence on the parameters of tunneling. The size of addition to time of identical particles tunneling, arising up because of their exchange interaction in a field of a rectangular quantum barrier is first counted. 17. Design and construction of a mode converter from TE10(rectangular) to TE11(circular) International Nuclear Information System (INIS) Tubbing, B.J.D. 1984-08-01 The design and manufacturing of a wavelength mode converter from the TE 10 (rectangular) mode in oversized rectangular to the TE 11 (circular) mode in oversized circular waveguide is described. A differential equation for the cross-sectional shape of the converter was solved numerically. A stainless-steel mandrel was produced on a numerically controlled milling machine. Sixteen converters were produced by means of electroforming on one mandrel. (Auth.) 18. Experimental investigation on carbon nano tubes coated brass rectangular extended surfaces International Nuclear Information System (INIS) Senthilkumar, Rajendran; Prabhu, Sethuramalingam; Cheralathan, Marimuthu 2013-01-01 Finned surface has been extensively used for free convection cooling of internal combustion engines and several electronic kits etc. Here rectangular brass fin was preferred for analysis. Thermocouples were attached all over the surface of the fin in equal distances. The measurement of surface temperature and calculated convective heat transfer rate were reported for several heat input values. The overall system performance can be improved by enhancing heat transfer rate of extended surfaces. Based on the above requirement, brass surface was coated by carbon nano tubes. The temperature and heat transfer characteristics were investigated using Taguchi method for experimental design. Finally the performances of coated and non-coated rectangular brass fins were compared. The average percentage of increase in heat transfer rate was proved around 12% for carbon nanocoated rectangular brass fins. - Graphical abstract: The designed Natural and Forced convection Heat Transfer Test Rig measures the enhanced rate of heat transfer for nano coated rectangular fins than in non-coated fins. Highlights: ► Rectangular brass fins were preferred for convective heat transfer process. ► The rectangular brass fins are coated with multi wall carbon nano tubes in EBPVD process with nanometer thickness. ► Temperature and heat transfer rate were investigated for nanocoated and non-coated fins by using Taguchi method. ► Multi wall carbon nanotubes act as a pin fin to enhance surface area for effective convective heat transfer rate. 19. Novel high-frequency energy-efficient pulsed-dc generator for capacitively coupled plasma discharge Science.gov (United States) Mamun, Md Abdullah Al; Furuta, Hiroshi; Hatta, Akimitsu 2018-03-01 The circuit design, assembly, and operating tests of a high-frequency and high-voltage (HV) pulsed dc generator (PDG) for capacitively coupled plasma (CCP) discharge inside a vacuum chamber are reported. For capacitive loads, it is challenging to obtain sharp rectangular pulses with fast rising and falling edges, requiring intense current for quick charging and discharging. The requirement of intense current generally limits the pulse operation frequency. In this study, we present a new type of PDG consisting of a pair of half-resonant converters and a constant current-controller circuit connected with HV solid-state power switches that can deliver almost rectangular high voltage pulses with fast rising and falling edges for CCP discharge. A prototype of the PDG is assembled to modulate from a high-voltage direct current (HVdc) input into a pulsed HVdc output, while following an input pulse signal and a set current level. The pulse rise time and fall time are less than 500 ns and 800 ns, respectively, and the minimum pulse width is 1 µs. The maximum voltage for a negative pulse is 1000 V, and the maximum repetition frequency is 500 kHz. During the pulse on time, the plasma discharge current is controlled steadily at the set value. The half-resonant converters in the PDG perform recovery of the remaining energy from the capacitive load at every termination of pulse discharge. The PDG performed with a high energy efficiency of 85% from the HVdc input to the pulsed dc output at a repetition rate of 1 kHz and with stable plasma operation in various discharge conditions. The results suggest that the developed PDG can be considered to be more efficient for plasma processing by CCP. 20. Novel high-frequency energy-efficient pulsed-dc generator for capacitively coupled plasma discharge. Science.gov (United States) Mamun, Md Abdullah Al; Furuta, Hiroshi; Hatta, Akimitsu 2018-03-01 The circuit design, assembly, and operating tests of a high-frequency and high-voltage (HV) pulsed dc generator (PDG) for capacitively coupled plasma (CCP) discharge inside a vacuum chamber are reported. For capacitive loads, it is challenging to obtain sharp rectangular pulses with fast rising and falling edges, requiring intense current for quick charging and discharging. The requirement of intense current generally limits the pulse operation frequency. In this study, we present a new type of PDG consisting of a pair of half-resonant converters and a constant current-controller circuit connected with HV solid-state power switches that can deliver almost rectangular high voltage pulses with fast rising and falling edges for CCP discharge. A prototype of the PDG is assembled to modulate from a high-voltage direct current (HVdc) input into a pulsed HVdc output, while following an input pulse signal and a set current level. The pulse rise time and fall time are less than 500 ns and 800 ns, respectively, and the minimum pulse width is 1 µs. The maximum voltage for a negative pulse is 1000 V, and the maximum repetition frequency is 500 kHz. During the pulse on time, the plasma discharge current is controlled steadily at the set value. The half-resonant converters in the PDG perform recovery of the remaining energy from the capacitive load at every termination of pulse discharge. The PDG performed with a high energy efficiency of 85% from the HVdc input to the pulsed dc output at a repetition rate of 1 kHz and with stable plasma operation in various discharge conditions. The results suggest that the developed PDG can be considered to be more efficient for plasma processing by CCP. 1. Interactions of pulsed electric fields with living organisms International Nuclear Information System (INIS) Vezinet, R.; Joly, J.C.; Meyer, O.; Gilbert, C.; Fourrier-Lamer, A.; Silve, A.; Mir, L.M.; Rols, M.P.; Chopinet, L.; Teissie, J.; Roux, D. 2013-01-01 Biologists are more and more involved in the study of the interactions of electromagnetic fields with human body for therapeutics and health applications. In this article we present 4 studies. The first study concerns the interaction between the electromagnetic field and the biochemical reaction of the hydrolysis of the acetylcholine, a primary neurotransmitter of the human body. It has been shown that a progressive slowing-down of the reaction appears when the pulse repetition frequency increases. The second study is dedicated to the effects of electromagnetic pulses at the cell membrane level. We know that electromagnetic pulses can alter the permeability of the cell membrane. We have used rectangular electromagnetic pulses to allow chemicals to enter the cell. In the case of cancer treatment the efficiency of a chemicals like bleomycin can be largely increased. The third study is dedicated to the use of 2 electromagnetic pulses of different duration to optimize gene transfer into the cell nucleus. The last study focuses on the analysis of plant reactions when facing electromagnetic pulses. An experiment performed on a sunflower shows that despite high electric fields no electro-physiological response of the plant has been measured when the sunflower was submitted to electromagnetic pulses 2. Generation of Quasi-Gaussian Pulses Based on Correlation Techniques Directory of Open Access Journals (Sweden) POHOATA, S. 2012-02-01 Full Text Available The Gaussian pulses have been mostly used within communications, where some applications can be emphasized: mobile telephony (GSM, where GMSK signals are used, as well as the UWB communications, where short-period pulses based on Gaussian waveform are generated. Since the Gaussian function signifies a theoretical concept, which cannot be accomplished from the physical point of view, this should be expressed by using various functions, able to determine physical implementations. New techniques of generating the Gaussian pulse responses of good precision are approached, proposed and researched in this paper. The second and third order derivatives with regard to the Gaussian pulse response are accurately generated. The third order derivates is composed of four individual rectangular pulses of fixed amplitudes, being easily to be generated by standard techniques. In order to generate pulses able to satisfy the spectral mask requirements, an adequate filter is necessary to be applied. This paper emphasizes a comparative analysis based on the relative error and the energy spectra of the proposed pulses. 3. Optimal design for rectangular isolated footings using the real soil pressure Directory of Open Access Journals (Sweden) Arnulfo Luévanos Rojas 2017-05-01 Full Text Available The standard design method (classical method for reinforced concrete rectangular footings is: First, a dimension is proposed and should comply with the allowable stresses; subsequently, the effective depth is obtained from the maximum moment and is checked against the bending shear and the punching shear until, it complies with these conditions and, then, steel reinforcement is obtained, but it is not guarantee that the minimum cost will be obtained. This paper shows an optimal design for reinforced concrete rectangular footings using the new model. A numerical experimentation is presented to show the model capability to estimate the minimum cost design of the materials used for a rectangular footing that supports an axial load and moments in two directions in accordance to the building code requirements for structural concrete and commentary (ACI 318-13. Also, a comparison is made between the optimal design and current design for rectangular footings. The solutions show that the optimal design is more economical and more precise with respect to the current design, because standard design is done by trial and error. Then, the optimal design should be used to obtain the minimum cost design for reinforced concrete rectangular footings. 4. Analysis of the rectangular resonator with butterfly MMI coupler using SOI Science.gov (United States) Kim, Sun-Ho; Park, Jun-Hee; Kim, Eudum; Jeon, Su-Jin; Kim, Ji-Hoon; Choi, Young-Wan 2018-02-01 We propose a rectangular resonator sensor structure with butterfly MMI coupler using SOI. It consists of the rectangular resonator, total internal reflection (TIR) mirror, and the butterfly MMI coupler. The rectangular resonator is expected to be used as bio and chemical sensors because of the advantages of using MMI coupler and the absence of bending loss unlike ring resonators. The butterfly MMI coupler can miniaturize the device compared to conventional MMI by using a linear butterfly shape instead of a square in the MMI part. The width, height, and slab height of the rib type waveguide are designed to be 1.5 μm, 1.5 μm, and 0.9 μm, respectively. This structure is designed as a single mode. When designing a TIR mirror, we considered the Goos-Hänchen shift and critical angle. We designed 3:1 MMI coupler because rectangular resonator has no bending loss. The width of MMI is designed to be 4.5 μm and we optimize the length of the butterfly MMI coupler using finite-difference time-domain (FDTD) method for higher Q-factor. It has the equal performance with conventional MMI even though the length is reduced by 1/3. As a result of the simulation, Qfactor of rectangular resonator can be obtained as 7381. 5. Random pulse generator International Nuclear Information System (INIS) Guo Ya'nan; Jin Dapeng; Zhao Dixin; Liu Zhen'an; Qiao Qiao; Chinese Academy of Sciences, Beijing 2007-01-01 Due to the randomness of radioactive decay and nuclear reaction, the signals from detectors are random in time. But normal pulse generator generates periodical pulses. To measure the performances of nuclear electronic devices under random inputs, a random generator is necessary. Types of random pulse generator are reviewed, 2 digital random pulse generators are introduced. (authors) 6. Band-selective shaped pulse for high fidelity quantum control in diamond International Nuclear Information System (INIS) Chang, Yan-Chun; Xing, Jian; Liu, Gang-Qin; Jiang, Qian-Qing; Li, Wu-Xia; Zhang, Fei-Hao; Gu, Chang-Zhi; Pan, Xin-Yu; Long, Gui-Lu 2014-01-01 High fidelity quantum control of qubits is crucially important for realistic quantum computing, and it becomes more challenging when there are inevitable interactions between qubits. We introduce a band-selective shaped pulse, refocusing BURP (REBURP) pulse, to cope with the problems. The electron spin of nitrogen-vacancy centers in diamond is flipped with high fidelity by the REBURP pulse. In contrast with traditional rectangular pulses, the shaped pulse has almost equal excitation effect in a sharply edged region (in frequency domain). So the three sublevels of host 14 N nuclear spin can be flipped accurately simultaneously, while unwanted excitations of other sublevels (e.g., of a nearby 13 C nuclear spin) is well suppressed. Our scheme can be used for various applications such as quantum metrology, quantum sensing, and quantum information process. 7. Band-selective shaped pulse for high fidelity quantum control in diamond Energy Technology Data Exchange (ETDEWEB) Chang, Yan-Chun; Xing, Jian; Liu, Gang-Qin; Jiang, Qian-Qing; Li, Wu-Xia [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Zhang, Fei-Hao [Tsinghua National Laboratory for Information Science and Technology, Beijing 100084 (China); State Key Laboratory of Low-Dimensional Physics and Department of Physics, Tsinghua University, Beijing 100084 (China); Gu, Chang-Zhi; Pan, Xin-Yu, E-mail: [email protected] [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Collaborative Innovation Center of Quantum Matter, Beijing 100871 (China); Long, Gui-Lu [Tsinghua National Laboratory for Information Science and Technology, Beijing 100084 (China); State Key Laboratory of Low-Dimensional Physics and Department of Physics, Tsinghua University, Beijing 100084 (China); Collaborative Innovation Center of Quantum Matter, Beijing 100871 (China) 2014-06-30 High fidelity quantum control of qubits is crucially important for realistic quantum computing, and it becomes more challenging when there are inevitable interactions between qubits. We introduce a band-selective shaped pulse, refocusing BURP (REBURP) pulse, to cope with the problems. The electron spin of nitrogen-vacancy centers in diamond is flipped with high fidelity by the REBURP pulse. In contrast with traditional rectangular pulses, the shaped pulse has almost equal excitation effect in a sharply edged region (in frequency domain). So the three sublevels of host {sup 14}N nuclear spin can be flipped accurately simultaneously, while unwanted excitations of other sublevels (e.g., of a nearby {sup 13}C nuclear spin) is well suppressed. Our scheme can be used for various applications such as quantum metrology, quantum sensing, and quantum information process. 8. Programmable pulse generator International Nuclear Information System (INIS) Xue Zhihua; Lou Binqiao; Duan Xiaohui 2002-01-01 The author introduces the design of programmable pulse generator that is based on a micro-controller and controlled by RS232 interface of personal computer. The whole system has good stability. The pulse generator can produce TTL pulse and analog pulse. The pulse frequency can be selected by EPLD. The voltage amplitude and pulse width of analog pulse can be adjusted by analog switches and digitally-controlled potentiometers. The software development tools of computer is National Instruments LabView5.1. The front panel of this virtual instrumentation is intuitive and easy-to-use. Parameters can be selected and changed conveniently by knob and slide 9. Versatile Stimulation Back-End With Programmable Exponential Current Pulse Shapes for a Retinal Visual Prosthesis. Science.gov (United States) 2016-11-01 This paper reports on the design, implementation, and test of a stimulation back-end, for an implantable retinal prosthesis. In addition to traditional rectangular pulse shapes, the circuit features biphasic stimulation pulses with both rising and falling exponential shapes, whose time constants are digitally programmable. A class-B second generation current conveyor is used as a wide-swing, high-output-resistance stimulation current driver, delivering stimulation current pulses of up to ±96 μA to the target tissue. Duration of the generated current pulses is programmable within the range of 100 μs to 3 ms. Current-mode digital-to-analog converters (DACs) are used to program the amplitudes of the stimulation pulses. Fabricated using the IBM 130 nm process, the circuit consumes 1.5×1.5 mm 2 of silicon area. According to the measurements, the DACs exhibit DNL and INL of 0.23 LSB and 0.364 LSB, respectively. Experimental results indicate that the stimuli generator meets expected requirements when connected to electrode-tissue impedance of as high as 25 k Ω. Maximum power consumption of the proposed design is 3.4 mW when delivering biphasic rectangular pulses to the target load. A charge pump block is in charge of the upconversion of the standard 1.2-V supply voltage to ±3.3V. 10. Numerical investigation of the effect of driving voltage pulse shapes on the characteristics of low-pressure argon dielectric barrier discharge International Nuclear Information System (INIS) Eslami, E.; Barjasteh, A.; Morshedian, N. 2015-01-01 In this work, we numerically compare the effect of a sinusoidal, triangular, and rectangular pulsed voltage profile on the calculated particle production, electric current, and gas voltage in a dielectric barrier discharge. The total argon gas pressure of 400 Pa, the distance between dielectrics of 5 mm, the dielectric thickness of 0.7 mm, and the temperature of T = 300 K were considered as input parameters. The different driving voltage pulse shapes (triangular, rectangular, and sinusoidal) are considered as applied voltage with a frequency of 7 kHz and an amplitude of 700 V peak to peak. It is shown that applying a rectangular voltage, as compared with a sinusoidal or triangle voltage, increases the current peak, while the peak width is decreased. Higher current density is related to high production of charged particles, which leads to the generation of some highly active species, such as Ar* (4s level), and Ar** (4p level) in the gap 11. PERFORMANCE ANALYSIS OF RECTANGULAR MPA USING DIFFERENT SUBSTRATE MATERIALS FOR WLAN APPLICATION Directory of Open Access Journals (Sweden) E Aravindraj 2017-03-01 Full Text Available In this paper, a rectangular microstrip patch antenna (MPA is designed using different substrate materials for analyzing the performance of the MPA. Alumina (Al2O3, Bakelite, Beryllium oxide (BeO, Gallium Arsenide (GaAs, RT-Duroid and Flame Retardant 4 (FR-4 are the six different substrate used in the design. The size of the rectangular microstrip patch antenna varies according to the dielectric constant of substrate materials used. The operating frequency taken for this analysis is 5.8 GHz. The proposed design provides the study on the performance of rectangular microstrip patch antenna for different substrate materials using the same frequency. This study conveys that which substrate material provides better performance. Moreover, this comparative study conveys that which substrate material provides better performance. The simulation parameters are investigated using HFSS. 12. Exact thermal representation of multilayer rectangular structures by infinite plate structures using the method of images Science.gov (United States) Palisoc, Arthur L.; Lee, Chin C. 1988-12-01 Using the method of images and the analytical temperature solution to the multilayer infinite plate structure, the thermal profile over finite rectangular multilayer integrated circuit devices can be calculated exactly. The advantage of using the image method lies in the enhanced capability of arriving at an analytical solution for structures where analytical solutions do not apparently exist, e.g., circular or arbitrarily oriented rectangular sources over multilayered rectangular structures. The new approach results in large savings in computer CPU time especially for small sources over large substrates. The method also finds very important applications to integrated circuit devices with heat dissipating elements close to the edge boundaries. Results from two examples indicate that the edge boundaries of a device may also be utilized to remove heat from it. This additional heat removing capability should have important applications in high power devices. 13. One-dimensional nonlinear theory for rectangular helix traveling-wave tube Energy Technology Data Exchange (ETDEWEB) Fu, Chengfang, E-mail: [email protected]; Zhao, Bo; Yang, Yudong; Ju, Yongfeng [Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huai' an 223003 (China); Wei, Yanyu [School of Physical Electronics, University of Electronic and Technology of China, Chengdu 610054 (China) 2016-08-15 A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length. 14. DNB Mechanistic model assessment based on experimental data in narrow rectangular channel International Nuclear Information System (INIS) Zhou Lei; Yan Xiao; Huang Yanping; Xiao Zejun; Huang Shanfang 2011-01-01 The departure from nuclear boiling (DNB) is important concerning about the safety of a PWR. Lacking assessment by experimental data points, it's doubtful whether the existing models can be used in narrow rectangular channels or not. Based on experimental data points in narrow rectangular channels, two kinds of classical DNB models, which include liquid sublayer dryout model (LSDM) and bubble crowding model (BCM), were assessed. The results show that the BCM has much wider application range than the LSDM. Several thermal parameters show systematical influences on the calculated results by the models. The performances of all the models deteriorate as the void fraction increases. The reason may be attributed to the geometrical differences between a circular tube and narrow rectangular channel. (authors) 15. Rainfall height stochastic modelling as a support tool for landslides early warning Science.gov (United States) Capparelli, G.; Giorgio, M.; Greco, R.; Versace, P. 2009-04-01 intervals. More useful for this issue are the so-called DRIP (Disaggregated Rectangular Intensity Pulse) and NSRP (Neymann-Scott Rectangular Pulse) model [Heneker et al., 2001; Cowpertwait et al., 2002], usually adopted to generate synthetic point rainfall series. In this paper, the DRIP model approach is adopted in conjunction with FLAIR model to calculate the probability of flowslides occurrence. The final aim of the study is in fact to provide a useful tool to implement an early warning system for hydrogeological risk management. Model calibration has been carried out with hourly rainfall hieght data provided by the rain gauges of Campania Region civil protection agency meteorological warning network. So far, the model has been applied only to data series recorded at a single rain gauge. Future extension will deal with spatial correlation between time series recorded at different gauges. ACKNOWLEDGEMENTS The research was co-financed by the Italian Ministry of University, by means of the PRIN 2006 PRIN program, within the research project entitled ‘Definition of critical rainfall thresholds for destructive landslides for civil protection purposes'. REFERENCES Box, G.E.P. and Jenkins, G.M., 1976. Time Series Analysis Forecasting and Control, Holden-Day, San Francisco. Cowpertwait, P.S.P., Kilsby, C.G. and O'Connell, P.E., 2002. A space-time Neyman-Scott model of rainfall: Empirical analysis of extremes, Water Resources Research, 38(8):1-14. Salas, J.D., 1992. Analysis and modeling of hydrological time series, in D.R. Maidment, ed., Handbook of Hydrology, McGraw-Hill, New York. Heneker, T.M., Lambert, M.F. and Kuczera G., 2001. A point rainfall model for risk-based design, Journal of Hydrology, 247(1-2):54-71. Versace, P., Sirangelo. B. and Capparelli, G., 2003. Forewarning model of landslides triggered by rainfall. Proc. 3rd International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment, Davos. 16. Review of Critical Heat Flux Correlations for Upward Flow in a Vertical Thin Rectangular Channel Energy Technology Data Exchange (ETDEWEB) Choi, Gil Sik; Chang, Soon Heung [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of) 2014-05-15 From the view point of safety, this type of fuel has higher resistance to earthquake and external impact. The cross section of coolant flow channel in the reactor core composed with the plate fuel is a thin rectangular shape. Thermal-hydraulic characteristics of this thin rectangular channel are different with those of general circular rod fuel bundle flow channel. Accordingly it could be thought that the CHF correlation in a thin rectangular channel is different with that in a circular channel, for which a large number of researches on CHF prediction have been carried out. The objective of this paper is to review previous researches on CHF in a thin rectangular channel, summarize the important conclusion and propose the new simple CHF correlation, which is based on the data set under high pressure and high flow rate condition. The researches on CHF in rectangular channel have been partially carried out according to the pressure, heated surface number, heated surface wettability effect, flow driving force and flow direction conditions. From the literature researches on CHF for upward flow in a vertical thin rectangular channel, some CHF prediction methods were reviewed and compared. There is no universal correlation which can predict CHF at all conditions, but generally, Katto empirical correlation is known to be useful at high pressure and high flow rate. The new simple correlation was developed from the restricted data set, the CHF prediction capacity of which is better than that of Katto. Even though the prediction consistency of the new simple correlation is lower, MAE and RMS error decreased quite. For the more development of the new simple CHF correlation, the more advanced regression analysis method and theoretical analysis should be studied in future. 17. Review of Critical Heat Flux Correlations for Upward Flow in a Vertical Thin Rectangular Channel International Nuclear Information System (INIS) Choi, Gil Sik; Chang, Soon Heung 2014-01-01 From the view point of safety, this type of fuel has higher resistance to earthquake and external impact. The cross section of coolant flow channel in the reactor core composed with the plate fuel is a thin rectangular shape. Thermal-hydraulic characteristics of this thin rectangular channel are different with those of general circular rod fuel bundle flow channel. Accordingly it could be thought that the CHF correlation in a thin rectangular channel is different with that in a circular channel, for which a large number of researches on CHF prediction have been carried out. The objective of this paper is to review previous researches on CHF in a thin rectangular channel, summarize the important conclusion and propose the new simple CHF correlation, which is based on the data set under high pressure and high flow rate condition. The researches on CHF in rectangular channel have been partially carried out according to the pressure, heated surface number, heated surface wettability effect, flow driving force and flow direction conditions. From the literature researches on CHF for upward flow in a vertical thin rectangular channel, some CHF prediction methods were reviewed and compared. There is no universal correlation which can predict CHF at all conditions, but generally, Katto empirical correlation is known to be useful at high pressure and high flow rate. The new simple correlation was developed from the restricted data set, the CHF prediction capacity of which is better than that of Katto. Even though the prediction consistency of the new simple correlation is lower, MAE and RMS error decreased quite. For the more development of the new simple CHF correlation, the more advanced regression analysis method and theoretical analysis should be studied in future 18. Pulsed water jet generated by pulse multiplication Czech Academy of Sciences Publication Activity Database Dvorský, R.; Sitek, Libor; Sochor, T. 2016-01-01 Roč. 23, č. 4 (2016), s. 959-967 ISSN 1330-3651 R&D Projects: GA MŠk(CZ) LO1406; GA MŠk ED2.1.00/03.0082 Institutional support: RVO:68145535 Keywords : high- pressure pulses * pulse intensifier * pulsed water jet * water hammer effect Subject RIV: JQ - Machines ; Tools Impact factor: 0.723, year: 2016 http://hrcak.srce.hr/163752?lang=en 19. Modeling on bubbly to churn flow pattern transition for vertical upward flows in narrow rectangular channel International Nuclear Information System (INIS) Wang Yanlin; Chen Bingde; Huang Yanping; Wang Junfeng 2011-01-01 A theoretical model was developed to predict the bubbly to churn flow pattern transition for vertical upward flows in narrow rectangular channel. The model was developed based on the imbalance theory of Helmholtz and some reasonable assumptions. The maximum ideal bubble in narrow rectangular channel and the thermal hydraulics boundary condition leading to bubbly flow to churn flow pattern transition was calculated. The model was validated by experimental data from previous researches. Comparison between predicted result and experimental result shows a reasonable good agreement. (author) 20. Transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations International Nuclear Information System (INIS) Sugano, Y. 1980-01-01 The transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations on two edges are studied by means of the Airy stress function. The purposes of this paper are to present a method of determing the transient thermal stresses in an orthographic rectangular plate with four edges of distinct thermal boundary condition of the third kind which exactly satisfy the traction-free conditions of shear stress over all boundaries including four corners of the plate, and to consider the effects of the anisotropies of material properties and the convective heat transfer on the upper and lower surfaces on the thermal stress distribution. (orig.) 1. A study on liquid lithium flow in rectangular duck perpendicular to a intense magnetic field International Nuclear Information System (INIS) Shen Xiuzhong; Chen Ke; Liu Yang; Zhang Qinshun 2001-01-01 A research on high-speed liquid-metal lithium flow through a non-expanding rectangular duck under uniform intense magnetic field is presented. A equations set with Poisson equation and Helmholtz equation, which control the electrical field and flow field respectively, has been deduced by analysis and PHsolver, a program to solve the equations set, has also been finished. The current density distribution and flow field in the non-expanding rectangular channel with intense magnetic field have been obtained from PHsolver by applying the wall-function in the boundary wall. The velocity profile in the duck appears M-shaped 2. Dual cameras acquisition and display system of retina-like sensor camera and rectangular sensor camera Science.gov (United States) Cao, Nan; Cao, Fengmei; Lin, Yabin; Bai, Tingzhu; Song, Shengyu 2015-04-01 For a new kind of retina-like senor camera and a traditional rectangular sensor camera, dual cameras acquisition and display system need to be built. We introduce the principle and the development of retina-like senor. Image coordinates transformation and interpolation based on sub-pixel interpolation need to be realized for our retina-like sensor's special pixels distribution. The hardware platform is composed of retina-like senor camera, rectangular sensor camera, image grabber and PC. Combined the MIL and OpenCV library, the software program is composed in VC++ on VS 2010. Experience results show that the system can realizes two cameras' acquisition and display. 3. HIGH QUALITY FACADE SEGMENTATION BASED ON STRUCTURED RANDOM FOREST, REGION PROPOSAL NETWORK AND RECTANGULAR FITTING Directory of Open Access Journals (Sweden) K. Rahmani 2018-05-01 Full Text Available In this paper we present a pipeline for high quality semantic segmentation of building facades using Structured Random Forest (SRF, Region Proposal Network (RPN based on a Convolutional Neural Network (CNN as well as rectangular fitting optimization. Our main contribution is that we employ features created by the RPN as channels in the SRF.We empirically show that this is very effective especially for doors and windows. Our pipeline is evaluated on two datasets where we outperform current state-of-the-art methods. Additionally, we quantify the contribution of the RPN and the rectangular fitting optimization on the accuracy of the result. 4. The time of discrete spectrum identical particles tunneling at their simultaneous passing over rectangular quantum barrier International Nuclear Information System (INIS) Martsenyuk, L.S. 2010-01-01 Research of influence of exchange interaction of identical particles for the time of their simultaneous tunneling through a rectangular quantum barrier is lead. The account of identity leads to necessity of symmetrisation of wave function owing to what in the formula describing interaction of two particles, arises an additional element. In result the parameters of tunneling, including time of tunneling change. Time of tunneling is calculated from the formula received in work from the size of exchange interaction of two particles simultaneously crossing a rectangular quantum barrier. 5. On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism Science.gov (United States) Lyashko, A. D. 2017-11-01 A new analytical presentation of the solution for steady-state oscillations of orthotopic rectangular prism is found. The corresponding infinite system of linear algebraic equations has been deduced by the superposition method. A countable set of precise eigenfrequencies and elementary eigenforms is found. The identities are found which make it possible to improve the convergence of all the infinite series in the solution of the problem. All the infinite series in presentation of solution are analytically summed up. Numerical calculations of stresses in the rectangular orthotropic prism with a uniform along the border and harmonic in time load on two opposite faces have been performed. 6. Natural Frequency of F.G. Rectangular Plate by Shear Deformation Theory International Nuclear Information System (INIS) Shahrjerdi, Ali; Sapuan, S M; Shahzamanian, M M; Mustapha, F; Zahari, R; Bayat, M 2011-01-01 Natural frequency of functionally graded (F.G.) rectangular plate is carried out by using second-order shear deformation theory (SSDT). The material properties of functionally graded rectangular plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution. The equations of motion are obtained by energy method. Numerical results for functionally graded plates are given in dimensionless graphical forms and the effects of material properties on natural frequency are determined. 7. Precipitation extremes on multiple timescales - Bartlett-Lewis rectangular pulse model and intensity-duration-frequency curves Science.gov (United States) Ritschel, Christoph; Ulbrich, Uwe; Névir, Peter; Rust, Henning W. 2017-12-01 For several hydrological modelling tasks, precipitation time series with a high (i.e. sub-daily) resolution are indispensable. The data are, however, not always available, and thus model simulations are used to compensate. A canonical class of stochastic models for sub-daily precipitation are Poisson cluster processes, with the original Bartlett-Lewis (OBL) model as a prominent representative. The OBL model has been shown to well reproduce certain characteristics found in observations. Our focus is on intensity-duration-frequency (IDF) relationships, which are of particular interest in risk assessment. Based on a high-resolution precipitation time series (5 min) from Berlin-Dahlem, OBL model parameters are estimated and IDF curves are obtained on the one hand directly from the observations and on the other hand from OBL model simulations. Comparing the resulting IDF curves suggests that the OBL model is able to reproduce the main features of IDF statistics across several durations but cannot capture rare events (here an event with a return period larger than 1000 years on the hourly timescale). In this paper, IDF curves are estimated based on a parametric model for the duration dependence of the scale parameter in the generalized extreme value distribution; this allows us to obtain a consistent set of curves over all durations. We use the OBL model to investigate the validity of this approach based on simulated long time series. 8. Development of a 100 KV 10 a pulse generator on the basis of electron tubes for plasma immersion ion implantation International Nuclear Information System (INIS) Kaur, Mandeep; Barve, D.N.; Chakravarthy, D.P. 2006-01-01 The design of a high-voltage pulsing system on the basis of hard tube of hard tube for a plasma immersion ion implantation (PIII) facility is presented. A list of requirements, which have to be fulfilled by a high-voltage pulse generator to get best results and an optimum operation of the PIII system, is given. The requirement for the pulse generator can be fulfilled well using a pulse generator design, which employs a hard tube switch. The pulse generator design presented is optimized for PIII systems. The hard tube control can produce nearly rectangular pulses of any duration and repetition frequencies and is especially optimized for obtaining voltage rise times as short as possible. (author) 9. Laser pulse stacking method Science.gov (United States) Moses, E.I. 1992-12-01 A laser pulse stacking method is disclosed. A problem with the prior art has been the generation of a series of laser beam pulses where the outer and inner regions of the beams are generated so as to form radially non-synchronous pulses. Such pulses thus have a non-uniform cross-sectional area with respect to the outer and inner edges of the pulses. The present invention provides a solution by combining the temporally non-uniform pulses in a stacking effect to thus provide a more uniform temporal synchronism over the beam diameter. 2 figs. 10. Pulse to pulse klystron diagnosis system International Nuclear Information System (INIS) Nowak, J.; Davidson, V.; Genova, L.; Johnson, R.; Reagan, D. 1981-03-01 This report describes a system used to study the behavior of SLAC high powered klystrons operating with a twice normal pulse width of 5 μs. At present, up to eight of the klystrons installed along the accelerator can be operated with long pulses and monitored by this system. The report will also discuss some of the recent findings and investigations 11. 76 FR 64312 - Light-Walled Welded Rectangular Carbon Steel Tubing From Taiwan: Final Results of the Expedited... Science.gov (United States) 2011-10-18 ... Rectangular Carbon Steel Tubing From Taiwan: Final Results of the Expedited Sunset Review of the Antidumping... the antidumping duty order on light-walled welded rectangular carbon steel tubing from Taiwan pursuant... steel tubing from Taiwan pursuant to section 751(c) of the Act. See Initiation of Five-Year (Sunset... 12. 77 FR 5240 - Light-Walled Welded Rectangular Carbon Steel Tubing From Taiwan: Continuation of Antidumping Duty... Science.gov (United States) 2012-02-02 ... Rectangular Carbon Steel Tubing From Taiwan: Continuation of Antidumping Duty Order AGENCY: Import... revocation of the antidumping duty order on light-walled welded rectangular carbon steel tubing from Taiwan would likely lead to a continuation or recurrence of dumping and material injury to an industry in the... 13. Optical implementation of (3, 3, 2) regular rectangular CC-Banyan optical network Science.gov (United States) Yang, Junbo; Su, Xianyu 2007-07-01 CC-Banyan network plays an important role in the optical interconnection network. Based on previous reports of (2, 2, 3) the CC-Banyan network, another rectangular-Banyan network, i.e. (3, 3, 2) rectangular CC-Banyan network, has been discussed. First, according to its construction principle, the topological graph and the routing rule of (3, 3, 2) rectangular CC-Banyan network have been proposed. Then, the optically experimental setup of (3, 3, 2) rectangular CC-Banyan network has been designed and achieved. Each stage of node switch consists of phase spatial light modulator (PSLM) and polarizing beam-splitter (PBS), and fiber has been used to perform connection between adjacent stages. PBS features that s-component (perpendicular to the incident plane) of the incident light beam is reflected, and p-component (parallel to the incident plane) passes through it. According to switching logic, under the control of external electrical signals, PSLM functions to control routing paths of the signal beams, i.e. the polarization of each optical signal is rotated or not rotated 90° by a programmable PSLM. Finally, the discussion and analysis show that the experimental setup designed here can realize many functions such as optical signal switch and permutation. It has advantages of large number of input/output-ports, compact in structure, and low energy loss. Hence, the experimental setup can be used in optical communication and optical information processing. 14. The Effects of a Rectangular Rapid-Flashing Beacon on Vehicle Speed Science.gov (United States) VanWagner, Michelle; Van Houten, Ron; Betts, Brian 2011-01-01 In 2008, nearly 31% of vehicle fatalities were related to failure to adhere to safe vehicle speeds (National Highway Traffic Safety Administration [NHTSA], 2009). The current study evaluated the effect of a rectangular rapid-flashing beacon (RRFB) triggered by excessive speed on vehicle speed using a combined alternating treatments and reversal… 15. Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices NARCIS (Netherlands) Sman, van der R.G.M. 2006-01-01 In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the 16. Scattering of E Polarized Plane Wave by Rectangular Cavity With Finite Flanges Science.gov (United States) 2017-11-01 The rigorous Method of Regularization is implemented for accurate analysis of wave scattering by rectangular cavity with finite flanges. The solution is free from limitations on problem parameters. The calculation of the induced surface current, bistatic radar cross section (RCS) and frequency dependence of monostatic RCS are performed with controlled accuracy in a wide frequency band. 17. Square and Rectangular Arrays from Directed Assembly of Sphere-forming Diblock Copolymers in Thin Films Science.gov (United States) Ji, Shengxiang; Nagpal, Umang; Liao, Wen; de Pablo, Juan; Nealey, Paul 2010-03-01 Patterns of square and rectangular arrays with nanoscale dimensions are scientifically and technologically important. Fabrication of square array patterns in thin films has been demonstrated by directed assembly of cylinder-forming diblock copolymers on chemically patterned substrates, supramolecular assembly of diblock copolymers, and self-assembly of triblock terpolymers. However, a macroscopic area of square array patterns with long-range order has not been achieved, and the fabrication of rectangular arrays has not been reported so far. Here we report a facile approach for fabricating patterns of square and rectangular arrays by directing the assembly of sphere-forming diblock copolymers on chemically patterned substrates. On stripe patterns, a square arrangement of half spheres, corresponding to the (100) plane of the body-centred cubic (BCC) lattice, formed on film surfaces. When the underlying pattern periods mismatched with the copolymer period, the square pattern could be stretched (up to ˜60%) or compressed (˜15%) to form rectangular arrays. Monte Carlo simulations have been further used to verify the experimental results and the 3-dimensional arrangements of spheres. 18. Rectangular optical filter based on high-order silicon microring resonators Science.gov (United States) Bao, Jia-qi; Yu, Kan; Wang, Li-jun; Yin, Juan-juan 2017-07-01 The rectangular optical filter is one of the most important optical switching components in the dense wavelength division multiplexing (DWDM) fiber-optic communication system and the intelligent optical network. The integrated highorder silicon microring resonator (MRR) is one of the best candidates to achieve rectangular filtering spectrum response. In general, the spectrum response rectangular degree of the single MRR is very low, so it cannot be used in the DWDM system. Using the high-order MRRs, the bandwidth of flat-top pass band, the out-of-band rejection degree and the roll-off coefficient of the edge will be improved obviously. In this paper, a rectangular optical filter based on highorder MRRs with uniform couplers is presented and demonstrated. Using 15 coupled race-track MRRs with 10 μm in radius, the 3 dB flat-top pass band of 2 nm, the out-of-band rejection ratio of 30 dB and the rising and falling edges of 48 dB/nm can be realized successfully. 19. Rectangular optical filter based on high-order silicon microring resonators Institute of Scientific and Technical Information of China (English) BAO Jia-qi; YU Kan; WANG Li-jun; YIN Juan-juan 2017-01-01 The rectangular optical filter is one of the most important optical switching components in the dense wavelength division multiplexing (DWDM) fiber-optic communication system and the intelligent optical network.The integrated highorder silicon microring resonator (MRR) is one of the best candidates to achieve rectangular filtering spectrum response.In general,the spectrum response rectangular degree of the single MRR is very low,so it cannot be used in the DWDM system.Using the high-order MRRs,the bandwidth of flat-top pass band,the out-of-band rejection degree and the roll-off coefficient of the edge will be improved obviously.In this paper,a rectangular optical filter based on highorder MRRs with uniform couplers is presented and demonstrated.Using 15 coupled race-track MRRs with 10 μm in radius,the 3 dB flat-top pass band of 2 nm,the out-of-band rejection ratio of 30 dB and the rising and falling edges of 48 dB/nm can be realized successfully. 20. Analytical study of a reversed-field pinch with rectangular cross section International Nuclear Information System (INIS) Zhang Peng 1990-01-01 An analyic solution of the force-free equation for a toroidal configuration of rectangular cross section is presented. It is shown that the critical value of contraction ratio for the appearance of a reversed field as well as of the ohmic current increases as the elongation of the cross section increases 1. Hydrodynamics of slug flow in a vertical narrow rectangular channel under laminar flow condition International Nuclear Information System (INIS) Wang, Yang; Yan, Changqi; Cao, Xiaxin; Sun, Licheng; Yan, Chaoxing; Tian, Qiwei 2014-01-01 Highlights: • Slug flow hydrodynamics in a vertical narrow rectangular duct were investigated. • The velocity of trailing Taylor bubble undisturbed by the leading one was measured. • Correlation of Taylor bubble velocity with liquid slug length ahead it was proposed. • Evolution of length distributions of Taylor bubble and liquid slug was measured. • The model of predicted length distributions was applied to the rectangular channel. - Abstract: The hydrodynamics of gas–liquid two-phase slug flow in a vertical narrow rectangular channel with the cross section of 2.2 mm × 43 mm is investigated using a high speed video camera system. Simultaneous measurements of velocity and duration of Taylor bubble and liquid slug made it possible to determine the length distributions of the liquid slug and Taylor bubble. Taylor bubble velocity is dependent on the length of the liquid slug ahead, and an empirical correlation is proposed based on the experimental data. The length distributions of Taylor bubbles and liquid slugs are positively skewed (log-normal distribution) at all measuring positions for all flow conditions. A modified model based on that for circular tubes is adapted to predict the length distributions in the present narrow rectangular channel. In general, the experimental data is well predicted by the modified model 2. Numerical analysis and optimization of 3D magnetohydrodynamic flows in rectangular U-bend Energy Technology Data Exchange (ETDEWEB) He, Qingyun, E-mail: [email protected]; Feng, Jingchao; Chen, Hongli, E-mail: [email protected] 2016-11-01 Highlights: • MHD flows in rectangular U bends have been investigated under specific magnetic field. • U bends analyzed with different aspect ratio, distance of U bends and the wall conductance ratio. • Pressure optimization of rectangular U bends at corner region. • Studying different inclination of magnetic field cases according to original MHD flows. - Abstract: Liquid metal flow in rectangular bends is a common phenomenon of fusion liquid metal blanket operation, in which the velocity distributions and magnetohydrodynamic (MHD) pressure drop are considered as critical issues. Previous studies mainly aimed at specific fixed geometry for bend flows in LM blanket. The present investigation focuses on numerical analysis of MHD flow in 3D rectangular bends at laminar conditions, which is aimed to reduce MHD pressure drop caused by electromagnetic coupling in conductive flow, especially in bend corner region. The used code has been developed by University of Science and Technology of China (USTC) and validated by recommended benchmark cases such as Shercliff, ALEX experiments and KIT experiment cases, etc. In order to search the optimal duct bending, certain parameters such as different aspect ratio of the duct corner area cross-section, distance of import and export from the elbow and wall conductance ratio have been considered to investigate the pressure drop of MHD flow. Moreover, the effects of different magnetic field direction relative to flow distribution between bends have also been analyzed. 3. Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate Directory of Open Access Journals (Sweden) Minghui Yao 2014-01-01 Full Text Available This paper investigates the multipulse heteroclinic bifurcations and chaotic dynamics of a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. According to the von Karman type equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. The method of multiple scales and Galerkin’s approach are applied to the partial differential governing equation. Then, the four-dimensional averaged equation is obtained for the case of 1 : 3 internal resonance and primary parametric resonance. The extended Melnikov method is used to study the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multipulse chaotic dynamics are analytically obtained. From the investigation, the geometric structure of the multipulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multipulse chaotic motions can occur. To sum up, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists for the laminated composite piezoelectric rectangular plate. 4. Comparison of rectangular and dual-planar positron emission mammography scanners International Nuclear Information System (INIS) Qi, Jinyi; Kuo, Chaincy; Huesman, Ronald H.; Klein, Gregory J.; Moses, William W.; Reutter, Bryan W. 2002-01-01 Breast imaging using dedicated positron emission tomography (PEM) has gained much interest in the medical imaging field. In this paper, we compare the performance between a rectangular geometry and a parallel dual-planar geometry. Both geometries are studied with depth of interaction (DOI) detectors and non- DOI detectors. We compare the Fisher-information matrix, lesion detection, and quantitation of the four systems. The lesion detectability is measured by the signal-to-noise ratio (SNR) of a prewhitening numerical observer for detecting a known hot spot on a uniform background. Results show that the rectangular system with DOI has the highest SNR for the detection task and the lowest bias at any given noise level for the quantitation task. They also show that for small simulated lesions the parallel dual-planar system with DOI detectors outperforms the rectangular system with non-DOI detectors, while the rectangular system with non-DOI detectors can outperform the parallel dual-planar system with DOI detectors for large simulated lesions 5. Edge Effects in a Composite Weakly Reinforced with Fibers of Rectangular Cross Section Science.gov (United States) Boichuk, V. Yu. 2001-05-01 This paper deal with the edge effect in a composite weakly reinforced with fibers of rectangular cross section and subjected to biaxial uniform loading. The edge effects due to the difference between Poisson's ratios of the composite components are studied. Numerical results are presented 6. From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation NARCIS (Netherlands) Bastiaans, M.J.; Leest, van A.J. 1998-01-01 Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, 7. Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation NARCIS (Netherlands) Bastiaans, M.J.; Leest, van A.J. 1998-01-01 Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays 8. Numerical analysis and optimization of 3D magnetohydrodynamic flows in rectangular U-bend International Nuclear Information System (INIS) He, Qingyun; Feng, Jingchao; Chen, Hongli 2016-01-01 Highlights: • MHD flows in rectangular U bends have been investigated under specific magnetic field. • U bends analyzed with different aspect ratio, distance of U bends and the wall conductance ratio. • Pressure optimization of rectangular U bends at corner region. • Studying different inclination of magnetic field cases according to original MHD flows. - Abstract: Liquid metal flow in rectangular bends is a common phenomenon of fusion liquid metal blanket operation, in which the velocity distributions and magnetohydrodynamic (MHD) pressure drop are considered as critical issues. Previous studies mainly aimed at specific fixed geometry for bend flows in LM blanket. The present investigation focuses on numerical analysis of MHD flow in 3D rectangular bends at laminar conditions, which is aimed to reduce MHD pressure drop caused by electromagnetic coupling in conductive flow, especially in bend corner region. The used code has been developed by University of Science and Technology of China (USTC) and validated by recommended benchmark cases such as Shercliff, ALEX experiments and KIT experiment cases, etc. In order to search the optimal duct bending, certain parameters such as different aspect ratio of the duct corner area cross-section, distance of import and export from the elbow and wall conductance ratio have been considered to investigate the pressure drop of MHD flow. Moreover, the effects of different magnetic field direction relative to flow distribution between bends have also been analyzed. 9. The Effect of Mandrel Configuration on the Warpage in Pultrusion of Rectangular Hollow Profiles NARCIS (Netherlands) Baran, Ismet; Hattel, Jesper H.; Akkerman, Remko 2014-01-01 Thermo-mechanical process simulation of an industrially pultruded rectangular hollow profile is presented. Glass/polyester is used for the continuous filament mat (CFM) and the uni-directional (UD) layers. The process induced residual distortions together with the temperature and degree of cure are 10. A CPW-Fed Rectangular Ring Monopole Antenna for WLAN Applications Directory of Open Access Journals (Sweden) Sangjin Jo 2014-01-01 Full Text Available We present a simple coplanar waveguide- (CPW- fed rectangular ring monopole antenna designed for dual-band wireless local area network (WLAN applications. The antenna is based on a simple structure composed of a CPW feed line and a rectangular ring. Dual-band WLAN operation can be achieved by controlling the distance between the rectangular ring and the ground plane of the CPW feed line, as well as the horizontal vertical lengths of the rectangular ring. Simulated and measured data show that the antenna has a compact size of 21.4×59.4 mm2, an impedance bandwidths of 2.21–2.70 GHz and 5.04–6.03 GHz, and a reflection coefficient of less than −10 dB. The antenna also exhibits an almost omnidirectional radiation pattern. This simple compact antenna with favorable frequency characteristics therefore is attractive for applications in dual-band WLAN. 11. Regimes of Vorticity in the Wake of a Rectangular Vortex Generator DEFF Research Database (Denmark) Velte, Clara Marika; Okulov, Valery; Hansen, Martin Otto Laver 2011-01-01 This paper concerns the study of the secondary structures generated in the wake of a wall mounted rectangular vane, commonly referred to as a vortex generator. The study has been conducted by Stereoscopic PIV measurements in a wind tunnel and supplementary flow visualizations in a water channel... 12. Behavior of thin rectangular ANCF shell elements in various mesh configurations DEFF Research Database (Denmark) Hyldahl, Per; Mikkola, Aki M.; Balling, Ole 2014-01-01 a thorough review of three available formulations, they are used in three different convergence studies. Initially a reference study is conducted to determine how the ANCF performs in an uniform and rectangular mesh. Subsequently, the ANCF methods sensitivity to irregular mesh is investigated and finally... 13. Ultra-narrow band diode lasers with arbitrary pulse shape modulation (Conference Presentation) Science.gov (United States) Ryasnyanskiy, Aleksandr I.; Smirnov, Vadim; Mokhun, Oleksiy; Glebov, Alexei L.; Glebov, Leon B. 2017-03-01 Wideband emission spectra of laser diode bars (several nanometers) can be largely narrowed by the usage of thick volume Bragg gratings (VBGs) recorded in photo-thermo-refractive glass. Such narrowband systems, with GHz-wide emission spectra, found broad applications for Diode Pumped Alkali vapor Lasers, optically pumped rare gas metastable lasers, Spin Exchange Optical Pumping, atom cooling, etc. Although the majority of current applications of narrow line diode lasers require CW operation, there are a variety of fields where operation in a different pulse mode regime is necessary. Commercial electric pulse generators can provide arbitrary current pulse profiles (sinusoidal, rectangular, triangular and their combinations). The pulse duration and repetition rate however, have an influence on the laser diode temperature, and therefore, the emitting wavelength. Thus, a detailed analysis is needed to understand the correspondence between the optical pulse profiles from a diode laser and the current pulse profiles; how the pulse profile and duty cycle affects the laser performance (e.g. the wavelength stability, signal to noise ratio, power stability etc.). We present the results of detailed studies of the narrowband laser diode performance operating in different temporal regimes with arbitrary pulse profiles. The developed narrowband (16 pm) tunable laser systems at 795 nm are capable of operating in different pulse regimes while keeping the linewidth, wavelength, and signal-to-noise ratio (>20 dB) similar to the corresponding CW modules. 14. Neutronic studies on decoupled hydrogen moderator for a short-pulse spallation source International Nuclear Information System (INIS) Harada, Masahide; Watanabe, Noboru; Teshigawara, Makoto; Kai, Tetsuya; Ikeda, Yujiro 2005-01-01 Neutronic studies of decoupled hydrogen moderators were performed by calculations taking into account para hydrogen content, decoupling energy, moderator dimensions/shapes and reflector material. Low-energy parts of calculated spectral intensities with different para hydrogen contents were analyzed by a modified Maxwell function to characterize neutron spectra. The result shows that a 100% para hydrogen moderator gives the highest pulse peak intensity together with the narrowest pulse width and the shortest decay times. Pulse broadening with a reflector was explained by time distributions of source neutrons entering into the moderator through a decoupler. Material dependence of time distribution was studied. A decoupling energy higher than 1 eV does not bring about a large improvement in pulse widths and decay times, even at a large penalty in the peak intensity. The optimal moderator thickness was also discussed for a rectangular parallelepipe-shaped and a canteen-shaped moderator 15. Fast and efficient STT switching in MTJ using additional transient pulse current Science.gov (United States) Pathak, Sachin; Cha, Jongin; Jo, Kangwook; Yoon, Hongil; Hong, Jongill 2017-06-01 We propose a profile of write pulse current-density to switch magnetization in a perpendicular magnetic tunnel junction to reduce switching time and write energy as well. Our simulated results show that an overshoot transient pulse current-density (current spike) imposed to conventional rectangular-shaped pulse current-density (main pulse) significantly improves switching speed that yields the reduction in write energy accordingly. For example, we could dramatically reduce the switching time by 80% and thereby reduce the write energy over 9% in comparison to the switching without current spike. The current spike affects the spin dynamics of the free layer and reduces the switching time mainly due to spin torque induced. On the other hand, the large Oersted field induced causes changes in spin texture. We believe our proposed write scheme can make a breakthrough in magnetic random access memory technology seeking both high speed operation and low energy consumption. 16. Rectangular waveguide-to-coplanar waveguide transitions at U-band using e-plane probe and wire bonding DEFF Research Database (Denmark) Dong, Yunfeng; Johansen, Tom Keinicke; Zhurbenko, Vitaliy 2016-01-01 This paper presents rectangular waveguide-to-coplanar waveguide (CPW) transitions at U-band (40–60 GHz) using E-plane probe and wire bonding. The designs of CPWs based on quartz substrate with and without aluminum cover are explained. The single and double layer rectangular waveguide-to-CPW trans......This paper presents rectangular waveguide-to-coplanar waveguide (CPW) transitions at U-band (40–60 GHz) using E-plane probe and wire bonding. The designs of CPWs based on quartz substrate with and without aluminum cover are explained. The single and double layer rectangular waveguide......-to-CPW transitions using E-plane probe and wire bonding are designed. The proposed rectangular waveguide-to-CPW transition using wire bonding can provide 10 GHz bandwidth at U-band and does not require extra CPWs or connections between CPWs and chips. A single layer rectangular waveguide-to-CPW transition using E......-plane probe with aluminum package has been fabricated and measured to validate the proposed transitions. To the authors' best knowledge, this is the first time that a wire bonding is used as a probe for rectangular waveguide-to-CPW transition at U-band.... 17. Low frequency sound field control for loudspeakers in rectangular rooms using CABS (Controlled Acoustical Bass System) DEFF Research Database (Denmark) 2010-01-01 Rectangular rooms are the most common shape for sound reproduction, but at low frequencies the reflections from the boundaries of the room cause large spatial variations in the sound pressure level. Variations up to 30 dB are normal, not only at the room modes, but basically at all frequencies....... As sound propagates in time, it seems natural that the problems can best be analyzed and solved in the time domain. A time based room correction system named CABS (Controlled Acoustical Bass System) has been developed for sound reproduction in rectangular listening rooms. It can control the sound...... sound field in the whole room, and short impulse response. In a standard listening room (180 m3) only 4 loudspeakers are needed, 2 more than a traditional stereo setup. CABS is controlled by a developed DSP system. The time based approached might help with the understanding of sound field control... 18. Magnetohydrodynamic flow of generalized Maxwell fluids in a rectangular micropump under an AC electric field Energy Technology Data Exchange (ETDEWEB) Zhao, Guangpu [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Jian, Yongjun, E-mail: [email protected] [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Chang, Long [School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, Inner Mongolia 010051 (China); Buren, Mandula [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China) 2015-08-01 By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed. 19. On Stability of Exact Transparent Boundary Condition for the Parabolic Equation in Rectangular Computational Domain Science.gov (United States) Feshchenko, R. M. Recently a new exact transparent boundary condition (TBC) for the 3D parabolic wave equation (PWE) in rectangular computational domain was derived. However in the obtained form it does not appear to be unconditionally stable when used with, for instance, the Crank-Nicolson finite-difference scheme. In this paper two new formulations of the TBC for the 3D PWE in rectangular computational domain are reported, which are likely to be unconditionally stable. They are based on an unconditionally stable fully discrete TBC for the Crank-Nicolson scheme for the 2D PWE. These new forms of the TBC can be used for numerical solution of the 3D PWE when a higher precision is required. 20. Image properties of list mode likelihood reconstruction for a rectangular positron emission mammography with DOI measurements International Nuclear Information System (INIS) Qi, Jinyi; Klein, Gregory J.; Huesman, Ronald H. 2000-01-01 A positron emission mammography scanner is under development at our Laboratory. The tomograph has a rectangular geometry consisting of four banks of detector modules. For each detector, the system can measure the depth of interaction information inside the crystal. The rectangular geometry leads to irregular radial and angular sampling and spatially variant sensitivity that are different from conventional PET systems. Therefore, it is of importance to study the image properties of the reconstructions. We adapted the theoretical analysis that we had developed for conventional PET systems to the list mode likelihood reconstruction for this tomograph. The local impulse response and covariance of the reconstruction can be easily computed using FFT. These theoretical results are also used with computer observer models to compute the signal-to-noise ratio for lesion detection. The analysis reveals the spatially variant resolution and noise properties of the list mode likelihood reconstruction. The theoretical predictions are in good agreement with Monte Carlo results 1. Sound absorption effects in a rectangular enclosure with the foamed aluminum sheet absorber International Nuclear Information System (INIS) Oh, Jae Eung; Chung, Jin Tai; Kim, Sang Hun; Chung, Kyung Ryul 1998-01-01 For the purpose of finding out the optimal thickness of sound absorber and the sound absorption effects due to the selected thickness at an interested frequency range, the analytical study identifies the interior and exterior sound field characteristics of a rectangular enclosure with foamed aluminum lining and the experimental verification is performed with random noise input. By using a two-microphone impedance tube, we measure experimentally the absorption coefficient and the impedance of simple sound absorbing materials. Measured acoustical parameters of the test samples are applied to the theoretical analysis to predict sound pressure field in the cavity. The sound absorption effects from measurements are compared to predicted ones in both cases with and without foamed aluminum lining in the cavity of the rectangular enclosure 2. Integral transform solution of bending problem of clamped orthotropic rectangular plates International Nuclear Information System (INIS) An, C.; Gu, J.-J.; Su, J. 2011-01-01 The generalized integral transform technique (GITT) is employed to obtain an exact solution for the bending problem of fully clamped orthotropic rectangular plates. The use of the GITT approach in the analysis of the transverse deflection equation leads to a coupled system of fourth order differential equations in the dimensionless longitudinal spatial variable. The resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from IMSL Library. Numerical results with automatic global accuracy control are produced for different values of aspect ratio. Critical comparisons with previously reported numerical results are performed with excellent agreement. Several sets of reference results for clamped orthotropic rectangular plates are also provided for future covalidation purposes. (author) 3. Plasmonic band-stop filter with asymmetric rectangular ring for WDM networks International Nuclear Information System (INIS) 2013-01-01 We proposed a simple asymmetric rectangular band-stop filter based on metal–insulator–metal plasmonic waveguides. It is shown that the performance of the structure as a filter strongly depends on the asymmetry of the rectangular structure. An analytical model based on the analogy between MDM waveguides and the microwave transmission line is used to calculate the resonance wavelengths and explain the behavior of the filter. The bandwidth of spectra can be easily manipulated by adjusting the topological parameters of the filter. It is also demonstrated that by adjusting the bandwidth, the filter can be used for CWDM standard channels. The filter behavior is verified using the numerical finite difference time domain (FDTD) method. The filter is compact and has a footprint of 1 μm × 0.5 μm, which is suitable for integrated optical circuits. (paper) 4. Comparison of air-standard rectangular cycles with different specific heat models International Nuclear Information System (INIS) Wang, Chao; Chen, Lingen; Ge, Yanlin; Sun, Fengrui 2016-01-01 Highlights: • Air-standard rectangular cycle models are built and investigated. • Finite-time thermodynamics is applied. • Different dissipation models and variable specific heats models are adopted. • Performance characteristics of different cycle models are compared. - Abstract: In this paper, performance comparison of air-standard rectangular cycles with constant specific heat (SH), linear variable SH and non-linear variable SH are conducted by using finite time thermodynamics. The power output and efficiency of each cycle model and the characteristic curves of power output versus compression ratio, efficiency versus compression ratio, as well as power output versus efficiency are obtained by taking heat transfer loss (HTL) and friction loss (FL) into account. The influences of HTL, FL and SH on cycle performance are analyzed by detailed numerical examples. 5. Critical heat flux of subcooled flow boiling in narrow rectangular channels International Nuclear Information System (INIS) Kureta, Masatoshi; Akimoto, Hajime 1999-01-01 In relation to the high-heat-load devices such as a solid-target cooling channel of a high-intensity neutron source, burnout experiments were performed to obtain critical heat flux (CHF) data systematically for vertical upward flow in one-side heated rectangular channels. One of the objectives of this study was to study an extensibility of existing CHF correlations and models, which were proposed for a round tube, to rectangular channels for design calculation. Existing correlations and models were reviewed and compared with obtained data. Sudo's thin liquid layer dryout model, Griffel correlation and Bernath correlation were in good agreement with the experimental data for short-heated-length and low inlet water temperature conditions. (author) 6. Influence of old rectangular repair patches on the burst pressure of a gas pipeline International Nuclear Information System (INIS) Fazzini, Pablo Gabriel; Otegui, Jose Luis 2006-01-01 Seven full scale hydrostatic burst tests were carried out on pipes extracted from an API 5LX52 gas pipeline that contained rectangular and elliptical fillet welded patches and other repairs of different geometries. All breaks took place after widespread yielding. This analysis shows that the patches that generate greater risks are those that: (1) were attached to the pipeline at very low pressure (2) were placed to repair large defects (3) are rectangular, long in the direction of the pipe, and narrow (4) the quality of the weld is doubtful. Based on data reported by In Line Inspection (ILI), of the four conditions mentioned above, only the third can be assessed in order to quantify risks and to schedule replacements 7. Aeroacoustics of rectangular T-junctions subject to combined grazing and bias flows - An experimental investigation Science.gov (United States) Holmberg, Andreas; Karlsson, Mikael; Åbom, Mats 2015-03-01 Scattering matrices are determined experimentally and used to study the low-amplitude interaction, between the acoustic and the hydrodynamic fields in a T-junction of rectangular ducts. In particular, combinations of grazing and bias flows are investigated in the study. It is observed that for all flow combinations, waves incident on the junction at the downstream side only are attenuated, while waves incident at the other branches may be amplified or attenuated, depending on the Strouhal number. When bias in-flow is introduced to a grazing flow, there is first an increase and then a decrease in both amplification and attenuation, as the bias in-flow Mach number is increased. Comparing with T-junctions of circular ducts, the interaction is stronger for rectangular duct junctions. 8. Study on critical heat flux based on wavelet transform in rectangular narrow channels International Nuclear Information System (INIS) Zhou Tao; Ju Zhongyun; Zhang Lei; Li Jingjing; Sheng Cheng; Xiao Zejun 2014-01-01 Critical heat flux is very important for the safety of nuclear reactor, and observing temperature rise rate is a feasible method. The wavelet transform is used to analyze the CHF temperature rise curves in rectangular narrow channels, which can remove relative weaker interference and effectively judge CHF. Rectangular narrow channel can strengthen heat transfer and reduce CHF, whose characteristics are proved by temperature rise curves analyzed by wavelet transform. Respectively applying Daubechies function and Haar function is to guarantee the accuracy of the wavelet analysis, and Daubechies function is more accurate than Haar function in the detail signal processing from results. While the wavelet analysis and experimental results are compared and found in good agreement with the experimental results. (authors) 9. Study on critical heat flux based on wavelet transform in rectangular narrow channels International Nuclear Information System (INIS) Zhou Tao; Ju Zhongyun; Zhang Lei; Li Jingjing; Sheng Cheng; Xiao Zejun 2014-01-01 Critical heat flux is very important for nuclear reactor safety, and observing temperature rise rate is a feasible method. Through using the wavelet transform to analyze the CHF temperature rise curves in rectangular narrow channels, it can remove relative weaker interference and effectively judge CHF. Rectangular narrow channel can strengthen heat transfer and reduce CHF, whose characteristics are proved by, temperature rise curves analyzed by wavelet transform. Respectively applying Daubechies function and Haar function is for guarantee the accuracy of the wavelet analysis, and Daubechies function is more accurate than Haar function in the detail signal processing from results. While the wavelet analysis and experimental results are compared and found in good agreement with the experimental results. (authors) 10. Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme KAUST Repository Shen, Yang 2016-11-01 The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space–time conservation element and solution element (CE/SE) scheme. The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes. As the cross-sectional size decreases, critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines. Furthermore, multiple cellular structures are observed through examples with typical aspect ratios. Utilizing the visualization of detailed three-dimensional structures, their formation mechanism is further analyzed. 11. Positronium behaviour in elongated PPT, rectangular MgO and spherical Si nanocavities International Nuclear Information System (INIS) Eijt, S.W.H.; Falub, C.V.; Mijnarends, P.E.; Veen, A. van 2001-01-01 The 2D-ACAR para-Ps (p-Ps) spectrum of PPT aramid fibres, which contain structural elongated open spaces in the unit cell, is compared with the spectrum calculated for a Ps wave function in a rectangular cavity. Helium ion implantation in MgO and Si single crystals creates thin layers of nanosize rectangular and spherical cavities, respectively. Depth-selective 2D-ACAR experiments at the positron centre Delft allow the extraction of the p-Ps contribution from the spectra. In both samples p-Ps is not thermalised and has an average energy of the order of a few eV. The energy and momentum distribution of the Ps atoms are extracted and compared with Maxwell distributions. (orig.) 12. Positronium behaviour in elongated PPT, rectangular MgO and spherical Si nanocavities Energy Technology Data Exchange (ETDEWEB) Eijt, S.W.H.; Falub, C.V.; Mijnarends, P.E.; Veen, A. van [Interfaculty Reactor Inst., Delft Univ. of Technology (Netherlands) 2001-07-01 The 2D-ACAR para-Ps (p-Ps) spectrum of PPT aramid fibres, which contain structural elongated open spaces in the unit cell, is compared with the spectrum calculated for a Ps wave function in a rectangular cavity. Helium ion implantation in MgO and Si single crystals creates thin layers of nanosize rectangular and spherical cavities, respectively. Depth-selective 2D-ACAR experiments at the positron centre Delft allow the extraction of the p-Ps contribution from the spectra. In both samples p-Ps is not thermalised and has an average energy of the order of a few eV. The energy and momentum distribution of the Ps atoms are extracted and compared with Maxwell distributions. (orig.) Directory of Open Access Journals (Sweden) Zhong-Qi Yue 2012-01-01 14. Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme International Nuclear Information System (INIS) Shen Yang; Liu Kai-Xin; Chen Pu; Shen Hua; Zhang De-Liang 2016-01-01 The three-dimensional premixed H 2 -O 2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space–time conservation element and solution element (CE/SE) scheme. The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes. As the cross-sectional size decreases, critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines. Furthermore, multiple cellular structures are observed through examples with typical aspect ratios. Utilizing the visualization of detailed three-dimensional structures, their formation mechanism is further analyzed. (paper) 15. Realization of Rectangular Artificial Spin Ice and Direct Observation of High Energy Topology. Science.gov (United States) Ribeiro, I R B; Nascimento, F S; Ferreira, S O; Moura-Melo, W A; Costa, C A R; Borme, J; Freitas, P P; Wysin, G M; de Araujo, C I L; Pereira, A R 2017-10-25 In this work, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by a and b respectively). Arrays with three different aspect ratios γ = a/b = [Formula: see text], [Formula: see text] and [Formula: see text] are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy topology (doubly-charged monopoles) does not emerge in our theoretical model, while they are seen in experiments for large enough γ. Our results also insinuate that the string tension connecting two magnetic monopoles in a pair vanishes in rectangular lattices with a critical ratio γ = γ c = [Formula: see text], supporting previous theoretical predictions. 16. Tabu Search-based Synthesis of Digital Microfluidic Biochips with Dynamically Reconfigurable Non-rectangular Devices DEFF Research Database (Denmark) Maftei, Elena; Pop, Paul; Madsen, Jan 2010-01-01 they are highly reconfigurable and scalable. A digital biochip is composed of a two-dimensional array of cells, together with reservoirs for storing the samples and reagents. Several adjacent cells are dynamically grouped to form a virtual device, on which operations are performed. So far, researchers have...... assumed that throughout its execution, an operation is performed on a rectangular virtual device, whose position remains fixed. However, during the execution of an operation, the virtual device can be reconfigured to occupy a different group of cells on the array, forming any shape, not necessarily...... rectangular. In this paper, we present a Tabu Search metaheuristic for the synthesis of digital microfluidic biochips, which, starting from a biochemical application and a given biochip architecture, determines the allocation, resource binding, scheduling and placement of the operations in the application... 17. MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts International Nuclear Information System (INIS) Sidorenkov, S.I.; Hua, T.Q.; Araseki, H. 1994-01-01 Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. Argonne National Laboratory and The Efremov Institute have jointly defined several benchmark problems for code validation. The problems, described in this paper, are based on two series of rectangular duct experiments conducted at ANL; one of the series is a joint ANL/Efremov experiment. The geometries consist of variation of aspect ratio and wall thickness (thus wall conductance ratio). The transverse magnetic fields are uniform and nonuniform in the axial direction 18. Size effect of the elastic modulus of rectangular nanobeams: Surface elasticity effect International Nuclear Information System (INIS) Yao Hai-Yan; Fan Wen-Liang; Yun Guo-Hong 2013-01-01 The size-dependent elastic property of rectangular nanobeams (nanowires or nanoplates) induced by the surface elasticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 100 nm. It is also found that the theoretical results calculated by a modified core-shell model have more obvious advantages than those by other models (core-shell model and core-surface model) by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers. (condensed matter: structural, mechanical, and thermal properties) 19. Magnetohydrodynamic flow of generalized Maxwell fluids in a rectangular micropump under an AC electric field International Nuclear Information System (INIS) Zhao, Guangpu; Jian, Yongjun; Chang, Long; Buren, Mandula 2015-01-01 By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed 20. Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide. Science.gov (United States) Huang, Yen-Chieh; Wang, Tsong-Dong; Lin, Yen-Hou; Lee, Ching-Han; Chuang, Ming-Yun; Lin, Yen-Yin; Lin, Fan-Yi 2011-11-21 We report forward and backward THz-wave difference frequency generations at 197 and 469 μm from a PPLN rectangular crystal rod with an aperture of 0.5 (height in z) × 0.6 (width in y) mm(2) and a length of 25 mm in x. The crystal rod appears as a waveguide for the THz waves but as a bulk material for the optical mixing waves near 1.54 μm. We measured enhancement factors of 1.6 and 1.8 for the forward and backward THz-wave output powers, respectively, from the rectangular waveguide in comparison with those from a PPLN slab waveguide of the same length, thickness, and domain period under the same pump and signal intensity of 100 MW/cm(2). © 2011 Optical Society of America 1. Resonant frequency function of thickness-shear vibrations of rectangular crystal plates. Science.gov (United States) Wang, Ji; Yang, Lijun; Pan, Qiaoqiao; Chao, Min-Chiang; Du, Jianke 2011-05-01 The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers. By satisfying the major boundary conditions of the dominant thickness-shear mode, three wavenumber solutions are obtained and the frequency equation is constructed. It is shown the resonant frequency of thickness-shear mode is a second-order polynomial of aspect ratios. This conforms to known results in the simplest form and is applicable to further analytical and experimental studies of the frequency equation of quartz crystal resonators. 2. Effect of aspect ratio on the laminar-to-turbulent transition in rectangular channel International Nuclear Information System (INIS) Wang Chang; Gao Puzhen; Tan Sichao; Xu Chao 2012-01-01 Highlights: ► Effect of aspect ratio on the transition Reynolds number in rectangular channel is studied. ► Prediction correlation for transition Reynolds number is proposed. ► The initiation location of flow transition is studied. - Abstract: The critical Reynolds number of the laminar-to-turbulent transition in the rectangular channel is investigated based on the energy gradient method. The results show that the critical Reynolds number decreases with the increasing aspect ratio. However, the relative location of laminar breakdown does not migrate significantly with the variation of the aspect ratio. In addition, a theoretical correlation as a function of the aspect ratio is proposed to calculate the transition Reynolds number, and the predicted values are in good agreement with the experimental data obtained in the published literatures. 3. Rectangular illumination using a secondary optics with cylindrical lens for LED street light. Science.gov (United States) Chen, Hsi-Chao; Lin, Jun-Yu; Chiu, Hsuan-Yi 2013-02-11 The illumination pattern of an LED street light is required to have a rectangular distribution at a divergence-angle ratio of 7:3 for economical illumination. Hence, research supplying a secondary optics with two cylindrical lenses was different from free-form curvature for rectangular illumination. The analytical solution for curvatures with different ratio rectangles solved this detail by light tracing and boundary conditions. Similarities between the experiments and the simulation for a single LED and a 9-LED module were analyzed by Normalized Cross Correlation (NCC), and the error rate was studied by the Root Mean Square (RMS). The tolerance of position must be kept under ± 0.2 mm in the x, y and z directions to ensure that the relative illumination is over 99%. 4. Turbulent slurry flow measurement using ultrasonic Doppler method in rectangular pipe Science.gov (United States) Bareš, V.; Krupička, J.; Picek, T.; Brabec, J.; Matoušek, V. 2014-03-01 Distribution of velocity and Reynolds stress was measured using ultrasonic velocimetry in flows of water and Newtonian water-ballotini slurries in a pressurized Plexiglas pipe. Profiles of the measured parameters were sensed in the vertical plane at the centreline of a rectangular cross section of the pipe. Reference measurements in clear water produced expected symmetrical velocity profiles the shape of which was affected by secondary currents developed in the rectangular pipe. Slurry-flow experiments provided information on an effect of the concentration of solid grains on the internal structure of the flow. Strong attenuation of velocity fluctuations caused by a presence of grains was identified. The attenuation increased with the increasing local concentration of the grains. 5. Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme KAUST Repository Shen, Yang; Shen, Hua; Liu, Kai Xin; Chen, Pu; Zhang, De Liang 2016-01-01 The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space–time conservation element and solution element (CE/SE) scheme. The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes. As the cross-sectional size decreases, critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines. Furthermore, multiple cellular structures are observed through examples with typical aspect ratios. Utilizing the visualization of detailed three-dimensional structures, their formation mechanism is further analyzed. 6. Aperture and counting rate of rectangular telescopes for single and multiple parallel particles. [Spark chamber telescopes Energy Technology Data Exchange (ETDEWEB) D' Ettorre Piazzoli, B; Mannocchi, G [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Melone, S [Istituto di Fisica dell' Universita, Ancona, Italy; Picchi, P; Visentin, R [Comitato Nazionale per l' Energia Nucleare, Frascati (Italy). Laboratori Nazionali di Frascati 1976-06-01 Expressions for the counting rate of rectangular telescopes in the case of single as well as multiple particles are given. The aperture for single particles is obtained in the form of a double integral and analytical solutions are given for some cases. The intensity for different multiplicities of parallel particles is related to the geometry of the detectors and to the features of the radiation. This allows an absolute comparison between the data recorded by different devices. 7. Direct solution of the biharmonic equation on rectangular regions and the Poisson equation on irregular regions International Nuclear Information System (INIS) Buzbee, B.L.; Dorr, F.W. 1974-01-01 The discrete biharmonic equation on a rectangular region and the discrete Poisson equation on an irregular region can be treated as modifications to matrix problems with very special structure. It is shown how to use the direct method of matrix decomposition to formulate an effective numerical algorithm for these problems. For typical applications the operation count is O(N 3 ) for an N x N grid. Numerical comparisons with other techniques are included. (U.S.) 8. Air-water upward flow in prismatic channel of rectangular base International Nuclear Information System (INIS) Carvalho Tofani, P. de. 1984-01-01 Experiments had carried out to investigate the two-phase upward air-water flow structure, in a rectangular test section, by using independent measuring techniques, which comprise direct viewing and photography, electrical probes and gamma-ray attenuation. Flow pattern maps and correlations for flow pattern transitions, void fraction profiles, liquid film thickness and superficial average void fraction are proposed and compared to available data. (Author) [pt 9. Simulation of natural convection in a rectangular loop using finite elements International Nuclear Information System (INIS) Pepper, D.W.; Hamm, L.L.; Kehoe, A.B. 1984-01-01 A two-dimensional finite-element analysis of natural convection in a rectangular loop is presented. A psi-omega formulation of the Boussinesque approximation to the Navier-Stokes equation is solved by the false transient technique. Streamlines and isotherms at Ra = 10 4 are shown for three different modes of heating. The results indicate that corner effects should be considered when modeling flow patterns in thermosyphons 10. Slug-annular transition with particular reference to narrow rectangular ducts International Nuclear Information System (INIS) Jones, O.C. Jr.; Zuber, N. 1978-01-01 The transition from slug-flow to annular-flow in two-phase, gas-liquid mixtures is analyzed. A transition equation is derived which agrees well when compared with objective data determined from the disappearance of the low-void peak in the void fluctuation probability density in a rectangular duct. Application to other geometries is suggested and tabular recommendations given for determination of the drift flux coefficient, K, based on results in the literature 11. Forced convective boiling heat transfer of water in vertical rectangular narrow channel International Nuclear Information System (INIS) Chen, Chong; Gao, Pu-zhen; Tan, Si-chao; Chen, Han-ying; Chen, Xian-bing 2015-01-01 Highlights: • Chen correlation cannot well predict the coefficient of rectangular channel. • Kim and Mudawar correlation is the best one among the Chen type correlations. • Lazarek and Black correlation predicted 7.0% of data within the ±30% error band. • The new correlation can well predict the coefficient with a small MAE of 14.4%. - Abstract: In order to research the characteristics of boiling flows in a vertical rectangular narrow channel, a series of convective boiling heat transfer experiments are performed. The test section is made of stainless steel with an inner diameter of 2 × 40 mm and heated length of 1100 mm. The 3194 experimental data points are obtained for a heat flux range of 10–700 kW/m 2 , a mass flux range of 200–2400 kg/m 2 s, a system pressure range of 0.1–2.5 MPa, and a quality range of 0–0.8. Eighteen prediction models are used to predict the flow boiling heat transfer coefficient of the rectangular narrow channel and the predicted value is compared against the database including 3194 data points, the results show that Chen type correlations and Lazarek and Black type correlations are not suitable for the rectangular channel very much. The Kim and Mudawar correlation is the best one among the 18 models. A new correlation is developed based on the superposition concept of nucleate boiling and convective boiling. the new correlation is shown to provide a good prediction against the database, evidenced by an overall MAE of 14.4%, with 95.2% and 98.6% of the data falling within ±30% and ±35% error bands, respectively 12. Rectangular Gusset Plate Behaviour in Cold-Formed I-Type Steel Connections Directory of Open Access Journals (Sweden) Bučmys Ž. 2017-06-01 Full Text Available Cold-formed structure connections utilizing gusset plates are usually semi-rigid. This paper investigates the behaviours of rectangular gusset plates in cold-formed connections of elements whose columns and beams are made with lipped back-to-back C-sections. Methods of calculating strength and stiffness are necessary for such semi-rigid joints. The main task of this paper is to determine a method capable of calculating these characteristics. The proposed analytical method could then be easily adapted to the component method that is described in part 1993-1-8 of the Eurocode. This method allows us to calculate both the strength and stiffness of rectangular gusset plates, assuming that the joint deforms only in plane. This method of design moment resistance calculation was presented taking into account that an entire cross-section shall reach its yield stress. A technique of stiffness calculation was presented investigating the sum of deformations acquired at the bending moment and from shear forces which are transmitted from each beam bolt group. Calculation results according to the suggested method show good agreement of laboratory experimental results of specimens with numerical simulations. Two specimens of beam-to-column connections were tested in the laboratory. Lateral supports were used on the specimens to prevent lateral displacements in order to better investigate the behaviour of the rectangular gusset plate in plane. Experiments were simulated by modelling rectangular gusset plates using standard finite element software ANSYS Workbench 14.0. Three-dimensional solid elements were used for modelling and both geometric and material nonlinear analysis was performed. 13. Total reflection and cloaking by zero index metamaterials loaded with rectangular dielectric defects KAUST Repository Wu, Ying 2013-05-06 In this work, we investigate wave transmission property through a zero index metamaterial (ZIM) waveguide embedded with rectangular dielectric defects. We show that total reflection and total transmission (cloaking) can be achieved by adjusting the geometric sizes and/or permittivities of the defects. Our work provides another possibility of manipulating wave propagation through ZIM in addition to the widely studied dielectric defects with cylindrical geometries. 14. Release of metal ions from round and rectangular NiTi wires Directory of Open Access Journals (Sweden) Arash Azizi 2016-04-01 Full Text Available Abstract Background The aim of this study was to evaluate the amount of nickel and titanium ions released from two wires with different shapes and a similar surface area. Methods Forty round nickel-titanium (NiTi arch wires with the diameter of 0.020 in. and 40 rectangular NiTi arch wires with the diameter of 0.016 × 0.016 in. were immersed in artificial saliva during a 21-day period. The surface area of both wires was 0.44 in.2. Wires were separately dipped into polypropylene tubes containing 50 ml of buffer solution and were incubated and maintained at 37 °C. Inductively coupled plasma atomic emission spectrometry (ICP-AES was used to measure the amount of ions released after exposure lengths of 1 h, 24 h, 1 week, and 3 weeks. Repeated measures ANOVA and Tukey tests were used to evaluate the data. Results The results indicated that the amount of nickel and titanium concentrations was significantly higher in the rectangular wire group. The most significant release of all metals was measured after the first hour of immersion. In the rectangular wire group, 243 ± 4.2 ng/ml of nickel was released after 1 h, while 221.4 ± 1.7 ng/ml of nickel was released in the round wire group. Similarly, 243.3 ± 2.8 ng/ml of titanium was released in the rectangular wire group and a significantly lower amount of 211.9 ± 2.3 ng/ml of titanium was released in the round wire group. Conclusions Release of metal ions was influenced by the shape of the wire and increase of time. 15. Thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion International Nuclear Information System (INIS) Sumi, N. 1981-01-01 On the basis of the complex variable method for determining the stationary two-dimensional thermal stresses, the thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion under a steady state temperature field is considered. The solution is found by the analytic continuation argument and the modified mapping-collocation technique. Numerical results indicate a dependence of the orthotropic stress intensity factors on the thermal, elastic and geometrical constants over a certain parameter range. (orig.) 16. Influence of a circular jet arrangement in a rectangular tank on flow and suspended sediment release OpenAIRE Althaus, Jenzer; Isabella, Jolanda Maria 2011-01-01 With the objective of high sediment release out of a rectangular tank the performance of a circular jet arrangement has been investigated. Therefore, experiments with four jets arranged in a horizontal circle placed in water with quasi homogeneous sediment concentration were conducted. The induced circulation was analysed by measuring the flow field. The influence of the flow circulation on suspension and on sediment release through the water intake was studied and discussed. The offbottom cl... 17. Transmission line model for coupled rectangular double split‐ring resonators DEFF Research Database (Denmark) Yan, Lei; Tang, Meng; Krozer, Viktor 2011-01-01 In this work, a model based on a coupled transmission line formulation is developed for microstrip rectangular double split‐ring resonators (DSRRs). This model allows using the physical dimensions of the DSRRs as an input avoiding commonly used extraction of equivalent parameters. The model inclu...... simulations of the DSRR structures. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1311–1315, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25988... 18. Numerical investigation of boiling heat transfer on hydrocarbon mixture refrigerant in vertical rectangular minichannel OpenAIRE Huixing Li; Yu Liu 2016-01-01 In order to investigate the characteristics of boiling heat transfer for hydrocarbon mixture refrigerant in plate-fin heat exchanger which is used in the petrochemical industry field, a model was established on boiling heat transfer in vertical rectangular channel. The simulated results were compared with the experimental data from literature. The results show that the deviation between the simulated results and experimental data is within ±15%. Meanwhile, the characteristic of boiling heat t... 19. Estimation of Equivalent Thermal Conductivity for Impregnated Electrical Windings Formed from Profiled Rectangular Conductors OpenAIRE Ayat, Sabrina S; Wrobel, Rafal; Goss, James; Drury, David 2016-01-01 In order to improve accuracy and reduce model setting-up, and solving time in thermal analysis of electrical machines, transformers and wound passive components, the multi-material winding region is frequently homogenised. The existing winding homogenization techniques are predo-minantly focused on winding constructions with round conductors, where thermal conductivity across conductors is usually assumed to be isotropic. However, for the profiled rectangular conductors that assumption is no ... 20. Experimental verification of the axial and lateral stiffness of large W7-X rectangular bellows International Nuclear Information System (INIS) Reich, J.; Cardella, A.; Koppe, T.; Missal, B.; Capriccioli, A.; Loehrer, W.; Langone, S.; Sassone, P.C. 2006-01-01 The WENDELSTEIN 7-X (W7-X) is a super-conducting helical advanced stellarator. W7-X is provided with 299 ports, which connect the plasma vessel with the outer vessel. All the ports are equipped with bellows, which, during bake-out and final adjustment, compensate the relative movements of the vessels. The bellows have different shapes and dimensions ranging from 100 mm circular to 1170 x 570 mm rectangular sizes. During various load-cases the axial and lateral stiffness of all bellows will create a resulting spring-force which acts on the supports of the vessels directly. The higher the stiffness the more is the significant influence on the supports. The lateral stiffness which was calculated with the established standard EJMA-code (Expansion Joint Manufacturers Association) seemed to be relatively small. This appeared to be not correct in particular for non circular bellows. That is why the stiffness of rectangular, multi-layer bellows have then been re-calculated with the Finite Element Method (FEM) code ANSYS. The maximum difference between the FEM and EJMA code resulted to be up to 250 % in particular with movements along the longer side of the bellows. In order to clarify the differences a test-campaign with the largest rectangular bellows was performed. A special test rack allowed predefined displacements in pure lateral and axial directions taking into consideration of the friction in the moving elements. During the tests the load-displacement diagram was recorded permanently. The outcome of the FEM-results was then verified by the tests in axial and lateral directions. The EJMA-code is well proved for circular bellows. The tests showed that instead any calculation of rectangular bellows has to be confirmed by experiments. The paper summarises the calculation, describes the test activities, the apparatus and reports the final results. (author) 1. Environmental Effects on Flutter Characteristics of Laminated Composite Rectangular and Skew Panels Directory of Open Access Journals (Sweden) T.V.R. Chowdary 1996-01-01 Full Text Available A finite element method is presented for predicting the flutter response of laminated composite panels subjected to moisture concentration and temperature. The analysis accounts for material properties at elevated temperature and moisture concentration. The analysis is based on the first-order approximation to the linear piston theory and laminated plate theory that includes shear deformation. Both rectangular and skew panels are considered. Stability boundaries at moisture concentrations and temperatures for various lamination schemes and boundary conditions are discussed. 2. On the evaluation of rectangular plane-extended sources and their associated radiation fields International Nuclear Information System (INIS) Oner, Feda 2007-01-01 The objective of this paper is to provide an efficient and reliable analytical procedure for the evaluation of rectangular plane-extended sources and their associated radiation fields. Integrals with integer and non-integer values appear in the evaluation of the radiation field distribution. The latter results from a homogeneous rectangular plane target bombarded by hollow-cylindrical ion beams, the elementary areas anisotropically emitting in non-dispersive media, and fast neutrons produced in non-dispersive media by sealed-off neutron generating tubes (NGT) in an axi-symmetric situation [Hubbell, J.H., Bach, R.L., Lamkin, J.C., 1960. Radiation from a rectangular source. J. Res. NBS 64C (2), 121-137; Hubbell, J.H., 1963a. A power series buildup factor formulation. Application to rectangular and offaxis disk source problems. J. Res. NBS 67C, 291-306, Hubbell, J.H., 1963b. Dose fields from plane sources using point-source data. Nucleonics 21 (8), 144-148; Timus et al., 2005a. Plane rectengular tritium target response to excitation by uniform distributed normal accelerated deuteron beam. Appl. Radiat. Isot. 63, 823-839; Timus et al., 2005b. Analytical characterization of radiation fields generated by certain witch-type distributed axi-symmetrical ion beams. Arab J. Nucl. Sci. Appl. 38(I) 253-264]. In these references, the resulting expressions are represented as infinite linear combinations of basic J q (a, b, z) integrals. With the help of relation for J q (a, b, z), we can evaluate the high terms of energy expressions, which have been proposed in the above-mentioned references. The extensive test calculations show that the proposed algorithm in this work is the most efficient one in practical computations 3. Total reflection and cloaking by zero index metamaterials loaded with rectangular dielectric defects KAUST Repository Wu, Ying; Li, Jichun 2013-01-01 In this work, we investigate wave transmission property through a zero index metamaterial (ZIM) waveguide embedded with rectangular dielectric defects. We show that total reflection and total transmission (cloaking) can be achieved by adjusting the geometric sizes and/or permittivities of the defects. Our work provides another possibility of manipulating wave propagation through ZIM in addition to the widely studied dielectric defects with cylindrical geometries. 4. The influence of streamwise vortices on turbulent heat transfer in rectangular ducts with various aspect ratios International Nuclear Information System (INIS) Choi, Hang Seok; Park, Tae Seon 2013-01-01 Highlights: ► With changing aspect ratio, the effect of secondary flows on the turbulent heat transfer is scrutinized by a LES. ► The conditional sampling technique of instantaneous near-wall streamwise vortices is developed. ► Clockwise and counter-clockwise rotating streamwise vortices are sampled and discussed with the wall heat transfer. ► The hot-sweep motions of CW and CCW vortices clearly appear with increasing aspect ratio. -- Abstract: The effect of aspect ratio of rectangular duct on the turbulent flow and heat transfer is very important for its engineering applications. But the turbulent thermal fields have not been fundamentally scrutinized in spite of its engineering significance especially for cooling device. Hence, in the present study, large eddy simulation is applied to the turbulent flow and heat transfer in rectangular ducts with varying aspect ratio. The turbulent statistics of the flow and thermal quantities are calculated and the characteristics of wall Nusselt number are investigated for each rectangular duct. Especially, to scrutinize near-wall streamwise vortices, a conditional sampling technique is developed and adopted. Clockwise and counter-clockwise rotating streamwise vortices are sampled and the probability density function of the vortex circulation Reynolds number and wall Nusselt number are calculated. From the results, the time-averaged secondary flow caused by instantaneous vortical motions has a great effect on the heat and momentum transport of the flow in the rectangular ducts. Hence, the wall Nusselt number is enhanced near the downwash flow region of the secondary flow. However, with increasing the aspect ratio, the effects of the hot-sweep flow of the clockwise and counter-clockwise rotating vortices become equally dominant near the wall normal bisector of the ducts. During time averaging process, these two counter-rotating vortices are canceled out each other diminishing a secondary flow but they still enhance the 5. SiPM response to long and intense light pulses Energy Technology Data Exchange (ETDEWEB) Vinogradov, S., E-mail: [email protected] [University of Liverpool and Cockcroft Institute, Sci-Tech Daresbury, Keckwick Lane, Warrington WA4 4AD (United Kingdom); P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 119991 Leninskiy prospekt 53, Moscow (Russian Federation); Arodzero, A. [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139 (United States); RadiaBeam Technologies Inc., 1717 Stewart St., Santa Monica, CA 90404 (United States); Lanza, R.C. [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139 (United States); Welsch, C.P. [University of Liverpool and Cockcroft Institute, Sci-Tech Daresbury, Keckwick Lane, Warrington WA4 4AD (United Kingdom) 2015-07-01 Recently Silicon Photomultipliers (SiPMs) have become well recognized as the detector of choice for various applications which demand good photon number resolution and time resolution of short weak light pulses in the nanosecond time scale. In the case of longer and more intensive light pulses, SiPM performance gradually degrades due to dark noise, afterpulsing, and non-instant cell recovering. Nevertheless, SiPM benefits are expected to overbalance their drawbacks in applications such as X-ray cargo inspection using Scintillation-Cherenkov detectors and accelerator beam loss monitoring with Cherenkov fibres, where light pulses of a microsecond time scale have to be detected with good amplitude and timing resolution in a wide dynamic range of 10{sup 5}–10{sup 6}. This report is focused on transient characteristics of a SiPM response on a long rectangular light pulse with special attention to moderate and high light intensities above the linear dynamic range. An analytical model of the transient response and an initial consideration of experimental results in comparison with the model are presented. 6. Buoyancy effects in vertical rectangular duct with coplanar magnetic field and single sided heat load Science.gov (United States) Kostichev, P. I.; Poddubnyi, I. I.; Razuvanov, N. G. 2017-11-01 In some DEMO blanket designs liquid metal flows in vertical ducts of rectangular cross-section between ceramic breeder units providing their cooling. Heat exchange in these conditions is governed by the influence of magnetic field (coplanar) and by buoyancy effects that depend on the flow orientation to the gravity vector (downward and upward flow). Magnetohydrodynamic and heat transfer of liquid metal in vertical rectangular ducts is not well researched. Experimental study of buoyancy effects in rectangular duct with coplanar magnetic field for one-sided heat load and downward and upward flowsis presented in this paper. The detail research with has been done on mercury MHD close loop with using of the probe technique allow to discover several advantageous and disadvantageous effects. The intensive impact of buoyancy force has been observed in a few regime of downward flow which has been laminarized by magnetic field. Due to the development in the flow of the secondary large-scale vortices heat transfer improved and the temperature fluctuations of the abnormally high intensity have been fixed. On the contrary, in the upward flow the buoyancy force stabilized the flow which lead to decreasing of the turbulence heat transfer ratio and, consequently, deterioration of heat transfer. 7. Fluid Flow and Infrared Image Analyses on Endwall Fitted with Short Rectangular Plate Fin Institute of Scientific and Technical Information of China (English) Kenyu OYAKAWA; Islam Md. DIDARUL; Minoru YAGA 2006-01-01 An experimental investigation is carried out to study fluid flow and heat transfer characteristics on the endwall fitted with arrays ( 7 × 7 ) of short rectangular plate fins of different pattern (co-angular and zigzag) for different pitch ratio. Experiments were conducted in a rectangular duct of 50 mm height for an air flow of Reynolds number ranged from 18750 to 62500 based on the equivalent diameter and air velocity of the duct. Infrared image analysis technique was employed to make clear the characteristics of local heat transfer coefficients on fin base, endwall and overall surface. Flow pattern around the short rectangular plates were visualized by inducing fluorescent dye in a water channel and longitudinal vortices were observed. Increasing the distance between plates in flow direction causes heat transfer enhancement for co-angular pattern, while decreasing the distance causes heat transfer enhancement for zigzag pattern. Zigzag pattern with pitch ratio 2 is found to be more effective in heat transfer enhancement than any other cases investigated. 8. Development of a design methodology for hydraulic pipelines carrying rectangular capsules International Nuclear Information System (INIS) Asim, Taimoor; Mishra, Rakesh; Abushaala, Sufyan; Jain, Anuj 2016-01-01 The scarcity of fossil fuels is affecting the efficiency of established modes of cargo transport within the transportation industry. Efforts have been made to develop innovative modes of transport that can be adopted for economic and environmental friendly operating systems. Solid material, for instance, can be packed in rectangular containers (commonly known as capsules), which can then be transported in different concentrations very effectively using the fluid energy in pipelines. For economical and efficient design of such systems, both the local flow characteristics and the global performance parameters need to be carefully investigated. Published literature is severely limited in establishing the effects of local flow features on system characteristics of Hydraulic Capsule Pipelines (HCPs). The present study focuses on using a well validated Computational Fluid Dynamics (CFD) tool to numerically simulate the solid-liquid mixture flow in both on-shore and off-shore HCPs applications including bends. Discrete Phase Modelling (DPM) has been employed to calculate the velocity of the rectangular capsules. Numerical predictions have been used to develop novel semi-empirical prediction models for pressure drop in HCPs, which have then been embedded into a robust and user-friendly pipeline optimisation methodology based on Least-Cost Principle. - Highlights: • Local flow characteristics in a pipeline transporting rectangular capsules. • Development of prediction models for the pressure drop contribution of capsules. • Methodology developed for sizing of Hydraulic Capsule Pipelines. • Implementation of the developed methodology to obtain optimal pipeline diameter. 9. Lattice Boltzmann Simulation of the Hydrodynamic Entrance Region of Rectangular Microchannels in the Slip Regime Directory of Open Access Journals (Sweden) Niya Ma 2018-02-01 Full Text Available Developing a three-dimensional laminar flow in the entrance region of rectangular microchannels has been investigated in this paper. When the hydrodynamic development length is the same magnitude as the microchannel length, entrance effects have to be taken into account, especially in relatively short ducts. Simultaneously, there are a variety of non-continuum or rarefaction effects, such as velocity slip and temperature jump. The available data in the literature appearing on this issue is quite limited, the available study is the semi-theoretical approximate model to predict pressure drop of developing slip flow in rectangular microchannels with different aspect ratios. In this paper, we apply the lattice Boltzmann equation method (LBE to investigate the developing slip flow through a rectangular microchannel. The effects of the Reynolds number (1 < Re < 1000, channel aspect ratio (0 < ε < 1, and Knudsen number (0.001 < Kn < 0.1 on the dimensionless hydrodynamic entrance length, and the apparent friction factor, and Reynolds number product, are examined in detail. The numerical solution of LBM can recover excellent agreement with the available data in the literature, which proves its accuracy in capturing fundamental fluid characteristics in the slip-flow regime. 10. The analysis of radiation parameters dependence of rectangular waveguide on its dimensions change Directory of Open Access Journals (Sweden) Manoilov V.P. 2016-04-01 Full Text Available Analysis of radiation from 3 centimeter waveband rectangular waveguide at the change of the side sizes is carried out for the purpose of efficiency estimation of its use as reflector parabolic antenna exciter. Some performance characteristics of radioelectronic systems depend on antennas types which are used. Recently, the development of antenna systems occurred mainly not by creating new, and by improving the parameters and characteristics of existing antennas. Therefore, there is a practical need to find ways to improve their elements. A detailed analysis of the radiation from the open end of the rectangular waveguide allows to specify exactly which of its parameters and characteristics need to be improved. Dependence charts of directional diagram (DD in planes E and H, radiation power, directivity upon variation of side sizes a, b are received. Dependence charts of attenuation coefficient upon frequency for wave types H10, H01, H02, H11, E11 are drawn up. Estimation of reasonability of using rectangular waveguide as reflector parabolic antenna exciter is received. 11. Experimental investigation on flow instability of forced circulation in a vertical mini-rectangular channel International Nuclear Information System (INIS) Yu Zhiting; Tan Sichao; Yuan Hongsheng; Zhuang Nailiang; Chen Hanying 2015-01-01 An experimental study was conducted to investigate the flow instability in a vertical mini-rectangular channel with distilled water as the working fluid. The rotational speed of the primary pump is gradually reduced to lower the inlet flow rate until the flow becomes unstable, while maintaining all other thermal parameters unchanged. Three types of instability, characterized by large amplitude oscillation, small amplitude oscillation and flow excursion, were identified from the experimental data. A stability map for the vertical mini-rectangular channel under forced circulation was established based on the Subcooling number and Phase Change number. The oscillation periods were correlated with the fluid transit time and the boiling delay time. A flow pattern map for vertical upward flow in a mini-rectangular channel was applied to confirm the flow patterns during the oscillation. The mechanisms of the three types of instability were obtained by considering several types of flow instabilities and comparing them with the oscillations observed in this work. (author) 12. VIBRATION CONTROL OF RECTANGULAR CROSS-PLY FRP PLATES USING PZT MATERIALS Directory of Open Access Journals (Sweden) DILEEP KUMAR K 2017-12-01 Full Text Available Piezoelectric materials are extensively employed in the field of structures for condition monitoring, smart control and testing applications. The piezoelectric patches are surface bonded to a composite laminate plate and used as vibration actuators. The coupling effects between the mechanical and electric properties of piezoelectric materials have drawn significant attention for their potential applications. In the present work, an analytical solution of the vibration response of a simply supported laminate rectangular plate under time harmonic electrical loading is obtained and a concept is developed for an approximate dynamic model to the vibration response of the simply supported orthotropic rectangular plates excited by a piezoelectric patch of variable rectangular geometry and location. A time harmonic electric voltages with the same magnitude and opposite sign are applied to the two symmetric piezoelectric actuators, which results in the bending moment on the plate. The main objective of the work is to obtain an analytical solution for the vibration amplitude of composite plate predicted from plate theory. The results demonstrate that the vibration modes can be selectively excited and the geometry of the PZTactuator shape remarkably affects the distribution of the response among modes. Thus according to the desired degree shape control it is possible to tailor the shape, size and properly designed control algorithm of the actuator to either excite or suppress particular modes. 13. Rectangular Schlumberger resistivity arrays for delineating vadose zone clay-lined fractures in shallow tuff International Nuclear Information System (INIS) Miele, M.; Laymon, D.; Gilkeson, R.; Michelotti, R. 1996-01-01 Rectangular Schlumberger arrays can be used for 2-dimensional lateral profiling of apparent resistivity at a unique current electrode separation, hence single depth of penetration. Numerous apparent resistivity measurements are collected moving the potential electrodes (fixed MN spacing) within a rectangle of defined dimensions. The method provides a fast, cost-effective means for the collection of dense resistivity data to provide high-resolution information on subsurface hydrogeologic conditions. Several rectangular Schlumberger resistivity arrays were employed at Los Alamos National Laboratory (LANL) from 1989 through 1995 in an area adjacent to and downhill from an outfall pipe, septic tank, septic drainfield, and sump. Six rectangular arrays with 2 AB spacings were used to delineate lateral low resistivity anomalies that may be related to fractures that contain clay and/or vadose zone water. Duplicate arrays collected over a three year time period exhibited very good data repeatability. The properties of tritium make it an excellent groundwater tracer. Because tritium was present in discharged water from all of the anthropogenic sources in the vicinity it was used for this purpose. One major low resistivity anomaly correlates with relatively high tritium concentrations in the tuff. This was determined from borehole samples collected within and outside of the anomalous zone. The anomaly is interpreted to be due to fractures that contain clay from the soil profile. The clay was deposited in the fractures by aeolian processes and by surface water infiltration. The fractures likely served as a shallow vadose zone groundwater pathway 14. Numerical investigation of boiling heat transfer on hydrocarbon mixture refrigerant in vertical rectangular minichannel Directory of Open Access Journals (Sweden) Huixing Li 2016-05-01 Full Text Available In order to investigate the characteristics of boiling heat transfer for hydrocarbon mixture refrigerant in plate-fin heat exchanger which is used in the petrochemical industry field, a model was established on boiling heat transfer in vertical rectangular channel. The simulated results were compared with the experimental data from literature. The results show that the deviation between the simulated results and experimental data is within ±15%. Meanwhile, the characteristic of boiling heat transfer was investigated in vertical rectangular minichannel of plate-fin heat exchanger. The results show that the boiling heat transfer coefficient increases with the increase in quality and mass flux and is slightly impacted by the heat flux. This is because that the main boiling mechanism is forced convective boiling while the contribution of nucleate boiling is slight. The correlation of Liu and Winterton is in good agreement with the simulation results. The deviation between correlation calculations and simulation results is mostly less than ±15%. These results will provide some constructive instructions for the understanding of saturated boiling mechanism in a vertical rectangular minichannel and the prediction of heat transfer performance in plate-fin heat exchanger. 15. Premature and stable critical heat flux for downward flow in a narrow rectangular channel International Nuclear Information System (INIS) Lee, Juhyung; Chang, Soon Heung; Jeong, Yong Hoon; Jo, Daeseong 2014-01-01 It has been recommended that RRs and MTRs be designed to have sufficient margins for CHF and the onset of FI as well, since unstable flow could leads to premature CHF under very low wall heat flux in comparison to stable CHF. Even the fact and previous studies, however, the understanding of relationship among FI, premature CHF and stable CHF is not sufficient to date. In this regards, subcooled flow boiling in a vertical rectangular channel was experimentally investigated to enhance the understanding of the CHF and the effect of the two-phase flow instability on it under low pressure conditions, especially for downward flow which was adopted for Jordan Research and Training Reactor (JRTR) and Kijang research reactor (KJRR) to achieve easier fuel and irradiation rig loading. In this study, CHF for downward flow of water under low pressure in narrow rectangular channel was experimentally investigated. For conditions such as downward flow, narrow rectangular channel and low pressure, it has been deduced from literature that flow instability could largely influence on triggering CHF at lower heat flux, i. e. premature CHF. Total 54 CHF data, which includes premature and stable data was obtained for various fluid conditions and system configurations including inlet stiffness. The upper and lower boundaries of CHF were newly proposed based on the experiment 16. Ultrashort Laser Pulse Phenomena CERN Document Server Diels, Jean-Claude 2006-01-01 Ultrashort Laser Pulse Phenomena, 2e serves as an introduction to the phenomena of ultra short laser pulses and describes how this technology can be used to examine problems in areas such as electromagnetism, optics, and quantum mechanics. Ultrashort Laser Pulse Phenomena combines theoretical backgrounds and experimental techniques and will serve as a manual on designing and constructing femtosecond (""faster than electronics"") systems or experiments from scratch. Beyond the simple optical system, the various sources of ultrashort pulses are presented, again with emphasis on the basic 17. Design and fabrication of a large rectangular magnetic cusp plasma source for high intensity neutral beam injectors International Nuclear Information System (INIS) Biagi, L.A.; Berkner, K.H.; Ehlers, K.W.; Paterson, J.A.; Porter, J.R. 1979-11-01 The design and fabrication techniques for a large, rectangular magnetic bucket plasma source are described. This source is compatible with the accelerator structures for the TFTR and DIII neutral-beam systems 18. Effect of a Finite Trailing Edge Thickness on the Drag of Rectangular and Delta Wings at Supersonic Speeds National Research Council Canada - National Science Library Klunker, E 1952-01-01 The effect of a finite trailing-edge thickness on the pressure drag of rectangular and delta wings with truncated diamond-shaped airfoil sections with a given thickness ratio is studied for supersonic... 19. Analysis of some coplanar transmission lines: coplanar coupled lines, coplanar coupled striplines, and coplanar coupled lines with rectangular microshield Science.gov (United States) Yuan, Naichang; He, Jianguo; Yao, Demiao; Dai, Qin; Lin, Weigan 1995-06-01 Two types of coplanar transmission lines, rectangular microshield coplanar coupled lines (RMCCL) and coplanar coupled rectangular microshield lines (CCRML), are proposed for MMIC applications. These are developed from coplanar coupled lines (CCL) and coplanar coupled strip lines (CCS). Analytic formulas are presented for calculating the quasistatic TEM parameters of these coupled lines by means of exact conformal mapping techniques. Numerical results are also presented to illustrate the properties of these coplanar transmission lines. International Nuclear Information System (INIS) Jonah, C.D.; Andong Liu; Mulac, W.A. 1987-01-01 Gas phase pulse radiolysis, a technique which can be used to study many different phenomena in chemistry and physics, is discussed. As a source of small radicals, pulse radiolysis is important to the field of chemistry, particularly to combustion and atmospheric kinetics. The reactions of 1,3-butadiene, allene, ethylene and acetylene with OH are presented. 52 refs., 1 fig., 1 tab 1. Pulse duration discriminator International Nuclear Information System (INIS) Kosakovskij, L.F. 1980-01-01 Basic circuits of a discriminator for discrimination of pulses with the duration greater than the preset one, and of a multifunctional discriminator allowing to discriminate pulses with the duration greater (tsub(p)>tsub(s)) and lesser (tsub(p) tsub(s) and with the duration tsub(p) [ru International Nuclear Information System (INIS) Sauer, M.C. Jr. 1981-01-01 Characteristics of various sources of pulsed radiation are examined from the viewpoint of their importance to the radiation chemist, and some examples of uses of such sources are mentioned. A summary is given of the application of methods of physical dosimetry to pulsed sources, and the calibration of convenient chemical dosimeters by physical dosimetry is outlined. 7 figures, 1 table 3. Pulsed neutron generator International Nuclear Information System (INIS) Bespalov, D.F.; Bykovskii, Yu.A.; Vergun, I.I.; Kozlovskii, K.I.; Kozyrev, Yu.P.; Leonov, R.K.; Simagin, B.I.; Tsybin, A.S.; Shikanov, A.Ie. 1986-03-01 The paper describes a new device for generating pulsed neutron fields, utilized in nuclear geophysics for carrying out pulsed neutron logging and activation analysis under field conditions. The invention employs a sealed-off neutron tube with a laser ion source which increases neutron yield to the level of 10 neutrons per second or higher. 2 refs., 1 fig 4. Bipolar pulse generator for intense pulsed ion beam accelerator International Nuclear Information System (INIS) Ito, H.; Igawa, K.; Kitamura, I.; Masugata, K. 2007-01-01 A new type of pulsed ion beam accelerator named ''bipolar pulse accelerator'' (BPA) has been proposed in order to improve the purity of intense pulsed ion beams. To confirm the principle of the BPA, we developed a bipolar pulse generator for the bipolar pulse experiment, which consists of a Marx generator and a pulse forming line (PFL) with a rail gap switch on its end. In this article, we report the first experimental result of the bipolar pulse and evaluate the electrical characteristics of the bipolar pulse generator. When the bipolar pulse generator was operated at 70% of the full charge condition of the PFL, the bipolar pulse with the first (-138 kV, 72 ns) and the second pulse (+130 kV, 70 ns) was successfully obtained. The evaluation of the electrical characteristics indicates that the developed generator can produce the bipolar pulse with fast rise time and sharp reversing time 5. Pulse induction heating Energy Technology Data Exchange (ETDEWEB) Vasiliev, A S; Kachanov, B Y; Kogan, B V 1993-12-31 Induction heating and three types of pulse processes were studied. It was found that in pulse processes the frequency and pulse duration of heat treatments do not remain constant. High frequency pulse heat treatments can be used on sprayed coatings; such treatments will result in stronger surfaces with no cracks. For induction hardening, the rate of specific power was 1 to 1.5 kW/sq.cm, for forging it was 0.2 to 0.3 kW/sq.cm and for melting it was 0.05 to 0.1 kW/sq.cm. The application of pulse heating will result in higher rates of specific power. 6. Pulse Distortion in Saturated Fiber Optical Parametric Chirped Pulse Amplification DEFF Research Database (Denmark) Lali-Dastjerdi, Zohreh; Da Ros, Francesco; Rottwitt, Karsten 2012-01-01 Fiber optical parametric chirped pulse amplification is experimentally compared for different chirped pulses in the picosecond regime. The amplified chirped pulses show distortion appearing as pedestals after recompression when the amplifier is operated in saturation.......Fiber optical parametric chirped pulse amplification is experimentally compared for different chirped pulses in the picosecond regime. The amplified chirped pulses show distortion appearing as pedestals after recompression when the amplifier is operated in saturation.... 7. The effect of the two tailored femtosecond laser pulses in the enhancement of methane dissociation International Nuclear Information System (INIS) Sadighi-Bonabi, R.; Dehghani, Z.; Irani, E. 2010-01-01 Complete text of publication follows. Based on the gradient optimization method a useful approach for dissociation of the methane molecule is introduced. This analytical model produces an optimized two tailored rectangular laser pulses which dissociates the molecular ion CH 4 + with maximum probability of 1. In this approach the field assisted dissociation is used by a semi-classical view. It is assumed that only the selective dissociative bond is in direction of the laser electric field are effective. Saturation is found for dissociation of the mentioned molecular bond, where the first pulse should have higher intensity than the second pulse. In addition to that, the sensitivity of the dissociation probability to the initial bond length and the control of the desired product channel by variation of the laser intensity and its duration of laser field is presented. 8. Method for measuring the resistive transition and critical current in superconductors using pulsed current International Nuclear Information System (INIS) McGinnis, W.C.; Jones, T.E. 1993-01-01 A method is described for measuring the intragranular critical current of a granular superconductive material, comprising the steps of: conducting a substantially rectangular electronic pulse through said material so as to conduct a current through said material such that when said intragranular critical current of said material is exceeded, any grains present in said material are in a superconducting state when said current is less than said intragranular critical current, said material having a critical temperature; measuring said current through said material while conducting said pulse; measuring a voltage difference across said material while conducting said pulse; and determining said intragranular critical current through said material by varying said current to discern a current level at which an electrical resistance of said material increases to that of a non-superconducting state as the grains of said material transition from said superconducting to said non-superconducting state 9. Analog Amplitude Modulation of a High Voltage, Solid State Inductive Adder, Pulse Generator Using MOSFETS International Nuclear Information System (INIS) Gower, E J; Sullivan, J S 2002-01-01 10. Time and Frequency Localized Pulse Shape for Resolution Enhancement in STFT-BOTDR Directory of Open Access Journals (Sweden) Linqing Luo 2016-01-01 Full Text Available Short-Time Fourier Transform-Brillouin Optical Time-Domain Reflectometry (STFT-BOTDR implements STFT over the full frequency spectrum to measure the distributed temperature and strain along the optic fiber, providing new research advances in dynamic distributed sensing. The spatial and frequency resolution of the dynamic sensing are limited by the Signal to Noise Ratio (SNR and the Time-Frequency (T-F localization of the input pulse shape. T-F localization is fundamentally important for the communication system, which suppresses interchannel interference (ICI and intersymbol interference (ISI to improve the transmission quality in multicarrier modulation (MCM. This paper demonstrates that the T-F localized input pulse shape can enhance the SNR and the spatial and frequency resolution in STFT-BOTDR. Simulation and experiments of T-F localized different pulses shapes are conducted to compare the limitation of the system resolution. The result indicates that rectangular pulse should be selected to optimize the spatial resolution and Lorentzian pulse could be chosen to optimize the frequency resolution, while Gaussian shape pulse can be used in general applications for its balanced performance in both spatial and frequency resolution. Meanwhile, T-F localization is proved to be useful in the pulse shape selection for system resolution optimization. 11. Optical pulse compression International Nuclear Information System (INIS) Glass, A.J. 1975-01-01 The interest in using large lasers to achieve a very short and intense pulse for generating fusion plasma has provided a strong impetus to reexamine the possibilities of optical pulse compression at high energy. Pulse compression allows one to generate pulses of long duration (minimizing damage problems) and subsequently compress optical pulses to achieve the short pulse duration required for specific applications. The ideal device for carrying out this program has not been developed. Of the two approaches considered, the Gires--Tournois approach is limited by the fact that the bandwidth and compression are intimately related, so that the group delay dispersion times the square of the bandwidth is about unity for all simple Gires--Tournois interferometers. The Treacy grating pair does not suffer from this limitation, but is inefficient because diffraction generally occurs in several orders and is limited by the problem of optical damage to the grating surfaces themselves. Nonlinear and parametric processes were explored. Some pulse compression was achieved by these techniques; however, they are generally difficult to control and are not very efficient. (U.S.) 12. RF Pulsed Heating Energy Technology Data Exchange (ETDEWEB) Pritzkau, David P. 2002-01-03 RF pulsed heating is a process by which a metal is heated from magnetic fields on its surface due to high-power pulsed RF. When the thermal stresses induced are larger than the elastic limit, microcracks and surface roughening will occur due to cyclic fatigue. Pulsed heating limits the maximum magnetic field on the surface and through it the maximum achievable accelerating gradient in a normal conducting accelerator structure. An experiment using circularly cylindrical cavities operating in the TE{sub 011} mode at a resonant frequency of 11.424 GHz is designed to study pulsed heating on OFE copper, a material commonly used in normal conducting accelerator structures. The high-power pulsed RF is supplied by an X-band klystron capable of outputting 50 MW, 1.5 {micro}s pulses. The test pieces of the cavity are designed to be removable to allow testing of different materials with different surface preparations. A diagnostic tool is developed to measure the temperature rise in the cavity utilizing the dynamic Q change of the resonant mode due to heating. The diagnostic consists of simultaneously exciting a TE{sub 012} mode to steady-state in the cavity at 18 GHz and measuring the change in reflected power as the cavity is heated from high-power pulsed RF. Two experimental runs were completed. One run was executed at a calculated temperature rise of 120 K for 56 x 10{sup 6} pulses. The second run was executed at a calculated temperature rise of 82 K for 86 x 10{sup 6} pulses. Scanning electron microscope pictures show extensive damage occurring in the region of maximum temperature rise on the surface of the test pieces. 13. Use of rectangular grid miniplates for fracture fixation at the mandibular angle. Science.gov (United States) Hochuli-Vieira, Eduardo; Ha, Thi Khanh Linh; Pereira-Filho, Valfrido Antonio; Landes, Constantin Alexander 2011-05-01 14. One-dimensional acoustic standing waves in rectangular channels for flow cytometry. Science.gov (United States) Austin Suthanthiraraj, Pearlson P; Piyasena, Menake E; Woods, Travis A; Naivar, Mark A; Lόpez, Gabriel P; Graves, Steven W 2012-07-01 Flow cytometry has become a powerful analytical tool for applications ranging from blood diagnostics to high throughput screening of molecular assemblies on microsphere arrays. However, instrument size, expense, throughput, and consumable use limit its use in resource poor areas of the world, as a component in environmental monitoring, and for detection of very rare cell populations. For these reasons, new technologies to improve the size and cost-to-performance ratio of flow cytometry are required. One such technology is the use of acoustic standing waves that efficiently concentrate cells and particles to the center of flow channels for analysis. The simplest form of this method uses one-dimensional acoustic standing waves to focus particles in rectangular channels. We have developed one-dimensional acoustic focusing flow channels that can be fabricated in simple capillary devices or easily microfabricated using photolithography and deep reactive ion etching. Image and video analysis demonstrates that these channels precisely focus single flowing streams of particles and cells for traditional flow cytometry analysis. Additionally, use of standing waves with increasing harmonics and in parallel microfabricated channels is shown to effectively create many parallel focused streams. Furthermore, we present the fabrication of an inexpensive optical platform for flow cytometry in rectangular channels and use of the system to provide precise analysis. The simplicity and low-cost of the acoustic focusing devices developed here promise to be effective for flow cytometers that have reduced size, cost, and consumable use. Finally, the straightforward path to parallel flow streams using one-dimensional multinode acoustic focusing, indicates that simple acoustic focusing in rectangular channels may also have a prominent role in high-throughput flow cytometry. Copyright © 2012 Elsevier Inc. All rights reserved. 15. Modeling the interference of vortex-induced vibration and galloping for a slender rectangular prism Science.gov (United States) Mannini, Claudio; Massai, Tommaso; Marra, Antonino Maria 2018-04-01 Several bluff bodies in an airflow, such as rectangular cylinders with moderate side ratio, in particular conditions of mass and damping can experience the interference of vortex-induced vibration (VIV) and galloping. This promotes a combined instability, which one may call "unsteady galloping", with peculiar features and possibly large vibration amplitudes in flow speed ranges where no excitation is predicted by classical theories. The mathematical model proposed between the 70's and the 80's by Prof. Y. Tamura to simulate this phenomenon was considered here for the case study of a two-dimensional rectangular cylinder with a side ratio of 1.5, having the shorter section side perpendicular to the smooth airflow. This wake-oscillator model relies on the linear superposition of the unsteady wake force producing VIV excitation and the quasi-steady force that is responsible for galloping. The model formulation was slightly modified, and the way to determine a crucial parameter was changed, revealing a previously unexplored behavior of the equations. In the present form, the model is able to predict the dynamic response of the rectangular cylinder with a satisfactory qualitative and, to a certain extent, quantitative agreement with the experimental data, although the limitations of the present approach are clearly highlighted in the paper. The mathematical modeling of unsteady galloping and the analysis of the results offer a deep insight into this complicated phenomenon and its nonlinear features. The model also represents a useful engineering tool to estimate the vibration of a structure or structural element for which the interference of VIV and galloping is envisaged. 16. Polydisperse particle-driven gravity currents in non-rectangular cross section channels Science.gov (United States) Zemach, T. 2018-01-01 We consider a high-Reynolds-number gravity current generated by polydisperse suspension of n types of particles distributed in a fluid of density ρi. Each class of particles in suspension has a different settling velocity. The current propagates along a channel of non-rectangular cross section into an ambient fluid of constant density ρa. The bottom and top of the channel are at z = 0, H, and the cross section is given by the quite general form -f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. The flow is modeled by the one-layer shallow-water equations obtained for the time-dependent motion. We solve the problem by a finite-difference numerical code to present typical height h, velocity u, and mass fractions of particle (concentrations) (ϕ( j), j = 1, …, n) profiles. The runout length of suspensions in channels of power-law cross sections is analytically predicted using a simplified depth-averaged "box" model. We demonstrate that any degree of polydispersivity adds to the runout length of the currents, relative to that of equivalent monodisperse currents with an average settling velocity. The theoretical predictions are supported by the available experimental data. The present approach is a significant generalization of the particle-driven gravity current problem: on the one hand, now the monodisperse current in non-rectangular channels is a particular case of n = 1. On the other hand, the classical formulation of polydisperse currents for a rectangular channel is now just a particular case, f(z) = const., in the wide domain of cross sections covered by this new model. 17. Numerical Simulation of Passage of a Neutrophil through a Rectangular Channel with a Moderate Constriction Science.gov (United States) Shirai, Atsushi; Masuda, Sunao 2013-01-01 The authors have previously presented a mathematical model to predict transit time of a neutrophil through an alveolar capillary segment which was modeled as an axisymmetric arc-shaped constriction settled in a cylindrical straight pipe to investigate the influence of entrance curvature of a capillary on passage of the cell. The axially asymmetric cross section of a capillary also influences the transit time because it requires three-dimensional deformation of a cell when it passes through the capillary and could lead to plasma leakage between the cell surface and the capillary wall. In this study, a rectangular channel was introduced, the side walls of which were moderately constricted, as a representative of axially asymmetric capillaries. Dependence of transit time of a neutrophil passing through the constriction on the constriction geometry, i.e., channel height, throat width and curvature radius of the constriction, was numerically investigated, the transit time being compared with that through the axisymmetric model. It was found that the transit time is dominated by the throat hydraulic diameter and curvature radius of the constriction and that the throat aspect ratio little affects the transit time with a certain limitation, indicating that if an appropriate curvature radius is chosen, such a rectangular channel model can be substituted for an axisymmetric capillary model having the same throat hydraulic diameter in terms of the transit time by choosing an appropriate curvature radius. Thus, microchannels fabricated by the photolithography technique, whose cross section is generally rectangular, are expected to be applicable to in vitro model experiments of neutrophil retention and passage in the alveolar capillaries. PMID:23527190 18. Dynamic pulse difference circuit International Nuclear Information System (INIS) Erickson, G.L. 1978-01-01 A digital electronic circuit of especial use for subtracting background activity pulses in gamma spectrometry is disclosed which comprises an up-down counter connected to count up with signal-channel pulses and to count down with background-channel pulses. A detector responsive to the count position of the up-down counter provides a signal when the up-down counter has completed one scaling sequence cycle of counts in the up direction. In an alternate embodiment, a detector responsive to the count position of the up-down counter provides a signal upon overflow of the counter 19. Coaxial pulse matching transformer International Nuclear Information System (INIS) Ledenev, V.V.; Khimenko, L.T. 1986-01-01 This paper describes a coaxial pulse matching transformer with comparatively simple design, increased mechanical strength, and low stray inductance. The transformer design makes it easy to change the turns ratio. The circuit of the device and an expression for the current multiplication factor are presented; experiments confirm the efficiency of the transformer. Apparatus with a coaxial transformer for producing high-power pulsed magnetic fields is designed (current pulses of 1-10 MA into a load and a natural frequency of 100 kHz) 20. Pulse-width discriminators International Nuclear Information System (INIS) Budyashov, Yu.G.; Grebenyuk, V.M.; Zinov, V.G. 1978-01-01 A pulse duration discriminator is described which is intended for processing signals from multilayer scintillators. The basic elements of the scintillator are: an input gate, a current generator, an integrating capacitor, a Schmidt trigger and an anticoincidence circuit. The basic circuit of the discriminator and its time diagrams explaining its operating are given. The discriminator is based on microcircuits. Pulse duration discrimination threshold changes continuously from 20 to 100 ns, while its amplitude threshold changes within 20 to 100 mV. The temperature instability of discrimination thresholds (both in pulse width and in amplitude) is better than 0.1 per cent/deg C 1. Multimode pulse counter International Nuclear Information System (INIS) Natanzon, D.D. 1982-01-01 A pulse counter with code conversion is described. The counter is based on the integrated circuits of direct-counting devices of medium integration. The counter ensures various modes of pulse counting depending on the logical control signals: reversible, two-channel summing, one-channel summing binary, summing with ''storage'' signal code fixation without interrupting pulse counting. Arrangement of the suggested structure as a microcircuit of medium integration might contribute to reduction in the counter type nomenclature in digital families of widely used integrated circuits 2. Pulsed atomic soliton laser International Nuclear Information System (INIS) Carr, L.D.; Brand, J. 2004-01-01 It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a nondispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments 3. DogPulse DEFF Research Database (Denmark) Skovgaard, Christoffer; Thomsen, Josephine Raun; Verdezoto, Nervo 2015-01-01 This paper presents DogPulse, an ambient awareness system to support the coordination of dog walking among family members at home. DogPulse augments a dog collar and leash set to activate an ambient shape-changing lamp and visualize the last time the dog was taken for a walk. The lamp gradually...... changes its form and pulsates its lights in order to keep the family members aware of the dog walking activity. We report the iterative prototyping of DogPulse, its implementation and its preliminary evaluation. Based on our initial findings, we present the limitations and lessons learned as well... 4. Critical heat flux for free convection boiling in thin rectangular channels International Nuclear Information System (INIS) Cheng, Lap Y.; Tichler, P.R. 1991-01-01 A review of the experimental data on free convection boiling critical heat flux (CHF) in vertical rectangular channels reveals three mechanisms of burnout. They are the pool boiling limit, the circulation limit, and the flooding limit associated with a transition in flow regime from churn to annular flow. The dominance of a particular mechanism depends on the dimensions of the channel. Analytical models were developed for each free convection boiling limit. Limited agreement with data is observed. A CHF correlation, which is valid for a wide range of gap sizes, was constructed from the CHFs calculated according to the three mechanisms of burnout. 17 refs., 7 figs 5. Low frequency sound field enhancement system for rectangular rooms using multiple low frequency loudspeakers DEFF Research Database (Denmark) 2006-01-01 an enhancement system with extra loudspeakers the sound pressure level distribution along the listening area presents a significant improvement in the subwoofer frequency range. The system is simulated and implemented on the three different rooms and finally verified by measurements on the real rooms.......Rectangular rooms have strong influence on the low frequency performance of loudspeakers. Simulations of three different room sizes have been carried out using finite-difference time-domain method (FDTD) in order to predict the behaviour of the sound field at low frequencies. By using... 6. Vector rectangular-shape laser based on reduced graphene oxide interacting with a long fiber taper. Science.gov (United States) Gao, Lei; Zhu, Tao; Huang, Wei; Zeng, Jing 2014-10-01 A vector dual-wavelength rectangular-shape laser (RSL) based on a long fiber taper deposited with reduced graphene oxide is proposed, where nonlinearity is enhanced due to a large evanescent-field-interacting length and strong field confinement of an 8 mm fiber taper with a waist diameter of 4 μm. Graphene flakes are deposited uniformly on the taper waist with light pressure effect, so this structure guarantees both excellent saturable absorption and high nonlinearity. The RSL with a repetition rate of 7.9 MHz shows fast polarization switching in two orthogonal polarization directions, and temporal and spectral characteristics are investigated. 7. Finite element analysis of crack growth from rectangular notch in mixed mode loading International Nuclear Information System (INIS) Mohd Rawi Mohd Zin 2002-01-01 The direction of crack growth from rectangular notch for ductile material is determined in this paper. The ductile material is assumed to exhibit the elastic-plastic behaviour. In the model, the crack is assumed to start when the J-integral fracture criterion exceeded the critical value during the application of load and the crack tip propagated to a priori. The direction of the crack is characterised by maximum principles stress criterion and the mechanism of crack propagation is simulated by deleted element technique. The model is validated with experimental results and it shows good agreement. (Author) 8. Experimental study on downward two-phase flow in narrow rectangular channel Energy Technology Data Exchange (ETDEWEB) Kim, T.H.; Jeong, J.H. [Pusan National Univ., Busan (Korea, Republic of) 2014-07-01 Adiabatic vertical two-phase flow of air and water through narrow rectangular channels was investigated. This study involved the observation of flow using a high speed camera and flow regimes were determined by image processing program using a MATLAB. The flows regimes in channel with downward flow are similar to those found by previous studies with upward flow. The flow regimes in downward flow at low liquid velocity are different from the previous studies in upward flow. The flow regimes can be classified into bubbly, cap-bubbly, slug and churn flow. (author) 9. Oscillating-flow loss test results in rectangular heat exchanger passages Science.gov (United States) Wood, J. Gary 1991-01-01 Test results of oscillating flow losses in rectangular heat exchanger passages of various aspect ratios are given. This work was performed in support of the design of a free-piston Stirling engine (FPSE) for a dynamic space power conversion system. Oscillating flow loss testing was performed using an oscillating flow rig, which was based on a variable stroke and variable frequency linear drive motor. Tests were run over a range of oscillating flow parameters encompassing the flow regimes of the proposed engine design. Test results are presented in both tabular and graphical form and are compared against analytical predictions. 10. FLOW VISUALIZATION OF RECTANGULAR SLOT AIR JET IMPINGEMENT ON FLAT SURFACES OpenAIRE Satheesha V *1, B. K. Muralidhra2, Abhilash N3, C. K. Umesh4 2018-01-01 Jet impingement near the mid-chord of the gas turbine blade is treated as a flat plate. Experimental and numerical investigations are carried out for a single slot air jet impinging on flat surface for two different rectangular slots of dimension (3mm x 65 mm) and (5mm x 65 mm). Experimentation is done to study the flow pattern topography on the flat target plate, with varying the flow rate from 20 LPM to 50 LPM by varying the nozzle to plate distance from 9 mm to 24 mm for slot jet of 3mm an... 11. Comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates Energy Technology Data Exchange (ETDEWEB) Reddy, J N; Chao, W C [Virginia Polytechnic Inst. and State Univ., Blacksburg (USA). Dept. of Engineering Science and Mechanics 1981-04-01 In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration. 12. Visualization experimental investigation on long stripe coherent structure in small-scale rectangular channel International Nuclear Information System (INIS) Su Jiqiang; Sun Zhongning; Fan Guangming; Wang Shiming 2013-01-01 The long stripe coherent structure of the turbulent boundary layer in a small- scale vertical rectangular channel was observed by using hydrogen bubble flow trace visualization technique. The statistical properties of the long stripe in the experimental channel boundary layer were compared with that in the smooth flat plate boundary layer. The pitch characteristics were explained by the formation mechanism of the long stripe. It was analyzed that how the change of y + affected the distribution of the long stripe. In addition, the frequency characteristics of the long stripe were also investigated, and the correlation of the long stripe frequency in such a flow channel was obtained. (authors) 13. Traffic of leukocytes in microfluidic channels with rectangular and rounded cross-sections. Science.gov (United States) Yang, Xiaoxi; Forouzan, Omid; Burns, Jennie M; Shevkoplyas, Sergey S 2011-10-07 Traffic of leukocytes in microvascular networks (particularly through arteriolar bifurcations and venular convergences) affects the dynamics of capillary blood flow, initiation of leukocyte adhesion during inflammation, and localization and development of atherosclerotic plaques in vivo. Recently, a growing research effort has been focused on fabricating microvascular networks comprising artificial vessels with more realistic, rounded cross-sections. This paper investigated the impact of the cross-sectional geometry of microchannels on the traffic of leukocytes flowing with human whole blood through a non-symmetrical bifurcation that consisted of a 50 μm mother channel bifurcating into 30 μm and 50 μm daughter branches. Two versions of the same bifurcation comprising microchannels with rectangular and rounded cross-sections were fabricated using conventional multi-layer photolithography to produce rectangular microchannles that were then rounded in situ using a recently developed method of liquid PDMS/air bubble injection. For microchannels with rounded cross-sections, about two-thirds of marginated leukocytes traveling along a path in the top plane of the bifurcation entered the smallest 30 μm daughter branch. This distribution was reversed in microchannels with rectangular cross-sections--the majority of leukocytes traveling along a similar path continued to follow the 50 μm microchannels after the bifurcation. This dramatic difference in the distribution of leukocyte traffic among the branches of the bifurcation can be explained by preferential margination of leukocytes towards the corners of the 50 μm mother microchannels with rectangular cross-sections, and by the additional hindrance to leukocyte entry created by the sharp transition from the 50 μm mother microchannel to the 30 μm daughter branch at the intersection. The results of this study suggest that the trajectories of marginated leukocytes passing through non-symmetrical bifurcations are 14. Early results of microwave transmission experiments through an overly dense rectangular plasma sheet with microparticle injection Energy Technology Data Exchange (ETDEWEB) Gillman, Eric D., E-mail: [email protected] [National Research Council Postdoctoral Associate at the U.S. Naval Research Laboratory, Washington, DC 20375 (United States); Amatucci, W. E. [U.S. Naval Research Laboratory, Washington, DC 20375 (United States) 2014-06-15 These experiments utilize a linear hollow cathode to create a dense, rectangular plasma sheet to simulate the plasma layer surrounding vehicles traveling at hypersonic velocities within the Earth's atmosphere. Injection of fine dielectric microparticles significantly reduces the electron density and therefore lowers the electron plasma frequency by binding a significant portion of the bulk free electrons to the relatively massive microparticles. Measurements show that microwave transmission through this previously overly dense, impenetrable plasma layer increases with the injection of alumina microparticles approximately 60 μm in diameter. This method of electron depletion is a potential means of mitigating the radio communications blackout experienced by hypersonic vehicles. 15. LUGS, Stress Analysis, Flexibility Factors for Rectangular Attachment on Thin Shell International Nuclear Information System (INIS) Dodge, W.G. 1977-01-01 1 - Description of problem or function: LUGS calculates stresses, stress indices, and flexibility factors for a rectangular attachment on a cylindrical shell. 2 - Method of solution: The program implements Bijlaard's series solution to the thin-shell equations. 3 - Restrictions on the complexity of the problem: Caution is recommended in using the code for attachments on very thin shells that have large circumferential dimension and small longitudinal dimension (GAMMA.GE.80, BETA2.LE.0.05, and BETA1.GE.0.3) as series convergence and/or numeric problems seem to exist 16. Energy characteristics of the double slot in the narrow wall of a rectangular waveguide OpenAIRE Martynenko, S. A. 2005-01-01 Based on approximation of the half-wave field distribution in the slots, an expression is derived for internal mutual conductance of closely-spaced slots, which form a double inclined slot in the narrow wall of a rectangular waveguide. The narrow wall has cut-outs reaching the broad wall. With the use of the method of induced magnetomotive forces, a mathematical model is devised for calculating the energy characteristics of the double slot. The impact of angle of inclination of the slots, dim... 17. Linear theory of a dielectric-loaded rectangular Cerenkov maser with a sheet electron beam International Nuclear Information System (INIS) Chen Ye; Wan Xiao-Sheng; Zhao Ding; Liu Wen-Xin; Wang Yong 2012-01-01 A three-dimensional model of a dielectric-loaded rectangular Cerenkov maser with a sheet electron beam for the beam-wave interaction is proposed. Based on this model, the hybrid-mode dispersion equation is derived with the Borgnis potential function by using the field-matching method. Its approximate solution is obtained under the assumption of a dilute electron beam. By using the Ansoft high frequency structural simulator (HFSS) code, the electromagnetic field distribution in the interaction structure is given. Through numerical calculations, the effects of beam thickness, beam and dielectric-layer gap distance, beam voltage, and current density on the resonant growth rate are analysed in detail 18. Theory of the special Smith-Purcell radiation from a rectangular grating Energy Technology Data Exchange (ETDEWEB) Liu, Weihao, E-mail: [email protected]; He, Zhigang, E-mail: [email protected]; Jia, Qika [National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui, 230029 (China); Li, Weiwei [National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui, 230029 (China); Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, via E. Fermi 40, 00044 Frascati, RM (Italy) 2015-12-15 The recently uncovered special Smith-Purcell radiation (S-SPR) from the rectangular grating has significantly higher intensity than the ordinary Smith-Purcell radiation (SPR). Its monochromaticity and directivity are also much better. Here we explored the mechanism of the S-SPR by applying the fundamental electromagnetic theory and simulations. We have confirmed that the S-SPR is exactly from the radiating eigen modes of the grating. Its frequency and direction are well correlated with the beam velocity and structure parameters, which indicates its promising applications in tunable wave generation and beam diagnostic. 19. Numerical modelling of flexible pavement incorporating cross-anisotropic material properties. Part II: Surface rectangular loading OpenAIRE Maina, J W; Kawana, F; Matsui, K 2017-01-01 In order to better understand the impact of increased loading on roads, studies on tyre-road interaction have gained prominence in recent years. Tyres form an essential interface between vehicles and road pavement surfaces. These are the only parts of the vehicle that are in contact with the road and transmit the vehicle loading to the road surface. The use of the Cartesian coordinate system is convenient in dealing with a uniform/non-uniform tyre load acting over a rectangular area, but few ... 20. Buckling Analysis of Rectangular Plates with Variable Thickness Resting on Elastic Foundation International Nuclear Information System (INIS) Viswanathan, K K; Aziz, Z A; Navaneethakrishnan, P V 2015-01-01 Buckling of rectangular plates of variable thickness resting in elastic foundation is analysed using a quintic spline approximation technique. The thickness of the plate varies in the direction of one edge and the variations are assumed to be linear, exponential and sinusoidal. The plate is subjected to in plane load of two opposite edges. The buckling load and the mode shapes of buckling are computed from the eigenvalue problem that arises. Detailed parametric studies are made with different boundary conditions and the results are presented through the diagram and discussed 1. A Green's function solution for a rectangular heat source on an infinite plate International Nuclear Information System (INIS) Bainbridge, B.L. 1989-01-01 The applications associated with a rectangular heat source on an infinite plate range from integrated circuits to thin film heat flux sensors on thin substrates. The particular problem from which the solution is developed concerns the use of a resistive strip for monitoring currents generated in circuits exposed to electromagnetic fields. The Green's function formulation is solved by using early and late time approximations for which analytical solutions can be derived. In this paper expressions are developed for three sets of boundary conditions and compared to the experimental performance of a physical device 2. Alternating current loss reduction for rectangular busbars by covering their edges with low permeable magnetic caps Energy Technology Data Exchange (ETDEWEB) Sasada, Ichiro, E-mail: [email protected] [Applied Science for Electronics and Materials, Kyushu University, Kasuga (Japan) 2014-05-07 A method to reduce ac conductive losses in a thin rectangular busbar made of copper is presented. The method is based on a technique, which makes the distribution of the ac current in the cross section of a busbar flatter. Edges of a thin busbar are covered with low permeability magnetic thin layers as caps. The magnetic cap makes the impedance experienced by the current flowing near the edge comparatively larger so that currents cannot get crowded near the edges of a busbar. This method is numerically verified. 3. On the calibration of rectangular atomic force microscope cantilevers modified by particle attachment and lamination International Nuclear Information System (INIS) Bowen, James; Zhang, Zhibing; Adams, Michael J; Cheneler, David; Ward, Michael C L; Walliman, Dominic; Arkless, Stuart G 2010-01-01 A simple but effective method for estimating the spring constant of commercially available atomic force microscope (AFM) cantilevers is presented, based on estimating the cantilever thickness from knowledge of its length, width, resonant frequency and the presence or absence of an added mass, such as a colloid probe at the cantilever apex, or a thin film of deposited material. The spring constant of the cantilever can then be estimated using standard equations for cantilever beams. The results are compared to spring constant calibration measurements performed using reference cantilevers. Additionally, the effect of the deposition of Cr and Ti thin films onto rectangular Si cantilevers is investigated 4. Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium Directory of Open Access Journals (Sweden) R. Ellahi 2012-01-01 Full Text Available We have examined the peristaltic flow of Carreau fluid in a rectangular channel through a porous medium. The governing equations of motion are simplified by applying the long wavelength and low Reynolds number approximations. The reduced highly nonlinear partial differential equations are solved jointly by homotopy perturbation and Eigen function expansion methods. The expression for pressure rise is computed numerically by evaluating the numerical integration. The physical features of pertinent parameters have been discussed by plotting graphs of velocity, pressure rise, pressure gradient, and stream functions. 5. Discharge coefficient of a rectangular sharp-edged broad-crested weir OpenAIRE Zachoval Zbyněk; Knéblová Michaela; Roušar Ladislav; Rumann Ján; Šulc Jan 2014-01-01 his paper is concerned with the determination of the relationship for the calculation of the discharge coefficient at free overflow over a rectangular sharp-edged broad-crested weir without lateral contraction. The determination was made on the basis of new measurement in a range of the relative thickness of the weir from 0.12 to 0.30 and newly in a large range of relative height of the weir extremely from 0.24 to 6.8 which greatly expands the application possibilities of low weirs. In additi... 6. Analytical Modeling of Natural Convection in a Tall Rectangular Enclosure with Multiple Disconnected Partitions Directory of Open Access Journals (Sweden) Youngmin Bae 2016-08-01 Full Text Available In this study, laminar natural circulation and heat transfer in a tall rectangular enclosure with disconnected vertical partitions inside were investigated. Analytical expressions were developed to predict the circulation flow rate and the average Nusselt number in a partially partitioned enclosure with isothermal side walls at different temperatures and insulated top and bottom walls. The proposed formulas are then validated against numerical results for modified Rayleigh numbers of up to 106. The impacts of the governing parameters are also examined along with a discussion of the heat transfer regimes. 7. A method for reconstruction of electromagnetic shower parameters in a calorimeter with a rectangular cellular structure International Nuclear Information System (INIS) Chernov, N.I.; Ososkov, G.A.; Russakovich, N.A.; Velev, G. 1989-01-01 The Shower Hodoscopic Detector (SHD) is an important part of the HYPERON detector, as well as many other up-to-date detectors. It is a calorimeter with rectangular cells. In the present paper we consider a model of the distribution of energy release in the SHD cells and propose analytical solution of the problem of fitting the model distribution to experimental data. The corresponding programme is included in the HYPERON software and allows one to raise the rate of the data processing 8-9 times with about 10% reliability increase. 8 refs.; 8 figs 8. Solution of the two- dimensional heat equation for a rectangular plate Directory of Open Access Journals (Sweden) Nurcan BAYKUŞ SAVAŞANERİL 2015-11-01 Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions. 9. Numerical simulation of sloshing in rectangular tanks with OpenFOAM CFD Package International Nuclear Information System (INIS) Andreski, Filip; Markov, Zoran; Diebold, Louis; Gazzola, Thomas 2009-01-01 The aim of this paper is to simulate the sloshing phenomenon using OpenFOAM CFD software package. The present paper treats a 2D numerical simulation of a partially filled tank that is located on a LNG carrier. Experiments were done on a rectangular tank excited with different excitation periods and amplitudes and the pressure was measured at certain locations on the tank walls. The goal of this research is to compare the experimental data for the pressure with the pressure results obtained with the CFD software. It is shown that the obtained results match well with the experimental data. 10. The effect of thermal conductance of vertical walls on natural convection in a rectangular enclosure International Nuclear Information System (INIS) Kikuchi, Y.; Yoshino, A.; Taii, K. 2004-01-01 This paper deals with the experimental results of natural convective heat transfer in a rectangular water layer bounded by vertical walls of different thermal conductance. The vertical walls were made of copper or stainless steel. A minimum was observed in the horizontal distribution of temperature near the heating wall since a secondary reverse flow occurred outside the boundary layer. For copper case the experimental results of Nusselt number agreed well with calculations under an isothermal wall condition. For stainless steel case, however, the measured values were lower than the calculations since a three-dimensional effect appeared in convection due to non-uniformity in wall temperature. (author) 11. Wakefield accelerator with hybrid plasma-dielectric structure of rectangular cross-section International Nuclear Information System (INIS) Kiselev, V.A.; Linnik, A.F.; Mirnyj, V.I.; Onishchenko, I.N.; Uskov, V.V. 2010-01-01 Increase of wakefield intensity at its excitation by a long train of relativistic electron bunches in the rectangular dielectric structure when it is filled with plasma of resonant density was experimentally observed. The first portion of the bunches, produced by electron linac 'Almaz-2', ionizes gas at atmospheric pressure so that plasma frequency becomes equal to bunch repetition frequency and to the frequency of principal Eigen mode of the dielectric structure. Excitation enhancement at such resonant conditions is being studied taking into account the improvement of bunch train propagation in the transit channel caused by charge compensation with plasma and the electrodynamics change of the dielectric structure at filling with plasma. 12. Larmor precession and dwell time of a relativistic particle scattered by a rectangular quantum well CERN Document Server Li, Z J; Liang, J J; Liang, J Q 2003-01-01 The Larmor precession of a relativistic neutral spin particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time in the first-order approximation of the infinitesimal field limit. The comparison of the time in a potential well with that in free space shows apparent superluminality. 13. Theory of the special Smith-Purcell radiation from a rectangular grating International Nuclear Information System (INIS) Liu, Weihao; He, Zhigang; Jia, Qika; Li, Weiwei 2015-01-01 The recently uncovered special Smith-Purcell radiation (S-SPR) from the rectangular grating has significantly higher intensity than the ordinary Smith-Purcell radiation (SPR). Its monochromaticity and directivity are also much better. Here we explored the mechanism of the S-SPR by applying the fundamental electromagnetic theory and simulations. We have confirmed that the S-SPR is exactly from the radiating eigen modes of the grating. Its frequency and direction are well correlated with the beam velocity and structure parameters, which indicates its promising applications in tunable wave generation and beam diagnostic 14. Effects of an external magnetic field in pulsed laser deposition Science.gov (United States) García, T.; de Posada, E.; Villagrán, M.; Ll, J. L. Sánchez; Bartolo-Pérez, P.; Peña, J. L. 2008-12-01 Thin films were grown by pulsed laser deposition, PLD, on Si (1 0 0) substrates by the ablation of a sintered ceramic SrFe 12O 19 target with and without the presence of a nonhomogeneous magnetic field of μ0H = 0.4 T perpendicular to substrate plane and parallel to the plasma expansion axis. The field was produced by a rectangular-shaped Nd-Fe-B permanent magnet and the substrate was just placed on the magnet surface (Aurora method). An appreciable increment of optical emission due to the presence of the magnetic field was observed, but no film composition change or thickness increment was obtained. It suggests that the increment of the optical emission is due mainly to the electron confinement rather than confinement of ionic species. 15. Effects of an external magnetic field in pulsed laser deposition Energy Technology Data Exchange (ETDEWEB) Garcia, T. [Universidad Autonoma de la Ciudad de Mexico (UACM), Prolongacion San Isidro 151, Col. San Lorenzo Tezonco, C.P. 09790, Mexico DF (Mexico)], E-mail: [email protected]; Posada, E. de [CINVESTAV-IPN Unidad Merida, Applied Physics Department, A.P. 73, Cordemex, C.P. 97130 Merida, Yuc. (Mexico); Villagran, M. [CCADET, Universidad Nacional Autonoma de Mexico (UNAM), A.P. 70-186, C.P. 04510, Mexico DF (Mexico); Ll, J.L. Sanchez [Laboratorio de Magnetismo, Facultad de Fisica-IMRE, Universidad de La Habana, La Habana 10400 (Cuba); Bartolo-Perez, P.; Pena, J.L. [CINVESTAV-IPN Unidad Merida, Applied Physics Department, A.P. 73, Cordemex, C.P. 97130 Merida, Yuc. (Mexico) 2008-12-30 Thin films were grown by pulsed laser deposition, PLD, on Si (1 0 0) substrates by the ablation of a sintered ceramic SrFe{sub 12}O{sub 19} target with and without the presence of a nonhomogeneous magnetic field of {mu}{sub 0}H = 0.4 T perpendicular to substrate plane and parallel to the plasma expansion axis. The field was produced by a rectangular-shaped Nd-Fe-B permanent magnet and the substrate was just placed on the magnet surface (Aurora method). An appreciable increment of optical emission due to the presence of the magnetic field was observed, but no film composition change or thickness increment was obtained. It suggests that the increment of the optical emission is due mainly to the electron confinement rather than confinement of ionic species. 16. Synthetic aperture radar imaging simulator for pulse envelope evaluation Science.gov (United States) Balster, Eric J.; Scarpino, Frank A.; Kordik, Andrew M.; Hill, Kerry L. 2017-10-01 A simulator for spotlight synthetic aperture radar (SAR) image formation is presented. The simulator produces radar returns from a virtual radar positioned at an arbitrary distance and altitude. The radar returns are produced from a source image, where the return is a weighted summation of linear frequency-modulated (LFM) pulse signals delayed by the distance of each pixel in the image to the radar. The imagery is resampled into polar format to ensure consistent range profiles to the position of the radar. The SAR simulator provides a capability enabling the objective analysis of formed SAR imagery, comparing it to an original source image. This capability allows for analysis of various SAR signal processing techniques previously determined by impulse response function (IPF) analysis. The results suggest that IPF analysis provides results that may not be directly related to formed SAR image quality. Instead, the SAR simulator uses image quality metrics, such as peak signal-to-noise ratio (PSNR) and structured similarity index (SSIM), for formed SAR image quality analysis. To showcase the capability of the SAR simulator, it is used to investigate the performance of various envelopes applied to LFM pulses. A power-raised cosine window with a power p=0.35 and roll-off factor of β=0.15 is shown to maximize the quality of the formed SAR images by improving PSNR by 0.84 dB and SSIM by 0.06 from images formed utilizing a rectangular pulse, on average. 17. Energy constraints in pulsed phase control of chaos Energy Technology Data Exchange (ETDEWEB) Meucci, R., E-mail: [email protected] [Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze (Italy); Euzzor, S. [Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze (Italy); Zambrano, S. [Università Vita-Salute San Raffaele, Via Olgettina 58, 20132 Milano (Italy); Pugliese, E. [Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze (Italy); Dipartimento di Scienze della Terra, Università di Firenze, Via G. La Pira 4, 50100 Firenze (Italy); Francini, F. [Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze (Italy); Arecchi, F.T. [Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze (Italy); Università di Firenze, Firenze (Italy) 2017-01-15 Phase control of chaos is a powerful technique but little is known about its physical constraints, relevant for real systems. As a fact, it has not been explored whether this technique can also be applied when the controlling perturbation is not harmonic. Here we apply phase control on a driven double well Duffing oscillator using periodic rectangular pulsed perturbations instead of the classical sinusoidal perturbations. Experimental measurements and numerical simulations show that this kind of perturbation is also able to stabilize the chaotic orbits for an adequate selection of the phase. Furthermore, as the duty cycle of the perturbation (that is, the fraction of the time that the periodically pulsed control is active) is increased, two separate regimes occur. In the first one, the perturbations leading to stabilization of periodic solutions are of constant energy (taken as the product of the duty cycle and the amplitude) and in the second one, a saturation phenomenon occurs, implying that increasing energy values of the perturbations are wasted. Our results unveil the versatility of the pulsed phase control scheme and the importance of energy constraints. 18. Energy constraints in pulsed phase control of chaos International Nuclear Information System (INIS) Meucci, R.; Euzzor, S.; Zambrano, S.; Pugliese, E.; Francini, F.; Arecchi, F.T. 2017-01-01 Phase control of chaos is a powerful technique but little is known about its physical constraints, relevant for real systems. As a fact, it has not been explored whether this technique can also be applied when the controlling perturbation is not harmonic. Here we apply phase control on a driven double well Duffing oscillator using periodic rectangular pulsed perturbations instead of the classical sinusoidal perturbations. Experimental measurements and numerical simulations show that this kind of perturbation is also able to stabilize the chaotic orbits for an adequate selection of the phase. Furthermore, as the duty cycle of the perturbation (that is, the fraction of the time that the periodically pulsed control is active) is increased, two separate regimes occur. In the first one, the perturbations leading to stabilization of periodic solutions are of constant energy (taken as the product of the duty cycle and the amplitude) and in the second one, a saturation phenomenon occurs, implying that increasing energy values of the perturbations are wasted. Our results unveil the versatility of the pulsed phase control scheme and the importance of energy constraints. 19. A laminated-iron fast-pulsed magnet CERN Document Server Faugeras, Paul E; Mayer, M; Schröder, G H 1977-01-01 In the SPS Beam Dumping System , two pairs of fast pulsed magnets deflect the circulating beam vertically and horizontally from its normal closed orbit, and onto a large absorber block. Two MKDV kickers produce a quasi-rectangular field pulse of 23 µs duration (this being the SPS revolution period) causing a vertical deflection of 44 mm at the absorber block, while two MKDH sweepers give a horizontal deflection ramping during 23 µs to a peak of 25 mm. On the 'flat top' of the MKDV pulse, oscillations of ± 10 % of the primary deflection are introduced. The proton beam is thus dumped into the absorber block during one revolution. Dumping may occur at any energy, but the dumping of a 400 GeV/c pencil beam of $10^{13}$ proton would produce thermal shock waves which would ultimately deform any solid absorber. The sweeper's 25 mm horizontal deflection and the kicker's 10 % oscillations were introduced to sweep the dumped beam over an area of about 200 $mm^{2}$ giving a reduction of one to two orders of magnitude... 20. Rapid thermal pulse annealing International Nuclear Information System (INIS) Miller, M.G.; Koehn, B.W.; Chaplin, R.L. 1976-01-01 Characteristics of recovery processes have been investigated for cases of heating a sample to successively higher temperatures by means of isochronal annealing or by using a rapid pulse annealing. A recovery spectra shows the same features independent of which annealing procedure is used. In order to determine which technique provides the best resolution, a study was made of how two independent first-order processes are separated for different heating rates and time increments of the annealing pulses. It is shown that the pulse anneal method offers definite advantages over isochronal annealing when annealing for short time increments. Experimental data by means of the pulse anneal techniques are given for the various substages of stage I of aluminium. (author) 1. Pulse holographic measurement techniques International Nuclear Information System (INIS) Kim, Cheol Jung; Baik, Seong Hoon; Hong, Seok Kyung; Kim, Jeong Moog; Kim, Duk Hyun 1992-01-01 With the development of laser, remote inspection techniques using laser have been growing on. The inspection and measurement techniques by pulse holography are well-established technique for precise measurement, and widely used in various fields of industry now. In nuclear industry, this technology is practically used because holographic inspection is remote, noncontact, and precise measurement technique. In relation to remote inspection technology in nuclear industry, state-of-the art of pulse HNDT (Holographic non-destructive testing) and holographic measurement techniques are examined. First of all, the fundamental principles as well as practical problems for applications are briefly described. The fields of pulse holography have been divided into the HNDT, flow visualization and distribution study, and other application techniques. Additionally holographic particle study, bubble chamber holography, and applications to other visualization techniques are described. Lastly, the current status for the researches and applications of pulse holography to nuclear industry which are carried out actively in Europe and USA, is described. (Author) 2. IAE pulsed electrostatic accelerator International Nuclear Information System (INIS) Afanas'ev, V.P.; Ganzhelyuk, M.L.; Kozlov, L.D.; Koltypin, E.A.; Molchanov, Yu.D.; Otroshchenko, G.A.; Yan'kov, G.B. 1976-01-01 The modernized pulse electrostatic accelerator using the klystron ion grouping and the beam interruption system prior to acceleration is described. The accelerator is modernized in order to improve parameters of a current pulse and to decrease the background in the measurement room. The ion beam of needed dimensions is obtained with the help of a high-frequency source and a beam grouping and deflection system. The general view of the beam grouping and deflection system is shown. The ion beam forming process is considered in detail. The modernized electrostatic accelerator permits to obtain a pulse current with a pulse length of 1.5 ns and an amplitude of 1.5 - 2 μA. With the repetition frequency of 2 MHz, the average target current is about 6 μA 3. International Year of Pulses 2016 \| 2016 International Year of Pulses Science.gov (United States) the Year in collaboration with Governments, relevant organizations, non-governmental organizations and the composition of pulses Image 4 Wrapping up the International Year of Pulses The 5 key messages to food security Infographic Pulses and climate change International Year of Pulses 2016 The 68th UN 4. Realtime aspects of pulse-to-pulse modulation International Nuclear Information System (INIS) Steiner, R.; Riedel, C.; Roesch, W. 1992-01-01 The pulse-to-pulse modulation of the SIS-ESR control system is described. Fast response to operator interaction and to changes in process conditions is emphasized as well as the essential part played by the timing system in pulse-to-pulse modulation. (author) 5. Pulsed spallation Neutron Sources International Nuclear Information System (INIS) Carpenter, J.M. 1994-01-01 This paper reviews the early history of pulsed spallation neutron source development at Argonne and provides an overview of existing sources world wide. A number of proposals for machines more powerful than currently exist are under development, which are briefly described. The author reviews the status of the Intense Pulsed Neutron Source, its instrumentation, and its user program, and provides a few examples of applications in fundamental condensed matter physics, materials science and technology 6. Pulsed spallation neutron sources International Nuclear Information System (INIS) Carpenter, J.M. 1996-01-01 This paper reviews the early history of pulsed spallation neutron source development ar Argonne and provides an overview of existing sources world wide. A number of proposals for machines more powerful than currently exist are under development, which are briefly described. The author reviews the status of the Intense Pulsed Neutron Source, its instrumentation, and its user program, and provide a few examples of applications in fundamental condensed matter physics, materials science and technology 7. Theoretical modeling of electroosmotic flow in soft microchannels: A variational approach applied to the rectangular geometry Science.gov (United States) 2018-03-01 Modeling of fluid flow in polyelectrolyte layer (PEL)-grafted microchannels is challenging due to their two-layer nature. Hence, the pertinent studies are limited only to circular and slit geometries for which matching the solutions for inside and outside the PEL is simple. In this paper, a simple variational-based approach is presented for the modeling of fully developed electroosmotic flow in PEL-grafted microchannels by which the whole fluidic area is considered as a single porous medium of variable properties. The model is capable of being applied to microchannels of a complex cross-sectional area. As an application of the method, it is applied to a rectangular microchannel of uniform PEL properties. It is shown that modeling a rectangular channel as a slit may lead to considerable overestimation of the mean velocity especially when both the PEL and electric double layer (EDL) are thick. It is also demonstrated that the mean velocity is an increasing function of the fixed charge density and PEL thickness and a decreasing function of the EDL thickness and PEL friction coefficient. The influence of the PEL thickness on the mean velocity, however, vanishes when both the PEL thickness and friction coefficient are sufficiently high. 8. Near field vorticity distributions from a sharp-edged rectangular jet International Nuclear Information System (INIS) Vouros, Alexandros P.; Panidis, Thrassos; Pollard, Andrew; Schwab, Rainer R. 2015-01-01 Highlights: • Axial mean vorticity equation terms are calculated from experimental data. • Appearance of ridges, dumbbell shape and saddleback velocity profiles is highlighted. • Explanations are provided using terms from the vorticity equation. - Abstract: Experimental results on the near field development of a free rectangular jet with aspect ratio 10 are presented. The jet issues from a sharp-edged orifice attached to a rectangular settling chamber at Re h ∼ 23,000, based on slot width, h. Measurements on cross plane grids were obtained with a two-component hot wire anemometry probe, which provided information on the three dimensional characteristics of the flow field. Two key features of this type of jet are mean axial velocity profiles presenting two off axis peaks, commonly mentioned as saddleback profiles, and a predominant dumbbell shape as described by, for example, a contour of the axial mean velocity. The saddleback shape is found to be significantly influenced by the vorticity distribution in the transverse plane of the jet, while the dumbbell is traced to two terms in the axial mean vorticity transport equation that diffuse fluid from the centre of the jet towards its periphery. At the farthest location where measurements were taken, 30 slot widths from the jet exit, the flow field resembles that of an axisymmetric jet 9. Wave-filter-based approach for generation of a quiet space in a rectangular cavity Science.gov (United States) Iwamoto, Hiroyuki; Tanaka, Nobuo; Sanada, Akira 2018-02-01 This paper is concerned with the generation of a quiet space in a rectangular cavity using active wave control methodology. It is the purpose of this paper to present the wave filtering method for a rectangular cavity using multiple microphones and its application to an adaptive feedforward control system. Firstly, the transfer matrix method is introduced for describing the wave dynamics of the sound field, and then feedforward control laws for eliminating transmitted waves is derived. Furthermore, some numerical simulations are conducted that show the best possible result of active wave control. This is followed by the derivation of the wave filtering equations that indicates the structure of the wave filter. It is clarified that the wave filter consists of three portions; modal group filter, rearrangement filter and wave decomposition filter. Next, from a numerical point of view, the accuracy of the wave decomposition filter which is expressed as a function of frequency is investigated using condition numbers. Finally, an experiment on the adaptive feedforward control system using the wave filter is carried out, demonstrating that a quiet space is generated in the target space by the proposed method. 10. Simplified Method for the Characterization of Rectangular Straw Bales (RSB) Thermal Conductivity Science.gov (United States) Conti, Leonardo; Goli, Giacomo; Monti, Massimo; Pellegrini, Paolo; Rossi, Giuseppe; Barbari, Matteo 2017-10-01 This research aims to design and implement tools and methods focused at the assessment of the thermal properties of full size Rectangular Straw Bales (RSB) of various nature and origin, because their thermal behaviour is one of the key topics in market development of sustainable building materials. As a first approach a method based on a Hot-Box in agreement with the ASTM C1363 - 11 standard was adopted. This method was found to be difficult for the accurate measurement of energy flows. Instead, a method based on a constant energy input was developed. With this approach the thermal conductivity of a Rectangular Straw-Bale (RSB λ) can be determined by knowing the thermal conductivity of the materials used to build the chamber and the internal and external temperature of the samples and of the chamber. A measurement a metering chamber was built and placed inside a climate chamber, maintained at constant temperature. A known quantity of energy was introduced inside the metering chamber. A series of thermopiles detects the temperature of the internal and external surfaces of the metering chamber and of the specimens allowing to calculate the thermal conductivity of RSB in its natural shape. Different cereal samples were tested. The values were found consistent with those published in scientific literature. 11. Measurements of time-dependent liquid-metal magnetohydrodynamic flows in a flat rectangular duct International Nuclear Information System (INIS) Buehler, L.; Horanyi, S. 2009-01-01 In the helium-cooled lead lithium (HCLL) blanket, which has been chosen as a reference concept for a liquid-metal breeding blanket to be tested in ITER, the heat is removed by helium cooled plates aligned with the strong toroidal magnetic field that confines the fusion plasma. The liquid breeder lead lithium circulates through gaps of rectangular cross-section between the cooling plates to transport the generated tritium towards external extraction facilities. Under the action of the strong magnetic field, liquid metal flows in conducting rectangular ducts exhibit jet-like velocity profiles in the thin boundary layers near the side walls, which are parallel to the magnetic field like the cooling plates in HCLL blankets. The velocity in these side layers may exceed several times the mean velocity in the duct and it is known that these layers become unstable for sufficiently high Reynolds numbers. The present paper summarizes experimental results for such unstable time-dependent flows in strong magnetic fields, which have been obtained in the MEKKA liquid metal laboratory of the Forschungszentrum Karlsruhe. In particular, spatial and temporal scales of perturbation patterns are identified. The results suggest that the flow between cooling plates in a HCLL blanket is laminar and stable. The observed time-dependent flow behavior appears at larger velocities so that the present results are more relevant for applications in dual coolant concepts where high-velocity jets have been predicted along side walls. 12. Discharge Coefficient of Rectangular Short-Crested Weir with Varying Slope Coefficients Directory of Open Access Journals (Sweden) Yuejun Chen 2018-02-01 Full Text Available Rectangular short-crested weirs are widely used for simple structure and high discharge capacity. As one of the most important and influential factors of discharge capacity, side slope can improve the hydraulic characteristics of weirs at special conditions. In order to systemically study the effects of upstream and downstream slope coefficients S1 and S2 on overflow discharge coefficient in a rectangular short-crested weir the Volume of Fluid (VOF method and the Renormalization Group (RNG κ-ε turbulence model are used. In this study, the slope coefficient ranges from V to 3H:1V and each model corresponds to five total energy heads of H0 ranging from 8.0 to 24.0 cm. Comparisons of discharge coefficients and free surface profiles between simulated and laboratory results display a good agreement. The simulated results show that the difference of discharge coefficients will decrease with upstream slopes and increase with downstream slopes as H0 increases. For a given H0, the discharge coefficient has a convex parabolic relation with S1 and a piecewise linearity relation with S2. The maximum discharge coefficient is always obtained at S2 = 0.8. There exists a difference between upstream and downstream slope coefficients in the influence range of free surface curvatures. Furthermore, a proposed discharge coefficient equation by nonlinear regression is a function of upstream and downstream slope coefficients. 13. Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir Directory of Open Access Journals (Sweden) Junfeng Ding 2018-04-01 Full Text Available Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions. 14. The testing of the Rectangular Pivot-point bellows for the PPPL Tokamak fusion test reactor International Nuclear Information System (INIS) Haughian, J.; Fong, M.; Greer, J.; Lou, K.; Scalise, D.T. 1983-01-01 The Neutral Beam Pivot Point Bellows (PPB) is installed in the duct which connects the Neutral Beam Enclosure to the Torus. This bellows, located at the pivot point, must fit the severely limited space available at the pivot-point location. Consequently, it has to be made rectangular in cross section with a large inside area for beam access. This leads to small convolutions with high stress concentrations. The function of the bellows is to permit change in the angular positioning of the neutral beam line with respect to the Tokamak, to isolate the Neutral Beam Line from the deflection of the Torus during bake out, and to allow for all misalignments. Internally the bellows will have a vacuum along with such gases such as hydrogen or deuterium. Externally, air or nitrogen gas will be present. It is constructed of Inconel 718 convolutions welded together to provide a clear rectangular opening of 23.4 by 32.2 inches, joined to a 625 Inconel flange at each end 15. Spectral Optical Readout of Rectangular-Miniature Hollow Glass Tubing for Refractive Index Sensing. Science.gov (United States) Rigamonti, Giulia; Bello, Valentina; Merlo, Sabina 2018-02-16 For answering the growing demand of innovative micro-fluidic devices able to measure the refractive index of samples in extremely low volumes, this paper presents an overview of the performances of a micro-opto-fluidic sensing platform that employs rectangular, miniature hollow glass tubings. The operating principle is described by showing the analytical model of the tubing, obtained as superposition of different optical cavities, and the optical readout method based on spectral reflectivity detection. We have analyzed, in particular, the theoretical and experimental optical features of rectangular tubings with asymmetrical geometry, thus with channel depth larger than the thickness of the glass walls, though all of them in the range of a few tens of micrometers. The origins of the complex line-shape of the spectral response in reflection, due to the different cavities formed by the tubing flat walls and channel, have been investigated using a Fourier transform analysis. The implemented instrumental configuration, based on standard telecom fiberoptic components and a semiconductor broadband optical source emitting in the near infrared wavelength region centered at 1.55 µm, has allowed acquisition of reflectivity spectra for experimental verification of the expected theoretical behavior. We have achieved detection of refractive index variations related to the change of concentration of glucose-water solutions flowing through the tubing by monitoring the spectral shift of the optical resonances. 16. Combined Transverse Steel-External FRP Confinement Model for Rectangular Reinforced Concrete Columns Directory of Open Access Journals (Sweden) Ahmed Al-Rahmani 2016-02-01 Full Text Available Recently, the need to increase the strength of reinforced concrete members has become a subject that civil engineers are interested in tackling. Of the many proposed solutions, fiber-reinforced polymer (FRP materials have attracted attention due to their superior properties, such as high strength-to-weight ratio, high energy absorption and excellent corrosion resistance. FRP wrapping of concrete columns is done to enhance the ultimate strength due to the confinement effect, which is normally induced by steel ties. The existence of the two confinement systems changes the nature of the problem, thus necessitating specialized nonlinear analysis to obtain the column’s ultimate capacity. Existing research focused on a single confinement system. Furthermore, very limited research on rectangular sections was found in the literature. In this work, a model to estimate the combined behavior of the two systems in rectangular columns is proposed. The calculation of the effective lateral pressure is based on the Lam and Teng model and the Mander model for FRP wraps and steel ties, respectively. The model then generates stress-strain diagrams for both the concrete core and the cover. The model was developed for the analysis in extreme load events, where all possible contributions to the column’s ultimate capacity should be accounted for without any margin of safety. The model was validated against experiments, and the results obtained showed good agreement with almost all of the available experimental data. 17. Validation Plan of Turbulence Models for Internal Gas Flow Analysis in a Heated Rectangular Riser Duct Energy Technology Data Exchange (ETDEWEB) Kim, Sin-Yeob; Shin, Dong-Ho; Park, Goon-Cherl; Cho, Hyoung Kyu [Seoul National Univ., Seoul (Korea, Republic of); Kim, Chan-Soo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of) 2016-10-15 VHTR being developed at Korea Atomic Energy Research Institute adopts an air-cooled Reactor Cavity Cooling System (RCCS) incorporating rectangular riser channels to remove the afterheat emitted from the reactor vessel. Because the performance of RCCS is determined by heat removal rate through the RCCS riser, it is important to understand the heat transfer phenomena in the RCCS riser to ensure the safety of the reactor. In the mixed convection, due to the buoyance force induced by temperature and density differences, local flow structure and heat transfer mode near the heated wall have significantly dissimilar characteristics from both forced convection and free convection. In this study, benchmark calculation was conducted to reproduce the previous statements that V2F turbulence model can capture the mixed convection phenomena with the Shehata's experimental data. Then, the necessity of the model validation for the mixed convection phenomena was confirmed with the CFD analyses for the geometry of the prototype RCCS riser. For the purpose of validating the turbulence models for mixed convection phenomena in the heated rectangular riser duct, validation plan with three experimental tests was introduced. Among them, the flow visualization test facility with preserved cross-section geometry was introduced and a preliminary test result was shown. 18. Analysis of counter current flow limitation during the cooling process at the rectangular narrow boundary International Nuclear Information System (INIS) 2013-01-01 Experimental studies to study the mechanism of boiling heat transfer in narrow rectangular channel under severe accident scenarios of TMI-2 nuclear power plant necessary for the understanding of management-related accidents. The research aims to obtain heat flux values and the critical heat flux (CHF) during the process of boiling heat transfer in narrow rectangular channel. Research methods experimentally using the HEATING-02 test section with cooling fluid is water temperature 98 °C. Experiments performed by varying the hot plate initial temperature of 100 °C, 200 °C and 300 °C with channel size 1 mm. Boiling during the cooling process was recorded by a transient temperature on the hot plate. Temperature data used to calculate the heat flux and wall temperature, the results are represented through the boiling curve. The results show that the higher plate temperature, the narrower width of the curve will be narrower and its mean that the plate surface cooling time will be slower. Results visualization is seen that the CCF occurred at the hot plate initial temperature of 100 °C, 200 °C and 300 °C with channel size 1 mm. (author) 19. Inertial migrations of cylindrical particles in rectangular microchannels: Variations of equilibrium positions and equivalent diameters Science.gov (United States) Su, Jinghong; Chen, Xiaodong; Hu, Guoqing 2018-03-01 Inertial migration has emerged as an efficient tool for manipulating both biological and engineered particles that commonly exist with non-spherical shapes in microfluidic devices. There have been numerous studies on the inertial migration of spherical particles, whereas the non-spherical particles are still largely unexplored. Here, we conduct three-dimensional direct numerical simulations to study the inertial migration of rigid cylindrical particles in rectangular microchannels with different width/height ratios under the channel Reynolds numbers (Re) varying from 50 to 400. Cylindrical particles with different length/diameter ratios and blockage ratios are also concerned. Distributions of surface force with the change of rotation angle show that surface stresses acting on the particle end near the wall are the major contributors to the particle rotation. We obtain lift forces experienced by cylindrical particles at different lateral positions on cross sections of two types of microchannels at various Re. It is found that there are always four stable equilibrium positions on the cross section of a square channel, while the stable positions are two or four in a rectangular channel, depending on Re. By comparing the equilibrium positions of cylindrical particles and spherical particles, we demonstrate that the equivalent diameter of cylindrical particles monotonously increases with Re. Our work indicates the influence of a non-spherical shape on the inertial migration and can be useful for the precise manipulation of non-spherical particles. 20. Effects of anisotropic properties on bursting behavior of rectangular cup with a V-notch Energy Technology Data Exchange (ETDEWEB) Kim, Jeong Tai [R and D Center, TERA Co. Ltd., Seoul (Korea, Republic of); Kim, Sang Mok [R and D Center, Hyosung Power and Industrial Systems PG, Changwon (Korea, Republic of); Kang, Beom Soo [Dept. of Aerospace Engineering, Pusan National University, Busan (Korea, Republic of); Ku, Tae Wan [Engineering Research Center of Innovative Technology on Advanced Forming, Pusan National University, Busan (Korea, Republic of) 2016-09-15 Effects of mechanical anisotropic properties on bursting failure and its pressure of rectangular deep-drawn cup fabricated by using AA3005-H14 thin sheet are investigated to utilize for electrolyte container of lithium-ion secondary batteries. The V-notch shape with a depth of 0.1 mm and an angle of 20.0 degrees is defined on the rectangular cup, which has a thickness of 0.20 mm on the major surface and that of 0.30 mm on the minor surface. With the measured mechanical properties by uni-axial tensile tests and the defined V-notch geometry, a series of numerical prediction models considering isotropic, planar and normal anisotropic characteristics, are built-up and the bursting simulations are performed. Thereafter, the bursting fracture behavior is investigated by adopting ductile fracture criterion proposed by Cockcroft and Latham. The results predicted for the planar and the normal anisotropic models show that the bursting fracture pressure is well matched to 0.400 MPa, and the isotropic and the planar anisotropic models present a bursting fracture height of about 4.95 mm and 4.92 mm, respectively. A series of experimental investigations are undertaken to verify the bursting deformation that had been predicted. The bursting pressure and its height during experimental verifications are shown to be in good agreement with each variation of about 5.88% and roughly 0.20% with respect to the numerical results obtained using the planar anisotropic model. 1. Fully developed liquid-metal flow in multiple rectangular ducts in a strong uniform magnetic field International Nuclear Information System (INIS) Molokov, S. 1993-01-01 Fully developed liquid-metal flow in a straight rectangular duct with thin conducting walls is investigated. The duct is divided into a number of rectangular channels by electrically conducting dividing walls. A strong uniform magnetic field is applied parallel to the outer side walls and dividing walls and perpendicular to the top and the bottom walls. The analysis of the flow is performed by means of matched asymptotics at large values of the Hartmann number M. The asymptotic solution obtained is valid for arbitrary wall conductance ratio of the side walls and dividing walls, provided the top and bottom walls are much better conductors than the Hartmann layers. The influence of the Hartmann number, wall conductance ratio, number of channels and duct geometry on pressure losses and flow distribution is investigated. If the Hartmann number is high, the volume flux is carried by the core, occupying the bulk of the fluid and by thin layers with thickness of order M -1/2 . In some of the layers, however, the flow is reversed. As the number of channels increases the flow in the channels close to the centre approaches a Hartmann-type flow with no jets at the side walls. Estimation of pressure-drop increase in radial ducts of a self-cooled liquid-metal blanket with respect to flow in a single duct with walls of the same wall conductance ratio gives an upper limit of 30%. (author). 13 refs., 10 figs., 1 tab 2. Experimental study of falling film evaporation in large scale rectangular channel International Nuclear Information System (INIS) Huang, X.G.; Yang, Y.H.; Hu, P. 2015-01-01 Highlights: • This paper studies the falling film evaporation in large scale rectangular channel experimentally. • The effects of air flow rate, film temperature and film flow rate on falling film evaporation are analyzed. • Increasing the air flow rate is considered as an efficient method to enhance the evaporation rate. • A correlation including the wave effect for falling film evaporation is derived based on heat and mass transfer analogy. - Abstract: The falling film evaporation in a large scale rectangular channel is experimentally studied in this paper for the design and improvement of passive containment cooling system. The evaporation mass transfer coefficient h D is obtained by the evaporation rate and vapor partial pressure difference of film surface and air bulk. The experimental results indicate that increasing of air flow rate appears to enhance h D , while the film temperature and film flow rate have little effect on h D . Since the wave effect on evaporation is noticed in experiment, the evaporation mass transfer correlation including the wave effect is developed on the basis of heat and mass transfer analogy and experimental data 3. Conversion of output factor from square field into rectangular field in electron beam CERN Document Server Wang Jian Hua; Xu Yi Fei 2002-01-01 Objective: A simple and accurate calculation method was designed to convert output factor from square field into rectangular field in electron beam, which can be easily implemented in clinical practice. Methods: 6, 12, 15 MeV electron beam, field size 6.0 cm x 7.5 cm, 5.0 cm x 10.0 cm, 6.0 cm x 12.0 cm, TL3000C dosimeter and source-to-surface distance method were used in dose measurement. The measured dose values were compared with the calculated ones from three theoretical equations with the conformation evaluated. Results: The calculated dose values from three theoretical equations differed from the measured ones by 0.23%, 1.30% and 1.10% (6 MeV), 0.63%, 0.90% and 0.73% (12 MeV), 0.50%, 1.80% and 3.40% (15 MeV), conforming best to the equation OUF (X, Y)=[OUF(X,X). OUF(Y,Y)] sup 1 sup / sup 2. When the size of the field was longer than Rp, the difference between the calculated values and measured ones was relatively very small. Conclusions: The output factor in rectangular fields can be accurately calculate... 4. Evaluation of the ultimate pressure capacity of rectangular HVAC ducts for nuclear pwoer plants International Nuclear Information System (INIS) Wedellsborg, B.W. 1984-01-01 Typical Category I HVAC ducts in a nuclear plant must be designed for loads and load combinations including positive and negative pressure loads which are generated due to the normal operation and postulated accident conditions. These pressure loads most often govern the design of the HVAC ducts. Structural design criteria are presently based on the AISI Code which limits the duct panel width-to-thickness ratio to a maximum of 500 and the maximum height-to-thickness ratio to 200, unless it can be shown by structural tests that larger ratios can be used. Test Programs performed on rectangular HVAC ducts subjected to vacumm loads have substantiated the use of ducts having panel width to thickness ratios of up to 1600. The results of the test programs were subsequently incorporated into the design through a more rational analytical design method which was developed from and correlates well with the test results. The purpose of this paper is to present the analytical design method and its correlation with the test results. Simple formulae for the design of rectangular HVAC ducts are presented. Lower bound values of duct sheet, and stiffener ultimate loads are derived, and correlated with recent test results. Analytically predicted ultimate pressures are also compared with other available duct test data 5. Influence of Fluid–Thermal–Structural Interaction on Boundary Layer Flow in Rectangular Supersonic Nozzles Directory of Open Access Journals (Sweden) Kalyani Bhide 2018-03-01 Full Text Available The aim of this work is to highlight the significance of Fluid–Thermal–Structural Interaction (FTSI as a diagnosis of existing designs, and as a means of preliminary investigation to ensure the feasibility of new designs before conducting experimental and field tests. The novelty of this work lies in the multi-physics simulations, which are, for the first time, performed on rectangular nozzles. An existing experimental supersonic rectangular converging/diverging nozzle geometry is considered for multi-physics 3D simulations. A design that has been improved by eliminating the sharp throat is further investigated to evaluate its structural integrity at design Nozzle Pressure Ratio (NPR 3.67 and off-design (NPR 4.5 conditions. Static structural analysis is performed by unidirectional coupling of pressure loads from steady 3D Computational Fluid Dynamics (CFD and thermal loads from steady thermal conduction simulations, such that the simulations represent the experimental set up. Structural deformation in the existing design is far less than the boundary layer thickness, because the impact of Shock wave Boundary Layer Interaction (SBLI is not as severe. FTSI demonstrates that the discharge coefficient of the improved design is 0.99, and its structural integrity remains intact at off-design conditions. This proves the feasibility of the improved design. Although FTSI influence is shown for a nozzle, the approach can be applied to any product design cycle, or as a prelude to building prototypes. 6. Numerical simulation of double-diffusive mixed convective flow in rectangular enclosure with insulated moving lid Energy Technology Data Exchange (ETDEWEB) Teamah, M.A. [Faculty of Engineering, Alexandria University, Mech. Eng. Dept, Alexandria (Egypt); El-Maghlany, W.M. [Faculty of Engineering, Suez Canal University, Ismailia (Egypt) 2010-09-15 The present study is concerned with the mixed convection in a rectangular lid-driven cavity under the combined buoyancy effects of thermal and mass diffusion. Double-diffusive convective flow in a rectangular enclosure with moving upper surface is studied numerically. Both upper and lower surfaces are being insulated and impermeable. Constant different temperatures and concentration are imposed along the vertical walls of the enclosure, steady state laminar regime is considered. The transport equations for continuity, momentum, energy and spices transfer are solved. The numerical results are reported for the effect of Richardson number, Lewis number, and buoyancy ratio on the iso-contours of stream line, temperature, and concentration. In addition, the predicted results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for 0.1 <= Le <= 50 and Prandtl number Pr = 0.7. Through out the study the Grashof number and aspect ratio are kept constant at 10{sup 4} and 2 respectively and -10 <= N <= 10, while Richardson number has been varied from 0.01 to 10 to simulate forced convection dominated flow, mixed convection and natural convection dominated flow. (authors) 7. Counter-current gas-liquid two-phase flow in a narrow rectangular channel International Nuclear Information System (INIS) Sohn, Byung Hu; Kim, Byong Joo 2000-01-01 A study of counter-current two-phase flow in a narrow rectangular channel has been performed. Two-phase flow patterns and void fractions were experimentally studied in a 760 mm long and 100 mm wide test section with 3.0 mm gap. The resulting data have been compared to previous transition criteria and empirical correlations. The comparison of experimental data to the transition criteria developed by Taitel and Barnea showed good agreement for the bubbly-to-slug transition. For the criteria of Mishima and Ishii to be applicable to the slug to churn transition, a new model seems to be needed for the accurate prediction of the distribution parameter for the counter-current flow in narrow rectangular channels. For the churn-to-annular transition the model of Taitel and Barnea was found to be close to the experimental data. However the model should be improved in conjunction with the channel geometry to accurately predict the counter-current flow limitation and flow transition. It was verified the distribution parameter was well-correlated by the drift-flux model. The distribution parameter for the present study was found to be about 1.2 for all flow regimes except 1.0 for an annular flow. (author) 8. Parametrisation of the collimator scatter correction factors of square and rectangular photon beams International Nuclear Information System (INIS) Jager, H.N.; Heukelom, S.; Kleffens, H.J. van; Gasteren, J.J.M. van; Laarse, R. van der; Venselaar, J.L.M.; Westermann, C.F. 1995-01-01 Collimator scatter correction factors S c have been measured with a cylindrical mini-phantom for five types of dual photon energy accelerators with energies between 6 and 25 MV. Using these S c -data three methods to parametrize S c of square fields have been compared including a third-order polynomial of the natural logarithm of the fieldsize normalised by the fieldsize of 10 cm 2 . Also six methods to calculate S c of rectangular fields have been compared including a new one which determines the equivalent fieldsize by extending Sterling's method. The deviation between measured and calculated S c for every accelerator, energy and all methods are determined resulting in the maximum and average deviation per method. Applied to square fields the maximum and average deviation were for the method of Chen 0.64% and 0.15%, of Szymzcyk 0.98% and 0.21%, and of this work 0.41% and 0.10%. For the rectangular fields the deviations were for the method of Sterling 1.89% and 0.50%, of Vadash 1.60% and 0.28%, of Szymczyk et al. 1.21% and 0.25%, of Chen 1.84% and 0.31% and of this work 0.79% and 0.20%. Finally, a recommendation is given how to limit the number of fields at which S c should be measured 9. Phase distribution measurements in narrow rectangular channels using image processing techniques International Nuclear Information System (INIS) Bentley, C.; Ruggles, A. 1991-01-01 Many high flux research reactor fuel assemblies are cooled by systems of parallel narrow rectangular channels. The HFIR is cooled by single phase forced convection under normal operating conditions. However, two-phase forced convection or two phase mixed convection can occur in the fueled region as a result of some hypothetical accidents. Such flow conditions would occur only at decay power levels. The system pressure would be around 0.15 MPa in such circumstances. Phase distribution of air-water flow in a narrow rectangular channel is examined using image processing techniques. Ink is added to the water and clear channel walls are used to allow high speed still photographs and video tape to be taken of the air-water flow field. Flow field images are digitized and stored in a Macintosh 2ci computer using a frame grabber board. Local grey levels are related to liquid thickness in the flow channel using a calibration fixture. Image processing shareware is used to calculate the spatially averaged liquid thickness from the image of the flow field. Time averaged spatial liquid distributions are calculated using image calculation algorithms. The spatially averaged liquid distribution is calculated from the time averaged spatial liquid distribution to formulate the combined temporally and spatially averaged fraction values. The temporally and spatially averaged liquid fractions measured using this technique compare well to those predicted from pressure gradient measurements at zero superficial liquid velocity 10. Springback Mechanism Analysis and Experiments on Robotic Bending of Rectangular Orthodontic Archwire Science.gov (United States) Jiang, Jin-Gang; Han, Ying-Shuai; Zhang, Yong-De; Liu, Yan-Jv; Wang, Zhao; Liu, Yi 2017-11-01 Fixed-appliance technology is the most common and effective malocclusion orthodontic treatment method, and its key step is the bending of orthodontic archwire. The springback of archwire did not consider the movement of the stress-strain-neutral layer. To solve this problem, a springback calculation model for rectangular orthodontic archwire is proposed. A bending springback experiment is conducted using an orthodontic archwire bending springback measurement device. The springback experimental results show that the theoretical calculation results using the proposed model coincide better with the experimental testing results than when movement of the stress-strain-neutral layer was not considered. A bending experiment with rectangular orthodontic archwire is conducted using a robotic orthodontic archwire bending system. The patient expriment result show that the maximum and minimum error ratios of formed orthodontic archwire parameters are 22.46% and 10.23% without considering springback and are decreased to 11.35% and 6.13% using the proposed model. The proposed springback calculation model, which considers the movement of the stress-strain-neutral layer, greatly improves the orthodontic archwire bending precision. 11. An analytical solution for Dean flow in curved ducts with rectangular cross section Science.gov (United States) Norouzi, M.; Biglari, N. 2013-05-01 In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels. 12. Si nanostructures grown by picosecond high repetition rate pulsed laser deposition International Nuclear Information System (INIS) Pervolaraki, M.; Komninou, Ph.; Kioseoglou, J.; Athanasopoulos, G.I.; Giapintzakis, J. 2013-01-01 One-step growth of n-doped Si nanostructures by picosecond ultra fast pulsed laser deposition at 1064 nm is reported for the first time. The structure and morphology of the Si nanostructures were characterized by X-ray diffraction, scanning electron microscopy and atomic force microscopy. Transmission electron microscopy studies revealed that the shape of the Si nanostructures depends on the ambient argon pressure. Fibrous networks, cauliflower formations and Si rectangular crystals grew when argon pressure of 300 Pa, 30 Pa and vacuum (10 −3 Pa) conditions were used, respectively. In addition, the electrical resistance of the vacuum made material was investigated 13. Si nanostructures grown by picosecond high repetition rate pulsed laser deposition Energy Technology Data Exchange (ETDEWEB) Pervolaraki, M., E-mail: [email protected] [Nanotechnology Research Center and Department of Mechanical and Manufacturing Engineering, University of Cyprus, 75 Kallipoleos Av., PO Box 20537, 1678 Nicosia (Cyprus); Komninou, Ph.; Kioseoglou, J. [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Athanasopoulos, G.I. [Nanotechnology Research Center and Department of Mechanical and Manufacturing Engineering, University of Cyprus, 75 Kallipoleos Av., PO Box 20537, 1678 Nicosia (Cyprus); Giapintzakis, J., E-mail: [email protected] [Nanotechnology Research Center and Department of Mechanical and Manufacturing Engineering, University of Cyprus, 75 Kallipoleos Av., PO Box 20537, 1678 Nicosia (Cyprus) 2013-08-01 One-step growth of n-doped Si nanostructures by picosecond ultra fast pulsed laser deposition at 1064 nm is reported for the first time. The structure and morphology of the Si nanostructures were characterized by X-ray diffraction, scanning electron microscopy and atomic force microscopy. Transmission electron microscopy studies revealed that the shape of the Si nanostructures depends on the ambient argon pressure. Fibrous networks, cauliflower formations and Si rectangular crystals grew when argon pressure of 300 Pa, 30 Pa and vacuum (10{sup −3} Pa) conditions were used, respectively. In addition, the electrical resistance of the vacuum made material was investigated. 14. Particle acceleration by electromagnetic pulses International Nuclear Information System (INIS) Lai, H.M. 1982-01-01 Particle interaction with plane electromagnetic pulses is studied. It is shown that particle acceleration by a wavy pulse, depending on the shape of the pulse, may not be small. Further, a diffusive-type particle acceleration by multiple weak pulses is described and discussed. (author) 15. Dynamics of traveling reaction pulses International Nuclear Information System (INIS) Dovzhenko, A. Yu.; Rumanov, E. N. 2007-01-01 The growth of activator losses is accompanied by the decay of a traveling reaction pulse. In a ring reactor, this propagation threshold is present simultaneously with a threshold related to the ring diameter. The results of numerical experiments with pulses of an exothermal reaction reveal the transition from pulse propagation to a homogeneous hot regime, established regimes with periodic variations of the pulse velocity, and oscillatory decay of the pulse. When the medium becomes 'bistable' as a result of the variation in parameters, this factor does not prevent the propagation of pulses, but leads to changes in the pulse structure 16. Effect of the configuration of the corner in a narrow rectangular channel on flow and heat transfer International Nuclear Information System (INIS) Xu Jianjun; Chen Bingde; Wang Xiaojun 2009-01-01 In order to further understand the effect of the configuration of the corner in a narrow rectangular channel on flow and heat transfer, flow field and temperature field in a narrow rectangular channel were numerical simulated by using CFD code CFX10.0. The results show under the condition of equal quantity of heat of solid which is obtained by decreasing the solid of the corner, the distributions of inside wall temperature for the orthogonal and circular type configurations of the corner are almost the same as that of the archetypal configuration, and those can simulate heat transfer of the archetypal con- figuration. Under the condition of equal Re, secondary flow and friction pressure of the orthogonal type configuration are almost the same as those of the circular type configuration, which shows that the circular type configuration of the corner in a narrow channel can substituted for the archetypal configuration to simulate flow and heat transfer in a narrow rectangular channel. (authors) 17. Effect on two-phase flow frictional pressure drop characteristic in narrow rectangular channel at fluctuant condition International Nuclear Information System (INIS) Li Changwei; Cao Xiaxin; Sun Licheng; Jin Guangyuan 2013-01-01 Based on the data of two-phase flow in narrow rectangular channel, the influence of the two-phase flow friction characteristic under the different fluctuant states was analyzed. Through analyzing the experimental data, it is shown that the fluctuant amplitude of the friction pressure drop is affected slightly by the fluctuant period in narrow rectangular channel, but the frequency of the friction pressure drop fluctuation is changed. However, the change of fluctuant period is of little effect on the average frictional pressure drop. Comparing the φ l 2 (φ g 2 )-X variation curves at static condition with the ones at fluctuant condition, using the L-M method, it's found that the two phase frictional pressure drop in the narrow rectangular channel under the fluctuant state can be calculated by the φ l 2 (φ g 2 )-X variation curve at static condition. (authors) 18. Research on the comparison of extension mechanism of cellular automaton based on hexagon grid and rectangular grid Science.gov (United States) Zhai, Xiaofang; Zhu, Xinyan; Xiao, Zhifeng; Weng, Jie 2009-10-01 Historically, cellular automata (CA) is a discrete dynamical mathematical structure defined on spatial grid. Research on cellular automata system (CAS) has focused on rule sets and initial condition and has not discussed its adjacency. Thus, the main focus of our study is the effect of adjacency on CA behavior. This paper is to compare rectangular grids with hexagonal grids on their characteristics, strengths and weaknesses. They have great influence on modeling effects and other applications including the role of nearest neighborhood in experimental design. Our researches present that rectangular and hexagonal grids have different characteristics. They are adapted to distinct aspects, and the regular rectangular or square grid is used more often than the hexagonal grid. But their relative merits have not been widely discussed. The rectangular grid is generally preferred because of its symmetry, especially in orthogonal co-ordinate system and the frequent use of raster from Geographic Information System (GIS). However, in terms of complex terrain, uncertain and multidirectional region, we have preferred hexagonal grids and methods to facilitate and simplify the problem. Hexagonal grids can overcome directional warp and have some unique characteristics. For example, hexagonal grids have a simpler and more symmetric nearest neighborhood, which avoids the ambiguities of the rectangular grids. Movement paths or connectivity, the most compact arrangement of pixels, make hexagonal appear great dominance in the process of modeling and analysis. The selection of an appropriate grid should be based on the requirements and objectives of the application. We use rectangular and hexagonal grids respectively for developing city model. At the same time we make use of remote sensing images and acquire 2002 and 2005 land state of Wuhan. On the base of city land state in 2002, we make use of CA to simulate reasonable form of city in 2005. Hereby, these results provide a proof of 19. Global field synchronization in gamma range of the sleep EEG tracks sleep depth: Artifact introduced by a rectangular analysis window. Science.gov (United States) Rusterholz, Thomas; Achermann, Peter; Dürr, Roland; Koenig, Thomas; Tarokh, Leila 2017-06-01 Investigating functional connectivity between brain networks has become an area of interest in neuroscience. Several methods for investigating connectivity have recently been developed, however, these techniques need to be applied with care. We demonstrate that global field synchronization (GFS), a global measure of phase alignment in the EEG as a function of frequency, must be applied considering signal processing principles in order to yield valid results. Multichannel EEG (27 derivations) was analyzed for GFS based on the complex spectrum derived by the fast Fourier transform (FFT). We examined the effect of window functions on GFS, in particular of non-rectangular windows. Applying a rectangular window when calculating the FFT revealed high GFS values for high frequencies (>15Hz) that were highly correlated (r=0.9) with spectral power in the lower frequency range (0.75-4.5Hz) and tracked the depth of sleep. This turned out to be spurious synchronization. With a non-rectangular window (Tukey or Hanning window) these high frequency synchronization vanished. Both, GFS and power density spectra significantly differed for rectangular and non-rectangular windows. Previous papers using GFS typically did not specify the applied window and may have used a rectangular window function. However, the demonstrated impact of the window function raises the question of the validity of some previous findings at higher frequencies. We demonstrated that it is crucial to apply an appropriate window function for determining synchronization measures based on a spectral approach to avoid spurious synchronization in the beta/gamma range. Copyright © 2017 Elsevier B.V. All rights reserved. 20. Pulsed rf excited spectrometer having improved pulse width control International Nuclear Information System (INIS) 1977-01-01 RF excitation for a spectrometer is obtained by pulse width modulating an RF carrier to produce the desired broadband RF exciting spectrum. The RF excitation includes a train of composite RF pulses, each composite pulse having a primary pulse portion of a first RF phase and a second pulse portion of a second RF phase opposite that of the first. In this manner, the finite rise and fall times of the primary pulse portion are compensated for by the corresponding rise and fall times of the secondary pulse portion. The primary pulse portion is lengthened by an amount equal to the secondary pulse portion so that the secondary pulse portion cancels the added primary pulse portion. In a spectrometer, the compensating second pulse component removes certain undesired side bands of the RF excitation caused by the finite rise and fall times of the applied RF pulses. The compensating second pulse component removes certain undesired side bands associated with each of the resonant lines of the excited resonance spectrum of the sample under analysis, particularly for wide band RF excitation 1. Impact of different rectangular wires on torsional expression of different sizes of buccal tube. Science.gov (United States) Ajami, Shabnam; Boroujeni, Afshar-Rasti 2018-01-01 Torsions in rectangular wires are the essential part of corrections in the finishing stage of treatment. Moreover the greatest amounts of torques are applied in the molar areas. a clinically effective moment is between 5 and 20 Nmm. In this study we have decided to evaluate the impact of different tube sizes and different dimensions of wires with different modulus of elasticities on the amount torsional bond strength of molar tubes. 60 human impacted molar teeth were collected. A buccal tube was bonded on the buccal surface of all the samples by using light cured adhesive resin. After that, the teeth were mounted in a hard acrylic block. According to the size of buccal tube and the rectangular wires to be tested 4 groups will be designed. Torsional force was applied by instron machine. The torque angle at 5Nmm and at 20Nmm point will be calculated: which means, how many degrees of torque is required to reach the maximum 20Nmm moment from the minimum 5Nmm.One-way ANOVA was used to compare torque angle in all of the groups. The least amount of clinically significant angle was 2.2 ᵒ in the 0.017×0.025 SS and the largest amount of it was 23.7 ᵒ in the 0.017×0.025 TMA in 0.018×0.025 slot molar tube. But, this angle was 19.9 ᵒand 13.6 ᵒ in 0.019×0.025 SS and 0.019×0.025 TMA archwire in 0.022×0.028 molar tube. The 0.017×0.025 SS archwire in 0.018×0.025 molar tube had the lowest clinically significant angle. The largest amount was seen in group 0.017×0.025 TMA in 0.018×0.025 slot molar tube. Key words: Torsional efficacy, rectangular wires, buccal tubes, torque angle. 2. On the prediction of single-phase forced convection heat transfer in narrow rectangular channels International Nuclear Information System (INIS) Ghione, Alberto; Noel, Brigitte; Vinai, Paolo; Demazière, Christophe 2014-01-01 In this paper, selected heat transfer correlations for single-phase forced convection are assessed for the case of narrow rectangular channels. The work is of interest in the thermal-hydraulic analysis of the Jules Horowitz Reactor (JHR), which is a research reactor under construction at CEA-Cadarache (France). In order to evaluate the validity of the correlations, about 300 tests from the SULTAN-JHR database were used. The SULTAN-JHR program was carried out at CEA-Grenoble and it includes different kinds of tests for two different vertical rectangular channels with height of 600 mm and gap of 1.51 and 2.16 mm. The experimental conditions range between 2 - 9 bar for the pressure; 0.5 - 18 m/s for the coolant velocity and 0.5 - 7.5 MW/m 2 for the heat flux (whose axial distribution is uniform). Forty-two thermocouples and eight pressure taps were placed at several axial locations, measuring wall temperature and pressure respectively. The analysis focused on turbulent flow with Reynolds numbers between 5.5 x 10 3 - 2.4 x 10 5 and Prandtl numbers between 1.5 - 6. It was shown that standard correlations as the Dittus-Boelter and Seider-Tate significantly under-estimate the heat transfer coefficient, especially at high Reynolds number. Other correlations specifically designed for narrow rectangular channels were also taken into account and compared. The correlation of Popov-Petukhov in the form suggested by Siman-Tov still under-estimates the heat transfer coefficient, even if slight improvements could be seen. A better agreement for the tests with gap equal to 2.16 mm could be found with the correlation of Ma and the one of Liang. However the heat transfer coefficient when the gap is equal to 1.51 mm could not be predicted accurately. Furthermore these correlations were based on data at low Reynolds numbers (up to 13000) and low heat flux, so the use of them for SULTAN-JHR may be questionable. According to the authors’ knowledge, existing models of heat transfer 3. Herophilus on pulse Directory of Open Access Journals (Sweden) Afonasin, Eugene 2015-01-01 Full Text Available The first detailed study of the pulse (sphygmology is associated in antiquity with Herophilus (the end of the 4th century BCE, an Alexandrian physician, renowned for his anatomical discoveries. The scholars also attribute to him a discovery of a portable and adjustable water-clock, used for measuring ‘natural’ and ‘unnatural’ pulse and, accordingly, temperature of the patient. In the article we translate the principal ancient evidences and comment upon them. We study both the practical aspects of ancient sphygmology and the theoretical speculations associated with it. Ancient theory of proportion and musical harmony allowed to build a classification of the pulses, but the medical experience did not fit well in the Procrustean bed of this rather simple theory. 4. Current Extensions on PULSE Directory of Open Access Journals (Sweden) Sanda Dragos 2010-09-01 Full Text Available Using a learning management system (LMS is a common practise nowadays. Such instruments are used in educational institutions to enhance and support the teaching act as well as in industry for training purposes. In a computer science department of an university such instrument tends to be a basic requirement. That is because not only it allows a better management of courses and a better communication between students and professors, but can also serve as a perfect instrument for presenting teaching related materials for computer science subjects. During the years I have created and used several such instruments: a System with Interactive ackNowledgement and Evaluation of students work during laboratory sessions (SINE, a Php Utility used in Laboratories for Student Evaluation (PULSE, and PULSE Extended. The aim of this paper is to present the current enhancements of PULSE. 5. Millimicrosecond pulse techniques CERN Document Server Lewis, Ian A D 1959-01-01 Millimicrosecond Pulse Techniques, Second Edition focuses on millimicrosecond pulse techniques and the development of devices of large bandwidth, extending down to comparatively low frequencies (1 Mc/s). Emphasis is on basic circuit elements and pieces of equipment of universal application. Specific applications, mostly in the field of nuclear physics instrumentation, are considered. This book consists of eight chapters and opens with an introduction to some of the terminology employed by circuit engineers as well as theoretical concepts, including the laws of circuit analysis, Fourier analysi 6. Pulsed Plasma Electron Sources Science.gov (United States) Krasik, Yakov 2008-11-01 Pulsed (˜10-7 s) electron beams with high current density (>10^2 A/cm^2) are generated in diodes with electric field of E > 10^6 V/cm. The source of electrons in these diodes is explosive emission plasma, which limits pulse duration; in the case E Saveliev, J. Appl. Phys. 98, 093308 (2005). Ya. E. Krasik, A. Dunaevsky, and J. Felsteiner, Phys. Plasmas 8, 2466 (2001). D. Yarmolich, V. Vekselman, V. Tz. Gurovich, and Ya. E. Krasik, Phys. Rev. Lett. 100, 075004 (2008). J. Z. Gleizer, Y. Hadas and Ya. E. Krasik, Europhysics Lett. 82, 55001 (2008). 7. Spallation neutrons pulsed sources International Nuclear Information System (INIS) Carpenter, J. 1996-01-01 This article describes the range of scientific applications which can use these pulsed neutrons sources: Studies on super fluids, measures to verify the crawling model for the polymers diffusion; these sources are also useful to study the neutron disintegration, the ultra cold neutrons. In certain applications which were not accessible by neutrons diffusion, for example, radiations damages, radionuclides production and activation analysis, the spallation sources find their use and their improvement will bring new possibilities. Among others contributions, one must notice the place at disposal of pulsed muons sources and neutrinos sources. (N.C.). 3 figs CERN Document Server Alabaster, Clive 2012-01-01 This book is a practitioner's guide to all aspects of pulse Doppler radar. It concentrates on airborne military radar systems since they are the most used, most complex, and most interesting of the pulse Doppler radars; however, ground-based and non-military systems are also included. It covers the fundamental science, signal processing, hardware issues, systems design and case studies of typical systems. It will be a useful resource for engineers of all types (hardware, software and systems), academics, post-graduate students, scientists in radar and radar electronic warfare sectors and milit 9. Pulse Synchronization System (PSS) International Nuclear Information System (INIS) 1977-06-01 This document is intended to serve as an operations manual, as well as a documentation of the backup analyses pertinent to the design as delivered. A history of earlier unsuccessful versions of the Pulse Synchronization System (PSS) is not included. The function of the PSS is to synchronize the time of arrival at the fusion target of laser pulses that are propagated through the 20 amplifier chains of the SHIVA laser. The positional accuracy requirement is +-1.5 mm (+-5 psec), and is obtained by the PSS with a wide margin factor 10. Physical model of reactor pulse International Nuclear Information System (INIS) Petrovic, A.; Ravnik, M. 2004-01-01 Pulse experiments have been performed at J. Stefan Institute TRIGA reactor since 1991. In total, more than 130 pulses have been performed. Extensive experimental information on the pulse physical characteristics has been accumulated. Fuchs-Hansen adiabatic model has been used for predicting and analysing the pulse parameters. The model is based on point kinetics equation, neglecting the delayed neutrons and assuming constant inserted reactivity in form of step function. Deficiencies of the Fuchs-Hansen model and systematic experimental errors have been observed and analysed. Recently, the pulse model was improved by including the delayed neutrons and time dependence of inserted reactivity. The results explain the observed non-linearity of the pulse energy for high pulses due to finite time of pulse rod withdrawal and the contribution of the delayed neutrons after the prompt part of the pulse. The results of the improved model are in good agreement with experimental results. (author) 11. Performance of an inclined solar still with rectangular grooves and ridges International Nuclear Information System (INIS) Anburaj, P.; Kalidasa, Murugavel K.; Samuel Hansen, R. 2013-01-01 This work investigates the experimental performance of a new type inclined solar still with rectangular grooves and ridges in absorber plate. The still was fabricated and tested for various inclination angles of 25, 30 and 35 facing south with absorber plate. Performances of the still were compared with different wick materials (Black cotton cloth, Jute cloth, and Waste cotton pieces) on the absorber plate. The effect of placing porous material (Clay pot) and energy storing material (Mild steel pieces) in the grooves were studied. The results demonstrate that 30 inclination is optimum which yielded 3.77 L/day production. Compared to different wick materials, black cotton cloth helps to achieve maximum productivity of 4.21 L/day. The addition of permeable materials and energy absorbing materials also enhances the distillate output to 4.27 L/day. (authors) 12. Investigation on flow and heat transfer characteristics in rectangular channel with drop-shaped pin fins Directory of Open Access Journals (Sweden) Fengming Wang 2012-12-01 Full Text Available The flow and heat transfer characteristics inside a rectangular channel embedded with pin fins were numerically and experimentally investigated. Several differently shaped pin fins (i.e., circular, elliptical, and drop-shaped with the same cross-sectional areas were compared in a staggered arrangement. The Reynolds number based on the obstructed section hydraulic diameter (defined as the ratio of the total wetted surface area to the open duct volume available for flow was varied from 4800 to 8200. The more streamlined drop-shaped pin fins were better at delaying or suppressing separation of the flow passing through them, which decreased the aerodynamic penalty compared to circular pin fins. The heat transfer enhancement of the drop-shaped pin fins was less than that of the circular pin fins. In terms of specific performance parameters, drop-shaped pin fins are a promising alternative configuration to circular pin fins. 13. Methods of Experimental Investigation of Cavitation in a Convergent - Divergent Nozzle of Rectangular Cross Section Directory of Open Access Journals (Sweden) Jablonská Jana 2016-08-01 Full Text Available Cavitation is a phenomenon with both positive and negative effects and with dynamic manifestations in hydraulic, food, chemical and other machinery. This article deals with the detection and dynamic behavior of cavitation clouds in water flows through a rectangular cross-section convergent-divergent nozzle. Cavitation was measured by methods applicable in engineering practice. Pressure, flow rate, noise, vibration, and amount of air dissolved in the liquid were measured and cavitation region was recorded with a high-speed camera. Evaluation of acquired images in connection with measured pressure pulsations and mechanical vibrations was performed with the use of the FFT method. In certain cases, dimensionless parameters were used to generalize the measurements. The results will be used to specify multiphase mathematical cavitation model parameters. 14. Liquid-metal flow in a rectangular duct with a non-uniform magnetic field International Nuclear Information System (INIS) Walker, J.S. 1986-04-01 This paper treats liquid-metal flow in rectangular ducts with thin conducting walls. A transverse magnetic field changes from a uniform strength upstream to a weaker uniform strength downstream. The Hartmann number and the interaction parameter are assumed to be large, while the magnetic Reynolds number is assumed to be small. If the magnetic field changes gradually over a long duct length, the velocity and pressure are nearly uniform in each cross section and the flow differs slightly from locally fully developed flow. If the magnetic field changes more abruptly over a shorter duct length, the velocity and pressure are much larger near the walls parallel to the magnetic field than in the central part of duct. Solutions for the pressure drops due to the magnetic field change are presented 15. Flame Quenching Dynamics of High Velocity Flames in Rectangular Cross-section Channels KAUST Repository Mahuthannan, Ariff Magdoom; Lacoste, Deanna; Damazo, Jason; Kwon, Eddie; Roberts, William L. 2017-01-01 Understanding flame quenching for different conditions is necessary to develop safety devices like flame arrestors. In practical applications, the speed of a deflagration in the lab-fixed reference frame will be a strong function of the geometry through which the deflagration propagates. This study reports on the effect of the flame speed, at the entrance of a quenching section, on the quenching distance. A 2D rectangular channel joining two main spherical vessels is considered for studying this effect. Two different velocity regimes are investigated and referred to as configurations A, and B. For configuration A, the velocity of the flame is 20 m/s, while it is about 100 m/s for configuration B. Methane-air stoichiometric mixtures at 1 bar and 298 K are used. Simultaneous dynamic pressure measurements along with schlieren imaging are used to analyze the quenching of the flame. Risk assessment of re-ignition is also reported and analyzed. 16. An approach to global equalisation in a rectangular room at low frequencies DEFF Research Database (Denmark) Orozco, Arturo 1999-01-01 The motivation of this study is the fact that sound reproduced in a room undergoes a spectral colouration, which is undesirable. This effect is particularly severe at low frequencies in small enclosures.A theoretical study based on computer simulations is presented. The listening area is a contin......The motivation of this study is the fact that sound reproduced in a room undergoes a spectral colouration, which is undesirable. This effect is particularly severe at low frequencies in small enclosures.A theoretical study based on computer simulations is presented. The listening area...... is a continuous region in a rectangular room that occupies almost the entire room. A travelling wave is generated by feeding a number of loudspeakes with the signal to be reproduced passed through digital filters. The problem of designing these filters is investigated both in the frequency domain and in the time... 17. Pool Boiling Characteristics on the Microstructure surfaces with Both Rectangular Cavities and Channels Energy Technology Data Exchange (ETDEWEB) Kim, Dong Eok; Myung, Byung-Soo [Kyungpook Nat’l Univ., Daegu (Korea, Republic of); Park, Su Cheong; Yu, Dong In [POSTECH, Pohang (Korea, Republic of); Kim, Moo Hwan [Korea Institute of Nuclear Safety (KINS), Daejeon (Korea, Republic of); Ahn, Ho Seon [Incheon Nat’l Univ., Incheon (Korea, Republic of) 2016-06-15 Based on a surface design with rectangular cavities and channels, we investigated the effects of gravity and capillary pressure on pool-boiling Critical Heat Flux (CHF). The microcavity structures could prevent liquid flow by the capillary pressure effect. In addition, the microchannel structures contributed to induce one-dimensional liquid flow on the boiling surface. The relationship between the CHF and capillary flow was clearly established. The driving potentials for the liquid supply into a boiling surface can be generated by the gravitational head and capillary pressure. Through an analysis of pool boiling and visualization data, we reveal that the liquid supplement to maintain the nucleate boiling condition on a boiling surface is closely related to the gravitational pressure head and capillary pressure effect. 18. Scanning tunneling microscopic images and scanning tunneling spectra for coupled rectangular quantum corrals International Nuclear Information System (INIS) Mitsuoka, Shigenori; Tamura, Akira 2011-01-01 Assuming that an electron confined by double δ-function barriers lies in a quasi-stationary state, we derived eigenstates and eigenenergies of the electron. Such an electron has a complex eigenenergy, and the imaginary part naturally leads to the lifetime of the electron associated with tunneling through barriers. We applied this point of view to the electron confined in a rectangular quantum corral (QC) on a noble metal surface, and obtained scanning tunneling microscopic images and a scanning tunneling spectrum consistent with experimental ones. We investigated the electron states confined in coupled QCs and obtained the coupled states constructed with bonding and anti-bonding states. Using those energy levels and wavefunctions we specified scanning tunneling microscope (STM) images and scanning tunneling spectra (STS) for the doubly and triply coupled QCs. In addition we pointed out the feature of resonant electron states associated with the same QCs at both ends of the triply coupled QCs. 19. A comparison of Landsat point and rectangular field training sets for land-use classification Science.gov (United States) Tom, C. H.; Miller, L. D. 1984-01-01 Rectangular training fields of homogeneous spectroreflectance are commonly used in supervised pattern recognition efforts. Trial image classification with manually selected training sets gives irregular and misleading results due to statistical bias. A self-verifying, grid-sampled training point approach is proposed as a more statistically valid feature extraction technique. A systematic pixel sampling network of every ninth row and ninth column efficiently replaced the full image scene with smaller statistical vectors which preserved the necessary characteristics for classification. The composite second- and third-order average classification accuracy of 50.1 percent for 331,776 pixels in the full image substantially agreed with the 51 percent value predicted by the grid-sampled, 4,100-point training set. 20. Two-phase upward air water flow in a prismatic channel with rectangular base International Nuclear Information System (INIS) Carvalho Tofani, P. de 1984-01-01 Two-phase liquid-gas mixtures provide suitable means to simulate water-water vapor flows, which may occur in nuclear reactor cores. The mastery of physical transport phenomena is of great importance, as far as the analysis of such thermal systems is concerned. Within the framework of thermal-hydraulic programs, experiments have been carried out to investigate the two-phase upward air-water flow structure, in a rectangular test section, by using independent measuring techniques, which comprise direct viewing and photography, electrical probes and gamma-ray attenuation. In this paper, flow pattern maps and correlations for flow pattern transitions, void fraction profiles, liquid film thickness and superficial average void fraction are proposed and compared to available data. (Author) [pt 1. Progress in electrical and mechanical properties of rectangular MgB2 wires International Nuclear Information System (INIS) Kovac, P; Melisek, T; Kopera, L; Husek, I; Polak, M; Kulich, M 2009-01-01 Critical current densities and mechanical resistance of MgB 2 wires made by the rectangular wire-in-tube technique (RWIT) have been studied. Wires prepared from different precursor powders and variable sheath materials are compared. The best electrical performance (10 4 A cm -2 at 11.3 T) was measured for the wire with mechanically alloyed powder doped by SiC. While the critical current densities, J c , at 4.2 K are considerably influenced by the powder used, the differences at 20 K are much smaller. Flattened wires show different levels of critical current anisotropy influenced by the precursor powder used. Stress-strain characteristics and critical current degradation are strongly affected by the applied metallic materials and also by the filament's strength. The highest irreversible strain ε irr = 0.55% was measured for Ti/Cu/Monel sheathed wire with filaments from mechanically alloyed powder. 2. Topology optimization for elastic base under rectangular plate subjected to moving load Directory of Open Access Journals (Sweden) Jilavyan Samvel H. 2015-09-01 Full Text Available Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two- dimensional Heaviside‘s function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented. 3. Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions Directory of Open Access Journals (Sweden) Huimin Liu 2017-01-01 Full Text Available This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique. 4. Three-dimensional numerical simulations of turbulent cavitating flow in a rectangular channel Science.gov (United States) Iben, Uwe; Makhnov, Andrei; Schmidt, Alexander 2018-05-01 Cavitation is a phenomenon of formation of bubbles (cavities) in liquid as a result of pressure drop. Cavitation plays an important role in a wide range of applications. For example, cavitation is one of the key problems of design and manufacturing of pumps, hydraulic turbines, ship's propellers, etc. Special attention is paid to cavitation erosion and to performance degradation of hydraulic devices (noise, fluctuations of the mass flow rate, etc.) caused by the formation of a two-phase system with an increased compressibility. Therefore, development of a model to predict cavitation inception and collapse of cavities in high-speed turbulent flows is an important fundamental and applied task. To test the algorithm three-dimensional simulations of turbulent flow of a cavitating liquid in a rectangular channel have been conducted. The obtained results demonstrate the efficiency and robustness of the formulated model and the algorithm. 5. Experimental study of gas-liquid flow local characteristics in rectangular microchannel Directory of Open Access Journals (Sweden) Bartkus German 2017-01-01 Full Text Available Using high-speed video recording and the method of dual laser scanning the gas-liquid flow was investigated in a rectangular microchannel with an aspect ratio of 0.74 (cross section 269×362 μm. The T-mixer was used at the channel’s inlet for the two-phase flow formation. The peculiarity of this work is using a number of liquids (ethanol, distilled water, 40% aqueous ethanol with different physical properties, including surface tension, viscosity, and density, with nitrogen. Experiments were carried out for the vertically upward and horizontal flow. Using laser scanning method the maps of flow patterns were obtained for all mixtures. 6. Experimental investigation of onset of nucleate boiling in this rectangular channels International Nuclear Information System (INIS) Belhadj, M.; Christensen, R.N.; Aldemir, T. 1988-01-01 The 10 kW, HEU fueled Ohio State University Research Reactor (OSURR) will be upgraded to operate with plate type LEU U 3 Si 2 , fuel elements in the power range 250-500 kW. The core will be cooled by natural convection and an onset of nucleate boiling (ONB) margin of 1.2 will be maintained in the hot channel under steady-state operation. The validity of the correlations used for predicting ONB in plate type research reactors is not known for low heat flux-low velocity flows. An experiment has been set up at The Ohio State University to investigate ONB for laminar flow in this rectangular channels. The results show that: The Bergles-Rohsenow correlation and the correlation proposed by Ricque and Siboul predict higher and lower ONB fluxes than actual, respectively. The ONB heat flux is flow velocity dependent 7. Laser--Doppler anemometry technique applied to two-phase dispersed flows in a rectangular channel International Nuclear Information System (INIS) Lee, S.L.; Srinivasan, J. 1979-01-01 A new optical technique using Laser--Doppler anemometry has been applied to the local measurement of turbulent upward flow of a dilute water droplet--air two-phase dispersion in a vertical rectangular channel. Individually examined were over 20,000 droplet signals coming from each of a total of ten transversely placed measuring points, the closest of which to the channel wall was 250 μ away from the wall. Two flows of different patterns due to different imposed flow conditions were investigated, one with and the other without a liquid film formed on the channel wall. Reported are the size and number density distribution and the axial and lateral velocity distributions for the droplets as well as the axial and lateral velocity distributions for the air 8. Active control of radiated sound power from a baffled, rectangular panel DEFF Research Database (Denmark) Mørkholt, Jakob 1996-01-01 with an array of eleven microphones in front of the panel, is very close to minimising the actual radiated sound power. Practical experiments where such an array estimate has been minimised using the filtered X LMS algorithm have shown that substantial reductions of radiated sound power can be obtained over......Active control of radiated sound power from a rectangular baffled panel by minimisation of an accurate power estimate, using piezoceramic actuators, has been investigated. Computer simulations have shown that minimising a power estimate obtained by discretised integration of the far field intensity...... a broad frequency range using few piezoceramic actuators, provided that an accurate estimate of the sound power is available for minimisation.... 9. Three-dimensional MHD [magnetohydrodynamic] flows in rectangular ducts of liquid-metal-cooled blankets International Nuclear Information System (INIS) Hua, T.Q.; Walker, J.S.; Picologlou, B.F.; Reed, C.B. 1988-07-01 Magnetohydrodynamic flows of liquid metals in rectangular ducts with thin conducting walls in the presence of strong nonuniform transverse magnetic fields are examined. The interaction parameter and Hartmann number are assumed to be large, whereas the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined in very thin boundary layers adjacent to the walls. A significant fraction of the fluid flow is concentrated in the boundary layers adjacent to the side walls which are parallel to the magnetic field. This paper describes the analysis and numerical methods for obtaining 3-D solutions for flow parameters outside these layers, without solving explicitly for the layers themselves. Numerical solutions are presented for cases which are relevant to the flows of liquid metals in fusion reactor blankets. Experimental results obtained from the ALEX experiments at Argonne National Laboratory are used to validate the numerical code. In general, the agreement is excellent. 5 refs., 14 figs 10. Characteristic of local parameter of bubbly flow in rectangular channel under inclined and rolling conditions International Nuclear Information System (INIS) Yan Changqi; Jin Guangyuan; Sun Licheng; Wang Yang 2015-01-01 Characteristics of local parameters of bubbly flow were investigated in rectangular channel (40 mm × 3 mm) under inclined and rolling conditions. Under vertical condition, the distribution type 'wall peak' and 'core peak' are observed, and 'core peak' exists when the liquid superficial velocity is low and the gas superficial velocity is high. Under inclined condition, the peaks of two distribution types get strengthened at the top of the channel, and weakened at the bottom. Under rolling condition, the peaks of two distribution types get strengthened compared with the same angle under inclined condition when the angle is getting larger. The influence from rolling motion gets stronger on the peak of two distribution types when the rolling movement is more violent. (authors) 11. Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads Science.gov (United States) Viswanathan, A. V.; Tamekuni, M.; Baker, L. L. 1974-01-01 A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution. 12. Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory Directory of Open Access Journals (Sweden) Alireza Shooshtari Full Text Available Abstract Free vibration of a magnetoelectroelastic rectangular plate is investigated based on the Reddy's third-order shear deformation theory. The plate rests on an elastic foundation and it is considered to have different boundary conditions. Gauss's laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single partial differential equation and then by using the Galerkin method, the ordinary differential equation of motion as well as an analytical relation for the natural frequency of the plate is obtained. Some numerical examples are presented to validate the proposed model and to investigate the effects of several parameters on the vibration frequency of the considered smart plate. 13. Experimental visualization coalesced interaction of sliding bubble near wall in vertical narrow rectangular channel International Nuclear Information System (INIS) Xu Jianjun; Chen Bingde; Wang Xiaojun 2011-01-01 The characteristic of the coalesced sliding bubble was visually observed by wide side and narrow side of the narrow rectangular channel using high speed digital camera. The results show that the coalesced time among the sliding bubbles is quick, and the new formation of coalesced bubble is not lift-off, and it continues to slide along the heated surface in low heat flux for the isolated bubble region. The influence region is about 2 times projected area of the sliding bubble when the sliding bubbles begin to interact. The sliding bubble velocities increase duo to the interaction among the bubbles, which contributes to enhance heat transfer of this region. Finally, the effect of coalesced interaction of growing bubble in the nucleation sites on bubble lift-off was discussed and analysed. (authors) 14. Computationally Efficient 2D DOA Estimation with Uniform Rectangular Array in Low-Grazing Angle Directory of Open Access Journals (Sweden) Junpeng Shi 2017-02-01 Full Text Available In this paper, we propose a computationally efficient spatial differencing matrix set (SDMS method for two-dimensional direction of arrival (2D DOA estimation with uniform rectangular arrays (URAs in a low-grazing angle (LGA condition. By rearranging the auto-correlation and cross-correlation matrices in turn among different subarrays, the SDMS method can estimate the two parameters independently with one-dimensional (1D subspace-based estimation techniques, where we only perform difference for auto-correlation matrices and the cross-correlation matrices are kept completely. Then, the pair-matching of two parameters is achieved by extracting the diagonal elements of URA. Thus, the proposed method can decrease the computational complexity, suppress the effect of additive noise and also have little information loss. Simulation results show that, in LGA, compared to other methods, the proposed methods can achieve performance improvement in the white or colored noise conditions. 15. Heat transfer of natural convection in a rectangular cavity with vertical walls of different temperatures International Nuclear Information System (INIS) Seki, Nobuhiro; Fukusako, Shoichiro; Inaba, Hideo 1978-01-01 In the present study the behavior of heat transfer in a rectangular cavity with one isothermal vertical wall heated and the other cooled is investigated. Heat transfer coefficients on the vertical walls are measured for fluids with Prandtl number Pr of 3 to 40,000 in case of aspect-ratio H/W from 5 to 47.5 and their correlated results are presented for laminar, transition and turbulent regions, respectively. It is shown that the present arrangement (Nu sub(H) - Ra sub(H)) using the height of cavity as a representative length may significantly be useful in the various heat transfer modes accompanied with flow patterns of them. (auth.) 16. Harmonic Suppressed Slot Antennas Using Rectangular/Circular Defected Ground Structures Directory of Open Access Journals (Sweden) 2012-01-01 Full Text Available Two wide rectangle-shaped microstrip-fed 2.6-GHz slot antennas using defected ground structures (DGSs with a low design complexity are proposed to achieve wideband harmonic suppression. To accomplish this, two rectangular DGSs (RDGSs in the first antenna and two circular DGSs (CDGSs in the second one with various dimensions are etched into the ground plane, which could have a wideband-stop characteristic. Simulated and measured reflection coefficients indicate that the two proposed structures effectively suppress the second and third harmonics up to 23 dB between 3.5 and 10.5 GHz with a maximum ripple of 2.4 dB. In addition, the radiation patterns and peak gains of the antennas can be suppressed at least 17 dB and 7.1 dBi, respectively, at the third harmonic frequency of 7.86 GHz. 17. A Novel CPW BandPass Filter Integrating Periodic Rectangular Slot Cells Directory of Open Access Journals (Sweden) 2015-12-01 Full Text Available In this paper, we introduce the design and the achievement of a Bandpass filter structure based on the use of rectangular slot cell. The originality of this work is to achieve a coplanar filter easy to integrate with microwave planar circuits and having a wide frequency bandwidth. The proposed bandpass filter is a low cost and compact planar filter structure. The final circuit is simulated by using two electromagnetic solvers, ADS and HFSS. The validation into simulation is based on using optimization methods integrated into the both solvers. Simulations have taken into account a high meshing density to cover the whole circuit. The fabricated bandpass filter has an area of 35X31mm2 and having a good insertion loss around -0.75dB in the bandwidth. The comparison between simulation and measurement results presents a good agreement. 18. Evanescently Coupled Rectangular Microresonators in Silicon-on-Insulator with High Q-Values: Experimental Characterization Directory of Open Access Journals (Sweden) Manuel Mendez-Astudillo 2017-04-01 Full Text Available We report on evanescently coupled rectangular microresonators with dimensions up to 20 × 10 μm2 in silicon-on-insulator in an add-drop filter configuration. The influence of the geometrical parameters of the device was experimentally characterized and a high Q value of 13,000 was demonstrated as well as the multimode optical resonance characteristics in the drop port. We also show a 95% energy transfer between ports when the device is operated in TM-polarization and determine the full symmetry of the device by using an eight-port configuration, allowing the drop waveguide to be placed on any of its sides, providing a way to filter and route optical signals. We used the FDTD method to analyze the device and e-beam lithography and dry etching techniques for fabrication. 19. Discharge coefficient of a rectangular sharp-edged broad-crested weir Directory of Open Access Journals (Sweden) Zachoval Zbyněk 2014-06-01 Full Text Available This paper is concerned with the determination of the relationship for the calculation of the discharge coefficient at free overflow over a rectangular sharp-edged broad-crested weir without lateral contraction. The determination was made on the basis of new measurement in a range of the relative thickness of the weir from 0.12 to 0.30 and newly in a large range of relative height of the weir extremely from 0.24 to 6.8 which greatly expands the application possibilities of low weirs. In addition, the effects of friction and surface tension on the value of the discharge coefficient were evaluated as well as the effect of the relative thickness of the weir. The new equation for discharge coefficient, expressed using the relative height of the weir, was subjected to verification made by an independent laboratory which confirmed its accuracy. 20. CFD analysis of premixed hydrogen/air combustion in an upright, rectangular shaped combustion chamber International Nuclear Information System (INIS) Gera, B.; Singh, R.K.; Vaze, K.K. 2014-01-01 Premixed hydrogen/air combustion in an upright, rectangular shaped combustion chamber has been performed numerically using commercial CFD code CFD-ACE+. The combustion chamber had dimensions 1 m X 0.024 m X 1 m. Simulations were carried out for 10% (v/v) hydrogen concentration for which experimental results were available. Effect of different boundary condition and ignition position on flame propagation was studied. Time dependent flame propagation in the chamber was predicted by CFD code. The computed transient flame propagation in the chamber was in good agreement with experimental results. The present work demonstrated that the available commercial CFD codes are capable of modeling hydrogen deflagration in a realistic manner. (author) 1. Flame Quenching Dynamics of High Velocity Flames in Rectangular Cross-section Channels KAUST Repository Mahuthannan, Ariff Magdoom 2017-01-05 Understanding flame quenching for different conditions is necessary to develop safety devices like flame arrestors. In practical applications, the speed of a deflagration in the lab-fixed reference frame will be a strong function of the geometry through which the deflagration propagates. This study reports on the effect of the flame speed, at the entrance of a quenching section, on the quenching distance. A 2D rectangular channel joining two main spherical vessels is considered for studying this effect. Two different velocity regimes are investigated and referred to as configurations A, and B. For configuration A, the velocity of the flame is 20 m/s, while it is about 100 m/s for configuration B. Methane-air stoichiometric mixtures at 1 bar and 298 K are used. Simultaneous dynamic pressure measurements along with schlieren imaging are used to analyze the quenching of the flame. Risk assessment of re-ignition is also reported and analyzed. 2. The investigation of ferromagnetic resonance linewidth in Ni80Fe20 films with submicron rectangular elements Directory of Open Access Journals (Sweden) D. Zhang 2016-05-01 Full Text Available Patterned magnetic films with nano-scaled dots exhibit some special magnetic properties. In this paper, we investigate the in-plane shape anisotropy and the magnetization dynamic damping in permalloy (Ni80Fe20 arrays of submicron rectangular elements using ferromagnetic resonance (FMR. The FMR linewidth exhibits a dependence on the element size, and mainly comes from the contribution of the intrinsic damping. Also the contribution of two-magnon scattering plays an important role and is reduced with increasing aspect ratio. The damping coefficient decreases from 0.0129 to 0.0118 with the element length increasing from 300 nm to 1200 nm, and the theoretical calculation suggests that the change of damping results from the longitudinal and transverse interlayer spin current due to the spatially inhomogeneous magnetization dynamics. 3. Experimental study on transition characteristics of pulsating flow in narrow rectangular channel International Nuclear Information System (INIS) Zhang Chuan; Tan Sichao; Liu Yusheng; Gao Puzhen; Zhao Jianing; Zhang Hong 2013-01-01 Experimental study of flow characteristic in smooth narrow rectangular channel under harmonic pulsating flow which covers laminar to turbulent flow (Reynolds number 7504-450) was carried out. The experimental results show that the frictional factors in acceleration phase of pulsating flow are higher than that in steady state, but lower than that in deceleration phase. Womersley parameter has a significant influence on the critical Reynolds number. The critical Reynolds number decreases with the increase of Womersley parameter in acceleration phase and it is opposite in deceleration phase. An empirical correlation was developed to predict the critical Reynolds number based on the experimental data, and the correlation can fit with critical Reynolds number in steady state. (authors) 4. Pressure drop of magnetohydrodynamic two-phase annular flow in rectangular channel International Nuclear Information System (INIS) Kumamaru, Hiroshige; Fujiwara, Yoshiki; Ogita, Kenji 1999-01-01 Numerical calculations have been performed on magnetohydrodynamic (MHD) two-phase annular flow in a rectangular channel with a small aspect ratio, i.e.a small ratio of the channel side perpendicular to the applied magnetic field and the side parallel to the field. Results of the present calculation agree nearly with Inoue et al.'s experimental results in the region of large liquid Reynolds numbers and large Hartmann numbers. Calculation results also show that the pressure drop ratio, i.e. the ratio of pressure drop of two-phase flow to that of single-phase flow under the same liquid flow rate and applied magnetic field, becomes lower than ∼0.02 for conditions of a fusion reactor plant. (author) 5. Influence of the synchrotron radiation on particle dynamics in a rectangular undulator International Nuclear Information System (INIS) Chin, Yong Ho. 1989-03-01 This paper is concerned with the synchrotron radiation from an undulating electron beam in a rectangular waveguide. It is shown analytically and numerically that the radiated energy spectrum may differ significantly from the free space result when the undulator length divided by the Lorentz factor of the electron beam is larger than the transverse size of the waveguide. The undulator radiation is identified with the awake field in beam instabilities. The concepts of wake function and impedance are introduced to formulate the present problem in the same manner as the beam instability problem. It is shown that the obtained impedances satisfy the Panofsky-Wenzel theorem and other properties inevitable for wake fields. 5 refs., 2 figs 6. Vacuum stress tensor of a scalar field in a rectangular waveguide International Nuclear Information System (INIS) Rodrigues, R.B.; Svaiter, N.F.; Paola, R.D.M. de 2001-11-01 Using the heat Kernel method and the analytical continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, {T μν (vector x)} and {Θ μν (vector x)}, associated with a massless scalar field confined in the interior of an infinity long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using {T 00 (vector x)} and {Θ 00 (vector x)}. From the stress tensors we obtain the local casimir forces in all walls by introducing a particular external configuration. It is hown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations. (author) 7. Transmission properties of terahertz waves through asymmetric rectangular aperture arrays on carbon nanotube films Directory of Open Access Journals (Sweden) Yue Wang 2016-04-01 Full Text Available Transmission spectra of terahertz waves through a two-dimensional array of asymmetric rectangular apertures on super-aligned multi-walled carbon nanotube films were obtained experimentally. In this way, the anisotropic transmission phenomena of carbon nanotube films were observed. For a terahertz wave polarization parallel to the orientation of the carbon nanotubes and along the aperture short axis, sharp resonances were observed and the resonance frequencies coincided well with the surface plasmon polariton theory. In addition, the minima of the transmission spectra were in agreement with the location predicted by the theory of Wood’s anomalies. Furthermore, it was found that the resonance profiles through the carbon nanotube films could be well described by the Fano model. 8. Unsteady cavity flow around a rectangular cylinder; Kakuchu mawari no hiteijo cavitation nagare Energy Technology Data Exchange (ETDEWEB) Takahashi, T.; Kaga, T.; Ota, T. [Tohoku University, Sendai (Japan). Faculty of Engineering; Mori, T. [Hachinohe Institute of Technology, Aomori (Japan) 1995-08-25 Unsteady cavity flow around a rectangular cylinder was observed using a high-speed camera. To clarify the correlation between the cavity behavior and fluid dynamic characteristics in the transitional region and supercavitation, fluctuating forces and surface pressures on the cylinder surface were recorded simultaneously. The tested cylinder has a critical width-to-height ration 2.8, in which the shear layer separated from the leading edge intermittently reattaches near the trailing edge. Bubbly cloud originating from the separated region near the leading edge causes fluctuation of cavity termination and induces large oscillations of fluid forces and pressures. As the cavitation number decreases, the low-frequency fluctuation of the cavity developing downstream of the rear surface increases in the fluid dynamic behavior. 24 refs., 12 figs. 9. Magnetic field from arbitrarily shaped flat coils with filamentary, ribbon, and rectangular cross sections International Nuclear Information System (INIS) Weissenburger, D.W.; Christensen, U.R. 1975-01-01 This report describes the derivation of three groups of equations: (1) Field components from an arbitrarily shaped filament lying in a plane. (2) Field components from an arbitrarily shaped ribbon of infinitesimal thickness with center line lying in a plane. (3) Field components from an arbitrarily shaped bar of rectangular cross section with its center line lying in a plane. In all three cases analytical expressions for the field components were found for an infinitesimal element of the cross section. These expressions are then integrated numerically along the arbitrarily shaped center line of the coil to obtain the three field components. As a check for accuracy the calculated field values of an elliptically shaped coil were compared to an existing analytic expression for a filamentary elliptical coil 10. Characterizing the attenuation of coaxial and rectangular microwave-frequency waveguides at cryogenic temperatures Energy Technology Data Exchange (ETDEWEB) Kurpiers, Philipp; Walter, Theodore; Magnard, Paul; Salathe, Yves; Wallraff, Andreas [ETH Zuerich, Department of Physics, Zuerich (Switzerland) 2017-12-15 Low-loss waveguides are required for quantum communication at distances beyond the chip-scale for any low-temperature solid-state implementation of quantum information processors. We measure and analyze the attenuation constant of commercially available microwave-frequency waveguides down to millikelvin temperatures and single photon levels. More specifically, we characterize the frequency-dependent loss of a range of coaxial and rectangular microwave waveguides down to 0.005 dB/m using a resonant-cavity technique. We study the loss tangent and relative permittivity of commonly used dielectric waveguide materials by measurements of the internal quality factors and their comparison with established loss models. The results of our characterization are relevant for accurately predicting the signal levels at the input of cryogenic devices, for reducing the loss in any detection chain, and for estimating the heat load induced by signal dissipation in cryogenic systems. (orig.) 11. Investigation of friction in rectangular Nitrile-Butadiene Rubber (NBR) hydraulic rod seals for defence applications Energy Technology Data Exchange (ETDEWEB) Bhaumik, Shankar; Guruprasad, S.; Bhandari, P. [R and DE , Dighi (India); Kumaraswamy, A. [Defence Institute of Advanced Technology, Girinagar (India) 2015-11-15 Contact based FE simulations have been carried out to estimate the contact pressure distribution at seal/rod interface at sealed oil pressures of 10, 20 and 30 MPa and constant rod velocity of 0.12 m/s. Oil film thickness at the interface was then computed analytically at various combinations of oil pressures and rod velocities. Seal contact pressure and oil film thickness data along with surface roughness, intermolecular interaction between seal/rod interfaces has been perused to estimate the friction in Nitrile-Butadiene Rubber (NBR) rectangular hydraulic rod seals using theoretical models such as Inverse hydrodynamic lubrication (IHL), Greenwood-Williamson (GW) and Wassink's models. The friction at seal/rod interface was also measured experimentally using a specially designed test rig. The comparison of theoretical and experimental data revealed that, friction computed from GW and Wassink's models had good agreement with the experimental results. 12. Testing of the rectangular pivot-point bellows for the PPPL tokamak fusion test reactor International Nuclear Information System (INIS) Haughian, J.; Lou, K.; Greer, J.; Fong, M.; Scalise, D.T. 1983-12-01 The Neutral Beam Pivot Point Bellows (PPB) is installed in the duct which connects the Neutral Beam Enclosure to the Torus. This bellows, located at the pivot point, must fit the severely limited space available at the pivot-point location. Consequently, it has to be made rectangular in cross section with a large inside area for beam access. This leads to small convolutions with high stress concentrations. The function of the bellows is to permit change in the angular positioning of the neutral beam line with respect to the Tokamak, to isolate the Neutral Beam Line from the deflection of the Torus during bake out, and to allow for all misalignments. Internally the bellows will have a vacuum along with such gases such as hydrogen or deuterium. Tests parameters are described 13. Gap states and edge properties of rectangular graphene quantum dot in staggered potential Science.gov (United States) Jeong, Y. H.; Eric Yang, S.-R. 2017-09-01 We investigate edge properties of a gapful rectangular graphene quantum dot in a staggered potential. In such a system gap states with discrete and closely spaced energy levels exist that are spatially located on the left or right zigzag edge. We find that, although the bulk states outside the energy gap are nearly unaffected, spin degeneracy of each gap state is lifted by the staggered potential. We have computed the occupation numbers of spin-up and -down gap states at various values of the strength of the staggered potential. The electronic and magnetic properties of the zigzag edges depend sensitively on these numbers. We discuss the possibility of applying this system as a single electron spintronic device. 14. Finite Element Analysis of Simple Rectangular Microstrip Sensor for Determination Moisture Content of Hevea Rubber Latex Science.gov (United States) Yahaya, NZ; Ramli, MR; Razak, NNANA; Abbas, Z. 2018-04-01 The Finite Element Method, FEM has been successfully used to model a simple rectangular microstrip sensor to determine the moisture content of Hevea rubber latex. The FEM simulation of sensor and samples was implemented by using COMSOL Multiphysics software. The simulation includes the calculation of magnitude and phase of reflection coefficient and was compared to analytical method. The results show a good agreement in finding the magnitude and phase of reflection coefficient when compared with analytical results. Field distributions of both the unloaded sensor as well as the sensor loaded with different percentages of moisture content were visualized using FEM in conjunction with COMSOL software. The higher the amount of moisture content in the sample the more the electric loops were observed. 15. Mixed convection heat transfer simulation in a rectangular channel with a variable speed rotational cylinder Science.gov (United States) Khan, Md Imran; Billah, Md. Mamun; Rahman, Mohammed Mizanur; Hasan, Mohammad Nasim 2017-12-01 Numerical simulation of steady two-dimensional heat transfer in a rectangular channel with a centered variable speed cylinder has been performed in this paper. In this setup, an isoflux heater is placed at the bottom wall of the channel while the upper wall is kept isothermal with a low temperature. The cylinder's peripheral speed to maximum inlet fluid velocity ratio (ξ) is varied from 0.5 to 1.5 for both clockwise and anticlockwise rotational cases. Air has been considered as working fluid while other system parameters such as Grashof and Reynolds numbers are varied. The effects of rotational speed, Grashof and Reynolds numbers on the streamline pattern, isothermal lines, local and average Nusselt number are analyzed and presented. It is observed the cylinder's rotational direction and speed has a significant effect on the flow pattern, temperature distribution as well as heat transfer characteristics. 16. Light scattering of rectangular slot antennas: parallel magnetic vector vs perpendicular electric vector Science.gov (United States) Lee, Dukhyung; Kim, Dai-Sik 2016-01-01 We study light scattering off rectangular slot nano antennas on a metal film varying incident polarization and incident angle, to examine which field vector of light is more important: electric vector perpendicular to, versus magnetic vector parallel to the long axis of the rectangle. While vector Babinet’s principle would prefer magnetic field along the long axis for optimizing slot antenna function, convention and intuition most often refer to the electric field perpendicular to it. Here, we demonstrate experimentally that in accordance with vector Babinet’s principle, the incident magnetic vector parallel to the long axis is the dominant component, with the perpendicular incident electric field making a small contribution of the factor of 1/\|ε\|, the reciprocal of the absolute value of the dielectric constant of the metal, owing to the non-perfectness of metals at optical frequencies. 17. Analysis of flow distribution instability in parallel thin rectangular multi-channel system Energy Technology Data Exchange (ETDEWEB) Xia, G.L. [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an City 710049 (China); Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin City 150001 (China); Su, G.H., E-mail: [email protected] [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an City 710049 (China); Peng, M.J. [Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin City 150001 (China) 2016-08-15 Highlights: • Flow distribution instability in parallel thin rectangular multi-channel system is studied using RELAP5 codes. • Flow excursion may bring parallel heating channel into the density wave oscillations region. • Flow distribution instability is more likely to happen at low power/flow ratio conditions. • The increase of channel number will not affect the flow distribution instability boundary. • Asymmetry inlet throttling and heating will make system more unstable. - Abstract: The flow distribution instability in parallel thin rectangular multi-channel system has been researched in the present study. The research model of parallel channel system is established by using RELAP5/MOD3.4 codes. The transient process of flow distribution instability is studied at imposed inlet mass flow rate and imposed pressure drop conditions. The influence of heating power, mass flow rate, system pressure and channel number on flow distribution instability are analyzed. Furthermore, the flow distribution instability of parallel two-channel system under asymmetric inlet throttling and heating power is studied. The results show that, if multi-channel system operates at the negative slope region of channel ΔP–G curve, small disturbance in pressure drop will lead to flow redistribution between parallel channels. Flow excursion may bring the operating point of heating channel into the density-wave oscillations region, this will result in out-phase or in-phase flow oscillations. Flow distribution instability is more likely to happen at low power/flow ratio conditions, the stability of parallel channel system increases with system pressure, the channel number has a little effect on system stability, but the asymmetry inlet throttling or heating power will make the system more unstable. 18. Heat Transfer Characteristics during Boiling of Immiscible Liquids Flowing in Narrow Rectangular Heated Channels Directory of Open Access Journals (Sweden) Yasuhisa Shinmoto 2017-11-01 Full Text Available The use of immiscible liquids for cooling of surfaces with high heat generation density is proposed based on the experimental verification of its superior cooling characteristics in fundamental systems of pool boiling and flow boiling in a tube. For the purpose of practical applications, however, heat transfer characteristics due to flow boiling in narrow rectangular channels with different small gap sizes need to be investigated. The immiscible liquids employed here are FC72 and water, and the gap size is varied as 2, 1, and 0.5 mm between parallel rectangular plates of 30 mm × 175 mm, where one plate is heated. To evaluate the effect of gap size, the heat transfer characteristics are compared at the same inlet velocity. The generation of large flattened bubbles in a narrow gap results in two opposite trends of the heat transfer enhancement due to thin liquid film evaporation and of the deterioration due to the extension of dry patch in the liquid film. The situation is the same as that observed for pure liquids. The latter negative effect is emphasized for extremely small gap sizes if the flow rate ratio of more-volatile liquid to the total is not reduced. The addition of small flow rate of less-volatile liquid can increase the critical heat flux (CHF of pure more-volatile liquid, while the surface temperature increases at the same time and assume the values between those for more-volatile and less-volatile liquids. By the selection of small flow rate ratio of more-volatile liquid, the surface temperature of pure less-volatile liquid can be decreased without reducing high CHF inherent in the less-volatile liquid employed. The trend of heat transfer characteristics for flow boiling of immiscible mixtures in narrow channels is more sensitive to the composition compared to the flow boiling in a round tube. 19. AMELIORATE OF BANDWIDTH AND RETURN LOSS OF RECTANGULAR PATCH ANTENNA USING METAMATERIAL STRUCTURE FOR RFID TECHNOLOGY Directory of Open Access Journals (Sweden) RAJESH SAHA 2016-09-01 Full Text Available Radio Frequency Identification is an emerging research topic to identify any object automatically and it has applications in many fields like manufacture industry, business, animal tracking, vehicle tracking etc. In automatic identification system, the main role of radio frequency identification system is radiation and detection. The reader and the tag are the important components in radio frequency identification technology. In radio frequency identification system, antenna plays very significant role to transmit and receive data in both direction (i.e., from reader to tag and vice versa. An antenna with high gain, high directivity, high bandwidth and more down in negative S11 (dB value works as an effective antenna. So design and optimization of an effective antenna is very necessary for any application. In this paper, firstly itdesigned a rectangular patch antenna and simulated through High Frequency Structure Simulator. In next step, it designed a metamaterial structure having U shape Split Ring Resonator with both one and two port, on the rectangular patch antenna to improve the return loss and bandwidth of patch antenna; so that the performance of the tag can be increased for the radio frequency identification system. By simulation it has been seen that, two port antenna provides maximum return loss and bandwidth of - 41.2dB and 870MHz respectively. Finally, the output parameters such as return loss, gain, directivity that are obtained from simulation of the metamaterial Split Ring Resonator structure antenna are compared with the network output of Artificial Neural Network to find the Mean Square Error between the simulated output and Artificial Neural Network output. 20. Viscoelastic-gravitational deformation by a rectangular thrust fault in a layered earth International Nuclear Information System (INIS) Rundle, J.B. 1982-01-01 Previous papers in this series have been concerned with developing the numerical techniques required for the evaluation of vertical displacements which are the result of thrust faulting in a layered, elastic-gravitational earth model. This paper extends these methods to the calculation of fully time-dependent vertical surface deformation from a rectangular, dipping thrust fault in an elastic-gravitational layer over a viscoelastic-gravitational half space. The elastic-gravitational solutions are used together with the correspondence principle of linear viscoelasticity to give the solution in the Laplace transform domain. The technique used here to invert the displacements into the time domain is the Prony series technique, wherein the transformed solution is fit to the transformed representation of a truncated series of decaying exponentials. Purely viscoelastic results obtained are checked against results found previously using a different inverse transform method, and agreement is excellent. A series of results are obtained for a rectangular, 30 0 dipping thrust fault in an elastic-gravitational layer over viscoelastic-gravitational half space. Time-dependent displacements are calculated out to 50 half space relaxation times tau/sub a/, or 100 Maxwell times 2tau/sub m/ = tau/sub a/. Significant effects due to gravity are shown to exist in the solutions as early as several tau/sub a/. The difference between the purely viscoelastic solution and the viscoelastic-gravitational solutions grows as time progresses. Typically, the solutions with gravity reach an equilibrium value after 10--20 relaxation times, when the purely viscoelastic solutions are still changing significantly. 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https://meta.wikimedia.org/wiki/Wikivoyage/Logo_2013/Submissions	# Wikivoyage/Logo 2013/Submissions Jump to navigation Jump to search Wikivoyage Logo Election 2013 The following discussion is closed. Please do not modify it. This page is for organizing and discussing initial submissions for the 2013 Wikivoyage logo selection. Please see that page for general information, including rules of participation. All contributors are invited to submit potential logos for review, in accordance with the rules set out there and at Wikivoyage/Logo 2013. Please note that entering a submission constitutes your acceptance of those rules. Logo submissions should be listed and discussed here. If you submit multiple different proposals, please indicate clearly which should be taken before the submission period ends. Otherwise all will be added to the voting-gallery; but remember that voters have only 3 votes in total and adding lots of similar proposals may diminish the chances (this depends on how the voters behave, of course). Further information available at the talk page. ## Recommendations The ideal new Wikivoyage logo should be distinct from other logos, including other Wikimedia logos! It should be something unique, with a clear relation to Wikivoyage's mission and culture. Creativity is also highly encouraged with the choice of color scheme. Keep in mind that this is a multilingual project with a strong international slant (as it is a travel site!) so consider whether a logo would be appropriate for all language versions, including those with non-Latin scripts. ## Option 1 - Flowing Arrow I'm not quite sure how to format this, so please feel free to move it around a bit. Author: Nick talk This suggested logo has popped up previously, but here it is again; an abstract arrow. You can read a full (slightly tongue-in-cheek) explanation of my reasoning and see some implementations, other language versions and the SVG version that Peter very kindly made, here. Comments welcome! --Nick talk 18:38, 10 July 2013 (UTC) ### Discussion It's a really nice logo and I really like the baby blue colour, but in order to make it more in line with other Wikimedia projects, I would very much prefer for it to use the same colours as other recent logos, e.g. the Wikimedia logo itself. I also agree with the comments previously voiced that making it somewhat more like both a compass needle and the Eiffel Tower at the same time would make it even more powerful. PrinceGloria (talk) 19:36, 10 July 2013 (UTC) Thanks for your comments! :) I confess, I deliberately didn't use the WMF colours as none of the other 'consumer' (that's not the right word) wikis use the WMF colour scheme; if anything, blue is the more popular colour, but I used a brighter shade to differentiate ourselves; I know that some members of the community were not particularly keen on sharing colours with the 'meta' projects. I would personally be a little wary of making it look more like the Eiffel Tower and would prefer to keep the shape a little ambiguous in that respect: we don't want to be confused for the Parisian tourist board! I think it's nice that different people might see different things in the shape, but all of them are hopefully travel related. --Nick talk 19:54, 10 July 2013 (UTC) I agree. PrinceGloria, I really have no idea what you're thinking with your suggestions. Look at the logos for Wikipedia, Wikibooks, Wiktionary, and Wikiversity. The only thing they have in common is that none of them use the colors of the Wikimedia logo! So why should Wikivoyage? I'm also not sure what's 'powerful' about looking like the Eiffel Tower; can you elaborate? LtPowers (talk) 23:17, 10 July 2013 (UTC) I basically like this logo: color, form and thought. It works okay at a small size, but even in the gallery above I think that the version without the wordmark is too simple. I'm not sure what I'd add, but I think it needs something so that it's not a flat circle in bigger versions. Perhaps add continents to the globe (almost invisible at small sizes) or gradients. //Shell 09:27, 11 July 2013 (UTC) Too simple?? I'm guessing you don't have formal training in graphic design. One of the most basic precepts of design (graphic or otherwise) is simplicity. LtPowers (talk) 18:13, 11 July 2013 (UTC) Thanks for your thoughts //Shell! As LtPowers has said, I've aimed to keep this logo as simple as possible in order to make it more powerful: a strong, confident symbol for the project. Some of the most iconic logos in the world are composed of very simple elements. Hopefully this simplicity means that it works well at many different sizes, which is important for a project like this. --Nick talk 19:16, 11 July 2013 (UTC) I appreciate the goal to have a simple logo. I still feel that it needs something at the size it will be viewed in most (135px wide with wordmark) and I think this logo is simpler than all other Wikimedia projects'. The Github mark (the silhouette) is one that I like very much - it's simple, yet contains details that make it interesting when large. Nick, what would you consider an iconic logo? //Shell 21:58, 11 July 2013 (UTC) Thanks for responding. I'd like to think it's about as simple as the Wikiquote and Wikidata emblems; not unusually so. The GitHub mark, whilst nice, doesn't seem that much more 'exciting' than the logo above and a cat-octopus hybrid might look a tad incongruous here. Personally, I like 'clean' design and that's what I've aimed for here. The use of a world map would, I fear, make the logo seem a little 'fussy', whilst gradients are rather losing their vogue at present - a flat icon can be timeless. Some examples of simple logos that I would deem iconic are: the Apple logo, the Pepsi logo, the Mercedes-Benz logo, the Bell System logo, the British Rail logo and the Nike tick. I believe that simplicity makes a mark memorable and stronger. In reality, it's likely that the image in the top left corner is the largest resolution at which this logo is going to be seen. As such, it is important that it can be reproduced faithfully at a range of much smaller sizes too - if small details were introduced, there's a chance that they could be compressed and unpleasant or lost entirely. --Nick talk 22:24, 11 July 2013 (UTC) I'll quote myself just once more as a general statement of support for this submission: it suggests a V for Voyage, flight, a compass, and even a bit of ocean waves, while being very simple and sleek. Nick also explained that part of his inspiration was the three step evolution of our project and community, first developing at Wikitravel, then migrating (i.e., fleeing) to Wikivoyage, and then happily under the umbrella of the WMF. Thinking of the icon this way, the "arrow" acts not just as a compass needle, but also a pointer forward, which could be read as an allegory for our project's forward movement, or movement in general (and travel is, of course, movement). To respond to PrinceGloria and //Shell above, I think that simplicity and distinctiveness should actually be primary goals in creating a new logo, as these qualities imbue the icon with more power and "catchiness." I certainly hope to have the opportunity to look at more submissions, which hopefully are on the way, but I can say I'd be happy with this one, as long as there are no legal obstacles this time. Great start to the submissions! --Peter Talk 20:26, 11 July 2013 (UTC) I think that this is an attractive logo, I just feel that if I saw it without the Wikivoyage label at the bottom, I wouldn't know it was for Wikivoyage. Qardys (talk) 01:19, 12 July 2013 (UTC) (edit conflict) Thanks for your comments! Personally, I don't think a logo should be used to try and convey exactly what a project's about; after a while, any logo would become synonymous with WV simply by association. Other WMF logos seem to have been made with this in mind as well: either that or Wikipedia's developing spherical jigsaw puzzles and Wikisource is building an iceberg! A logo should, to my mind, convey the abstract spirit of a project , rather than explicitly say what an organisation stands for. If you look at the selection of logos I posted for //Shell above, none of them states what the company in question does, but gives a pictorial representation which might be used to identify them. That's what I've tried to create for Wikivoyage here. --Nick talk 07:38, 12 July 2013 (UTC) I would reuse the font of the current logo. This would be a link with the current one. --Andyrom75 (talk) 07:20, 12 July 2013 (UTC) In the context of travelling, the logo reminds me more of a paper plane than an arrow. And a paper plane looks strange in contrast to the massive pollution real aircrafts cause. --Nicor (talk) 09:03, 12 July 2013 (UTC) @Nick: Wikiquote & Wikidata have simpler shapes, but the colors make them more interesting to me. My point about the Github silhouette was that the details in the tail make it interesting at high resolutions while lo-res versions are still clear. Those logos are rarely seen as simplified as the versions you linked: Apple's is often on their products, where the logo has some gloss/texture; Pepsi's on a can, also giving gloss; Mercedes-Benz's is chromium-plated and 3D; Nike's on shoes/clothes which give texture/interesting background (don't know about Bell/British Rail). Contrast that with the Wikivoyage logo, which will be viewed on a gray background with no more gloss/texture than it has from the start. I guess Microsoft's new icons are a better comparison, but even those are usually in a smaller format. //Shell 12:06, 12 July 2013 (UTC) I created a version showing my idea. To me the continents make it interesting at hi-res, while not taking anything away from the lo-res situations. (I'm not sure whether I can submit this version for Wikivoyage since it uses continents from here) //Shell 14:20, 12 July 2013 (UTC) Shell, your version with continent outlines in the blue disk is very interesting. I'd like to see what that looks like with the continents more prominently displayed, maybe like, or not like, a blue marble. --Rogerhc (talk) 19:11, 12 July 2013 (UTC) Rogerhc, I don't understand what you mean by "blue marble". Would you like a version with a darker outline? //Shell 19:40, 12 July 2013 (UTC) Thanks for posting that //Shell! I'm still not completely sure of it myself: I still like plain and simple, but I do appreciate your input and it is interesting to see! :) Personally, I like bold, simple shapes and 'unfussy' design, even though it's not necessarily everyone's cup of tea. I'd like the logo to look the same at all resolutions if possible, but your opinion is just as valid as mine! --Nick talk 12:50, 13 July 2013 (UTC) Under the terms of this process Shell can submit a derivative with those changes as an alternative proposal. · · · Peter (Southwood) (talk): 14:17, 13 July 2013 (UTC) Absolutely! Shell's more than welcome to submit a derivative; the above is just my personal opinion. --Nick talk 14:35, 13 July 2013 (UTC) Quite so, and for what it's worth I prefer the plainer version. If I can make a suggestion, the curves of the gaps in the arrow could be harmonized a little. This one is on my short list at present. · · · Peter (Southwood) (talk): 15:08, 13 July 2013 (UTC) Thanks! I am, unfortunately, away from my computer for the next couple of weeks (doing this on my phone), but once I get back, I'll try and smooth out some of the logo's rougher edges. :) --Nick talk 15:50, 13 July 2013 (UTC) Peter, Am I though? My version is a combination of Nick's idea and a map. The map wasn't submitted here, so I don't believe I can submit my version without creating my own map or replacing it with one in the public domain. I'm not skilled enough to create my own, so either somebody else can create one or we'll have to find a better one. //Shell 18:28, 13 July 2013 (UTC) The shape of the earth is not copyrighted, just find a PD source and use that. You will want an svg anyway. cheers, · · · Peter (Southwood) (talk): 18:47, 13 July 2013 (UTC) Shell I like your improvement on Nick's idea. Give yourself a try and submit it. --Andyrom75 (talk) 23:06, 13 July 2013 (UTC) I find Shell's version unnecessairly complicated. The power of Nick's version is its simplicity, relative uniqueness (it SUGGESTS a few things, but isn't one, so it has potential to become a universally recognized logo) and scalability (it works just as well as a thumb icon as it does as fullsize logo). PrinceGloria (talk) 19:18, 14 July 2013 (UTC) I made one more version, this time with a split color. I don't intend to submit either variant now, since that would just confuse voters, but some people like the idea, I'll do something for the final round if this submission makes it that far. //Shell 20:11, 17 July 2013 (UTC) • I don't like it. The arrow is broken for my POV. Though, I think, it is possible to see something like sail in this arrow and to rework/redraw logo in this direction. Alex Spade (talk) 12:03, 16 July 2013 (UTC) • It's a little reminiscent to the OpenOffice.org ball logo, but probably not too much. Superm401 \| Talk 23:47, 16 July 2013 (UTC) Can we see what it would look like as a favicon? Maybe even with an actual page having it as a favicon, not just a small picture? Thanks! 81.14.76.167 00:05, 19 July 2013 (UTC) Thanks very much for your comments everyone! I'm afraid I'm currently away from my PC and only have my phone, so I'm not going to be able to create a page to use the favicon; however, as soon as I return, I'd be happy to create one for you. Any more comments or questions would be welcome! --Nick talk 02:27, 19 July 2013 (UTC) If you'd like to see it at small icon size, here's a 16 x 16 px version, though when I return to my computer I'll probably tweak it a little. --Nick talk 20:58, 21 July 2013 (UTC) Good idea; making the white parts a bit thicker/bigger may make for a clearer favicon at the expense of mathematical precision in relation to the normal-sized icon. I'd be okay with that. I still think this is an outstanding logo. LtPowers (talk) 19:32, 23 July 2013 (UTC) Thanks very much LtPowers! I really appreciate your comments! As soon as I get access to a computer I'll get working on an improved and slightly edited favicon. --Nick talk 19:56, 23 July 2013 (UTC) ## Option 2 - Info ### Discussion The "information desk" icon is used widely. The extra markers around the circle look like old maps. --NaBUru38 (talk) 22:11, 11 July 2013 (UTC) Have you tried to reuse the current color palette? This maybe could fit better with some color choices that has been done in the past for maps & articles. --Andyrom75 (talk) 07:21, 12 July 2013 (UTC) I believe that this submission breaks the rules: it was created by User:Digr while submitted by User:NaBUru38. //Shell 07:31, 13 July 2013 (UTC) I think Option 11 - Compass Rose with Globe is better. Alex Spade (talk) 12:04, 16 July 2013 (UTC) ## Option 3 - Plane 2 ### Discussion It looks like both an open book and an airplane. It invites to open, read and write. --NaBUru38 (talk) 22:12, 11 July 2013 (UTC) I feel like you don't need to confine yourself to the Wikimedia shades. Was that your natural choice for both logos, or was it to reinforce brand identity? Qardys (talk) 23:22, 11 July 2013 (UTC) I remember this logo, and I really like the excellet idea that is behind it. Maybe (although I don't know how) I would graphically enforce these two concept, because without the explanation they don't arrive immediately. Once you know them, are clear, and are clear as well after several observation, but in my opinion a logo should be clear since the first glance. --Andyrom75 (talk) 07:26, 12 July 2013 (UTC) To me it looks like neither an open book nor an aircraft, even when I am told it should. I can see the attempted resemblance, but for me it just does not gel. That which makes it look somewhat like an aircraft, detracts from the book-like aspects and vice versa. · · · Peter (Southwood) (talk): 09:46, 12 July 2013 (UTC) I can see the book but no aircraft. Wikivoyage is not Wikibooks, I dont want confusion. --Pyfisch (talk) 10:09, 12 July 2013 (UTC) Great idea. It was my first choice during the first round already and it will be my first choice. Really like it. -- 13:16, 12 July 2013 (UTC) I believe that this submission breaks the rules: it was created by User:Isatis78 while submitted by User:NaBUru38. //Shell 07:31, 13 July 2013 (UTC) User:Isatis78 has now confirmed agreement to the logo submission rules here. Restoring this one to discussion. I've retitled this section according to the creator's original title. --Maggie Dennis (WMF) (talk) 20:53, 14 July 2013 (UTC) • I don't see plane, I see only book. Good idea, bad realization. Alex Spade (talk) 12:06, 16 July 2013 (UTC) • I like it very much. --Pequod76(talk) 08:36, 23 July 2013 (UTC) • Very Wiki! I vastly prefer this to something 100% travel-generic, even if it might be slightly difficult to interpret for some viewers. Pratyeka (talk) 03:53, 24 July 2013 (UTC) • Interesting, I see a bird into it, and it reminds me of the logo of Partij voor de Vrijheid (Freedom Party), a controversial Dutch political party. Obviously, it doesn't have my preference. Effeietsanders (talk) 11:05, 24 July 2013 (UTC) ## Option 4 - Next Generation Compass ### Discussion A simple compass logo. Known as Rbrown on Wikivoyage. Youtube2000 (talk) 05:11, 12 July 2013 (UTC) • Does not show up very well · · · Peter (Southwood) (talk): 09:42, 12 July 2013 (UTC) I cropped the image - now it's better visible. //Shell 09:22, 13 July 2013 (UTC) Thank you Shell. Youtube2000 (talk) 05:27, 14 July 2013 (UTC) • Too simple. Unoriginal. Сolour match "salad green on white background" is unacceptable. Alex Spade (talk) 12:12, 16 July 2013 (UTC) • It's a good idea but not very original, unfortunately. A lot of GPS and navigation devices and software use compass icons. Even web browsers. --TMg 23:22, 16 July 2013 (UTC) ## Option 5 - The Old Logo ### Discussion The logo is well known. And the WMF is already the owner. --RolandUnger (talk) 13:43, 12 July 2013 (UTC) I believe that this submission breaks the rules: it was created by Hansm and Unger , but submitted by RolandUnger 81.178.165.241 12:09, 13 July 2013 (UTC) I think submission of the old logo is not a problem. It is created by Hansm and Unger, but the ownership is transferred to the wikivoyage community and if one of them wants it back that should not be made a big problem. Carsrac (talk) 17:18, 14 July 2013 (UTC) I think that might be stretching the point a bit, only one person can make an edit, or do you dispute that Unger and RolandUnger are the same person?· · · Peter (Southwood) (talk): 12:58, 13 July 2013 (UTC) Unger and RolandUnger are the same person. I had to change my name because of SUL. --RolandUnger (talk) 18:32, 14 July 2013 (UTC) The weak point of this logo and other logo's based on the latin script that wikivoyage is project that is not a latin only project. The Greek and the Hebrew language version would look very funny with this logo. Carsrac (talk) 17:26, 14 July 2013 (UTC) Virgin Airlines? Alex Spade (talk) 12:20, 16 July 2013 (UTC) ## Option 6 - Plane(t) 6i. Flying plane This is my submission for the Wikivoyage logo selection process. The logo emphasizes that Wikivoyage is a free, world-wide travel guide. The airplane represents travel, and considering we're a world-wide travel guide, it is flying around the Earth. The "free" bit is only slightly hinted at, as the airplane is flying in a half-moon-shaped reversed "c", a nod to our copyleft license. The logo shows not one, but two planets, because we are a project that's a coming together of two worlds (two communities), now operating together in union. That's why the airplane is flying around both planets as if they are one. I chose orange because it's a unique color not used by any other WMF project. But we can make dozens of variations with many different colors. I'm open for your comments and suggestions. Globe-trotter (talk) 16:07, 12 July 2013 (UTC) ### Discussion Seems like the Death Star with a bigger hole. ~~EBE123~~ talkContribs 21:58, 12 July 2013 (UTC) Very nice but it remind me the expedia logo. Inkey (talk) 11:52, 13 July 2013 (UTC) I think it's a bit similar to Expedia's previous logo, but not their current. //Shell 18:37, 13 July 2013 (UTC) Generally speaking I like the logo, but it doesn't makes me think to a WMF site (I don't recall at all the expedia's one, so I'm not referring to it). Try to use all the RGB colors just to see what comes out. --Andyrom75 (talk) 21:57, 13 July 2013 (UTC) I'm a fan of this, but would like to see some other versions. The planets to me look more like an eyeball, which probably isn't what you're going for. I don't think the swooshed plane, which I like a lot, is too similar to the old Expedia logo (the whole look is very different). --Peter Talk 19:19, 16 July 2013 (UTC) The two planets were no success, so I uploaded a couple of different versions of the logo. I thought it might be an idea to make the plane loop, as it makes the logo a bit more playful and shows how fun travel is (just like how making loops is fun). Globe-trotter (talk) 03:41, 17 July 2013 (UTC) Upturned planes on 6f and 6h lead to aerophobia. Alex Spade (talk) 15:58, 17 July 2013 (UTC) I don't like most of the alternative versions you made, but 6i is excellent, I like a lot! PS The above Alex comment cracks me up! :-D --Andyrom75 (talk) 17:21, 17 July 2013 (UTC) These are by far my favorite logos here (enough to make me make my first edit on Meta). Simple but interesting, and (my pet peeve) actually has good typography. 6d, 6g, and 6i are my favorites.—Kelvinsong (talk) 18:20, 17 July 2013 (UTC) These are very intriguing. I really like 6i out of all the options, but would also like to see a version of 6e flipped vertically (so the plane flies forward to the right) and changed to blue. JamesA (talk) 07:53, 18 July 2013 (UTC) This is generally a very nice logo, very dynamic. Only it took me while to recognize the plane in it - it looked like a lizard to me at first :) And also I am not sure if a plane represents traveling very well, it doesn't work with me, anyway. --Danapit (talk) 13:56, 18 July 2013 (UTC) You improved it greatly in the later variations, namely 6i. The use of orange and bright blue is really dynamic. On that note, is it possible for us to see 6i in orange? Nick1372 (talk) 15:03, 18 July 2013 (UTC) What about some more color? Doc James (talk · contribs · email) 11:32, 19 July 2013 (UTC) 6i is my favorite, and it seems like a few others agree with me. The problem with it is when it needs to be shown without the word Wikivoyage & small, i.e. a favicon. Frankly, it would make a terrible favicon. I like it a lot, though. Does anyone know if it's possible to have a slightly different favicon than full logo? 6g would make a nice favicon. Nick1372 (talk) 06:25, 21 July 2013 (UTC) No reason we can't, I guess. Wikipedia does it. JamesA (talk) 12:01, 21 July 2013 (UTC) Great concept, but the plane instantly reminded me of a shark swimming in the water...? Globe-trotter, this is a really good idea for a logo and I love the way it evolved to become more simple and poignant. If you already don't, I believe you could make a living as a graphic / corporate identity designer. This is one of my favourites, because it looks really cool and professional, which will make people think Wikivoyage is not just a bunch of nutters writing crazy stuff about things they didn't like in Tblisi. Just a few remarks: • I am a strong believer in using Wikimedia standard colours for newer projects to make clear their association with the foundation. Worked for Species, Commons and Data, should work well for us, because the point we want to make online is that while there are other wiki-based travel sites online, we are the only one thus far that is genuinely free in every sense and run according to all of the Wikimedia principles. Would you be able to try to use the RGB colours on a version of the logo? • There might be some concern about suggesting travel = airplanes, which is somehow something we might want to avoid, being very inclusive of all modes and types of travelling and throwing cliches outta the door. That said, I am a quite cliche traveller myself and I like planes :) • I agree I get this "I've seen that somewhere" vibe and you may want to check out whether there aren't some similar logos around • I absolutely believe the only way the plane should be pointing is upwards and it should point in one direction both in the general logo and favicon, although I am all for having a different favicon than general logo, or even many versions of it, as long as they are instantly recognizable. • As a sidenote, we may want to later reuse the "inverted plane" logo (6h I believe) or the "plane + mountains" logo from another proposal whenever we would be looking for a logo for WikiAirCrashInvestigation All from me now. Over and out, PrinceGloria (talk) 15:11, 22 July 2013 (UTC) I agree with PrinceGloria that using RGB could highlight the sense of a greated community that we are a part of. Maybe "wiki" and "voyage" could be colored with the two missing color, because I think that the remaining part of the logo is nice as it is. --Andyrom75 (talk) 20:04, 22 July 2013 (UTC) What complete rubbish. Wikipedia doesn't use RGB. Wiktionary doesn't use it. Wikibooks doesn't use it. Wikinews doesn't use it. Wikisource doesn't use it. Are they any less a part of the community? Wikipedia especially? Why would we want to look like a meta project? LtPowers (talk) 19:34, 23 July 2013 (UTC) Thank you for your kind words. The aformentioned projects, perhaps excluding Wikisource, are very popular in their own right. You can see that the less popular / newer the project, the more coherent its logo is with the general theme (e.g. same shades of blue, similar style). We would want to look "like a meta project" for the reasons mentioned above - for people to immediately know and become familiar with the idea, that this IS a Wikimedia project, not just yet another travel site / wiki. PrinceGloria (talk) 05:33, 24 July 2013 (UTC) When I first saw Wikivoyage’s current logo I thought "this looks like an internal project of the Wikimedia foundation, probably something boring and not something useful like Wikipedia or Wiktionary" (of course I was wrong, but having those colors on the logo was very confusing) Fractal (talk) 15:47, 24 July 2013 (UTC) ## Option 7 - WV logo 20 px rendering , 16 px rendering , 10 px rendering Colour could be anything that provides sufficient contrast. I like blue or green, which are particularly suitable for the negative version (white on colour or transparent on colour). · · · Peter (Southwood) (talk): 18:57, 12 July 2013 (UTC) Text is optional and can be chosen by the language version. · · · Peter (Southwood) (talk): 10:48, 14 July 2013 (UTC) Reminds me of the Northrop Grumman B-2 Spirit bomber too much. odder (talk) 20:52, 12 July 2013 (UTC) It actually does look a little like that, but I don't think many people would think of that when looking at this logo. It's a bit like the w:Rorschach test. ;) If other people agree with that, though, we might want to use a different logo. PiRSquared17 (talk) 01:49, 13 July 2013 (UTC) This invites a cease and desist from the VVV. PrinceGloria (talk) 10:45, 13 July 2013 (UTC) Their logo is three separate V's in a triangle in a square, this is a combined W and V in a circle. colours are different and can be changed, negative version differs even more. · · · Peter (Southwood) (talk): 08:09, 14 July 2013 (UTC) It is also different from the Mitsubishi logo, the Volkswagen logo, the Triangle health and fitness logo, Wyoming valley anthracite logo, West Virginia University logo, VVV Venlo logo and Anton May logo. · · · Peter (Southwood) (talk): 11:13, 14 July 2013 (UTC) Modified logo it's definitely better that the original one. --Andyrom75 (talk) 13:02, 14 July 2013 (UTC) I thought the simplicity of the original would be better, but now I have got used to the change I think you are right. · · · Peter (Southwood) (talk): 13:38, 14 July 2013 (UTC) Our current logo is far more different from the WTC logo than this one from VVV, but it still invited a cease and desist. And the new version bears even more similarity to the VVV, which was born basically of the same idea. I like it, but I would be mega-cautious. PrinceGloria (talk) 19:13, 14 July 2013 (UTC) Legal department will make that decision I guess. · · · Peter (Southwood) (talk): 08:48, 16 July 2013 (UTC) I don't like it. Very similar with WC room signs or with Volkswagen logo. Alex Spade (talk) 12:53, 16 July 2013 (UTC) Which WC room signs would that be? · · · Peter (Southwood) (talk): 14:14, 16 July 2013 (UTC) I didn't say, that it was WC room sign. It has similar design for me, I see in proposed logo smth like this with two changes - C on right transformed to V on bottom, or woman triangle (like here) without head. Alex Spade (talk) 16:10, 17 July 2013 (UTC) I looked at your examples, and I don't think there is any similarity at all. · · · Peter (Southwood) (talk): 20:15, 23 July 2013 (UTC) While I like this, particularly some ideas that come to mind using the very simple and stylized version in the first thumb, I share some worries about its similarity to other logos. In particular, the versions with the components separated a bit remind a lot of the Volkswagen logo. The other issue is that the WV initials don't apply to many language versions both currently and going forward. But if the logo is sufficiently abstracted, that is less of an issue. --Peter Talk 19:23, 16 July 2013 (UTC) My imediate first thought when seeing this one was the sports teams of the University of West Virginia. I'm not versed enough in the law to know if it is close enough to matter, though. (Aside, the problems mentioned elsewhere about this one not being logical for non-latin script projects holds here.) Courcelles 03:00, 17 July 2013 (UTC) I also had the VVV association immediately. --Danapit (talk) 13:57, 18 July 2013 (UTC) ## Option 8 - Get Escape 16px rendering: 20px rendering: 24px rendering: I imagine a logo that could resemble a bird while spreading its wings and the letters "W" and "V" (WikiVoyage's initials) at the same time. Moreover, my logo wants to express the escape from the ordinary when someone takes a journey and the possibility to choose different paths before starting a trip. --Mess (talk) 22:55, 12 July 2013 (UTC) I like it! Uses the WMF color, it has the circle that recall the world and other WM logos, furthermore there's a W that recall Wikivoyage. Try to make some other alternatives on these theme, don't stop on the first idea. --Andyrom75 (talk) 23:09, 13 July 2013 (UTC) Hey, did you maybe read on my mind? I just thought about a squared version this night (dropping out the circle), et voila... --Mess (talk) 08:20, 14 July 2013 (UTC) Between the two I'd like more the first one. In the second one there's "too many angles", with the round shape is more balanced (IMO). --Andyrom75 (talk) 13:01, 14 July 2013 (UTC) Nice the third version, but I would let let arrows goes out from the circle to give more the idea of freedom. --Andyrom75 (talk) 12:40, 16 July 2013 (UTC) I don't see any geo-themed object in this logo. Alex Spade (talk) 12:45, 16 July 2013 (UTC) As with some other submissions, I think it would be nice to get away from the WV initials, since they do not apply to many language versions--especially those with non-Latin writing systems. That said, this could be the starting point for a more abstracted logo focusing on the elements of motion out of one's individual sphere and into the rest of the globe. --Peter Talk 19:25, 16 July 2013 (UTC) @Andyrom: OK, I'll try to adjust it as soon as possible. @Alex Spade: and so? What's the point? I don't think that some other submissions are strictly connected to a geographic theme. @Peter: it's true, you can see a WV at first sight on my logo, but I took into account non-Latin languages and I render it in order to be seen also as a route that from a starting point could take different directions around the world. Anyway, I thank you and Alex for the critics, maybe I'll create another version that might fit your needs. --Mess (talk) 21:59, 16 July 2013 (UTC) Here we go! I revised the third version and added a new one featuring 2 arrows that look like the Tropics (in addition, it recalls in a different key WikiVoyage's current logo). --Mess (talk) 08:16, 17 July 2013 (UTC) Update: I build another one from #4, using 4 crossed arrows that form a Union Jack-like pattern. --Mess (talk) 12:38, 17 July 2013 (UTC) Yes, some other submissions are not connected to a geographic theme too. But they have another, more important weaknesses (important for my POV). Alex Spade (talk) 16:14, 17 July 2013 (UTC) #5 looks like a Xmas ball :-D ... but I think you can work on #4 Try to put a "world" on that sphere, and maybe try also to work on those arrows giving them a more "mellifluous" style. --Andyrom75 (talk) 17:08, 17 July 2013 (UTC) Do you mean an abstract representation of Earth? I don't know, it would be too... messy! XD I just want to use simple geometric shapes in order to have a clean work (above all on small icons). --Mess (talk) 20:02, 17 July 2013 (UTC) Not abstract, just the map. Regarding the small icon, if you are not too convinced, it could be slightly different form the big one, I meant, with just the blue sphere. --Andyrom75 (talk) 20:28, 17 July 2013 (UTC) Map as background? Hmmm... It can be interesting solution. Alex Spade (talk) 21:57, 17 July 2013 (UTC) OK, as you wish. Here it is the 6th version, with a map of the Earth that I extracted from this (I specified into the file's description that it's a derivative work, but I don't know if there are copyright issues, I don't want to infringe anything). --Mess (talk) 09:23, 18 July 2013 (UTC) I don't think that anyone has the copyright on the world! (Just joking :-D .... in any case we can easily find a free globe map) I like a lot how is it coming out, but I would still work on the arrows. Initially I'll keep the two different colors and, like the current one, running into the different rotation direction of the world giving the idea of "roaming around". Secondly I'll change the shape of the arrows with a more gentle shape. --Andyrom75 (talk) 12:52, 18 July 2013 (UTC) Believe me, I don't get how much "gentle" would be the arrows for you. Can you give me an example, please? Regarding the colors, I decided to use the dark red to both the arrows because there's already a lot of green for the lands and blue for the water, so I wanted to balance these 3 colors. --Mess (talk) 14:52, 18 July 2013 (UTC) Maybe for the color you are right. Being not good at drawing I can't tell you in detail what to do. I've just describe my feeling looking at it. Try to enlarge the top for a better proportion. Then I don't know if shadow/3D effect can help. --Andyrom75 (talk) 16:47, 18 July 2013 (UTC) I retouched the arrows. I hope you like them now. --Mess (talk) 08:38, 19 July 2013 (UTC) Much more better! What about a third red line in the middle like a spiral? Try several version, like with just one arrow peak, another increasing the dimension from the tail to the head, or other ideas... --Andyrom75 (talk) 14:41, 19 July 2013 (UTC) What do you think about a spiral of 4 arrows? I build it with 3 different backgrounds. --Mess (talk) 22:58, 19 July 2013 (UTC) Arrows this time are perefect, very nice, but the latest tries gives me the idea of a dangerous typhoon so the willing of stay at home and not to travel :-D Coming back to 8.6, when I've said spiral, I was thinking on an third line parallel to the others two and positioned in between. So the spiral is something that is not over the globe, but it's all around. --Andyrom75 (talk) 08:14, 20 July 2013 (UTC) Ah, I understand what you were thinking now. Well, I made a test with this third line, but looking all together it resembles too much either the WTO logo or the Java one (IMHO), so I prefered to give up this solution. Meanwhile, I discarded the versions #4 and #5 and I redrew them as different variations of #6. --Mess (talk) 13:24, 20 July 2013 (UTC) [a capo] I see a good potential in 8.4, but the arrows should be "fatter". --Pequod76(talk) 16:35, 20 July 2013 (UTC) Thanks for the tip, I enlarged them. --Mess (talk) 20:23, 21 July 2013 (UTC) Anyway, which of my logos do you like much? I would like to choose up to 3, because I don't want to submit too much proposals. --Mess (talk) 17:40, 23 July 2013 (UTC) I'd be careful with the four red arrows - it gets a bit close to a swastika - and especially with the red color give a bad vibe. If you do part green, part red, it is much less. Effeietsanders (talk) 11:08, 24 July 2013 (UTC) You're perfectly right, they look very ambiguous with that configuration. I choose to withdraw that design (together with other proposals), so I'll keep only #1, #4 and #6 for the contest. --Mess (talk) 13:22, 24 July 2013 (UTC) ## Option 9 - sailboat Created by Isarra (talk · contribs) in R1 of the original contest. I like it, so I think it deserves another shot. ono 05:06, 13 July 2013 (UTC) Reopened. Isarra has consented to the submission rules, here. --Maggie Dennis (WMF) (talk) 00:44, 16 July 2013 (UTC) This is a nice design, and the colors work well together. It fits the theme of Wikivoyage of being free, etc., and it's a bonus that it depicts and actual voyage. Could I possibly see it with the word Wikivoyage under it? Nick1372 (talk) 02:09, 16 July 2013 (UTC) While pretty, and suggesting travel quite well, it is a bit cluttered and may not work as an icon or in greyscale. How does it look to the colourblind? · · · Peter (Southwood) (talk): 07:10, 16 July 2013 (UTC) I agree with Peter S. that this looks pretty, but a little cluttered. Maybe we could try it without the circles, just the boat? --Peter Talk 20:15, 16 July 2013 (UTC) This is far and beyond my favorite. Ed [talk] [en] 00:13, 17 July 2013 (UTC) Love the blue version! Pratyeka (talk) 03:49, 24 July 2013 (UTC) I really do like this one, and would like to see a verson with "Wikivoyage" written under it. It looks good to the colourblind as well (speaking as an expert on being colour blind) - the colours are different enough that the brain can separate which is which, even in the red/blue/green version. 142.109.6.2 17:34, 24 July 2013 (UTC) ## Option 11 - Compass Rose with Globe I liked this one too. ono 05:06, 13 July 2013 (UTC) I liked it (second one). Alex Spade (talk) 12:21, 16 July 2013 (UTC) I agree with Alex: the second one is better. --Andyrom75 (talk) 12:44, 16 July 2013 (UTC) I like version 0.4a.--Patafisik (talk) 15:11, 16 July 2013 (UTC) While I like this a lot when considered independently, I think it's (much) too similar to the Meta logo. While that doesn't present trademark issues, since the WMF would own both, it still fails to give our project a unique look. (Actually, given Wikivoyage's greater visibility than Meta, it might be better to say that we'd be robbing Meta of its unique look!) At a minimum, I think the globe element would need to be completely rethought. The compass element in 0.4a is really nice, though. --Peter Talk 20:19, 16 July 2013 (UTC) I like Version 0.4a even if it is similar to the Meta log: Meta's looks concentrating and stable, this one moving outward dynamically.--miya (talk) 05:08, 17 July 2013 (UTC) Second one really elegant. Jon Davies (WMUK) (talk) 07:51, 17 July 2013 (UTC) I have said, I liked it (0.4a), but image must be cleared (see full size on image description page). Alex Spade (talk) 22:40, 17 July 2013 (UTC) Version 0.2 delete. We can change Globe. Digr (talk) 19:14, 18 July 2013 (UTC) I like this one. --Alex rollin (talk) 18:26, 22 July 2013 (UTC) I like it . good work.Kbda3200 Though it looks good, in fact it is totally generic and uninspiring. As a creative community we should be able to do far better than this. Pratyeka (talk) 03:54, 24 July 2013 (UTC) ## Option 12 - Arrows - Favicon proposal - - better favicon proposal in 16, 24 and 32px My proposal for the new logo. The arrows represent the directions of travel, I took the colours from Wikimedia Design guidelines. Best --AleXXw (talk) 23:57, 13 July 2013 (UTC) Very nice. Doc James (talk · contribs · email) 01:01, 14 July 2013 (UTC) I agree. Very nice. -- 04:54, 14 July 2013 (UTC) Very striking. The text can be translated while the logo remains recognizable for all languages. Works for me. · · · Peter (Southwood) (talk): 07:59, 14 July 2013 (UTC) I agree. Beautiful and versatile. Nice work. --Nanae (talk) 09:43, 14 July 2013 (UTC) Great. Simplicity is the best. Re the favicon: suggesting to remove either preferrably both letters (ie. as the last example is - some languages even don't use latin alphabet and ie. chinese/japanese characters probably wouldn't be legible, or consider azbuka, where the first letter is similar to latin B) or at least the "V" (mind translations, where "voyage" could be translated to the word beginning with the different letter). Favicons should be icons (preferably of the logotype) only. In any case, again, very nice work! Technical: What is the font and is it free? Danny B. 12:38, 14 July 2013 (UTC) Beautiful! I like a lot this one! In particular the first version (i.e. main logo)! It has all the feature that I was looking for (i.e. WMF logo & recall to the current one), furthermore, for future use it can be streched to the "only arrows version". Currently it's my favourite! Regarding the letters I don't consider it a problem, because we can have exactly the same approach of the wikipedia logo: an image with a text translated in each language. (e.g. ko, it, fa)--Andyrom75 (talk) 12:57, 14 July 2013 (UTC) It would work well with a wide variety of fonts, so that would be a separate issue. Each language could make their own decision on what best suits their name. · · · Peter (Southwood) (talk): 13:44, 14 July 2013 (UTC) Thx for your feedback! • I was not thinking about different character systems at the moment of creating the favicon, I think just the arrows will work better. • If anyone here could translate wikivoyage to a language with different character systems (hebrew, any asian, kyrilic,...) I'd love to present them as demo. • To clarify: the first three logo versions are the same logo for different purposes. • The font I used was Gill Sans bold. The creator Eric Gill died in 1940, so it should be free in most countries. If there is any problem: I think most of the bold sanserif typeface would work as well. Best --AleXXw (talk) 20:28, 14 July 2013 (UTC) Slightly new version using DejaVu sans, an open source font, the other languages for demo. Which version do you like more? Best --AleXXw (talk) 05:54, 15 July 2013 (UTC) There is one simple rule in typeface design and it is that Gill Sans always wins. Seriously though - drop the bold, it doesn't look good. Either Sans is fine to me, but not with bold. A very good design, I am only slightly worried it is not very travel-themed and could just as well be used by many other projects. PrinceGloria (talk) 19:04, 15 July 2013 (UTC) I don't like concept "Three arrows". Four arrows are classic for geo-projects. Alex Spade (talk) 12:23, 16 July 2013 (UTC) I confirm my appreciation for this logo, so I suggest you to invest part of your time in searching over the web if there's any similar registered logos that may arise legal issues. --Andyrom75 (talk) 12:54, 16 July 2013 (UTC) And I like the three arrows because it is different from the conventional four directions arrows and allows use of the three primary colours. · · · Peter (Southwood) (talk): 13:43, 16 July 2013 (UTC) I think this is a very attractive, strong submission. The idea of an unconventional compass (which maybe I'm projecting onto the submission), is really cool. Working the name into the center of the logo is also a cool step. How would this work with a caption, if we choose to use one (we don't have to). --Peter Talk 20:23, 16 July 2013 (UTC) I wasn't expecting to like anything better than Nick's arrow, but I like this submission best of all the ones that have been submitted so far. Ikan Kekek (talk) 20:08, 17 July 2013 (UTC) I like the plain 3 arrows (favicon) (also produces a closure illustion of a cube!) Shyamal (talk) 11:36, 18 July 2013 (UTC) Very pretty. Simple and flexible. --Danapit (talk) 13:50, 18 July 2013 (UTC) It's a good looking logo, but why the hell does everyone want to use red, green, and blue?? Of all the content (as opposed to meta) projects, only Wikispecies uses this color scheme, and theirs is muted. If we use red, green, blue, we look like a meta project. LtPowers (talk) 01:38, 19 July 2013 (UTC) I see a great potential on this logo. I was thinking on video where the 3 arrows goes out to show something in the middle, and/or to draw something on their trails as they pass by. Or, in static pages, the smallest ones (with no letter inside), could be used as bullet points on some institutional list or brochure. --Andyrom75 (talk) 08:21, 20 July 2013 (UTC) I agree. Very nice... -- 08:11, 22 July 2013 (UTC) Answer to LtPowers: Because it's pretty. Ikan Kekek (talk) 22:28, 23 July 2013 (UTC) I really like this logo – very clean and striking. I like the font of the original version better than the DejuVu Sans one. I've never been a fan of the clunky-looking DejuVu Sans, open source or not. Kaldari (talk) 04:56, 31 July 2013 (UTC) ## Option 13 - W-route • All removed from submission by 6 icon, on submitter request 16 px favicon: My logo shows a dynamic route (in shape of a curved "W") on a globe. The text uses the same font as the original logo (with new kerning). The structure is the same as in the Wikipedia- or the Wikimedia logo: A round sign at the top und the text at the bottom. The preceding unsigned comment was added by Giweddah (talk • contribs) . I suggest a more obvious "W" for the "route". · · · Peter (Southwood) (talk): first it is a route – and with a little fantasy it becomes a "W". I like logos with a slight "secret": for example the (bavarian) air-screw in the BMW logo or air/land/water in the Mercedes star. Giweddah It has a vague similarity to the GE logo :-) --Andyrom75 (talk) 12:54, 14 July 2013 (UTC) Maybe it is because of the color. Here are some variations: I don't like "W" in this logo. It is very Arabic-like. Moreover, first logo (wroute2) is still GE-like. Second variant... (my proxy-server cutted out it). Third one (wroute4) is similar to Eurovision Baku (Azerbaijan) logo. Alex Spade (talk) 12:36, 16 July 2013 (UTC) "Baku" is over and what is wrong with arabic? Proposed variant of "W" letter is similar with Arabic letters. Such imitation (accidental or intentional) is good for Arabic organization or for travel agency working with Arabic states. And it is not good for international, interlanguage project about all countries of the World. Alex Spade (talk) 22:10, 17 July 2013 (UTC) Maybe I'm still conditioned from the first impression but I still see the GE logo. Have you consider to modify the "dynamic route"? --Andyrom75 (talk) 12:52, 16 July 2013 (UTC) Consider: yes. But I like the actual form. And I see no "vague similarity" to the GE logo in the later suggestions, yes there are white lines in a circle – but that is the only similarity. Giweddah I like this conceptually and visually, particularly in the third thumb above using our soon-to-be discarded logo's colors. The path is stylized/abstracted enough where I don't think using a W is problematic for language versions that do not use a Latin W in their name. But I also share concerns about the similarity to the GE logo. I guess that will be a question for Legal. --Peter Talk 20:26, 16 July 2013 (UTC) It probably doesn't help much but I like the very first one very much. A path around a globe that forms a W, all made with so less strokes. This is brilliant. I also like the dark blue color. Number 5 confuses me a bit. It's like the stroke is going the wrong direction, getting thinner from right to left. Maybe it's because the tip of the brush that forms the stroke is mirrored. You can't use a brush that way when you are right handed. Yea, I know, this is nitpicking. ;-) --TMg 19:29, 18 July 2013 (UTC) ## Option 14 - Lines and Arrow Okay. This is the first of several designs I will be presenting. This one is an arrow formed with four lines, each one representing something. The grey line represents the roads, the green line the forests and national parks, the red line represents the attractions, and the blue line, the water. Together, they form an arrow, a symbol used to point directions across the globe, and well-known in the traveling world. The red semi-circle (which I originally planned to be blue, though) represents the land above which all those elements coexist; e.g. the earth. Any thoughts? — ΛΧΣ21 02:01, 15 July 2013 (UTC) ### Second version I have done this little tweak that I do like and adds a different meaning to the logo. Cheers. — ΛΧΣ21 08:27, 16 July 2013 (UTC) Generally speaking it doesn't inspire me, because the logo itself, doesn't give me the idea of the voyage, and with the wiki.label is applied below of it, they screech a little bit, because I don't perceive them as a whole thing. --Andyrom75 (talk) 12:49, 16 July 2013 (UTC) I like that this is very visually distinct, but share Andyrom75's concern that it's relation to travel is pretty hard to discern without an explanation. --Peter Talk 20:29, 16 July 2013 (UTC) I don't like these. I see smth like "subway/railroad map" here (in both sections). It can be good for land transport system (subway or railroad company), but it is not good for WV. Alex Spade (talk) 22:32, 17 July 2013 (UTC) This may also have trademark problems; it looks a lot like the British Rail logo to me. Daniel Case (talk) 19:26, 23 July 2013 (UTC) I'm sorry to say that but the lines look like something is broken. They don't form something bigger, they are fighting each other. The second version is a bit better because it's more balanced. But it still reminds me of this. --TMg 19:37, 18 July 2013 (UTC) ## Option 15 - Feet At 20px: My logo is based on the primitivity primality (thanks en:User:AshLin) of feet in travel placed on a globe with some jut, here not accurately placed but could be designed with more geometrical accuracy and suggesting the same jigsaw theme of Wikipedia and using the same colour scheme (not adjusted exactly in the first version). Variants based on this can be considered. Shyamal (talk) 05:32, 15 July 2013 (UTC) I like it. Give us an example without the grey disc. It might be a more powerful image. · · · Peter (Southwood) (talk): 15:36, 15 July 2013 (UTC) Have added two other variants. Shyamal (talk) Versions 2 and 3 are very much like a logo that I saw on a google search for "Footprints logo", so may be a Copyvio or TM issue. 4 is OK, but would still like to see a clean version of the first with only the footprints. The original version is evocative of going out in various directions from a centre, it is fresh and dynamic, whereas the others all suggest a circularity of motion. I think an outward looking logo is most appropriate to our project. There is no need to dilute the message with any circular component. The grey disc will reduce legibility in greyscale and B&W. A simple clean graphic works best as an icon. First version without circle has potential for all these things. Try icons at 16 or 20px to see what I mean. · · · Peter (Southwood) (talk): 07:06, 16 July 2013 (UTC) Added simple version. Shyamal (talk) 07:31, 16 July 2013 (UTC) I think it is the best of the variants. Crisp and clean and most clear at small sizes. · · · Peter (Southwood) (talk): 08:41, 16 July 2013 (UTC) Very nice and original. My favourite is #4. That said, it doesn't recall me a "voyage". --Andyrom75 (talk) 12:31, 16 July 2013 (UTC) Good idea on the whole, but small icons is very muddy. May be, it is possible to use only one feet for small variant (heel is green, toes are red or smth like this). Alex Spade (talk) 12:43, 16 July 2013 (UTC) I like version 3, clean work.--Patafisik (talk) 15:13, 16 July 2013 (UTC) Love version 4! It also looks good when shrunk... sort of like a rattan ball! Pratyeka (talk) 03:57, 24 July 2013 (UTC) ## Option 17 - Take off • 4 V3 icon the only submission from this section on submitter request 16 px favicon: The logo shows an arrow (in Wikimedia colors) that starts to a voyage. The text uses the same font as the original logo (with new kerning). Giweddah I find version 1 more interesting. Version is is more like "come with me" while version 2 is "go that way". Try to make the gaps between the three colors a bit wider. --TMg 14:26, 16 July 2013 (UTC) Thank you. In version 3 the gaps are a little bit wider and the curve has a new form (a real ellipse). Giweddah I have to say I like this one a lot (the curved one) - probably my favourite on this page! Nice and simple. However it is possible that I only think this way because of its resemblance to the previous logo? -- Chuq (talk) 23:32, 16 July 2013 (UTC) I like this idea and I think it isn't so linked to the previous logo (in the old one we have a globe with arrows, in this one we have only an arrow). It could be a good point for start. -- Yiyi (talk) 22:26, 23 July 2013 (UTC) I liked the first more. I'm not sure about the colors but the 3D like effect is nice. It's like the arrow is coming from the back. --TMg 16:44, 24 July 2013 (UTC) ## Option 18 - Simplified sailboat I liked #Option 9 - sailboat but found it to complicated. This is my first try to make it simpler. Please tell me what you think. I will try to add more versions depending on the input I get. --TMg 14:24, 16 July 2013 (UTC) Why aren't all of the sections of the outside the same color? I think it would be better just as one color. I'm slightly concerned about how a sailboat design will be when the logo has to be small, so can wee see it small? Nick1372 (talk) 21:17, 16 July 2013 (UTC) The green section is an island in the distance, blue is the water. The Wikimedia logo uses similar coloring. But you are right, I could try a single color. --TMg 23:09, 16 July 2013 (UTC) The wave below the boat can be stylized better. Shyamal (talk) 01:58, 17 July 2013 (UTC) Despite its name, Wikivoyage is not primarily about sailing (although coverage of sailing is most welcome!). That said, if you'd like to try simplifying the design even more, let's have a look. Ikan Kekek (talk) 20:13, 17 July 2013 (UTC) This is my favourite of the sailboat ones :) Ross Hill (talk) 17:31, 18 July 2013 (UTC) I added two color variations. I also retouched the wave and made the sail a bit smaller in the new versions. --TMg 19:17, 18 July 2013 (UTC) I like version 2.2 best of all submissions in there. Wikivoyage is not about sailing but I think that sail boat says voyage like no other logos in here. Colour theme goes well with Wikimedia's other projects. I think it is working well in small size too. – linnea (talk) 10:06, 19 July 2013 (UTC) I agree that 2.2 it's the better version beacuse it's leaner. --Andyrom75 (talk) 14:44, 19 July 2013 (UTC) ## Option 19 - Snake on a magic towel Snake on a magic towel. Ok guys, I admit it, I draw terribly, but damn all those logos look so boring for a fun, comunity-driven travelling site! I bring you a traveller snake, it still doesn't have name, it is up to the Wikivoyagers to decide how to call it. It flies on a towel and goes everywhere! That is why it is so happy. It could even have the tongue out like a dog enjoying a car ride with the windows down. The colors can be taken from the official scheme, and this snake likes to form a W, the magic word (how else could a magic towel fly?!). Sometimes it likes to pose sideways and then you have a stilized W with a towel underscoring it. Artists, designers... help! This snake is angry at me for such a poor rendition, it says it can look much better! Materials used: pen on post-it. --Micru (talk) 16:04, 16 July 2013 (UTC) Totally agree most of these logos are boring and generic - go snakey! Pratyeka (talk) 04:00, 24 July 2013 (UTC) There is a big, big smile on my face :) --Peter Talk 20:33, 16 July 2013 (UTC) As a general rule, logos should be as simple as possible, but I am definitely intrigued. If you get someone to "computerize" it, it could have potential. Nick1372 (talk) 21:21, 16 July 2013 (UTC) It is such a cute "mascot" idea that I had to help out :) Shyamal (talk) 01:27, 17 July 2013 (UTC) A girly snake with long eyelashes ! Yeahhhh Anthere (talk) 05:48, 17 July 2013 (UTC) Oh! Really great, Shyamal and Micro. Just one thing bothers me about the new image - the tongue is a bit longue proportional to the body. (And forked on both ends?) 11:01, 17 July 2013 (UTC) Too complicated for a wiki logo that has to be instantly recognizable, even when it's very small. However, this could be Wikivoyage's unofficial (or even official) mascot, our version of Wikipe-tan. Simon Peter Hughes (talk) 13:56, 17 July 2013 (UTC) Not for the logo, but it could be a nice and funny mascot :-) --Andyrom75 (talk) 17:00, 17 July 2013 (UTC) I like the sketch better ;)--Arnaugir (talk) 17:21, 17 July 2013 (UTC) I'd be happy to keep snakey as a mascot floating around the site either way, but I still think this could be made into an icon. It would just have to be simplified a good bit. Unfortunately, my icon generating skills are poor. --Peter Talk 19:14, 17 July 2013 (UTC) I don't think there's any potential as a logo, but it's fantastic as a mascot for the site, something we would significantly benefit from. Any reason it is a snake, though? They seem to have a negative, dangerous and poisonous connotation. JamesA (talk) 07:48, 18 July 2013 (UTC) By the way, I just wanted to commend Micru for bringing up the tone aspect to our logo considerations. There are 3-4 extremely strong logo submissions above, but all are pretty masculine and "techy." The masculine, techy demographic is not one we Wikimedians have trouble attracting. Having something really fun, bright, and whimsical (like a snake on a flying carpet) could be a good way to make our project more approachable for other demographics that we need to fill out a well-rounded travel guide to the world with lively writing—I hope we see some more submissions in this vein. Despite not being all that good at it, I'm going to try and vectorize and scale down this idea. Hopefully I'll generate something useful. --Peter Talk 01:52, 18 July 2013 (UTC) Thank you all for your positive feedback :) The new drawing looks so, so much better! And we even have some name proposals "Snakey" or "Hoopy". I have a friend who is designer and said that he would also try to do a "logo-ified" version. So exciting! --Micru (talk) 14:15, 18 July 2013 (UTC) I LOVE the Snakey! We need more fun in the projects! :D --Waithamai (talk) 02:06, 20 July 2013 (UTC) Why not take Option 6 up there and replace the plane around the Wikivoyage word by Snakey? Or you could even use Snakey as the W and spell out the rest of Wikivoyage name beside him (her?). Amqui (talk) 17:25, 23 July 2013 (UTC) If I could draw better I would do it! You can also take a look to the stylized versions below :) --Micru (talk) 23:19, 23 July 2013 (UTC) ### Cartoonish version This is an eleventh hour attempt to keep this idea alive ;) If you have suggestions, well, I won't be around to make the fixes until after the submission period ends today! I tried to preserve the cartoonishness of the original drawing, hopefully people like it. I think it works very well with a handwriting style font like Lenka (which we use in our current, soon-to-be defunct logo). --Peter Talk 21:39, 23 July 2013 (UTC) Great submission, Peter! I like the choice of colors and the style has improved a lot :) --Micru (talk) 23:19, 23 July 2013 (UTC) I agree this is important to keep alive and develop further! I can see the potential of using it as a tool to explain geography and foreign cultures to children. Pratyeka (talk) 04:02, 24 July 2013 (UTC) ### Simple version I made version where the W shape of snake is clearer and voyage is text on towel. This is free drawn with finger (didn't find stylus) on my tablet. I agree that sometimes logos can be fun. Now looking preview of the small version of this it kinda looks like ticket. --– linnea (talk) 22:59, 23 July 2013 (UTC) Thanks for the submission! What about adding one eye :) or better said .) --Micru (talk) 23:24, 23 July 2013 (UTC) I think this is a great logo with only one flaw--I don't think it will work well for language versions that use non-Latin scripts. How would Викигид work with that? Or ויקימסע? --Peter Talk 00:44, 24 July 2013 (UTC) ### Stylized versions These are the stylized versions that my friend Lluis has made for Wikivoyage: a fantasy ballon, two stylish snakes and a book plane.--Micru (talk) 23:19, 23 July 2013 (UTC) I have moved the balloon and all the comments to option 46.--Micru (talk) 18:23, 24 July 2013 (UTC) ## Option 20 - Suitcase You might recognize this logo from Wikivoyage/Logo/Round 1#Option 8 Suitcase. It´s simple and recognizable, even in a small version, as a logo should be. Some logos are to generic, it could be a logo for just anything, or they make the viewer associate it to something else than travels. All people think of travelling when they see a suitcase, it couldnt be about anything else. / Elinnea (talk) 13:43, 17 July 2013 (UTC) Maybe I've been spoiled by wheeled rollaboards, but I see a briefcase here, not a suitcase. Courcelles 17:43, 17 July 2013 (UTC) Coming from someone that carries suitcases on a flight like a man (), I like this concept. It's unique enough that I don't think there's going to be any issues this time around. Signalizing (talk) 19:24, 17 July 2013 (UTC) I respect the effort that went into creating and submitting this proposed logo, but I don't find it elegant. There's a lot more to travel than luggage. Travel, to me, is above all about flexibility, imagination, discovery, and people learning more about the rest of the human race. Ikan Kekek (talk) 20:10, 17 July 2013 (UTC) Exactly! Travel is motion. Luggage is hand/legcuffs. Alex Spade (talk) 22:17, 17 July 2013 (UTC) ## Option 21 - Compass Rose Variation Two variations with the Compass rose. Lionel Allorge (talk) 11:50, 18 July 2013 (UTC) Although it's not my favourite, I can state that it's very nice, in particular the second one that recall me a dynamic "Catherine wheel" (I hope the word it's correct :-P). --Andyrom75 (talk) 13:00, 18 July 2013 (UTC) I like number 2. Maybe bigger , and wider triangles would look better. Ross Hill (talk) 17:36, 18 July 2013 (UTC) Ugly. Version 2 it's swastika. Digr (talk) 19:10, 18 July 2013 (UTC) Too much like the Wikitravel logo, and the colours don't suit it. · · · Peter (Southwood) (talk): 13:55, 22 July 2013 (UTC) Not a big fan of this one, but the left one (with the border) is definitely clearer than the right one. Effeietsanders (talk) 11:12, 24 July 2013 (UTC) ## Option 22 - The dhow (II) Already proposed last October. This is a proposal which focuses on the dhow, a vessel used in the Red Sea and Indian Ocean region, imho an excellent example of crosscultural connector. I was unhappy with the old version, made for the last year contest, because it wasn't enough "rounded". I've tried to smooth it out. I'm just an amateur graphic designer, so please help me with suggestions and svg-ification. --Pequod76(talk) 21:00, 18 July 2013 (UTC) The red line needs a white border or something if you but it on a colored background. --TMg 21:06, 18 July 2013 (UTC) Thank you. I've put a white background. --Pequod76(talk) 21:35, 18 July 2013 (UTC) I definitely prefer the old version, since the new one looks to have grabbed an element directly from the Meta logo. --Peter Talk 20:59, 19 July 2013 (UTC) Definitely true. But... don't you think that the old one is too less rounded? Maybe I can quit the grabbed elements and leave the new version with no borders? I perceive the new versione better centered. Thanks for your comment. --Pequod76(talk) 11:54, 20 July 2013 (UTC) There's a third option now. :) These are all sketches, bad realized in terms of graphic technique. --Pequod76(talk) 16:06, 20 July 2013 (UTC) And a fourth. --Pequod76(talk) 16:28, 20 July 2013 (UTC) I don't see any need for a circle in the logo. The first option looks cleanest and simplest to me, and those are things to aim for! --Peter Talk 18:12, 20 July 2013 (UTC) Thank you for your suggestions. I've put a fifth attempt. --Pequod76(talk) 23:34, 20 July 2013 (UTC) Fifth option is by far the best. Simple, but dynamic. Nick1372 (talk) 22:14, 21 July 2013 (UTC) I agree with Nick: 5° it's the best (same reasons) --Andyrom75 (talk) 23:25, 21 July 2013 (UTC) That is a very strange rig. Does not look like any lateen I have ever seen. What is the blue supposed to be? · · · Peter (Southwood) (talk): 13:53, 22 July 2013 (UTC) Hi! This was my point of departure. I've seen myself some dhows in East Africa, but with many different sets of rigs. (I'm not an expert!). --Pequod76(talk) 07:55, 23 July 2013 (UTC) I see. The sails are set in opposite directions. Very strange. I wonder if they ever actually do that. the yards would more normally be set parallel. · · · Peter (Southwood) (talk): 09:50, 23 July 2013 (UTC) It seems you are right. Anyway, it's easy to divert the blue lateen, in order to give it the same shape as the green one. Do you think is it worth it? :) --Pequod76(talk) 20:58, 23 July 2013 (UTC) ## Option 23 - W-Plane Author : User:Hugo Salt Here's my entry : A plane to symbolize "Voyage" with the "W" in the background for "Wiki". Two color schemes proposed. As proposed by Andyrom75 , the version B includes a thicker circle (looks much nicer I think). Version C is lighter as the "W" background was removed. 21:11, 18 July 2013‎ User:Hugo Salt ### Discussion Maybe make another version with either are darker background, or W. 99.245.192.218 23:07, 18 July 2013 (UTC) I like the plane. Less the background. I would increase also the thickness of the circle. --Andyrom75 (talk) 06:20, 19 July 2013 (UTC) Road sign? 81.178.175.163 19:50, 19 July 2013 (UTC) While it has an attractive simplicity to it, I don't like the W for two reasons. The "crashed V" font looks very similar to Wikipedia's W icon, and as mentioned for other submissions, W is not used in non-Latin language versions. --Peter Talk 21:05, 19 July 2013 (UTC) C are far and away better than the previous one. I like them. Although you would sacrifice their simplicity (that is one strong point of that version), try to think on versions with one or two elements more, just to enrich it a little bit. I don't have tremendous idea at the moment :-) make&post some try, for example with four compass triangles on the circle (with the peak versus the outside), or maybe just two arrows with the head pointing the line of the circle itself as if the circle is rotating (to give an idea of moving). Something like that. --Andyrom75 (talk) 08:30, 20 July 2013 (UTC) I like the C blue (I don’t really like the colors of C classic). Maybe you could try to add a shape of mountain under the plane? Fractal (talk) 10:07, 20 July 2013 (UTC) Here is something like what I have in mind: http://commons.wikimedia.org/wiki/File:HugoWikiVoyage1C-bis.png. Feel free to do whatever you want with it. Fractal (talk) 10:30, 20 July 2013 (UTC) I'm not feeling very good about the width of the circle. The first proposal is so skinny that it's kind of hard to see, but I prefer it over the wider circle, which is clunky and too obvious. Can I see it with a circle with a width in between the two? Nick1372 (talk) 06:14, 21 July 2013 (UTC) With the red circle, it looks like a "no airplanes taking off" or perhaps "no airplane traffic allowed" traffic-sign-style sign to European eyes. Amusing, but not really good for a Wikivoyage logo, I believe. In terms of logos comprising airplanes (slightly questionable - as if travel was only by airplane), I prefer Globe-trotter's submission by far. PrinceGloria (talk) 06:22, 21 July 2013 (UTC) version Mountain Classic it's very nice. --Andyrom75 (talk) 23:23, 21 July 2013 (UTC) The mountains are nice, thanks! But please, do not use the Meta-Wiki colors, Wikivoyage has nothing to do with Meta-Wiki and using the same colors is very confusing (at least I found it very confusing when I discovered Wikivoyage with the current logo). Fractal (talk) 13:52, 22 July 2013 (UTC) Thanks everyone for your comments. Now I have to decide which one to submit. I'm still not sure whereas I should submit two color variations or only one logo. I think the mountain versions are the best looking indeed.HugoSalt 19:21, 22 July 2013 (UTC) I think you should submit version "Mountain Blue". It's the best, IMO. If it gets accepted, you can always submit other colors in Round 2. Nick1372 (talk) 19:51, 23 July 2013 (UTC) It's quite unlikely a passenger aircraft could achieve such a high climb angle, and if it could, it wouldn't do so anyway. --YMS (talk) 20:33, 23 July 2013 (UTC) This is a logo, not a technical illustration, It is not required to be realistic. · · · Peter (Southwood) (talk): 20:54, 23 July 2013 (UTC) I like the blue one with mountains. Very nice. Ikan Kekek (talk) 22:30, 23 July 2013 (UTC) I also think that the version Mountain Blue is the best one Fractal (talk) 15:36, 24 July 2013 (UTC) Thanks everyone for your feedbacks :). --Hugo Salt 19:59, 24 July 2013 (UTC) Of course a logo doesn't have to be realistic, but if it says "We're not going to survive this", I don't think it's a good logo. --YMS (talk) 20:21, 24 July 2013 (UTC) Sorry to say that but they all look like information signs on an airport. --TMg 16:49, 24 July 2013 (UTC) And aren't airports among the most used areas when traveling ? If it reminds airports, then it reminds travel, then it fits well the term "Voyage" ;). --Hugo Salt 19:59, 24 July 2013 (UTC) ## Option 24 - Circle and arrows Meant to look similar to Meta logo, with arrows like on a compass rose. I don't know why it turned out so small. Ross Hill (talk) 00:08, 19 July 2013 (UTC) Why in the world would we want a logo similar to Meta-Wiki's?? LtPowers (talk) 01:44, 19 July 2013 (UTC) I agree--we want a distinctive and unique logo. Given that Meta and Wikivoyage are incredibly different projects, why would Wikivoyage inspire a similar design? --Peter Talk 21:01, 19 July 2013 (UTC) I think you could reasonably say we don't want a logo that looks like any of the other WMF logos in shape or colour, we want a logo that is distinctive and different, like Wikipedia, Wikiversity, Wikisource etc. · · · Peter (Southwood) (talk): 13:49, 22 July 2013 (UTC) Why? Half of the icons of Wikimedia projects (including Wikidata and Wikispecies) use the same colors. And Wikivoyage is a Wikimedia project! What's wrong with the colors? If it would a specification not to use the Wikimedia colors, why couldn't I read someting about it in the contest rules? Logos: http://www.wikimedia.org (i'm not a native speaker. Please feel free to correct my text)Giweddah There is no rule that you can't use these colors, but Wikivoyagers have consistently said that they prefer a more unique logo, with a color scheme that is aims to be more reflective of the culture individual project in question, which probably means brighter colors, or colors in some way inspired by the idea of travel. (That recommendation is now at the top of this page.) Since the vote will be weighted towards Wikivoyagers, it might be worthwhile to take this preference seriously ;) --Peter Talk 18:43, 23 July 2013 (UTC) ## Option 25 - White-blue world I prefere the white-blue logo. Which one do you prefere? let me know because I would like to use only one of them. Thank you in advance. Ah, Is the meaning of the image understandable? Horizon, mountains, route and W of Wikivoyage...Polloepollo (talk) 10:27, 24 July 2013 (UTC) It's a very good idea and has a lot of potential. The problem is that W. You cannot integrate the latin alphabet into the design, because not all countries covered by Wikipedia use it. Try to replace the W with something else and put the word Wikivoyage on the bottom. By the way, I like the first one far better. Try keeping it one solid color. Nick1372 (talk) 15:05, 20 July 2013 (UTC) Thank you Nick for your advices. I think you are right, so I came up with this new logo, which is my favorite one. The third is the best. As a thumbnail, it is hard to say if it looks good : . Cantons-de-l'Est (talk) 02:40, 23 July 2013 (UTC) I like the third, but I'm slightly concerned about the fact that taking away the W broke the circle-ness (is that a word?). I could get used to it, though. Nick1372 (talk) 04:02, 23 July 2013 (UTC) Maybe "circularity". :P πr2 (tc) 04:08, 23 July 2013 (UTC) Yes, The logos are not perfect, but I ran out of (simple) ideas and the deadline is tomorrow. So I added a W in the first logo and then I'm going to wait for voting response. Thank you both for your hints. Finally it's my intention to submit to the voting only the logo with the constellations and the white-blue logo with the "W" mountain and the entire name wikivoyage written on the right (So it can be written in any alphabet). I'm sorry, but with all of the options above it takes me a lot of staring and reading the description to understand what it depicts. Not the strongest contender in its current shape I'm afraid. Effeietsanders (talk) 11:14, 24 July 2013 (UTC) • If the blue-green-red is used, I think it would be better for it to be the Wikimedia colors. Also, integrating the "W" right in the logo is a bit problematic for other languages. --Yair rand (talk) 11:50, 24 July 2013 (UTC) It's supposed to be upside-down mountains, not really a W. It's been brought up already.Nick1372 (talk) 20:27, 24 July 2013 (UTC) ## Option 26 - Travel modes My first submission. Don't know if it is to be my last. After going over the other submissions, I'm surprised none have use the plane and boat together yet! As per advice from other people, I've been gathering some details needed, and this is end result #1. I need some room for improvisation, though, like the square version. As for the font, I have no idea of it yet. I'm also planning to add a tagline, but just like the main one, I'm not sure of the font here, too... NJKFalcon (talk) 18:00, 19 July 2013 (UTC) ...Why two couple of brackets? It's a "wiki" reference. Don't know exactly how to put it in a way... NJKFalcon (talk) 18:00, 19 July 2013 (UTC) Similar idea to the MediaWiki logo. PiRSquared17 (talk) 18:11, 19 July 2013 (UTC) It's an In joke is it not? That's not helpful when reaching out to the public 81.178.175.163 19:38, 19 July 2013 (UTC) Honestly I don't like it, but I'm writing you for a general suggestion. Wiki-brackets works for an internal logo, where all the audience knows exactly what they are (like the MediaWiki one). Wikivoyage has a different target, a much more wider one, that potentially they don't know how to write a wiki-article and they will never do, so for them the brackets will remain meaningless. Try something different. --Andyrom75 (talk) 08:36, 20 July 2013 (UTC) I don't mind the brackets themselves, but they need to go. They're making the central part of the design way too small. Nick1372 (talk) 15:09, 20 July 2013 (UTC) Vertically stretch the brackets and remove the bold (not [[ ]], but [[ ]]). Put them in gray. They could be like less square, more round, like a wind symbol (${\displaystyle \approx }$). You should be able to enlarge the boat-plane. Cantons-de-l'Est (talk) 02:17, 23 July 2013 (UTC) ## Option 27 - Top-Plane Author : User:Hugo Salt (I decided to submit only version 1, I've removed version 2 from the voting gallery.) Here's a second entry : A plane seen from top. We can find this kind of plane top-view representation in airports. Here are two variations. Looks like a road sign 81.178.175.163 19:39, 19 July 2013 (UTC) As with some other submissions above, this is very similar to the Meta logo, and I think we should be going for something unique, and more inspired by Wikivoyage itself. --Peter Talk 21:02, 19 July 2013 (UTC) The right one (version 2) is much clearer than version 1. However, I don't like the plane so much as symbol here. It looks too much like an airport-sign at the side of the road to me. It also suggests that Wikivoyage is only for 'far travels' which is (as far as i know) not necessarily the case. Effeietsanders (talk) 11:16, 24 July 2013 (UTC) ## Option 28 - V for voyage • Only 2 submitted, per submitter request The logo shows 3 colored pieces that forms a globe and a "V" for voyage. Giweddah I really like this one! --Stryn (talk) 14:13, 20 July 2013 (UTC) The problem is that the V is not used in all of the languages that Wikivoyage covers. Therefore, in half the world, it will just be two lines and a circle... Nick1372 (talk) 15:14, 20 July 2013 (UTC) I know, but this is still nice. --Stryn (talk) 16:19, 20 July 2013 (UTC) I think, it is not a big problem. VW, Mazda or Lexus sell cars in China and no one there can read the letters (VW, M, L) in the logos. A logo has to be unique and simple but not necessarily readable. Giweddah I share Nick's concern, though--I think we should be an assertively multilingual project. Also, would you mind experimenting a bit with the colors. It's a little sad to see the Meta logo colors used in so many submissions! But yes, otherwise a nice, clean logo ;) --Peter Talk 18:21, 20 July 2013 (UTC) Clean and nice as a logo should be. I don't see as a problem the presence of latin characters, an infinity of global successful logo have. --Andyrom75 (talk) 21:02, 20 July 2013 (UTC) As a sidenote, I believe that Japanese pupils learn the Latin alphabet at school, so it is not true to say "no one there can read the letters". There is a fair amount of Latin characters and whole words and phrases written out using them in Japanese everyday life. That said, I am with Peter and Nick. PrinceGloria (talk) 06:25, 21 July 2013 (UTC) The same for chinese pupils, AFAIK. :) --Pequod76(talk) 09:54, 21 July 2013 (UTC) Which one is better (straight vs curves, red vs grey)? Giweddah In my opinion #2 non both counts 81.178.173.30 12:51, 22 July 2013 (UTC) I immediately thought of the South African flag, but really it is not very much like it at all. Maybe I am biased. · · · Peter (Southwood) (talk): 13:41, 22 July 2013 (UTC) I think I will submit the second one – it looks softer. And the meaning of the (second) three colors: blue stands for water/sea, green stands for (natural) land and grey stands for man-made travel destinations (e.g. Buildings, cities) Giweddah ## Option 29 - Earth Compass This logo shows a compass on the Earth. I tried to make it quite simple. (Drawn with Adobe Illustrator) Alexander95015 ### Discussion Sorry, but that's barely distinguishable as the Earth. The shapes don't really look like continents. Can you try it again? Nick1372 (talk) 18:14, 21 July 2013 (UTC) Thanks for the feedback. How do you think it can be more recognizable as continents? Alexander95015 (talk) 01:32, 22 July 2013 (UTC) http://commons.wikimedia.org/wiki/Category:Maps_of_the_world and http://commons.wikimedia.org/wiki/Category:Earth Giweddah Perhaps you could shape the continents to look like the actual continents? Top left could resemble North America, bottom left could be South America, top right could be Europe, etc. Just remember to keep it simple… Nick1372 (talk) 19:58, 23 July 2013 (UTC) ## Option 30 - Means of transport 10 px icons: 16 px icons: 20 px icons: 24 px icons: 10 px basic logos: 16 px basic logos: 20 px basic logos: 24 px basic logos: This logo shows three means of transport: aeroplane, bus and ship. Ship is blue, as water is blue. Bus (I thought about a car first, but I think the bus is "more community" mean of transport, as Wikivoyage is a community peoject) is green, as grass on land is green. And aeroplane is red because red is just last color recommended by Wikimedia Foundation Design. I hope you find it enough simple to become a logo and enough nice to look at it so often. --Mimarik 17:00, 22 July 2013 (UTC) ### Discussion Nice concept. I like the ship and the bus. My problem is with the plane. It's really an unappealing shape. Can you just change that? In addition, please do not limit yourself to WMF colors!! There are so many other colors that would look better, and we want to show uniqueness in our logo. Nick1372 (talk) 22:09, 21 July 2013 (UTC) I just don't know what colors to use! Has anybody an opinion? --Mimarik 17:00, 22 July 2013 (UTC) Ask for help on the en:Portal:Color. Cantons-de-l'Est (talk) 02:30, 23 July 2013 (UTC) I have an idea for the colors. Can you try this for the plane, this for the bus, and this for the ship? Each recalls where each mode of transportation is used (sky, land, ocean), yet share a primary color to show how they're all connected. Nick1372 (talk) 04:49, 23 July 2013 (UTC) What does it mean when you say "primary color"? Background? Color inside suitcase? --Mimarik (talk) 18:19, 23 July 2013 (UTC) Sorry, I meant that using the colors of dark green, light blue, and blue-green are similar colors, binding them together. It doesn't need a background color. Nick1372 (talk) 20:10, 23 July 2013 (UTC) half of the icons of Wikimedia projects (including Wikidata and Wikispecies) uses the same colors. And Wikivoyage is a Wikimedia project. What's wrong with it? Logos: http://www.wikimedia.org Giweddah I agree. Good reason to use WMF colors. --Mimarik (talk) 18:19, 23 July 2013 (UTC) With the exception of Wikispecies (which uses muted versions of the usual RGB), all of the projects that use the RGB colors are meta-projects, not projects that end users use. LtPowers (talk) 19:40, 23 July 2013 (UTC) Most people haven't a clue what the Wikimedia Foundation is. If non-users have ventured into the MetaWiki site (or any other meta project) , they were probably very confused (as I was when I first became a user). If Wikivoyage were to have the same colors, they might recall those feelings of confusion and decide it wouldn't be worth the trouble to explore Wikivoyage. Nick1372 (talk) 20:10, 23 July 2013 (UTC) This submission is interesting but somehow seems a little busy to me, probably because there are three many means of transport that seem too close to each other for my taste. Ikan Kekek (talk) 22:34, 23 July 2013 (UTC) I agree, a bit too busy. However, the ones with windows are much clearer than the ones without (especially the train becomes hard to recognize). At the same time, leaving out the suitcase helps too. Effeietsanders (talk) 11:17, 24 July 2013 (UTC) ## Option 31 - circular path ### Discussion Nice designs, but too much details. --Andyrom75 (talk) 20:10, 22 July 2013 (UTC) I've fixed the submission in the gallery. I would try something without text in order to see how it is at 20px. I like them all. Who is the author? :) --Pequod76(talk) 08:49, 23 July 2013 (UTC) ## Option 32 - Satellite view The idea was to see the world more global, like pictures from a satellite. ### Discussion What exactly is it? All I see is a green box and some arrows. Nick1372 (talk) 04:27, 23 July 2013 (UTC) ## Option 33 - Flying Proa (20px) And now for something (not quite) completely different. A silhouette of a more exotic (Wiki)voyager in a flying proa. A bit rough as it is a first draft. Romance, adventure and a different colour scheme. · · · Peter (Southwood) (talk): 15:34, 22 July 2013 (UTC) (50px)(75px) ### Discussion Number 2 is nice. The thumbnail is easy to remember. Cantons-de-l'Est (talk) 02:33, 23 July 2013 (UTC) I like the third one a lot. Nick1372 (talk) 04:25, 23 July 2013 (UTC) I like this too, and think that Lenka or fonts with a similar feel work well with the, ah, curvaceousness of the icon. Could we see how this looks when small? --Peter Talk 05:34, 23 July 2013 (UTC) How small? legibility of text is lost at 50px, but that would happen for many logos with text. At 75 it is marginal. The graphic does quite well at both 50 and 75px because of the clean lines, low clutter and high contrast. Lenka has an organic feel which goes well with the boat type. · · · Peter (Southwood) (talk): 07:32, 23 July 2013 (UTC) As small as the icons that get placed in browser tabs, I guess, which don't need to have text. --Peter Talk 18:46, 23 July 2013 (UTC) The colors are very high-contrast... very 16-bit. Less saturation and less contrast between them would improve this logo significantly. LtPowers (talk) 19:42, 23 July 2013 (UTC) Colour change is easy. The main point was to avoid WMF colour combination. High contrast can be useful for small icons, but name your colours and I will run up a sample. · · · Peter (Southwood) (talk): 20:27, 23 July 2013 (UTC) Yellow and blue are fine, but try decreasing the saturation on them. Maybe move one of them a tad closer to green. LtPowers (talk) 20:11, 24 July 2013 (UTC) It's not necessary to decrease the size of the blue section. It might even create problems with other languages, which could possibly have longer names. Nick1372 (talk) 20:21, 24 July 2013 (UTC) ## Option 34 - A walker on the globe I propose two logos: the silhouette of a walker with his bag on a background of globe with the colors of wikimedia. --Dyolf77 (talk) 17:15, 22 July 2013 (UTC) ### Discussion I like a lot the shape of a walking man, but the background doesn't convince me. --Andyrom75 (talk) 20:12, 22 July 2013 (UTC) The same. Try removing the grid. Cantons-de-l'Est (talk) 02:35, 23 July 2013 (UTC) Don't feel forced to use WMF colors. Are there others you'd rather use? Nick1372 (talk) 04:30, 23 July 2013 (UTC) I tried with a new background in C. --Dyolf77 (talk) 07:37, 23 July 2013 (UTC) I like this idea a lot too, but why is he walking in front of the Meta logo? ;) --Peter Talk 05:32, 23 July 2013 (UTC) I love the Meta logo :) --Dyolf77 (talk) 07:37, 23 July 2013 (UTC) • I like "B". Digr (talk) 11:48, 23 July 2013 (UTC) C is a huge improvement and is something we could really work with. The 'W' needs to go, though. LtPowers (talk) 19:43, 23 July 2013 (UTC) • C without "W" --Dyolf77 (talk) 20:45, 23 July 2013 (UTC) • (20px)(50px) (75px) C without the W is by far the best. I like it. Nick1372 (talk) 21:48, 23 July 2013 (UTC) • While the logo looks OK, I dislike it because it focuses on (A) men; and (B) walking/budget travel/backpacking. We should not alienate our potential audience with the logo. Pratyeka (talk) 04:04, 24 July 2013 (UTC) • Sorry about that, but I think it is not a question of sexism, at the first sight we feel that this is a traveler. Besides, if you look closely at the silhouette you can not say 100% that this is a man :) Thanks for the review. Regards Dyolf77 (talk) 16:42, 24 July 2013 (UTC) My favourite is B without grid. --Andyrom75 (talk) 06:47, 24 July 2013 (UTC) One of the better submissions. I strongly prefer without grid and without W. Both B-without and C-without I could live with. I am unsure if this would start a discussion about gender equality though, possibly best to run this by some more people, and see if you can adjust for that. Effeietsanders (talk) 11:20, 24 July 2013 (UTC) Here a new version with B & C (20px)(50px) (75px) --Dyolf77 (talk) 16:42, 24 July 2013 (UTC) Oh, I like this one !! The contrast is good. Might require a bit more refinement on the edges of the silhouette, but for me this is definitely one of the best proposals ! TheDJ (talk) 10:02, 2 August 2013 (UTC) Hi, I like this logo but I'm afraid it's pretty close to the Guide du Routard logo. Risky one. --Flappiefh (talk) 17:52, 10 August 2013 (UTC) ## Option 35 Kite I propose the concept of Kite to show the attitude of traveller. It is freely flying kite same as freely wondering traveller. Note: I do not have computer right now and i dont know coreldraw also. Anybody can help by redrawing concept and modofying it to suit as a logo. Here is just proposed concept. I have drawn it in mobile app so its poor. Just consider the concept. Please help me artists here. Thanks. -Nizil Shah (talk) 08:12, 23 July 2013 (UTC) I suggest that you upload cropped versions and mark them to be added to the voting gallery only. -- Rillke (talk) 22:58, 23 July 2013 (UTC) cropped version added but still waiting to be computerised by someone. :( -Nizil Shah (talk) 16:08, 24 July 2013 (UTC) ## Option 36 - Shoe mark I propose this shoe mark as a concept here. Travellers leave their shoe marks everywhere. Note: I have just added concept pic here as i do not have computer. It is drawn in mobile app so its poor. Just consider the concepts. Anybody can redraw it to suit as a logo. Artists are welcome. Thanks. -Nizil Shah (talk) 10:12, 23 July 2013 (UTC) ## Option 37 - Simple Wikivoyage Quite a simple design. -Alexander95015 ### Discussion How is it linked to sense of Wikivoyage? --Mimarik (talk) 18:12, 23 July 2013 (UTC) It has nothing to do with travel. It's possible to be too simple, you know. Nick1372 (talk) 20:16, 23 July 2013 (UTC) ## Option 38 - The geographical zones 20 px rendering , 16 px rendering This logo looks like the current logo that we are forced to change. I thought about the geographical zones that divide the Earth and I associated them with the colour of the Wikimedia logo: blue (that is a cool colour) stand for the frigid zones, green (that recall the forests, or the nature) represent the temperate zones, and red (a warm colour) is the torrid zone. In order to give the idea of traveling around the world i added an arrow in the second version. --Mystère Martin (talk) 16:39, 23 July 2013 (UTC) Nice logo, I like it. It's not easy to reproduce a globe without copying directly the MetaWiki globe. --Mess (talk) 17:47, 23 July 2013 (UTC) It's not bad, but I think we need a cleaner break from the current logo, if only to satisfy the WTO. LtPowers (talk) 19:45, 23 July 2013 (UTC) Nice logo that is a perfect link between the current voy logo e the wikimedia one. Despite Lt observation I don't see any kind of similarities with the WTO one. Maybe I would only apply some variation on the arrows that doesn't convince me too much. --Andyrom75 (talk) 06:45, 24 July 2013 (UTC) I uploaded a new version with a better arrow, thinner and with rounded corners. Moreover, I think that my logo is very different from the WTO one, but it recalls the current logo that I've always liked. --Mystère Martin (talk) 09:04, 24 July 2013 (UTC) I like 2.1 and 3. I would mix them. Add an arrow (don't know where :-) ...mayb in the same position) on 3, because I like the torsion, but without the arrow it seems "static". Try two version, one with the same arrow (the latest) and another one longer that would reach near the end of the globe on the opposite side. --Andyrom75 (talk) 14:03, 24 July 2013 (UTC) I made the fourth version. These are the 20 px renderings: and --Mystère Martin (talk) 14:34, 24 July 2013 (UTC) I didn't say it looked like the WTO logo. I'm saying the WTO may not be satisfied that this logo is sufficiently different from the one to which they objected. LtPowers (talk) 20:06, 24 July 2013 (UTC) ## Option 39 - Travel Bag I propose a Travel Bag for Wikivoyage Logo. It captures the concept of going places.Imadmemon (talk) 07:32, 24 July 2013 (UTC) added by Imadmemon (talk · contribs), 19:30, 23. Jul. 2013‎ Unsigned entry may not be valid. · · · Peter (Southwood) (talk): 21:03, 23 July 2013 (UTC) Where is this stated? The contribs are recorded in the revision history, though it is inconvenient digging through it. -- Rillke (talk) 23:03, 23 July 2013 (UTC) Can someone kindly guide me how to submit a Signed Entry. Type four tildes ~~~~ at the end of your edit. · · · Peter (Southwood) (talk): 06:24, 24 July 2013 (UTC) Greatly appreciated.Imadmemon (talk) 07:34, 24 July 2013 (UTC) ## Option 40 - Flying Witch Not sure why but a Wicked Witch flying across the globe seems appropriate to me as Wikivoyage Logo. May be its the rhyming sound of a Wicked witch & Wiki :)Imadmemon (talk) 07:36, 24 July 2013 (UTC) added by Imadmemon (talk · contribs), 19:30, 23. Jul. 2013‎ Unsigned entry may not be valid. · · · Peter (Southwood) (talk): 21:04, 23 July 2013 (UTC) Funny but not appropriate :-) --Andyrom75 (talk) 13:56, 24 July 2013 (UTC) Maybe we could use this on Halloween or something. ;) I don't think this would give a good impression of Wikivoyage. PiRSquared17 (talk) 18:35, 24 July 2013 (UTC) Make the witch larger. A lot larger. --TMg 17:04, 24 July 2013 (UTC) ## Option 41 - Exploring World I've tried to capture the concept of exploring the world in this logo. The magnifying glass symbolizes the exploration & search part.Imadmemon (talk) 07:37, 24 July 2013 (UTC) added by Imadmemon (talk · contribs), 19:30, 23. Jul. 2013‎ Unsigned entry may not be valid. · · · Peter (Southwood) (talk): 21:04, 23 July 2013 (UTC) It really represents what is Wikivoyage. Amqui (talk) 00:00, 24 July 2013 (UTC) Thanks Amqui. Imadmemon (talk) 07:37, 24 July 2013 (UTC) The idea is simple and perfect. I like the style of drawing, but it's a kind of style that I don't see very fitting with a logo concept. --Andyrom75 (talk) 13:55, 24 July 2013 (UTC) Very sorry to say that but this is one of the most common ideas in the world. Magnifying glasses on globes were used many, many times before. Definitely not a good idea to copy that. --TMg 17:03, 24 July 2013 (UTC) ## Option 42 - Par Avion Just like a letter sent via Air Mail, the users of Wikivoyage can travel across the globe. That's the concept behind this logo.Imadmemon (talk) 07:38, 24 July 2013 (UTC) added by Imadmemon (talk · contribs), 19:30, 23. Jul. 2013‎ Unsigned entry may not be valid. · · · Peter (Southwood) (talk): 21:05, 23 July 2013 (UTC) I will be grateful if you can explain how to submit signed entry. Type four tildes ~~~~ at the end of your edit. Thanks again Peter. Imadmemon (talk) 07:38, 24 July 2013 (UTC) I may be wrong but this looks like a copyright violation for me. It looks like you edited an existing picture of an envelope. --TMg 16:59, 24 July 2013 (UTC) ## Option 43 - Navigational Sextant Author: Michelle This logo of a navigational sextant depicts the idea of travel and exploration. The blue circle symbolizes the Earth, as the majority of our planet is water. It's clean, simple design is easily recognizable and can be scaled down considerably while maintaining it's quality. The colors were chosen for several reasons - 1) Primary colors being easy to detect by the human eye. 2) The red and blue also ties into the nautical theme in which the sailors used these sextants which in turn relates to 'voyage' in Wikivoyage. 3) These colors would also work when converted to gray-scale or be viewed by someone that is colorblind. 208.50.124.65 10:57, 24 July 2013 (UTC) ### Discussion Sorry but it seems a masonic logo :-P --Andyrom75 (talk) 06:41, 24 July 2013 (UTC) There is no sextant on a masonic logo, they use a divider and square. · · · Peter (Southwood) (talk): 07:30, 24 July 2013 (UTC) I haven't said that is equal, I've said that it recalls that symbol at the first glance. ...well, also at the second glance :-D --Andyrom75 (talk) 13:52, 24 July 2013 (UTC) ## Option 44 - Compass Face Here are my submissions for the new logo. I could think of nothing better to represent travel and freedom than a compass. I tried to incorporate 'flat' design (seeing as its so popular nowadays). Enjoy! Hardwigg (talk) 23:58, 23 July 2013 (UTC) ## Option 45 - WV Arrow For my submission, I combined some other suggestions i found intersting : - wikimedia colors - Arrow (option 1) - WV logo (option 7) - Compass (options 4, 11, 44) the result like a Compass with a green arrow made of WV letters into the red and blue Wikimedia Circle Raznow (talk) 09:16, 24 July 2013 (UTC) Nice combination. --Andyrom75 (talk) 13:52, 24 July 2013 (UTC) Really nice. Would the Latin initials translatable to other non-Latin scripts though? Bennylin 18:48, 27 July 2013 (UTC) ## Option 46 - Fantasy balloon These are the stylized balloon that my friend did (originally option 19).--Micru (talk) 18:23, 24 July 2013 (UTC) The balloon is a surprise, and a really good one. It's simple, stylish, appropriate, and unique! That would be a great logo. --Peter Talk 00:39, 24 July 2013 (UTC) What about Snakey in the cradle? Amqui (talk) 04:26, 24 July 2013 (UTC) Unbelivable how we have arrived here from "Snake on a magic towel". Simply amazing! Good job and very nice result. --Andyrom75 (talk) 06:51, 24 July 2013 (UTC) That balloon is so great idea! The colors are done so nicely. I also like the last snakey, it shows the W shape great. – linnea (talk) 09:09, 24 July 2013 (UTC) I realy liked Balloon. Its surprising how Snakey lead us to such a nice design with great colors. I liked Cartoonish snakey too. It should be turned into mascot of WV. Well done Micru and friends.-Nizil Shah (talk) 16:26, 24 July 2013 (UTC) I love them all, especially the balloon and the "burning" snake. The colors are great. There is no need to stick to the same colors again and again for such a project. I will definitely vote for these. --TMg 16:48, 24 July 2013 (UTC) I think balloon should be submitted separately as it has a potential to be chosen as a logo. It has W and V nicely woven into ballon. Great colors. Simplicity. Recognisable. Appropriate to travel. I will vote for this even thaught I have submitted some ideas. Awesome. -Nizil Shah (talk) 16:53, 24 July 2013 (UTC) I added a cropped version of the balloon. This should be definitely added to the voting as a separate entry. --TMg 17:34, 24 July 2013 (UTC) Sepparated and added SVG. If anyone could crop that one too it would be great. The font is Arista 2.0 Alternate light.ttf --Micru (talk) 18:28, 24 July 2013 (UTC) Done. -- Rillke (talk) 19:45, 24 July 2013 (UTC) I really, really like this submission. The icon reminds of a hot air balloon, which is probably the coolest way to travel, with plenty of thematic possibilities that we can make use of in various on-site promotions (Jules Verne-ish ideas coming to mind). It also reminds of a parachute, which makes me think of parachuting off into unknown lands. That dovetails really nicely with our motto of voy:Wikivoyage:Plunge forward! The color scheme is distinct, classy, and yet still fun. The snakey connection is just icing on the cake. --Peter Talk 20:42, 24 July 2013 (UTC) ## Option 47 - Feet of the world A cheerful concept that is meant to represent the spirit of traveling. The footprint represents the most ecologically sensitive way to travel. Along with the blue globe background, the feet represents the east and west of the modern world and how traveling makes us one. The typeface used is Courgette Regular (open source) and was chosen for its adventurous character. 3 color artwork and unique features makes it identifiable even in small size --Planemad (talk) 21:09, 24 July 2013 (UTC) ## Option 48 - Azimuthal map 16px: 32px: I used WMF logo's blue color and an azimuthal map similar to the one used in United Nations' emblem, you can check the 16 and 32 pixel favicon sizes above. please visit the file pages to see the logos with text. ■ MMXX talk 21:50, 24 July 2013 (UTC) I've added designs A and C to the voting gallery. ■ MMXX talk 22:27, 24 July 2013 (UTC) While very attractive, I think it is too similar to the UN logo. (Which is a concern, given that our current problems stem from being too similar to that of another international organization!) --Peter Talk 22:30, 24 July 2013 (UTC) Maybe you should compare it side-by-side with the UN logo, although the map is taken from the UN logo, but they are very different IMO. please also see the Wikinews logo which uses the exact same map, it is more similar to the UN logo, but we didn't have any issue with using it. ■ MMXX talk 22:54, 24 July 2013 (UTC) The above discussion is preserved as an archive. 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http://www.onlineprediction.net/?n=Main.KernelMethods	# Kernel Methods Kernel methods are a powerful tool of modern learning. This article provides an introduction to kernel methods through a motivating example of kernel ridge regression, defines reproducing kernel Hilbert spaces (RKHS), and then sketches a proof of the fundamental existence theorem. Some results that appear to be important in the context of learning are also discussed. # 1. A Motivating Example: Kernel Ridge Regression In this section we will introduce kernels in the context of ridge regression. The reader may skip this section and proceed straight to the next session if he is only interested in the formal theory of RKHSs. A more detailed discussion of Ridge Regression and kernels can be found in Section 3 of Steve Busuttil's dissertation. ## 1.1 The Problem Suppose we are given a set of examples , where are signals and are outcomes or labels. We want to find a dependency between signals and outcomes and to be able to predict given a new . This problem is often referred to as the regression problem 1. Let us start by restricting ourselves to linear dependencies of the form , where , is the standard scalar product in , and the prime stands for transposition (by default all vectors are assumed to be column vectors). The class of linear functions is not too reach, and we will need to progress to more sophisticated classes later. ## 1.2 Least Squares and Ridge Regression The least squares is a natural, popular, and time-honoured (apparently going back to Legendre and Gauss) approach to finding . Let us take an minimising the sum of squared discrepancies Minimising this expression is equivalent to projecting of the vector on the subspace of generated by vectors , where consists of -th coordinates of s. The projection on the subspace is always unique and well-defined. However if the vectors are linearly dependent (which always happens if the sample is small and ) this unique projection has multiple representations as their linear combination. The method of least squares thus does not necessarily define a unique regressor. Consider a more general problem. Let us take and consider the expression A vector minimising this is called a solution of the ridge regression problem (for reasons that will become apparent later). The least squares approach is a special case of the ridge regression approach, namely, that of . Why would anyone want to use ? There are three main reasons. First, ridge regression with always specifies a unique regressor as will be shown below. Secondly, a positive value of makes the problem easier computationally. These properties will be shown later in this section. Thirdly, the term performs the regularisation function. It penalises the growth of coefficients of and urges us to look for "simpler" solutions. ## 1.3 Solution: Primary Form Let us find the solution of the ridge regression problem with . It is convenient to introduce a matrix ; the rows of are vectors (and the columns are vectors mentioned above). We get By differentiating w.r.t. and equating the result to 0 we get and where is the identity matrix. This must be a solution; indeed, as coefficients of approach infinity, and therefore must go to infinity. Let us analyse this expression. The matrices , , and have the size . The matrix is positive semi-definite, i.e., for all (this follows from ). By adding we make the matrix positive definite, i.e., we have for all (indeed, ). Because every positive definite matrix is non-singular 2, must have the inverse. If , a solution to the ridge regression problem always exists and it is unique. If and , the matrix becomes singular 3. The geometrical interpretation of this situation was discussed above. As approach 0, the matrix may become close to singular. The numerical routines for finding will then become less and less stable: they will have to deal with very big or very small values and make large round-up errors. Taking a larger thus stabilises the computation as mentioned above. Let us attempt a rough hypothetical analysis of the predictive performance of ridge regression for different values of . If is very big, the term completely overshadows and the predictive performance deteriorates. If is very small, we may encounter numerical problems. An optimal value should thus be neither too big no too small. In some sense it must be comparable in size to elements of . The exact choice of depends on the particular dataset. Finally, let us go back to the term "ridge regression". One of the versions of its etymology is that the diagonal of forms a "ridge" added on top of the least squares matrix . ## 1.4 Solution: Dual Form Using the matrix identity we can rewrite the ridge regression solution as follows. For an arbitrary the outcome suggested by ridge regression is and this can be rewritten as This formula is called the dual form of the ridge regression solution. Similar arguments concerning non-singularity apply to . The matrix has the size . This might seem a disadvantage compared to the primary form: it is natural to expect that in practice would be fixed and not too big, while the size of the sample may be quite large. However this formula allows us to develop important generalisations. We can say that in the dual form. However there is a more interesting way to interpret the dual form formula. We have where is the matrix of mutual scalar products and is the vector of scalar products of by : Note that all s and appear in this formula only in mutual scalar product. This observation has important consequences. ## 1.5 Non-linear Regression Now let us try to extend the class of functions we use and consider a wider class. Suppose that , i.e., all s are numbers and we are interested in approximations by polynomials of degree , i.e., functions of the form . Of course we can write down for this case, perform the differentiation and find the solution as we did before. However there is a simpler argument based on the dual form. Let us map into as follows: . Once we have done this, we can do linear regression on new "long" signals. If we use the dual form, we do not even have to perform the transformations explicitly. Because we only need scalar products, we can compute all the necessary products and substitute them into the dual form formula. Let us write down a formal generalisation. The signals do not have to come from any longer. Let them be drawn from some arbitrary set 4 . Suppose that we have a mapping , where is some vector space equipped with a scalar product (dot-product space); the space is sometimes referred to as the feature space. We can use ridge regression in the feature space. The prediction of ridge regression on a signal can be written as where and the function is given by . The space does not have to be finite-dimensional. However since every vector space with a scalar product can be embedded into a Hilbert space (see below for a definition) we can assume that it is Hilbert. The transformation is of no particular importance to us. Once we know the kernel , we can perform regression with it. A justification for the ridge regression in the kernel case will be obtained below in Subsection 5.3. ## 1.6 Mappings and Kernels It would be nice to have a characterisation of all without a reference to . A characterisation of this kind can be given. It is easy to see that has the following properties: • it is symmetric: for all ; this follows from the symmetry of the scalar product ; • it is positive semi-definite: for every positive integer and every the matrix is positive semi-definite 5; indeed, is the Gram matrix of the images 6. Surprisingly these two simple properties are sufficient. Let us call a function satisfying these two properties a kernel. Then the following theorem can be formulated. Theorem 1. For any set a function is a kernel, i.e., it is symmetric and positive semi-definite, if and only if there is a mapping from into a Hilbert space with a scalar product such that for all . We proved the "if" part when we defined kernels. The "only if" part follows from the results of the next sections, where we will show that the class of kernels coincides with the class of so called reproducing kernels. # 2. Reproducing Kernel Hilbert Spaces In this section we introduce reproducing kernel Hilbert spaces (RKHS) and show some of their basic properties. The presentation is based mainly on [Aronszajn, 1943] and [Aronszajn, 1950] and the reader may consult these papers for more details; note that the former paper is in French. ## 2.1 Hilbert Space A set of some elements is a Hilbert space if 1. is a vector space over (Hilbert spaces over the complex plain can also be considered, but we shall restrict ourselves to in this article); 2. is equipped with a scalar product (i.e., with a symmetric positive definite bilinear form); 3. is complete w.r.t. the metric generated by the scalar product, i.e., every fundamental sequence of elements of converges. Some authors require a Hilbert space to be separable, t.e., to have a countable dense subset. For example, [Aronszajn, 1943] reserves the name "Hilbert". We shall not impose this requirement by default. As a matter of fact all separable Hilbert spaces are isomorphic (the situation is similar to that with finite-dimensional spaces; the separable Hilbert space is "countable-dimensional"). A typical (though not particularly relevant to this article) example of a Hilbert space is provided by , which is the space of all real-valued functions on such that is Lebesgue-integrable w.r.t. the measure on with the scalar product . Another example is given by , which is the set of infinite sequences , , such that the sum converges. Both and on with the standard Lebesgue measure are separable; therefore they are isomorphic. ## 2.2 Reproducing Kernel Hilbert Spaces: a Definition Let be a Hilbert space consisting of functions on a set . A function is a reproducing kernel (r.k.) for if • for every the function (i.e., as the function of the second argument with fixed) belongs to • the reproducing property holds: for every and every we have . A space admitting a reproducing kernel is called a reproducing kernel Hilbert space (RKHS). ## 2.3 Reproducing Kernel Hilbert Spaces: Some Properties Let us formulate and prove some basic properties of reproducing kernels. Theorem 2. 1. If a r.k. for exists, it is unique. 2. If is a reproducing kernel for , then for all and we have . 3. If is a RKHS, then convergence in implies pointwise convergence of corresponding functions. Proof: In order to prove (1) suppose that there are two r.k. and for the same space . For every the function belongs to and, applying linearity and the reproducing property, we get The definition of a Hilbert space implies that coincides with and therefore they are equal everywhere as functions. Property (2) follows immediately from the reproducing property and the Cauchy(-Schwarz-Bunyakovsky) inequality. Property (3) follows from (2). Indeed, for all and we have We shall now give an important "internal" characterisation of reproducing kernel Hilbert spaces. Let consisting of real-valued functions on be a Hilbert space. Take and consider the functional mapping into . It is linear (in ) and is called the evaluation functional. Note that the evaluation functional is not defined on : the elements of are in fact equivalence classes of functions that coincide everywhere up to a set of measure 0, and thus they are not really defined at every point 7. Theorem 3. A Hilbert space consisting of real-valued functions on is a RKHS if and only if for every the corresponding evaluation functional is continuous. Proof: The "only if" part follows from (2) from the previous theorem. In order to prove the "if" part we need the Riess-Fischer Representation Theorem, which states that every continuous linear functional on a Hilbert space can be represented as the scalar product by some element of the space. Take . Because the evaluation functional is continuous, there is a unique such that . We can define a mapping by . Let . We have and thus . On the other hand for every and we have Therefore is a r.k. for . This criterion is quite important. The continuity of the evaluation functional means that it is consistent with the norm: functions and that are close with respect to the norm evaluate to values and that are close. If we consider functions from some space as hypotheses in machine learning and the norm on the space as a measure of complexity, it is natural to require the continuity of the evaluation functional. The theorem shows that all "natural" Hilbert spaces of functions are in fact reproducing kernel Hilbert spaces. ## 2.4 Existence Theorem We have shown that a r.k. can be represented as . This implies that is • symmetric due to the symmetry of the scalar product; • positive semi-definite, i.e., for all the matrix is positive semi-definite; this holds since is the Gram matrix. Thus is a kernel according to the definition from the previous section. The following theorem shows that the classes of kernels and reproducing kernels coincide. Theorem 4. Let is a real-valued function of two arguments on . Then is a reproducing kernel for some Hilbert space of functions on if and only if • is symmetric • is positive semi-definite. If there is a space admitting as its reproducing kernel, it is unique. # 3. Proof of the Existence Theorem In this section we will prove the existence theorem. Let be a kernel. ## 3.1 Linear Combinations: A Dot Product Space We start the proof by constructing a linear space of functions consisting of linear combinations , where is a positive integer, and . The linearity follows by construction. The scalar product is defined after the following fashion. Let (by adding terms with zero coefficients we can ensure that the linear combinations have equal numbers of terms and that all in the combinations are the same). We need to prove that the scalar product is well-defined, i.e., to show that it is independent of particular representations of factors (recall that we are constructing a space of functions rather than formal linear combinations). Let and . We have We see that the scalar product can be expressed in terms of values of and thus is independent of a particular representation of as a linear combination. A similar argument can be applied to . The independence follows. The function is symmetric because is symmetric. For from above we have because is positive semi-definite. Therefore is positive semi-definite. We have shown that it is a positive semi-definite symmetric bilinear form. One final step is necessary to prove that it is positive definite and therefore a scalar product. Let us evaluate , where and is some element from . We get The form and thus satisfy the reproducing property. Because the form is positive semi-definite, the Cauchy(-Schwarz-Bunyakovsky) inequality holds for it and where is defined as . Combining this with the reproducing property yields Therefore implies that for an arbitrary . We have thus shown that is actually positive definite and therefore a scalar product. The construction is not finished yet because is not necessarily complete. It remains to construct a completion of . It is well known that every linear space with a scalar product has a completion, which is a Hilbert space. However this argument cannot be applied here 8: we need a completion of a specific form, namely, consisting of functions . Note that, however, we have already proved Theorem 1 from Section 1: we can map into some Hilbert space so that the value of the kernel is given by the scalar product of images. The mapping is given by the obvious . ## 3.2 Completion In this subsection we will construct a completion of . Let be a fundamental sequence. For every the inequalities which follow from the previous subsection, imply that the sequence of values is fundamental and therefore has a limit. We can define a function by . Let consist of all functions thus obtained. Clearly, since each from is the pointwise limit of the sequence . The scalar product on can be introduced as follows. If is the pointwise limit of and is the pointwise limit of , then . Let us show that this limit exists. For all positive integers , , and we have Because the norms of elements of a fundamental sequence are uniformly bounded, the difference can be made as close to 0 as necessary for sufficiently large , , and . Thus there is even a double limit in the sense that for all sufficiently big and the difference becomes arbitrarily small. Let us show that the scalar product is independent of a choice of fundamental sequences converging to and . Consider two pairs of fundamental sequences, and converging to and and converging to . Consider the expression . The sequence consisting of functions is clearly fundamental, therefore, as shown above, there must exist a limit . Let us evaluate this limit. There are coefficients and elements such that ( may change as varies). We have Since and converge pointwise to 0, this expression converges to zero as . Thus Similarly Therefore the difference converges to 0 as . Our definition is thus independent of a particular choice of fundamental sequences. The bilinearity of on is easy to check. The number is non-negative as a limit of non-negative numbers. More precisely, let be a fundamental sequence converging to pointwise. Because the equality implies that for all . We have shown that is indeed a linear space with a scalar product. Clearly, and the scalar product on extends that on . Let us show that is complete. First, let be a fundamental sequence of elements of converging pointwise to . We have This converges to 0 as and thus is the limit of in . Secondly, consider a fundamental sequence of elements of . For each there is such that . The sequence is fundamental in and therefore has a limit in . It must be the limit of too. It remains to show that the reproducing property holds of . It follows by continuity. Let be a fundamental sequence of elements of converging pointwise to . We have We have constructed a RKHS for . Note that constructed in the previous subsection is dense in it. ## 3.3 Uniqueness Let us show that the RKHS for a particular kernel is unique. Let be the RKHS constructed above and be some other RKHS for the same kernel . The definition of an RKHS implies that all functions must belong to . The same must be true of their linear combinations . Thus as a set. Since the reproducing property holds on , on elements of the scalar product must coincide with scalar product we constructed above. Thus is a subspace of . Because is complete, all fundamental sequences from should have limits in . In RKHSs convergence implies pointwise convergence and thus all pointwise limits of fundamental sequences from belong to . Thus as a set. Because the scalar product is continuous w.r.t. itself, we have for all sequences and such that and in as . Thus the scalar product on coincides with that on , or, in other terms, is a closed subspace of . Let . We can represent it as , where and is orthogonal to and therefore to all functions , which belong to . Because the reproducing property holds on , we get Thus coincides with everywhere on and . # 4. What RKHSs are and What They are not In this section we provide a selection of minor results and counterexamples concerning RKHSs. They will help the reader to get a better intuition of an RKHS and perhaps dissolve some misconceptions. ## 4.1 Continuity and Separability Suppose that is a topological space and is continuous (in both the arguments, i.e., on ). One can claim that any feature mapping associated with is continuous. Indeed, The continuity of implies that as approach , the expression approaches 0. We have shown that is continuous 9. If moreover is separable, then the RKHS is separable. Indeed we have shown in the proof of the existence theorem that finite linear combinations are dense in . The coefficients can be taken to be rational. Take a countable dense subset . Because the mapping is a feature mapping, it is continuous, and we can approximate any with some . In most natural cases signals are strings of reals, i.e., and the kernel is continuous and therefore the RKHS is separable. Note however that inseparable RKHSs exist. Indeed, consider the space . It consists of functions such that everywhere except, perhaps, for a countable set and The scalar product is defined by It is easy to see that this space is Hilbert. The only non-trivial bit is completeness. Let be a fundamental sequence. By taking the union of all supports we can obtain a countable set such that all vanish outside . The sequences belong to the "usual" and we can reduce the question of completeness of to completeness of . The space is an RKHS. Indeed, consider (here is the indicator function of a set ). This is clearly a kernel. On the other hand is not separable. Indeed, the functions , , form an uncountable orthonormal system. ## 4.2 Pointwise Convergence in RKHSs As we know from Theorem 2, convergence in an RKHS implies pointwise convergence of functions. Let us show that the opposite is not true. A simple counterexample is provided by considered as a set of functions on the set of positive integers . It is an RKHS with as above. Consider the sequence of functions We have as , which implies pointwise and even uniform convergence to equal to 0 everywhere. On the other hand . Requiring to be continuous and the domain to be connected will not change the situation; the counterexample can be easily extended to cover this possibility. Indeed, take . For each positive integer consider the "tooth" function equal to 0 outside , 1 at and linear on and . Let the space consist of functions , where . A function is continuous on , its values at integer points form a sequence from and the value at is given by , . Let the scalar product be induced by : . This space is isomorphic to . The space is an RKHS with the following kernel. For a positive integer we have and for all . For , where is a positive integer, . This kernel is continuous on . On the other hand pointwise (and uniform) convergence does not imply convergence in the norm. It is easy to do a further step and show that can be connected and compact. Note that for any sequence we have as and therefore for any we have as . We can define by continuity. The set can be mapped onto by . The following intuition may be helpful. As explained above, an RKHS may be thought of as a Hilbert space of hypotheses and the norm as the hypothesis complexity. The functions uniformly close to zero but having non-zero norms correspond to overcomplicated hypotheses with no real explanatory power. ## 4.3 RKHSs with the Same Sets of Functions We know from part 1 of Theorem 2 that for each RKHS there is a unique kernel, i.e., if two kernels, and , specify the same RKHS, then they coincide. Here the words "the same RKHS" mean the same set of functions with the same scalar product on them. What if the scalar product is different? Can two different kernels specify RKHSs with the same sets of functions? It is easy to construct a trivial example. The kernel specifies the same set of functions as the kernel . Indeed, recall the construction from the existence theorem. The kernels and specify the same set of finite linear combinations with equivalent norms. A sequence is fundamental in one space if and only if it is fundamental in another and the completions, consisting of pointwise limits, will coincide. A slightly less trivial example may be constructed as follows. Let and is given by . If is equipped with the standard Euclidean scalar product , we get a kernel . The RKHS corresponding to this kernel consists of functions of the form , where . Let is given by . It specifies the kernel , which is not a multiple of . The RKHS corresponding to consists of functions of the form , where . It is easy to see that the set of functions is the set of polynomials of degree 1, just as in the first case. The kernels specifying the RKHSs with the same sets of functions thus do not have to be multiples of each other. This argument can be generalised further as follows. Let specify kernel and let be a bounded linear operator in the Hilbert space . Consider the mapping and the kernel . The RKHS corresponding to this kernel consists of functions of the form . This can be rewritten as , where is the operator adjoint to . If (and therefore ) is invertible, ranges over the whole space and the RKHS for consists of the same functions as that for . The following observation can also be made. Theorem 5. The set of kernels on specifying the RKHS with the same set of functions is closed under multiplication by a positive constant and addition, i.e., 1. for every kernel and , the kernel specifies the RKHS with the same set of functions as the RKHS for ; 2. for every two kernels and on specifying the RKHSs with the same set of functions, the kernel specifies the RKHS with the same set of functions. Proof: The multiplicative part has been already proved above. Let us prove the additive part (the multiplicative part can be proved in the same fashion). Let and be feature mappings corresponding to and . Consider the Hilbert space with the "componentwise" scalar product (here and are the scalar products on and , respectively). Clearly the mapping given by specifies the kernel . The corresponding RKHS consists of functions of the form , where and . Since or can be equal to 0, the RKHS contains the RKHSs for and as sets. Since the two sets of functions are equal, adding them up does not produce anything new. # 5. RKHSs and Prediction in Feature Spaces We have shown that the three definitions of a kernel are equivalent: • a positive semi-definite symmetric function; • a reproducing kernel; • the scalar product in a feature space, i.e., , where maps into a Hilbert space . The RKHS for a particular kernel is unique. Note that uniqueness holds in a very strong sense: it is a unique set of functions with a uniquely defined scalar product; there are no isomorphisms or equivalences involved. The mapping in the third definition is by no means unique. Indeed, let . Consider a right shift defined by . The composition will produce the same kernel as . However there is some degree of uniqueness. Let be the closure of the linear span of all images , . It is isomorphic to the RKHS. ## 5.1 RKHS Inside a Feature Space Theorem 6. For every mapping , where is a Hilbert space, the closure of the linear span of the image of , i.e., , is isomorphic to the RKHS of the kernel . There is a canonical isomorphism mapping onto from the RKHS. Proof: Let us denote the closure of the span by and the RKHS by . Let be the set of finite sums of the form , where and are some coefficients, as in the construction above. We start by constructing the isomorphism of and . Put and, by linearity, . We need to show that is well-defined. Let for some coefficients and and elements . Then for every we have i.e., by the definition of . This means that the functions and coincide everywhere and thus is well-defined. The mapping preserves the scalar product: The mapping is surjective. Indeed, each sum has an inverse image. The mapping is also injective. Assume the converse. Then there is a point such that but in the RKHS. This is a contradiction because preserves the scalar product and therefore the norm. Thus is a bijection. Let us extend to the isomorphism of and . Let converge to . The sequence is fundamental in . Since preserves the scalar product on , the images form a fundamental sequence in . It should converge. Put . Suppose that there are two sequences and converging to . Let us mix the sequences into (e.g., by letting and , ). The sequence converges to and is therefore fundamental. The images of must form a fundamental sequence in and must have a limit. All its subsequences should converge to the same limit. Thus and is well-defined. The scalar product is preserved by continuity. The surjectivity can be shown as follows. Let and let converge to . The inverse images of must form a fundamental sequence in and must have a limit . It follows from the definition that . The injectivity on follows from the same argument as on . The theorem follows. The mapping can be extended to the mapping of the whole by letting , where is the projection operator. The mapping is no longer injective (unless coincides with ) and no longer preserves the scalar product. However we have , where the minimum is attained on the projection . ## 5.2 Another Definition of RKHS The above construction allows us to construct an interpretation of RKHS important for machine learning. In competitive prediction we prove consistency results of the following type. We do not assume the existence of a "correct" hypothesis but rather show that our method competes well with a class of some other predictors, such as all linear regressors. Therefore identifying and describing such natural classes is an important task. In Hilbert spaces we have a natural equivalent of linear regressors. Those are linear functionals, or, as the Riess-Fischer Representation Theorem shows, scalar products by an element . After we have mapped into a Hilbert space , we can consider predictors of the form . Theorem 6 immediately implies that the class of such functions coincides with the RKHS. Indeed, there is a unique decomposition , where is the projection of on and is orthogonal to . We have where belongs to the RKHS. We may want to assign the norm to the predictor ; clearly . The space of predictors thus obtained does not exceed the RKHS and the norms of predictors are equal to or greater than those of the elements of the RKHS. Thus regressors in the feature space have no more power than functions from the RKHS. We get the following theorem as a bonus. Theorem 7. Let be a mapping into a Hilbert space . The space of functions defined by , where , equipped with the norm coincides with the reproducing kernel Hilbert space for the kernel defined by . ## 5.3 Ridge Regression in Feature Spaces; the Representer Theorem In this section we revisit the ridge regression problem from Section 1 and present one argument of great importance for competitive prediction. Suppose that we have a sequence of signals and outcomes as in Section 1. On top of that suppose that we have a mapping from the set of signals into a Hilbert feature space . Take ; as we said before, it can be considered as a regressor yielding the dependency . We may ask if there is minimising the expression with . Consider the predictor where and It qualifies as a regressor of the above type. Indeed, it is a linear combination of . Let us show that it minimises . Let be a subspace of consisting of all linear combinations of (it is closed because it is finite-dimensional). Take . It can be decomposed into a sum , where is orthogonal to . For all we have ; we also have . Therefore . When minimising we can restrict ourselves to predictors from , i.e., linear combinations of ! Because is finite-dimensional, the arguments from Section 1 apply and the ridge regression turns out to provide the minimum of over (or the minimum of over the corresponding RKHS). This argument can be generalised to the representer theorem. We shall formulate two variants of it. Theorem 8. Let be a mapping into a Hilbert space and be given by where is a function from to nondecreasing in the last argument and are some fixed elements. Then for every there is a linear combination , where are constants, such that . If is strictly increasing in the last argument and does not itself have the form , there is a linear combination such that . Proof: The proof is by observing that the projection of on the subspace has the same scalar products with elements , and a smaller norm . Corollary 1. Let be a kernel and the corresponding RHKS; let be given by where is a function from to nondecreasing in the last argument and . Then for every there is a linear combination , where are some constants, such that . If is strictly increasing in the last argument and does not itself have the form , there is a linear combination such that . # 6. Hierarchies of Kernels ## 6.1 Subspaces of RKHSs and Sums of Kernels Consider an RKHS corresponding to a kernel . Let be a subspace of . Clearly, is a RKHS. This can be shown as follows. The evaluation functional is continuous on . Its restriction on should remain continuous and therefore is a RKHS. This does not contradict the uniqueness theorem. If is a proper subspace of , it is an RKHS for a different kernel . Suppose that itself is a subspace of some Hilbert space of functions . As we discussed above, in applications such as machine learning it does not make much sense to consider spaces where the evaluation functional is not continuous, and therefore should be an RKHS with its own kernel too. One can say that RKHSs form hierarchies: larger spaces have more power than smaller spaces. However each of them has its own kernel. In competitive prediction the natural competitors of a kernel method are the functions from the corresponding RKHS. Other RKHSs require the use of a different kernel. The rest of this section contains some results clarifying the structure of this hierarchy. Theorem 9. Let a space of real-valued functions on be the RKHS corresponding to a kernel . If is a subspace of , then is an RKHS and has a kernel . If is the orthogonal complement of , then it is also an RKHS and it has the kernel such that for all . Proof: Let and be the projection operators from to and , respectively. Take a point . The evaluation functional on equals the scalar product by . It is easy to see that plays the same role in . Indeed, and for every function we have Put . Let us prove that it is the kernel for We do this by showing that as a function of coincides with . Fix and denote the function by . We have . The above argument implies that for every and thus . The reproducing property follows. Similarly is the kernel for . Let . We have and ; therefore By taking and we get . Theorem 10. Let be three kernels on such that for all . Then the RKHSs and corresponding to the kernels and are subsets (but not necessarily subspaces) of the RKHS corresponding to the kernel . For each there are functions and such that and for its norm we have the equality If and have only the identical zero function in common (i.e., ), then they are subspaces of and each one is the orthogonal complement of the other. It is easy to see that does not have to be a subspace of . Indeed, let and . Clearly if we take the set of functions constituting and equip it with the scalar product , we get the RKHS for . It is a subset but not a subspace of . Proof: Let and mapping into Hilbert spaces and , respectively, be feature maps giving rise to the kernels and , i.e., Let be the Hilbert space consisting of pairs such that and with the scalar product given by Take defined by It is easy to see that The results of Subsect. 5.2 imply that the RKHS for coincides with the set of functions , where . Similarly, the RKHSs for and consist of all functions and , respectively, where and . For every the element belongs to ( is the zero element of here). We have and therefore as a set; the same argument applies to . The decomposition implies that each can be decomposed into the sum of and . We have The minimum is taken over pairs of ; clearly, we can take the minimum over all pairs of and such that ; indeed, . Now let . Under this assumption every has a unique decomposition , where and . Indeed, if , then . The function of the left-hand side belongs to and the function on the right-hand side belongs to and therefore they are both equal to zero. Thus for every pair and we have . Take . Then this equality implies that . Taking leads to . The norms on and coincide with the norm on ; the same should apply to the scalar product and thus and are subspaces rather than just subsets of . Picking arbitrary and and applying Pythagoras theorem yields . Comparing this with the above equality implies that , i.e., and are orthogonal subspaces. Let us introduce a relation on kernels on a set . We will write if the difference is a kernel. If this relation holds, then for all . Indeed, since is a kernel, the matrix is positive semi-definite, i.e., . This observation justifies the notation to some extent and implies that is antisymmetric. Indeed, if and then for we get for all . Theorem 2 implies that for every from the RKHS of and every we have and thus is identically zero. This implies that . Clearly, is transitive: if , then . The theorems above imply that for kernels is closely linked with the relation on their RKHSs. However no direct correspondence has been shown. The following results close the gap. Theorem 11. Let and be two kernels on the same set and let and be their RKHSs. If , then as a set and for every we have This theorem follows from our previous results. Indeed, the square is given by the minimum of taken over all decompositions , where is the RKHS corresponding to the difference . Every can be represented as , which implies the inequality in the theorem. The opposite result holds. Theorem 12. Let and be its RKHSs. If as a set and forms a Hilbert space w.r.t. a norm such that for every , then is an RKHS and its reproducing kernel satisfies . It is easy to see that the inequality on the norms cannot be omitted. Consider some kernel on and let . Let be the RKHS for . For every we have and therefore that coincides with as a set and has the scalar product is the RKHS for . We have . However let us consider as a subset of . It satisfies the conditions of the theorem apart from the norm clause but . The proof of the theorem is beyond the scope of this article and can be found in [Aronszajn, 1950], pp.355-356. ## 6.2 Subsets of the Domain The representer theorem provides a motivation to the following analysis important for learning. Suppose that we have a kernel and let be its RKHS. Consider a subset and let be the restriction of to . It is easy to see that is still a kernel. What can one say about the RKHS corresponding to ? This question is important for learning for the following reason. Suppose that we are given a training sample (or a history of past signals and outcomes, if we are using an on-line protocol) and a new signal . One can consider different sets containing the observed signals . What effect will the choice of a particular have on the consistency analysis of a learning method? The representer theorem above suggests that the choice of is essentially irrelevant. Padding does not really change much. (Of course the situation becomes different if we need to make a statement valid for all s that can possibly occur.) We shall see that this is generally true. Let us try and clarify the situation. First, does contain more functions on ? Are restrictions of functions from form a set richer than ? This is easy to answer if we use the definition of a RKHS provided by Theorem 7. Let be a mapping such that for all (here is a Hilbert space as usual). Then coincides with the set of functions of the form , where ranges over and the norm of is the minimum of the norms of all elements corresponding to . Clearly represents as well as : we have for all . Thus consists of functions of the form restricted to . This implies that the restrictions of all functions from to belong to . On the other hand for every there is such that and we can extend to by considering scalar products with the same . Therefore each function from is a restriction of some function from . The norm of does not exceed that of each extension; on the other hand it equals to the norm of some and therefore to the norm of some extension. Theorem 13. Let a space of real-valued functions on be the RKHS corresponding to a kernel and let . Then the RKHS corresponding to the kernel coincides with the set of restrictions to of functions from and the norm on it is given by . The mapping from to provided by the restriction operator does not have to be injective. Indeed two elements can have the same scalar products with all elements from but different scalar products with some elements of . One can easily identify a subspace of isomorphic to though. Theorem 14. Let a space of real-valued functions on be the RKHS corresponding to a kernel and let . Then the closure of the set of finite linear combinations of the form , where and , i.e., the subspace is isomorphic to the RKHS corresponding to the kernel and an isomorphism is given by the restriction of functions from to . Proof: Let us denote the restriction operator by . It maps each into its restriction . We already know that maps into and it does not increase the norm. It is easy to see that it is linear. We need to show that as a mapping from into is injective, surjective, and actually preserves the norm. Consider the set of finite linear combinations of the form , where . We can consider them as elements of and elements of . It is easy to see that "" these linear combinations, i.e., (note that on the left the combination is considered as an element of and on the right the same combination is an element of ). Let us show that restricted to functions that are finite linear combinations of the above form is an isomorphism. Its surjectivity follows from the above. On the other hand we have The mapping thus preserves the norm of a linear combination. This implies that is injective because cannot map a non-zero element into zero. Now consider on the subspace . Let ; it can be approximated by a linear combination to any degree of precision w.r.t. the norm . However does not increase the norm and we therefore have Because , the norm of is also preserved, which immediately implies that is an injection on . To prove the surjectivity we need to remember that the finite linear combinations are dense in . If , it is the limit of a sequence of finite linear combinations. Their inverse images (i.e., the same combinations) in will form a fundamental sequence because the norm is preserved and therefore will converge. The image of the limit has to be the original . Corollary 2. The orthogonal complement of w.r.t. consists of all functions such that for all . Proof: Consider and . We have . If is orthogonal to , it is orthogonal to each and therefore for all . If on , then it is orthogonal to all , where , all their linear combinations and therefore to all elements of . # 7. Tensor Products of Kernels Suppose that we have two kernels and . Let be the Cartesian product . We can consider the function defined by We will call it the tensor product 10 of and and use the notation . We will show that the tensor product is also a kernel and construct the corresponding RKHS. Theorem 15. If and are kernels then their tensor product , where , defined by is also a kernel. We shall prove this theorem later. Let us first derive some corollaries. Corollary 3. Let and be two kernels defined on the same domain . Then their componentwise product defined by is also a kernel. Proof: Inside the direct product consider the "diagonal" set defined by . The restriction of the tensor product coincides with the componentwise product on . Clearly, it is therefore a kernel. Theorem 13 implies that the RKHS corresponding to the componentwise product consists of restrictions of functions from the RKHS corresponding to the tensor product to . We obtain the following linear algebra result as a bonus. Corollary 4. The componentwise product of two symmetric positive-definite matrices is symmetric and positive-definite. The corollary can be proved by considering a symmetric positive-definite matrix as a kernel on a finite set. Let us prove the theorem about the tensor product. We shall prove it by constructing the RKHS for the product . The space is the tensor product of RKHSs with the scalar product corresponding to and with the scalar product corresponding to . We cannot employ the standard construction (see e.g., [Weidmann, 1980], Section 3.4) directly because we need to ensure that the resulting space is still a space of functions rather than a generic Hilbert space. Consider the set of functions on of the form , where and . As often happens when we try to construct a tensor product of some spaces, this set is not necessarily closed under addition. Therefore let us consider the space of finite sums , where is a positive integer, and . It is clearly a vector space. Let us define the scalar product of and by We need to show that the scalar product is well-defined, i.e., it depends on functions rather than their representations in the form of sums of products. We have The inner sum is a function on . We have We can thus get rid of a particular representation of as a sum of products; only the values of matter. Clearly, the same argument applies to . The scalar product is thus well-defined. It still remains to show that satisfies the properties of a scalar product. It is easy to check that it is a bilinear form. We need to show that and vanishes only for . Let us take and apply an orthonormalisation procedure (e.g., the Gram-Schmidt method) to in and to in . After renaming the functions, we get a representation , where, for both and , the equality holds for all and holds for all . For the scalar product we have If , all are 0 and therefore . Let us now find out the role of the product of kernels defined by Fix and . The function is a product of functions from and , i.e., has the form , where and . For we get The resulting space with a scalar product can be incomplete, so we need to construct its completion; the situation is somehow similar to that with the existence theorem. We cannot use the standard result about completions of pre-Hilbert spaces, because we need to obtain a space of functions. In order to construct the completion, we need to recall some facts about orthonormal bases in Hilbert spaces. Let be a (pre-)Hilbert space with a scalar product . An orthonormal system is a system of vectors , where is some index set, not necessarily countable, such that equals 0 for and 1 for . It is easy to check that all finite subsets of an orthonormal system are linearly independent. If is an orthonormal system, then for each only countably many scalar products are non-zero and the Bessel inequality holds. An orthonormal system is an orthonormal base, if its span (the set of all finite linear combinations of its elements) is dense in , i.e., . An orthonormal system is an orthonormal base if and only if for every the Parseval equality holds. The Parseval equality implies that . (The convergence of this series can be understood as follows. If , is a sequence of (pairwise different) indexes including all such that , then as .) The scalar product of is given by . This generalises the finite-dimensional facts about the coordinate decomposition of a vector and its length. Each Hilbert space has an orthonormal base; this follows from Zorn's lemma. This system is countable if and only if is separable. Let vectors , form an orthonormal system in a Hilbert space. The series converges if and only if the sequence belongs to . Each separable Hilbert space is thus isomorphic to . As a matter of fact, any Hilbert space is isomorphic to , where is the index set of its orthonormal base. The space consists of systems of reals , where only countably many elements are non-zero and . The addition and multiplication by a constant are defined componentwise. The scalar product of and is . Let us now build the completion. Take an orthonormal base in and an orthonormal base in . The index sets and do not have to be countable 11 Consider the class of functions of the form , where only countably many coefficients are non-zero and . Let us show that this series is absolutely convergent for each . Fix ; the Cauchy(-Schwarz-Bunyakovsky) inequality implies that where the first sum on the left-hand side must converge and second is still to be analysed. Recall that is an RKHS and the evaluation functional at a point corresponds to the scalar product by . Thus . The Bessel inequality implies that and therefore Repeating the same argument, we get Take and fix the first coordinate. The function belongs to as a converging sum of . (Indeed, the sum converges and .) We can calculate the scalar product This expression considered as a function of belongs to . Clearly its scalar product with equals . The coordinates are thus uniquely defined by the function . We can define a scalar product as the sum of the products of corresponding coordinates. The resulting space is isomorphic to . Let us denote if by . It is easy to see that it is complete and therefore Hilbert. Let us show that contains all products of the form , where and . Indeed, if and then and the sum converges. Finite linear combinations of functions of this form are dense in ; indeed, the expression for can be truncated to a finite number of terms. The scalar product we introduced on functions coincides with the product in . Indeed, let , , , and . We have By linearly this property can be extended to finite linear combinations. One can conclude, by continuity, that is a reproducing kernel for the Hilbert space of functions . # 8. Some Popular Kernels In this section we summarise some sufficient conditions for a function to be a kernel and obtain some popular kernels. Let us recall the facts we know and formulate simple corollaries. Theorem 16. A function is a kernel if and only if it is symmetric and positive-semidefinite. This is Theorem 4 or the existence theorem. Corollary 5. If is a kernel and , then is a kernel. Corollary 6. If and are kernels on the same set, then their sum is a kernel on the set. Corollary 7. The pointwise limit of kernels is a kernel. Proof: Let be the pointwise limit of and each is a kernel. Because is symmetric, is symmetric too. For any finite array and we have . As , we get and thus is positive semi-definite. Theorem 17. If and are kernels on the same set, then their product is a kernel on the set. This was proven as Corollary 3. Corollary 8. Let be a kernel and is a polynomial with positive coefficients. Then is a kernel. Note the requirement that the coefficients should be positive. Indeed, is not a kernel unless is identically equal to zero. Corollary 9. If is a kernel, then is a kernel. Proof: The exponent can be decomposed into Taylor's series on . The function is a pointwise limit of polynomials on and all these polynomials have positive coefficients. Theorem 18. A function is a kernel if and only if there is a mapping , where is a vector space with a scalar product , such that . Corollary 10. If is a real vector-function on , then is a kernel on . Corollary 11. The function is a kernel on , . This fact is obvious and can be derived by many different ways. We can now obtain Vapnik's inhomogeneous polynomial kernel. Corollary 12. For any positive integer the function is a kernel on . Proof: Indeed, is a kernel and is a polynomial with positive coefficients. The following corollary introduces radial-basis function (rbf) kernel. Corollary 13. For any , the function , where is the Euclidean norm, is a kernel on . Proof: We have The product of the first two terms is a kernel generated by the mapping . The third term is a kernel as the exponent of a kernel. The product of two kernels is also a kernel. 1 As different, for example, to the classification problem, where s belong to a finite set. 2 Indeed, let be positive definite. If is singular, for some , but this implies . 3 The condition is not just sufficient, but necessary for to be singular. Indeed, if is singular, it is not positive definite and for some . This implies , i.e., columns of are linearly dependent. 4 It is important that no particular structure is postulated on ; throughout the most of this article it is just a set. 5 A definition and a discussion were given above. 6 We have . 7 Thus is not an RKHS according to our definition: it is disqualified without a substantive consideration. 8 The book [Schölkopf and Smola 2002] uses this argument in Section 2.2.3, p. 35-36, in a rather misleading way. 9 Proposition 2.14 from [Schölkopf and Smola 2002] states that continuous maps exist with a reference to [Parthasary and Smith, 1972], where the stronger statement is proven, but the weaker statement is claimed. 10 Aronszajn uses the term "direct product". The reason why we use the term "tensor product" will become apparent later 11 Paper [Aronszajn, 1950] considers only the countable case and its proof is formally valid only for separable RKHSs. However minor amendments can make it valid everywhere.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9875653386116028, "perplexity": 276.39847266850103}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423785.29/warc/CC-MAIN-20170721142410-20170721162410-00376.warc.gz"}
http://ufldl.stanford.edu/wiki/index.php?title=Softmax_Regression&diff=next&oldid=610	# Softmax Regression (Difference between revisions) Revision as of 23:24, 7 May 2011 (view source)Zellyn (Talk \| contribs)m (→Parameterization)← Older edit Revision as of 23:26, 7 May 2011 (view source)Zellyn (Talk \| contribs) m (→Binary Logistic Regression)Newer edit → Line 190: Line 190: &= &= - \frac{e^{ \Theta_1^T x^{(1)} } }{ 1 + e^{ \Theta_1^T x^{(i)} } } + \frac{e^{ \Theta_1^T x^{(i)} } }{ 1 + e^{ \Theta_1^T x^{(i)} } } \cdot \cdot - \frac{1}{e^{ \Theta_1^T x^{(1)} } } + \frac{1}{e^{ \Theta_1^T x^{(i)} } } \begin{bmatrix} \begin{bmatrix} e^{ \Theta_1^T x^{(i)} } \\ e^{ \Theta_1^T x^{(i)} } \\ ## Introduction Softmax regression, also known as multinomial logistic regression, is a generalisation of logistic regression to problems where there are more than 2 class labels. Recall that in logistic regression, our hypothesis was of the form: \begin{align} h_\theta(x) = \frac{1}{1+\exp(-\theta^Tx)}, \end{align} where we trained the logistic regression weights to optimize the (conditional) log-likelihood of the dataset using p(y \| x) = hθ(x). In softmax regression, we are interested in multi-class problems where each example (input image) is assigned to one of k labels. One example of a multi-class classification problem would be classifying digits on the MNIST dataset where each example has label 1 of 10 possible labels (i.e., where it is the digit 0, 1, ... or 9). To extend the logistic regression framework which only outputs a single probability value, we consider a hypothesis that outputs K values (summing to 1) that represent the predicted probability distribution. Formally, let us consider the classification problem where we have m k-dimensional inputs $x^{(1)}, x^{(2)}, \ldots, x^{(m)}$ with corresponding class labels $y^{(1)}, y^{(2)}, \ldots, y^{(m)}$, where $y^{(i)} \in \{1, 2, \ldots, n\}$, with n being the number of classes. Our hypothesis hθ(x), returns a vector of probabilities, such that \begin{align} h(x^{(i)}) = \begin{bmatrix} P(y^{(i)} = 1 \| x^{(i)}) \\ P(y^{(i)} = 2 \| x^{(i)}) \\ \vdots \\ P(y^{(i)} = n \| x^{(i)}) \end{bmatrix} = \frac{1}{ \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} } \begin{bmatrix} e^{ \theta_1^T x^{(i)} } \\ e^{ \theta_2^T x^{(i)} } \\ \vdots \\ e^{ \theta_n^T x^{(i)} } \\ \end{bmatrix} \end{align} where $\theta_1, \theta_2, \ldots, \theta_n$ are each k-dimensional column vectors that constitute the parameters of our hypothesis. Notice that $\frac{1}{ \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} }$ normalizes the distribution so that it sums to one. Strictly speaking, we only need n − 1 parameters for n classes, but for convenience, we use n parameters in our derivation. Now, this hypothesis defines a predicted probability distribution given some x, P(y \| x(i)) = h(x(i)). Thus to train the model, a natural choice is to maximize the (conditional) log-likelihood of the data, $l(\theta; x, y) = \sum_{i=1}^{m} \ln { P(y^{(i)} \| x^{(i)}) }$. Motivation: One reason for selecting this form of hypotheses comes from connections to linear discriminant analysis. In particular, if one assumes a generative model for the data in the form $p(x,y) = p(y) \times p(x \| y)$ and selects for p(x \| y) a member of the exponential family (which includes Gaussians, Poissons, etc.) it is possible to show that the conditional probability p(y \| x) has the same form as our chosen hypotheses h(x). For more details, see the CS 229 Lecture 2 Notes. ## Optimizing Softmax Regression Expanding the log-likelihood expression, we find that: \begin{align} \ell(\theta) &= \ln L(\theta; x, y) \\ &= \ln \prod_{i=1}^{m}{ P(y^{(i)} \| x^{(i)}) } \\ &= \sum_{i=1}^{m}{ \ln \frac{ e^{ \theta^T_{y^{(i)}} x^{(i)} } }{ \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} } } \\ &= \theta^T_{y^{(i)}} x^{(i)} - \ln \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} \end{align} Unfortunately, there is no closed form solution to this optimization problem (although it is concave), and we usually use an off-the-shelf optimization method (e.g., L-BFGS, stochastic gradient descent) to find the optimal parameters. Using these optimization methods require computing the gradient ($\ell(\theta)$ w.r.t. θk), which can can be derived as follows: \begin{align} \frac{\partial \ell(\theta)}{\partial \theta_k} &= \frac{\partial}{\partial \theta_k} \theta^T_{y^{(i)}} x^{(i)} - \ln \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} \\ &= I_{ \{ y^{(i)} = k\} } x^{(i)} - \frac{1}{ \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} } \cdot e^{ \theta_k^T x^{(i)} } \cdot x^{(i)} \qquad \text{(where } I_{ \{ y^{(i)} = k\} } \text{is 1 when } y^{(i)} = k \text{ and 0 otherwise) } \\ &= x^{(i)} ( I_{ \{ y^{(i)} = k\} } - P(y^{(i)} = k \| x^{(i)}) ) \end{align} With this, we can now find a set of parameters that maximizes $\ell(\theta)$, for instance by using L-BFGS with minFunc. ### Weight Regularization When using softmax regression in practice, it is important to use weight regularization. In particular, if there exists a linear separator that perfectly classifies all the data points, then the softmax-objective is unbounded (given any θ that separates the data perfectly, one can always scale θ to be larger and obtain a better objective value). With weight regularization, one penalizes the weights for being large and thus avoids these degenerate situations. Weight regularization is also important as it often results in models that generalize better. In particular, one can view weight regularization as placing a (Gaussian) prior on θ so as to prefer θ with smaller values. In practice, we often use a L2 weight regularization on the weights where we penalize the squared value of each element of θ. Formally, we use: \begin{align} w(\theta) = \frac{\lambda}{2} \sum_{i}{ \sum_{j}{ \theta_{ij}^2 } } \end{align} This regularization term is added together with the log-likelihood function to give a cost function, J(θ), which we want to minimize (note that we want to minimize the negative log-likelihood, which corresponds to maximizing the log-likelihood): \begin{align} J(\theta) = -\ell(\theta) + \frac{\lambda}{2} \sum_{i}{ \sum_{j}{ \theta_{ij}^2 } } \end{align} The gradients with respect to the cost function must then be adjusted to account for the weight decay term: \begin{align} \frac{\partial J(\theta)}{\partial \theta_k} &= x^{(i)} ( I_{ \{ y^{(i)} = k\} } - P(y^{(i)} = k \| x^{(i)}) ) + \lambda \theta_k \end{align} Minimizing J(θ) now performs regularized softmax regression. ## Parameterization We noted earlier that we actually only need n − 1 parameters to model n classes. To see why this is so, consider our hypothesis again: \begin{align} h(x^{(i)}) &= \frac{1}{ \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} } \begin{bmatrix} e^{ \theta_1^T x^{(i)} } \\ e^{ \theta_2^T x^{(i)} } \\ \vdots \\ e^{ \theta_n^T x^{(i)} } \\ \end{bmatrix} \\ &= \frac{e^{ \theta_n^T x^{(i)} } }{ \sum_{j=1}^{n}{e^{ \theta_j^T x^{(i)} }} } \cdot \frac{1}{e^{ \theta_n^T x^{(i)} } } \begin{bmatrix} e^{ \theta_1^T x^{(i)} } \\ e^{ \theta_2^T x^{(i)} } \\ \vdots \\ e^{ \theta_n^T x^{(i)} } \\ \end{bmatrix} \\ &= \frac{1}{ \sum_{j=1}^{n}{e^{ (\theta_j^T - \theta_n^T) x^{(i)} }} } \begin{bmatrix} e^{ (\theta_1^T - \theta_n^T) x^{(i)} } \\ e^{ (\theta_2^T - \theta_n^T) x^{(i)} } \\ \vdots \\ e^{ (\theta_n^T - \theta_n^T) x^{(i)} } \\ \end{bmatrix} \\ \end{align} Letting Θj = θj − θn for $j = 1, 2 \ldots n - 1$ gives \begin{align} h(x^{(i)}) &= \frac{1}{ 1 + \sum_{j=1}^{n-1}{e^{ \Theta_j^T x^{(i)} }} } \begin{bmatrix} e^{ \Theta_1^T x^{(i)} } \\ e^{ \Theta_2^T x^{(i)} } \\ \vdots \\ 1 \\ \end{bmatrix} \\ \end{align} Showing that only n − 1 parameters are required. In practice, however, it is often easier to implement the version which is over-parametrized although both methods will lead to the same classifier. ### Binary Logistic Regression In the special case where n = 2, one can also show that softmax regression reduces to logistic regression: \begin{align} h(x^{(i)}) &= \frac{1}{ 1 + e^{ \Theta_1^T x^{(i)} } } \begin{bmatrix} e^{ \Theta_1^T x^{(i)} } \\ 1 \\ \end{bmatrix} \\ &= \frac{e^{ \Theta_1^T x^{(i)} } }{ 1 + e^{ \Theta_1^T x^{(i)} } } \cdot \frac{1}{e^{ \Theta_1^T x^{(i)} } } \begin{bmatrix} e^{ \Theta_1^T x^{(i)} } \\ 1 \\ \end{bmatrix} \\ &= \frac{1}{ e^{ -\Theta_1^T x^{(i)} } + 1 } \begin{bmatrix} 1 \\ e^{ -\Theta_1^T x^{(i)} } \\ \end{bmatrix} \\ \end{align}	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000097751617432, "perplexity": 3002.1959747435826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221214713.45/warc/CC-MAIN-20180819070943-20180819090943-00228.warc.gz"}
http://www.dolfin-adjoint.org/en/latest/documentation/maths/1-foreword.html	# Foreword¶ Written by Patrick E. Farrell Far too often, maths books launch into their subject without explaining to the novice reader why he or she should care about it in the first place. So, before diving into the details, let’s take a few minutes to motivate why adjoint techniques were invented. Suppose an aeronautical engineer wishes to design a wing. The wing is parametrised by a vector $$m$$; for example, suppose each entry of $$m$$ is the coefficient of a Bézier curve. For any potential wing design $$m$$, the Euler equations can be solved, and the lift-to-drag ratio $$J$$ of the design computed. With an adjoint, the engineer can do far more: the adjoint computes the derivative of the drag with respect to the design parameters. This can be used to guide a human designer, or can be passed to an automated optimisation algorithm to automatically compute an optimal shape. [jameson1988] [giles2000]. In the literature, this concept is referred to as adjoint design optimisation. Suppose a meteorologist wishes to improve a forecast by constraining the weather model to match atmospheric observations. The state of the atmosphere at the initial time is partially known (from weather stations), but in order to initialise the model an initial condition for the whole world is required. For any guess of the (unknown) initial state of the atmosphere $$m$$, the Navier-Stokes and related equations can be solved, and the weighted misfit $$J$$ between the observed values and the simulation results can be computed. With an adjoint, the meteorologist can systematically update their guess for the initial state of the atmosphere to match the observations [ledimet1986] [talagrand1987]. In the literature, this concept is referred to as variational data assimilation, 3D-Var and 4D-Var. Suppose an oceanographer wishes to understand the impact of bottom topography on transport through the Drake passage. Bottom topography (the shape of the sea floor) is quite poorly known; many areas of the world are sparsely observed, and observations from over a century ago are still used in some places. The bottom topography is represented as a scalar field $$m$$, the Navier-Stokes and related equations are solved, and the average net transport through the Drake passage $$J$$ computed. With an adjoint, the oceanographer can see where the transport is most sensitive to the topography, and so quantify where the uncertainty matters most [losch2007]. In the literature, this concept is referred to as sensitivity analysis. Suppose a nuclear engineer working for a government regulator wishes to examine a proposed new nuclear reactor design. To do this, a forward model of the Boltzmann transport equations will be used to simulate the proposed design and verify its safety. However, all simulations inherently come with discretisation errors, and unless those errors are quantified, the simulations cannot be relied upon to make decisions upon which millions of lives and billions of pounds depend. With an adjoint, the engineer can quantify the impact of discretisation errors on the criticality rate, and decide to what extent the simulations may be trusted [becker2001]. In the literature, this concept is referred to as goal-based error estimation, or goal-based adaptivity. Suppose a mathematician wishes to understand the stability of some physical system. The traditional approach to this problem is to linearise the operator and investigate its eigenvalues, which determine the long-term behaviour of the system (as $$t \rightarrow \infty$$). However, systems that are eigenvalue-stable can exhibit unexpected transient growth of small perturbations, which in turn can cause the system to become unstable (through nonlinear effects) [trefethen1993]. By computing the singular value decomposition of the tangent linear model, the transient growth of the system to such perturbations can be quantified, and the optimally growing perturbations identified [farrell1996]. The computation of the singular value decomposition in turn requires the adjoint. In the literature, this approach is referred to as generalised stability theory. As you can see, adjoints show up in many applications, and in many computational techniques. One of the reasons why adjoints have a reputation for being difficult is because their discussion is performed in many different areas of science, usually with their own specialised terminology. Reading the literature, there are almost as many ways to approach the topic as there are practitioners! With this introduction, I hope to strike to the heart of the matter, and clear some of the confusion with the minimum of application– or technique–specific lingo. ## A note on the exposition¶ I have chosen to motivate adjoints via a discussion of PDE-constrained optimisation for two reasons. The first is that this approach encapsulates many important applications of adjoints in a general way, and so the reader will be well-equipped to understand much adjoint-related mathematics in the literature. The second is the elegance of the result: most people are amazed when they first learn that it is possible to compute the gradient of a functional $$\widehat{J}(m)$$ in a cost independent of the number of parameters $$\textrm{dim}(m)$$! The topic of adjoints is intriguing, counterintuitive and beautiful; any exposition should try to live up to that. The focus of the exposition will be on getting the core ideas across, and for this reason the discussion will sometimes neglect technicalities. For example, I will implicitly assume that all problems are well-posed, that all necessary derivatives exist and are sufficiently smooth, etc. Occasionally, to build intuition, I will refer to objects as matrices and vectors, although the exposition holds in exactly the same way for their analogues in functional analysis. For an advanced in-depth technical treatment of PDE-constrained optimisation, see the excellent book of Hinze et al. [hinze2009]. ## Notation¶ The notation is mostly inspired by Gunzburger [gunzburger2003]. Symbol Meaning $$m$$ the vector of parameters $$u$$ the solution of the PDE $$F(u, m)$$ the PDE relating $$u$$ and $$m$$: $$F \equiv 0$$ $$J(u, m)$$ a functional of interest $$\widehat{J}(m)$$ the functional considered as a pure function of $$m$$: $$\widehat{J}(m) = J(u(m), m)$$ In the next section, we introduce the PDE-constrained optimisation problem and give a broad overview of how it may be tackled. References [1M-BR01] R. Becker and R. Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numerica, 10:1–102, 2001. doi:10.1017/S0962492901000010. [1M-FI96] B. F. Farrell and P. J. Ioannou. Generalized stability theory. Part I: Autonomous operators. Journal of the Atmospheric Sciences, 53(14):2025–2040, 1996. doi:10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2. [1M-GP00] M. B. Giles and N. A. Pierce. An introduction to the adjoint approach to design. Flow, Turbulence and Combustion, 65(3-4):393–415, 2000. doi:10.1023/A:1011430410075. [1M-Gun03] M. D. Gunzburger. Perspectives in Flow Control and Optimization. Advances in Design and Control. SIAM, 2003. ISBN 089871527X. [1M-HPUU09] M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich. Optimization with PDE constraints. Volume 23 of Mathematical Modelling: Theory and Applications. Springer, 2009. ISBN 978-1-4020-8838-4. [1M-Jam88] A. Jameson. Aerodynamic design via control theory. Journal of Scientific Computing, 3(3):233–260, 1988. doi:10.1007/BF01061285. [1M-LDT86] F.-X. Le Dimet and O. Talagrand. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A, 38A(2):97–110, 1986. doi:10.1111/j.1600-0870.1986.tb00459.x. [1M-LH07] M. Losch and P. Heimbach. Adjoint sensitivity of an ocean general circulation model to bottom topography. Journal of Physical Oceanography, 37(2):377–393, 2007. doi:10.1175/JPO3017.1. [1M-TC87] O. Talagrand and P. Courtier. Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory. Quarterly Journal of the Royal Meteorological Society, 113(478):1311–1328, 1987. doi:10.1002/qj.49711347812. [1M-TTRD93] L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll. Hydrodynamic stability without eigenvalues. Science, 261(5121):578–584, 1993. doi:10.1126/science.261.5121.578.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8665491342544556, "perplexity": 945.0198298603748}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396089.30/warc/CC-MAIN-20200528104652-20200528134652-00159.warc.gz"}
https://math.stackexchange.com/questions/58890/similarity-between-special-matrices-and-special-complex-numbers	# Similarity between special matrices and special complex numbers From Wikipedia: It is occasionally useful (but sometimes misleading) to think of the relationships of different kinds of normal matrices as analogous to the relationships between different kinds of complex numbers: • Invertible matrices are analogous to non-zero complex numbers • Unitary matrices are analogous to complex numbers whose absolute value is 1 • Hermitian matrices are analogous to real numbers • Hermitian positive definite matrices are analogous to positive real numbers • Skew Hermitian matrices are analogous to purely imaginary numbers I also happen to see that the number analogy of each kind of special matrices also agree with their eigenvalues: • eigenvalues of invertible matrices are non-zero complex numbers • eigenvalues of Unitary matrices are complex numbers whose absolute value is 1 • eigenvalues of Hermitian matrices are real numbers • eigenvalues of Hermitian positive definite matrices are positive real numbers • eigenvalues of Skew Hermitian matrices are purely imaginary numbers I wonder 1. if the relation between the eigenvalues of special matrices and their number analogy is just coincidence, or there are something inherent, fundamental and more than analogy? 2. if there are other ways than eigenvalues by which the special matrices and special numbers are similar to each other? (I actually don't quite understand what Wikipedia means by analogy. The example in terms of eigenvalues is just my guess. The author may have other things in mind and there may be other possibilities.) 3. if there are other kinds of special matrices not mentioned in the list have similar analogy to special numbers? (Hermitian negative definite is too trivial to mention.) 4. if there are some relevant references? (It seems that this kind of analogy is mentioned in Halmos "Linear Algebra", but cannot find where it is.) Thanks and regards! • Your entire list is based on the identification of $\mathbb{C}$ with the complex $1 \times 1$ matrices. The analogy is obtained by replacing $1$ by $n$ throughout. I'll remove the (elementary-number-theory) tag and before you ask: elementary number theory is generally used for properties of natural numbers or integers, divisibility, etc. – t.b. Aug 21 '11 at 22:56 • Something related... – J. M. is a poor mathematician Aug 21 '11 at 22:56 • Re: reference in Halmos: section 71, page 139 "[...] Hermitian matrices play the same role as real numbers." It seems that much of the part on orthogonality is built around the analogy you ask about. – t.b. Aug 21 '11 at 23:01 • @Theo: Thanks! The first quote mentioned "different kinds of normal matrices as analogous to the relationships between different kinds of complex numbers" followed by "invertible matrices are analogous to non-zero complex numbers". I was wondering if invertible matrices are not all normal matrices, and the quote meant "invertible normal matrices" when saying "invertible matrices"? – Tim Aug 23 '11 at 22:26 • Normal matrices are diagonalizable, invertible matrices aren't in general: e.g. $\begin{bmatrix} 1 & 1 \\ 0 & 1\end{bmatrix}$ is invertible but not normal (check this!). No, I don't think Halmos meant to write invertible normal matrices, as the invertible normal $n \times n$-matrices don't form a group under matrix multiplication if $n \geq 2$ while the invertible matrices do. – t.b. Aug 23 '11 at 22:31 The complex numbers and the algebra of all $n \times n$ complex matrices are particular examples of (complex) Banach algebras with involution. The involution is somewhat (though not always perfectly) analogous to complex conjugation. The algebra of bounded linear operators on a Hilbert space is one example of such an algebra (mentioned in the reference of Halmos in Theo's comment), which includes both these cases as subcase. In that case, the involution sends an operator to its adjoint, and the analogy with complex conjugation is quite strong. The behaviour of an operator with respect to this involution is strongly reflected in the behaviour of its spectrum (in the case of finite dimensional vector spaces, spectrum of a matrix equates to the set of eigenvalues of that matrix). However, the complex numbers is unique among (complex) Banach algebras, in that the only Banach division algebra (that is, Banach algebra in which every non-zero element has a multiplicative inverse) up to isomorphism is the complex numbers itself (this is the Banach-Mazur theorem). I think what you're noticing about eigenvalues comes down to this: if $\lambda$ is an eigenvalue of $A$, with corresponding eigenvector $\bf v$, then multiplying $\bf v$ by $A$ is the same as multiplying $\bf v$ by $\lambda$, that is, $A{\bf v}=\lambda{\bf v}$. Also, if $A$ has a dominant eigenvalue $\lambda$ (an eigenvalue exceeding all the others in modulus), then the entries of $A^n$ grow as $\lambda^n$ as $n$ increases, and the length of $A^n{\bf v}$ is (in the limit) proportional to $\lambda^n$ for all $\bf v$ outside of a proper subspace. So in these senses, matrices behave like their eigenvalues.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9314733743667603, "perplexity": 381.0924428389173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526489.6/warc/CC-MAIN-20190720070937-20190720092937-00071.warc.gz"}
https://www.science.gov/topicpages/n/nuclear+hamiltonian+ab.html	#### Sample records for nuclear hamiltonian ab 1. The nuclear monopole Hamiltonian Duflo, J.; Zuker, A. P. 1999-05-01 The monopole Hamiltonian Hm is defined as the part of the interaction that reproduces the average energies of configurations. After separating the bulk contributions, we propose a minimal form for Hm containing six parameters adjusted to reproduce the spectra of particle and hole states on doubly magic cores. The mechanism of shell formation is then explained. The reliability of the parametrization is checked by showing that the predicted particle-hole gaps are consistent with experimental data, and that the monopole matrix elements obtained provide the phenomenological cure made necessary by the bad saturation and shell properties of the realistic NN interaction. Predictions are made for the yet unobserved levels around 132Sn, 22O, 34,42Si, 68,78Ni, and 100Sn and for the particle-hole gaps in these nuclei. 2. Construction of diabatic Hamiltonian matrix from ab initio calculated molecular symmetry adapted nonadiabatic coupling terms and nuclear dynamics for the excited states of Na3 cluster. PubMed 2013-04-25 We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (2(2)E' and 1(2)A1') of Na3 cluster, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO). The signs of the NACTs at each point of the configuration space (CS) are determined by employing appropriate irreducible representations (IREPs) arising due to MS group, and such terms are incorporated into the adiabatic to diabatic transformation (ADT) equations to obtain the ADT angles. Since those sign corrected NACTs and the corresponding ADT angles demonstrate the validity of curl condition for the existence of three-state (2(2)E' and 1(2)A1') sub-Hilbert space, it becomes possible to construct the continuous, single-valued, symmetric, and smooth 3 × 3 diabatic Hamiltonian matrix. Finally, nuclear dynamics has been carried out on such diabatic surfaces to explore whether our MS-based treatment of diabatization can reproduce the pattern of the experimental spectrum for system B of Na3 cluster. 3. Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory SciTech Connect Vary, J. P.; Maris, P.; Honkanen, H.; Li, J.; Shirokov, A. M.; Brodsky, S. J.; Harindranath, A. 2009-12-17 Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually, we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements. 4. Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory SciTech Connect Vary, J.P.; Maris, P.; Shirokov, A.M.; Honkanen, H.; li, J.; Brodsky, S.J.; Harindranath, A.; Teramond, G.F.de; /Costa Rica U. 2009-08-03 Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually,we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements. 5. Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions. PubMed Changlani, Hitesh J; Zheng, Huihuo; Wagner, Lucas K 2015-09-14 We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models. 6. Ab initio calculation of excitonic Hamiltonian of light-harvesting complex LH1 of Thermochromatium tepidum Kozlov, Maxim I.; Poddubnyy, Vladimir V.; Glebov, Ilya O.; Belov, Aleksandr S.; Khokhlov, Daniil V. 2016-02-01 The electronic properties of light-harvesting complexes determine the efficiency of energy transfer in photosynthetic antennae. Ab initio calculations of the electronic properties of bacteriochlorophylls (composing the LH1 complex of the purple bacteria Thermochromatium tepidum) were performed. Based on these calculations, the excitonic Hamiltonian of a native cyclic complex and the Hamiltonians of open complexes with several removed bacteriochlorophylls were constructed. Absorption spectra calculated based on these Hamiltonians agree well with the experimental data. We found that the parameters of interaction between the neighboring bacteriochlorophylls are significantly larger than the empirical parameters suggested previously. 7. Relativistic k .p Hamiltonians for centrosymmetric topological insulators from ab initio wave functions Nechaev, I. A.; Krasovskii, E. E. 2016-11-01 We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films. 8. Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions SciTech Connect Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K. 2015-09-14 We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models. 9. Unified ab initio approaches to nuclear structure and reactions DOE PAGES Navratil, Petr; Quaglioni, Sofia; Hupin, Guillaume; ... 2016-04-13 The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD-employing Hamiltonians constructed within chiral effective field theory. After a brief overview of the field, we focus on ab initio many-body approaches—built upon the no-core shell model—that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the 6He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of 9Be. Further, we discuss applications to the 7Bemore » $${({\\rm{p}},\\gamma )}^{8}{\\rm{B}}$$ radiative capture. Lastly, we highlight our efforts to describe transfer reactions including the 3H$${({\\rm{d}},{\\rm{n}})}^{4}$$He fusion.« less 10. Ab Initio Effective Rovibrational Hamiltonians for Non-Rigid Molecules via Curvilinear VMP2 Changala, Bryan; Baraban, Joshua H. 2017-06-01 Accurate predictions of spectroscopic constants for non-rigid molecules are particularly challenging for ab initio theory. For all but the smallest systems, brute force'' diagonalization of the full rovibrational Hamiltonian is computationally prohibitive, leaving us at the mercy of perturbative approaches. However, standard perturbative techniques, such as second order vibrational perturbation theory (VPT2), are based on the approximation that a molecule makes small amplitude vibrations about a well defined equilibrium structure. Such assumptions are physically inappropriate for non-rigid systems. In this talk, we will describe extensions to curvilinear vibrational Møller-Plesset perturbation theory (VMP2) that account for rotational and rovibrational effects in the molecular Hamiltonian. Through several examples, we will show that this approach provides predictions to nearly microwave accuracy of molecular constants including rotational and centrifugal distortion parameters, Coriolis coupling constants, and anharmonic vibrational and tunneling frequencies. 11. Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation Chibotaru, L. F.; Ungur, L. 2012-08-01 A methodology for the rigorous nonperturbative derivation of magnetic pseudospin Hamiltonians of mononuclear complexes and fragments based on ab initio calculations of their electronic structure is described. It is supposed that the spin-orbit coupling and other relativistic effects are already taken fully into account at the stage of quantum chemistry calculations of complexes. The methodology is based on the establishment of the correspondence between the ab initio wave functions of the chosen manifold of multielectronic states and the pseudospin eigenfunctions, which allows to define the pseudospin Hamiltonians in the unique way. Working expressions are derived for the pseudospin Zeeman and zero-field splitting Hamiltonian corresponding to arbitrary pseudospins. The proposed calculation methodology, already implemented in the SINGLE_ANISO module of the MOLCAS-7.6 quantum chemistry package, is applied for a first-principles evaluation of pseudospin Hamiltonians of several complexes exhibiting weak, moderate, and very strong spin-orbit coupling effects. 12. Comparison of nuclear Hamiltonians using spectral function sum rules Rios, A.; Carbone, A.; Polls, A. 2017-07-01 Background: The energy weighted sum rules of the single-particle spectral functions provide a quantitative understanding of the fragmentation of nuclear states due to short-range and tensor correlations. Purpose: The aim of this paper is to compare on a quantitative basis the single-particle spectral function generated by different nuclear Hamiltonians in symmetric nuclear matter using the first three energy-weighted moments. Method: The spectral functions are calculated in the framework of the self-consistent Green's function approach at finite temperature within a ladder resummation scheme. We analyze the first three moments of the spectral function and connect these to the correlations induced by the interactions between the nucleons in symmetric nuclear matter. In particular, the variance of the spectral function is directly linked to the dispersive contribution of the self-energy. The discussion is centered around two- and three-body chiral nuclear interactions, with and without renormalization, but we also provide results obtained with the traditional phase-shift-equivalent CD-Bonn and Av18 potentials. Results: The variance of the spectral function is particularly sensitive to the short-range structure of the force, with hard-core interactions providing large variances. Chiral forces yield variances which are an order of magnitude smaller and, when tamed using the similarity renormalization group, the variance reduces significantly and in proportion to the renormalization scale. The presence of three-body forces does not substantially affect the results. Conclusions: The first three moments of the spectral function are useful tools in analyzing the importance of correlations in nuclear ground states. In particular, the second-order moment provides a direct insight into dispersive contributions to the self-energy and its value is indicative of the fragmentation of single-particle states. 13. Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory SciTech Connect Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Shirokov, A.M.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Ng, E.G.; Yang, C.; Sosonkina, M.; /Ames Lab 2012-06-22 Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory. 14. Ab initio calculations of nuclear reactions important for astrophysics Navratil, Petr; Dohet-Eraly, Jeremy; Calci, Angelo; Horiuchi, Wataru; Hupin, Guillaume; Quaglioni, Sofia 2016-09-01 In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD employing Hamiltonians constructed within chiral effective field theory. One of the newly developed approaches is the No-Core Shell Model with Continuum (NCSMC), capable of describing both bound and scattering states in light nuclei simultaneously. We will present NCSMC results for reactions important for astrophysics that are difficult to measure at relevant low energies, such as 3He(α,γ)7Be and 3H(α,γ)7Li and 11C(p,γ)12N radiative capture, as well as the 3H(d,n)4He fusion. We will also address prospects of calculating the 2H(α,γ)6Li capture reaction within the NCSMC formalism. Prepared in part by LLNL under Contract DE-AC52-07NA27344. Supported by the U.S. DOE, OS, NP, under Work Proposal No. SCW1158, and by the NSERC Grant No. SAPIN-2016-00033. TRIUMF receives funding from the NRC Canada. 15. Toward eliminating the electronic structure bottleneck in nonadiabatic dynamics on the fly: An algorithm to fit nonlocal, quasidiabatic, coupled electronic state Hamiltonians based on ab initio electronic structure data Zhu, Xiaolei; Yarkony, David R. 2010-03-01 An algorithm for constructing a quasidiabatic, coupled electronic state Hamiltonian, in a localized region of nuclear coordinate space, suitable for determining bound state spectra, is generalized to determine a nonlocal Hamiltonian capable of describing, for example, multichannel nonadiabatic photodissociation. For Nstate coupled electronic states, the Hamiltonian, Hd, is a symmetric Nstate×Nstate matrix whose elements are polynomials involving: decaying exponentials exp(-ari,jn) n =1,2, where ri,j=Ri-Rj, ri,j=\|ri,j\|, Rj locates the jth nucleus; and scaled dot-cross product coordinates, proportional to ri,j×ri,k•ri,l. The constructed Hamiltonian is constrained to reproduce, exactly, the ab initio data, energies, gradients, and derivative coupling at selected points, or nodes, in nuclear coordinate space. The remainder of the ab initio data is approximated in a least-squares sense using a normal equations approach. The fitting procedure includes a damping term that precludes oscillations due to the nodal constraints or local excesses of parameters. To illustrate the potential of the fitting procedure an Hd is constructed, with the full nuclear permutation-inversion symmetry, which describes portions of the 1,2 A1 potential energy surfaces of NH3, including the minimum energy point on the 1,2 A1 seam of conical intersection and the NH2+H asymptote. Ab initio data at 239 nuclear configurations was used in the construction which was tested at 48 additional nuclear configurations. While the energy range on the ground and excited potential energy surface is each individually ˜45 000 cm-1, the root mean square error for the energies at all points is only 93.6 cm-1. The location and local conical topography of the minimum energy conical intersection is exactly reproduced. The derivative couplings are shown to be well reproduced, justifying the attribute quasidiabatic. 16. From Model Hamiltonians to ab Initio Hamiltonians and Back Again: Using Single Excitation Quantum Chemistry Methods To Find Multiexciton States in Singlet Fission Materials. PubMed Mayhall, Nicholas J 2016-09-13 Due to the promise of significantly enhanced photovoltaic efficiencies, significant effort has been directed toward understanding and controlling the singlet fission mechanism. Although accurate quantum chemical calculations would provide a detail-rich view of the singlet fission mechanism, this is complicated by the multiexcitonic nature of one of the key intermediates, the (1)(TT) state. Being described as two simultaneous and singlet-coupled triplet excitations on a pair of nearest neighbor monomers, the (1)(TT) state is inherently a multielectronic excitation. This fact renders most single-reference ab initio quantum chemical methods incapable of providing accurate results. This paper serves two purposes: (1) to demonstrate that the multiexciton states in singlet fission materials can be described using a spin-only Hamiltonian and with each monomer treated as a biradical and (2) to propose a very simple procedure for extracting the values for this Hamiltonian from single-reference calculations. Numerical examples are included for a number of different systems, including dimers, trimers, tetramers, and a cluster comprised of seven chromophores. 17. Dipole and transition moments of SiH, PH and SH by ab initio effective valence shell Hamiltonian method Park, Jong Keun; Sun, Hosung 1992-07-01 The ab initio effective valence shell Hamiltonian method, based on quasi-degenerate many-body perturbation theory, is generalized to calculate molecular properties as well as the valence state energies. The procedure requires the evaluation of effective operators for each molecular property. Effective operators are perturbatively expanded in powers of correlation and contain contributions from excitations outside of the multireference valence space. To demonstrate the validity of this method, calculations for dipole moments of and transition moments between several low lying valence states of SiH, SiH +, PH, PH +, SH, and SH + to the lowest nontrivial order in the correlations have been performed and compared with other theoretical calculations. 18. Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator SciTech Connect Szalay, Viktor 2015-05-07 A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed. 19. Unified ab initio approaches to nuclear structure and reactions SciTech Connect Navratil, Petr; Quaglioni, Sofia; Hupin, Guillaume; Romero-Redondo, Carolina; Calci, Angelo 2016-04-13 The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD-employing Hamiltonians constructed within chiral effective field theory. After a brief overview of the field, we focus on ab initio many-body approaches—built upon the no-core shell model—that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the 6He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of 9Be. Further, we discuss applications to the 7Be ${({\\rm{p}},\\gamma )}^{8}{\\rm{B}}$ radiative capture. Lastly, we highlight our efforts to describe transfer reactions including the 3H${({\\rm{d}},{\\rm{n}})}^{4}$He fusion. 20. Unified ab initio approaches to nuclear structure and reactions SciTech Connect Navratil, Petr; Quaglioni, Sofia; Hupin, Guillaume; Romero-Redondo, Carolina; Calci, Angelo 2016-04-13 The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD-employing Hamiltonians constructed within chiral effective field theory. After a brief overview of the field, we focus on ab initio many-body approaches—built upon the no-core shell model—that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the 6He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of 9Be. Further, we discuss applications to the 7Be ${({\\rm{p}},\\gamma )}^{8}{\\rm{B}}$ radiative capture. Lastly, we highlight our efforts to describe transfer reactions including the 3H${({\\rm{d}},{\\rm{n}})}^{4}$He fusion. 1. Some implications of the Hartree product treatment of the quantum nuclei in the ab initio nuclear-electronic orbital methodology Gharabaghi, Masumeh; Shahbazian, Shant 2016-12-01 In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally. 2. Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework Kim, Ilki; von Spakovsky, Michael R. 2017-08-01 Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intrarelaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time is valid as well for time-independent Hamiltonians as a special case and makes the description provided by the SEAQT framework more robust at the fundamental level. In addition, the SEAQT framework is used to help resolve a fundamental issue of thermodynamics in the quantum domain, namely, that concerning the unique definition of process-dependent work and heat functions. The developments presented lead to the conclusion that this framework is not just an alternative approach to thermodynamics in the quantum domain but instead one that uniquely sheds new light on various fundamental but as of yet not completely resolved questions of thermodynamics. 3. Advances in ab initio theories for nuclear reactions Quaglioni, Sofia 2016-09-01 Driven by high-performance computing and new ideas, in recent years ab initio theory has made great strides in achieving a unified description of nuclear structure, clustering and reactions from the constituent nucleons and their strong and electroweak interactions. This is giving access to forefront tools and new fertile grounds to further our understanding of the nuclear force and electroweak currents in nuclei in terms of effective degrees of freedom. A fundamental understanding of nuclear reaction mechanisms and a new capability to accurately compute their properties is also relevant for nuclear astrophysics, terrestrial applications of nuclear fusion, and for using nuclei as probes of fundamental physics through, for example, neutrino-nucleus scattering. In this talk, I will present recent highlights and reflect on future perspectives for this area of nuclear theory. Prepared by LLNL under Contract No. DE-AC52-07NA27344. 4. Ab initio calculations of nuclear structure and reactions with chiral two- and three-nucleon interactions Navratil, Petr; Langhammer, Joachim; Hupin, Guillaume; Quaglioni, Sofia; Calci, Angelo; Roth, Robert; Soma, Vittorio; Cipollone, Andrea; Barbieri, Carlo; Duguet, T. 2014-09-01 The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In recent years, a significant progress has been made in developing ab initio many-body approaches capable of describing both bound and scattering states in light and medium mass nuclei based on input from QCD employing Hamiltonians constructed within chiral effective field theory. We will present calculations of proton-10C scattering and resonances of the exotic nuclei 11N and 9He within the no-core shell model with continuum. Also, we will discuss calculations of binding and separation energies of neutron rich isotopes of Ar, K, Ca, Sc and Ti within the self-consistent Gorkov-Green's function approach. The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In recent years, a significant progress has been made in developing ab initio many-body approaches capable of describing both bound and scattering states in light and medium mass nuclei based on input from QCD employing Hamiltonians constructed within chiral effective field theory. We will present calculations of proton-10C scattering and resonances of the exotic nuclei 11N and 9He within the no-core shell model with continuum. Also, we will discuss calculations of binding and separation energies of neutron rich isotopes of Ar, K, Ca, Sc and Ti within the self-consistent Gorkov-Green's function approach. Support from the NSERC Grant No. 401945-2011 is acknowledged. This work was prepared in part by the LLNL under Contract No. DE-AC52-07NA27344. 5. Study of Nuclear Clustering from an Ab Initio Perspective Kravvaris, Konstantinos; Volya, Alexander 2017-08-01 We put forward a new ab initio approach that seamlessly bridges the structure, clustering, and reactions aspects of the nuclear quantum many-body problem. The configuration interaction technique combined with the resonating group method based on a harmonic oscillator basis allows us to treat the reaction and multiclustering dynamics in a translationally invariant way and preserve the Pauli principle. Our presentation includes studies of Be,108 and an exploration of 3 α clustering in 12C. 6. Ab initio study of the Zener polaron spectrum of half-doped manganites: Comparison of several model Hamiltonians Bastardis, Roland; Guihéry, Nathalie; de Graaf, Coen 2006-07-01 The low-energy spectrum of the Zener polaron in half-doped manganite is studied by means of correlated ab initio calculations. It is shown that the electronic structure of the low-energy states results from a subtle interplay between double-exchange configurations and O 2pσ to Mn 3d charge-transfer configurations that obey a Heisenberg logic. The comparison of the calculated spectrum to those predicted by the Zener Hamiltonian reveals that this simple description does not correctly reproduces the Zener polaron physics. A better reproduction of the calculated spectrum is obtained with either a Heisenberg model that considers a purely magnetic oxygen or the Girerd-Papaefthymiou double-exchange model. An additional significant improvement is obtained when different antiferromagnetic contributions are combined with the double-exchange model, showing that the Zener polaron spectrum is actually ruled by a refined double-exchange mechanism where non-Hund atomic states play a non-negligible role. Finally, eight states of a different nature have been found to be intercalated in the double-exchange spectrum. These states exhibit an O to Mn charge transfer, implying a second O 2p orbital of approximate π character instead of the usual σ symmetry. A small mixing of the two families of states occurs, accounting for the final ordering of the states. 7. Ab Initio Nuclear Structure and Reaction Calculations for Rare Isotopes SciTech Connect Draayer, Jerry P. 2014-09-28 We have developed a novel ab initio symmetry-adapted no-core shell model (SA-NCSM), which has opened the intermediate-mass region for ab initio investigations, thereby providing an opportunity for first-principle symmetry-guided applications to nuclear structure and reactions for nuclear isotopes from the lightest p-shell systems to intermediate-mass nuclei. This includes short-lived proton-rich nuclei on the path of X-ray burst nucleosynthesis and rare neutron-rich isotopes to be produced by the Facility for Rare Isotope Beams (FRIB). We have provided ab initio descriptions of high accuracy for low-lying (including collectivity-driven) states of isotopes of Li, He, Be, C, O, Ne, Mg, Al, and Si, and studied related strong- and weak-interaction driven reactions that are important, in astrophysics, for further understanding stellar evolution, X-ray bursts and triggering of s, p, and rp processes, and in applied physics, for electron and neutrino-nucleus scattering experiments as well as for fusion ignition at the National Ignition Facility (NIF). 8. Nuclear motion effects on the density matrix of crystals: An ab initio Monte Carlo harmonic approach Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto 2012-07-01 In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated. 9. Nuclear motion effects on the density matrix of crystals: an ab initio Monte Carlo harmonic approach. PubMed Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto 2012-07-28 In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated. 10. Ab initio calculations of nuclear widths via an integral relation Nollett, Kenneth M. 2012-10-01 I describe the computation of energy widths of nuclear states using an integral over the interaction region of ab initio variational Monte Carlo wave functions, and I present calculated widths for many states. I begin by presenting relations that connect certain short-range integrals to widths. I then present predicted widths for 5⩽A⩽9 nuclei, and I compare them against measured widths. They match the data more closely and with less ambiguity than estimates based on spectroscopic factors. I consider the consequences of my results for identification of observed states in 8B, 9He, and 9Li. I also examine failures of the method and conclude that they generally involve broad states and variational wave functions that are not strongly peaked in the interaction region. After examining bound-state overlap functions computed from a similar integral relation, I conclude that overlap calculations can diagnose cases in which computed widths should not be trusted. 11. Isoscalar monopole resonance of the alpha particle: a prism to nuclear Hamiltonians. PubMed Bacca, Sonia; Barnea, Nir; Leidemann, Winfried; Orlandini, Giuseppina 2013-01-25 We present an ab initio study of the isoscalar monopole excitations of (4)He using different realistic nuclear interactions, including modern effective field theory potentials. In particular we concentrate on the transition form factor F(M) to the narrow 0(+) resonance close to threshold. F(M) exhibits a strong potential model dependence, and can serve as a kind of prism to distinguish among different nuclear force models. Compared to the measurements obtained from inelastic electron scattering off ^{4}He, one finds that the state-of-the-art theoretical transition form factors are at variance with experimental data, especially in the case of effective field theory potentials. We discuss some possible reasons for such a discrepancy, which still remains a puzzle. 12. Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules Rey, M.; Nikitin, A. V.; Tyuterev, Vl. G. 2010-08-01 A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY3 molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH3 where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)]. 13. Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller-Plesset perturbation theory Changala, P. Bryan; Baraban, Joshua H. 2016-11-01 We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We apply this method to and demonstrate its accuracy on two molecules: Si2C, a quasilinear triatomic with significant bending anharmonicity, and CH3NO2, which contains a completely unhindered methyl rotor. In addition to these two examples, we discuss several key technical aspects of the method, including an efficient implementation of Eckart and quasi-Eckart frame embedding that does not rely on numerical finite differences. 14. Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller-Plesset perturbation theory. PubMed Changala, P Bryan; Baraban, Joshua H 2016-11-07 We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We apply this method to and demonstrate its accuracy on two molecules: Si2C, a quasilinear triatomic with significant bending anharmonicity, and CH3NO2, which contains a completely unhindered methyl rotor. In addition to these two examples, we discuss several key technical aspects of the method, including an efficient implementation of Eckart and quasi-Eckart frame embedding that does not rely on numerical finite differences. 15. Vibrational dynamics of zero-field-splitting hamiltonian in gadolinium-based MRI contrast agents from ab initio molecular dynamics SciTech Connect Lasoroski, Aurélie; Vuilleumier, Rodolphe; Pollet, Rodolphe 2014-07-07 The electronic relaxation of gadolinium complexes used as MRI contrast agents was studied theoretically by following the short time evolution of zero-field-splitting parameters. The statistical analysis of ab initio molecular dynamics trajectories provided a clear separation between static and transient contributions to the zero-field-splitting. For the latter, the correlation time was estimated at approximately 0.1 ps. The influence of the ligand was also probed by replacing one pendant arm of our reference macrocyclic complex by a bulkier phosphonate arm. In contrast to the transient contribution, the static zero-field-splitting was significantly influenced by this substitution. 16. Accurate ab initio tight-binding Hamiltonians: Effective tools for electronic transport and optical spectroscopy from first principles D'Amico, Pino; Agapito, Luis; Catellani, Alessandra; Ruini, Alice; Curtarolo, Stefano; Fornari, Marco; Nardelli, Marco Buongiorno; Calzolari, Arrigo 2016-10-01 The calculations of electronic transport coefficients and optical properties require a very dense interpolation of the electronic band structure in reciprocal space that is computationally expensive and may have issues with band crossing and degeneracies. Capitalizing on a recently developed pseudoatomic orbital projection technique, we exploit the exact tight-binding representation of the first-principles electronic structure for the purposes of (i) providing an efficient strategy to explore the full band structure En(k ) , (ii) computing the momentum operator differentiating directly the Hamiltonian, and (iii) calculating the imaginary part of the dielectric function. This enables us to determine the Boltzmann transport coefficients and the optical properties within the independent particle approximation. In addition, the local nature of the tight-binding representation facilitates the calculation of the ballistic transport within the Landauer theory for systems with hundreds of atoms. In order to validate our approach we study the multivalley band structure of CoSb3 and a large core-shell nanowire using the ACBN0 functional. In CoSb3 we point the many band minima contributing to the electronic transport that enhance the thermoelectric properties; for the core-shell nanowire we identify possible mechanisms for photo-current generation and justify the presence of protected transport channels in the wire. 17. Spin-orbit decomposition of ab initio nuclear wave functions Johnson, Calvin W. 2015-03-01 Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum j , leading to j -j coupling, decades ago phenomenological models suggested that a simpler picture for 0 p -shell nuclides can be realized via coupling of the total spin S and total orbital angular momentum L . I revisit this idea with large-basis, no-core shell-model calculations using modern ab initio two-body interactions and dissect the resulting wave functions into their component L - and S -components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly 50 years and six orders of magnitude in basis dimensions. I suggest that L -S decomposition may be a useful tool for analyzing ab initio wave functions of light nuclei, for example, in the case of rotational bands. 18. Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei; Kawashima, Naoki; Sota, Shigetoshi; Tohyama, Takami; Imada, Masatoshi 2017-08-01 We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), 10.1103/PhysRevLett.113.107201], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid. 19. Ab Initio Calculations Of Nuclear Reactions And Exotic Nuclei SciTech Connect Quaglioni, S. 2014-05-05 Our ultimate goal is to develop a fundamental theory and efficient computational tools to describe dynamic processes between nuclei and to use such tools toward supporting several DOE milestones by: 1) performing predictive calculations of difficult-to-measure landmark reactions for nuclear astrophysics, such as those driving the neutrino signature of our sun; 2) improving our understanding of the structure of nuclei near the neutron drip line, which will be the focus of the DOE’s Facility for Rare Isotope Beams (FRIB) being constructed at Michigan State University; but also 3) helping to reveal the true nature of the nuclear force. Furthermore, these theoretical developments will support plasma diagnostic efforts at facilities dedicated to the development of terrestrial fusion energy. 20. Ab initio nuclear structure from lattice effective field theory SciTech Connect Lee, Dean 2014-11-11 This proceedings article reviews recent results by the Nuclear Lattice EFT Collaboration on an excited state of the {sup 12}C nucleus known as the Hoyle state. The Hoyle state plays a key role in the production of carbon via the triple-alpha reaction in red giant stars. We discuss the structure of low-lying states of {sup 12}C as well as the dependence of the triple-alpha reaction on the masses of the light quarks. 1. Extension of the MIRS computer package for the modeling of molecular spectra: From effective to full ab initio ro-vibrational Hamiltonians in irreducible tensor form Nikitin, A. V.; Rey, M.; Champion, J. P.; Tyuterev, Vl. G. 2012-07-01 The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version [Nikitin AV, Champion JP, Tyuterev VlG. The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules. J Quant Spectrosc Radiat Transf 2003;82:239-49.] was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possibilities for spectra calculations and modeling by getting rid of several previous limitations particularly for the size of polyads and the number of tensors involved. It allows dealing with overlapping polyads and includes more efficient and faster algorithms for the calculation of coefficients related to molecular symmetry properties (6C, 9C and 12C symbols for C3v, Td, and Oh point groups) and for better convergence of least-square-fit iterations as well. The new version is not limited to polyad effective models. It also allows direct predictions using full ab initio ro-vibrational normal mode Hamiltonians converted into the irreducible tensor form. Illustrative examples on CH3D, CH4, CH3Cl, CH3F and PH3 are reported reflecting the present status of data available. It is written in C++ for standard PC computer operating under Windows. The full package including on-line documentation and recent data are freely available at http://www.iao.ru/mirs/mirs.htm or http://xeon.univ-reims.fr/Mirs/ or http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/MIRS.html and as supplementary data from the online version of the article. 2. Quantifying statistical uncertainties in ab initio nuclear physics using Lagrange multipliers Carlsson, B. D. 2017-03-01 Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, I here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass nuclei to highlight any differences between the presented methods. The main conclusion is that the LM method is more robust, while covariance-based methods are less demanding in their evaluation. 3. Realistic collective nuclear Hamiltonian Dufour, Marianne; Zuker, Andrés P. 1996-10-01 The residual part of the realistic forces-obtained after extracting the monopole terms responsible for bulk properties-is strongly dominated by pairing and quadrupole interactions, with important στ.στ, octupole, and hexadecapole contributions. Their forms retain the simplicity of the traditional pairing plus multipole models, while eliminating their flaws through a normalization mechanism dictated by a universal A-1/3 scaling. Coupling strengths and effective charges are calculated and shown to agree with empirical values. Comparisons between different realistic interactions confirm the claim that they are very similar. 4. Nuclear quantum effect on intramolecular hydrogen bond of hydrogen maleate anion: An ab initio path integral molecular dynamics study Kawashima, Yukio; Tachikawa, Masanori 2013-05-01 Ab initio path integral molecular dynamics simulation was performed to understand the nuclear quantum effect on the hydrogen bond of hydrogen malonate anion. Static calculation predicted the proton transfer barrier as 0.12 kcal/mol. Conventional ab initio molecular dynamics simulation at 300 K found proton distribution with a double peak on the proton transfer coordinate. Inclusion of thermal effect alone elongates the hydrogen bond length, which increases the barrier height. Inclusion of nuclear quantum effect washes out this barrier, and distributes a single broad peak in the center. H/D isotope effect on the proton transfer is also discussed. 5. Symmetry-Adapted Ab Initio Shell Model for Nuclear Structure Calculations Draayer, J. P.; Dytrych, T.; Launey, K. D.; Langr, D. 2012-05-01 An innovative concept, the symmetry-adapted ab initio shell model, that capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. This framework is expected to inform the leading features of nuclear structure and reaction data for light and medium mass nuclei, which are currently inaccessible by theory and experiment and for which predictions of modern phenomenological models often diverge. We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon-nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A = 16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. This, in turn, points to the importance of using a symmetry-adapted framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation. 6. Hamiltonian purification SciTech Connect Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo; Pascazio, Saverio; Nakazato, Hiromichi; Yuasa, Kazuya; Giovannetti, Vittorio 2015-12-15 The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided. 7. Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects. PubMed Sumner, Isaiah; Iyengar, Srinivasan S 2007-10-18 We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities. 8. Integration of ab-initio nuclear calculation with derivative free optimization technique SciTech Connect Sharda, Anurag 2008-01-01 Optimization techniques are finding their inroads into the field of nuclear physics calculations where the objective functions are very complex and computationally intensive. A vast space of parameters needs searching to obtain a good match between theoretical (computed) and experimental observables, such as energy levels and spectra. Manual calculation defies the scope of such complex calculation and are prone to error at the same time. This body of work attempts to formulate a design and implement it which would integrate the ab initio nuclear physics code MFDn and the VTDIRECT95 code. VTDIRECT95 is a Fortran95 suite of parallel code implementing the derivative-free optimization algorithm DIRECT. Proposed design is implemented for a serial and parallel version of the optimization technique. Experiment with the initial implementation of the design showing good matches for several single-nucleus cases are conducted. Determination and assignment of appropriate number of processors for parallel integration code is implemented to increase the efficiency and resource utilization in the case of multiple nuclei parameter search. 9. Semi-empirical and ab initio DFT modeling of the spin-Hamiltonian parameters for Fe6+: K2MO4 (M = S, Cr, Se) Avram, N. M.; Brik, M. G.; Andreici, E.-L. 2014-09-01 In this paper we calculated the spin-Hamiltonian parameters (g factors {{g}\|\|}, {{g}\\bot } and zero field splitting parameter D) for Fe6+ ions doped in K2MO4 (M = S, Cr, Se) crystals, taking into account the actual site symmetry of the Fe6+ impurity ion. The suggested method is based on the successful application of two different approaches: the crystal field theory (CFT) and density functional based (DFT). Within the CFT model we used the cluster approach and the perturbation theory method, based on the crystal field parameters, which were calculated in the superposition model. Within the DFT approach the calculations were done at the self-consistent field (SCF) by solving the coupled perturbed SCF equations. Comparison with experimental data shows that the obtained results are quite satisfactory, which proves applicability of the suggested calculating technique. 10. Input/Output of ab-initio nuclear structure calculations for improved performance and portability SciTech Connect Laghave, Nikhil 2010-01-01 Many modern scientific applications rely on highly computation intensive calculations. However, most applications do not concentrate as much on the role that input/output operations can play for improved performance and portability. Parallelizing input/output operations of large files can significantly improve the performance of parallel applications where sequential I/O is a bottleneck. A proper choice of I/O library also offers a scope for making input/output operations portable across different architectures. Thus, use of parallel I/O libraries for organizing I/O of large data files offers great scope in improving performance and portability of applications. In particular, sequential I/O has been identified as a bottleneck for the highly scalable MFDn (Many Fermion Dynamics for nuclear structure) code performing ab-initio nuclear structure calculations. We develop interfaces and parallel I/O procedures to use a well-known parallel I/O library in MFDn. As a result, we gain efficient I/O of large datasets along with their portability and ease of use in the down-stream processing. Even situations where the amount of data to be written is not huge, proper use of input/output operations can boost the performance of scientific applications. Application checkpointing offers enormous performance improvement and flexibility by doing a negligible amount of I/O to disk. Checkpointing saves and resumes application state in such a manner that in most cases the application is unaware that there has been an interruption to its execution. This helps in saving large amount of work that has been previously done and continue application execution. This small amount of I/O provides substantial time saving by offering restart/resume capability to applications. The need for checkpointing in optimization code NEWUOA has been identified and checkpoint/restart capability has been implemented in NEWUOA by using simple file I/O. 11. Ab Initio Enhanced calphad Modeling of Actinide-Rich Nuclear Fuels SciTech Connect Morgan, Dane; Yang, Yong Austin 2013-10-28 The process of fuel recycling is central to the Advanced Fuel Cycle Initiative (AFCI), where plutonium and the minor actinides (MA) Am, Np, and Cm are extracted from spent fuel and fabricated into new fuel for a fast reactor. Metallic alloys of U-Pu-Zr-MA are leading candidates for fast reactor fuels and are the current basis for fast spectrum metal fuels in a fully recycled closed fuel cycle. Safe and optimal use of these fuels will require knowledge of their multicomponent phase stability and thermodynamics (Gibbs free energies). In additional to their use as nuclear fuels, U-Pu-Zr-MA contain elements and alloy phases that pose fundamental questions about electronic structure and energetics at the forefront of modern many-body electron theory. This project will validate state-of-the-art electronic structure approaches for these alloys and use the resulting energetics to model U-Pu-Zr-MA phase stability. In order to keep the work scope practical, researchers will focus on only U-Pu-Zr-{Np,Am}, leaving Cm for later study. The overall objectives of this project are to: Provide a thermodynamic model for U-Pu-Zr-MA for improving and controlling reactor fuels; and, Develop and validate an ab initio approach for predicting actinide alloy energetics for thermodynamic modeling. 12. Spectroscopic fingerprints of toroidal nuclear quantum delocalization via ab initio path integral simulations. PubMed Schütt, Ole; Sebastiani, Daniel 2013-04-05 We investigate the quantum-mechanical delocalization of hydrogen in rotational symmetric molecular systems. To this purpose, we perform ab initio path integral molecular dynamics simulations of a methanol molecule to characterize the quantum properties of hydrogen atoms in a representative system by means of their real-space and momentum-space densities. In particular, we compute the spherically averaged momentum distribution n(k) and the pseudoangular momentum distribution n(kθ). We interpret our results by comparing them to path integral samplings of a bare proton in an ideal torus potential. We find that the hydroxyl hydrogen exhibits a toroidal delocalization, which leads to characteristic fingerprints in the line shapes of the momentum distributions. We can describe these specific spectroscopic patterns quantitatively and compute their onset as a function of temperature and potential energy landscape. The delocalization patterns in the projected momentum distribution provide a promising computational tool to address the intriguing phenomenon of quantum delocalization in condensed matter and its spectroscopic characterization. As the momentum distribution n(k) is also accessible through Nuclear Compton Scattering experiments, our results will help to interpret and understand future measurements more thoroughly. 13. Ab initio statistical mechanics of surface adsorption and desorption. II. Nuclear quantum effects. PubMed Alfè, D; Gillan, M J 2010-07-28 We show how the path-integral formulation of quantum statistical mechanics can be used to construct practical ab initio techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum nuclear effects. The techniques we describe are based on the computation of the potential of mean force on a chosen molecule and generalize the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalized-gradient exchange-correlation functional for the case of H(2)O on the MgO (001) surface at low coverage. We note that the very high vibrational frequencies of the H(2)O molecule would normally require very large numbers of time slices (beads) in path-integral calculations, but we show that this requirement can be dramatically reduced by employing the idea of thermodynamic integration with respect to the number of beads. The validity and correctness of our path-integral calculations on the H(2)O/MgO(001) system are demonstrated by supporting calculations on a set of simple model systems for which quantum contributions to the free energy are known exactly from analytic arguments. 14. Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory. PubMed Marsalek, Ondrej; Markland, Thomas E 2016-02-07 Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost. 15. Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory SciTech Connect Marsalek, Ondrej; Markland, Thomas E. 2016-02-07 Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost. 16. Why Dynamic Simulations are Needed to Calculate Thermally Averaged Spin Hamiltonians Weitekamp, Daniel P.; Mueller, Leonard J. 1998-03-01 The spin Hamiltonian needed to describe nearly all magnetic resonance experiments is an average over rapidly relaxing spatial degrees of freedom. This has previously been taken to be a Boltzmann average of quantities calculable from the time-independent Hamiltonian describing the system. We show why this approach is conceptually flawed and describe the physics of previously unsuspected, intrinsically dynamic, contributions to the spin Hamiltonian for this ubiquitous situation. Numerical estimates indicate that these new terms are required in order to simulate nuclear magnetic resonance spectra at the resolution with which they are routinely measured. An approach is outlined in which ab initio electronic structures may be combined with a tractable semi-classical description of rovibrational relaxation to give the necessary dynamic corrections, which are described by an average Liouvillian born as the result of spatial susceptibility (ALBATROSS). 17. Ab initio calculations of the intermolecular chemical shift in nuclear magnetic resonance in the gas phase and for adsorbed species Jameson, Cynthia J.; de Dios, Angel C. 1992-07-01 The chemical shifts observed in nuclear magnetic resonance experiments are the differences in shielding of the nuclear spin in different electronic environments. These are known to depend on intermolecular interactions as evidenced by density-dependent chemical shifts in the gas phase, gas-to-liquid shifts, and adsorption shifts on surfaces. We present the results of the first ab initio intermolecular chemical shielding function calculated for a pair of interacting atoms for a wide range of internuclear separations. We used the localized orbital local origin (LORG) approach of Hansen and Bouman and also investigated the second-order electron correlation contributions using second-order LORG (SOLO). The 39Ar shielding in Ar2 passes through zero at some very short distance, going through a minimum, and asymptotically approaches zero at larger separations. The 21Ne shielding function in Ne2 has a similar shape. The Drude model suggests a method of scaling that portion of the shielding function that is weighted most heavily by exp[-V(R)/kT]. The scaling factors, which have been verified in the comparison of 21Ne in Ne2 against 39Ar in Ar2 ab initio results, allows us to project out from the same 39Ar in Ar2 ab initio values the appropriate 129Xe shielding functions in the Xe-Ar, Xe-Kr, and Xe-Xe interacting pairs. These functions lead to temperature-dependent second virial coefficients of chemical shielding which agree with experiments in the gas phase. Ab initio calculations of 39Ar shielding in clusters of argon are used to model the observed 129Xe chemical shifts of Xe, Xe2,...,Xe8 trapped in the cages of zeolite NaA. 18. Determining quasidiabatic coupled electronic state Hamiltonians using derivative couplings: A normal equations based method. PubMed Papas, Brian N; Schuurman, Michael S; Yarkony, David R 2008-09-28 A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC. 19. Communication: XFAIMS—eXternal Field Ab Initio Multiple Spawning for electron-nuclear dynamics triggered by short laser pulses SciTech Connect Mignolet, Benoit; Curchod, Basile F. E.; Martinez, Todd J. 2016-11-17 Attoscience is an emerging field where attosecond pulses or few cycle IR pulses are used to pump and probe the correlated electron-nuclear motion of molecules. We present the trajectory-guided eXternal Field Ab Initio Multiple Spawning (XFAIMS) method that models such experiments “on-the-fly,” from laser pulse excitation to fragmentation or nonadiabatic relaxation to the ground electronic state. For the photoexcitation of the LiH molecule, we show that XFAIMS gives results in close agreement with numerically exact quantum dynamics simulations, both for atto- and femtosecond laser pulses. As a result, we then show the ability of XFAIMS to model the dynamics in polyatomic molecules by studying the effect of nuclear motion on the photoexcitation of a sulfine (H2CSO). 20. Communication: XFAIMS—eXternal Field Ab Initio Multiple Spawning for electron-nuclear dynamics triggered by short laser pulses DOE PAGES Mignolet, Benoit; Curchod, Basile F. E.; Martinez, Todd J. 2016-11-17 Attoscience is an emerging field where attosecond pulses or few cycle IR pulses are used to pump and probe the correlated electron-nuclear motion of molecules. We present the trajectory-guided eXternal Field Ab Initio Multiple Spawning (XFAIMS) method that models such experiments “on-the-fly,” from laser pulse excitation to fragmentation or nonadiabatic relaxation to the ground electronic state. For the photoexcitation of the LiH molecule, we show that XFAIMS gives results in close agreement with numerically exact quantum dynamics simulations, both for atto- and femtosecond laser pulses. As a result, we then show the ability of XFAIMS to model the dynamics inmore » polyatomic molecules by studying the effect of nuclear motion on the photoexcitation of a sulfine (H2CSO).« less 1. Weakly Hamiltonian actions Martínez Torres, David; Miranda, Eva 2017-05-01 In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting. 2. Ab Initio Calculations Of Light-Ion Reactions SciTech Connect Navratil, P; Quaglioni, S; Roth, R; Horiuchi, W 2012-03-12 The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of nuclear forces, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD employing Hamiltonians constructed within chiral effective field theory. In this contribution, we present one of such promising techniques capable of describing simultaneously both bound and scattering states in light nuclei. By combining the resonating-group method (RGM) with the ab initio no-core shell model (NCSM), we complement a microscopic cluster approach with the use of realistic interactions and a microscopic and consistent description of the clusters. We discuss applications to light nuclei scattering, radiative capture and fusion reactions. 3. The isotropic Hamiltonian formalism SciTech Connect Vaisman, Izu 2011-02-10 A Hamiltonian formalism is a procedure that allows to associate a dynamical system to a function and that includes classical Hamiltonian mechanics as a particular case. The present, expository paper gives a survey of the Hamiltonian formalism defined by an isotropic subbundle of TM+TM, in particular, by a Dirac structure. We discuss reduction and geometric quantization of the Hamiltonian dynamical systems provided by this formalism. 4. Precise Lifetime Measurements in Light Nuclei for Benchmarking Modern Ab-initio Nuclear Structure Models SciTech Connect Lister, C.J.; McCutchan, E.A. 2014-06-15 A new generation of ab-initio calculations, based on realistic two- and three-body forces, is having a profound impact on our view of how nuclei work. To improve the numerical methods, and the parameterization of 3-body forces, new precise data are needed. Electromagnetic transitions are very sensitive to the dynamics which drive mixing between configurations. We have made a series of precise (< 3%) measurements of electromagnetic transitions in the A=10 nuclei {sup 10}C and {sup 10}Be by using the Doppler Shift Attenuation method carefully. Many interesting features can be reproduced including the strong α clustering. New measurements on {sup 8}Be and {sup 12}Be highlight the interplay between the alpha clusters and their valence neutrons. 5. Ab initio determination of the nuclear relaxation contribution to the second hyperpolarizability of carbon disulfide Champagne, Benoı̂t 1998-04-01 Although basis set saturation, electron correlation and frequency dispersion have been addressed thoroughly, the electronic second hyperpolarizability of carbon disulfide computed by K. Ohta, T. Sakaguchi, K. Kamada and T. Fukumi (Chem. Phys. Lett. 274 (1997) 306) is not in agreement with experiment. In this Letter the potentially substantial nuclear relaxation contribution is evaluated within the Møller-Plesset scheme limited to second order by using the 6-31G basis set augmented by three diffuse functions (1p and 2d). Within the enhanced approximation, the nuclear relaxation contribution to the static, dc-Kerr and ESHG second hyperpolarizability turns out to amount to 26.5%, 6.8% and -0.8% of the pure static electronic counterpart, respectively. The remaining gap between theory and experiment suggests new experiments should be carried out. 6. Ab initio simulation of radiation damage in nuclear reactor pressure vessel materials 2012-02-01 Using Kinetic Monte Carlo we developed a code to study point defect hopping in BCC metallic alloys using energetics and attempt frequencies calculated using VASP, an electronic structure software package. Our code provides a way of simulating the effects of neutron radiation on potential reactor materials. Specifically we will compare the Molybdenum-Chromium alloy system to steel alloys for use in nuclear reactor pressure vessels. 7. Modelling the local atomic structure of molybdenum in nuclear waste glasses with ab initio molecular dynamics simulations. PubMed Konstantinou, Konstantinos; Sushko, Peter V; Duffy, Dorothy M 2016-09-21 The nature of chemical bonding of molybdenum in high level nuclear waste glasses has been elucidated by ab initio molecular dynamics simulations. Two compositions, (SiO2)57.5-(B2O3)10-(Na2O)15-(CaO)15-(MoO3)2.5 and (SiO2)57.3-(B2O3)20-(Na2O)6.8-(Li2O)13.4-(MoO3)2.5, were considered in order to investigate the effect of ionic and covalent components on the glass structure and the formation of the crystallisation precursors (Na2MoO4 and CaMoO4). The coordination environments of Mo cations and the corresponding bond lengths calculated from our model are in excellent agreement with experimental observations. The analysis of the first coordination shell reveals two different types of molybdenum host matrix bonds in the lithium sodium borosilicate glass. Based on the structural data and the bond valence model, we demonstrate that the Mo cation can be found in a redox state and the molybdate tetrahedron can be connected with the borosilicate network in a way that inhibits the formation of crystalline molybdates. These results significantly extend our understanding of bonding in Mo-containing nuclear waste glasses and demonstrate that tailoring the glass composition to specific heavy metal constituents can facilitate incorporation of heavy metals at high concentrations. 8. Photoexcited Nuclear Dynamics with Ab Initio Electronic Structure Theory: Is TD-DFT Ready For the Challenge? Subotnik, Joseph In this talk, I will give a broad overview of our work in nonadiabatic dynamics, i.e. the dynamics of strongly coupled nuclear-electronic motion whereby the relaxation of a photo-excited electron leads to the heating up of phonons. I will briefly discuss how to model such nuclear motion beyond mean field theory. Armed with the proper framework, I will then focus on how to calculate one flavor of electron-phonon couplings, known as derivative couplings in the chemical literature. Derivative couplings are the matrix elements that couple adiabatic electronic states within the Born-Oppenheimer treatment, and I will show that these matrix elements show spurious poles using formal (frequency-independent) time-dependent density functional theory. To correct this TD-DFT failure, a simple approximation will be proposed and evaluated. Finally, time permitting, I will show some ab initio calculations whereby one can use TD-DFT derivative couplings to study electronic relaxation through a conical intersection. 9. Direct assessment of quantum nuclear effects on hydrogen bond strength by constrained-centroid ab initio path integral molecular dynamics Walker, Brent; Michaelides, Angelos 2010-11-01 The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)2 is about 30% weaker when quantum nuclear effects are included, while that in (H2O)2 is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation. 10. Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes. PubMed Equbal, Asif; Shankar, Ravi; Leskes, Michal; Vega, Shimon; Nielsen, Niels Chr; Madhu, P K 2017-03-14 Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient (1)H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the (1)H-(1)H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of (1)H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme. 11. Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes Equbal, Asif; Shankar, Ravi; Leskes, Michal; Vega, Shimon; Nielsen, Niels Chr.; Madhu, P. K. 2017-03-01 Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the 1H-1H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of 1H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme. 12. Hamiltonian Light-Front Ffield Theory in a Basis Function Approach SciTech Connect Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C. 2009-05-15 Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach, present illustrative features of some non-interacting systems in a cavity and discuss the computational challenges. 13. Open-shell nuclei and excited states from multireference normal-ordered Hamiltonians Gebrerufael, Eskendr; Calci, Angelo; Roth, Robert 2016-03-01 We discuss the approximate inclusion of three-nucleon (3 N ) interactions into ab initio nuclear structure calculations using a multireference formulation of normal ordering and Wick's theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multireference normal ordering opens a path to open-shell nuclei and excited states. Based on different multideterminantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p -shell nuclei, including 6Li,12C, and 10B. We find that this multireference normal-ordered two-body approximation is able to capture the effects of the 3 N interaction with sufficient accuracy, both for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies. 14. Fitting and using model Hamiltonian in non-adiabatic molecular dynamics simulations Smale, Jonathan Ross In order to study computationally increasingly complex systems using theoretical methods model, Hamiltonians are required to accurately describe the potential energy surface they represent. Also ab-initio methods improve the calculation of the excited states of these complex systems becomes increasingly feasible. One such model Hamiltonian described herein, the Vibronic Coupling Hamiltonian, has previously shown its versatility and ability to describe a variety of non-adiabatic problems. This thesis describes a new method, a genetic algorithm, for the parameterisation of the Vibronic Coupling Hamiltonian to describe both previously calculated potential energy surfaces (allene and pentatetraene) and newly calculated (cyclo-butadiene and toluene) potential energy surfaces. In order to test this genetic algorithm, quantum nuclear dynamics calculations were performed using the multi-configurational time dependent Hartree method and the results compared to experiment.. 15. Ab initio Study of Nuclear Quadrupole Interactions in Selenium and Tellurium Maharjan, N. B.; Paudyal, D. D.; Mishra, D. R.; Byahut, S. P.; Cho, Hwa-Suck; Scheicher, R. H.; Jeong, Junho; Das, T. P. 2004-03-01 We are systematically studying the influence of impurities in calcogenide glasses on the glass transition temperature using the first-principles Hartree-Fock cluster method. Results of our calculations on the electronic structures of pure selenium and tellurium chain systems, and with Te and Se impurities respectively, will be reported. By comparing the theoretically obtained nuclear quadrupole interaction (NQI) tensors for ^77Se and ^125Te with available experimental NQI tensors, we were able to test the accuracy of the calculated electronic structures. Good agreement for both the pure and the impurity systems has been found. We have also studied ^125Te NQI tensors in Te-Thiourea and compared our result with experimental data to check on the choice of the ^125Te quadrupole moment used. 16. MO-AB-207-03: ACR Update in Nuclear Medicine SciTech Connect Harkness, B. 2015-06-15 A goal of an imaging accreditation program is to ensure adequate image quality, verify appropriate staff qualifications, and to assure patient and personnel safety. Currently, more than 35,000 facilities in 10 modalities have been accredited by the American College of Radiology (ACR), making the ACR program one of the most prolific accreditation options in the U.S. In addition, ACR is one of the accepted accreditations required by some state laws, CMS/MIPPA insurance and others. Familiarity with the ACR accreditation process is therefore essential to clinical diagnostic medical physicists. Maintaining sufficient knowledge of the ACR program must include keeping up-to-date as the various modality requirements are refined to better serve the goals of the program and to accommodate newer technologies and practices. This session consists of presentations from authorities in four ACR accreditation modality programs, including magnetic resonance imaging, computed tomography, nuclear medicine, and mammography. Each speaker will discuss the general components of the modality program and address any recent changes to the requirements. Learning Objectives: To understand the requirements of the ACR MR Accreditation program. The discussion will include accreditation of whole-body general purpose magnets, dedicated extremity systems well as breast MRI accreditation. Anticipated updates to the ACR MRI Quality Control Manual will also be reviewed. To understand the requirements of the ACR CT accreditation program, including updates to the QC manual as well as updates through the FAQ process. To understand the requirements of the ACR nuclear medicine accreditation program, and the role of the physicist in annual equipment surveys and the set up and supervision of the routine QC program. To understand the current ACR MAP Accreditation requirement and present the concepts and structure of the forthcoming ACR Digital Mammography QC Manual and Program. 17. MO-AB-207-00: ACR Update in MR, CT, Nuclear Medicine, and Mammography SciTech Connect 2015-06-15 A goal of an imaging accreditation program is to ensure adequate image quality, verify appropriate staff qualifications, and to assure patient and personnel safety. Currently, more than 35,000 facilities in 10 modalities have been accredited by the American College of Radiology (ACR), making the ACR program one of the most prolific accreditation options in the U.S. In addition, ACR is one of the accepted accreditations required by some state laws, CMS/MIPPA insurance and others. Familiarity with the ACR accreditation process is therefore essential to clinical diagnostic medical physicists. Maintaining sufficient knowledge of the ACR program must include keeping up-to-date as the various modality requirements are refined to better serve the goals of the program and to accommodate newer technologies and practices. This session consists of presentations from authorities in four ACR accreditation modality programs, including magnetic resonance imaging, computed tomography, nuclear medicine, and mammography. Each speaker will discuss the general components of the modality program and address any recent changes to the requirements. Learning Objectives: To understand the requirements of the ACR MR Accreditation program. The discussion will include accreditation of whole-body general purpose magnets, dedicated extremity systems well as breast MRI accreditation. Anticipated updates to the ACR MRI Quality Control Manual will also be reviewed. To understand the requirements of the ACR CT accreditation program, including updates to the QC manual as well as updates through the FAQ process. To understand the requirements of the ACR nuclear medicine accreditation program, and the role of the physicist in annual equipment surveys and the set up and supervision of the routine QC program. To understand the current ACR MAP Accreditation requirement and present the concepts and structure of the forthcoming ACR Digital Mammography QC Manual and Program. 18. Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics John, Christopher; Spura, Thomas; Habershon, Scott; Kühne, Thomas D. 2016-04-01 We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems. 19. Ab initio nuclear many-body perturbation calculations in the Hartree-Fock basis Hu, B. S.; Xu, F. R.; Sun, Z. H.; Vary, J. P.; Li, T. 2016-07-01 Starting from realistic nuclear forces, the chiral N3LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, 4He and 16O. The two-body N3LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the antisymmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation probabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available and find good agreement. This supports the conclusion that our methods produce reasonably converged results with these interactions. We also compare our results with experimental data. 20. The Role of Anharmonicity and Nuclear Quantum Effects in the Pyridine Molecular Crystal: An ab initio Molecular Dynamics Study Ko, Hsin-Yu; Distasio, Robert A., Jr.; Santra, Biswajit; Car, Roberto Molecular crystal structure prediction has posed a substantial challenge to first-principles methods and requires sophisticated electronic structure methods to determine the stabilities of nearly degenerate polymorphs. In this work, we demonstrate that the anharmonicity from van der Waals interactions is relevant to the finite-temperature structures of pyridine and pyridine-like molecular crystals. Using such an approach, we find that the equilibrium structures are well captured with classical ab initio molecular dynamics (AIMD), despite the presence of light atoms such as hydrogen. Employing path integral AIMD simulations, we demonstrate that the success of classical AIMD results from a separation of nuclear quantum effects between the intermolecular and intramolecular degrees of freedom. In this separation, the quasiclassical and anharmonic intermolecular degrees of freedom determine the equilibrium structure, while the quantum and harmonic intramolecular degrees of freedom are averaging to the correct intramolecular structure. This work has been supported by the Department of Energy under Grants No. DE-FG02-05ER46201 and DE-SC0008626. 1. Vibrational circular dichroism from ab initio molecular dynamics and nuclear velocity perturbation theory in the liquid phase. PubMed Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel 2016-08-28 We report the first fully ab initio calculation of dynamical vibrational circular dichroism spectra in the liquid phase using nuclear velocity perturbation theory (NVPT) derived electronic currents. Our approach is rigorous and general and thus capable of treating weak interactions of chiral molecules as, e.g., chirality transfer from a chiral molecule to an achiral solvent. We use an implementation of the NVPT that is projected along the dynamics to obtain the current and magnetic dipole moments required for accurate intensities. The gauge problem in the liquid phase is resolved in a twofold approach. The electronic expectation values are evaluated in a distributed origin gauge, employing maximally localized Wannier orbitals. In a second step, the gauge invariant spectrum is obtained in terms of a scaled molecular moments, which allows to systematically include solvent effects while keeping a significant signal-to-noise ratio. We give a thorough analysis and discussion of this choice of gauge for the liquid phase. At low temperatures, we recover the established double harmonic approximation. The methodology is applied to chiral molecules ((S)-d2-oxirane and (R)-propylene-oxide) in the gas phase and in solution. We find an excellent agreement with the theoretical and experimental references, including the emergence of signals due to chirality transfer from the solute to the (achiral) solvent. 2. Nuclear Quantum Effects in Liquid Water: A Highly Accurate ab initio Path-Integral Molecular Dynamics Study Distasio, Robert A., Jr.; Santra, Biswajit; Ko, Hsin-Yu; Car, Roberto 2014-03-01 In this work, we report highly accurate ab initio path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (via the colored-noise generalized Langevin equation). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation, in light of the experimental deep inelastic neutron scattering (DINS) measurements. DOE: DE-SC0008626, DOE: DE-SC0005180. 3. Modelling the local atomic structure of molybdenum in nuclear waste glasses with ab initio molecular dynamics simulations SciTech Connect None, None 2016-01-01 The nature of chemical bonding of molybdenum in high level nuclear waste glasses has been elucidated by ab initio molecular dynamics simulations. Two compositions, (SiO2)57.5 – (B2O3)10 – (Na2O)15 – (CaO)15 – (MoO3)2.5 and (SiO2)57.3 – (B2O3)20 – (Na2O)6.8 – (Li2O)13.4 – (MoO3)2.5 , were considered in order to investigate the effect of ionic and covalent components on the glass structure and the formation of the crystallisation precursors (Na2MoO4 and CaMoO4). The coordination environments of Mo cations and the corresponding bond lengths calculated from our model are in excellent agreement with experimental observations. The analysis of the first coordination shell reveals two different types of molybdenum host matrix bonds in the lithium sodium borosilicate glass. Based on the structural data and the bond valence model, we demonstrate that the Mo cation can be found in a redox state and the molybdate tetrahedron can be connected with the borosilicate network in a way that inhibits the formation of crystalline molybdates. These results significantly extend our understanding of bonding in Mo-containing nuclear waste glasses and demonstrate that tailoring the glass composition to specific heavy metal constituents can facilitate incorporation of heavy metals at high concentrations. K.K. was supported through the Impact Studentship scheme at UCL co-funded by the IHI Corporation and UCL. P.V.S. thanks the Royal Society, which supported preliminary work on this project, and the Laboratory Directed Research and Development program at PNNL, a multiprogram national laboratory operated by Battelle for the U.S. Department of Energy. Via our membership of the UK's HEC Materials Chemistry Consortium, which is funded by EPSRC (EP/L000202), this work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk). 4. Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning. PubMed Pandey, Manoj Kumar; Krishnan, Mangala Sunder 2010-11-07 Spin dynamics under magic angle spinning has been studied using different theoretical approaches and also by extensive numerical simulation programs. In this article we present a general theoretical approach that leads to analytic forms for effective Hamiltonians for an N-spin dipolar and quadrupolar coupled system under magic angle spinning (MAS) conditions, using a combination of Floquet theory and van Vleck (contact) transformation. The analytic forms presented are shown to be useful for the study of MAS spin dynamics in solids with the help of a number of simulations in two, three, and four coupled, spin-1/2 systems as well as spins in which quadrupolar interactions are also present. 5. Path Integrals and Hamiltonians Baaquie, Belal E. 2014-03-01 1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index. 6. Branched Hamiltonians and supersymmetry DOE PAGES Curtright, Thomas L.; Zachos, Cosmas K. 2014-03-21 Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail. 7. Supersymmetry of tridiagonal Hamiltonians Yamani, Hashim A.; Mouayn, Zouhair 2014-07-01 A positive semi-definite Hamiltonian H that has a tridiagonal matrix representation in a basis set, allows a definition of forward- and backward-shift operators that can be used to define the matrix representation of its supersymmetric partner Hamiltonian H( + ) with respect to the same basis. We find explicit relationships connecting the matrix elements of both Hamiltonians. We present a method to obtain the orthogonal polynomials in the eigenstate expansion problem attached to H( + ) starting from those polynomials arising in the same problem for H. This connection is established by using the notion of kernel polynomials. We apply the obtained results to two known solvable models with different kinds of spectrum. 8. Dynamical supersymmetric Dirac Hamiltonians SciTech Connect Ginocchio, J.N. 1986-01-01 Using the language of quantum electrodynamics, the Dirac Hamiltonian of a neutral fermion interacting with a tensor field is examined. A supersymmetry found for a general Dirac Hamiltonian of this type is discussed, followed by consideration of the special case of a harmonic electric potential. The square of the Dirac Hamiltonian of a neutral fermion interacting via an anomalous magnetic moment in an electric potential is shown to be equivalent to a three-dimensional supersymmetric Schroedinger equation. It is found that for a potential that grows as a power of r, the lowest energy of the Hamiltonian equals the rest mass of the fermion, and the Dirac eigenfunction has only an upper component which is normalizable. It is also found that the higher energy states have upper and lower components which form a supersymmetric doublet. 15 refs. (LEW) 9. Stimulated Raman signals at conical intersections: Ab initio surface hopping simulation protocol with direct propagation of the nuclear wave function. PubMed Kowalewski, Markus; Mukamel, Shaul 2015-07-28 Femtosecond Stimulated Raman Spectroscopy (FSRS) signals that monitor the excited state conical intersections dynamics of acrolein are simulated. An effective time dependent Hamiltonian for two C-H vibrational marker bands is constructed on the fly using a local mode expansion combined with a semi-classical surface hopping simulation protocol. The signals are obtained by a direct forward and backward propagation of the vibrational wave function on a numerical grid. Earlier work is extended to fully incorporate the anharmonicities and intermode couplings. 10. Stimulated Raman signals at conical intersections: Ab initio surface hopping simulation protocol with direct propagation of the nuclear wave function SciTech Connect Kowalewski, Markus Mukamel, Shaul 2015-07-28 Femtosecond Stimulated Raman Spectroscopy (FSRS) signals that monitor the excited state conical intersections dynamics of acrolein are simulated. An effective time dependent Hamiltonian for two C—H vibrational marker bands is constructed on the fly using a local mode expansion combined with a semi-classical surface hopping simulation protocol. The signals are obtained by a direct forward and backward propagation of the vibrational wave function on a numerical grid. Earlier work is extended to fully incorporate the anharmonicities and intermode couplings. 11. Ab initio path integral simulations for the fluoride ion-water clusters: competitive nuclear quantum effect between F(-)-water and water-water hydrogen bonds. PubMed Kawashima, Yukio; Suzuki, Kimichi; Tachikawa, Masanori 2013-06-20 Small hydrated fluoride ion complexes, F(-)(H2O)n (n = 1-3), have been studied by ab initio hybrid Monte Carlo (HMC) and ab initio path integral hybrid Monte Carlo (PIHMC) simulations. Because of the quantum effect, our simulation shows that the average hydrogen-bonded F(-)···HO distance in the quantum F(-)(H2O) is shorter than that in the classical one, while the relation inverts at the three water molecular F(-)(H2O)3 cluster. In the case of F(-)(H2O)3, we have found that the nuclear quantum effect enhances the formation of hydrogen bonds between two water molecules. In F(-)(H2O)2 and F(-)(H2O)3, the nuclear quantum effect on two different kinds of hydrogen bonds, F(-)-water and water-water hydrogen bonds, competes against each other. In F(-)(H2O)3, thus, the nuclear quantum effect on the water-water hydrogen bond leads to the elongation of hydrogen-bonded F(-)···HO distance, which we suggest this as the possible origin of the structural inversion from F(-)(H2O) to F(-)(H2O)3. 12. Nuclear polarization corrections to the μ4He+ Lamb shift. PubMed Ji, C; Nevo Dinur, N; Bacca, S; Barnea, N 2013-10-04 Stimulated by the proton radius conundrum, measurements of the Lamb shift in various light muonic atoms are planned at PSI. The aim is to extract the rms charge radius with high precision, limited by the uncertainty in the nuclear polarization corrections. We present an ab initio calculation of the nuclear polarization for μ(4)He(+) leading to an energy correction in the 2S-2P transitions of δ(pol)(A)=-2.47 meV ±6%. We use two different state-of-the-art nuclear Hamiltonians and utilize the Lorentz integral transform with hyperspherical harmonics expansion as few-body methods. We take into account the leading multipole contributions, plus Coulomb, relativistic, and finite-nucleon-size corrections. Our main source of uncertainty is the nuclear Hamiltonian, which currently limits the attainable accuracy. Our predictions considerably reduce the uncertainty with respect to previous estimates and should be instrumental to the μ(4)He(+) experiment planned for 2013. 13. Allene and pentatetraene cations as models for intramolecular charge transfer: vibronic coupling Hamiltonian and conical intersections. PubMed Markmann, Andreas; Worth, Graham A; Cederbaum, Lorenz S 2005-04-08 We consider the vibronic coupling effects involving cationic states with degenerate components that can be represented as charge localized at either end of the short cumulene molecules allene and pentatetraene. Our aim is to simulate dynamically the charge transfer process when one component is artificially depopulated. We model the Jahn-Teller vibronic interaction within these states as well as their pseudo-Jahn-Teller coupling with some neighboring states. For the manifold of these states, we have calculated cross sections of the ab initio adiabatic potential energy surfaces along all nuclear degrees of freedom, including points at large distances from the equilibrium to increase the physical significance of our model. Ab initio calculations for the cationic states of allene and pentatetraene were based on the fourth-order Møller-Plesset method and the outer valence Green's function method. In some cases we had to go beyond this method and use the more involved third-order algebraic diagrammatic construction method to include intersections with satellite states. The parameters for a five-state, all-mode diabatic vibronic coupling model Hamiltonian were least-square fitted to these potentials. The coupling parameters for the diabatic model Hamiltonian are such that, in comparison to allene, an enhanced preference for indirect charge transfer is predicted for pentatetraene. 14. Determination of nuclear quadrupole moments – An example of the synergy of ab initio calculations and microwave spectroscopy SciTech Connect 2015-01-22 Highly correlated scalar relativistic calculations of electric field gradients at nuclei in diatomic molecules in combination with accurate nuclear quadrupole coupling constants obtained from microwave spectroscopy are used for determination of nuclear quadrupole moments. 15. Stochastic surrogate Hamiltonian Katz, Gil; Gelman, David; Ratner, Mark A.; Kosloff, Ronnie 2008-07-01 The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath. 16. Stochastic surrogate Hamiltonian SciTech Connect Katz, Gil; Kosloff, Ronnie; Gelman, David; Ratner, Mark A. 2008-07-21 The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath. 17. Experimental quantum Hamiltonian learning Wang, Jianwei; Paesani, Stefano; Santagati, Raffaele; Knauer, Sebastian; Gentile, Antonio A.; Wiebe, Nathan; Petruzzella, Maurangelo; O'Brien, Jeremy L.; Rarity, John G.; Laing, Anthony; Thompson, Mark G. 2017-06-01 The efficient characterization of quantum systems, the verification of the operations of quantum devices and the validation of underpinning physical models, are central challenges for quantum technologies and fundamental physics. The computational cost of such studies could be improved by machine learning enhanced by quantum simulators. Here we interface two different quantum systems through a classical channel--a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre--and use the former to learn the Hamiltonian of the latter via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately 10-5. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model. We implement an interactive version of the protocol and experimentally show its ability to characterize the operation of the quantum photonic device. 18. Machine-learned approximations to Density Functional Theory Hamiltonians PubMed Central Hegde, Ganesh; Bowen, R. Chris 2017-01-01 Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471 19. Machine-learned approximations to Density Functional Theory Hamiltonians Hegde, Ganesh; Bowen, R. Chris 2017-02-01 Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. 20. Machine-learned approximations to Density Functional Theory Hamiltonians. PubMed Hegde, Ganesh; Bowen, R Chris 2017-02-15 Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. 1. Hamiltonian Engineering for High Fidelity Quantum Operations Ribeiro, Hugo; Baksic, Alexandre; Clerk, Aashish High-fidelity gates and operations are crucial to almost every aspect of quantum information processing. In recent experiments, fidelity is mostly limited by unwanted couplings with states living out of the logical subspace. This results in both leakage and phase errors. Here, we present a general method to deal simultaneously with both these issues and improve the fidelity of quantum gates and operations. Our method is applicable to a wide variety of systems. As an example, we can correct gates for superconducting qubits, improve coherent state transfer between a single NV centre electronic spin and a single nitrogen nuclear spin, improve control over a nuclear spin ensemble, etc. Our method is intimately linked to the Magnus expansion. By modifying the Magnus expansion of an initially given Hamiltonian Hi, we find analytically additional control Hamiltonians Hctrl such that Hi +Hctrl leads to the desired gate while minimizing both leakage and phase errors. 2. Which grids are Hamiltonian SciTech Connect Hedetniemi, S. M.; Hedetniemi, S. T.; Slater, P. J. 1980-01-01 A complete grid G/sub m,n/ is a graph having m x n pertices that are connected to form a rectangular lattice in the plane, i.e., all edges of G/sub m,n/ connect vertices along horizontal or vertical lines. A grid is a subgraph of a complete grid. As an illustration, complete grids describe the basic pattern of streets in most cities. This paper examines the existence of Hamiltonian cycles in complete grids and complete grids with one or two vertices removed. It is determined for most values of m,n greater than or equal to 1, which grids G/sub m,n/ - (u) and G/sub m,n/ - (u,v) are Hamiltonian. 12 figures. (RWR) 3. Hamiltonian spinfoam gravity Wieland, Wolfgang M. 2014-01-01 This paper presents a Hamiltonian formulation of spinfoam gravity, which leads to a straightforward canonical quantization. To begin with, we derive a continuum action adapted to a simplicial decomposition of space-time. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise—in the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may still miss an additional constraint. Finally, we canonically quantize and recover the EPRL (Engle-Pereira-Rovelli-Livine) face amplitudes. Communicated by P R L V Moniz 4. An electromechanical Ising Hamiltonian PubMed Central Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi 2016-01-01 Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling. PMID:28861469 5. Approximate symmetries of Hamiltonians Chubb, Christopher T.; Flammia, Steven T. 2017-08-01 We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest. 6. Chaotic Hamiltonian Dynamics. Bialek, James Mark Chaotic behavior may be observed in deterministic Hamiltonian Systems with as few as three dimensions, i.e., X, P, and t. The amount of chaotic behavior depends on the relative influence of the integrable and non-integrable parts of the Hamiltonian. The Standard Map is such a system and the amount of chaotic behavior may be varied by adjusting a single parameter. The global phase space portrait is a complicated mixture of quiescent and chaotic regions. First a new calculational method, characterized by a Fractal Diagram, is presented. This allows the quantitative prediction of the boundaries between regular and chaotic regions in phase space. Where these barriers are located gives qualitative insight into diffusion in phase space. The method is illustrated with the Standard Map but may be applied to any Hamiltonian System. The second phenomenon is the Universal Behavior predicted to occur for all area preserving maps. As a parameter is varied causing the mapping to become more chaotic a pattern is observed in the location and stability of the fixed points of the maps. The fixed points undergo an infinite sequence of period doubling bifurcations in a finite range of the parameter. The relative locations of the fixed point bifurcation and the parameter intervals between bifurcations both asymptotically approach constants which are Universal in that the same constants keep appearing in different problems. Predictions of Universal Behavior have been based on the study of algebraic mappings. The problem we examine has a Hamiltonian given by H = p^2 over {2} - lambda over{2pi}sin(2pi x)sin(2pit). This Hamiltonian describes the motion of a compass needle in a sinusoidally varying magnetic field or, equally well, the one dimensional motion of a particle in a standing wave potential. By treating the magnitude(lambda ) of the time dependent potential as a parameter and by examining the trajectories of the system in a Poincare surface of section, the resulting differential 7. Hamiltonian cosmology of bigravity Soloviev, V. O. 2017-03-01 This article is written as a review of the Hamiltonian formalism for the bigravity with de Rham-Gabadadze-Tolley (dRGT) potential, and also of applications of this formalism to the derivation of the background cosmological equations. It is demonstrated that the cosmological scenarios are close to the standard ΛCDM model, but they also uncover the dynamical behavior of the cosmological term. This term arises in bigravity regardless on the choice of the dRGT potential parameters, and its scale is given by the graviton mass. Various matter couplings are considered. 8. Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of ^{99}Ru and ^{101}Ru Mishra, S. N. 2017-08-01 The nuclear quadrupole moments, Q, for the ground and first excited states in ^{99}Ru and ground state of ^{101}Ru have been determined by comparing the experimentally observed quadrupole interaction frequencies ν _Q with calculated electric field gradient (EFG) for a large number of Ru-based compounds. The ab-initio calculations of EFG were performed using the all-electron augmented plane wave + local orbital (APW + lo) method of the density functional theory (DFT). From the slope of the linear correlation between theoretically calculated EFGs and experimentally observed ν _Q, we obtain the quadrupole moment for the (5/2^+) ground state in ^{99}Ru and ^{101}Ru as 0.0734(17) b and 0.431(14) b respectively, showing excellent agreement with the values reported in literature. For 3/2^+, the quadrupole moment of the first excited state in ^{99}Ru is obtained as +0.203(3) b, which is considerably lower than the commonly accepted literature value of +0.231(12) b. The results presented in this paper would be useful for the precise determination of quadrupole moment of high spin states in other Ru isotopes and is likely to stimulate further shell model calculations for an improved understanding of nuclear shape in these nuclei. 9. Nuclear Zero Point Effects as a Function of Density in Ice-like Structures and Liquid Water from vdW-DF Ab Initio Calculations Pamuk, Betül; Allen, Philip B.; Soler, Jose M.; Fernández-Serra, Marivi 2014-03-01 The contributions of nuclear zero point vibrations to the structures of liquid water and ice are not negligible. Recently, we have explained the source of an anomalous isotope shift in hexagonal ice, representing itself as an increase in the lattice volume when H is replaced by D, by calculating free energy within the quasiharmonic approximation, with ab initio density functional theory. In this work, we extend our studies to analyze the zero point effect in other ice-like structures under different densities: clathrate hydrates, LDL and HDL-like amorphous ices with different densities, and a highly dense ice phase, ice VIII. We show that there is a transition from anomalous isotope effect to normal isotope effect as the density increases. We also analyze nuclear zero point effects in liquid water using different vdW-DFs and make connections to this anomalous-normal isotope effect transition in ice. This work is supported by DOE Early Career Award No. DE-SC0003871. 10. Hamiltonian light-front field theory in a basis function approach SciTech Connect Vary, J. P.; Honkanen, H.; Li Jun; Maris, P.; Brodsky, S. J.; Harindranath, A.; Sternberg, P.; Ng, E. G.; Yang, C. 2010-03-15 Hamiltonian light-front quantum field theory constitutes a framework for the nonperturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories is obtained that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present illustrative features of some noninteracting systems in a cavity. We illustrate the first steps toward solving quantum electrodynamics (QED) by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges. 11. Ab initio studies of the nuclear magnetic resonance chemical shifts of a rare gas atom in a zeolite Jameson, Cynthia J.; Lim, Hyung-Mi 1995-09-01 The intermolecular chemical shift of a rare gas atom inside a zeolite cavity is calculated by ab initio analytical derivative theory using gauge-including atomic orbitals (GIAO) at the Ar atom and the atoms of selected neutral clusters each of which is a 4-, 6-, or 8-ring fragment of the zeolite cage. The Si, Al, O atoms and the charge-balancing counterions (Na+, K+, Ca2+) of the clusters (from 24 to 52 atoms) are at coordinates taken from the refined single crystal x-ray structure of the NaA, KA, and CaA zeolites. Terminating OH groups place the H atom at an appropriate O-H distance along the bond to the next Si or Al atom in the crystal. The chemical shift of the Ar atom located at various positions relative to the cluster is calculated using Boys-Bernardi counterpoise correction at each position. The dependence of the rare gas atom chemical shift on the Al/Si ratio of the clusters is investigated. The resulting shielding values are fitted to a pairwise additive form to elicit effective individual Ar-O, Ar-Na, Ar-K, Ar-Ca intermolecular shielding functions of the form σ(39Ar, Ar...Ozeol)= a6r-6+a8r-8+a10r-10+a12r -12, where r is the distance between the Ar and the O atom. A similar form is used for the counterions. The dependence of the Ar shielding on the Al/Si ratio is established (the greater the Al content, the higher the Ar chemical shift), which is in agreement with the few experimental cases where the dependence of the 129Xe chemical shift on the Al/Si ratio of the zeolite has been observed. 12. Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: The Interplay of Nuclear and Electronic Quantum Effects. PubMed Marsalek, Ondrej; Markland, Thomas E 2017-04-06 Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with on-the-fly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lower-level density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments. 13. Drift Hamiltonian in magnetic coordinates SciTech Connect White, R.B.; Boozer, A.H.; Hay, R. 1982-02-01 A Hamiltonian formulation of the guiding-center drift in arbitrary, steady state, magnetic and electric fields is given. The canonical variables of this formulation are simply related to the magnetic coordinates. The modifications required to treat ergodic magnetic fields using magnetic coordinates are explicitly given in the Hamiltonian formulation. 14. Robust online Hamiltonian learning Granade, Christopher E.; Ferrie, Christopher; Wiebe, Nathan; Cory, D. G. 2012-10-01 In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance. 15. Heterogeneous nuclear ribonucleoprotein A/B and G inhibits the transcription of gonadotropin-releasing-hormone 1 PubMed Central Zhao, Sheng; Korzan, Wayne J.; Chen, Chun-Chun; Fernald, Russell D. 2008-01-01 Gonadotropin releasing hormone 1 (GnRH1) causes the release of gonadotropins from the pituitary to control reproduction. Here we report that two heterogeneous nuclear ribonucleoproteins (hnRNP-A/B and hnRNP-G) bind to the GnRH-I upstream promoter region in a cichlid fish, Astatotilapia burtoni. We identified these binding proteins using a newly developed homology based method of mass spectrometric peptide mapping. We show that both hnRNP-A/B and hnRNP-G co-localize with GnRH1 in the pre-optic area of the hypothalamus in the brain. We also demonstrated that these ribonucleoproteins exhibit similar binding capacity in vivo, using immortalized mouse GT1-7 cells where overexpression of either hnRNP-A/B or hnRNP-G significantly down-regulate GnRH1 mRNA levels in GT1-7 cells, suggesting that both act as repressors in GnRH1 transcriptional regulation. PMID:17920292 16. Ab initio no core shell model SciTech Connect Barrett, Bruce R.; Navrátil, Petr; Vary, James P. 2012-11-17 A long-standing goal of nuclear theory is to determine the properties of atomic nuclei based on the fundamental interactions among the protons and neutrons (i.e., nucleons). By adopting nucleon-nucleon (NN), three-nucleon (NNN) and higher-nucleon interactions determined from either meson-exchange theory or QCD, with couplings fixed by few-body systems, we preserve the predictive power of nuclear theory. This foundation enables tests of nature's fundamental symmetries and offers new vistas for the full range of complex nuclear phenomena. Basic questions that drive our quest for a microscopic predictive theory of nuclear phenomena include: (1) What controls nuclear saturation; (2) How the nuclear shell model emerges from the underlying theory; (3) What are the properties of nuclei with extreme neutron/proton ratios; (4) Can we predict useful cross sections that cannot be measured; (5) Can nuclei provide precision tests of the fundamental laws of nature; and (6) Under what conditions do we need QCD to describe nuclear structure, among others. Along with other ab initio nuclear theory groups, we have pursued these questions with meson-theoretical NN interactions, such as CD-Bonn and Argonne V18, that were tuned to provide high-quality descriptions of the NN scattering phase shifts and deuteron properties. We then add meson-theoretic NNN interactions such as the Tucson-Melbourne or Urbana IX interactions. More recently, we have adopted realistic NN and NNN interactions with ties to QCD. Chiral perturbation theory within effective field theory ({chi}EFT) provides us with a promising bridge between QCD and hadronic systems. In this approach one works consistently with systems of increasing nucleon number and makes use of the explicit and spontaneous breaking of chiral symmetry to expand the strong interaction in terms of a dimensionless constant, the ratio of a generic small momentum divided by the chiral symmetry breaking scale taken to be about 1 GeV/c. The resulting NN 17. Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: momentum representation, coupled electron-nuclear dynamics, and external fields. PubMed Pacheco, Alexander B; Iyengar, Srinivasan S 2011-02-21 We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al(27) - C(7) - Al(27) nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed. 18. Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: Momentum representation, coupled electron-nuclear dynamics, and external fields Pacheco, Alexander B.; Iyengar, Srinivasan S. 2011-02-01 We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al27 - C7 - Al27 nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed. 19. Nuclear, Virescent Mutants of Zea mays L. with High Levels of Chlorophyll (a/b) Light-Harvesting Complex during Thylakoid Assembly 1 PubMed Central Polacco, Mary L.; Chang, M. T.; Neuffer, M. Gerald 1985-01-01 We have found nuclear, recessive mutants in Zea mays L. where assembly of the major chlorophyll (a/b) light-harvesting complex (LHC) was not delayed relative to most other thylakoid protein complexes during thylakoid biogenesis. This contrasts with the normal development of maize chloroplasts (NR Baker, R Leech 1977 Plant Physiol 60: 640-644). All four mutants examined were allelic and virescent, and displayed visibly higher yields of leaf Chl fluorescence during greening. Fully greened mutants had normal leaf Chl fluorescence yield and normal levels of LHC, and grew to maturity under field conditions. Therefore, delayed LHC assembly is not an obligate feature of thylakoid differentiation. Assigning the molecular basis for the mutation should provide information concerning reguation of LHC assembly. Several possibilities are discussed. The pleiotropic mutant phenotype is not attributable to defects in thylakoid glycerolipid synthesis. Thylakoids isolated from greening mutant leaf sections had elevated glycerolipid/Chl ratios. In addition, both the molar distribution and acyl composition of four major glycerolipids were normal for developing mutant thylakoids. Images Fig. 2 PMID:16664140 20. Nuclear, Virescent Mutants of Zea mays L. with High Levels of Chlorophyll (a/b) Light-Harvesting Complex during Thylakoid Assembly. PubMed Polacco, M L; Chang, M T; Neuffer, M G 1985-04-01 We have found nuclear, recessive mutants in Zea mays L. where assembly of the major chlorophyll (a/b) light-harvesting complex (LHC) was not delayed relative to most other thylakoid protein complexes during thylakoid biogenesis. This contrasts with the normal development of maize chloroplasts (NR Baker, R Leech 1977 Plant Physiol 60: 640-644). All four mutants examined were allelic and virescent, and displayed visibly higher yields of leaf Chl fluorescence during greening. Fully greened mutants had normal leaf Chl fluorescence yield and normal levels of LHC, and grew to maturity under field conditions. Therefore, delayed LHC assembly is not an obligate feature of thylakoid differentiation.Assigning the molecular basis for the mutation should provide information concerning reguation of LHC assembly. Several possibilities are discussed. The pleiotropic mutant phenotype is not attributable to defects in thylakoid glycerolipid synthesis. Thylakoids isolated from greening mutant leaf sections had elevated glycerolipid/Chl ratios. In addition, both the molar distribution and acyl composition of four major glycerolipids were normal for developing mutant thylakoids. 1. Effective Hamiltonians for phosphorene and silicene DOE PAGES Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; ... 2015-02-01 We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene.We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, itmore » is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector.We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k · p parameters.« less 2. Effective Hamiltonians for phosphorene and silicene SciTech Connect Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; Zhang, Y.; Willatzen, M. 2015-02-01 We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene.We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector.We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k · p parameters. 3. Effective Hamiltonians of polymethineimine, polyazine and polyazoethene: A density matrix variation approach Chen, GuanHua; Su, ZhongMin; Shen, ZhenWen; Yan, YiJing 1998-08-01 A new variation method is proposed to determine the effective Hamiltonians for conjugated π-electron systems. This method is based on the minimization of the difference between the ground state reduced single electron density matrix calculated from the effective Hamiltonian and its ab initio counterpart under a set of well-defined constraints. Applications are made to various oligomers of polymethineimine (PMI), polyazine (PAZ) and polyazoethene (PAE) at the Hartree-Fock level. Calculated are also the optical gaps of these oligomers. The effective Hamiltonians contain electron-electron Coulomb interactions and are suitable for the study of excited state dynamic processes such as nonlinear optical properties in π-conjugated systems. 4. A partial Hamiltonian approach for current value Hamiltonian systems Naz, R.; Mahomed, F. M.; Chaudhry, Azam 2014-10-01 We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions. 5. Robust Online Hamiltonian Learning Granade, Christopher; Ferrie, Christopher; Wiebe, Nathan; Cory, David 2013-05-01 In this talk, we introduce a machine-learning algorithm for the problem of inferring the dynamical parameters of a quantum system, and discuss this algorithm in the example of estimating the precession frequency of a single qubit in a static field. Our algorithm is designed with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online, during experimental data collection, or can be used as a tool for post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. Finally, we discuss the performance of the our algorithm by appeal to the Cramer-Rao bound. This work was financially supported by the Canadian government through NSERC and CERC and by the United States government through DARPA. NW would like to acknowledge funding from USARO-DTO. 6. Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians Subasi, Yigit; Jarzynski, Christopher The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l < k . This technique works best for Hamiltonians with a few interactions with very large k and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C. 7. Solutions of the Bohr Hamiltonian, a compendium Fortunato, L. 2005-10-01 The Bohr Hamiltonian, also called collective Hamiltonian, is one of the cornerstones of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the V(β,γ) potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in γ-unstable and γ-stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei. 8. Collective Hamiltonian for wobbling modes Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.; Meng, J. 2014-10-01 The simple, longitudinal, and transverse wobblers are systematically studied within the framework of a collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach. Solving the collective Hamiltonian by diagonalization, the energies and the wave functions of the wobbling states are obtained. The obtained results are compared with those by the harmonic approximation formula and particle rotor model. The wobbling energies calculated by the collective Hamiltonian are closer to the exact solutions by the particle rotor model than the harmonic approximation formula. It is confirmed that the wobbling frequency increases with the rotational frequency in simple and longitudinal wobbling motions while decreases in transverse wobbling motion. These variation trends are related to the stiffness of the collective potential in the collective Hamiltonian. 9. Time-dependent drift Hamiltonian SciTech Connect Boozer, A.H. 1983-03-01 The lowest-order drift equations are given in a canonical magnetic coordinate form for time-dependent magnetic and electric fields. The advantages of the canonical Hamiltonian form are also discussed. 10. Hamiltonian description of the ideal fluid SciTech Connect Morrison, P.J. 1994-01-01 Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems. 11. Hamiltonian formulation of general relativity. Teitelboim, Claudio The following sections are included: * INTRODUCTION * HAMILTONIAN FORMULATION OF GAUGE THEORIES (PRE-BRST) * BRST HAMILTONIAN FORMULATION OF GAUGE THEORIES * DYNAMICS OF GRAVITATIONAL FIELD * DOES THE HAMILTONIAN VANISH? GENERAL COVARIANCE AS AN "ORDINARY" GAUGE INVARIANCE * GENERALLY COVARIANT SYSTEMS * TIME AS A CANONICAL VARIABLE. ZERO HAMILTONIAN * Parametrized Systems * Zero Hamiltonian * Parametrization and Explicit Time Dependence * TIME REPARAMETRIZATION INVARIANCE * Form of Gauge Transformations * Must the Hamiltonian be Zero for a Generally Covariant System? * Simple Example of a Generally Covariant System with a Nonzero Hamiltonian * "TRUE DYNAMICS" VERSUS GAUGE TRANSFORMATIONS * Interpretation of the Formalism * Reduced Phase Space * MUST TIME FLOW? * GAUGE INDEPENDENCE OF PATH INTEGRAL FOR A PARAMETRIZED SYSTEM ILLUSTRATED. EQUIVALENCE OF THE GAUGES t = τ AND t = 0 * Reduced Phase Space Transition Amplitude as a Reduced Phase Space Path Integral * Canonical Gauge Conditions * Gauge t = 0 * Gauge t α τ * BRST CHARGE OF GRAVITATIONAL FIELD * ELEMENTS OF BRST THEORY * THE GHOST, YOU'VE COME A LONG WAY BABY * Introduction * Quantum mechanics, the art of finding and combining simple elementary processes * Ghosts necessary to keep elementary processes simple * BRST symmetry: ghosts and matter become different components of single geometrical object * BRST SYMMETRY IN CLASSICAL MECHANICS * Ghosts have role in classical mechanics * Gauge invariance and constraints * Classical mechanics over Grassmann algebra necessary * Higher order structure functions * Rank defined. Open algebras * Ghosts. Ghost number. BRST generator as generating function for structure functions * A belianization of constraints. Existence of Ω * Uniqueness of Ω * Classical BRST cohomology * QUANTUM BRST THEORY * States and operators * Ghost number * BRST invariant states * Quantum BRST cohomology * Equivalence of the BRST physical subspace with the conventional gauge 12. Ab-Initio Shell Model with a Core SciTech Connect Lisetskiy, A F; Barrett, B R; Kruse, M; Navratil, P; Stetcu, I; Vary, J P 2008-06-04 We construct effective 2- and 3-body Hamiltonians for the p-shell by performing 12{h_bar}{Omega} ab initio no-core shell model (NCSM) calculations for A=6 and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0{h_bar}{Omega} space. We then separate these effective Hamiltonians into 0-, 1- and 2-body contributions (also 3-body for A=7) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective 3- and higher-body interactions for A > 6 is investigated and discussed. 13. Hamiltonian approach to frame dragging Epstein, Kenneth J. 2008-07-01 A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson-Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials. 14. Three-cluster dynamics within an ab initio framework DOE PAGES Quaglioni, Sofia; Romero-Redondo, Carolina; Navratil, Petr 2013-09-26 In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to amore » 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.« less 15. Can we perturbatively expand the \\Qcirc -box in the Bloch-Horowitz Hamiltonian? Shimizu, Genki; Takayanagi, Kazuo; Otsuka, Takaharu 2014-09-01 In nuclear many-body problems, it is impossible to diagonalize the Hamiltonian directly because of the huge Hilbert space. We introduce, therefore, the concept of the effective interaction. We first partition the whole Hilbert space into the model space of tractable size and its complement, and then look for the effective Hamiltonian defined in the model space that reproduces exact eigenenergies and model space projections of the corresponding eigenstates. Effective Hamiltonians are categorized into energy-independent and energy-dependent groups. The energy-independent effective Hamiltonian has been calculated by iterative methods, and has been used widely for a long time. The energy-dependent effective Hamiltonian is known as the Bloch-Horowitz (BH) Hamiltonian. Though it requires a self-consistent solution, it can, in principle, give all the eigenenergies of the Hamiltonian, if provided with the exact BH Hamiltonian. In actual calculations, however, we can calculate the \\Qcirc -box only up to a finite order of perturbation expansion. In this work, we clarify its convergence condition and examine what we can obtain with the approximate BH Hamiltonian, and what we cannot. 16. Characterization of DNA sequences that mediate nuclear protein binding to the regulatory region of the Pisum sativum (pea) chlorophyl a/b binding protein gene AB80: identification of a repeated heptamer motif. PubMed Argüello, G; García-Hernández, E; Sánchez, M; Gariglio, P; Herrera-Estrella, L; Simpson, J 1992-05-01 Two protein factors binding to the regulatory region of the pea chlorophyl a/b binding protein gene AB80 have been identified. One of these factors is found only in green tissue but not in etiolated or root tissue. The second factor (denominated ABF-2) binds to a DNA sequence element that contains a direct heptamer repeat TCTCAAA. It was found that presence of both of the repeats is essential for binding. ABF-2 is present in both green and etiolated tissue and in roots and factors analogous to ABF-2 are present in several plant species. Computer analysis showed that the TCTCAAA motif is present in the regulatory region of several plant genes. 17. First principles of Hamiltonian medicine. PubMed Crespi, Bernard; Foster, Kevin; Úbeda, Francisco 2014-05-19 We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease. 18. First principles of Hamiltonian medicine PubMed Central Crespi, Bernard; Foster, Kevin; Úbeda, Francisco 2014-01-01 We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease. PMID:24686937 19. Hamiltonians defined by biorthogonal sets Bagarello, Fabio; Bellomonte, Giorgia 2017-04-01 In some recent papers, studies on biorthogonal Riesz bases have found renewed motivation because of their connection with pseudo-Hermitian quantum mechanics, which deals with physical systems described by Hamiltonians that are not self-adjoint but may still have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed in some previous papers. However, in many physical models, one has to deal not with orthonormal bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of G -quasi basis, and we show a series of conditions under which a definition of non-self-adjoint Hamiltonian with purely point real spectra is still possible. 20. Variational identities and Hamiltonian structures SciTech Connect Ma Wenxiu 2010-03-08 This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws. 1. Generalized James' effective Hamiltonian method Shao, Wenjun; Wu, Chunfeng; Feng, Xun-Li 2017-03-01 James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems. This method only corresponds to the second-order perturbation theory and cannot be exploited to treat problems which should be solved by using the third- or higher-order perturbation theory. In this paper, we generalize James' effective Hamiltonian method to the higher-order case. Using the method developed here, we reexamine two recently published examples [L. Garziano et al., Phys. Rev. Lett. 117, 043601 (2016), 10.1103/PhysRevLett.117.043601; Ken K. W. Ma and C. K. Law, Phys. Rev. A 92, 023842 (2015), 10.1103/PhysRevA.92.023842]; our results turn out to be the same as the original ones derived from the third-order perturbation theory and adiabatic elimination method, respectively. For some specific problems, this method can simplify the calculating procedure and the resultant effective Hamiltonian is more general. 2. Ab initio calculation of the potential bubble nucleus 34Si Duguet, T.; Somà, V.; Lecluse, S.; Barbieri, C.; Navrátil, P. 2017-03-01 the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in 34Si varies significantly with the nuclear Hamiltonian used. However, demanding that the experimental charge density distribution and the root-mean-square radius of 36S be well reproduced, along with 34Si and 36S binding energies, only leaves the NNLOsat Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of 34Si, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1 /2--3 /2- splitting in the spectrum of 35Si as compared to 37S. Conclusions: The occurrence of a bubble structure in the charge distribution of 34Si is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of 34Si in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on 34Si and 36S in order to further test our theoretical spectral strength distributions over a wide energy range. 3. Collective Hamiltonian for chiral modes Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.; Jolos, R. V.; Meng, J. 2013-02-01 A collective model is proposed to describe the chiral rotation and vibration and applied to a system with one h11/2 proton particle and one h11/2 neutron hole coupled to a triaxial rigid rotor. The collective Hamiltonian is constructed from the potential energy and mass parameter obtained in the tilted axis cranking approach. By diagonalizing the collective Hamiltonian with a box boundary condition, it is found that for the chiral rotation, the partner states become more degenerate with the increase of the cranking frequency, and for the chiral vibrations, their important roles for the collective excitation are revealed at the beginning of the chiral rotation region. 4. Quasilocal Hamiltonians in general relativity SciTech Connect Anderson, Michael T. 2010-10-15 We analyze the definition of quasilocal energy in general relativity based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular, the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasilocal energy in general relativity requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations. 5. Lowest eigenvalues of random Hamiltonians SciTech Connect Shen, J. J.; Zhao, Y. M.; Arima, A.; Yoshinaga, N. 2008-05-15 In this article we study the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues is applicable to many different systems. We improve the accuracy of the formula by considering the third central moment. We show that these formulas are applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions. 6. Remembering AB Belyayev, S. T. 2013-06-01 In 1947 I became a second-year student at Moscow State University's Physics and Engineering Department, where a part of the week's classes were taught at base organizations. Our group's base was the future Kurchatov Institute, at that time known as the mysterious "Laboratory N^circ 2," and later as LIPAN. . Besides group lectures and practical work at the experimental laboratories, we also had access to the general seminars which Igor Vasilyevich Kurchatov tried to hold, with Leonid Vasilyevich Groshev filling in when he was absent. At the seminar, theorists spoke as welcome co-presenters and commentators. In 1949 I felt ready to approach A. B. Migdal to ask if I could transfer to his theoretical sector. In response, he suggested a number of simple qualitative problems, which I then successfully solved. (Incidentally, AB used the very same "introductory problems" for screening many generations of students.) So I wound up among AB's students. From 1952 on (for 10 years) I also served as an employee of the Migdal Sector. My memoirs here are mainly inspired by these years of constant communication with AB. After my departure for Novosibirsk in 1962, although our meetings still took place, they became occasional.... 7. Operator evolution for ab initio electric dipole transitions of 4He DOE PAGES Schuster, Micah D.; Quaglioni, Sofia; Johnson, Calvin W.; ... 2015-07-24 A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopic internucleon forces. A major element of such an effort is applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of ab initio calculations as a function of the model space size. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for nonscalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity renormalization group method and apply the renormalized matrix elements to the calculationmore » of the 4He total photoabsorption cross section and electric dipole polarizability. All observables are calculated within the ab initio no-core shell model. Furthermore, we find that, although seemingly small, the effects of evolved operators on the photoabsorption cross section are comparable in magnitude to the correction produced by including the chiral three-nucleon force and cannot be neglected.« less 8. A Note on Hamiltonian Graphs ERIC Educational Resources Information Center Skurnick, Ronald; Davi, Charles; Skurnick, Mia 2005-01-01 Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian… 9. Derivation of Hamiltonians for accelerators SciTech Connect Symon, K.R. 1997-09-12 In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables. 10. A Note on Hamiltonian Graphs ERIC Educational Resources Information Center Skurnick, Ronald; Davi, Charles; Skurnick, Mia 2005-01-01 Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian… 11. On third order integrable vector Hamiltonian equations Meshkov, A. G.; Sokolov, V. V. 2017-03-01 A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found. 12. Collective Hamiltonian for Chiral and Wobbling Modes Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.; Jolos, R. V.; Meng, J. The recent progresses of the collective Hamiltonian for chiral and wobbling modes are briefly introduced. The collective Hamiltonian is constructed from the collective potential and mass parameter obtained in the tilted axis cranking approach. The collective Hamiltonian can reproduce the exact solutions by the particle rotor model very well for both chiral and wobbling modes. 13. Systematic method for deriving effective Hamiltonians Swain, S. 1994-04-01 A systematic procedure for deriving effective Hamiltonians to any order is presented, which is applicable to any time-independent Hamiltonian. The method is based on a continued-fraction approach and avoids the singularities which may occur with perturbation theory. It is illustrated by deriving the effective Hamiltonian for the one-photon, dressed-state laser to second order. 14. Constructing Dense Graphs with Unique Hamiltonian Cycles ERIC Educational Resources Information Center Lynch, Mark A. M. 2012-01-01 It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs… 15. Geometric Hamiltonian structures and perturbation theory SciTech Connect Omohundro, S. 1984-08-01 We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging. 16. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories SciTech Connect Tronko, Natalia; Brizard, Alain J. 2015-11-15 A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections. 17. Hamiltonian formulation of teleparallel gravity Ferraro, Rafael; Guzmán, María José 2016-11-01 The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra. 18. A Hamiltonian approach to Thermodynamics SciTech Connect Baldiotti, M.C.; Fresneda, R.; Molina, C. 2016-10-15 In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations. 19. Computational power of symmetric Hamiltonians Kay, Alastair 2008-07-01 The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still bounded error, quantum polynomial time complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a universal quantum interface, a device which enables control of an arbitrary computation through the control of a fixed number of spins, and using it as a building block to entirely remove the need for control, except in the system initialization. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a Quantum-Merlin-Arthur-complete problem. 20. Core polarization and modern realistic shell-model Hamiltonians Coraggio, L.; Covello, A.; Gargano, A.; Itaco, N. The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called "bubble diagrams," may be provided calculating the Kirson-Babu-Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson-Babu-Brown induced interaction to derive the shell-model effective Hamiltonian for p-shell nuclei starting from a modern nucleon-nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies. 1. Core polarization and modern realistic shell-model Hamiltonians Coraggio, L.; Covello, A.; Gargano, A.; Itaco, N. The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called “bubble diagrams,” may be provided calculating the Kirson-Babu-Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson-Babu-Brown induced interaction to derive the shell-model effective Hamiltonian for p-shell nuclei starting from a modern nucleon-nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies. 2. Higher-dimensional Wannier functions of multiparameter Hamiltonians Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy 2015-05-01 When using Wannier functions to study the electronic structure of multiparameter Hamiltonians H(k ,λ ) carrying a dependence on crystal momentum k and an additional periodic parameter λ , one usually constructs several sets of Wannier functions for a set of values of λ . We present the concept of higher-dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multiparameter Hamiltonians based on a single set of HDWFs. The obstacle of nonorthogonality of Bloch functions at different λ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter λ . We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of λ : (i) the spin-spiral vector q and (ii) the direction of the ferromagnetic magnetization m ̂. Using the generalized interpolation of the energy, we extract the corresponding values of magnetocrystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization, and spin torques. 3. Contact symmetries and Hamiltonian thermodynamics SciTech Connect Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F. 2015-10-15 It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production. 4. Ab Initio and Ab Exitu No-Core Shell Model SciTech Connect Vary, J P; Navratil, P; Gueorguiev, V G; Ormand, W E; Nogga, A; Maris, P; Shirokov, A 2007-10-02 We outline two complementary approaches based on the no core shell model (NCSM) and present recent results. In the ab initio approach, nuclear properties are evaluated with two-nucleon (NN) and three-nucleon interactions (TNI) derived within effective field theory (EFT) based on chiral perturbation theory (ChPT). Fitting two available parameters of the TNI generates good descriptions of light nuclei. In a second effort, an ab exitu approach, results are obtained with a realistic NN interaction derived by inverse scattering theory with off-shell properties tuned to fit light nuclei. Both approaches produce good results for observables sensitive to spin-orbit properties. 5. Ab initio calculations of ^12C and neutron drops Pieper, Steven C. 2009-10-01 Ab initio calculations of nuclei, which treat a nucleus as a system of A nucleons interacting by realistic two- and three-nucleon forces, have made tremendous progress in the last 15 years. This is a result of better Hamiltonians, rapidly increasing computer power, and new or improved many-body methods. Three methods are principally being used: Green's function Monte Carlo (GFMC), no-core shell model, and coupled cluster. In the limit of large computer resources, all three methods produce exact eigenvalues of a given nuclear Hamiltonian. With DOE SciDAC and INCITE support, all three methods are using the largest computers available today. Under the UNEDF SciDAC grant, the Argonne GFMC program was modified to efficiently use more than 2000 processors. E. Lusk (Argonne), R.M. Butler (Middle Tennessee State U.) and I have developed an Asynchronous Dynamic Load-Balancing (ADLB) library. In addition all the cores in a node are used via OpenMP as one ADLB/MPI client. In this way we obtain very good scalability up to 30,000 processors on Argonne's IBM Blue Gene/P. Two systems of particular interest that require this computer power are ^12C and neutron drops. V.R. Pandharipande (UIUC, deceased), J. Carlson (LANL), R.B. Wiringa (Argonne), and I have developed new trial wave functions that explicitly contain the three-alpha particle structure of ^12C. These are being used with the Argonne V18 and Illinois-7 potentials which reproduce the energies of 51 states in 3<=A<=12 nuclei with an rms error of 600,eV. Neutron drops are collections of neutrons confined in an artificial external well and interacting with realistic NN and NNN potentials. Their properties can be used as experimental data'' for developing energy-density functionals. 6. Emergent properties of nuclei from ab initio coupled-cluster calculations SciTech Connect Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; Papenbrock, T. 2016-05-17 Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. Our endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. We review some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO${}_{{\\rm{sat}}}$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. Finally, the coupling to the continuum impacts the energies of the ${J}^{\\pi }=1/{2}^{-},3/{2}^{-},7/{2}^{-},3/{2}^{+}$ states in ${}^{\\mathrm{17,23,25}}$O, and—contrary to naive shell-model expectations—the level ordering of the ${J}^{\\pi }=3/{2}^{+},5/{2}^{+},9/{2}^{+}$ states in ${}^{\\mathrm{53,55,61}}$Ca. 7. Emergent properties of nuclei from ab initio coupled-cluster calculations SciTech Connect Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; Papenbrock, T. 2016-05-17 Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. Our endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. We review some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO${}_{{\\rm{sat}}}$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. Finally, the coupling to the continuum impacts the energies of the ${J}^{\\pi }=1/{2}^{-},3/{2}^{-},7/{2}^{-},3/{2}^{+}$ states in ${}^{\\mathrm{17,23,25}}$O, and—contrary to naive shell-model expectations—the level ordering of the ${J}^{\\pi }=3/{2}^{+},5/{2}^{+},9/{2}^{+}$ states in ${}^{\\mathrm{53,55,61}}$Ca. 8. Emergent properties of nuclei from ab initio coupled-cluster calculations Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; Papenbrock, T. 2016-06-01 Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. This endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. This paper reviews some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO{}{{sat}} is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon-nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. The coupling to the continuum impacts the energies of the {J}π =1/{2}-,3/{2}-,7/{2}-,3/{2}+ states in {}{17,23,25}O, and—contrary to naive shell-model expectations—the level ordering of the {J}π =3/{2}+,5/{2}+,9/{2}+ states in {}{53,55,61}Ca. ). 9. Killing symmetries as Hamiltonian constraints Lusanna, Luca 2016-02-01 The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive. 10. Staggered quantum walks with Hamiltonians Portugal, R.; de Oliveira, M. C.; Moqadam, J. K. 2017-01-01 Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties similar to the ones for quantum computers, though. Therefore, there is a strong motivation to develop new quantum-walk models which might be easier to implement. In this work we present an extension of the staggered quantum walk model that is fitted for physical implementations in terms of time-independent Hamiltonians. We demonstrate that this class of quantum walk includes the entire class of staggered quantum walk model, Szegedy's model, and an important subset of the coined model. 11. Canonical form of Hamiltonian matrices Zuker, A. P.; Waha Ndeuna, L.; Nowacki, F.; Caurier, E. 2001-08-01 On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines-within fluctuations and behavior very near the origin-smooth canonical matrices whose forms depend on the rank of the Hamiltonian, dimensionality of the vector space, and second and third moments. A framework emerges that amounts to a general Anderson model capable of dealing with ground state properties and strength functions. The smooth forms imply binomial level densities. A simplified approach to canonical thermodynamics is proposed. 12. Chasing Hamiltonian structure in gyrokinetic theory SciTech Connect Burby, J. W. 2015-09-01 Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a stochastic Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense. 13. Hamiltonian thermostats fail to promote heat flow Hoover, Wm. G.; Hoover, Carol G. 2013-12-01 Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model systems we treat are ϕ4 chains, with quartic tethers and quadratic nearest-neighbor Hooke's-law interactions. This model is known to satisfy Fourier's law. Our prototypical problem sandwiches a Newtonian subsystem between hot and cold Hamiltonian reservoir regions. We have characterized four different Hamiltonian reservoir types. There is no tendency for any of these two-temperature Hamiltonian simulations to transfer heat from the hot to the cold degrees of freedom. Evidently steady heat flow simulations require energy sources and sinks, and are therefore incompatible with Hamiltonian mechanics. 14. Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions Bonnaillie-Noël, V.; Helffer, B.; Hoffmann-Ostenhof, T. 2009-05-01 The spectral analysis of Aharonov-Bohm Hamiltonians with flux \\frac12 leads surprisingly to a new insight on some questions of isospectrality appearing for example in Jakobson et al (2006 J. Comput. Appl. Math. 194 141-55) and Levitin et al (J. Phys. A: Math. Gen. 39 2073-82) and of minimal partitions (Helffer et al 2009 Ann. Inst. H. Poincaré Anal. Non Linéaire 26 101-38). We will illustrate this point of view by discussing the question of spectral minimal 3-partitions for the rectangle \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big]{-}\\frac b2,\\frac b2\\big[ , with 0 < a <= b. It has been observed in Helffer et al (2009 Ann. Inst. H. Poincaré Anal. Non Linéaire 26 101-38) that when 0<\\frac ab < \\sqrt{\\vphantom{A^A}\\smash{\\\\frac 38}} the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big] {-}\\frac b2,-\\frac b6\\big[, \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big]{-}\\frac b6,\\frac b6\\big[ and \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big] \\frac b6, \\frac b2\\big[ . We will describe a possible mechanism of transition for increasing \\frac ab between these nodal minimal 3-partitions and non-nodal minimal 3-partitions at the value \\sqrt{\\vphantom{A^A}\\smash{\\\\frac 38}} and discuss the existence of symmetric candidates for giving minimal 3-partitions when \\sqrt{\\vphantom{A^A}\\smash{\\\\frac 38}} <\\frac ab \\leq 1 . Numerical analysis leads very naturally to nice questions of isospectrality which are solved by the introduction of Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle. 15. Hamiltonian approach to slip-stacking dynamics DOE PAGES Lee, S. Y.; Ng, K. Y. 2017-06-29 Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. As a result, the dynamics can also be applied to other accelerator complexes. 16. Local bulk physics from intersecting modular Hamiltonians 2017-06-01 We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces intersect at a point in the bulk then CFT operators which commute with both extended modular Hamiltonians must be localized at the intersection point. We use this to construct local bulk operators purely from CFT considerations, without knowing the bulk metric, using intersecting modular Hamiltonians. For conformal field theories at zero and finite temperature the appropriate modular Hamiltonians are known explicitly and we recover known expressions for local bulk observables. 17. Hamiltonian decomposition for bulk and surface states. PubMed Sasaki, Ken-Ichi; Shimomura, Yuji; Takane, Yositake; Wakabayashi, Katsunori 2009-04-10 We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts for honeycomb lattice systems. The Hamiltonian decomposition reveals that next-nearest-neighbor hopping causes sizable changes in the energy spectrum of surface states even if the correction to the energy spectrum of bulk states is negligible. By applying the Hamiltonian decomposition to edge states in graphene systems, we show that the next-nearest-neighbor hopping stabilizes the edge states. The application of Hamiltonian decomposition to a general lattice system is discussed. 18. Moment methods and nuclear level densities SciTech Connect Johnson, Calvin W. 2008-04-17 Working in a shell-model framework, I use moments of the nuclear many-body Hamiltonian to illustrate the importance of the residual interaction to microscopic calculations of the nuclear level density. 19. Ab initio excited states from the in-medium similarity renormalization group Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K. 2017-04-01 We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms. 20. Operator evolution for ab initio electric dipole transitions of 4He SciTech Connect Schuster, Micah D.; Quaglioni, Sofia; Johnson, Calvin W.; Jurgenson, Eric D.; Navartil, Petr 2015-07-24 A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopic internucleon forces. A major element of such an effort is applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of ab initio calculations as a function of the model space size. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for nonscalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity renormalization group method and apply the renormalized matrix elements to the calculation of the 4He total photoabsorption cross section and electric dipole polarizability. All observables are calculated within the ab initio no-core shell model. Furthermore, we find that, although seemingly small, the effects of evolved operators on the photoabsorption cross section are comparable in magnitude to the correction produced by including the chiral three-nucleon force and cannot be neglected. 1. Hamiltonian tomography of photonic lattices Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan 2017-06-01 In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between. 2. Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian Ripoche, J.; Lacroix, D.; Gambacurta, D.; Ebran, J.-P.; Duguet, T. 2017-01-01 internucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage of automatic access to the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N6) in system size. This method achieves unprecedented accuracy for the ground-state correlation energy, effective pairing gap, and one-body entropy as well as for the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a sufficiently strong motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate, and versatile ab initio description of mid-mass open-shell nuclei in the future. 3. Theoretical gas to liquid shift of (15)N isotropic nuclear magnetic shielding in nitromethane using ab initio molecular dynamics and GIAO/GIPAW calculations. PubMed Gerber, Iann C; Jolibois, Franck 2015-05-14 Chemical shift requires the knowledge of both the sample and a reference magnetic shielding. In few cases as nitrogen (15N), the standard experimental reference corresponds to its liquid phase. Theoretical estimate of NMR magnetic shielding parameters of compounds in their liquid phase is then mandatory but usually replaced by an easily-get gas phase value, forbidding direct comparisons with experiments. We propose here to combine ab initio molecular dynamic simulations with the calculations of magnetic shielding using GIAO approach on extracted cluster's structures from MD. Using several computational strategies, we manage to accurately calculate 15N magnetic shielding of nitromethane in its liquid phase. Theoretical comparison between liquid and gas phase allows us to extrapolate an experimental value for the 15N magnetic shielding of nitromethane in gas phase between -121.8 and -120.8 ppm. 4. Implicit variational principle for contact Hamiltonian systems Wang, Kaizhi; Wang, Lin; Yan, Jun 2017-02-01 We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions. 5. Bohr Hamiltonian with time-dependent potential 2016-04-01 In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant. 6. Generalized seniority from random Hamiltonians SciTech Connect Johnson, C. W.; Bertsch, G. F.; Dean, D. J.; Talmi, I. 2000-01-01 We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J=0 ground states and an energy gap, but the relationship between ground-state wave functions of neighboring nuclei shows signatures of pairing as well. Matrix elements of pair creation-annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required. (c) 1999 The American Physical Society. 7. Dynamical manifestations of Hamiltonian monodromy SciTech Connect Delos, J.B. Dhont, G. Sadovskii, D.A. Zhilinskii, B.I. 2009-09-15 Monodromy is the simplest obstruction to the existence of global action-angle variables in integrable Hamiltonian dynamical systems. We consider one of the simplest possible systems with monodromy: a particle in a circular box containing a cylindrically symmetric potential-energy barrier. Systems with monodromy have nontrivial smooth connections between their regular Liouville tori. We consider a dynamical connection produced by an appropriate time-dependent perturbation of our system. This turns studying monodromy into studying a physical process. We explain what aspects of this process are to be looked upon in order to uncover the interesting and somewhat unexpected dynamical behavior resulting from the nontrivial properties of the connection. We compute and analyze this behavior. 8. Universal two-body-Hamiltonian quantum computing Nagaj, Daniel 2012-03-01 We present a Hamiltonian quantum-computation scheme universal for quantum computation. Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of constant-norm, time-independent, two-body interaction terms. Furthermore, each qubit in the system interacts only with a constant number of other qubits in a three-layer, geometrically local layout. The computer runs in three steps—it starts in a simple initial product state, evolves according to a time-independent Hamiltonian for time of order L2 (up to logarithmic factors), and finishes with a two-qubit measurement. Our model improves previous universal two-local-Hamiltonian constructions, as it avoids using perturbation gadgets and large energy-penalty terms in the Hamiltonian, which would result in a large required run time. 9. Building A Universal Nuclear Energy Density Functional (UNEDF) SciTech Connect Joe Carlson; Dick Furnstahl; Mihai Horoi; Rusty Lusk; Witek Nazarewicz; Esmond Ng; Ian Thompson; James Vary 2012-09-30 During the period of Dec. 1 2006 - Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: first, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions. 10. Applications of Floquet-Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence. PubMed Mananga, Eugene Stephane 2013-01-01 This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented. © 2013 Elsevier Inc. All rights reserved. 11. Applications of Floquet-Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence PubMed Central Mananga, Eugene Stephane 2015-01-01 This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented. PMID:24034855 12. Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene Morrison, Adrian F.; Herbert, John M. 2017-06-01 Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission. 13. Ab Initio Infrared and Raman Spectra. DTIC Science & Technology 1982-08-01 tions. For parameters not depending on momenta, a parallel ab fhti Monte Carlo approach would use electronic energies and other parameters of... Monte Carlo approach. Specifically, as one of us has suggested,t I classical molecular dynamics may be integrated with ab iniHo quan- tum force...alternative approach, for phenomena which are not explicitly time dependent, is a Monte Carlo procedure in which at each trial nuclear configuration 14. Periodic ab initio calculation of nuclear quadrupole parameters as an assignment tool in solid-state NMR spectroscopy: applications to 23Na NMR spectra of crystalline materials. PubMed Johnson, Clive; Moore, Elaine A; Mortimer, Michael 2005-05-01 Periodic ab initio HF calculations using the CRYSTAL code have been used to calculate (23)Na NMR quadrupole parameters for a wide range of crystalline sodium compounds including Na(3)OCl. An approach is developed that can be used routinely as an alternative to point-charge modelling schemes for the assignment of distinct lines in (23)Na NMR spectra to specific crystallographic sodium sites. The calculations are based on standard 3-21 G and 6-21 G molecular basis sets and in each case the same modified basis set for sodium is used for all compounds. The general approach is extendable to other quadrupolar nuclei. For the 3-21 G calculations a 1:1 linear correlation between experimental and calculated values of C(Q)((23)Na) is obtained. The 6-21 G calculations, including the addition of d-polarisation functions, give better accuracy in the calculation of eta((23)Na). The sensitivity of eta((23)Na) to hydrogen atom location is shown to be useful in testing the reported hydrogen-bonded structure of Na(2)HPO(4). 15. Gauge-invariant hydrogen-atom Hamiltonian SciTech Connect Sun Weimin; Wang Fan; Chen Xiangsong; Lue Xiaofu 2010-07-15 For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle was recently provided by us [X.-S. Chen et al., Phys. Rev. Lett. 100, 232002 (2008)]. Based on the separation of the electromagnetic potential into pure-gauge and gauge-invariant parts, we have proposed a new set of momentum and Hamiltonian operators which satisfy both the requirement of gauge invariance and the relevant commutation relations. In this paper we report a check for the case of the hydrogen-atom problem: Starting from the Hamiltonian of the coupled electron, proton, and electromagnetic field, under the infinite proton mass approximation, we derive the gauge-invariant hydrogen-atom Hamiltonian and verify explicitly that this Hamiltonian is different from the Dirac Hamiltonian, which is the time translation generator of the system. The gauge-invariant Hamiltonian is the energy operator, whose eigenvalue is the energy of the hydrogen atom. It is generally time dependent. In this case, one can solve the energy eigenvalue equation at any specific instant of time. It is shown that the energy eigenvalues are gauge independent, and by suitably choosing the phase factor of the time-dependent eigenfunction, one can ensure that the time-dependent eigenfunction satisfies the Dirac equation. 16. WE-AB-204-11: Development of a Nuclear Medicine Dosimetry Module for the GPU-Based Monte Carlo Code ARCHER SciTech Connect Liu, T; Lin, H; Xu, X; Stabin, M 2015-06-15 Purpose: To develop a nuclear medicine dosimetry module for the GPU-based Monte Carlo code ARCHER. Methods: We have developed a nuclear medicine dosimetry module for the fast Monte Carlo code ARCHER. The coupled electron-photon Monte Carlo transport kernel included in ARCHER is built upon the Dose Planning Method code (DPM). The developed module manages the radioactive decay simulation by consecutively tracking several types of radiation on a per disintegration basis using the statistical sampling method. Optimization techniques such as persistent threads and prefetching are studied and implemented. The developed module is verified against the VIDA code, which is based on Geant4 toolkit and has previously been verified against OLINDA/EXM. A voxelized geometry is used in the preliminary test: a sphere made of ICRP soft tissue is surrounded by a box filled with water. Uniform activity distribution of I-131 is assumed in the sphere. Results: The self-absorption dose factors (mGy/MBqs) of the sphere with varying diameters are calculated by ARCHER and VIDA respectively. ARCHER’s result is in agreement with VIDA’s that are obtained from a previous publication. VIDA takes hours of CPU time to finish the computation, while it takes ARCHER 4.31 seconds for the 12.4-cm uniform activity sphere case. For a fairer CPU-GPU comparison, more effort will be made to eliminate the algorithmic differences. Conclusion: The coupled electron-photon Monte Carlo code ARCHER has been extended to radioactive decay simulation for nuclear medicine dosimetry. The developed code exhibits good performance in our preliminary test. The GPU-based Monte Carlo code is developed with grant support from the National Institute of Biomedical Imaging and Bioengineering through an R01 grant (R01EB015478) 17. Three-cluster dynamics within an ab initio framework SciTech Connect Quaglioni, Sofia; Romero-Redondo, Carolina; Navratil, Petr 2013-09-26 In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects. 18. Incomplete Dirac reduction of constrained Hamiltonian systems SciTech Connect Chandre, C. 2015-10-15 First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified. 19. Hamiltonian and Lagrangian theory of viscoelasticity Hanyga, A.; Seredyńska, M. 2008-03-01 The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity. 20. The gravity duals of modular Hamiltonians Jafferis, Daniel L.; Suh, S. Josephine 2016-09-01 In this work, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region. 1. The gravity duals of modular Hamiltonians SciTech Connect Jafferis, Daniel L.; Suh, S. Josephine 2016-09-12 In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region. 2. Symmetries and regular behavior of Hamiltonian systems. PubMed Kozlov, Valeriy V. 1996-03-01 The behavior of the phase trajectories of the Hamilton equations is commonly classified as regular and chaotic. Regularity is usually related to the condition for complete integrability, i.e., a Hamiltonian system with n degrees of freedom has n independent integrals in involution. If at the same time the simultaneous integral manifolds are compact, the solutions of the Hamilton equations are quasiperiodic. In particular, the entropy of the Hamiltonian phase flow of a completely integrable system is zero. It is found that there is a broader class of Hamiltonian systems that do not show signs of chaotic behavior. These are systems that allow n commuting "Lagrangian" vector fields, i.e., the symplectic 2-form on each pair of such fields is zero. They include, in particular, Hamiltonian systems with multivalued integrals. (c) 1996 American Institute of Physics. 3. Compressed quantum metrology for the Ising Hamiltonian Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B. 2016-12-01 We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation. 4. Quasi-Hamiltonian structure and Hojman construction Carinena, Jose F.; Guha, Partha; Ranada, Manuel F. 2007-08-01 Given a smooth vector field [Gamma] and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that [Gamma] is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction. 5. Momentum and Hamiltonian in Complex Action Theory Nagao, Keiichi; Nielsen, Holger Bech In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q. 6. Quantum mechanical hamiltonian models of turing machines Benioff, Paul 1982-11-01 Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex. 7. A Student's Guide to Lagrangians and Hamiltonians Hamill, Patrick 2013-11-01 Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index. 8. Hamiltonian surface charges using external sources SciTech Connect Troessaert, Cédric 2016-05-15 In this work, we interpret part of the boundary conditions as external sources in order to partially solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start by describing the hamiltonian structure of external symmetries preserving the action up to a transformation of the external sources of the theory. We then extend these results to the computation of surface charges for field theories with non-trivial boundary conditions. 9. Nonperturbative embedding for highly nonlocal Hamiltonians Subaşı, Yiǧit; Jarzynski, Christopher 2016-07-01 The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l Hamiltonian which is more local than the original one (using an analog device), and finally reverse the unitary transformation. The net effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. 10. Hamiltonian formulation of string field theory Siopsis, George 1987-09-01 Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude. 11. Hamiltonian vector fields on almost symplectic manifolds Vaisman, Izu 2013-09-01 Let (M, ω) be an almost symplectic manifold (ω is a nondegenerate, not closed, 2-form). We say that a vector field X of M is locally Hamiltonian if LXω = 0, d(i(X)ω) = 0, and it is Hamiltonian if, furthermore, the 1-form i(X)ω is exact. Such vector fields were considered in Fassò and Sansonetto ["Integrable almost-symplectic Hamiltonian systems," J. Math. Phys. 48, 092902 (2007)], 10.1063/1.2783937, under the name of strongly Hamiltonian, and a corresponding action-angle theorem was proven. Almost symplectic manifolds may have few, nonzero, Hamiltonian vector fields, or even none. Therefore, it is important to have examples and it is our aim to provide such examples here. We also obtain some new general results. In particular, we show that the locally Hamiltonian vector fields generate a Dirac structure on M and we state a reduction theorem of the Marsden-Weinstein type. A final section is dedicated to almost symplectic structures on tangent bundles. 12. Reaction Hamiltonian and state-to-state description of chemical reactions SciTech Connect Ruf, B.A.; Kresin, V.Z.; Lester, W.A. Jr. 1985-08-01 A chemical reaction is treated as a quantum transition from reactants to products. A specific reaction Hamiltonian (in second quantization formalism) is introduced. The approach leads to Franck-Condon-like factor, and adiabatic method in the framework of the nuclear motion problems. The influence of reagent vibrational state on the product energy distribution has been studied following the reaction Hamiltonian method. Two different cases (fixed available energy and fixed translational energy) are distinguished. Results for several biomolecular reactions are presented. 40 refs., 5 figs. 13. Geometric Construction of Quantum Hall Clustering Hamiltonians Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny 2015-10-01 Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU (n ) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties. 14. Hamiltonian Description of Multi-fluid Streaming Valls, C.; de La Llave, R.; Morrison, P. J. 2001-10-01 The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems. 15. Geometric construction of quantum hall clustering Hamiltonians DOE PAGES Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny 2015-10-08 In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-bodymore » interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less 16. Generalized index for Hamiltonian systems with applications Zevin, Alexandr A. 2005-09-01 Some classes of linear Hamiltonian equations with periodic coefficients (nondegenerate, strongly stable, completely unstable) are determined by the disposition of the Floquet multipliers. Periodic solutions of nonlinear equations (e.g. elliptic or hyperbolic solutions) are also defined by the multipliers of the corresponding variational equation. In this paper, we consider a general set M of linear Hamiltonian equations with multipliers satisfying some arbitrary conditions and a specific condition on the multiplier lying at some point of the unit circle (all known sets admit such a definition). We show that the set M consists of a finite number of subsets Mi which comprise a countable number of domains M_q^i within which any two Hamiltonians can be continuously deformed into each other. The corresponding integer index q is expressed through the eigenvalues of some self-adjoint problem. It is shown that this index (and, therefore, the known indices relating to specific sets) increases on increasing the Hamiltonian. Using the obtained results, some known and new sets are studied from the unified point of view. It is shown that for the sets of nondegenerate and completely unstable equations, the domains M_q^i are directionally convex; for strongly stable equations, necessary and sufficient conditions for directional convexity are found. The results are applied to problems of existence and stability of periodic solutions of nonlinear Hamiltonian equations. 17. Rovibrational molecular hamiltonian in mixed bond-angle and umbrella-like coordinates. PubMed Makarewicz, Jan; Skalozub, Alexander 2007-08-16 A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitude inversion and torsion motions is derived. The derivation is based on a division of a molecule into two parts: a frame and a top. The nuclei of the frame only are used to construct a molecular system of axes. The inversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion of the top is described by the nonstandard torsion angle defined in terms of the nuclear vectors and one of the molecular axes. The internal coordinates chosen take into account the properties of the inversion and torsion motions. Vibrational s and rotational Omega vectors obtained for the introduced internal coordinates determine the rovibrational tensor G defined by simple scalar products of these vectors. The Jacobian of the transformation from the Cartesian to the internal coordinates considered and the G tensor specify the rovibrational Hamiltonian. As a result, the Hamiltonian for penta-atomic molecules like NH2OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH2NH2 with two inverters, is reported. The approach considered is essentially general and sufficiently simple, as demonstrated by derivation of a polyatomic molecule Hamiltonian in polyspherical coordinates, obtained by other methods with much greater efforts. 18. Emergent properties of nuclei from ab initio coupled-cluster calculations DOE PAGES Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; ... 2016-05-17 Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. Our endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. We review some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLOmore » $${}_{{\\rm{sat}}}$$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. Finally, the coupling to the continuum impacts the energies of the $${J}^{\\pi }=1/{2}^{-},3/{2}^{-},7/{2}^{-},3/{2}^{+}$$ states in $${}^{\\mathrm{17,23,25}}$$O, and—contrary to naive shell-model expectations—the level ordering of the $${J}^{\\pi }=3/{2}^{+},5/{2}^{+},9/{2}^{+}$$ states in $${}^{\\mathrm{53,55,61}}$$Ca.« less 19. Geometric Hamiltonian quantum mechanics and applications Pastorello, Davide 2016-08-01 Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed. 20. Hamiltonian boundary term and quasilocal energy flux SciTech Connect Chen, C.-M.; Nester, James M.; Tung, R.-S. 2005-11-15 The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant. 1. Equivalent Hamiltonians with additional discrete states Chinn, C. R.; Thaler, R. M. 1991-01-01 Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations. 2. Gravitational surface Hamiltonian and entropy quantization Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav 2017-02-01 The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics. 3. The gravity duals of modular Hamiltonians DOE PAGES Jafferis, Daniel L.; Suh, S. Josephine 2016-09-12 In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less 4. Charge transfer in strongly correlated systems: An exact diagonalization approach to model Hamiltonians SciTech Connect Schöppach, Andreas; Gnandt, David; Koslowski, Thorsten 2014-04-07 We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths. 5. Charge transfer in strongly correlated systems: an exact diagonalization approach to model Hamiltonians. PubMed Schöppach, Andreas; Gnandt, David; Koslowski, Thorsten 2014-04-07 We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths. 6. The Legendre transformations in Hamiltonian optics Gitin, A. V. 2010-04-01 The Legendre transformations are an important tool in theoretical physics. They play a critical role in mechanics, optics, and thermodynamics. In Hamiltonian optics the Legendre transformations appear twice: as the connection between the Lagrangian and the Hamiltonian and as relations among eikonals. In this article interconnections between these two types of Legendre transformations have been investigated. Using the method of "transition to the centre and difference coordinates'' it is shown that four Legendre transformations which connect point, point-angle, angle-point, and angle eikonals of an optical system correspond to four Legendre transformations which connect four systems of equations: Euler's equations, Hamilton's equations, and two unknown before pairs of equations. 7. Exploring Hamiltonian dielectric solvent molecular dynamics Bauer, Sebastian; Tavan, Paul; Mathias, Gerald 2014-09-01 Hamiltonian dielectric solvent (HADES) is a recent method [7,25], which enables Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric continua. Sample simulations of an α-helical decapeptide with and without explicit solvent demonstrate the high efficiency of HADES-MD. Addressing the folding of this peptide by replica exchange MD we study the properties of HADES by comparing melting curves, secondary structure motifs and salt bridges with explicit solvent results. Despite the unoptimized ad hoc parametrization of HADES, calculated reaction field energies correlate well with numerical grid solutions of the dielectric Poisson equation. 8. Hamiltonian dynamics for complex food webs. PubMed Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno 2016-03-01 We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity. 9. Canonical transformations and Hamiltonian evolutionary systems SciTech Connect Al-Ashhab, Samer 2012-06-15 In many Lagrangian field theories, one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different cases. These three cases depend on the specific dimensions of the vector bundle of the theory and the associated Hamiltonian differential operator. We also show how a canonical transformation transforms a Hamiltonian evolutionary system and its conservation laws. Finally, we illustrate these ideas with three examples. 10. Reduction of pre-Hamiltonian actions De Nicola, Antonio; Esposito, Chiara 2017-05-01 We prove a reduction theorem for the tangent bundle of a Poisson manifold (M , π) endowed with a pre-Hamiltonian action of a Poisson-Lie group (G ,πG) . In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden-Ratiu reduction of M. If the manifold M is symplectic and simply connected, the reduced tangent bundle is integrable and its integral symplectic groupoid is the Marsden-Weinstein reduction of the pair groupoid M × M ¯ . 11. Hamiltonians generating optimal-speed evolutions 2009-01-01 We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric (inner product) dependence of the lower bound on the travel time and the universality (metric independence) of the upper bound on the speed of unitary evolutions. 12. Hamiltonian mechanics and planar fishlike locomotion Kelly, Scott; Xiong, Hailong; Burgoyne, Will 2007-11-01 A free deformable body interacting with a system of point vortices in the plane constitutes a Hamiltonian system. A free Joukowski foil with variable camber shedding point vortices in an ideal fluid according to a periodically applied Kutta condition provides a model for fishlike locomotion which bridges the gap between inviscid analytical models that sacrifice realism for tractability and viscous computational models inaccessible to tools from nonlinear control theory. We frame such a model in the context of Hamiltonian mechanics and describe its relevance both to the study of hydrodynamic interactions within schools of fish and to the realization of model-based control laws for biomimetic autonomous robotic vehicles. 13. Surface terms and the Gauss Bonnet Hamiltonian 2003-07-01 We derive the gravitational Hamiltonian starting from the Gauss Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the Hamiltonian give a remarkably simple expression for the total energy of a spacetime. This expression is consistent with energy expressions found in Preprint hep-th/0212292. However, we can apply our results whatever the choice of background and whatever the symmetries of the spacetime. 14. Hamiltonian dynamics for complex food webs Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno 2016-03-01 We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity. 15. Ostrogradski Hamiltonian approach for geodetic brane gravity SciTech Connect 2010-12-07 We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly. 16. Convergence to equilibrium under a random Hamiltonian. PubMed Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek 2012-09-01 We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration. 17. Ab initio valence-space theory for exotic nuclei Holt, Jason 2015-10-01 Recent advances in ab initio nuclear structure theory have led to groundbreaking predictions in the exotic medium-mass region, from the location of the neutron dripline to the emergence of new magic numbers far from stability. Playing a key role in this progress has been the development of sophisticated many-body techniques and chiral effective field theory, which provides a systematic basis for consistent many-nucleon forces and electroweak currents. Within the context of valence-space Hamiltonians derived from the nonperturbative in-medium similarity renormalization group (IM-SRG) approach, I will discuss the importance of 3N forces in understanding and making new discoveries in the exotic sd -shell region. Beginning in oxygen, we find that the effects of 3N forces are decisive in explaining why 24O is the last bound oxygen isotope, validating first predictions of this phenomenon from several years ago. Furthermore, 3N forces play a key role in reproducing spectroscopy, including signatures of doubly magic 22,24O, and physics beyond the dripline. Similar improvements are obtained in new spectroscopic predictions for exotic fluorine and neon isotopes, where agreement with recent experimental data is competitive with state-of-the-art phenomenology. Finally, I will discuss first applications of the IM-SRG to effective valence-space operators, such as radii and E 0 transitions, as well as extensions to general operators crucial for our future understanding of electroweak processes, such as neutrinoless double-beta decay. This work was supported by NSERC and the NRC Canada. 18. Suppressing qubit dephasing using real-time Hamiltonian estimation PubMed Central Harvey, S. P.; Nichol, J. M.; Bartlett, S. D.; Doherty, A. C.; Umansky, V.; Yacoby, A. 2014-01-01 Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and materials engineering, quantum error correction and dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in a qubit using real-time Hamiltonian parameter estimation. Using a rapidly converging Bayesian approach, we precisely measure the splitting in a singlet-triplet spin qubit faster than the surrounding nuclear bath fluctuates. We continuously adjust qubit control parameters based on this information, thereby improving the inhomogenously broadened coherence time from tens of nanoseconds to >2 μs. Because the technique demonstrated here is compatible with arbitrary qubit operations, it is a natural complement to quantum error correction and can be used to improve the performance of a wide variety of qubits in both meteorological and quantum information processing applications. PMID:25295674 19. Hamiltonian Approach to Nonlinear Travelling Whistler Waves SciTech Connect Webb, G.M.; McKenzie, J.F.; Dubinin, E.; Sauer, K. 2005-08-01 A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is discussed. The model is based on the equations of two-fluid electron-proton plasmas. In the cold gas limit, the complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable {phi} = {phi}p - {phi}e representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are obtained. The Hamiltonian integral H, is used to classify the trajectories in the ({phi}, w) phase plane, where {phi} and w = u2 are the canonical coordinates. Periodic, oscillation solitary wave and compacton solutions are obtained, depending on the value of the Hamiltonian integral H and the Alfven Mach number M of the travelling wave. The individual electron and proton phase variables {phi}e and {phi}p are determined in terms of {phi} and w. An alternative Hamiltonian formulation in which {phi}-tilde = {phi}p + {phi}e is the new independent variable replacing x is used to write the travelling wave solutions parametrically in terms of {phi}-tilde. 20. Mapping between dissipative and Hamiltonian systems Xing, Jianhua 2010-09-01 Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation recently introduced by Ao (2004 J. Phys. A: Math. Gen. 37 L25) is related to previous works of Graham (1977 Z. Phys. B 26 397) and Eyink et al (1996 J. Stat. Phys. 83 385), which can also be viewed as the generalized application of the Helmholtz theorem in vector calculus. We then show that systems described by ordinary stochastic differential equations with white noise can be mapped to thermostated Hamiltonian systems. A steady-state of a dissipative system corresponds to the equilibrium state of the corresponding Hamiltonian system. These results provide a solid theoretical ground for corresponding studies on nonequilibrium dynamics, especially on nonequilibrium steady state. Mapping permits the application of established techniques and results for Hamiltonian systems to dissipative non-Hamiltonian systems, those for thermodynamic equilibrium states to nonequilibrium steady states. We discuss several implications of this work. 1. Periodic Solutions of Hamiltonian Systems: A Survey. DTIC Science & Technology 1980-12-01 auto - nomous Hamiltonian system has the form: (0.) aH 8Hp -S-(p,q) q ( where d denotes This system can be represented more concisely as (HS) z = ZHz(Z...oscillazioni periodiche d’une sistema dinamico, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 19, (1934), 234-237. [15] Arnold, V. I 2. An underlying geometrical manifold for Hamiltonian mechanics Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M. 2017-02-01 We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion. 3. Lagrangian tetragons and instabilities in Hamiltonian dynamics Entov, Michael; Polterovich, Leonid 2017-01-01 We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium. 4. From Nonlinear to Hamiltonian via Feedback1 DTIC Science & Technology 2002-01-01 distribution unlimited. 13. Abstract Mechanical control systems are a very important class of nonlinear control systems . They posses a rich mathematical...methodologies developed for mechanical control systel logically rendering nonlinear control systems , mechanical by a proper choice of feedback. In particular, w...OF PA Nonlinear mechanical control systems , Hamiltonian Control Systems x 16. PRICE CODE 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19 5. Eigenfunction expansions for time dependent hamiltonians Jauslin, H. R.; Guerin, S.; Deroussiaux, A. We describe a generalization of Floquet theory for non periodic time dependent Hamiltonians. It allows to express the time evolution in terms of an expansion in eigenfunctions of a generalized quasienergy operator. We discuss a conjecture on the extension of the adiabatic theorem to this type of systems, which gives a procedure for the physical preparation of Floquet states. * DIRECT SUPPORT * A3418380 00004 6. Hamiltonian constraint in polymer parametrized field theory 2011-01-01 Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type “polymer” representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints. 7. Hamiltonian constraint in polymer parametrized field theory SciTech Connect 2011-01-15 Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints. 8. Hamiltonian gadgets with reduced resource requirements Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre 2015-01-01 9. Incomplete integrable Hamiltonian systems with complex polynomial Hamiltonian of small degree SciTech Connect Lepskii, Timur A 2010-12-07 Complex Hamiltonian systems with one degree of freedom on C{sup 2} with the standard symplectic structure {omega}C=dz and dw and a polynomial Hamiltonian function f=z{sup 2}+P{sub n}(w), n=1,2,3,4, are studied. Two Hamiltonian systems (M{sub i}, Re{omega}{sub C,i}, H{sub i}=Ref{sub i}), i=1,2, are said to be Hamiltonian equivalent if there exists a complex symplectomorphism M{sub 1}{yields}M{sub 2} taking the vector field sgradH{sub 1} to sgradH{sub 2}. Hamiltonian equivalence classes of systems are described in the case n=1,2,3,4, a completed system is defined for n=3,4, and it is proved that it is Liouville integrable as a real Hamiltonian system. By restricting the real action-angle coordinates defined for the completed system in a neighbourhood of any nonsingular leaf, real canonical coordinates are obtained for the original system. Bibliography: 9 titles. 10. The 2-alkyl-2H-indazole regioisomers of synthetic cannabinoids AB-CHMINACA, AB-FUBINACA, AB-PINACA, and 5F-AB-PINACA are possible manufacturing impurities with cannabimimetic activities. PubMed Longworth, Mitchell; Banister, Samuel D; Mack, James B C; Glass, Michelle; Connor, Mark; Kassiou, Michael 2016-01-01 Indazole-derived synthetic cannabinoids (SCs) featuring an alkyl substituent at the 1-position and l-valinamide at the 3-carboxamide position (e.g., AB-CHMINACA) have been identified by forensic chemists around the world, and are associated with serious adverse health effects. Regioisomerism is possible for indazole SCs, with the 2-alkyl-2H-indazole regioisomer of AB-CHMINACA recently identified in SC products in Japan. It is unknown whether this regiosiomer represents a manufacturing impurity arising as a synthetic byproduct, or was intentionally synthesized as a cannabimimetic agent. This study reports the synthesis, analytical characterization, and pharmacological evaluation of commonly encountered indazole SCs AB-CHMINACA, AB-FUBINACA, AB-PINACA, 5F-AB-PINACA and their corresponding 2-alkyl-2H-indazole regioisomers. Both regioisomers of each SC were prepared from a common precursor, and the physical properties, (1)H and (13)C nuclear magnetic resonance spectroscopy, gas chromatography-mass spectrometry, and ultraviolet-visible spectroscopy of all SC compounds are described. Additionally, AB-CHMINACA, AB-FUBINACA, AB-PINACA, and 5F-AB-PINACA were found to act as high potency agonists at CB1 (EC50 = 2.1-11.6 nM) and CB2 (EC50 = 5.6-21.1 nM) receptors in fluorometric assays, while the corresponding 2-alkyl-2H-indazole regioisomers demonstrated low potency (micromolar) agonist activities at both receptors. Taken together, these data suggest that 2-alkyl-2H-indazole regioisomers of AB-CHMINACA, AB-FUBINACA, AB-PINACA, and 5F-AB-PINACA are likely to be encountered by forensic chemists and toxicologists as the result of improper purification during the clandestine synthesis of 1-alkyl-1H-indazole regioisomers, and can be distinguished by differences in gas chromatography-mass spectrometry fragmentation pattern. 11. Hamiltonian time integrators for Vlasov-Maxwell equations He, Yang; Qin, Hong; Sun, Yajuan; Xiao, Jianyuan; Zhang, Ruili; Liu, Jian 2015-12-01 Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature. 12. Hamiltonian time integrators for Vlasov-Maxwell equations SciTech Connect He, Yang; Xiao, Jianyuan; Zhang, Ruili; Liu, Jian; Qin, Hong; Sun, Yajuan 2015-12-15 Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature. 13. Conformal killing tensors and covariant Hamiltonian dynamics SciTech Connect Cariglia, M.; Gibbons, G. W.; Holten, J.-W. van; Horvathy, P. A.; Zhang, P.-M. 2014-12-15 A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six. 14. Tangent lifts of bi-Hamiltonian structures Dobrogowska, Alina; Jakimowicz, Grzegorz 2017-08-01 We construct two Poisson structures πT M and π˜ T M on the tangent bundle TM to a Poisson manifold (M ,π ) using Lie algebroid (TM, qM, M). Next, we construct the Poisson manifold (T M ,πT M ,λ ) from a bi-Hamiltonian manifold (M ,π1,π2 ) . This structure can be considered as a deformation of the Poisson structure related to an algebroid structure. We show that the bi-Hamiltonian structure from M can be transferred to the manifold TM. Moreover we present how to construct the Casimir functions for structures πT M, πT M ,λ, π˜ T g, and π˜ T g*,λ from the Casimir functions for π1 and π2 and discuss some particular examples. 15. Hamiltonian deformations of Gabor frames: First steps. PubMed de Gosson, Maurice A 2015-03-01 Gabor frames can advantageously be redefined using the Heisenberg-Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed - as the title suggests - as the very first steps towards a general deformation theory for Gabor frames. 16. Hamiltonian deformations of Gabor frames: First steps PubMed Central de Gosson, Maurice A. 2015-01-01 Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed – as the title suggests – as the very first steps towards a general deformation theory for Gabor frames. PMID:25892903 17. General formalism for singly thermostated Hamiltonian dynamics. PubMed Ramshaw, John D 2015-11-01 A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed. 18. Diffusion in very chaotic hamiltonian systems SciTech Connect Abarbanel, Henry D. I.; Crawford, John David 1981-04-20 In this paper, we study nonintegrable hamiltonian dynamics: H(I,θ) = H0(I) + kH1(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I0, θ0, t0) that the system is at I, θ at t, given it was at I0, θ0 at t0. By discretizing time into steps of size ϵ, we show how to evaluate physical observables for large k, fixed ϵ. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Finally, passage to ϵ = 0, the original hamiltonian flow, is discussed. 19. Hamiltonian learning and certification using quantum resources. PubMed Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D G 2014-05-16 In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable. 20. Hamiltonian Approach To Dp-Brane Noncommutativity Nikolic, B.; Sazdovic, B. 2010-07-01 In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields. 1. NUCLEAR REACTORS DOEpatents Long, E.; Ashby, J.W. 1958-09-16 ABS>A graphite moderator structure is presented for a nuclear reactor compriscd of an assembly of similarly orientated prismatic graphite blocks arranged on spaced longitudinal axes lying in common planes wherein the planes of the walls of the blocks are positioned so as to be twisted reintive to the planes of said axes so thatthe unlmpeded dtrect paths in direction wholly across the walls of the blocks are limited to the width of the blocks plus spacing between the blocks. 2. Controlling Hamiltonian chaos via Gaussian curvature. PubMed Oloumi, A; Teychenné, D 1999-12-01 We present a method allowing one to partly stabilize some chaotic Hamiltonians which have two degrees of freedom. The purpose of the method is to avoid the regions of V(q(1),q(2)) where its Gaussian curvature becomes negative. We show the stabilization of the Hénon-Heiles system, over a wide area, for the critical energy E=1/6. Total energy of the system varies only by a few percent. 3. Hamiltonian anomalies of bound states in QED SciTech Connect Shilin, V. I.; Pervushin, V. N. 2013-10-15 The Bound State in QED is described in systematic way by means of nonlocal irreducible representations of the nonhomogeneous Poincare group and Dirac's method of quantization. As an example of application of this method we calculate triangle diagram Para-Positronium {yields} {gamma}{gamma}. We show that the Hamiltonian approach to Bound State in QED leads to anomaly-type contribution to creation of pair of parapositronium by two photon. 4. Hamiltonian theory of guiding-center motion SciTech Connect Littlejohn, R.G. 1980-05-01 A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion. 5. The Hamiltonian Mechanics of Stochastic Acceleration SciTech Connect Burby, J. W. 2013-07-17 We show how to nd the physical Langevin equation describing the trajectories of particles un- dergoing collisionless stochastic acceleration. These stochastic di erential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems. 6. mAbs PubMed Central 2009-01-01 The twenty two monoclonal antibodies (mAbs) currently marketed in the U.S. have captured almost half of the top-20 U.S. therapeutic biotechnology sales for 2007. Eight of these products have annual sales each of more than \$1 B, were developed in the relatively short average period of six years, qualified for FDA programs designed to accelerate drug approval, and their cost has been reimbursed liberally by payers. With growth of the product class driven primarily by advancements in protein engineering and the low probability of generic threats, mAbs are now the largest class of biological therapies under development. The high cost of these drugs and the lack of generic competition conflict with a financially stressed health system, setting reimbursement by payers as the major limiting factor to growth. Advances in mAb engineering are likely to result in more effective mAb drugs and an expansion of the therapeutic indications covered by the class. The parallel development of biomarkers for identifying the patient subpopulations most likely to respond to treatment may lead to a more cost-effective use of these drugs. To achieve the success of the current top-tier mAbs, companies developing new mAb products must adapt to a significantly more challenging commercial environment. PMID:20061824 7. Room temperature line lists for CO2 symmetric isotopologues with ab initio computed intensities Zak, Emil J.; Tennyson, Jonathan; Polyansky, Oleg L.; Lodi, Lorenzo; Zobov, Nikolay F.; Tashkun, Sergei A.; Perevalov, Valery I. 2017-03-01 Remote sensing experiments require high-accuracy, preferably sub-percent, line intensities and in response to this need we present computed room temperature line lists for six symmetric isotopologues of carbon dioxide: 13C16O2, 14C16O2, 12C17O2, 12C18O2, 13C17O2 and 13C18O2, covering the range 0-8000 cm-1. Our calculation scheme is based on variational nuclear motion calculations and on a reliability analysis of the generated line intensities. Rotation-vibration wavefunctions and energy levels are computed using the DVR3D software suite and a high quality semi-empirical potential energy surface (PES), followed by computation of intensities using an ab initio dipole moment surface (DMS). Four line lists are computed for each isotopologue to quantify sensitivity to minor distortions of the PES/DMS. Reliable lines are benchmarked against recent state-of-the-art measurements and against the HITRAN2012 database, supporting the claim that the majority of line intensities for strong bands are predicted with sub-percent accuracy. Accurate line positions are generated using an effective Hamiltonian. We recommend the use of these line lists for future remote sensing studies and their inclusion in databases. 8. Ab initio Approach to Effective Single-Particle Energies in Doubly Closed Shell Nuclei SciTech Connect Duguet, T. 2012-01-01 The present work discusses, from an ab initio standpoint, the definition, the meaning, and the usefulness of effective single-particle energies (ESPEs) in doubly closed shell nuclei. We perform coupled-cluster calculations to quantify to what extent selected closed-shell nuclei in the oxygen and calcium isotopic chains can effectively be mapped onto an effective independent-particle picture. To do so, we revisit in detail the notion of ESPEs in the context of strongly correlated many-nucleon systems and illustrate the necessity of extracting ESPEs through the diagonalization of the centroid matrix, as originally argued by Baranger. For the purpose of illustration, we analyze the impact of correlations on observable one-nucleon separation energies and nonobservable ESPEs in selected closed-shell oxygen and calcium isotopes. We then state and illustrate the nonobservability of ESPEs. Similarly to spectroscopic factors, ESPEs can indeed be modified by a redefinition of inaccessible quantities while leaving actual observables unchanged. This leads to the absolute necessity of employing consistent structure and reaction models based on the same nuclear Hamiltonian to extract the shell structure in a meaningful fashion from experimental data. 9. Optimal Hamiltonian Simulation by Quantum Signal Processing Low, Guang Hao; Chuang, Isaac L. 2017-01-01 The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d -sparse Hamiltonian H ^ for time-interval t with error ɛ is O [t d ∥H ^ ∥max+log (1 /ɛ ) /log log (1 /ɛ ) ] , which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H ^ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability. 10. Invariants for time-dependent Hamiltonian systems. PubMed Struckmeier, J; Riedel, C 2001-08-01 An exact invariant is derived for n-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special Ansatz for the invariant and determine its time-dependent coefficients. In the second approach, we perform a two-step canonical transformation of the initially time-dependent Hamiltonian to a time-independent one. The invariant is found to contain a function of time f(2)(t), defined as a solution of a linear third-order differential equation whose coefficients depend in general on the explicitly known configuration space trajectory that follows from the system's time evolution. It is shown that the invariant can be interpreted as the time integral of an energy balance equation. Our result is applied to a one-dimensional, time-dependent, damped non-linear oscillator, and to a three-dimensional system of Coulomb-interacting particles that are confined in a time-dependent quadratic external potential. We finally show that our results can be used to assess the accuracy of numerical simulations of time-dependent Hamiltonian systems. 11. Effective Hamiltonian for edge states in graphene. DOE PAGES Deshpande, H.; Winkler, R. 2017-06-03 Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Lambda in the Brillouin zone (BZ) with protected degeneracies at Lambda. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. We show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Lambda for the edge states without affecting the bulk spectrum.« less 12. Numerical Continuation of Hamiltonian Relative Periodic Orbits Wulff, Claudia; Schebesch, Andreas 2008-08-01 The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years, there has been rapid progress in the development of a bifurcation theory for dynamical systems with structure, such as symmetry or symplecticity. But as yet, there are few results on the numerical computation of those bifurcations. The methods we present in this paper are a first step toward a systematic numerical analysis of generic bifurcations of Hamiltonian symmetric periodic orbits and relative periodic orbits (RPOs). First, we show how to numerically exploit spatio-temporal symmetries of Hamiltonian periodic orbits. Then we describe a general method for the numerical computation of RPOs persisting from periodic orbits in a symmetry breaking bifurcation. Finally, we present an algorithm for the numerical continuation of non-degenerate Hamiltonian relative periodic orbits with regular drift-momentum pair. Our path following algorithm is based on a multiple shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré section and a tangential continuation method with implicit reparametrization. We apply our methods to continue the famous figure eight choreography of the three-body system. We find a relative period doubling bifurcation of the planar rotating eight family and compute the rotating choreographies bifurcating from it. 13. Redesign of the DFT/MRCI Hamiltonian SciTech Connect Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M. 2016-01-21 The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion. 14. Cylindrical coordinate representation for multiband Hamiltonians Takhtamirov, Eduard 2012-10-01 Rotationally invariant combinations of the Brillouin zone-center Bloch functions are used as basis function to express in cylindrical coordinates the valence-band and Kane envelope-function Hamiltonians for wurtzite and zinc-blende semiconductor heterostructures. For cylindrically symmetric systems, this basis allows to treat the envelope functions as eigenstates of the operator of projection of total angular momentum on the symmetry axis, with the operator's eigenvalue conventionally entering the Hamiltonians as a parameter. Complementing the Hamiltonians with boundary conditions for the envelope functions on the symmetry axis, we present for the first time a complete formalism for efficient modeling and description of multiband electron states in low-dimensional semiconductor structures with cylindrical symmetry. To demonstrate the potency of the cylindrical symmetry approximation and establish a criterion of its applicability for actual structures, we map the ground and several excited valence-band states in an isolated wurtzite GaN quantum wire of a hexagonal cross-section to the states in an equivalent quantum wire of a circular cross-section. 15. Dynamics of Hamiltonian Systems and Memristor Circuits Itoh, Makoto; Chua, Leon In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems. 16. Ab initio infrared and Raman spectra NASA Technical Reports Server (NTRS) Fredkin, D. R.; White, S. R.; Wilson, K. R.; Komornicki, A. 1983-01-01 It is pointed out that with increased computer power and improved computational techniques, such as the gradients developed in recent years, it is becoming practical to compute spectra ab initio, from the fundamental constants of nature, for systems of increasing complexity. The present investigation has the objective to explore several possible ab initio approaches to spectra, giving particular attention to infrared and nonresonance Raman. Two approaches are discussed. The sequential approach, in which first the electronic part and then later the nuclear part of the Born-Oppenheimer approximation is solved, is appropriate for small systems. The simultaneous approach, in which the electronic and nuclear parts are solved at the same time, is more appropriate for many-atom systems. A review of the newer quantum gradient techniques is provided, and the infrared and Raman spectral band contours for the water molecule are computed. 17. Formalisms for Electron Exchange Kinetics in Aqueous Solution, and the Role of Ab Initio Techniques in Their Implementation SciTech Connect Newton, M. D. 1980-01-01 Formalisms suitable for calculating the rate of electron exchange between transition metal complexes in aqueous solution are reviewed and implemented in conjunction with ab initio quantum chemical calculations which provide crucial off-diagonal Hamiltonian matrix elements as well as other relevant electronic structural data. Rate constants and activation parameters are calculated for the hex-aquo Fe2 +-Fe3+ system, using a simple activated complex theory, a non-adiabatic semi-classical model which includes nuclear tunnelling, and a more detailed quantum mechanical method based on the Golden Rule. Comparisons are made between calculated results and those obtained by extrapolating experimental data to zero ionic strength. All methods yield similar values for the overall rate constant (∾ 0.1 L/(mol-sec)). The experimental activation parameters (δH and δS) are in somewhat better agreement with the semi classical and quantum mechanical results than with those from the simple activated complex theory, thereby providing some indication that non-adiabaticity and nuclear tunnelling may be important in the Fe2+/3+ exchange reaction. It is concluded that a model based on direct metal-metal overlap can account for the observed reaction kinetics provided the reactants are allowed to approach well within the traditional contact distance of 6.9 Å. 6 figures, 7 tables. 18. A self-consistent and environment-dependent Hamiltonian for large-scale simulations of complex nanostructures Yu, Ming; Wu, S. Y.; Jayanthi, C. S. 2009-11-01 This review is devoted to the development of a robust semi-empirical Hamiltonian for quantum-mechanics-based simulations. The Hamiltonian referred as self-consistent (SC) and environment-dependent (ED) Hamiltonian is developed in the framework of linear combination of atomic orbitals (LCAO) and includes multi-center electron-ion and electron-electron interactions. Furthermore, the framework allows for a self-consistent treatment of charge-redistributions. The parameterized Hamiltonian matrix elements and overlap functions are obtained by fitting them to accurate first-principles database of properties corresponding to clusters and bulk phases of materials. The total energy includes the band structure energy, the correction term from the double-counting of electrons, and ion-ion repulsions, where the band structure energy is obtained by solving a generalized eigenvalue equation. Linear scaling algorithms for large-scale simulations of materials have also been incorporated. The present approach goes beyond the traditional two-center tight-binding Hamiltonians in terms of its accuracy and transferability and allows the study of system sizes that are beyond the scope of ab-initio simulations. We have studied a wide-variety of complex materials and complex phenomena using the SCED-LCAO MD that include: (i) the structure and stability of bucky-diamond carbon clusters and their phase transformations upon annealing, (ii) the initial stage of growth of single-wall carbon nanotubes (SWCNTs), and (iii) structural and electronic properties of bucky-diamond SiC clusters and SiC nanowires (NWs). The successful outcome of these case studies is a testament to the transferability of the Hamiltonian to different types of atomic environments ( i.e., co-ordinations and bonding configurations). 19. The Use of Ab Initio Wavefunctions in Line-Shape Calculations for Water Vapor Gamache, Robert R.; Lamouroux, Julien; Schwenke, David W. 2014-06-01 In semi-classical line-shape calculations, the internal motions of the colliding pair are treated via quantum mechanics and the collision trajectory is determined by classical dynamics. The quantum mechanical component, i.e. the determination of reduced matrix elements (RME) for the colliding pair, requires the wavefunctions of the radiating and the perturbing molecules be known. Here the reduced matrix elements for collisions in the ground vibrational state of water vapor are calculated by two methods and compared. First, wavefunctions determined by diagonalizing an effective (Watson) Hamiltonian are used to calculate the RMEs and, second, the ab initio wavefunctions of Partridge and Schwenke are used. While the ground vibrational state will yield the best approximation of the wavefunctions from the effective Hamiltonian approach, this study clearly identifies problems for states not included in the fit of the Hamiltonian and for extrapolated states. RMEs determined using ab initio wavefunctions use ˜100000 times more computational time; however, all ro-vibrational interactions are included. Hence, the ab initio approach will yield better RMEs as the number of vibrational quanta exchanged in the optical transition increases, resulting in improvements in calculated half-widths and line shifts. It is important to note that even for pure rotational transitions the use of ab initio wavefunctions will yield improved results. 20. Ab initio infrared and Raman spectra Fredkin, Donald R.; Komornicki, Andrew; White, Steven R.; Wilson, Kent R. 1983-06-01 We discuss several ways in which molecular absorption and scattering spectra can be computed ab initio, from the fundamental constants of nature. These methods can be divided into two general categories. In the first, or sequential, type of approach, one first solves the electronic part of the Schrödinger equation in the Born-Oppenheimer approximation, mapping out the potential energy, dipole moment vector (for infrared absorption) and polarizability tensor (for Raman scattering) as functions of nuclear coordinates. Having completed the electronic part of the calculation, one then solves the nuclear part of the problem either classically or quantum mechanically. As an example of the sequential ab initio approach, the infrared and Raman rotational and vibrational-rotational spectral band contours for the water molecule are computed in the simplest rigid rotor, normal mode approximation. Quantum techniques are used to calculate the necessary potential energy, dipole moment, and polarizability information at the equilibrium geometry. A new quick, accurate, and easy to program classical technique involving no reference to Euler angles or special functions is developed to compute the infrared and Raman band contours for any rigid rotor, including asymmetric tops. A second, or simultaneous, type of ab initio approach is suggested for large systems, particularly those for which normal mode analysis is inappropriate, such as liquids, clusters, or floppy molecules. Then the curse of dimensionality prevents mapping out in advance the complete potential, dipole moment, and polarizability functions over the whole space of nuclear positions of all atoms, and a solution in which the electronic and nuclear parts of the Born-Oppenheimer approximation are simultaneously solved is needed. A quantum force classical trajectory (QFCT) molecular dynamic method, based on linear response theory, is described, in which the forces, dipole moment, and polarizability are computed quantum 1. Hierarchical structure of noncanonical Hamiltonian systems Yoshida, Z.; Morrison, P. J. 2016-02-01 Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of ‘equipartition’ may bear no specific structure. Fluid turbulence is a typical example—while turbulent mixing seems to increase entropy, a variety of sustained vortical structures can emerge. In Hamiltonian formalism, some topological constraints are represented by Casimir invariants (for example, helicities of a fluid or a plasma), and then, the effective phase space is reduced to the Casimir leaves. However, a general constraint is not necessarily integrable, which precludes the existence of an appropriate Casimir invariant; the circulation is an example of such an invariant. In this work, we formulate a systematic method to embed a Hamiltonian system in an extended phase space; we introduce phantom fields and extend the Poisson algebra. A phantom field defines a new Casimir invariant, a cross helicity, which represents a topological constraint that is not integrable in the original phase space. Changing the perspective, a singularity of the extended system may be viewed as a subsystem on which the phantom fields (though they are actual fields, when viewed from the extended system) vanish, i.e., the original system. This hierarchical relation of degenerate Poisson manifolds enables us to see the ‘interior’ of a singularity as a sub Poisson manifold. The theory can be applied to describe bifurcations and instabilities in a wide class of general Hamiltonian systems (Yoshida and Morrison 2014 Fluid Dyn. Res. 46 031412). 2. Erythema ab igne. PubMed Miller, Kristen; Hunt, Raegan; Chu, Julie; Meehan, Shane; Stein, Jennifer 2011-10-15 Erythema ab igne is a reticulated, erythematous or hyperpigmented dermatosis that results from chronic and repeated exposure to low levels of infrared radiation. Multiple heat sources have been reported to cause this condition, which include heated reclining chairs, heating pads, hot water bottles, car heaters, electric space heaters, and, more recently, laptop computers. Treatment consists of withdrawing the inciting heat source. Although erythema ab igne carries a good prognosis, it is not necessarily a self-limited diagnosis as patients are at long-term risk of developing subsequent cutaneous malignant conditions, which include squamous cell and merkel-cell carcinomas. 3. The quantization of the Rabi Hamiltonian Vandaele, Eva R. J.; Arvanitidis, Athanasios; Ceulemans, Arnout 2017-03-01 The Rabi Hamiltonian addresses the proverbial paradigmatic case of a two-level fermionic system coupled to a single bosonic mode. It is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which rationalize the spectrum by relating the solutions to the Juddian baselines. The relationship with Braak’s integrability claim (Braak 2011 Phys. Rev. Lett. 107 100401) is discussed. 4. Quantum Hamiltonian Identification from Measurement Time Traces Zhang, Jun; Sarovar, Mohan 2014-08-01 Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings. 5. Hamiltonian analysis of BHT massive gravity Blagojević, M.; Cvetković, B. 2011-01-01 We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants ( Λ 0, m 2), our canonical analysis reveals the special role of the condition Λ 0/ m 2 ≠ -1. In this sector, the dimension of the physical phase space is found to be N ∗ = 4, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra. 6. Forced Oscillations of Nonlinear Hamiltonian Systems, II. DTIC Science & Technology 1979-12-01 Rabinowitz (J8], 9]). The author obtained similar results ([6]), by using a variational method devised b.: F. Clarke and himself for convex subquadratic...and satisfying, for some constants bl > a’ > 0 and 5 > 2: (39) a’ ixi-21Y 2 _< (V"(x)yy) < b’ lxiy-21yj 2, all x ev , y c ip Then for any T > 0, there is...34Linear operators", Wiley. [6] I. Ekeland, "Periodic Hamiltonian trajectories and a theorem of P. Rabinowitz ", 1978, to appear in Journal of Differential 7. Exact two-component Hamiltonians revisited. PubMed Liu, Wenjian; Peng, Daoling 2009-07-21 Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schrodinger picture. The two formulations become equivalent after the mistake is corrected. 8. Exact two-component Hamiltonians revisited SciTech Connect Liu Wenjian; Peng Daoling 2009-07-21 Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schroedinger picture. The two formulations become equivalent after the mistake is corrected. 9. Hamiltonian Description of Convective-cell Generation SciTech Connect J.A. Krommes and R.A. Kolesnikov 2004-03-11 The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted. 10. Perturbation Theory for Parent Hamiltonians of Matrix Product States Szehr, Oleg; Wolf, Michael M. 2015-05-01 This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013). 11. Wigner quantization of some one-dimensional Hamiltonians SciTech Connect Regniers, G.; Van der Jeugt, J. 2010-12-15 Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those we have the ubiquitous relation with Lie superalgebras and their representations. In this paper, we study two one-dimensional Hamiltonians for which the Wigner quantization is related with the orthosymplectic Lie superalgebra osp(1\|2). One of them, the Hamiltonian H=xp, is popular due to its connection with the Riemann zeros, discovered by Berry and Keating on the one hand and Connes on the other. The Hamiltonian of the free particle, H{sub f}=p{sup 2}/2, is the second Hamiltonian we will examine. Wigner quantization introduces an extra representation parameter for both of these Hamiltonians. Canonical quantization is recovered by restricting to a specific representation of the Lie superalgebra osp(1\|2). 12. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians SciTech Connect Buljubasich, Lisandro; Dente, Axel D.; Levstein, Patricia R.; Chattah, Ana K.; Pastawski, Horacio M.; Sánchez, Claudia M. 2015-10-28 We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor \|k\| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors \|k\|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed. 13. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians Buljubasich, Lisandro; Sánchez, Claudia M.; Dente, Axel D.; Levstein, Patricia R.; Chattah, Ana K.; Pastawski, Horacio M. 2015-10-01 We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor \|k\| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors \|k\|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed. 14. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians. PubMed Buljubasich, Lisandro; Sánchez, Claudia M; Dente, Axel D; Levstein, Patricia R; Chattah, Ana K; Pastawski, Horacio M 2015-10-28 We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor \|k\| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors \|k\|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed. 15. Nucleus-Dependent Valence-Space Approach to Nuclear Structure Stroberg, S. R.; Calci, A.; Hergert, H.; Holt, J. D.; Bogner, S. K.; Roth, R.; Schwenk, A. 2017-01-01 We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture three-nucleon (3 N ) forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper p and s d shells. Finally, we address the 1+/3+ inversion problem in 22Na and 46V. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei. 16. Norm-square localization for Hamiltonian LG-spaces Loizides, Yiannis 2017-04-01 We prove a formula for twisted Duistermaat-Heckman distributions associated to a Hamiltonian LG-space. The terms of the formula are localized at the critical points of the norm-square of the moment map, and can be computed in cross-sections. Our main tools are the theory of quasi-Hamiltonian G-spaces, as well as the Hamiltonian cobordism approach to norm-square localization introduced recently by Harada and Karshon. 17. Hamiltonian and non-Hamiltonian perturbation theory for nearly periodic motion 1986-02-01 Kruskal's asymptotic theory of nearly period motion [M. Kruskal, J. Math. Phys. 4, 806 (1962)] (with applications to nonlinear oscillators, guiding center motion, etc.) is generalized and modified. A new more natural recursive formula, with considerable advantages in applications, determining the averaging transformations and the drift equations is derived. Also almost quasiperiodic motion is considered. For a Hamiltonian system, a manifestly Hamiltonian extension of Kruskal's theory is given by means of the phase-space Lagrangian formulation of Hamiltonian mechanics. By performing an averaging transformation on the phase-space Lagrangian for the system (L → L¯) and adding a total derivative dS/dτ, a nonoscillatory Lagrangian Λ=L¯+dS/dτ is obtained. The drift equations and the adiabatic invariant are now obtained from Λ. By truncating Λ to some finite order in the small parameter ɛ, manifestly Hamiltonian approximating systems are obtained. The utility of the method for treating the guiding-center motion is demonstrated in a separate paper. 18. Ab initio derivation of model energy density functionals Dobaczewski, Jacek 2016-08-01 I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results. 19. Hamiltonian description of closed configurations of the vacuum magnetic field SciTech Connect Skovoroda, A. A. 2015-05-15 Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov. 20. Entanglement Hamiltonians for Chiral Fermions with Zero Modes Klich, Israel; Vaman, Diana; Wong, Gabriel 2017-09-01 In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in (1 +1 )D . We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy. 1. Position-dependent mass quantum Hamiltonians: general approach and duality Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F. 2016-03-01 We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article. 2. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy SciTech Connect Sugny, D.; Jauslin, H. R.; Mardesic, P.; Pelletier, M.; Jebrane, A. 2008-04-15 Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskii, and Zhilinskii, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); and Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m:-n resonant systems. 3. How is Lorentz invariance encoded in the Hamiltonian? Kajuri, Nirmalya 2016-07-01 One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available. 4. Hamiltonian theory of nonlinear waves in planetary rings NASA Technical Reports Server (NTRS) Stewart, G. R. 1987-01-01 The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle. 5. Action with Acceleration i: Euclidean Hamiltonian and Path Integral Baaquie, Belal E. 2013-10-01 An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated. 6. Dressed qubits in nuclear spin baths SciTech Connect Wu Lianao 2010-04-15 We present a method to encode a dressed qubit into the product state of an electron spin localized in a quantum dot and its surrounding nuclear spins via a dressing transformation. In this scheme, the hyperfine coupling and a portion of a nuclear dipole-dipole interaction become logic gates, while they are the sources of decoherence in electron-spin qubit proposals. We discuss errors and corrections for the dressed qubits. Interestingly, the effective Hamiltonian of nuclear spins is equivalent to a pairing Hamiltonian, which provides the microscopic mechanism to protect dressed qubits against decoherence. 7. Classical Hamiltonian structures in wave packet dynamics Gray, Stephen K.; Verosky, John M. 1994-04-01 The general, N state matrix representation of the time-dependent Schrödinger equation is equivalent to an N degree of freedom classical Hamiltonian system. We describe how classical mechanical methods and ideas can be applied towards understanding and modeling exact quantum dynamics. Two applications are presented. First, we illustrate how qualitative insights may be gained by treating the two state problem with a time-dependent coupling. In the case of periodic coupling, Poincaré surfaces of section are used to view the quantum dynamics, and features such as the Floquet modes take on interesting interpretations. The second application illustrates computational implications by showing how Liouville's theorem, or more generally the symplectic nature of classical Hamiltonian dynamics, provides a new perspective for carrying out numerical wave packet propagation. We show how certain simple and explicit symplectic integrators can be used to numerically propagate wave packets. The approach is illustrated with an application to the problem of a diatomic molecule interacting with a laser, although it and related approaches may be useful for describing a variety of problems. 8. Strong coupling expansions for nonintegrable hamiltonian systems SciTech Connect Abarbanel, Henry D. I.; Crawford, John David 1982-09-01 In this paper, we present a method for studying nonintegrable Hamiltonian systems H(I,θ) = H0(I) + kH1(I,θ) (I, θ are action-angle variables) in the regime of large k. Our central tool is the conditional probability P(I,θ,t \| I00,t0) that the system is at I. θ at time t given that it resided at I0, θ0 at t0. An integral representation is given for this conditional probability. By discretizing the Hamiltonian equations of motion in small time steps, ϵ, we arrive at a phase volume-preserving mapping which replaces the actual flow. When the motion on the energy surface E = H(I,θ) is bounded we are able to evaluate physical quantities of interest for large k and fixed ϵ. We also discuss the representation of P (I,θ,t \| I00t0) when an external random forcing is added in order to smooth the singular functions associated with the deterministic flow. Explicit calculations of a “diffusion” coefficient are given for a non-integrable system with two degrees of freedom. Finally, the limit ϵ → 0, which returns us to the actual flow, is subtle and is discussed. 9. Thermalization Time Bounds for Pauli Stabilizer Hamiltonians Temme, Kristan 2017-03-01 We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven. 10. A Hamiltonian Five-Field Gyrofluid Model Keramidas Charidakos, Ioannis; Waelbroeck, Francois; Morrison, Philip 2015-11-01 Reduced fluid models constitute versatile tools for the study of multi-scale phenomena. Examples include magnetic islands, edge localized modes, resonant magnetic perturbations, and fishbone and Alfven modes. Gyrofluid models improve over Braginskii-type models by accounting for the nonlocal response due to particle orbits. A desirable property for all models is that they not only have a conserved energy, but also that they be Hamiltonian in the ideal limit. Here, a Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of electron and ion densities, the parallel component of ion and electron velocities and ion temperature. Quasineutrality and Ampere's law determine respectively the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated to five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models. This work was funded by U.S. DOE Contract No. DE-FG02-04ER-54742. 11. AB initio infrared and Raman spectra Fredkin, D. R.; Komornicki, A.; White, S. R.; Wilson, K. R. 1982-08-01 We discuss several ways in which molecular absorption and scattering spectra can be computed ab initio, from the fundamental constants of nature. These methods can be divided into two general categories. In the first, or sequential, type of approach, one first solves the electronic part of the Schroedinger equation in the Born-Oppenheimer approximation, mapping out the potential energy, dipole moment vector (for infrared absorption) and polarizability tensor (for Raman scattering) as functions of nuclear coordinates. Having completed the electronic part of the calculation, one then solves the nuclear part of the problem either classically or quantum mechanically. As an example of the sequential ab initio approach, the infrared and Raman rotational and vibrational-rotational spectral band contours for the water molecule are computed in the simplest rigid rotor, normal mode approximation. Quantum techniques, are used to calculate the necessary potential energy, dipole moment, and polarizability information at the equilibrium geometry. A new quick, accurate, and easy to program classical technique involving no reference to Euler angles or special functions is developed to compute the infrared and Raman angles or special functions is developed to compute the infrared and Raman band contours for any rigid rotor, including asymmetric tops. A second, or simultaneous, type of ab initio approach is suggested for large systems, particularly those for which normal mode analysis is inappropriate, such as liquids, clusters, or floppy molecules. 12. Multiple time step integrators in ab initio molecular dynamics SciTech Connect Luehr, Nathan; Martínez, Todd J.; Markland, Thomas E. 2014-02-28 Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions are described by empirical potentials is now well established, their application to ab initio molecular dynamics calculations has been limited by difficulties associated with splitting the ab initio potential into fast and slowly varying components. Here we present two schemes that enable efficient time-scale separation in ab initio calculations: one based on fragment decomposition and the other on range separation of the Coulomb operator in the electronic Hamiltonian. We demonstrate for both water clusters and a solvated hydroxide ion that multiple time-scale molecular dynamics allows for outer time steps of 2.5 fs, which are as large as those obtained when such schemes are applied to empirical potentials, while still allowing for bonds to be broken and reformed throughout the dynamics. This permits computational speedups of up to 4.4x, compared to standard Born-Oppenheimer ab initio molecular dynamics with a 0.5 fs time step, while maintaining the same energy conservation and accuracy. 13. Vibrational analysis of HOCl up to 98{percent} of the dissociation energy with a Fermi resonance Hamiltonian SciTech Connect Jost, R.; Joyeux, M.; Skokov, S.; Bowman, J. 1999-10-01 We have analyzed the vibrational energies and wave functions of HOCl obtained from previous {ital ab initio} calculations [J. Chem. Phys. {bold 109}, 2662 (1998); {bold 109}, 10273 (1998)]. Up to approximately 13&hthinsp;000 cm{sup {minus}1}, the normal modes are nearly decoupled, so that the analysis is straightforward with a Dunham model. In contrast, above 13&hthinsp;000 cm{sup {minus}1} the Dunham model is no longer valid for the levels with no quanta in the OH stretch (v{sub 1}=0). In addition to v{sub 1}, these levels can only be assigned a so-called polyad quantum number P=2v{sub 2}+v{sub 3}, where 2 and 3 denote, respectively, the bending and OCl stretching normal modes. In contrast, the levels with v{sub 1}{ge}2 remain assignable with three v{sub i} quantum numbers up to the dissociation (D{sub 0}=19&hthinsp;290&hthinsp;cm{sup {minus}1}). The interaction between the bending and the OCl stretch ({omega}{sub 2}{congruent}2{omega}{sub 3}) is well described with a simple, fitted Fermi resonance Hamiltonian. The energies and wave functions of this model Hamiltonian are compared with those obtained from {ital ab initio} calculations, which in turn enables the assignment of many additional {ital ab initio} vibrational levels. Globally, among the 809 bound levels calculated below dissociation, 790 have been assigned, the lowest unassigned level, No. 736, being located at 18&hthinsp;885 cm{sup {minus}1} above the (0,0,0) ground level, that is, at about 98{percent} of D{sub 0}. In addition, 84 {open_quotes}resonances{close_quotes} located above D{sub 0} have also been assigned. Our best Fermi resonance Hamiltonian has 29 parameters fitted with 725 {ital ab initio} levels, the rms deviation being of 5.3 cm{sup {minus}1}. This set of 725 fitted levels includes the full set of levels up to No. 702 at 18&hthinsp;650 cm{sup {minus}1}. The {ital ab initio} levels, which are assigned but not included in the fit, are reasonably predicted by the model Hamiltonian, but with a 14. Spectral Properties of Fractional Quantum Hall Hamiltonians Weerasinghe, Amila The fractional quantum Hall (FQH) effect plays a prominent role in the study of topological phases of matter and of strongly correlated electron systems in general. FQH systems have been demonstrated to show many interesting novel properties such as fractional charges, and are believed to harbor even more intriguing phenomena such as fractional statistics. However, there remain many interesting questions to be addressed in this regime. The work reported in this thesis aims to push the envelope of our understanding of the low-energy properties of FQH states using microscopic principles. In the first part of the thesis, we present a systematic perturbative approach to study excitations in the thin cylinder/torus limit of the quantum Hall states. The approach is applied to the Haldane-Rezayi and Gaffnian quantum Hall states, which are both expected to have gapless excitations in the usual two-dimensional thermodynamic limit. For the Haldane-Rezayi state, we confirm that gapless excitations are present also in the "one-dimensional" thermodynamic limit of an infinite thin cylinder, in agreement with earlier considerations based on the wave functions alone. In contrast, we identify the lowest excitations of the Gaffnian state in the thin cylinder limit, and conclude that they are gapped, using a combination of perturbative and numerical means. We discuss possible scenarios for the cross-over between the two-dimensional and the one-dimensional thermodynamic limit in this case. In the second part of the thesis, we study the low energy spectral properties of positive center-of-mass conserving two-body Hamiltonians as they arise in models of FQH states. Starting from the observation that positive many-body Hamiltonians must have ground state energies that increase monotonously in particle number, we explore what general additional constraints can be obtained for two-body interactions with "center-of-mass conservation" symmetry, both in the presence and absence of particle 15. New relativistic Hamiltonian: the angular magnetoelectric coupling Paillard, Charles; Mondal, Ritwik; Berritta, Marco; Dkhil, Brahim; Singh, Surendra; Oppeneer, Peter M.; Bellaiche, Laurent 2016-10-01 Spin-Orbit Coupling (SOC) is a ubiquitous phenomenon in the spintronics area, as it plays a major role in allowing for enhancing many well-known phenomena, such as the Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, the Rashba effect, etc. However, the usual expression of the SOC interaction ħ/4m2c2 [E×p] • σ (1) where p is the momentum operator, E the electric field, σ the vector of Pauli matrices, breaks the gauge invariance required by the electronic Hamiltonian. On the other hand, very recently, a new phenomenological interaction, coupling the angular momentum of light and magnetic moments, has been proposed based on symmetry arguments: ξ/2 [r × (E × B)] M, (2) with M the magnetization, r the position, and ξ the interaction strength constant. This interaction has been demonstrated to contribute and/or give rise, in a straightforward way, to various magnetoelectric phenomena,such as the anomalous Hall effect (AHE), the anisotropic magnetoresistance (AMR), the planar Hall effect and Rashba-like effects, or the spin-current model in multiferroics. This last model is known to be the origin of the cycloidal spin arrangement in bismuth ferrite for instance. However, the coupling of the angular momentum of light with magnetic moments lacked a fundamental theoretical basis. Starting from the Dirac equation, we derive a relativistic interaction Hamiltonian which linearly couples the angular momentum density of the electromagnetic (EM) field and the electrons spin. We name this coupling the Angular MagnetoElectric (AME) coupling. We show that in the limit of uniform magnetic field, the AME coupling yields an interaction exactly of the form of Eq. (2), thereby giving a firm theoretical basis to earlier works. The AME coupling can be expressed as: ξ [E × A] • σ (3) with A being the vector potential. Interestingly, the AME coupling was shown to be complementary to the traditional SOC, and together they restore the gauge invariance of the 16. On the physical applications of hyper-Hamiltonian dynamics Gaeta, Giuseppe; Rodríguez, Miguel A. 2008-05-01 An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate—in suitable limits—the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin. 17. Higher-order Hamiltonian fluid reduction of Vlasov equation SciTech Connect Perin, M.; Chandre, C.; Morrison, P.J.; Tassi, E. 2014-09-15 From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of this model from the Poisson bracket of the Vlasov equation, and we discuss the associated Casimir invariants. 18. Boson Hamiltonians and stochasticity for the vorticity equation NASA Technical Reports Server (NTRS) Shen, Hubert H. 1990-01-01 The evolution of the vorticity in time for two-dimensional inviscid flow and in Lagrangian time for three-dimensional viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise. 19. A HAMILTONIAN FORMULATION FOR SPIRAL-SECTOR ACCELERATORS. SciTech Connect BERG,J.S. 2007-11-05 I develop a formulation for Hamiltonian dynamics in an accelerator with magnets whose edges follow a spiral. I demonstrate using this Hamiltonian that a spiral FFAG can be made perfectly 'scaling'. I examine the effect of tilting an RF cavity with respect a radial line from the center of the machine, potentially with a different angle than the spiral of the magnets. 20. Non-self-adjoint hamiltonians defined by Riesz bases SciTech Connect Bagarello, F.; Inoue, A.; Trapani, C. 2014-03-15 We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators. 1. Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings de León, Manuel; Jiménez, Fernando; Martín de Diego, David 2012-05-01 The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to the geometrical integration of Hamiltonian systems are obtained. 2. Hamiltonian structures for the Ostrovsky-Vakhnenko equation Brunelli, J. C.; Sakovich, S. 2013-01-01 We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko (OV) equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed. 3. Friction in a Model of Hamiltonian Dynamics Fröhlich, Jürg; Gang, Zhou; Soffer, Avy 2012-10-01 We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle's trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest. "A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion."—— Aristotle 4. Nonperturbative light-front Hamiltonian methods Hiller, J. R. 2016-09-01 We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations. 5. A Hamiltonian five-field gyrofluid model SciTech Connect Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. 2015-11-15 A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models. 6. Hamiltonian formalism and path entropy maximization Davis, Sergio; González, Diego 2015-10-01 Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference. 7. Hamiltonian formulations and symmetries in rod mechanics SciTech Connect Dichmann, D.J.; Li, Yiwei; Maddocks, J.H. 1996-12-31 This article provides a survey of contemporary rod mechanics, including both dynamic and static theories. Much of what we discuss is regarded as classic material within the mechanics community, but the objective here is to provide a self-contained account accessible to workers interested in modelling DNA. We also describe a number of recent results and computations involving rod mechanics that have been obtained by our group at the University of Maryland. This work was largely motivated by applications to modelling DNA, but our approach reflects a background of research in continuum mechanics. In particular, we emphasize the role that Hamiltonian formulations and symmetries play in the effective computation of special solutions, conservation laws of dynamics and integrals of statics. 41 refs., 10 figs. 8. Hamiltonian inclusive fitness: a fitter fitness concept PubMed Central Costa, James T. 2013-01-01 In 1963–1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's ‘special difficulty’—the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of ‘offspring ideas’ that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated. PMID:24132089 9. Using Hamiltonian control to desynchronize Kuramoto oscillators Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo 2017-02-01 Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model. 10. Discrete variable representation for singular Hamiltonians Schneider, Barry I.; Nygaard, Nicolai 2004-11-01 We discuss the application of the discrete variable representation (DVR) to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved, the boundary conditions are satisfied, and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions. 11. Fourier series expansion for nonlinear Hamiltonian oscillators. PubMed Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac 2010-06-01 The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate. 12. Finite Hamiltonian Systems: Linear Transformations and Aberrations Wolf, Kurt Bernardo 2008-11-01 In finite Hamiltonian systems, the operators of position, momentum, and energy have a finite number N of eigenvalues. These operators can be naturally realized as generators of the Lie algebra su(2), in a representation of spin j, of dimension N = 2j+1. Time evolution is rotation of a phase space sphere, whose projections perform the harmonic motion of an oscillator. The (centrally extended) group of rigid—linear—motions of this phase space is then U(2). On the other hand, N-point wavefunctions—signals—can be subject to a U(N) group of unitary matrices, containing the linear U(2); aberrations are transformations outside that subgroup. As in geometric optics, we classify the aberration multiplets by order and weight. Their action on phase space is displayed by means of a Wigner function on the sphere, to be compared with the corresponding geometric canonical transformations. 13. Hamiltonian formalism of minimal massive gravity Mahdavian Yekta, Davood 2015-09-01 In this paper, we study the three-dimensional minimal massive gravity (MMG) in the Hamiltonian formalism. At first, we define the canonical gauge generators as building blocks in this formalism and then derive the canonical expressions for the asymptotic conserved charges. The construction of a consistent asymptotic structure of MMG requires introducing suitable boundary conditions. In the second step, we show that the Poisson bracket algebra of the improved canonical gauge generators produces an asymptotic gauge group, which includes two separable versions of the Virasoro algebras. For instance, we study the Banados-Teitelboim-Zanelli (BTZ) black hole as a solution of the MMG field equations, and the conserved charges give the energy and angular momentum of the BTZ black hole. Finally, we compute the black hole entropy from the Cardy formula in the dual conformal field theory and show our result is consistent with the value obtained by using the Smarr formula from the holographic principle. 14. Discrete variable representation for singular Hamiltonians. PubMed Schneider, Barry I; Nygaard, Nicolai 2004-11-01 We discuss the application of the discrete variable representation (DVR) to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved, the boundary conditions are satisfied, and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions. 15. Hamiltonian description of composite fermions: Magnetoexciton dispersions Murthy, Ganpathy 1999-11-01 A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in fractional quantum hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the ν=13, 25, and 37 gapped fractions, and find approximate agreement with numerical results. I also analyze the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 25 and 37, and it is shown that the spin-polarized 25 state, in contrast to the spin-polarized 13 state, cannot be described as a simple quantum ferromagnet. 16. Hamiltonian Approach to the Dynamical Casimir Effect SciTech Connect Haro, Jaume; Elizalde, Emilio 2006-09-29 A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term--proportional to the mirrors' acceleration - which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors - while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out. 17. Geometric solitons of Hamiltonian flows on manifolds SciTech Connect Song, Chong; Sun, Xiaowei; Wang, Youde 2013-12-15 It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution. 18. Modal decomposition of Hamiltonian variational equations NASA Technical Reports Server (NTRS) Wiesel, William E. 1994-01-01 Over any finite arc of trajectory, the variational equations of a Hamiltonian system can be separated into 'normal' modes. This transformation is canonical, and the Lyapunov exponents over the trajectory arc occur as positive/negative pairs for conjugate modes, while the modal vectors remain unit vectors. This decomposition effectively solves the variational equations for any canonical, linear-dependent system. As an example, we study the Voyager I trajectory. In an interplanetary flyby, some of the modal variables increase by very large multiplicative factors, but this means that their conjugate modal variables decrease by those same very large multiplicative vectors. Maneuver strategies for this case are explored, and the minimum delta upsilon maneuver is found. SciTech Connect Malitsky, N.; Bourianoff, G.; Severgin, Yu. 1993-11-01 For the many applied tasks of accelerator physics, the 4D single particle pseudo-Hamiltonian may be presented as the Hamiltonian of the near-integrable system consisting of integrable and perturbed terms. The KAM theorem states that for sufficiently small perturbation the invariant surfaces continue to exist and, for the systems with two degrees of freedom, completely isolate the thin stochastic layers. As the perturbation strength increases, a transition can occur in which these surfaces disappear and the stochastic layers connect, resulting in globally stochastic motion. One of the important problems is to determine this {open_quotes}boundary{close_quotes} invariant surface. There are several approaches that may be used to describe the regular trajectories in the small limited region. The most powerful method is the perturbation theory which allows us to study the combined influence of the different multipoles. The inclusion of Lie operators improved this method and developed it up to high order perturbation. But the perturbation theory failed to describe the change in topology and since the regular trajectories depend discontinuously on choice of initial coordinates, it cannot be used in the whole region of the stable motion. The authors suggest to limit the attention to the study of the {open_quotes}boundary{close_quotes} invariant and implement the additional {open_quotes}local{close_quotes} transformation. The authors briefly review the well known theories, their advantages and imperfections, and the necessity of the {open_quotes}local{close_quotes} transformation. They present the comparison of the map tracking with the invariants determined by the perturbation methods. 20. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation SciTech Connect Fernández, Francisco M. 2016-06-15 We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition. 1. Simulating typical entanglement with many-body Hamiltonian dynamics SciTech Connect Nakata, Yoshifumi; Murao, Mio 2011-11-15 We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians. 2. Remarks on the Lagrangian representation of bi-Hamiltonian equations Pavlov, M. V.; Vitolo, R. F. 2017-03-01 The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components. 3. Hamiltonian analysis of higher derivative scalar-tensor theories Langlois, David; Noui, Karim 2016-07-01 We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective. 4. Investigation of non-Hermitian Hamiltonians in the Heisenberg picture Miao, Yan-Gang; Xu, Zhen-Ming 2016-05-01 The Heisenberg picture for non-Hermitian but η-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but η-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order Heisenberg equations of motion are complex, we can construct a Hermitian counterpart that gives the same second order equations of motion. In terms of a similarity transformation we verify the iso-spectral property of the Hermitian and non-Hermitian Hamiltonians and obtain the related eigenfunctions. This feature can be used to determine real eigenvalues for such non-Hermitian Hamiltonian systems. As an application, two new non-Hermitian Hamiltonians are constructed and investigated, where one is non-Hermitian and non-PT-symmetric and the other is non-Hermitian but PT-symmetric. Moreover, the complementarity and compatibility between our treatment and the PT symmetry are discussed. 5. Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks Baaquie, Belal E. 2013-10-01 The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks. 6. Quantum control by means of hamiltonian structure manipulation. PubMed Donovan, A; Beltrani, V; Rabitz, H 2011-04-28 A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited 7. Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform. 8. Trinucleon Electromagnetic Form Factors and the Light-Front Hamiltonian Dynamics SciTech Connect Baroncini, F.; Kievsky, A.; Pace, E.; Salme, G. 2008-10-13 This contribution briefly illustrates preliminary calculations of the electromagnetic form factors of {sup 3}He and {sup 3}H, obtained within the Light-front Relativistic Hamiltonian Dynamics, adopting i) a Poincare covariant current operator, without dynamical two-body currents, and ii) realistic nuclear bound states with S, P and D waves. The kinematical region of few (GeV/c){sup 2}, relevant for forthcoming TJLAB experiments, has been investigated, obtaining possible signatures of relativistic effects for Q{sup 2}>2.5(GeV/c){sup 2}. 9. Five-dimensional collective Hamiltonian with the Gogny force: An ongoing saga Libert, J.; Delaroche, J.-P.; Girod, M. 2016-07-01 We provide a sample of analyses for nuclear spectroscopic properties based on the five-dimensional collective Hamiltonian (5DCH) implemented with the Gogny force. The very first illustration is dating back to the late 70's. It is next followed by others, focusing on shape coexistence, shape isomerism, superdeformation, and systematics over the periodic table. Finally, the inclusion of Thouless-Valatin dynamical contributions to vibrational mass parameters is briefly discussed as a mean of strengthening the basis of the 5DCH theory. 10. Ab initio alpha-alpha scattering Elhatisari, Serdar; Lee, Dean; Rupak, Gautam; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A.; Luu, Thomas; Meißner, Ulf-G. 2015-12-01 Processes such as the scattering of alpha particles (4He), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars. In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei—nuclei with even and equal numbers of protons and neutrons—is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the ‘adiabatic projection method’ to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of 11. Ab initio alpha-alpha scattering. PubMed Elhatisari, Serdar; Lee, Dean; Rupak, Gautam; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A; Luu, Thomas; Meißner, Ulf-G 2015-12-03 Processes such as the scattering of alpha particles ((4)He), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars. In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei--nuclei with even and equal numbers of protons and neutrons--is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the 'adiabatic projection method' to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of 12. Computational studies of competing phases in model Hamiltonians Jiang, Mi Model Hamiltonians play an important role in our understanding of both quantum and classical systems, such as strongly correlated unconventional superconductivity, quantum magnetism, non-fermi liquid heavy fermion materials and classical magnetic phase transitions. The central problem is how models with many degrees of freedom choose between competing ground states, e.g. magnetic, superconducting, metallic, insulating as the degree of thermal and quantum fluctuations is varied. This dissertation focuses on the numerical investigation of several important model Hamiltonians. Specifically, we used the determinant Quantum Monte Carlo (DQMC) to study three Hubbard-like models: the Fermi-Hubbard model with two regions of different interaction strength, the Fermi-Hubbard model with a spin-dependent band structure, and the related periodic Anderson model (PAM). The first model used was to explore inter-penetration of metallic and Mott insulator physics across a Metal-Mott Insulator interface by computing the magnetic properties and spectral functions. As a minimal model of a half metallic magnet, the second model was used to explore the impact of on-site Hubbard interaction U, finite temperature, and an external (Zeeman) magnetic field on a bilayer tight-binding model with spin-dependent hybridization. We use PAM to study the Knight shift anomaly in heavy fermion materials found in Nuclear magnetic resonance (NMR) experiments and confirm several predictions of the two-fluid theory accounting for the anomaly. Another application of the Hubbard model described in this dissertation is the investigation on the effects of spin-dependent disorder on s-wave superconductors based on the attractive Hubbard model. Here we used the Bogoliubov-de Gennes (BdG) self-consistent approach instead of quantum simulations. The spin-dependent random potential was shown to induce distinct transitions at which the energy gap and average order parameter vanish, generating an intermediate gapless 13. Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems Vogl, M.; Pankratov, O.; Shallcross, S. 2017-07-01 We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states. 14. Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory Hirayama, Motoaki; Miyake, Takashi; Imada, Masatoshi; Biermann, Silke 2017-08-01 We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees of freedom in a controlled way by a perturbative scheme, we construct an effective Hamiltonian for a restricted low-energy target space incorporating the effects of high-energy degrees of freedom in an effective manner. The resulting effective Hamiltonian can afterwards be solved by accurate many-body solvers. We improve this "multiscale ab initio scheme for correlated electrons" (MACE) primarily in two directions by elaborating and combining two frameworks developed by Hirayama et al. [M. Hirayama, T. Miyake, and M. Imada, Phys. Rev. B 87, 195144 (2013), 10.1103/PhysRevB.87.195144] and Casula et al. [M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Phys. Rev. Lett. 109, 126408 (2012), 10.1103/PhysRevLett.109.126408]: (1) Double counting of electronic correlations between the DFT and the low-energy solver is avoided by using the constrained G W scheme; and (2) the frequency dependent interactions emerging from the partial trace summation are successfully separated into a nonlocal part that is treated following ideas by Hirayama et al. and a local part treated nonperturbatively in the spirit of Casula et al. and are incorporated into the renormalization of the low-energy dispersion. The scheme is favorably tested on the example of SrVO3. 15. Novel Exciton States in Monolayer MoS2: Unconventional Effective Hamiltonian da Jornada, Felipe; Qiu, Diana; Louie, Steven 2014-03-01 Recent well-converged ab inito GW-BSE calculations show that monolayer MoS2 has a large number of strongly bound excitons with varying characters. We show that these excitonic states cannot be even qualitatively described by an effective mass hydrogenic model without a detailed understanding of the 2D screening. Additionally, we identify and analyze one exciton series having an unusually high binding energy, which originates around the Γ point of the Brillouin zone. We show that this excitonic series arises from a fundamentally different effective Hamiltonian with a kinetic energy term resembling a Mexican hat in momentum space, which is responsible for the unusual ordering of the energy levels and distribution of oscillator strength. This work was supported by NSF grant No. DMR10-1006184 and the U.S. DOE under Contract No. DE-AC02-05CH11231. 16. Electronic properties, low-energy Hamiltonian, and superconducting instabilities in CaKFe4As4 Lochner, Felix; Ahn, Felix; Hickel, Tilmann; Eremin, Ilya 2017-09-01 We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe4As4 by combining an ab initio approach and a projection of the band structure to a low-energy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3 d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe4As4 and the parent systems CaFe2As2 and KFe2As2 . In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe4As4 by employing the leading angular harmonics approximation and find two potential A1 g-symmetry representations of the superconducting gap to be the dominant instabilities in this system. 17. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian Wahlen-Strothman, Jacob M.; Henderson, Thomas M.; Hermes, Matthew R.; Degroote, Matthias; Qiu, Yiheng; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E. 2017-02-01 Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime. 18. An effective Hamiltonian approach to quantum random walk Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti 2017-03-01 In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one. 19. Local Hamiltonians for quantitative Green's function embedding methods Rusakov, Alexander A.; Phillips, Jordan J.; Zgid, Dominika 2014-11-01 Embedding calculations that find approximate solutions to the Schrödinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective interactions approximating the low energy physics of the initial realistic system, (ii) mapping the model system onto an impurity Hamiltonian, and (iii) solving the impurity problem. We have developed a novel procedure for parametrizing the impurity Hamiltonian that avoids the mathematically uncontrolled step of constructing the low energy model system. Instead, the impurity Hamiltonian is immediately parametrized to recover the self-energy of the realistic system in the limit of high frequencies or short time. The effective interactions parametrizing the fictitious impurity Hamiltonian are local to the embedded regions, and include all the non-local interactions present in the original realistic Hamiltonian in an implicit way. We show that this impurity Hamiltonian can lead to excellent total energies and self-energies that approximate the quantities of the initial realistic system very well. Moreover, we show that as long as the effective impurity Hamiltonian parametrization is designed to recover the self-energy of the initial realistic system for high frequencies, we can expect a good total energy and self-energy. Finally, we propose two practical ways of evaluating effective integrals for parametrizing impurity models. 20. Nonunitary quantum computation in the ground space of local Hamiltonians Usher, Naïri; Hoban, Matty J.; Browne, Dan E. 2017-09-01 A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial. 1. Hamiltonian of a spinning test particle in curved spacetime SciTech Connect Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra 2009-11-15 Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S{sub Kerr}S (and S{sub Kerr}{sup 2}) through 3PN order, S{sub Kerr} being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order. 2. Hamiltonian of a spinning test-particle in curved spacetime Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra 2010-02-01 Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type SKerr, (and SKerr^2) through 3PN order, SKerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order. ) 3. Hamiltonian of a spinning test particle in curved spacetime Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra 2009-11-01 Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type SKerrS (and SKerr2) through 3PN order, SKerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order. 4. Enhancing sensitivity in quantum metrology by Hamiltonian extensions Fraïsse, Julien Mathieu Elias; Braun, Daniel 2017-06-01 A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form θ G . For such "phase-shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it is possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term from the original Hamiltonian. Neither method makes use of any ancillas, which shows that, for quantum channel estimation with an arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with nitrogen vacancy center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe. 5. Uncertainty relation for non-Hamiltonian quantum systems SciTech Connect Tarasov, Vasily E. 2013-01-15 General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications. 6. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions de Gosson, Maurice A.; Gröchenig, Karlheinz; Romero, José Luis 2016-06-01 We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sjöstrand class with bounded second-order derivatives. This answers a question raised in de Gosson (Appl Comput Harmonic Anal 38(2):196-221, 2015) 7. Transformation of Hamiltonians to near action-angle form SciTech Connect Boozer, A.H. 1985-04-01 A classical Hamiltonian would be solved by a transformation to action-angle variables I,theta in which the Hamiltonian is H-bar(I). Generally, such a transformation does not exist, and, at best, the Hamiltonian can be transformed to H-bar(I) + H(I,theta,t) with H being a sum of Fourier terms that resonate with H-bar. We give a set of ordinary differential equations in a parameter epsilon that carry out this transformation as the set is integrated from epsilon equal to zero to one. Although the differential equations can be integrated numerically, approximations give classical perturbation theory. 8. Covariant Hamiltonian for the electromagnetic two-body problem De Luca, Jayme 2005-09-01 We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem. 9. Covariant Hamiltonian for the electromagnetic two-body problem. PubMed De Luca, Jayme 2005-09-01 We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem. 10. Generic perturbations of linear integrable Hamiltonian systems Bounemoura, Abed 2016-11-01 In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invariant tori), the Nekhoroshev theorem (stability of the action variables for a finite but long interval of time) and Arnold diffusion (instability of the action variables). Whether the frequency of the integrable system is resonant or not, it is known that the KAM theorem does not hold true for all perturbations; when the frequency is resonant, it is the Nekhoroshev theorem that does not hold true for all perturbations. Our first result deals with the resonant case: we prove a result of instability for a generic perturbation, which implies that the KAM and the Nekhoroshev theorem do not hold true even for a generic perturbation. The case where the frequency is nonresonant is more subtle. Our second result shows that for a generic perturbation the KAM theorem holds true. Concerning the Nekhrosohev theorem, it is known that one has stability over an exponentially long (with respect to some function of ɛ -1) interval of time and that this cannot be improved for all perturbations. Our third result shows that for a generic perturbation one has stability for a doubly exponentially long interval of time. The only question left unanswered is whether one has instability for a generic perturbation (necessarily after this very long interval of time). 11. Surface Lifshits tails for random quantum Hamiltonians Kirsch, Werner; Raikov, Georgi 2017-03-01 We consider Schrödinger operators on L2(ℝd) ⊗L2 (ℝℓ) of the form Hω=H⊥⊗I∥ +I⊥⊗H∥ +Vω , where H⊥ and H∥ are Schrödinger operators on L2(ℝd) and L2(ℝℓ) , respectively, and Vω(x ,y ) :=∑ξ∈ℤdλξ(ω ) v (x -ξ ,y ) ,x ∈ℝd ,y ∈ℝℓ is a random "surface potential." We investigate the behavior of the integrated density of surface states of Hω near the bottom of the spectrum and near internal band edges. The main result of the current paper is that, under suitable assumptions, the behavior of the integrated density of surface states of Hω can be read off from the integrated density of states of a reduced Hamiltonian H⊥+Wω where Wω is a quantum mechanical average of Vω with respect to y ∈ℝℓ . We are particularly interested in cases when H⊥ is a magnetic Schrödinger operator, but we also recover some of the results from Kirsch and Warzel [J. Funct. Anal. 230, 222-250 (2006)] for non-magnetic H⊥. 12. Hamiltonian chaos in nonlinear optical polarization dynamics David, D.; Holm, D. D.; Tratnik, M. V. 1990-03-01 This paper applies Hamiltonian methods to the Stokes representation of the one-beam and two-beam problems of polarized optical pulses propagating as travelling waves in nonlinear media. We treat these two dynamical systems as follows. First, we use the reduction method of Marsden and Weinstein to map each of the systems to the two-dimensional sphere, S 2. The resulting reduced systems are then analyzed from the viewpoints of their stability properties and of bifurcations with symmetry; in particular, several degenerate bifurcations are found and described. We also establish the presence of chaotic dynamics in these systems by demonstrating the existence of Smale horseshoe maps in the three- and four-dimensional cases, as well as Arnold diffusion in the higher-dimensional cases. The method we use to establish such complex dynamics is the Mel'nikov technique, as extended by Holmes and Marsden, and Wiggins for the higher-dimensional cases. These results apply to perturbations of homoclinic and heteroclinic orbits of the reduced integrable problems for static, as well as travelling-wave, solutions describing either a single opt ical beam, or two such beams counterpropagating. Thus, we show that these optics problems exhibit complex dynamics and predict the experimental consequences of this dynamics. 13. Hamiltonian formalism for Perturbed Black Hole Spacetimes Mihaylov, Deyan; Gair, Jonathan 2017-01-01 Present and future gravitational wave observations provide a new mechanism to probe the predictions of general relativity. Observations of extreme mass ratio inspirals with millihertz gravitational wave detectors such as LISA will provide exquisite constraints on the spacetime structure outside astrophysical black holes, enabling tests of the no-hair property that all general relativistic black holes are described by the Kerr metric. Previous work to understand what constraints LISA observations will be able to place has focussed on specific alternative theories of gravity, or generic deviations that preserve geodesic separability. We describe an alternative approach to this problem--a technique that employs canonical perturbations of the Hamiltonian function describing motion in the Kerr metric. We derive this new approach and demonstrate its application to the cases of a slowly rotating Kerr black hole which is viewed as a perturbation of a Schwarzschild black hole, of coupled perturbations of black holes in the second-order Chern-Simons modified gravity theory, and several more indicative scenarios. Deyan Mihaylov is funded by STFC. 14. Laptop Induced Erythema Ab Igne PubMed Central Nayak, Sudhir U K; Shenoi, Shrutakirthi D; Prabhu, Smitha 2012-01-01 Erythema ab igne is a reticular, pigmented dermatosis caused by prolonged and repeated exposure to infrared radiation that is insufficient to produce a burn. The use of laptop computers has increased manifold in the recent past. Prolonged contact of the laptop with the skin can lead to the development of erythema ab igne. We present a case of erythema ab igne secondary to laptop use in an Indian student. PMID:22615512 15. Laptop induced erythema ab igne. PubMed Nayak, Sudhir U K; Shenoi, Shrutakirthi D; Prabhu, Smitha 2012-03-01 Erythema ab igne is a reticular, pigmented dermatosis caused by prolonged and repeated exposure to infrared radiation that is insufficient to produce a burn. The use of laptop computers has increased manifold in the recent past. Prolonged contact of the laptop with the skin can lead to the development of erythema ab igne. We present a case of erythema ab igne secondary to laptop use in an Indian student. 16. The Hamiltonian of Einstein affine-metric formulation of General Relativity Kiriushcheva, N.; Kuzmin, S. V. 2010-11-01 It is shown that the Hamiltonian of the Einstein affine-metric (first-order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as in the case of the second-order formulation. In the second-order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables ( arXiv:0809.0097 abs/arXiv:0809.0097" TargetType="URL"/> ). For the first-order formulation, the necessity of such a redefinition "to correspond to diffeomorphism invariance" (reported by Ghalati, arXiv:0901.3344 abs/arXiv:0901.3344" TargetType="URL"/> ) is just an artifact of using the Henneaux-Teitelboim-Zanelli ansatz (Nucl. Phys. B 332:169, 1990), which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani (Ann. Phys. 143:357, 1982) is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second-order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second- and first-order formulations of metric GR. The first-order formulation of Einstein-Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed. 17. PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics Fring, Andreas; Jones, Hugh; Znojil, Miloslav 2008-06-01 Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the 18. Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach. PubMed Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao 2013-09-10 Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data. 19. Estimation of many-body quantum Hamiltonians via compressive sensing SciTech Connect Shabani, A.; Rabitz, H.; Mohseni, M.; Lloyd, S.; Kosut, R. L. 2011-07-15 We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions. 20. Construction of Lagrangians and Hamiltonians from the Equation of Motion ERIC Educational Resources Information Center Yan, C. C. 1978-01-01 Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA) 1. Periodic equatorial water flows from a Hamiltonian perspective Ionescu-Kruse, Delia; Martin, Calin Iulian 2017-04-01 The main result of this paper is a Hamiltonian formulation of the nonlinear governing equations for geophysical periodic stratified water flows in the equatorial f-plane approximation allowing for piecewise constant vorticity. 2. Effective Hamiltonians of 2D Spin Glass Clusters Clement, Colin; Liarte, Danilo; Middleton, Alan; Sethna, James 2015-03-01 We have a method for directly identifying the clusters which are thought to dominate the dynamics of spin glasses. We also have a method for generating an effective Hamiltonian treating each cluster as an individual spin. We used these methods on a 2D Ising spin glass with Gaussian bonds. We study these systems by generating samples and correlation functions using a combination of Monte Carlo and high-performance numerically exact Pfaffian methods. With effective cluster Hamiltonians we can calculate the free energy asymmetry of the original clusters and perform a scaling analysis. The scaling exponents found are consistent with Domain-Wall Renormalization Group methods, and probe all length scales. We can also study the flow of these effective Hamiltonians by clustering the clustered spins, and we find that our hard spin Hamiltonians at high temperature retain accurate low-temperature fluctuations when compared to their parent models. 3. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy Sugny, D.; Mardešić, P.; Pelletier, M.; Jebrane, A.; Jauslin, H. R. 2008-04-01 Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskií, and Zhilinskií, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); Nekhoroshev, Sadovskií, and Zhilinskií, Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m :-n resonant systems. 4. Two time physics and Hamiltonian Noether theorem for gauge systems SciTech Connect Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M. 2006-09-25 Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. 5. Room Temperature Line Lists for CO_2 Isotopologues with AB Initio Computed Intensities Zak, Emil; Tennyson, Jonathan; Polyansky, Oleg; Lodi, Lorenzo; Zobov, Nikolay Fedorovich; Tashkun, Sergey; Perevalov, Valery 2016-06-01 We report 13 room temperature line lists for all major CO_2 isotopologues, covering 0-8000 wn. These line lists are a response to the need for line intensities of high, preferably sub-percent, accuracy by remote sensing experiments. Our scheme encompasses nuclear motion calculations supported by critical reliability analysis of the generated line intensities. Rotation-vibration wavefunctions and energy levels are computed using DVR3D and a high quality semi-empirical potential energy surface (PES) [1], followed by computation of intensities using a fully ab initio dipole moment surface (DMS). Cross comparison of line lists calculated using pairs of high-quality PES's and DMS's is used to assess imperfections in the PES, which lead to unreliable transition intensities between levels involved in resonance interactions. Four line lists are computed for each isotopologue to quantify sensitivity to minor distortions of the PES/DMS. This provides an estimate of the contribution to the overall line intensity error introduced by the underlying PES. Reliable lines are benchmarked against recent state-of-the-art measurements [2] and HITRAN-2012 supporting the claim that the majority of line intensities for strong bands are predicted with sub-percent accuracy [3]. Accurate line positions are generated using an effective Hamiltonian [4]. We recommend use of these line lists for future remote sensing studies and inclusions in databases. X. Huang, D. W. Schwenke, S. A. Tashkun, T. J. Lee, J. Chem. Phys. 136, 124311, 2012. O. L. Polyansky, K. Bielska, M. Ghysels, L. Lodi, N. F. Zobov, J. T. Hodges, J. Tennyson, PRL, 114, 243001, 2015. E. Zak, J. Tennyson, O. L. Polyansky, L. Lodi, S. A. Tashkun, V. I. Perevalov, JQSRT, in press and to be submitted. S. A. Tashkun, V. I. Perevalov, R. R. Gamache, J. Lamouroux, JQSRT, 152, 45-73, 2015. 6. Hamiltonian Light-front Field Theory Within an AdS/QCD Basis SciTech Connect Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C.; /LBL, Berkeley 2009-12-16 Non-perturbative Hamiltonian light-front quantum field theory presents opportunities and challenges that bridge particle physics and nuclear physics. Fundamental theories, such as Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) offer the promise of great predictive power spanning phenomena on all scales from the microscopic to cosmic scales, but new tools that do not rely exclusively on perturbation theory are required to make connection from one scale to the next. We outline recent theoretical and computational progress to build these bridges and provide illustrative results for nuclear structure and quantum field theory. As our framework we choose light-front gauge and a basis function representation with two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. 7. Global Calculations Using Potential Functions and Effective Hamiltonian Models for Vibration-Rotation Spectroscopy and Dynamics of Small Polyatomic Molecules 2010-06-01 It has become increasingly common to use accurate potential energy surfaces and dipole moment surfaces for predictions and assignment of high-resolution vibration-rotation molecular spectra. These surfaces are obtained either from high-level ab initio electronic structure calculations or from a direct fit to experimental spectroscopic data. The talk will continue a discussion of some recent advances in the domain of the "potentiology". The role of basis extrapolations, of the Born-Oppenheimer breakdown corrections , in particular for very highly excited vibration states will be considered. As effective polyad Hamiltonians and band transition moment operators are still widely used for data reductions in high-resolutions molecular spectroscopy, experimental spectra analyses invoke a need for accurate methods of building physically meaningful effective models from ab initio surfaces. This involves predictions for various spectroscopic constants, including vibration dependence of rotational and centrifugal distortion and resonance coupling parameters. Topics planned for discussion include: high-order Contact Transformations of rovibrational Hamiltonians and of the dipole moment for small polyatomic molecules; convergence issues; the role of the anharmonicity in a potential energy function and of resonance couplings on the normal mode mixing and on vib-rot assignments with application to high energy vibration levels of SO_2 and to ozone near the dissociation limit; intensity anomalies in H_2S / HDS / D_2S spectra, relation of the shape of ab initio dipole moment surfaces with a "mystery" of nearly vanishing symmetry allowed bands. A full account for symmetry properties requires efficient theoretical tools for transformations of molecular Hamiltonians such as irreducible tensor formalism, applications using phosphine and methane potentials will be discussed. Both potential functions and effective polyad Hamiltonians allow studying changes in quasi-classical vibration 8. Time and a physical Hamiltonian for quantum gravity. PubMed Husain, Viqar; Pawłowski, Tomasz 2012-04-06 We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. 9. Hyperbolic tori in Hamiltonian systems with slowly varying parameter SciTech Connect Medvedev, Anton G 2013-05-31 This paper looks at a Hamiltonian system which depends periodically on a parameter. For each value of the parameter the system is assumed to have a hyperbolic periodic solution. Using the methods in KAM-theory it is proved that if the Hamiltonian is perturbed so that the value of the parameter varies with constant small frequency, then the nonautonomous system will have hyperbolic 2-tori in the extended phase space. Bibliography: 12 titles. 10. Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD SciTech Connect Morrison, P.J.; Greene, J.M. 1980-04-01 A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables. 11. Applications of Noether conservation theorem to Hamiltonian systems Mouchet, Amaury 2016-09-01 The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics. 12. Applications of Noether conservation theorem to Hamiltonian systems SciTech Connect Mouchet, Amaury 2016-09-15 The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics. 13. The Lagrangian-Hamiltonian formalism for higher order field theories Vitagliano, Luca 2010-06-01 We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity. 14. MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD SciTech Connect K. HANSON 2001-02-01 The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy {var_phi}, where {var_phi} is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of {var_phi}, is proposed to measure the convergence of the MCMC sequence. 15. The rovibrational Hamiltonian for ammonia-like molecules. PubMed Makarewicz, Jan; Skalozub, Alexander 2002-03-01 A new exact quantum mechanical rovibrational Hamiltonian operator for ammonia-like molecules is derived. The Hamiltonian is constructed in a molecular system of axes, such that its z' axis makes a trisection of the pyramidal angle formed by three bond vectors with the vertex on the central atom. The introduced set of the internal rovibrational coordinates is adapted to facilitate a convenient description of the inversion motion. These internal coordinates and the molecular axis system have a remarkable property, namely, the internal vibrational angular momentum of the molecule equals zero. This property significantly reduces the Coriolis coupling and simplifies the form of the Hamiltonian. The correctness of this Hamiltonian is proved by a numerical procedure. The orthogonal Radau vectors allowing us to define a similar molecular axis system and the internal coordinates are considered. The Hamiltonian for the Radau parameterization takes a form simple enough to carry out effectively variational calculations of the molecular rovibrational states. Under the appropriate choice of the variational basis functions, the Hamiltonian matrix elements are fully factorizable and do not have any singularities. A convenient method of symmetrization of the basis functions is proposed. 16. Ab initio calculation of (hyper)polarizabilities using a sum-over-states formalism. Taylor, Caroline M.; Chaudhuri, Rajat K.; Potts, Davin M.; Freed, Karl F. 2001-03-01 Hyperpolarizabilities are relevant to a wide range of non-linear optical properties. Ab initio computations often require a high level of correlation for accurate determination of β and γ , and especially of thier frequency dependence. While sum-over-states methods are widely used within semi-empirical frameworks, they have not been employed with high level ab initio methods because of the computational costs associated with calculating a sufficient number of states. The effective valence shell Hamiltonian method (H^v) is a highly correlated, size-extensive, ab initio, multireference, perturbative (perturb-then-diagonalize'') method. A single H^v calculation yields a large number of states, making it ideal for use with the sum-over-states fomalism for determination of molecular properties. The method has been used to calculate the (hyper)polarizabilities of small polyene systems. 17. Leading-order relativistic effects on nuclear magnetic resonance shielding tensors. PubMed Manninen, Pekka; Ruud, Kenneth; Lantto, Perttu; Vaara, Juha 2005-03-15 We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe. 18. Global exploration and inversion of quantum Hamiltonian- Observable relationships Geremia, John Michael 2001-09-01 High-precision, quantitative knowledge of quantum Hamiltonians is a crucial prerequisite for accurately predicting and controlling molecular behavior. Understanding the physical connection between the quantum equations of motion and the physical observables measured in the laboratory is fundamental to bridging theory and experiment. However, Hamiltonian-Observable relationships are generally complex and nonlinear, making them difficult to represent, explore, and invert. A functional mapping concept that allows many nonlinear Hamiltonian-Observable relationships to be learned using a relatively small set of representative Hamiltonians is developed. Maps provide rationally organized response information that details how non-perturbative variations in the Hamiltonian affect physical observables. Nonlinear mapping techniques permit the application of global search algorithms to quantum inverse problems, such as Hamiltonian identification and control. The resulting map-facilitated inversion framework provides a new capability for identifying the full family of Hamiltonians consistent with a finite, noise-contaminated molecular objective. As a demonstration, potential energy surfaces for He-Ne, Na2, and Ar-HCl are extracted from spectral and scattering data. A facilitated laboratory control algorithm is introduced and it is demonstrated that maps provide a reliable dynamic analysis of strong-field control mechanisms. The framework of map-facilitated closed-loop inversion unifies the previously distinct fields of quantum Hamiltonian identification and coherent control. It also leads to a hybrid laboratory/computational algorithm that systematically determines the best experiments and data for global Hamiltonian identification. Conventional inversions have been limited to treating available data. Here, it is shown that optimal data, i.e., measurements with maximum information content, provides a superior means for studying molecular Hamiltonians. The concept of optimal 19. Nuclear Safety Information Center, Its Products and Services ERIC Educational Resources Information Center Buchanan, J. R. 1970-01-01 The Nuclear Safety Information Center (NSIC) serves as a focal point for the collection, analysis and dissemination of information related to safety problems encountered in the design, analysis, and operation of nuclear facilities. (Author/AB) 20. Nuclear Safety Information Center, Its Products and Services ERIC Educational Resources Information Center Buchanan, J. R. 1970-01-01 The Nuclear Safety Information Center (NSIC) serves as a focal point for the collection, analysis and dissemination of information related to safety problems encountered in the design, analysis, and operation of nuclear facilities. (Author/AB) 1. Toward spectroscopically accurate global ab initio potential energy surface for the acetylene-vinylidene isomerization SciTech Connect Han, Huixian; Li, Anyang; Guo, Hua 2014-12-28 A new full-dimensional global potential energy surface (PES) for the acetylene-vinylidene isomerization on the ground (S{sub 0}) electronic state has been constructed by fitting ∼37 000 high-level ab initio points using the permutation invariant polynomial-neural network method with a root mean square error of 9.54 cm{sup −1}. The geometries and harmonic vibrational frequencies of acetylene, vinylidene, and all other stationary points (two distinct transition states and one secondary minimum in between) have been determined on this PES. Furthermore, acetylene vibrational energy levels have been calculated using the Lanczos algorithm with an exact (J = 0) Hamiltonian. The vibrational energies up to 12 700 cm{sup −1} above the zero-point energy are in excellent agreement with the experimentally derived effective Hamiltonians, suggesting that the PES is approaching spectroscopic accuracy. In addition, analyses of the wavefunctions confirm the experimentally observed emergence of the local bending and counter-rotational modes in the highly excited bending vibrational states. The reproduction of the experimentally derived effective Hamiltonians for highly excited bending states signals the coming of age for the ab initio based PES, which can now be trusted for studying the isomerization reaction. 2. PREFACE: International Symposium on Exotic Nuclear Structure From Nucleons (ENSFN 2012) Honma, Michio; Utsuno, Yutaka; Shimizu, Noritaka 2013-07-01 The International Symposium on 'Exotic Nuclear Structure From Nucleons (ENSFN2012)' was held at the Koshiba Hall, the University of Tokyo, Japan, from October 10th to 12th, 2012. This symposium was supported by RIKEN Nishina Center (RNC) and the Center for Nuclear Study (CNS), University of Tokyo. This symposium was devoted to discussing recent achievement and perspectives in the structure of exotic nuclei from the viewpoint of the nuclear force. The following subjects were covered in this symposium from both theoretical and experimental sides: Evolution of shell structure and collectivity in exotic nuclei Ab-initio theory and its application to exotic nuclei Advancement in large-scale nuclear-structure calculations Effective Hamiltonian and energy density functional Spin-isospin responses New aspects of two- and three-body forces Impact on nuclear astrophysics Emphasis was placed on the development of large-scale nuclear-structure calculations and the new experimental information on exotic nuclei. Around 80 participants attended this symposium and we enjoyed 37 excellent invited talks and 9 selected oral presentations. A special talk was presented to celebrate the 60th birthday of professor Takaharu Otsuka, who has made invaluable contribution to the progress in the fields covered in this symposium. The organizing committee consisted of T Abe (Tokyo), M Honma (Aizu; chair), N Itagaki (YITP, Kyoto), T Mizusaki (Senshu), T Nakatsukasa (RIKEN), H Sakurai (Tokyo/RIKEN), N Shimizu (CNS, Tokyo; scientific secretary), S Shimoura (CNS, Tokyo), Y Utsuno (JAEA/CNS, Tokyo; scientific secretary). Finally, we would like to thank all the speakers and the participants as well as the other organizers for their contributions which made the symposium very successful. Michio Honma, Yutaka Utsuno and Noritaka Shimizu Editors Tokyo, April 2013 Sponsors logo1 Sponsors logo2 The PDF also contains the conference program. 3. Ab initio study of electron-phonon coupling in rubrene Ordejón, P.; Boskovic, D.; Panhans, M.; Ortmann, F. 2017-07-01 The use of ab initio methods for accurate simulations of electronic, phononic, and electron-phonon properties of molecular materials such as organic crystals is a challenge that is often tackled stepwise based on molecular properties calculated in gas phase and perturbatively treated parameters relevant for solid phases. In contrast, in this work we report a full first-principles description of such properties for the prototypical rubrene crystals. More specifically, we determine a Holstein-Peierls-type Hamiltonian for rubrene, including local and nonlocal electron-phonon couplings. Thereby, a recipe for circumventing the issue of numerical inaccuracies with low-frequency phonons is presented. In addition, we study the phenyl group motion with a molecular dynamics approach. 4. Exotic Nuclear Shapes: Dudek, J.; Schunck, N.; Dubray, N.; Góźdź, A. After recalling some in principle known but seldom mentioned facts about variety of concepts/notions of the nuclear shapes, we briefly summarize the results of the recent microscopic calculations predicting the existence of the large-elongation (hyper-deformed) nuclear configurations — as well as another series of calculations predicting that some nuclei should exhibit high-rank symmetries: the tetrahedral and the octahedral ones. The latter are associated with 48- and 96- symmetry elements, respectively, of the nuclear mean-field Hamiltonian. Obviously the physics motivations behind the hyper-deformation and the high-rank symmetry studies are not the observations of the new geometrical forms as such; in our opinion these motivations are much deeper and are given in the text. 5. Probing the symmetries of the Dirac Hamiltonian with axially deformed scalar and vector potentials by similarity renormalization group. PubMed Guo, Jian-You; Chen, Shou-Wan; Niu, Zhong-Ming; Li, Dong-Peng; Liu, Quan 2014-02-14 Symmetry is an important and basic topic in physics. The similarity renormalization group theory provides a novel view to study the symmetries hidden in the Dirac Hamiltonian, especially for the deformed system. Based on the similarity renormalization group theory, the contributions from the nonrelativistic term, the spin-orbit term, the dynamical term, the relativistic modification of kinetic energy, and the Darwin term are self-consistently extracted from a general Dirac Hamiltonian and, hence, we get an accurate description for their dependence on the deformation. Taking an axially deformed nucleus as an example, we find that the self-consistent description of the nonrelativistic term, spin-orbit term, and dynamical term is crucial for understanding the relativistic symmetries and their breaking in a deformed nuclear system. 6. Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches. PubMed Reta, Daniel; Moreira, Ibério de P R; Illas, Francesc 2016-07-12 In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical. 7. Hamiltonian thermodynamics of three-dimensional dilatonic black holes Dias, Gonçalo A. S.; Lemos, José P. S. 2008-08-01 The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free ω parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates {M,PM}, M being the mass parameter and PM its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrödinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton. 8. Periodic pseudo-Hermitian Hamiltonian: Nonadiabatic geometric phase Maamache, M. 2015-09-01 It is well known that Hermitian operators have real eigenvalues while non-Hermitian ones may have complex eigenvalues. Recently, numerical and analytical results indicated that the spectra of many non-Hermitians Hamiltonians H are indeed real if they are invariant under the combined action of self-adjoint parity P and time reversal T . The concept of a pseudo-Hermitian operator showed that the remarkable spectral properties of the P T -symmetric Hamiltonians follow from their pseudo-Hermiticity. It is possible to explain these observations by the concept of pseudo-Hermitian operators and to formulate completeness and orthonormality relations. Most of the effort has been devoted to study time-independent non-Hermitian systems. In this paper, we study the exactly solvable time-dependent periodic pseudo-Hermitian Hamiltonians. The method introduced, to make the reality of eigenvalues and phases, is based on a Floquet decomposition of the evolution operator UH(t ) =ZH(t ) exp(i MHt ) associated with the periodic pseudo-hermitian Hamiltonian H (t )=H (t +T ) . One of the results found in this paper concerns a calculation of Berry's phase for periodic, but not necessarily adiabatic, pseudo-Hermitian Hamiltonians. A two-level pseudo-Hermitian system is discussed as an illustrative example. 9. Ab Interno Trabeculectomy PubMed Central Pantcheva, Mina B.; Kahook, Malik Y. 2010-01-01 Anterior chamber drainage angle surgery, namely trabeculotomy and goniotomy, has been commonly utilized in children for many years. Its’ reported success has ranged between 68% and 100% in infants and young children with congenital glaucoma. However, the long-term success of these procedures has been limited in adults presumably due to the formation of anterior synechiae (AS) in the postoperative phase. Recently, ab interno trabeculectomy with the Trabectome™ has emerged as a novel surgical approach to effectively and selectively remove and ablate the trabecular meshwork and the inner wall of the Schlemm’s canal in an attempt to avoid AS formation or other forms of wound healing with resultant closure of the cleft. This procedure seems to have an appealing safety profile with respect to early hypotony or infection if compared to trabeculectomy or glaucoma drainage device implantation. This might be advantageous in some of the impoverish regions of the Middle East and Africa where patients experience difficulties keeping up with their postoperative visits. It is important to note that no randomized trial comparing the Trabectome to other glaucoma procedures appears to have been published to date. Trabectome surgery is not a panacea, however, and it is associated with early postoperative intraocular pressure spikes that may require additional glaucoma surgery as well as a high incidence of hyphema. Reported results show that postoperative intraocular pressure (IOP) remains, at best, in the mid-teen range making it undesirable in patients with low-target IOP goals. A major advantage of Trabectome surgery is that it does not preclude further glaucoma surgery involving the conjunctiva, such as a trabeculectomy or drainage device implantation. As prospective randomized long-term clinical data become available, we will be better positioned to elucidate the exact role of this technique in the glaucoma surgical armamentarium. PMID:21180426 10. Ab initio downfolding for electron-phonon-coupled systems: Constrained density-functional perturbation theory Nomura, Yusuke; Arita, Ryotaro 2015-12-01 We formulate an ab initio downfolding scheme for electron-phonon-coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme can be implemented by slightly modifying the density functional-perturbation theory (DFPT), which is one of the standard methods for calculating phonon properties from first principles. Our scheme, which we call the constrained DFPT, can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity, and multiferroicity. We believe that the constrained DFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed. 11. Many-body ab initio study of antiferromagnetic {Cr7M } molecular rings Chiesa, A.; Carretta, S.; Santini, P.; Amoretti, G.; Pavarini, E. 2016-12-01 Antiferromagnetic molecular rings are widely studied both for fundamental quantum-mechanical issues and for technological applications, particularly in the field of quantum information processing. Here we present a detailed first-principles study of two families—purple and green—of {Cr7M } antiferromagnetic rings, where M is a divalent transition metal ion (M =Ni2 + , Mn2 +, and Zn2 +). We employ a recently developed flexible and efficient scheme to build ab initio system-specific Hubbard models. From such many-body models we systematically derive the low-energy effective spin Hamiltonian for the rings. Our approach allows us to calculate isotropic as well as anisotropic terms of the spin Hamiltonian, without any a priori assumption on its form. For each compound we calculate magnetic exchange couplings, zero-field splitting tensors, and gyromagnetic tensors, finding good agreement with experimental results. 12. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry 2015-06-01 We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects. 13. Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei 2016-01-01 In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129). 14. Limit of small exits in open Hamiltonian systems. PubMed Aguirre, Jacobo; Sanjuán, Miguel A F 2003-05-01 The nature of open Hamiltonian systems is analyzed, when the size of the exits decreases and tends to zero. Fractal basins appear typically in open Hamiltonian systems, but we claim that in the limit of small exits, the invariant sets tend to fill up the whole phase space with the strong consequence that a new kind of basin appears, where the unpredictability grows indefinitely. This means that for finite, arbitrarily small accuracy, we can find uncertain basins, where any information about the future of the system is lost. This total indeterminism had only been reported in dissipative systems, in particular in the so-called intermingled riddled basins, as well as in the riddledlike basins. We show that this peculiar, behavior is a general feature of open Hamiltonian systems. 15. Distinguishing Lorenz and Chen Systems Based Upon Hamiltonian Energy Theory Cang, Shijian; Wu, Aiguo; Wang, Zenghui; Chen, Zengqiang Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. Moreover, the energy function and generalized Hamiltonian realization of the Lü system and a four-dimensional hyperchaotic Lorenz-type system are also discussed. 16. Reverse engineering of a Hamiltonian by designing the evolution operators PubMed Central Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie 2016-01-01 We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments. PMID:27444137 17. On the Hamiltonian formalism of the tetrad-connection gravity Lagraa, M. H.; Lagraa, M.; Touhami, N. 2017-06-01 We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamic part of the spatial connection is fixed to zero by an adequate gauge transformation. This new action leads to a coherent Hamiltonian formalism where the Lorentz, scalar and vectorial first-class constraints obey a closed algebra in terms of Poisson brackets. This algebra closes with structure constants instead of structure functions resulting from the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra of the reduced first-class constraints, where the second-class constraints are eliminated as strong equalities, is obtained in terms of Dirac brackets. These first-class constraints lead to the same physical degrees of freedom of the general relativity. 18. Riemannian geometry of Hamiltonian chaos: Hints for a general theory Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco 2008-10-01 We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam β model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity. 19. Effective Hamiltonian for protected edge states in graphene Winkler, R.; Deshpande, H. 2017-06-01 Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ . Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. We show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum. 20. Hamiltonian formalism of two-dimensional Vlasov kinetic equation PubMed Central Pavlov, Maxim V. 2014-01-01 In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo–Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo–Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented. PMID:25484603 1. Hamiltonian formalism of two-dimensional Vlasov kinetic equation. PubMed Pavlov, Maxim V 2014-12-08 In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented. 2. Reverse engineering of a Hamiltonian by designing the evolution operators Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie 2016-07-01 We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments. 3. Reverse engineering of a Hamiltonian by designing the evolution operators. PubMed Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie 2016-07-22 We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments. 4. Riemannian geometry of Hamiltonian chaos: hints for a general theory. PubMed Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco 2008-10-01 We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity. 5. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries Fernández, Francisco M.; Garcia, Javier 2014-03-01 We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C2v exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. 6. Effective Hamiltonians for fastly driven tight-binding chains Itin, A. P.; Neishtadt, A. I. 2014-02-01 We consider a single particle tunnelling in a tight-binding model with nearest-neighbour couplings, in the presence of a periodic high-frequency force. An effective Hamiltonian for the particle is derived using an averaging method resembling classical canonical perturbation theory. Three cases are considered: uniform lattice with periodic and open boundary conditions, and lattice with a parabolic potential. We find that in the latter case, interplay of the potential and driving leads to appearance of the effective next-nearest neighbour couplings. In the uniform case with periodic boundary conditions the second- and third-order corrections to the averaged Hamiltonian are completely absent, while in the case with open boundary conditions they have a very simple form, found before in some particular cases by S. Longhi (2008) [10]. These general results may found applications in designing effective Hamiltonian models in experiments with ultracold atoms in optical lattices, e.g. for simulating solid-state phenomena. 7. Autonomous Biological System (ABS) experiments. PubMed MacCallum, T K; Anderson, G A; Poynter, J E; Stodieck, L S; Klaus, D M 1998-12-01 Three space flight experiments have been conducted to test and demonstrate the use of a passively controlled, materially closed, bioregenerative life support system in space. The Autonomous Biological System (ABS) provides an experimental environment for long term growth and breeding of aquatic plants and animals. The ABS is completely materially closed, isolated from human life support systems and cabin atmosphere contaminants, and requires little need for astronaut intervention. Testing of the ABS marked several firsts: the first aquatic angiosperms to be grown in space; the first higher organisms (aquatic invertebrate animals) to complete their life cycles in space; the first completely bioregenerative life support system in space; and, among the first gravitational ecology experiments. As an introduction this paper describes the ABS, its flight performance, advantages and disadvantages. 8. Ab initio two-component Ehrenfest dynamics SciTech Connect Ding, Feizhi; Goings, Joshua J.; Liu, Hongbin; Lingerfelt, David B.; Li, Xiaosong 2015-09-21 We present an ab initio two-component Ehrenfest-based mixed quantum/classical molecular dynamics method to describe the effect of nuclear motion on the electron spin dynamics (and vice versa) in molecular systems. The two-component time-dependent non-collinear density functional theory is used for the propagation of spin-polarized electrons while the nuclei are treated classically. We use a three-time-step algorithm for the numerical integration of the coupled equations of motion, namely, the velocity Verlet for nuclear motion, the nuclear-position-dependent midpoint Fock update, and the modified midpoint and unitary transformation method for electronic propagation. As a test case, the method is applied to the dissociation of H{sub 2} and O{sub 2}. In contrast to conventional Ehrenfest dynamics, this two-component approach provides a first principles description of the dynamics of non-collinear (e.g., spin-frustrated) magnetic materials, as well as the proper description of spin-state crossover, spin-rotation, and spin-flip dynamics by relaxing the constraint on spin configuration. This method also holds potential for applications to spin transport in molecular or even nanoscale magnetic devices. 9. Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer Ajoy, Ashok; Rao, Rama Koteswara; Kumar, Anil; Rungta, Pranaw 2012-03-01 We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.230502 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries. 10. Ab Initio Multiple Spawning Method for Intersystem Crossing Dynamics: Spin-Forbidden Transitions between (3)B1 and (1)A1 States of GeH2. PubMed Fedorov, Dmitry A; Pruitt, Spencer R; Keipert, Kristopher; Gordon, Mark S; Varganov, Sergey A 2016-05-12 Dynamics at intersystem crossings are fundamental to many processes in chemistry, physics, and biology. The ab initio multiple spawning (AIMS) method was originally developed to describe internal conversion dynamics at conical intersections where derivative coupling is responsible for nonadiabatic transitions between electronic states with the same spin multiplicity. Here, the applicability of the AIMS method is extended to intersystem crossing dynamics in which transitions between electronic states with different spin multiplicities are mediated by relativistic spin-orbit coupling. In the direct AIMS dynamics, the nuclear wave function is expanded in the basis of frozen multidimensional Gaussians propagating on the coupled electronic potential energy surfaces calculated on the fly. The AIMS method for intersystem crossing is used to describe the nonadiabatic transitions between the (3)B1 and (1)A1 states of GeH2. The potential energies and gradients were obtained at the CASSCF(6,6)/6-31G(d) level of theory. The spin-orbit coupling matrix elements were calculated with the configuration interaction method using the two-electron Breit-Pauli Hamiltonian. The excited (3)B1 state lifetime and intersystem crossing rate constants were estimated by fitting the AIMS state population with the first-order kinetics equation for a reversible unimolecular reaction. The obtained rate constants are compared with the values predicted by the statistical nonadiabatic transition state theory with transition probabilities calculated using the Landau-Zener and weak coupling formulas. 11. Bounded stabilisation of stochastic port-Hamiltonian systems Satoh, Satoshi; Saeki, Masami 2014-08-01 This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances. 12. Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers Burgarth, Daniel; Ajoy, Ashok 2017-07-01 We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations. 13. Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers. PubMed Burgarth, Daniel; Ajoy, Ashok 2017-07-21 We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations. 14. Hamiltonian and Godunov structures of the Grad hierarchy. PubMed Grmela, Miroslav; Hong, Liu; Jou, David; Lebon, Georgy; Pavelka, Michal 2017-03-01 The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies, we also investigate relations between Hamiltonian and Godunov structures. 15. Lagrangian-Hamiltonian unified formalism for field theory Echeverría-Enríquez, Arturo; López, Carlos; Marín-Solano, Jesús; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso 2004-01-01 The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations. 16. Continuation of periodic orbits in symmetric Hamiltonian and conservative systems Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F. 2014-12-01 We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem. 17. Comments on HKT supersymmetric sigma models and their Hamiltonian reduction Fedoruk, Sergey; Smilga, Andrei 2015-05-01 Using complex notation, we present new simple expressions for two pairs of complex supercharges in HKT (‘hyper-Kähler with torsion’) supersymmetric sigma models. The second pair of supercharges depends on the holomorphic antisymmetric ‘hypercomplex structure’ tensor {{I}jk} which plays the same role for the HKT models as the complex structure tensor for the Kähler models. When the Hamiltonian and supercharges commute with the momenta conjugate to the imaginary parts of the complex coordinates, one can perform a Hamiltonian reduction. The models thus obtained represent a special class of quasicomplex sigma models introduced recently by Ivanov and Smilga (2013 SIGMA 9 069) 18. A Geometrical Version of the Maxwell-Vlasov Hamiltonian Structure Vittot, Michel; Morrison, Philip 2014-10-01 We present a geometrization of the Hamiltonian approach of classical electrodynamics, via (non-canonical) Poisson structures. This relativistic Hamiltonian framework (introduced by Morrison, Marsden, Weinstein) is a field theory written in terms of differential forms, independently of the gauge potentials. This algebraic and geometric description of the Vlasov kinetics is well suited for a perturbation theory, in a strong inhomogeneous magnetic field (expansion in 1/B, with all the curvature terms...), like in magnetically confined plasmas, and in any coordinates, for instance adapted to a Tokamak (toroidal coordinates, or else...). 19. Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics. PubMed Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A 2007-02-01 Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations. 20. Phase equilibria in polymer blend thin films: a Hamiltonian approach. PubMed Souche, M; Clarke, N 2009-12-28 We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films. 1. Characterizing Ground and Thermal States of Few-Body Hamiltonians Huber, Felix; Gühne, Otfried 2016-07-01 The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k -body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question of which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived. 2. The Hamilton-Jacobi method and Hamiltonian maps Abdullaev, S. S. 2002-03-01 A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, the general form of the symplectic maps is established. The generating function of the map is found by the perturbation method in the finite time intervals. The accuracy of the maps is studied for fully integrable and partially chaotic Hamiltonian systems and compared to that of the symplectic integration method. 3. Effective Hamiltonian for non-minimally coupled scalar fields Meşe, Emine; Pirinççiog˜Lu, Nurettin; Açıkgöz, Irfan; Binbay, Figen 2009-01-01 In the post Newtonian limit, a non-relativistic Hamiltonian is derived for scalar fields with quartic self-interaction and non-minimal coupling to the curvature scalar of the background spacetime. These effects are found to contribute to the non-relativistic Hamiltonian by adding nonlinearities and by modifying the gravitational Darwin term. As we discuss briefly in the text, the impact of these novel structures can be sizable in dense media like neutron star core, and can have observable signatures in phase transitions, for example. 4. Nonclassical degrees of freedom in the Riemann Hamiltonian. PubMed Srednicki, Mark 2011-09-02 The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros. 5. A parity breaking Ising chain Hamiltonian as a Brownian motor Cornu, F.; Hilhorst, H. J. 2014-10-01 We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed. 6. Effective Hamiltonian for a microwave billiard with attached waveguide. PubMed Stöckmann, H-J; Persson, E; Kim, Y-H; Barth, M; Kuhl, U; Rotter, I 2002-06-01 In a recent work the resonance widths in a microwave billiard with attached waveguide were studied in dependence on the coupling strength [E. Persson et al., Phys. Rev. Lett. 85, 2478 (2000)], and resonance trapping was experimentally found. In the present paper an effective Hamiltonian is derived that depends exclusively on billiard and waveguide geometry. Its eigenvalues give the poles of the scattering matrix provided that the system and environment are defined adequately. Further, we present the results of resonance trapping measurements where, in addition to our previous work, the position of the slit aperture within the waveguide was varied. Numerical simulations with the derived Hamiltonian qualitatively reproduce the experimental data. 7. Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories Román-Roy, Narciso 2009-11-01 This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems. 8. Quantifying the Effects of Higher Order Jahn-Teller Coupling Terms on a Quadratic Jahn-Teller Hamiltonian in the Case of NO_3 and Li_3. Tran, Henry; Stanton, John F.; Miller, Terry A. 2016-06-01 The Jahn-Teller (JT) effect represents an enormous complication in the understanding of many molecules. We have been able to assign ˜20 vibronic bands in the tilde{A}^2E'' ← tilde{X}^2A_2' transition of NO_3 and determine the linear and quadratic JT coupling terms for ν_3 and ν_4, indicating strong and weak JT coupling along these modes respectively. It was found that the experimental results quantitatively disagree with ones determined from a vibronic Hamiltonian based on high-level ab-initio theory. Typical analyses of experimental data use the quadratic JT Hamiltonian because limited measured levels tend to allow fitting only to coupling terms up to quadratic JT coupling. Hence, these analyses may neglect key contributions from cubic and quartic terms. To quantify this limitation, we have fit artificial spectra calculated with up to fourth order terms in the potential using a quadratic JT Hamiltonian and analyzed the results. The parameters chosen for this analysis are determined from ab-initio potentials for the tilde{A} state of NO_3 and tilde{X} state of Li_3 to gain further insight on these molecules. Our initial results concerning the limitations of the quadratic JT Hamiltonian will be presented. T. Codd, M.-W. Chen, M. Roudjane, J. F. Stanton, and T. A. Miller. Jet cooled cavity ringdown spectroscopy of the tilde{A}^2E'' ← tilde{X}^2A'_2 Transition of the NO_3 Radical. J. Chem. Phys., 142:184305, 2015 9. Ab initio calculations of light-ion fusion reactions SciTech Connect Hupin, G.; Quaglioni, S.; Navratil, P. 2012-10-20 The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. Above all nuclear scattering and reactions, which require the solution of the many-body quantum-mechanical problem in the continuum, represent an extraordinary theoretical as well as computational challenge for ab initio approaches. The ab initio No-Core Shell Model/Resonating-Group Method (NCSM/RGM) complements a microscopic cluster technique with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach is capable of describing simultaneously both bound and scattering states in light nuclei. Recent applications to light nuclei scattering and fusion reactions relevant to energy production in stars and Earth based fusion facilities, such as the deuterium-{sup 3}He fusion, are presented. Progress toward the inclusion of the three nucleon force into the formalism is outlined. 10. Ab Initio Calculation of the Hoyle State SciTech Connect Epelbaum, Evgeny; Krebs, Hermann; Lee, Dean; Meissner, Ulf-G. 2011-05-13 The Hoyle state plays a crucial role in the helium burning of stars heavier than our Sun and in the production of carbon and other elements necessary for life. This excited state of the carbon-12 nucleus was postulated by Hoyle as a necessary ingredient for the fusion of three alpha particles to produce carbon at stellar temperatures. Although the Hoyle state was seen experimentally more than a half century ago nuclear theorists have not yet uncovered the nature of this state from first principles. In this Letter we report the first ab initio calculation of the low-lying states of carbon-12 using supercomputer lattice simulations and a theoretical framework known as effective field theory. In addition to the ground state and excited spin-2 state, we find a resonance at -85(3) MeV with all of the properties of the Hoyle state and in agreement with the experimentally observed energy. 11. Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians Fring, Andreas; Frith, Thomas 2017-01-01 We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model. 12. Bohr Hamiltonian with a deformation-dependent mass term for the Davidson potential SciTech Connect Bonatsos, Dennis; Georgoudis, P. E.; Lenis, D.; Minkov, N.; Quesne, C. 2011-04-15 Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the {beta} variable, in the cases of {gamma}-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the deformation-dependent mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model. 13. Shapes and stability of algebraic nuclear models NASA Technical Reports Server (NTRS) Lopez-Moreno, Enrique; Castanos, Octavio 1995-01-01 A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes. 14. Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems Barth, A. M.; Vagov, A.; Axt, V. M. 2016-09-01 We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses. 15. TOPICAL REVIEW: Quadrupole collective states within the Bohr collective Hamiltonian Próchniak, L.; Rohoziński, S. G. 2009-12-01 The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed discussion of the model's kinematics. The quadrupole coordinates, momenta and angular momenta are defined and the structure of the isotropic tensor fields as functions of the tensor variables is investigated. After a comprehensive discussion of the quadrupole kinematics, the general form of the classical and quantum Bohr Hamiltonian is presented. The electric and magnetic multipole moment operators acting in the collective space are constructed and the collective sum rules are given. A discussion of the tensor structure of the collective wavefunctions and a review of various methods of solving the Bohr Hamiltonian eigenvalue equation are also presented. Next, the methods of derivation of the classical and quantum Bohr Hamiltonian from the microscopic many-body theory are recalled. Finally, the microscopic approach to the Bohr Hamiltonian is applied to interpret collective properties of 12 heavy even-even nuclei in the Hf-Hg region. Calculated energy levels and E2 transition probabilities are compared with experimental data. 16. A separable shadow Hamiltonian hybrid Monte Carlo method Sweet, Christopher R.; Hampton, Scott S.; Skeel, Robert D.; Izaguirre, Jesús A. 2009-11-01 Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc). 17. A separable shadow Hamiltonian hybrid Monte Carlo method. PubMed Sweet, Christopher R; Hampton, Scott S; Skeel, Robert D; Izaguirre, Jesús A 2009-11-07 Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc). 18. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries SciTech Connect Fernández, Francisco M. Garcia, Javier 2014-03-15 We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •PT-symmetric multidimensional oscillators appear to show PT phase transitions. •This transition was conjectured to be a high-energy phenomenon. •We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. •PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit. 19. Hamiltonian Noether theorem for gauge systems and two time physics Villanueva, V. M.; Nieto, J. A.; Ruiz, L.; Silvas, J. 2005-08-01 The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics. 20. Simulating Hamiltonian Dynamics with a Truncated Taylor Series Somma, Rolando 2015-03-01 One of the main motivations for quantum computers is their ability to efficiently simulate the dynamics of quantum systems. Since the mid-1990s, many algorithms have been developed to simulate Hamiltonian dynamics on a quantum computer, with applications to problems such as simulating spin models and quantum chemistry. While it is now well known that quantum computers can efficiently simulate Hamiltonian dynamics, ongoing work has improved the performance and expanded the scope of such simulations. In this talk, I will describe a very simple and efficient algorithm for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. This algorithm can simulate the time evolution of a wide variety of physical systems. The cost of this algorithm depends only logarithmically on the inverse of the desired precision, and can be shown to be optimal. Such a cost also represents an exponential improvement over known methods for Hamiltonian simulation based on, e.g., Trotter-Suzuki approximations. Roughly speaking, doubling the number of digits of accuracy of the simulation only doubles the complexity. The new algorithm and its analysis are highly simplified due to a technique for implementing linear combinations of unitary operations to directly apply the truncated Taylor series. This is joint work with Dominic Berry, Andrew Childs, Richard Cleve, and Robin Kothari. 1. The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach ERIC Educational Resources Information Center Likar, A.; Razpet, N. 2009-01-01 The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is… 2. The Hamiltonian property of the flow of singular trajectories SciTech Connect Lokutsievskiy, L V 2014-03-31 Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles. 3. Warped product Finsler manifolds from Hamiltonian point of view In this paper, the Finslerian warped product structures are introduced as Hamiltonian formalism without restricting Finsler functions to be absolutely homogeneous. Afterwards, the constituents of the related variational problem and Finslerian connections of this warped product are obtained according to those of its constructing Finsler manifolds. 4. The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach ERIC Educational Resources Information Center Likar, A.; Razpet, N. 2009-01-01 The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is… 5. Regularization of the Hamiltonian constraint compatible with the spinfoam dynamics Alesci, Emanuele; Rovelli, Carlo 2010-08-01 We introduce a new regularization for Thiemann’s Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearance of the 15j Wigner symbol in these. 6. Fractional Hamiltonian analysis of higher order derivatives systems SciTech Connect Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan 2006-10-15 The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives. 7. New bi-Hamiltonian systems on the plane Tsiganov, A. V. 2017-06-01 We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth, and sixth orders in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets, and recursion operators are also presented in the framework of the Jacobi method. 8. Estimating equilibrium properties from non-Hamiltonian dynamics VandeVondele, Joost; Rothlisberger, Ursula 2001-11-01 We derive an expression that enables the accurate estimation of equilibrium properties using non-Hamiltonian dynamics. The major advantage of our scheme is that a time average over a single non-Hamiltonian trajectory can be employed instead of an ensemble average. Hence, it can directly be used in standard molecular dynamics simulations. The connection between non-Hamiltonian dynamics and equilibrium properties is established by assigning to the individual frames of the trajectory a weight that is based on the fluctuations of the phase space compression factor. Additionally, a simple scheme that takes into account only fluctuation of a given maximum duration is introduced to reduce the statistical error. By systematically extending the duration of the allowed fluctuations, increasingly accurate results can be obtained. Non-Hamiltonian dynamics schemes that are capable to enhance sampling efficiency are applied to two model systems in order to demonstrate the practical performance of our approach for the calculation of equilibrium free energy differences and probability density profiles. 9. Model spin-orbit coupling Hamiltonians for graphene systems Kochan, Denis; Irmer, Susanne; Fabian, Jaroslav 2017-04-01 We present a detailed theoretical study of effective spin-orbit coupling (SOC) Hamiltonians for graphene-based systems, covering global effects such as proximity to substrates and local SOC effects resulting, for example, from dilute adsorbate functionalization. Our approach combines group theory and tight-binding descriptions. We consider structures with global point group symmetries D6 h, D3 d, D3 h, C6 v, and C3 v that represent, for example, pristine graphene, graphene miniripple, planar boron nitride, graphene on a substrate, and free standing graphone, respectively. The presence of certain spin-orbit coupling parameters is correlated with the absence of the specific point group symmetries. Especially in the case of C6 v—graphene on a substrate, or transverse electric field—we point out the presence of a third SOC parameter, besides the conventional intrinsic and Rashba contributions, thus far neglected in literature. For all global structures we provide effective SOC Hamiltonians both in the local atomic and Bloch forms. Dilute adsorbate coverage results in the local point group symmetries C6 v, C3 v, and C2 v, which represent the stable adsorption at hollow, top and bridge positions, respectively. For each configuration we provide effective SOC Hamiltonians in the atomic orbital basis that respect local symmetries. In addition to giving specific analytic expressions for model SOC Hamiltonians, we also present general (no-go) arguments about the absence of certain SOC terms. 10. Translation-Invariant Parent Hamiltonians of Valence Bond Crystals Huerga, Daniel; Greco, Andrés; Gazza, Claudio; Muramatsu, Alejandro 2017-04-01 We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S =1 /2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions. 11. Davidson potential and SUSYQM in the Bohr Hamiltonian SciTech Connect Georgoudis, P. E. 2013-06-10 The Bohr Hamiltonian is modified through the Shape Invariance principle of SUper-SYmmetric Quantum Mechanics for the Davidson potential. The modification is equivalent to a conformal transformation of Bohr's metric, generating a different {beta}-dependence of the moments of inertia. 12. Stochastic diffusion and Kolmogorov entropy in regular and random Hamiltonians SciTech Connect Isichenko, M.B. . Inst. for Fusion Studies Kurchatov Inst. of Atomic Energy, Moscow ); Horton, W. . Inst. for Fusion Studies); Kim, D.E.; Heo, E.G.; Choi, D.I. ) 1992-05-01 The scalings of the E x B turbulent diffusion coefficient D and the Kolmogorov entropy K with the potential amplitude {phi} {sup {approximately}} of the fluctuation are studied using the geometrical analysis of closed and extended particle orbits for several types of drift Hamiltonians. The high-amplitude scalings , D {proportional to} {phi} {sup {approximately} 2} or {phi} {sup {approximately} 0} and K {proportional to} log {phi} {sup {approximately}}, are shown to arise from different forms of a periodic (four-wave) Hamiltonian {phi}{sup {approximately}} (x,y,t), thereby explaining the controversy in earlier numerical results. For a quasi-random (six-wave) Hamiltonian numerical data for the diffusion D {proportional to} {phi} {sup {approximately} 0.92 {plus minus} 0.04} and the Kolmogorov entropy K {proportional to} {phi} {sup {approximately} 0.56 {plus minus} 0.17} are presented and compared with the percolation theory predictions D {sub p} {proportional to} {phi} {sup {approximately} 0.7}, K {sub p} {proportional to} {phi} {sup {approximately} 0.5}. To study the turbulent diffusion in a general form of Hamiltonian, a new approach of the series expansion of the Lagrangian velocity correlation function is proposed and discussed. 13. Stochastic diffusion and Kolmogorov entropy in regular and random Hamiltonians SciTech Connect Isichenko, M.B. \|; Horton, W.; Kim, D.E.; Heo, E.G.; Choi, D.I. 1992-05-01 The scalings of the E x B turbulent diffusion coefficient D and the Kolmogorov entropy K with the potential amplitude {phi} {sup {approximately}} of the fluctuation are studied using the geometrical analysis of closed and extended particle orbits for several types of drift Hamiltonians. The high-amplitude scalings , D {proportional_to} {phi} {sup {approximately} 2} or {phi} {sup {approximately} 0} and K {proportional_to} log {phi} {sup {approximately}}, are shown to arise from different forms of a periodic (four-wave) Hamiltonian {phi}{sup {approximately}} (x,y,t), thereby explaining the controversy in earlier numerical results. For a quasi-random (six-wave) Hamiltonian numerical data for the diffusion D {proportional_to} {phi} {sup {approximately} 0.92 {plus_minus} 0.04} and the Kolmogorov entropy K {proportional_to} {phi} {sup {approximately} 0.56 {plus_minus} 0.17} are presented and compared with the percolation theory predictions D {sub p} {proportional_to} {phi} {sup {approximately} 0.7}, K {sub p} {proportional_to} {phi} {sup {approximately} 0.5}. To study the turbulent diffusion in a general form of Hamiltonian, a new approach of the series expansion of the Lagrangian velocity correlation function is proposed and discussed. 14. Adaptive molecular resolution approach in Hamiltonian form: An asymptotic analysis. PubMed Zhu, Jinglong; Klein, Rupert; Delle Site, Luigi 2016-10-01 Adaptive molecular resolution approaches in molecular dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer (transition) region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined, and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size, and thus a Hamiltonian approach such as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes. 15. Translation-Invariant Parent Hamiltonians of Valence Bond Crystals. PubMed Huerga, Daniel; Greco, Andrés; Gazza, Claudio; Muramatsu, Alejandro 2017-04-21 We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S=1/2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions. 16. Hamiltonian evolutions of twisted polygons in {RP}^n Marì Beffa, Gloria; Wang, Jing Ping 2013-09-01 In this paper we find a discrete moving frame and their associated invariants along projective polygons in {RP}^n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W3-algebra), its projective realization in {RP}^2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the Wn-algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. 17. Integrable Hamiltonian systems on low-dimensional Lie algebras SciTech Connect Korotkevich, Aleksandr A 2009-12-31 For any real Lie algebra of dimension 3, 4 or 5 and any nilpotent algebra of dimension 6 an integrable Hamiltonian system with polynomial coefficients is found on its coalgebra. These systems are constructed using Sadetov's method for constructing complete commutative families of polynomials on a Lie coalgebra. Bibliography: 17 titles. 18. Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups DTIC Science & Technology 1981-07-28 478. V. I. Arnold [1964]. Inst"ility of dynamical systenms with several degrees of freedom, Dokl . Akad . Riuk. SSSR 156,9-12. V. I. Ar’nold [1966...a rigid body, Trans, oscow Math. Soc. 41, 287. S.L. Ziglin [1981]. Branching of solutions and nonexistence of integrals in Hamiltonian systems. Doklady Akad . Nauk . SSSR 257, 26-29. - J. I 19. LETTER TO THE EDITOR: On optimum Hamiltonians for state transformations Brody, Dorje C.; Hook, Daniel W. 2006-03-01 For a prescribed pair of quantum states \|ψIrang and \|ψFrang we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation \|ψIrang → \|ψFrang in the shortest duration. The derivation is geometric in character and does not rely on variational calculus. 20. Evolutionary approach for determining first-principles hamiltonians. PubMed Hart, Gus L W; Blum, Volker; Walorski, Michael J; Zunger, Alex 2005-05-01 Modern condensed-matter theory from first principles is highly successful when applied to materials of given structure-type or restricted unit-cell size. But this approach is limited where large cells or searches over millions of structure types become necessary. To treat these with first-principles accuracy, one 'coarse-grains' the many-particle Schrodinger equation into 'model hamiltonians' whose variables are configurational order parameters (atomic positions, spin and so on), connected by a few 'interaction parameters' obtained from a microscopic theory. But to construct a truly quantitative model hamiltonian, one must know just which types of interaction parameters to use, from possibly 10(6)-10(8) alternative selections. Here we show how genetic algorithms, mimicking biological evolution ('survival of the fittest'), can be used to distil reliable model hamiltonian parameters from a database of first-principles calculations. We demonstrate this for a classic dilemma in solid-state physics, structural inorganic chemistry and metallurgy: how to predict the stable crystal structure of a compound given only its composition. The selection of leading parameters based on a genetic algorithm is general and easily applied to construct any other type of complex model hamiltonian from direct quantum-mechanical results. 1. Hamiltonian flow in Coulomb gauge Yang-Mills theory SciTech Connect Leder, Markus; Reinhardt, Hugo; Pawlowski, Jan M.; Weber, Axel 2011-01-15 We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed. 2. Evolution of a Spin System Under a Periodic Hamiltonian Goldman, M. The expression of the density matrix for a spin system subjected to a periodic Hamiltonian is derived in the form of an expansion in powers of the inverse modulation frequency, an extension of a method devised by Ruishvili and Menabde and by Mehring. Its application to MAS experiments, as regards the contribution of the dipolar interactions to the sideband intensities, is discussed. 3. Spectral and resonance properties of the Smilansky Hamiltonian Exner, Pavel; Lotoreichik, Vladimir; Tater, Miloš 2017-02-01 We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. 4. Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling. PubMed Tosner, Zdenek; Glaser, Steffen J; Khaneja, Navin; Nielsen, Niels Chr 2006-11-14 We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments. 5. Fock-space diagonalization of the state-dependent pairing Hamiltonian with the Woods-Saxon mean field Molique, H.; Dudek, J. 1997-10-01 A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H⁁pair=∑αβGαβc†αc†α ¯cβ ¯cβ with an arbitrary set of matrix elements Gαβ. Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p~40 particles on n~80 levels and for several dozens of lowest lying states with precision ~(1-2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei. 6. The (100), (111) and (110) surfaces of diamond: an ab initio B3LYP study De La Pierre, Marco; Bruno, Marco; Manfredotti, Chiara; Nestola, Fabrizio; Prencipe, Mauro; Manfredotti, Claudio 2014-04-01 We present an accurate ab initio study of the structure and surface energy of the low-index (100), (111) and (110) diamond faces, by using the hybrid Hartree-Fock/density functional B3LYP Hamiltonian and a localised all-electron Gaussian-type basis set. A two-dimensional periodic slab model has been adopted, for which convergence on both structural and energetic parameters has been thoroughly investigated. For all the three surfaces, possible relaxations and reconstructions have been considered; a detailed geometrical characterisation is provided for the most stable structure of each orientation. Surface energy is discussed for all the investigated faces. 7. Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems Gong, Yuezheng; Wang, Qi; Wang, Zhu 2017-03-01 The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian system, a naive application of the POD method can destroy its Hamiltonian structure in the reduced-order model. In this paper, we develop a new reduce-order modeling approach for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but modifies the ROM so that the appropriate Hamiltonian structure is preserved. Since the POD truncation can degrade the approximation of the Hamiltonian function, we propose to use the POD basis from shifted snapshots to improve the Hamiltonian function approximation. We further derive a rigorous a priori error estimate of the structure-preserving ROM and demonstrate its effectiveness in several numerical examples. This approach can be readily extended to dissipative Hamiltonian systems, port-Hamiltonian systems etc. 8. Two-dimensional surrogate Hamiltonian investigation of laser-induced desorption of NO/NiO(100) SciTech Connect Dittrich, Soeren; Freund, Hans-Joachim; Koch, Christiane P.; Kosloff, Ronnie; Kluener, Thorsten 2006-01-14 The photodesorption of NO from NiO(100) is studied from first principles, with electronic relaxation treated by the use of the surrogate Hamiltonian approach. Two nuclear degrees of freedom of the adsorbate-substrate system are taken into account. To perform the quantum dynamical wave-packet calculations, a massively parallel implementation with a one-dimensional data decomposition had to be introduced. The calculated desorption probabilities and velocity distributions are in qualitative agreement with experimental data. The results are compared to those of stochastic wave-packet calculations where a sufficiently large number of quantum trajectories is propagated within a jumping wave-packet scenario. 9. Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes Dias, Gonçalo A. S.; Lemos, José P. S. 2008-10-01 The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free ω parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→±∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates {M,PM;Q,PQ}, where M is the mass parameter, which for ω<-(3)/(2) and for ω=±∞ needs a careful renormalization, PM is the conjugate momenta of M, Q is the charge parameter, and PQ is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrödinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field ϕ¯. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton. 10. First integrals of generalized Ermakov systems via the Hamiltonian formulation Mahomed, K. S.; Moitsheki, R. J. 2016-07-01 We obtain first integrals of the generalized two-dimensional Ermakov systems, in plane polar form, via the Hamiltonian approaches. There are two methods used for the construction of the first integrals, viz. the standard Hamiltonian and the partial Hamiltonian approaches. In the first approach, F(𝜃) and G(𝜃) in the Ermakov system are related as G(𝜃) + F‧(𝜃)/2 = 0. In this case, we deduce four first integrals (three of which are functionally independent) which correspond to the Lie algebra sl(2,R) ⊕ A1 in a direct constructive manner. We recover the results of earlier work that uses the relationship between symmetries and integrals. This results in the complete integrability of the Ermakov system. By use of the partial Hamiltonian method, we discover four new cases: F(𝜃) = G(𝜃)(c1sin 𝜃 + c3cos 𝜃)/(c1cos 𝜃 - c3sin 𝜃) with c2c3 = c1c4, c1≠0, c3≠0; F(𝜃) = G(𝜃)(c2sin 𝜃 + c4cos 𝜃)/(c2cos 𝜃 - c4sin 𝜃) with c1 = c3 = 0, c2≠0, c4≠0; F(𝜃) = -G(𝜃)cot 𝜃 with c1 = c2 = 0, c3, c4 arbitrary and F(𝜃) = G(𝜃)tan 𝜃 with c3 = c4 = 0, c1, c2 arbitrary, where the cis are constants in all cases. In the last two cases, we find that there are three operators each which give rise to three first integrals each. In both these cases, we have complete integrability of the Ermakov system. The first two cases each result in two first integrals each. For every case, both for the standard and partial Hamiltonian, the angular momentum type first integral arises and this is a consequence of the operator which depends on a momentum coordinate which is a generalized symmetry in the Lagrangian context. 11. Contact Transformations and Determinable Parameters in Spectroscopic Fitting Hamiltonians Mekhtiev, Mirza A.; Hougen, Jon T. 2000-02-01 In recent least-squares fits of torsion-rotation spectra of acetaldehyde and methanol it was found possible to adjust more fourth-order parameters than would be expected from traditional contact-transformation considerations. To investigate this discrepancy between theory and practice we have carried out numerical fitting experiments on the simpler three-dimensional (three-Eulerian-angle) asymmetric rotor problem, using J ≤ 20 unitless energy levels generated artificially from a full orthorhombic Hamiltonian with quadratic through octic operators in the angular momentum components. Results are analyzed using the condition number κ of the least-squares matrix, which is a measure of its invertibility in the presence of round-off and other errors. When κ is very large, parameters must be removed from the fit until κ becomes acceptably small, corresponding to procedures which lead to reduced Hamiltonians in molecular spectroscopy. We find that under certain circumstances κ can be decreased to an acceptable level for Hamiltonians which are only partially reduced when compared to Watson A and S reductions. Some insight into this behavior is obtained from classical mechanics and from the concept of delayed contact transformations. Transferring this numerical and algebraic understanding to the more complicated four-dimensional methyl-top internal rotor problem supports the empirical observation that presently existing data sets for methanol and acetaldehyde are most efficiently fit using partially reduced Hamiltonians and further suggests that expanding the methanol data set to transitions involving levels of higher J, K, and vt would favor even more strongly the use of partially reduced fourth-order Hamiltonians. 12. When a local Hamiltonian must be frustration-free. PubMed Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich 2016-06-07 A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory. 13. Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space Kim, Hwa Kil In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the Moreau-Yosida approximation and denote it by Hτ. We show that solutions of the Hamiltonian system for Hτ converge to a solution of the Hamiltonian system for H as τ converges to zero. We provide sufficient conditions on H to carry out this process. 14. Differential evolution algorithm for global optimizations in nuclear physics Qi, Chong 2017-04-01 We explore the applicability of the differential evolution algorithm in finding the global minima of three typical nuclear structure physics problems: the global deformation minimum in the nuclear potential energy surface, the optimization of mass model parameters and the lowest eigenvalue of a nuclear Hamiltonian. The algorithm works very effectively and efficiently in identifying the minima in all problems we have tested. We also show that the algorithm can be parallelized in a straightforward way. 15. Two integrable Hamiltonian hierarchies in sl(2 ,R ) and so(3 ,R ) with three potentials Gu, Xiang; Ma, Wen-Xiu; Zhang, Wen-Ying 2017-05-01 By introducing two specific matrix spectral problems associated with sl(2 ,R ) and so(3 ,R ) matrix Lie algebras, we generate two integrable Hamiltonian hierarchies with three potentials. The computation and analysis on their Hamiltonian structures by means of the trace identity show that the resulting hierarchies are Liouville integrable, namely, that each hierarchy consists of commuting Hamiltonian soliton equations. 16. On bi-Hamiltonian structure of two-component Novikov equation Li, Nianhua; Liu, Q. P. 2013-01-01 In this Letter, we present a bi-Hamiltonian structure for the two-component Novikov equation. We also show that proper reduction of this bi-Hamiltonian structure leads to the Hamiltonian operators found by Hone and Wang for the Novikov equation. 17. Targeting transcription factor Stat5a/b as a therapeutic strategy for prostate cancer PubMed Central Liao, Zhiyong; Nevalainen, Marja T 2011-01-01 Signal transducer and activator of transcription 5 (Stat5) is critical for the viability and growth of human prostate cancer cells in culture and for prostate xenograft tumors in nude mice. The expression of nuclear active Stat5a/b is associated with high histological grades of clinical prostate cancers, and the presence of active Stat5a/b in prostate cancer predicts early disease recurrence. Stat5a/b and androgen receptor signaling pathways functionally synergize in prostate cancer cells, and recent work suggests that Stat5a/b may be involved in the progression of prostate cancer to metastatic disease. Here, we review the biological functions of Stat5a/b in prostate cancer and potential strategies to target the prolactin receptor (PrlR)/Jak2/Stat5 signaling pathway for therapy development for prostate cancer. PMID:21416055 18. An investigation of ab initio shell-model interactions derived by no-core shell model Wang, XiaoBao; Dong, GuoXiang; Li, QingFeng; Shen, CaiWan; Yu, ShaoYing 2016-09-01 The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory (MBPT), the first work of which can be traced to Brown and Kuo's first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green's function Monte Carlo (GFMC), no-core shell model (NCSM), and coupled-cluster theory with single and double excitations (CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential (JISP) and chiral effective-field theory (EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body (3-bd) force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data. 19. Deuteron distribution in nuclear matter Benhar, O.; Fabrocini, A.; Fantoni, S.; Illarionov, A. Yu.; Lykasov, G. I. 2002-05-01 We analyze the properties of deuteron-like structures in infinite, correlated nuclear matter, described by a realistic hamiltonian containing the Urbana v14 two-nucleon and the Urbana TNI many-body potentials. The distribution of neutron-proton pairs, carrying the deuteron quantum numbers, is obtained as a function of the total momentum by computing the overlap between the nuclear matter in its ground state and the deuteron wave functions in correlated basis functions theory. We study the differences between the S- and D-wave components of the deuteron and those of the deuteron-like pair in the nuclear medium. The total number of deuteron type pairs is computed and compared with the predictions of Levinger's quasideuteron model. The resulting Levinger's factor in nuclear matter at equilibrium density is 11.63. We use the local density approximation to estimate the Levinger's factor for heavy nuclei, obtaining results which are consistent with the available experimental data from photoreactions. 20. Astrophysical jet dynamos based on spheromak, dusty plasma, and Hamiltonian concepts	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8473686575889587, "perplexity": 1470.9712621487988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806225.78/warc/CC-MAIN-20171120203833-20171120223833-00665.warc.gz"}
http://digre.pmf.unizg.hr/3956/	# Stable homotopy theory of dendroidal sets Bašić, Matija (2015) Stable homotopy theory of dendroidal sets. Doctoral thesis, Faculty of Science > Department of Mathematics. PDF Restricted to Repository staff only Language: English Download (829kB) \| Request a copy ## Abstract The main topic of this thesis is the stable homotopy theory of dendroidal sets. This topic belongs to the area of mathematics called algebraic topology. Algebraic topology studies the interaction between the algebraic and topological structures. Examples of topological spaces with a very rich algebraic structure are (iterated) loop spaces. Loop spaces carry an algebraic structure which is called an $A_{\infty}$-structure, while infinite loop spaces carry an $E_{\infty}$-structure. These structures consist of an infinite sequence of operations that satisfy various coherence laws. As it is difficult to grasp all these data, one usually uses topological operads to efficiently describe this information. One can think of operads as carrying “blueprints” for the algebraic structure which is realized in every space with that structure. The characterization results for (iterated) loop spaces using topological operads have been established in the early 1970’s by the work of P. May, M. Boardman and R. Vogt. In the 1990’s it became evident that it is important to understand the homotopy theory operads. The theory of dendroidal sets provides a new context for studying operads up to homotopy. Dendroidal sets were introduced in 2007 by I. Moerdijk and I. Weiss. Subsequent work of I. Moerdijk and D.-C. Cisinski shows that dendroidal sets indeed model topological/simplicial operads. An important advantage of dendroidal sets is that the theory is built in a natural way as a generalization of the theory of simplicial sets. The study of dendroidal sets is very combinatorial in its nature since it is based on the notion of trees (graphs with no loops). Also, as a category of presheaves, the category of dendroidal sets has nice categorical properties. Simplicial sets provide combinatorial models for spaces (think of it in terms of triangulations of spaces given by simplicial approximations) and dendroidal sets provide combinatorial models for infinite loops spaces as spaces together with complicated algebraic structure. In fact, the precise formulation of this idea is one of the main topics of this thesis. A precise formulation of our results is given in the language of Quillen’s model categories. Model categories provide a formalism to study and compare homotopy theories in various contexts (topological spaces, chain complexes, simplicial sets, operads etc.) One of the main results of this thesis is that the category of dendroidal sets admits a model structure such that the underlying homotopy theory is equivalent to the homotopy theory of infinite loop spaces (equivalently, of grouplike $E_{\infty}$-algebras or connective spectra). We call this model structure the stable model structure on dendroidal sets. Constructing a model structure is a tedious job. In our case it requires a great deal of technical combinatorial results about dendroidal sets (i.e. ab out trees). In order to simplify our arguments, in Chapter 4 we develop a combinatorial technique for proving results about dendroidal anodyne extensions. This technique can be viewed as a result in its own right as one might apply it also in different ways than it is used in the later chapters of the thesis. We give two constructions of the stable model model structure. The first construction is more elementary and has an advantage of providing a characterization of fibrations between fibrant objects. This construction is based on standard mo del-theoretical arguments and it is given in Chapter 5. The second construction, given in Chapter 6, is based on the work of G. Heuts. This approach makes it possible to show that the stable model structure on dendroidal sets is Quillen equivalent to a model structure on $E_{\infty}$-spaces with grouplike $E_{\infty}$-spaces as fibrant objects. The equivalence to grouplike $E_{\infty}$-objects (i.e. connective spectra) might be considered as a solution to the problem of geometric realization of dendroidal sets. Also, these results open new possibilities to investigate the connective part of classical stable homotopy theory. The results of the thesis presented in Chapter 7 go in that direction. In that final chapter we discuss homology groups of dendroidal sets. This homology theory generalizes the well-known homology theory of simplicial sets (i.e. the singular homology of spaces). The generalization is not straightforward because we work with non-planar trees, but we want to use a certain sign-convention for planar trees. After giving the definition, we establish that these homology groups are homotopy invariant and that they compute the standard homology of the corresponding connective spectrum. The results of Chapters 6 and 7 are joint work with T. Nikolaus. Item Type: Thesis (Doctoral thesis) Moerdijk, Ieke 2015 170 NATURAL SCIENCES > Mathematics > AlgebraNATURAL SCIENCES > Mathematics > Geometry and Topology ISBN 978-94-6259-634-4 Faculty of Science > Department of Mathematics Iva Prah 02 Jun 2015 09:16 02 Jun 2015 09:16 http://digre.pmf.unizg.hr/id/eprint/3956	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9169481992721558, "perplexity": 359.18281474604584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866733.77/warc/CC-MAIN-20180524170605-20180524190605-00195.warc.gz"}
https://computationstructures.org/notes/tradeoffs/notes.html	The circumspect engineer, given a problem to solve, inevitably faces a wide range of plausible alternative design choices. Typically, alternative paths to solving a problem differ in various cost and performance parameters, including • Hardware cost measures: circuit size, transistor count, etc. • Performance measures: Latency, throughput, clock speed. • Energy cost measures: average/maximum power dissipation, power supply and cooling requirements . • Engineering cost measures: design ease, simplicity, ease of maintenance/modification/extension. Engineering choices typically involve optimizing certain of these parameters, often at the expense of others. In this chapter we explore several examples of such tradeoffs. Optimizing Power 12.1. Optimizing Power We noted in Section 6.5 that the primary cause of power dissipation within CMOS logic circuitry is ohmic losses in the flow of current into and out of signal nodes during logic transitions. As observed in that section, the power dissipated is proportional to the frequency of transitions, which, in typical circuitry, is proportional to the clock frequency. In many situations we can improve the average (or maximum) energy dissipation by choosing a design that minimizes the number of logic transitions per second. A simple way to achieve that goal is by lowering the clock frequency, usually at a proportional loss of processing performance; indeed, some modern computers have low-power operating modes which simply slow the clock to a fraction of its maximal rate. Eliminating Unnecessary Transitions 12.1.1. Eliminating Unnecessary Transitions Can we lower the rate of transitions without commensurate performance degradation? Often the answer is yes. Consider, for example, the design of an Arithmetic Logic Unit (ALU), a high-level combinational building block you will be familiar with from the laboratory. An ALU is a computational Swiss army knife, performing any of a repertoire of operations on its input data based on a multi-bit function code (ALUFN) passed as a control input. Typical ALU Block Diagram The diagram to the right shows a typical top-level design for a combinational ALU: there are four subsystems responsible for different classes of operations (addition, Boolean, etc) each of which operates simultaneously on the input data. A final four-way multiplexor selects the computed result actually requested by the ALUFN code, discarding the values needlessly computed by the unselected subsystems. Assuming the requested operation is the exclusive or $A \oplus B$ of two 32-bit input operands $A$ and $B$, the 32-bit sum $A + B$ by the adder unit has simply wasted whatever power is taken for its computation. The redundant computation will automatically take place in our combinational circuit as soon as the $A$ and $B$ inputs take on new values, with many consequent transitions and power dissipation throughout the adder circuitry. Power-saving ALU Design We can eliminate these redundant transitions simply by not allowing the inputs to the adder to change unless an add operation has actually been selected. One way to accomplish this is shown to the left. In this approach, latches are placed in the data paths to each subsystem, and are gated by the particular combination of ALUFN bits that selects a computation by that subsystem. Using this scheme, the $A$ and $B$ inputs to unselected subsystems will be frozen, forcing internal logic nodes of these circuits to retain constant values and thereby dissipate very little power. Optimizing Latency 12.2. Optimizing Latency We can often use the mathematical properties of operations performed by circuit elements to rearrange their interconnection in a way that performs equivalent operations at lower latency. A common class of such rearrangements is the substitution of a tree for a linear chain of components that perform an associative binary operation, mentioned in Section 7.7.2. Parallel Prefix 12.2.1. Parallel Prefix We can generalize this approach to other binary operations. Suppose $\circledast$ is an associative binary operator, meaning that $a \circledast (b \circledast c) = (a \circledast b) \circledast c$. We can generalize this operator to $k$ operands $x_0, x_1, ... x_{n-1}$ by iteratively applying the binary $\circledast$ operator to successive prefixes of the operand sequence, computing each intermediate $x_j \circledast ... \circledast x_0$ by the recurrence $x_j \circledast (x_{j-1} \circledast ... \circledast x_0)$, generating values for each successive prefix of the argument sequence. This imposes a strict ordering on the component applications of the binary $\circledast$ operator; it requires that the result of applying $\circledast$ to the first $j-1$ arguments be completed before it is applied to $x_j$. In a sequential circuit implementation, the $k$-operand function would take $\theta(k)$ execution time, sufficient for a sequence of $k$ binary operations. A corresponding combinational circuit would have an input-output path going through all $k-1$ components, again implying a $\theta(k)$ latency. The associativity of $\circledast$, however, affords some flexibility in the order of the component computations. We can use the fact that $$x_0 \circledast (x_1 \circledast (x_2 \circledast x_3)) = (x_0 \circledast x_1) \circledast (x_2 \circledast x_3)$$ to process pairs of arguments in parallel, reducing the number of operands to be combined by a factor of two in the time taken by one binary operation. Repeated application of this step -- halving the number of operands in a single constant-time step -- reduces the asymptotic latency from $\theta(k)$ to $\theta(log(k))$, a dramatic improvement. In a combinational implementation, it results in a tree structure like that of Section 7.7.2. The key to this (and other) latency reduction techniques is to identify a critical sequence of steps that constrains the total execution time, and break that sequence into smaller subsequences that can be performed concurrently. Returning to the problem of binary addition, we have observed that the critical sequence through the ripple-carry adder of Section 11.2 is the combinational path that propagates carry information through each full adder from low-order to high-order bit positions. We might (and generally do) aspire to minimize the delay along this path by careful design of our full adder component to produce the output carry as fast as possible; however, this optimization gives at best a constant factor improvement to our $\theta(N)$-bit latency. More dramatic improvements require that the carry chain somehow be broken into pieces that can be dealt with in parallel. Suppose we need a 32-bit adder, but are unhappy with the latency of a 32-bit ripple-carry adder. We might observe that the latency of a 16-bit adder is roughly half that number, owing to its shorter carry chain; thus we could double the speed of our 32-bit adder by breaking it into two 16-bit adders dealing in parallel with the low- and high-order halves of our addends. The problem is that the carry input to the high-order 16-bit adder is unknown until the low-order adder has completed its operation. To accommodate this uncertainty, we simply replicate two instances of the high-order 16-bit adder, as shown to the right. We supply one of the high-order adders with $0$ as the carry input, the other with $1$; this guarantees that the sum bits coming from one of these high-order adders will be correct. We of course can't know which high-order sums to select, until the carry output is produced by the low-order add. To this end, we use a multiplexor to select between the two high-order sums depending on the low-order carry output. The latency of this carry-select adder is that of the 16-bit adder plus the delay of the multiplexor, nearly a factor of two saving. It comes at a hardware cost of over 50%, however, owing to the redundant high-order adder. Of course the number of bits in the high- and low-order portions need not be equal; often the low-order portion has fewer bits, allowing time for its carry output to propagate through the multiplexors selecting the high-order outputs. An $N$-bit carry-select adder may be hierarchical -- that is, each of the three component adders may themselves be carry-select adders. If we make a deep hierarchy of carry-select adders in this fashion, we can make a $2 \cdot n$-bit adder whose latency is only a mux delay longer than its three component $n$-bit adders, doubling $n$ at a fixed cost at each level. The result is a family of hierarchical $n$-bit carry-select adders whose latency grows as $\theta(\log(n))$. It is tempting to try rearranging the full adders of a ripple-carry adder in a tree, in order to get the $\theta(log n)$ latency available to $n$-bit associative logical operations like AND and XOR. Of course, the functions performed by the full adders cannot be arbitrarily regrouped, since the full adder at each bit position takes as input a carry from the next lower-order position, and supplies a carry to the adjacent higher-order full adder. This would seem to rule out performing the function of the higher-order FAs simultaneously with that of lower-order ones. Clever reformulation of the building blocks used for our adders, however, can mitigate this constraint. The key to our new approach is to eliminate carry out signals, which necessarily depend on carry inputs (leading to the $\theta(n)$ carry chain), replacing them with alternative information that can be used to deduce higher-order carry inputs. We'd like the new outputs to have two key properties: • They can be generated from the $A_i$ and $B_i$ inputs available at each bit position from the start of the operation, not depending on outputs computed from other bit positions; • Information from two adjacent sequences of bit positions can be aggregated to characterize the carry behavior of their concatenation. Consider the carry output from a $k$-bit ripple-carry adder. Given only the $k$-bit $A$ and $B$ data inputs, what can we say about the carry output it would produce? We can identify three cases: • Generate: Given these $A$ and $B$ values, $C_{out} = 1$ always. • Kill: Given these $A$ and $B$ values, $C_{out} = 0$ always. • Propagate: Given these $A$ and $B$ values, $C_{out} = C_{in}$, where $C_{in}$ is the carry input to the low-order bit of the adder. These three cases characterize the carry output independently of the carry input (in the sense that the characterization is valid whatever the carry input turns out to be). This allows it to be determined independently of the carry input -- i.e., in parallel for various bit positions within the adder. Lets consider a family of $k$-bit adders that replace carry output signals with outputs that encode these three classes of carry behavior. Given 3 cases, at least 2 signals are required. We choose the following two: • G (generate): $1$ if the carry is $1$; • P (propagate): $1$ if the carry is $C_{in}$. If neither G or P is asserted, then the carry is $0$ independently of $C_{in}$. Given $G$ and $P$ signals and the input carry $C_{in}$, the carry output can be computed by $C_{out} = G + P \cdot C_{in}$. 1-bit CLA The full adder of our ripple-carry implementations can be replaced by a $1$-bit carry lookahead adder. whose icon is shown to the left. 1-bit CLA logic Its sum output is $A \oplus B \oplus C_{in}$ as in the full adder, but $P = A \oplus B$ and $G = A \cdot B$ as shown to the right; this reflects the observation that an output carry is propagated if either $A$ or $B$ is one, and $generated$ if they are both one. Next we turn to the problem of cascading two small (say, $n$-bit) carry lookahead adders to make a bigger ($2 \cdot n$-bit) carry lookahead adder. To facilitate cascading, we define a specialized commponent, called CL for carry lookahead. 2-bit CLA circuit Each CL instance combines $P$, $G$, and $C_{in}$ signals of two carry-lookahead adders (say, $k$-bit and $j$-bits, respectively) to make them appear as a single, wider $k+j$-bit carry lookahead adder. It takes as input the carry input $C_{in}$ to the combined adder, and produces as output the $P$ and $G$ signals for the combination. The diagram on the left shows its use to combine two 1-bit carry lookahead adders into the 2-bit adder whose icon is nearly identical to that of the CLA1. 2-bit CLA Note that the 2-bit carry lookahead adder follows the same terminal pattern as the 1-bit version, differing only in the number of bits in the data signals. We can combine two carry-lookahead adders of arbitrary sizes using a CL module. We allocate one component adder to the high-order portion of the sum and the other to the low-order, routing their $P$, $G$, and $C_{in}$ signals to the CL module. The CL module performs two separable functions: • CL GP logic It combines $G_h, P_h$ and $G_l, P_l$ signals from the high- and low-order component adders to generate appropriate $P$ and $G$ signals for their combination. The combined $P = P_h \cdot P_l$ and $G = G_h + P_h \cdot G_l$ are generated by the logic shown to the right. • It generates carry input signals $C_h$ and $C_l$ for the component adders. The carry input to the low-order component is just the carry input to CL carry logic the combined adder; it is the $C_{in}$ input to the CL component. The carry input to the high-order component is computed using the $P$ and $G$ inputs computed in the step above, using the pair of gates shown to the right. The observant reader might notice that the 2-bit CLA circuit shown above appears to contain combinational cycles: it takes $P$ and $G$ signals from the component adders, and produces $C_{in}$ signals that are routed back to each adder. However, the two combinational functions performed by our CL module are entirely independent of one another; they are simply combined, for convenience, in a single module. Separating the CL module into independent combinational devices would allow us to redraw the diagram in acyclic form, verifying that it is indeed a valid combinational circuit. 8-bit CLA We can combine two CLA2 modules (using another CL component) to make a 4-bit CLA4, two CLA4s to make an 8-bit CLA8, etc. Moreover, we can use a CL module to combine, say, 16-bit and 4-bit carry lookahead adders to make a 20-bit adder; the CL device operates independently of the number of bits in each component adder. Each time we use a single CL module to combine two adders, we are in effect adding a layer to a tree of logic. If we expand the diagram of an 8-bit adder made this way, we get the circuit shown below: 8-bit CLA, expanded Observe that we have added two gates to compute a carry output, $C_{out}$, from the $P$ and $G$ outputs of the bottommost CL block. This allows our carry lookahead adder to replace slower ripple-carry adders that produce carry outputs. Note that the "leaves" of the tree -- the 1-bit CLA1 components -- get all of their $A$ and $B$ data bits simultaneously at the start of the ADD operation, independently of the number of bits. They each produce $P$ and $G$ signals independently of their late-arriving $C_{in}$ inputs; these $P$ and $G$ values propagate to the root CL element in the tree, which computes $C_{in}$ values that propagate through the tree back to the leaves. Using this construction, we can build a $2^k$-bit adder with a tree of depth $k$. The worst-case propagation path through this circuit is the $P$, $G$ values to the root CL followed by carry propagation back to the leaves -- a path whose propagtion delay is proportional to the tree depth $k$ rather than the bit-width $2^k$. The latency of a $2^k$-bit adder built this way is thus $\theta(k)$, whence the latency of an $N$-bit adder is $\theta(log N)$. Optimizing Throughput 12.3. Optimizing Throughput The most obvious way to improve the throughput of a device that computes $P(X)$ from $X$ is brute-force replication: if the throughput of one device is $T_P$ computations/second, then $N$ copies of the device working in parallel can perform $N \cdot T_P$ computations/second. In Section 11.5 we introduced the notion of pipelining, which often affords cheaper throughput improvements by adding registers rather than replicating the logic that performs the actual complication. These two techniques can often be combined to optimize throughput at modest cost. However, computation-specific engineering choices can dramatically impact their effectiveness and the performance of the resulting design. N-bit Binary Multiplier 12.3.1. N-bit Binary Multiplier Consider, for example, the multiplication of two $N$-bit unsigned binary numbers $A_{N-1:0}$ and $B_{N-1:0}$ to produce a $2 \cdot N$-bit unsigned binary product $P_{2N-1:0}$. We may view this operation as the sum of $N$ partial products, each of the form $B_i \cdot A_{N-1:0} \cdot 2^i$ for $0 \leq i \lt N$. Observe that each partial product can be formed by $N$ AND gates, multiplying the bits of $A$ by a selected $B_i$. It remains to sum the $N$ partial products, which we can do using an array of full adders -- much like our $N$-bit by $M$-word adder of Section 11.4. To streamline our design, we devise a multipler "slice" component containing $N$ full adders with an AND gate on one sum input, and replicate this slice component for each of the $N$ partial products. Our resulting design has the following structure: 4-bit Multiplier Note the two-dimensional layout of the diagram. Each row or "slice" has four locations, forming the 4-bit partial product $A \cdot B_i$ for consecutive bits $B_i$ of $B$ in consecutive rows. Each row is offset to properly account for the weight of its contribution to the final product, and the rightmost bit of each partial product becomes part of the product formed at the bottom terminals. The topmost slice contains only AND gates, as it has no incoming value from rows above to add to the partial product it generates. Subsequent rows have a full adder at each bit position, to combine the incoming sum from above with the partial product generated by the AND gates. Each row effectively contains a ripple-carry adder as well as the AND gates that form the partial product. Although there are only 4 4-bit partial products, we use additional slices to propagate carries and form the full $2\cdot N$ bits of the final product. The full adders in these slices have unused data inputs connected to logical 0 (ground), representing that $B_i = 0$ for $i \geq 4$. As a result, these additional bit positions don't require the logic of a full adder, and could be simplified considerably; similarly, the rightmost full adder in each slice might be optimized in view of its carry input tied to 0. While such optimizations are straightforward, we will not pursue them here. Noting that these optimizations may reduce constant factors impacting the cost and performance parameters of our multiplier, they do not effect its asymptotic cost or performance. The above 4-bit multipler generalizes to an $N$ bit combinational multipler, whose two-dimensional structure reflects an asymptotic hardware cost of A$\theta(N^2)$. Like the $N$-bit by $M$-word adder of , the signal flow through the array of full adders is top-to-bottom and right-to-left, leading to a longest-path propagation delay that grows as the sum of the array's width and height -- each $\theta(N)$. Thus the latency of our combinational multiplier is $\theta(N+N) = \theta(N)$, and its throughput is $\theta(1/N)$. Pipelined Multiplier 12.3.1.1. Pipelined Multiplier If we have a large number of independent multiplications to perform, it seems logical to pipeline our $n$-bit combinational multiplier to improve its $\theta(1/N)$ throughput. Quick inspection of the $4$-bit multiplier diagram above suggests an obvious partitioning of the combinational circuit into pipeline stages: each horizontal slice, that forms a 4-bit partial product and adds it to the sum coming from slices above, might constitute a pipeline stage. Indeed, we could pipeline our multiplier by drawing stage boundaries between horizontal slices, and inserting registers wherever a data path intersects a stage boundary. Unfortunately, such a pipelining approach would not result in improved performance. Since each multiplier slice effectively contains an $N$-bit ripple-carry adder, it requires $\theta(N)$ time for the carry to propagate from right to left through all $\theta(N)$ bits. The maximal clock period is thus $\theta(N)$, and the throughput of our naively pipelined multiplier remains at $\theta(1/N)$. Since there are $\theta(N)$ stages, however, the latency has now been degraded from $\theta(N)$ to $\theta(N^2)$. To materially improve performance, we must find a way to break long ($\theta(N)$) paths within each pipeline stage. The problem with our naive pipeline is that our horizontal pipeline boundaries failed to break up the horizontal carry chains within each slice. We might address this problem by making either the pipeline stage boundaries or the carry chains less horizontal, so that they intersect. The latter approach is deceptively simple: rather than routing the carry output from each full adder to the full adder on its immediate left, we route the carry to the corresponding full adder in the slice below. 4-bit Multiplier, pipelined With this minor change, horizontal pipeline stage boundaries intersect both the vertical path of the sum formation and the diagonal path of carry propagation. The worst-case propagation delay through each slice is constant -- $\theta(1)$ -- rather than $\theta(N)$, allowing a constant clock frequency independently of the number $N$ of operand bits. Making this design work requires careful attention to a number of details we gloss over here. Among these is the need for pipeline registers at points where data lines are implicit in the diagram -- for example, those carrying the 4-bit $A$ operand to the various pipeline stages. Sequential Multiplier 12.3.1.2. Sequential Multiplier The $N$-bit pipelined multipler just sketched can be built using $\theta(N)$ idential "slices", each a module containing $N$ each AND gates and full adders; we note that the topmost slice in our diagram omits the full adders, optimizing for the case when the sum coming from the slice above is zero. In pursuit of high throughput, at any instant each of the identical slices of our pipelined problem will be working on a different multiplication operation; hence any single multiplication is only using one of the slices at a time. 4-bit Sequential Multiplier This observation leads us to one approach to a sequential multiplier, made using a single slice which gets re-used during successive clock cycles to play the role of each of our pipeline stages. A sketch of this approach appears on the right: it uses a single pipeline stage supplying data to a pipeline register; however, most signals from this register are connected to the inputs of this single stage rather than of the next stage in the pipeline. In order to deal with the consecutive bits of the $B$ operand needed by successive pipeline stages, we load $B[3:0]$ into a shift register whose contents are shifted by one bit position at each active clock edge. Another shift register is used to collect successive bits of the product in an output register over the $2 \cdot N$ cycles it takes to do an $N$x$N$-bit multiplication. Again, we gloss over a number of details. But such a design can be used to build an $N$-bit multiplier at a hardware cost proportional to $N$ and having a latency of $\theta(N)$ since the clock period is independent of $N$. Multiplier Recap 12.3.1.3. Multiplier Recap The design of state-of-the-art multipliers involves a number of engineering techniques beyond our current scope; the three design examples here are chosen to illustrate tradeoffs typical of basic design decisions. Design Cost Latency Throughput Combinational $\theta(N^2)$ $\theta(N)$ $\theta(1/N)$ Pipelined $\theta(N^2)$ $\theta(N)$ $\theta(1)$ Sequential $\theta(N)$ $\theta(N)$ $\theta(1/N)$ Multiplier Designs The asymptotic parameters of the three design approaches we have sketched are summarized to the left. Of course, one must be careful making design decisions based on asymptotic performance: the additive and multiplicative constants ignored by the $\theta(...)$ abstraction may dominate cost/performance decisions for particular values of $N$. Our combinational multiplier maximizes latency, but as $N$ becomes large has lower throughput than the pipelined version and is more expensive than the sequential approach. Chapter Summary 12.4. Chapter Summary This chapter explores, via simple examples, the sorts of engineering tradeoffs confronted during the design process. Among the salient observations of this chapter: • Power dissipation, typically proportional to the frequency of logic transitions, can be optimized by minimizing the number of transitions made during a computation. • Minimization of combinational latency involves shortening the propagation delay along the longest input-output path. For a broad class of functions, this can be done using a tree structure, reducing the latency of an $N$-input function to $\theta(log N)$. • Pipelining improves throughput so long as stage boundaries break long combinational paths. • Sequential designs can exploit recurring structure replicating their function in time rather than in hardware, saving hardware cost.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.658024787902832, "perplexity": 1159.5262018804765}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304954.18/warc/CC-MAIN-20220126131707-20220126161707-00495.warc.gz"}
https://kb.osu.edu/dspace/handle/1811/10429	# $^{13}C$ MAGNETIC SHIELDING FROM BEAM MASER MEASURMENTS OF SPIN ROTATION INTERACTION IN $CH_{3}$ CN Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/10429 Files Size Format View 1978-MG-07.jpg 91.41Kb JPEG image Title: $^{13}C$ MAGNETIC SHIELDING FROM BEAM MASER MEASURMENTS OF SPIN ROTATION INTERACTION IN $CH_{3}$ CN Creators: Kukolich, Stephen G.; Lind, G.; Barfield, M.; Faehl, L.; Marshall, J. L. Issue Date: 1978 Publisher: Ohio State University Abstract: A beam maser spectrometer was used to make high resolution measurements (6 kHz f.w.h.m.) of $J=1\rightarrow 0$ transitions in $CH_{3}{^{13}}CN$. Spectra of $CH_{3}{^{12}}CN$. were obtained at higher resolution using Ramsey’s method of separated oscillating fields. Analysis of the spectra yielded values for quadrupole coupling, spin-rotation and spin-spin interaction strengths. The $^{13}C$ spin-rotation interaction strength was used to determine the paramagnetic contribution to the shielding tensor component $\sigma_{1}$. The diamagnetic contribution is obtained from molecular orbital calculations. Our results are compared with values obtained from liquid crystal and multiple pulse N.M.R. experiments. Description: Author Institution: Department of Chemistry, University of Arizona URI: http://hdl.handle.net/1811/10429 Other Identifiers: 1978-MG-07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7603302001953125, "perplexity": 8249.674979234162}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398453805.6/warc/CC-MAIN-20151124205413-00078-ip-10-71-132-137.ec2.internal.warc.gz"}
https://belljust.in/analyzing-return-times-ii-concurrent/	# Analyzing Return Times II - Concurrent This time we’ll discuss the concurrent model for aggregrating search results. In this post, we’re going to look at how to: • aggregate the results concurrently • model the algorithm run time as a random variable • find and evaluate the CDF of our model for a couple values This is part 2 in a series of posts that analyzes the return times of various randomized algorithms presented in a talk by Rob Pike. If you have not read the first post, I would encourage you to start there. ## Recap Last time we analyzed the sequential method of gathering our results. We wanted to know what percent of users would recieve their results in less than 1.5 seconds. After finding the PDF of the response time, we discovered that we could only expect half of users to hit our benchmark! The experimental results were even worse due to overhead in appending the results - only 46.0% make it. ## Concurrency and parallelism How can we do better? Well, our algorithm is just waiting for a response most of the time. If we launched all our searches and let them run at the same time, we would only wait as long as the longest search. Running these searches simultaneously is called parallel computing. Furthermore, getting the proper results does not matter when or in what order we get them. This means our algorithm can be designed concurrently. It is worth noting that concurrency and parallelism are not the same thing. These are often confused - so much so that Rob Pike has presented another talk on this very issue. • Parallelism is the simultaneous excecution of two or more processes • Concurrency is the property of an algorithm that allows it to be decomposed into multiple processes whose order of execution does not affect the correctness of the result Because our search is not actually being offloaded to other servers, it is not necessarily parallel (though it may be if you run it on a multi-core system!) fakeSearch is, however, sleeping most of the time. This means it will not block CPU execution and, for all practical purposes, seem to run in parallel with other fakeSearches. Now we get to the algorithm. 1func GoogleConcurrent(query string) (results []Result) { 2 c := make(chan Result) 3 go func() { c <- Web(query) }() 4 go func() { c <- Image(query) }() 5 go func() { c <- Video(query) }() 6 7 for i := 0; i < 3; i++ { 8 result := <-c 9 results = append(results, result) 10 } 11 return 12} The keyword chan denotes a channel in Go. 2 c := make(chan Result) Channels are pipes that allow you to send and recieve values between various threads of execution. Arrows pointing towards the channel, c <- foo, indicates the channel will be given a value. Arrows pointing away from the channel, foo := <-c, indicates a value should be recieved from the channel. The go keyword starts a new goroutine. 3 go func() { c <- Web(query) }() Goroutines are lightweight threads managed by the Go runtime. They are especially useful because it is practical to have hundreds of thousands running concurrently. Here we are using go to start an anonymous function that populates the channel with the search query result. Goroutines and channels are especially useful because they make it easy to aggregrate results without locks, condition variables, or difficult to follow callbacks. Even though this function starts several threads of execution, we can still read it more or less sequentially. ## GoogleConcurrent as a random variable In the sequential model, we had to wait for the first result then start the next search. This time we run all of them at the same time, meaning the total time we have to wait is the time the longest query takes to finish. Let’s model this as a random variable $$Y_{concurrent} = \text{max}(X_1, X_2, X_3)$$ Where $$X_i$$ is the time to complete a fakeSearch, which we modeled as a uniformly distributed random variable in the previous post. ## Cumulative Distribution Function (CDF) With the sequential method, we wanted to see the probability that a user would wait no more than 1.5 seconds. To do this we calculated the integral of the PDF, $$f_Y(y)$$, from $$-\infty$$ to 1.5. This is also known as the Cumulative Distribution Function (CDF), $$F_Y(y)$$, at $$y = 1.5$$ The relation between the probability of our event, the CDF, and the PDF is written like this: $$P(Y \leq y) = F_Y(y) = \int _{-\infty}^y f_Y(t) dt$$ Each term is read like such • the probability Y is less than or equal to y, which is equal to • the CDF of Y at y, which is equal to • the integral of the PDF of Y from negative infinity to y Now let’s find the probability that users wait no more than y seconds for the GoogleConcurrent algorithm. \begin{align} F_Y(y) & = P(Y \leq y) \\\ \\\ & = P(\text{max}(X_1, X_2, X_3) \leq y) \end{align} If y is greater than the largest X, it must also be greater than all X. Making this substitution allows us to decompose the problem further. \begin{align} P(\text{max}(X_1, X_2, X_3) \leq y) & = P(X_1 \leq y \cap X_2 \leq y \cap X_3 \leq y) \\\ \\\ & = P\left(\bigcap _{i=1}^3 X_i \leq y\right) \end{align} The intersection, $$\cap$$, of events means that each event must happen for the whole condition to succeed. Furthermore, each fakeSearch is independent, i.e. the time taken for one search does not affect the time taken for the other search.1 This special property implies the probability of all events happening is equal to the product of the probability of each event. \begin{align} P\left(\bigcap _{i=1}^3 X_i \leq y\right) & = P(X_1 \leq y)P(X_2 \leq y)P(X_3 \leq y) \\\ \\\ & = \prod _{i=1}^3P(X_i \leq y) = F_X(y)^3 \end{align} The rather satisfying result is the CDF of GoogleConcurrent simply equals the CDF of the uniform distribution cubed. $$F_Y(y) = \begin{cases} 0, & x < 0 \\\ x^3, & 0 < x < 1 \\\ 1, & x \geq 1 \\\ \end{cases}$$ Here’s a graph of the result ## How does it compare? With sequential, we got results back in 1.5 seconds or less 50% of the time here we get… $$F_Y(1.5) = 1$$ With GoogleConcurrent we can expect to get 100% of results back in under 1.5 seconds! Of course this makes sense: no one query takes longer than 1 second and we’re running all of them at the same time. But how fast can we get? Let’s evaluate the probability that GoogleConcurrent will finish before a few more time points: \begin{align} F_Y(0.5) &= 0.125 \\\ F_Y(0.8) &= 0.512 \\\ F_Y(0.9) &= 0.729 \\\ \end{align} Reading the second line, we can expect 51.2% of requests to be processed in 0.8 seconds or less Running an experiment with 2000 samples, 49.5% of requests were processed in 0.8 seconds. Once again the experimental results were slightly slower than the theoretical results - presumably due to overhead. In addition to the outstanding speed benefits we get from running the searches in parallel, we also give ourselves some room to expand. In the previous case, adding each additional search would increase the limit of our potential wait times by 1 second. With GoogleConcurrent even though our expected wait time will get closer and closer to 1 second with each additional search, our max wait time will never exceed that 1 second bound!2 The graph above shows us the CDF of Y as the number of different searches, $$n$$, increases. ## What next? Running the search in parallel significantly reduced our expected wait times. Can we do better? Until seeing Rob’s talk, I didn’t know how, but next post we’ll look at how using replicated services will allow us to improve even more! 1. This is another property of fakeSearch unlikely to be seen in the real world. E.g. our internet connection has slowed down, the service could be on the same overloaded server - these scenarios and more could make the services correlated and thereby dependent ↩︎ 2. Of course, in practice, appending the results will eventually take more than 1 second ↩︎	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7967878580093384, "perplexity": 926.6687931280417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572870.85/warc/CC-MAIN-20220817062258-20220817092258-00464.warc.gz"}
https://www.arxiv-vanity.com/papers/1302.5209/	# The Herschel††thanks: Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA PEP/HerMES Luminosity Function – I: Probing the Evolution of PACS selected Galaxies to z≃4 C. Gruppioni, F. Pozzi, G. Rodighiero, I. Delvecchio, S. Berta, L. Pozzetti, G. Zamorani, P. Andreani, A. Cimatti, O. Ilbert, E. Le Floc’h, D. Lutz, B. Magnelli, L. Marchetti, P. Monaco, R. Nordon, S. Oliver, P. Popesso, L. Riguccini, I. Roseboom, D.J. Rosario, M. Sargent, M. Vaccari, B. Altieri, H. Aussel, A. Bongiovanni, J. Cepa, E. Daddi, H. Domínguez-Sánchez, D. Elbaz, N. Förster Schreiber, R. Genzel, A. Iribarrem, M. Magliocchetti, R. Maiolino, A. Poglitsch, A. Pérez García, M. Sanchez-Portal, E. Sturm, L. Tacconi, I. Valtchanov, A. Amblard, V. Arumugam, M. Bethermin, J. Bock, A. Boselli, V. Buat, D. Burgarella, N. Castro-Rodríguez, A. Cava, P. Chanial, D.L. Clements, A. Conley, A. Cooray, C.D. Dowell, E. Dwek, S. Eales, A. Franceschini, J. Glenn, M. Griffin, E. Hatziminaoglou, E. Ibar, K. Isaak, R.J. Ivison, G. Lagache, L. Levenson, N. Lu, S. Madden, B. Maffei, G. Mainetti, H.T. Nguyen, B. O’Halloran, M.J. Page, P. Panuzzo, A. Papageorgiou C.P. Pearson, I. Pérez-Fournon, M. Pohlen, D. Rigopoulou, M. Rowan-Robinson, B. Schulz, D. Scott, N. Seymour, D.L. Shupe, A.J. Smith, J.A. Stevens, M. Symeonidis, M. Trichas, K.E. Tugwell, L. Vigroux, L. Wang, G. Wright, C.K. Xu, M. Zemcov, S. Bardelli, M. Carollo, T. Contini, O. Le Févre, S. Lilly, V. Mainieri, A. Renzini, M. Scodeggio, E. Zucca Accepted 2013 February 18. Received 2013 February 13; in original form 2012 October 23 ###### Abstract We exploit the deep and extended far-infrared data-sets (at 70, 100 and 160 m) of the Herschel GTO PACS Evolutionary Probe (PEP) Survey, in combination with the HERschel Multi-tiered Extragalactic Survey (HerMES) data at 250, 350 and 500 m, to derive the evolution of the rest-frame 35-m, 60-m, 90-m, and total infrared (IR) luminosity functions (LFs) up to 4. We detect very strong luminosity evolution for the total IR LF (L(1) up to 2, and (1) at 24) combined with a density evolution ((1) up to 1 and (1) at 14). In agreement with previous findings, the IR luminosity density () increases steeply to 1, then flattens between 1 and 3 to decrease at 3. Galaxies with different SEDs, masses and sSFRs evolve in very different ways and this large and deep statistical sample is the first one allowing us to separately study the different evolutionary behaviours of the individual IR populations contributing to . Galaxies occupying the well established SFR–stellar mass main sequence (MS) are found to dominate both the total IR LF and at all redshifts, with the contribution from off-MS sources (0.6 dex above MS) being nearly constant (20% of the total ) and showing no significant signs of increase with increasing over the whole 0.82.2 range. Sources with mass in the range 10log(/M)11 are found to dominate the total IR LF, with more massive galaxies prevailing at the bright end of the high- (2) LF. A two-fold evolutionary scheme for IR galaxies is envisaged: on the one hand, a starburst-dominated phase in which the SMBH grows and is obscured by dust , is followed by an AGN-dominated phase, then evolving toward a local elliptical. On the other hand, moderately star-forming galaxies containing a low-luminosity AGN have various properties suggesting they are good candidates for systems in a transition phase preceding the formation of steady spiral galaxies. ###### keywords: cosmology: observations – galaxies: active – galaxies: evolution – galaxies: luminosity function – galaxies: starburst – infrared: galaxies. pagerange: The Herschelthanks: Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA PEP/HerMES Luminosity Function – I: Probing the Evolution of PACS selected Galaxies to z4The Herschelthanks: Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA PEP/HerMES Luminosity Function – I: Probing the Evolution of PACS selected Galaxies to z4pubyear: 2012 ## 1 Introduction Understanding the origin and growth of the galaxies we observe today is one of the main problems of current cosmology. The luminosity function (LF) provides one of the fundamental tools to probe the distribution of galaxies over cosmological time, since it allows us to assess the statistical nature of galaxy formation and evolution. When computed at different redshifts, the LF constitutes the most direct method for exploring the evolution of a galaxy population, describing the relative number of sources of different luminosities counted in representative volumes of the Universe. The LF computed for different samples of galaxies can provide a crucial comparison between the distribution of different galaxy types, i.e. galaxies at different redshifts, in different enviroments or selected at different wavelengths. It has now become clear that we cannot understand galaxy evolution without accounting for the energy absorbed by dust and re-emitted at longer wavelengths (e.g, Genzel & Cesarsky 2000), in the infrared (IR) or sub-millimetre (sub-mm). Dust is responsible for obscuring the ultraviolet (UV) and optical light from galaxies: since star-formation occurs within dusty molecular clouds, far-IR and sub-mm data, where the absorbed radiation is re-emitted, are essential for providing a complete picture of the history of star-formation through cosmic time, which is one of the fundamental instruments we have to reconstruct how galaxies have evolved since their formation epoch. For these reasons, extragalactic surveys in the rest-frame IR represent a key tool for understanding galaxy formation and evolution. Surveys of dust emission performed with the former satellites exploring the Universe in the mid- and far-IR domain, i.e. the Infrared Astronomical Satellite (IRAS; Neugebauer 1984) and the Infrared Space Observatory (ISO; Kessler et al. 1996), allowed the first studies of the IR-galaxy LF at 0.3 (Saunders et al. 1990) and 1 (Pozzi et al. 2004), respectively. With Spitzer 24-m data, it was possible to study the evolution of the mid-IR LF up to 2 (e.g. Le Floc’h et al. 2005, Caputi et al. 2007, Rodighiero et al. 2010a), while, even with the deepest Spitzer Space Telescope (Werner et al. 2004) 70-m data, only 1–1.2 could be reached in the far-IR (Magnelli et al. 2009; Patel et al. 2012) ) – though Magnelli et al. (2011) reached 2 through stacking. Since the rest-frame IR spectral energy distributions (SEDs) of star-forming galaxies and AGN peak at 60–200 m, to measure their bolometric luminosity and evolution with we need to observe in the far-IR/sub-mm regime. However, the detection of large numbers of high- sources at the peak of their IR SED was not achievable before the Herschel Space Observatory (Pilbratt et al. 2010), due to source confusion and/or low detector sensitivity, and our knowledge of the far-IR luminosity function in the distant Universe is still affected by substantial uncertainties. Ground-based and balloon-borne observations in the mm/sub-mm range, probing the evolution of the most distant (2) and luminous dusty galaxies, have so far been limited to the identification of sources at the very bright end of the luminosity function (e.g., Chapman et al. 2005). All of these works detected strong evolution in both luminosity and/or density, indicating that IR galaxies were more luminous and/or more numerous in the past. Strong observational evidence of high rates of evolution for IR galaxies has been obtained also through the detection of a large amount of energy contained in the Cosmic Infrared Background (CIRB; Hauser & Dwek 2001), and the source counts from several deep cosmological surveys (from 15 m to 850 m) largely exceeding the no-evolution expectations (e.g. Smail et al. 1997; Elbaz et al. 1999; Papovich et al. 2004; Bethermin et al. 2010; Marsden et al. 2011). Both the CIRB and the source counts require a strong increase in the IR energy density between the present time and 1–2. At higher redshifts the total emissivity of IR galaxies is poorly constrained, due to the scarcity of Spitzer galaxies at 2, the large spectral extrapolations to derive the total IR luminosity from the mid-IR (see e.g. Elbaz et al. 2010, Nordon et al. 2010 and Nordon et al. 2012 for descriptions of the failure, at least at 1.5, of previous total IR luminosity extrapolations from the mid-IR, although we must note that this failure mainly affects luminosity-dependent methods like, e.g., that of Chary & Elbaz 2001) and the incomplete information on the -distribution of sub-mm sources (Chapman et al. 2005). Herschel, with its 3.5-m mirror, is the first telescope which allows us to detect the far-IR population to high redshifts (4–5) and to derive its rate of evolution through a detailed LF analysis. The new extragalactic surveys provided by Herschel in the far-IR/sub-mm domain, like the wide and shallow Herschel-ATLAS (Eales et al. 2010; Dunne et al. 2011), the complementary Herschel Multi-tiered Extragalactic Survey (HerMES; Oliver et al. 2012) and PACS Evolutionary Probe (PEP; Lutz et al. 2011) covering the most popular cosmological fields, and the deep, pencil beam, Herschel-GOODS project (Elbaz et al. 2011), will be crucial to assess galaxy and AGN evolution in the IR at 2. They will give us the opportunity to study in detail the population of IR galaxies and their evolution with cosmic time since the Universe was about a billion years old. In particular, the Photodetector Array Camera & Spectrometer (PACS; Poglitsch et al. 2010), with its high sensitivity and resolution at 70-m, 100-m and 160-m, is the best suited instrument to detect faint IR sources by overcoming the source confusion and blending problems that affected the previous far-IR missions. This is the first of two papers aiming at deriving the far- and total IR LFs from the Herschel PACSSpectral and Photometric Imaging Receiver (SPIRE; Griffin et al. 2010) data obtained within the PEP and HerMES extragalactic survey projects. In the present paper, we derive the rest-frame 35-m, 60-m, 90-m and total IR (8–1000 m) LFs from a sample selected at PACS 70, 100 and 160 m wavelengths in the GOODS (GOODS-S and GOODS-N), Extended Chandra Deep Field South (ECDFS) and COSMOS areas. We use the full 70–500 m PACSSPIRE data to determine and SED properties of the PACS selected sources. In a related paper, Vaccari et al. (in prep.) derive rest-frame 100-, 160- and 250-m and total IR LFs for a SPIRE selected sample. In addition, a third work aimed at studying the total IR LF based on the 24-m selected sample, using all the PEPHerMES data in the COSMOS field, is ongoing (Le Floc’h et al., in preparation). PEP is one of the major Herschel Guaranteed Time extragalactic key-projects, designed specifically to determine the cosmic evolution of dusty star-formation and of the IR luminosity function. It is structured as a “wedding cake”, based on four different layers covering different areas to different depths at 100 and 160 m (in the GOODS-S field also at 70 m), from the large and shallow COSMOS field to the deep, pencil beam GOODS-S field. PEP includes the most popular and widely studied extragalactic fields with extensive multi-wavelength coverage available, in particular deep optical, near-IR and Spitzer imaging and spectroscopic and photometric redshifts: COSMOS; Lockman Hole; Extended Groth Streep (EGS); ECDFS; GOODS-N; and GOODS-S (see Berta et al. 2010, Berta et al. 2011 and Lutz et al. 2011 for a detailed description of the fields and observations). Coordinated observations of the PEP fields at 250, 350 and 500 m with SPIRE have been obtained by the HerMES Survey (Oliver et al. 2012). HerMES, analogously to PEP but extending to a much wider area, is a legacy programme designed to map a set of nested fields (380 deg in total) of different sizes and depths, using SPIRE (at 250, 350 and 500 m), and PACS (at 100 and 160 m, shallower than PEP), with the widest component of 270 deg with SPIRE alone. In the fields covered by PEP, the two surveys are closely coordinated to provide an optimized sampling over wavelength. In Gruppioni et al. (2010) we started to determine the evolution with redshift of the galaxy and AGN LF in the far-IR domain by exploiting the PEP data obtained in GOODS-N by the PEP Science Demonstration Programme (SDP). Here we extend the analysis to the wider and shallower fields – COSMOS and ECDFS – and to the deepest field – GOODS-S – observed by PEP, and we also take advantage of the HerMES sub-mm data in the same fields to derive improved SED classifications and accurate total IR luminosities for our sources. This allows us to have statistically significant samples of IR galaxies at different redshifts and over a broad range of luminosities, to make a detailed study of the LF at several intervals, all the way from 0 to 4. The measure of the total IR luminosity obtained by integrating the SEDs, well constrained over the entire mid- and far-IR domain (and also in the sub-mm thanks to the available SPIRE data), allows us to derive the total IR LF and its evolution directly from far-IR data for unbiased samples selected at wavelengths close to the peak of dust emission. Moreover, the availability of deep multi-wavelength catalogues in the PEP fields is crucial for analysing the SEDs, obtaining k-corrections and total IR luminosities, and classifying the PEP sources into different IR populations, in order to separately study their LFs and evolutionary behaviour. This is the first study ever based on such a statistically wide and deep far-IR sample, to be able to provide LFs for different IR populations of galaxies and AGN. Here the evolution of the far- and total IR LFs (and luminosity density, hereafter ) are derived up to unprecedented high redshifts (4) both globally (e.g. for all the populations together) and separately, for each SED class. Despite the abundance of information available in the literature about the stellar mass function (MF; Fontana et al. 2004; Pozzetti et al. 2010; Ilbert et al. 2010; Dominguez-Sanchez et al. 2011), very little is known about the corresponding total IR LFs and star-formation rate (SFR) densities at different masses (an attempt based on Spitzer data was made by Pérez-González et al. 2005). From stellar MF studies one finds a clear increase with of the relative fraction of massive (log(/M11) star-forming objects, starting to contribute significantly to the massive-end of the MFs at 1 (Fontana et al. 2004; Ilbert et al. 2010). Their evolution and contribution to the total SFR history is however still uncertain, since only few studies have tried to reconstruct the evolution of the SF history of massive objects from optical/near-IR or mid-IR surveys (Juneau et al. 2005; Pérez-González et al. 2005; Santini et al. 2009; Fontanot et al. 2012) but none from far-IR selected surveys (providing a more direct indicator of the galaxy SF activity). In this work, we have derived the IR luminosity function and density in three different mass ranges (from log(/M)8.5 to log(/M)12), extending previous studies (limited to 1.8–2 for the most massive galaxies) to 4. Finally, our PEP data-sets have allowed us to quantify the relative contribution of the two main modes of star formation (a relatively steady one in disk-like galaxies, defining a tight SFR-stellar mass sequence, and a starburst mode in outliers) to the total IR LF and in three redshift intervals (0.81.25, 1.251.8 and 1.82.2) and to test the SED-classes belonging to each mode. The paper is structured as follows. The PEP Survey with the far-IR and multi-wavelength data, together with the SED characterisation and redshift distribution of the PEP sources, are described in Sect. 2. The LFs (rest-frame 35-m, 60-m, 90-m and total IR), their evolution (derived for different SED-classes, mass and specific star-formation rate intervals) are discussed in Sect. 3. In Sect. 4 we present the number and IR luminosity densities of the different galaxy types, while in Sect. 5 we discuss our results. In Sect. 6 we present our conclusions. Throughout this paper, we use a Chabrier initial mass function (IMF) and we assume a CDM cosmology with = 71 km s Mpc, = 0.27, and . ## 2 The Data The PEP fields where we computed the LFs are: COSMOS, 2 deg observed down to 3 depths of 5 mJy and 10.2 mJy at 100 m and 160 m, respectively; ECDFS, 700 arcmin down to 3 depths of 4.5 mJy and 8.5 mJy at 100 m and 160 m, respectively; GOODS-N, 300 arcmin to 3 and 5.7 mJy at 100 m and 160 m, respectively; and GOODS-S, 300 arcmin to 1.2 mJy, 1.2 mJy and 2.4 mJy at 70 m, 100 m and 160 m, respectively. Our reference samples are the blind catalogues at 70 (in GOODS-S only), 100 and 160 m to the level, which contain 373 (all in GOODS-S), 7176 (GOODS-S: 717, GOODS-N: 291, ECDFS: 813, COSMOS: 5355) and 7376 (GOODS-S: 867, GOODS-N: 316, ECDFS: 688, COSMOS: 5105) sources at 70, 100 and 160 m, respectively. We refer to Berta et al. (2010) and Berta et al. (2011) for a detailed description of the data catalogues and source counts. ### 2.1 Multi-wavelength Identification The PEP fields benefit from an extensive multi-wavelength coverage. We have therefore associated our sources to the ancillary catalogues by means of a multi-band likelihood ratio technique (Sutherland & Saunders 1992; Ciliegi et al. 2001), starting from the longest available wavelength (160 m, PACS) and progressively matching 100 m (PACS), 70 m (PACS, GOODS-S only) and 24 m (Spitzer/MIPS). In the GOODS-S field, we have associated to our PEP sources the 24-m catalogue by Magnelli et al. (2009), that we have matched with the opticalnear-IRIRAC MUSIC catalogue of Grazian et al. (2006), revised by Santini et al. (2009), which includes spectroscopic and photometric redshifts. To maximise the fraction of identifications, we limited our study to the area covered by the MUSIC catalogue (196 arcmin), obtaining 233, 468 and 492 sources at 70, 100 and 160 m, respectively, with flux density greater than the flux limits reported above (all with either spectroscopic or photometric redshifts). In the GOODS-N field, as described in Berta et al. (2010), Berta et al. (2011) and Gruppioni et al. (2010), a PSF-matched multi-wavelength catalogue111publicly available at http://www.mpe.mpg.de/ir/Research/PEP/publicdatareleases.php was created, including photometry from the far-UV (GALEX) to the mid-IR (Spitzer). As in GOODS-S, to maximise the identifications, we limited our study in GOODS-N to the area covered by the ACS (150 arcmin), obtaining 176 and 186 sources with flux density greater than the flux limit at 100 and 160 m, respectively (all with redshifts). We have matched our sources in the ECDFS with the multi-wavelength Survey by Yale-Chile (MUSYC) by Cardamone et al. (2010), obtaining 687 sources at 100 m and 625 sources at 160 m (578 and 547 with redshifts, 45% spectroscopic). Finally, in COSMOS, we have matched our catalogue with the deep 24-m sample of Le Floc’h et al. (2009) and with the IRAC-based catalogue of Ilbert et al. (2010), including optical and near-IR photometry and photometric redshifts. After the removal of PEP sources within flagged areas of the optical and/or IRAC COSMOS catalogues, we ended up with two catalogues consisting of 4110 and 4118 sources, with flux densities 5.0 and 10.2 mJy at 100 and 160 m respectively (3817 and 3849 with either spectroscopic or photometric redshifts). Throughout this paper and specifically for the SED fits described in Section 2.2, we adopt these spectroscopic or rest-frame UV to near-IR photometric redshifts for the various fields. The HerMES extragalactic survey (Oliver et al. 2012) performed coordinated observations with SPIRE at 250, 350 and 500 m in the same fields covered by PEP. In particular, in HerMES a prior source extraction was performed using the method presented in Roseboom et al. (2011), based on MIPS-24 m positions. The 24-m sources used as priors for SPIRE source extraction are the same as those associated with our PEP sources through the likelihood ratio technique. We have therefore associated the HerMES sources with the PEP sources by means of the 24-m sources matched to both samples. For most of our PEP sources (87 per cent) we found a 3 SPIRE counterpart in the HerMES catalogues. ### 2.2 Galaxy Classification We made use of all the available multi-wavelength data to derive the SEDs of our PEP sources, which we interpreted and classified by performing a fit (using the Le Phare code222available at http://www.cfht.hawaii.edu/arnouts/LEPHARE/lephare.html ; Arnouts et al. 2002 and Ilbert et al. 2006) with the semi-empirical template library of Polletta et al. (2007), representative of different classes of IR galaxies and AGN. To this library we added some templates modified in their far-IR part to better reproduce the observed Herschel data (see Gruppioni et al. 2010), and three starburst templates from Rieke et al. (2009). If required to improve the fit, different extinction values ( from 0.0 to 0.5) have been applied to the templates, by letting the code free to choose the most suitable extinction curve. The considered set of templates included SEDs of elliptical galaxies of different ages, lenticular, spirals (from Sa to Sdm), starburst galaxies (SB), type 1 QSOs, type 2 QSOs, Seyferts, LINERs and composite ULIRGs (containing both starburst and obscured AGN component), in the wavelength range between 0.1 and 1000 m. The latter templates, are empirical ones created to reproduce the SEDs of the heavily obscured AGN. Two of these SEDs (the broad absorption-line QSO Markarian 231 (Berta, 2005) and the Seyfert 2 galaxy IRAS 192547245 South (Berta et al., 2003)) are similar in shape, containing a powerful starburst component, mainly responsible for their far-IR emission, and an AGN component that contributes to – and dominates – the mid-IR (Farrah et al. 2003), reproducing the SEDs of “obscured” AGN regardless of their optical spectra (i.e. broad or narrow lines in the optical; Gruppioni et al. 2008). Hereafter, we will refer to this class of templates and to the sources reproduced by them as to type 2 AGN (AGN2). Three other empirical templates, reproducing the observed SEDs of nearby ULIRGs containing an obscured AGN (i.e. IRAS 20551-4250; IRAS 22491-1808; NGC 6240) have been associated to the Seyfert 1.8/2, LINER ones, since they all contain an AGN, but this AGN does not dominate the observed energetic output at any wavelength (from UV to far-IR/sub-mm), showing up just in the range where the host galaxy SED has a minimum (i.e. the mid-IR). The AGN in these objects is either obscured or of low luminosity. We refer to this class as to star-forming galaxies containing an AGN (SF-AGN), since their IR luminosity is largely dominated by star-formation. In our analysis, we make the basic assumption that the SED shapes seen at low redshifts are also able to represent the higher redshift objects. In any case, to further increase the range of SEDs in the fit, we have applied additional extinction with different extinction curves to our templates. All SED fits adopt fixed spectroscopic or photometric redshifts described in Section 2.1. The template library used to fit our data contains a finite number of SEDs (38), representative of given classes of local infrared objects, which do not vary with continuity from one class to another (there are large gaps in the parameter space). Therefore, the quality of the fit depends not only on the photometric errors, but also on the template SED uncertainties. For this reason, in our fitting procedure, in addition to the photometric errors on data, we need to take into account also the uncertainties due to the template SEDs discretisation and additional extinction. To do this, we have proceeded as described in detail by Gruppioni et al. (2008) and summarised as follows. First, we have run Le Phare on our PEP SEDs considering the nominal errors from catalogues, computing the distributions of the values in each of the considered photometric band (where and are the flux density and the relative error of the source, and the flux density of the template in the considered band), iteratively increasing the photometric errors until we have obtained a Gaussian distribution with 1. This corresponds to reduced distributions peaked around 1 (as expected in the case of good fit). With the new photometric uncertainties (on average, significantly increased mainly in the optical/near-IR and SPIRE bands), we have run Le Phare on our sources for the second time, obtaining what we have taken as the final SED-fitting results. The majority of our PEP sources are reproduced by templates of normal spiral galaxies (spiral), SB galaxies (starburst), and Seyfert2/1.8/LINERS/ULIRGsAGN (SF-AGN), although different classes prevail at different redshifts and luminosities. The spiral SEDs show no clear signs of enhanced SF or nuclear activity (see Fig. 1), the far-IR bump being characterised by relatively cold dust (20 K). On the other hand, SB templates are characterised by warmer (40–45 K), more pronounced far-IR bumps and significant UV extinction, indicative of intense star-formation activity. Templates of star-forming galaxies containing either a low-luminosity or obscured AGN (SF-AGN) are characterised by a “flattening” in the 3–10 m spectrum (suggesting detection of an AGN in the wavelength range where the host galaxy SED has a minimum) and a far-IR bump dominated by star-formation, which is intermediate (in terms of both energy and ) between spirals and SBs. Although they can be considered as star-forming galaxies at the wavelengths relevant to this work, we prefer to refer to them as SF-AGN throughout the paper, to keep in mind that they probably contain an AGN, whose presence, though not dominant in the far-IR, might be very important for analysis in other bands (e.g., in the X-rays or the mid-IR). We note that the well-studied high-z (2.3) SED of the strongly lensed sub-mm galaxy SMM J2135-0102, known as “the Cosmic Eyelash” (Ivison et al. 2010; Swinbank et al. 2010), best-fitted with our procedure by an extincted (E(B-V)0.2) IRAS 22491-1808 template (though rather poorly in the near-IR), does not represent the bulk of our population at high- (1.5), whose SEDs are indeed well reproduced by our library of templates. In fact, the considered template set provides very good fits to the SEDs of our PEP sources. In Fig. 1 we show the rest-frame SEDs (black dots) of the PEP sources belonging to the different “broad” SED classes (spiral, starburst, SF-AGN, AGN1 and AGN2), compared to the template SEDs of those classes normalised to the -band flux density. In Table 1 we report the fraction of sources belonging to each SED class: we find that in all the fields 41(38) per cent of the 100(160)-m sources are reproduced by a spiral template SED, 7(7) per cent with a starburst template SED, 45(48) per cent with a SF-AGN template SED, 2(3) per cent with an AGN2 SED and 5(4) per cent with an AGN1 SED. We note that the fraction of SF-AGN derived in this work is in agreement with results from mid-IR spectroscopy (with Spitzer-IRS) of local star-forming galaxies from the SINGS sample by Smith et al. (2007), who found that 50 per cent of local galaxies (though of lower luminosities than ours) do harbour low-luminosity AGN (of LINER or Seyfert types). Recently, Sajina et al. (2012) found an even higher fraction (70 per cent) of objects hosting an AGN in the mid-IR (Spitzer 24-m) selected samples (23 per cent AGN-dominated and 47 per cent showing both AGN and starburst activity). However, since the far-IR SED of the SF-AGN is dominated by star-formation and at these wavelengths resembles either starburst or spiral galaxy templates, we have also divided the SF-AGN class into SF-AGN(SB) and SF-AGN(Spiral) sub-classes, based of their far-IR/near-IR colours (e.g. /) and SED resemblance (apart from the rest-frame mid-IR flattening, which is detected in all of the SF-AGN SEDs). Specifically, galaxies best-fitted by the Seyfert2/1.8 templates (either the original ones from Polletta et al. 2007 or those modified by Gruppioni et al. 2010) have been classified as SF-AGN(Spiral), while galaxies best-fitted by the NGC 6240, IRAS 20551-4250 or IRAS 22491-1808 templates have been classified as SF-AGN(SB). The number of sources belonging to the former and the latter sub-classes are also reported in Table 1 as additional information. ### 2.3 Redshift Distribution A large number of spectroscopic redshifts have been measured in the GOODS, ECDFS and COSMOS regions. In the GOODS-S and ECDFS area a collection of more than 5000 spectroscopic redshifts are available (Cristiani et al. 2000; Croom et al. 2001; Bunker et al. 2003; Dickinson et al. 2004; Stanway et al. 2004; Strolger et al. 2004; Szokoly et al. 2004; van der Wel et al. 2004; Doherty et al. 2005; Le Fèvre et al. 2005; Mignoli et al. 2005; Vanzella et al. 2008; Popesso et al. 2009; Santini et al. 2009; Balestra et al. 2010; Cooper et al. 2012). In the GOODS-N area more than 2000 spectroscopic redshifts come from various observations (Cohen et al. 2000; Wirth et al. 2004; Cowie et al. 2004; Barger et al. 2008). Finally, in COSMOS we could use a collection of 3000 spectroscopic redshifts from either the public zCOSMOS bright database or the non-public zCOSMOS deep database (Lilly, S.J. et al. 2007; Lilly et al. 2009). For the PEP sources without spectroscopic redshift available, we have adopted the photometric redshifts derived from multi-wavelength (UV to near-IR) photometry by different authors in the different fields, as mentioned in Section 2.1. In the GOODS-S field the MUSIC photometric redshift catalogue (Grazian et al. 2006; Santini et al. 2009) provided photo-s for most of our PEP sources without spectroscopic data, while in the GOODS-N field, photo-s were obtained by Berta et al. (2010) for almost all the PEP sources within the ACS area. The Cardamone et al. (2010) and Ilbert et al. (2009) catalogues provided photometric redshifts for a large fraction of the PEP sources in the ECDFS and COSMOS areas, respectively. When considering both the spectroscopic and photometric redshifts, in our PEP fields the redshift incompleteness is very low. In particular, in the GOODS-S field we have either a spec- or a photo- for 100 per cent of the PEP sample within the MUSIC areas (80 per cent spectroscopic, though most of them lie at 2.5; see Berta et al. 2011). In the GOODS-N field we have a redshift completeness of 100 per cent of sources (70 per cent spectroscopic) within the ACS area. In the ECDFS and COSMOS fields we have a redshift completeness of 88 per cent and 93 per cent respectively (45 per cent and 40 per cent spectroscopic). The uncertainty in the photometric redshifts has been evaluated by means of a comparison with the available spec-s by the different authors providing photo- catalogues in the PEP fields. In particular, Berta et al. (2011) have compared the photometric and the available spectroscopic redshifts in GOODS-S, GOODS-N and COSMOS, finding a fraction of outliers, defined as objects having /(1)0.2, of 2 per cent for sources with a PACS detection. Most of these outliers are sources with few photometric points available, or SEDs not well reproduced by the available templates. The median absolute deviation of the /(1) distribution in the three fields analised by Berta et al. (2011) is 0.04 for the whole catalogue, and 0.038 for PACS-detected objects. In GOODS-S, Grazian et al. (2006) found an excellent agreement between photometric and spectroscopic redshifts over the fully accessible redshift range 06 (0.045), with a very limited number of catastrophic errors. In COSMOS, Ilbert et al. (2010) estimated the photometric redshift uncertainties of their 3.6-m catalogue matched with the COSMOS photo- multi-wavelength catalogue of Ilbert et al. (2009), finding 0.008 (and 1 per cent of catastrophic failures) at 22.5, 0.011 at 22.524 and 0.053 at 2425. In the ECDFS, by comparing non-X-ray sources with high-quality spectroscopic redshifts, Cardamone et al. 2010 found 0.008 to 1.2 0.027 at 1.23.7 and 0.016 at 3.7. Note that we have checked all the 2.5 photometric redshifts through Le Phare, assigning the Le Phare derived value in case of significant disagreement with that from the catalogue (though most resulted in very good agreement). The fractions of spectroscopic redshifts in the 2.53.0 interval amount to just 6% and 25% in COSMOS and GOODSS respectively, dropping to 4% and 6% at 3.04.2. We note that from our comparison between photo- and spec- (when available) we find a general good agreement in all fields. Photometric redshift errors may, in principle, affect the shape of the luminosity function at the bright end: by scattering objects to higher redshifts they make the steep fall-off at high luminosities appear shallower (e.g. Drory et al. 2003). To study the impact of redshift uncertainties on the inferred infrared LF, we have performed Monte Carlo simulations, as discussed in detail in Section 3.3. It is indeed very difficult to estimate the effect of catastrophic failures at 2.5, where mainly photometric redshifts are available and very little reliable spectroscopic data can be used to validate them. Moreover, for the limited high- samples with spectroscopic information, different results are found in the different fields: i.e., in GOODS-S Berta et al. (2011) found about 25 per cent of catastrophic failures for PACS detected sources above 2, with the tendency to have a higher than real photometric redshift, while in COSMOS the catastrophic failures (20 per cent) found by Ilbert et al. (2009) for MIPS selected sources at 23 were mostly for photo-’s smaller than spectroscopic ones. In addition to that, sometimes high- spectroscopic redshifts can be even more uncertain than photometric ones and great care must be taken when selecting spec-s for comparison (i.e. we need to choose those with high quality flags). For all these reasons, we limited our analysis of photo- uncertainties to the Monte Carlo simulations described in Section 3.3, without trying to derive uncertainties also due to catastrophic failures. In Section 3.2 we also note that the different (far-IR) photo-z approach of Lapi et al. (2011) produces consistent LF results in the common part of parameter space. The median redshift of the 70-m sample in GOODS-S is (70)0.67 (the mean is 0.86), while those of the 100- and 160-m samples are different in each of the fields, given the different flux density depths reached by PEP in each area. In Table 2 we report the median and the mean redshifts found for the different fields (and for the combined sample) at the different selection wavelengths. As expected, GOODS-S reaches the highest redshifts, while the surveys in the COSMOS and ECDFS fields are shallower and sample lower redshifts. On average, the 160-m selection favours higher redshifts than the 100-m one (see also Berta et al. 2011). In Fig. 2 we show the redshift distribution of the PEP sources selected at 100 m and 160 m in the four different fields. The black solid histogram is the total redshift distribution in the field (one for each row of the plot), while the filled histograms in different colours represent the redshift distributions of the different populations (green, spiral; cyan, starburst; red, SF-AGN; magenta, AGN2; blue, AGN1). The line-filled dashed histograms shown in the spiral and starburst panels represent the redshift distributions of the SF-AGN(Spiral) and SF-AGN(SB) sub-classes, respectively. In addition to the principal redshift peak, in GOODS-S a secondary peak centred at 2 is clearly visible at both 100 and 160 m. A similar result has been shown and discussed also by Berta et al. (2011), while an extensive analysis of PACS GOODS-S large-scale structure at 2–3 and of a 2.2 filamentary overdensity have been presented by Magliocchetti et al. (2011). ## 3 The Luminosity Function The sizes and depths of the PEP samples are such as to allow a direct and accurate determination of the far-IR LF in several redshift bins, from 0 up to 4. PEPHerMES is the unique Herschel survey to allow such analysis over such a wide redshift and luminosity range, sampling both the faint and bright ends of the far- and total IR LFs with sufficient statistics. Because of the redshift range covered by PEP, we would need to make significant extrapolations in wavelength when computing the rest-frame LFs at any chosen wavelengths. In order to apply the smallest extrapolations for the majority of our sources, we choose to derive the far-IR LFs at the rest-frame wavelengths corresponding to the median redshift of each sample. Given the median redshift of the 70-m sample in GOODS-S (0.67, see Table 2), we use that sample to derive the rest-frame luminosity function at 35 m. With the 100- and 160-m PEP samples (whose median redshifts are 0.64 and 0.73 respectively), we derived the rest-frame LFs at 60 and 90 m. Note that, given the excellent multi-wavelength coverage available for most of our sources (thanks also to the HerMES data available in all the PEP fields and providing reliable counterparts for most of our PEP sources), their SEDs are very well determined from the UV to the sub-mm. The extrapolations are therefore well constrained by accurately defined SEDs, even at high redshifts (i.e. at 3.5 the rest-frame 90-m luminosity corresponds to 400 m, which is still in the range covered by HerMES). ### 3.1 Method The LFs are derived using the method (Schmidt 1968). This method is non-parametric and does not require any assumptions on the LF shape, but derives the LF directly from the data. We have first derived the LFs in each field separately, in order to check for consistency and to test the role of cosmic variance. Successively, we have made use of the whole data-sets to derive the monochromatic and total IR LFs, by means of the Avni & Bahcall (1980) method for coherent analysis of independent data-sets. We have divided the samples into different redshift bins, over the range 04, selected to be almost equally populated, at least up to 2.5. In each redshift bin we have computed the comoving volume available to each source belonging to that bin, defined as , where is the minimum between the maximum redshift at which a source would still be included in the sample given the limiting flux of the survey (different for each field) and the upper boundary of the considered redshift bin, while is just the lower boundary of the considered redshift bin. When combining the four samples, we have constructed a complete sample over the whole GOODS-SGOODS-NECDFS(GOODS-S)COSMOS region, including all the observed objects (see details in Section 3.2). The depth of the sample is not constant throughout the region, but an object with a given flux density (included in the list of observed objects irrespective of the identity of its parent sample) can a priori be found in one (or more) region if its redshift is of that region (e.g. sources detected in the COSMOS area are detectable over the whole joint area, while the fainter sources detected in GOODS-S are detectable in GOODS-S only). The maximum volume of space which is available to such an object to be included in the joint sample is then defined by Vzmax,i = ΩGS4πVGSzmax+ΩGN4πVGNzmax+ΩE4πVEzmax+ +ΩC4πVCzmax (if zmax,i≤zCmax) = ΩGS4πVGSzmax+ΩGN4πVGNzmax+ΩE4πVEzmax (if zCmax where V (with =, , , corresponding to GOODS-S, GOODS-N, ECDFS and COSMOS, respectively) is the comoving volume available to each source in that field, in a given redshift bin, while is the solid angle subtended by that field sample on the sky. For each luminosity and redshift bin, the LF is given by: where is the comoving volume over which the - galaxy could be observed, is the size of the luminosity bin, and is the completeness correction factor of the - galaxy. These completeness correction factors are a combination of the completeness corrections given by Berta et al. (2010) and Berta et al. (2011), derived as described in Lutz et al. (2011), to be applied to each source as function of its flux density, together with a correction for redshift incompleteness (for the ECDFS and COSMOS only, see Section 2.3). Since, as mentioned in 2.3, the redshift incompleteness in the COSMOS and ECDFS areas is independent on PACS flux density, in these fields we have applied the corrections regardless of the source luminosity and redshift (i.e. by multiplying by 1.07 and 1.14 in COSMOS and ECDFS, respectively). However, the redshift incompleteness does not affect our conclusions, since 95 per cent of all our sources do have a redshift. Uncertainties in the infrared LF values depend on photometric redshift uncertainties. To quantify the effects of the uncertainties in photometric redshifts on our luminosity functions, we performed a set of Monte Carlo simulations, as described in Section 3.3. ### 3.2 The Rest-Frame 35-, 60- and 90-μm Luminosity Function By following the method described above, we have derived the 35-m, 60-m and 90-m rest-frame LFs from the 70-m (in GOODS-S only), 100-m and 160-m samples, respectively. In order to check the consistency between the catalogues and the effects of cosmic variance, we have first derived the monochromatic LFs in each field separately. Note that, since the 70-m data are available in the GOODS-S field only, to have a better sampling of the LF especially at the bright-end, we have also computed the rest-frame 35-m LF from the 100-m samples in the four fields and compared them with that obtained from the 70-m sample (see Fig 3; Table 3). The agreement between the two derivations is very good, implying correct extrapolations in wavelength due to the good and complete SED coverage. We have divided the samples into seven redshift bins: 0.00.4; 0.40.8; 0.81.2; 1.21.8; 1.82.5; 2.53.5; and 3.54.5. The results of the computation of our 35-m (reported in Table 3), 60-m and 90-m LFs are shown in Figs. 3, 4 and 5, respectively. The LFs in the four different fields appear to be consistent with each other within the error bars (1) in most of the common luminosity bins. The COSMOS and GOODS-S Surveys are complementary, with the faint end of the LFs being mostly determined by data in GOODS-S, and the bright end by COSMOS data. After having checked the field-to-field consistency, we have combined the 100- and 160-m samples in all fields, obtaining the global rest-frame 60- and 90-m LFs (reported in Tables 4 and 5, respectively). The data from each field in each -bin have been plotted (and considered in the combination) only in the luminosity bins where we expect our sample to be complete, given that at fainter luminosities not all galaxy types are observable (depending on their SEDs; Ilbert et al. 2004). For comparison, we overplot the LFs at 35 m from Magnelli et al. (2009) and Magnelli et al. (2011), the local LFs at 60 m from Saunders et al. (1990) and those at 90 m from Serjeant et al. (2004) and Sedgwick et al. (2011) and at 100 m from Lapi et al. (2011), respectively. The comparison between the 35-m LF, derived from the 70-m PEP sample in GOODS-S, and the results of Magnelli et al. (2009) and Magnelli et al. (2011), based on a 24-m prior extraction and stacking analysis on Spitzer maps, shows very good agreement, both with the data and with the double power-law fit. The 1.82.5 PEP LF is consistent within 1 with the Magnelli et al. (2011) data points, though the power-law fit at bright (10 L) seems to be slightly lower than our data. At 2.5 no comparison data from Spitzer are available, while our LF derivation can provide hints of evolution at the bright end of the LF. In the common redshift intervals (between 1 and 3.5), our 90-m LF is in very good agreement with the 100-m Lapi et al. (2011) derivation from the H-ATLAS survey (although their redshift bins are somewhat different than ours: 1.21.6; 1.62.0; 2.02.4; and 2.44.0) and with the previous PEP-SDP derivation (Gruppioni et al. 2010). The consistency between our 90-m LFs and the Lapi et al. (2011) ones (derived from a different sample, using a different template SED to fit the data and a rest-frame far-IR based method to derive photometric redshifts) gives us confidence that, at least up to 3.5, our computation is not significantly affected by incompleteness or by photo- uncertainties. ### 3.3 The Total Infrared Luminosity Function We integrate the best-fit SED of each source over 81000 m to derive the total IR luminosities ([8–1000 m]) in 11 redshift bins (0.0–0.3; 0.3–0.45; 0.45–0.6; 0.6–0.8; 0.8–1.0; 1.0–1.2; 1.2–1.7; 1.7–2.0; 2.0–2.5; 2.5–3.0; and 3.0–4.2), selected to be almost equally populated, at least up to 2.5. Our approach is similar to that of other studies based on mid-IR selected galaxy samples (e.g. Le Floc’h et al. 2005; Rodighiero et al. 2010a; Magnelli et al. 2011), but this is the first time that the SEDs have been accurately constrained by sufficiently deep data in the far-IR/sub-mm domain and not simply extrapolated from the mid-IR to the longer wavelengths or from average flux density ratios. As mentioned in Section 2.3, we have studied the impact of redshift uncertainties on the total IR LF by performing Monte Carlo simulations. As test cases, we used the COSMOS and GOODS-S samples (which are basically defining the bright and faint ends of the LF in an almost complementary way), and we checked the effect on the total IR luminosity function. We iterated the computation of the total IR LF by each time varying the photometric redshift of each source (assigning a randomly selected value, according to a Gaussian distribution, within the 68 per cent confidence interval). Each time, we then recomputed the monochromatic and total IR luminosities, as well as the value, but we did not perform the SED-fitting again, keeping the previously found best-fit template for each object (the effect on the k-correction is not relevant in the far-IR wavelength range). The results of this Monte Carlo simulation are reported in Fig. 6, where we show the total IR LFs derived in each of the PEP fields independently: the red and blue filled circles represent the estimates of the GOODS-S and COSMOS LFs, with their range of values derived with 20 iterations by allowing a change in photo- represented by the pink and sky-blue shaded areas, respectively. The comparison shows that the effect of the uncertainty of the photometric redshifts on the error bars is slightly larger than the simple Poissonian value (1/), and affects mainly the lower and the higher redshift bins (especially at low and high luminosities). Using these Monte Carlo simulations, we find no evident systematic offsets caused by the photometric redshift uncertainties (see Fig. 6). This is due to the very accurate photometric redshifts available in these fields. For the total uncertainty in each luminosity bin in GOODS-S and COSMOS, we have therefore assumed the dispersion given by the Monte Carlo simulations (as shown in Fig. 7). We note that at the higher (2.5), where we must rely on a majority of photometric redshifts, the true uncertainties (taking into account also catastrophic failures or incompleteness effects) might be larger than derived with simulations. The unavailability of a “true” comparison sample (i.e. a large comparison sample with accurate spectroscopic redshifts and fully representative for the PACS flux selection) at high z does not allow to properly quantify this statement. In Fig. 7 the total IR LFs obtained by combining the 160-m selected samples with the Avni & Bahcall (1980) technique is plotted and compared with other derivations available in the literature. The total IR LF of Sanders et al. (2003) is plotted as a local reference, in addition to the LFs of Le Floc’h et al. (2005), Rodighiero et al. (2010a), Caputi et al. (2007), Magnelli et al. (2009) and Magnelli et al. (2011) in various redshift intervals. Globally, data from surveys at different wavelengths agree relatively well over the common -range. No data for comparison are available at 2.5, apart from the IR LF of sub-mm galaxies from Chapman et al. (2005) and Wall et al. (2008) at 2.5, which represent reasonably well just the very bright end of the total IR LF. Our derivation is the first at such high redshifts, especially in the 34.2 range. Note the good agreement between our PEP-based total IR LF and the HerMES-based one derived by Vaccari et al. (in preparation), shown by the red open squares in Fig. 7. Though consistent within the error-bars, in the highest redshift bin the HerMES LF is slightly higher than ours. Since the 250-m HerMES selection favours the detection of higher redshift sources than the PEP one, it is more likely that the PEP LF in the higher-z bin is affected by some flux/redshift incompleteness rather than by the presence of low- sources erroneously placed at high- by incorrect photometric redshift assignment (catastrophic failures). The values of our total IR LF for each redshift and luminosity bin are reported in Table 6. ### 3.4 Evolution In order to study the evolution of the total IR LF, we derive a parametric estimate of the luminosity function at different redshifts. For the shape of the LF we assume a modified-Schechter function (i.e. Saunders et al. 1990), where is given by Φ(L)dlogL=Φ⋆(LL⋆)1−αexp[−12σ2log210(1+LL⋆)]dlogL, (3) behaving as a power law for and as a Gaussian in for . The adopted LF parametric shape depends on 4 parameters (, , and ), whose best fitting values and uncertainties have been found using a non-linear least squares fitting procedure. In detail, while in the first -bin all the parameters have been estimated, starting from the second -bin, the values of and have been frozen at the values found at lower redshift, leaving only and free to vary (see Table 7). Note that, in the highest redshift bin (3.04.2) we are not able to constrain the LF break, while we are up to 3. Therefore, the results found at this redshift are affected by larger uncertainties than the 3 ones. However, although there is some degeneracy in the values of and at 3.04.2, the range of allowed value combinations still giving a reasonable fit to the three observed data points (constraining the bright-end of the LF) is limited and do not significantly affect our results. In Fig. 8 we plot the total IR LFs at all redshifts with the 1 Poissonian uncertainty regions (different colours for different -intervals). There is a clear luminosity evolution with redshift, at least up to 3. The apparent “fall” of the 3 LF with respect to those at lower redshifts, if real, might imply a global negative evolution of the IR galaxies and/or AGN starting at 3. However, as mentioned above, we must point out that in the highest redshift bin PACS data could be affected by incompleteness, since with increasing redshift (and for intrinsically “cold” sources) the true PACS fluxes might fall below the detection limit (i.e. faint sources should be missed even if completeness corrections are perfect), while, if luminous enough, they can still be detectable by SPIRE. This effect is expected to be more relevant in COSMOS, where SPIRE data are quite deep relatively to PACS, while it should not happen in GOODS-S, where PACS data are very deep compared to the SPIRE ones (which are limited by confusion). The high- incompleteness of PACS surveys might also be emphasised by the redshift incompleteness of the COSMOS sample, that could affect the highest redshift bins more than the lower ones (although the redshift incompleteness seems to be independent of redshift; see Berta et al. 2011). However, we must point out that a decrease at 2.7–3 similar to that observed in our data, is also observed in the space density of X-ray (see Brusa et al. 2009; Civano et al. 2011) and optically selected AGN (Richards et al. 2006), and of sub-mm galaxies (Wall et al. 2008), as well as in the HerMES total IR LF – though less evident – (from 250-m data; Vaccari et al., in preparation: see Fig. 7). Moreover, our result is in agreement with the recent finding of Smit et al. (2012), that the characteristic value of the galaxy SFR exhibits a substantial, linear decrease as a function of redshift from 2 to 8. In Fig. 9 we show the values of and at different redshifts, with the best curve () fit to the data points. The values of the curve slopes and of the redshifts corresponding to evolutionary breaks have been chosen to be those which minimise the of the fit with two power-laws. We find a significant variation of L with , which increases as up to 1.85, and as between 1.85 and 4. The variation of with redshift starts with a slow decrease as up to 1.1, followed by a rapid decrease (1) at 1.1 and up to 4. Previous estimations of the evolution of and (i.e. Caputi et al. 2007, Bethermin et al. 2011 and Marsden et al. 2011) discussed a decrease in the density of far-IR sources between 1 and 2. In particular, Bethermin et al. (2011) and Marsden et al. (2011), by evolving a parameterised far-IR LF, explored the evolution required by the source counts in the parameter space. The results of these works (especially those of Bethermin et al. 2011, showing a decrease of at 1 and a flatter trend on the evolution of at 2), are close to ours, though with the source counts only it was not possible to constrain the evolution of IR sources at 2. ### 3.5 Evolution of the Different IR Populations The PEP survey, given its size and its coverage in luminosity and redshift, allows us to go further in investigating the evolution of the total IR LF: it gives us the opportunity to study the evolution of the different galaxy classes that compose the global IR population. To investigate the different evolutionary paths of the various IR populations, we have computed the 1/V LFs separately for the five galaxy classes defined by the SED-fitting analysis. In Fig. 10 we show the total IR LFs derived from the combined PEP samples for the different SED classes (coloured filled areas). The results of the fit to a modified Schechter function (see equation 3) for each population are overplotted on the data. In fact, by following the same procedure adopted for the global luminosity function, a parametric fit to the LFs at different redshifts has been performed also for the single populations. The and parameters, for each population, have been estimated at the redshift where the corresponding LF is best sampled (not necessarily at the lowest -bin as for the global LF). Subsequently, the values of and have been frozen at the values found in the “optimal” redshift bin, leaving only and free to vary. In Fig. 11, analogously to Fig. 9, we show the values of and at different redshifts for the different populations, with the best least square fitting curves () overplotted. The best-fitting values of , , and in the first redshift bin, together with the parameters describing the luminosity (, and : (1) to , (1) at ) and density evolution (, and : (1) out to , (1) at ) are reported in Table 8. A clear result of our analysis is that the evolution derived for the global IR LF is indeed a combination of different evolutionary paths: the far-IR population does not evolve all together “as a whole”, as it is often assumed in the literature, but is composed by different galaxy classes evolving differently and independently. As shown in Fig. 10, the normal spiral galaxy population dominates the luminosity function at low-, from the local Universe up to 0.5. Moving to higher redshifts, the number density of galaxies with spiral galaxy SEDs sharply decreases, while their luminosity continues to increase, at least up to 1 (see the and parameter trends shown in Fig. 11). We note that what we observe between 0 and 1 for the spiral SED galaxies is an increase of by a factor of 5, and a decrease of by a factor of 10. Since the two evolutions are not independent, the “total” evolutionary effect results from the combination of the two (as can be observed in the total IR luminosity density, see Section 4). A way to derive the ”total” effect of evolution on a LF is to fix at a given volume density value and see how the luminosity corresponding to that value changes: indeed we find an increases by a factor of 2.5 between 0 and 1 for the spiral LF, in good agreement with previous results, either empirical (for morphologically classified disky galaxies; Scarlata et al. 2007) or theoretical (from chemical evolution models of Milky Way-like galaxies; Colavitti, Matteucci & Murante 2008). Over the whole redshift range 0.53, the “totall” luminosity function is dominated by the SF-AGN population. The number density of SF-AGN is nearly constant from the local Universe up to 1–1.5, showing a slight decrease at higher redshifts, while their luminosities show positive evolution up to the highest redshifts (3.5–4). From Fig. 10 we note a sort of bimodality in the SF-AGN LFs (at 0.45, where we are able to cover a larger luminosity range). This bimodality is indeed to be ascribed to the crossing of two contributions: that of the SF-AGN(Spiral) population, responsible for the faint-end steepness of the LFs, and that of the SF-AGN(SB) population, dominating the bright-end of the SF-AGN LFs and declining at low (not reported in the figure). The starburst galaxy population never dominates. The redshift range where we observe the highest contribution from the starburst galaxies is at 1–2, while in the local Universe their contribution is almost negligible (i.e. their parameter shows an opposite trend with respect to that of spiral galaxies see Fig. 11). The AGN1 and AGN2 populations show a very similar evolutionary trend as a function of , both in and . These powerful AGN populations dominate only the very bright end of the total IR LF, although their number densities and luminosities keep increasing from the local Universe up to the higher redshifts. At 2.5 the AGN1 and AGN2 populations become as important as the SF-AGN one, with the total IR LF of PACS-selected sources in the redshift range 2.5–4 being totally dominated by objects containing an AGN. ### 3.6 Total IR LF in Mass and Specific Star-Formation Rate bins #### 3.6.1 Stellar masses and SFR from SED fitting The wealth of multi-wavelength data available in the cosmological fields included in our work allow us to perform a detailed SED fitting of all sources, in order to derive their most relevant physical parameters (e.g. stellar masses). To derive stellar masses we have fitted the broad-band SEDs of our sources using a modified version of MAGPHYS (Da Cunha et al. 2008), which is a code describing the SEDs using a combination of stellar light and emission from dust heated by stellar populations. In particular, the MAGPHYS software simultaneously fits the broad-band UV-to-far IR observed SED of each object, ensuring an energy balance between the absorbed UV light and that re-emitted in the far-IR regime. The main assumptions are that the energy re-radiated by dust is equal to that absorbed, and that starlight is the only significant source of dust heating. We refer to Da Cunha et al. (2008) for a thorough formal description of how galaxy SEDs are build. At each source’s redshift, the code chooses among different combinations of star formation histories, metallicities and dust contents, associating a wide range of optical models to a wide range of infrared spectra and comparing to observed photometry, seeking for minimization. Each star formation (SF) history is parameterised in terms of an underlying continuous model with exponentially declining star formation rate (SFR), on top of which are superimposed random bursts (see Da Cunha et al. 2008, Da Cunha et al. 2010). We note that, although the MAGPHYS assumption of exponentially declining SFR might not be the best to reproduce the SFR history of 1.5 star-forming galaxies (i.e. exponentially increasing or increasing SFR would be better choices, as widely discussed by Maraston et al. 2010 and Reddy et al. 2012), in our specific case it does not affect the results. In fact, we do not use the MAGPHYS derived SFRs, but we compute them by integrating the best-fitting SED (resulting from Le Phare). The models are distributed uniformly in metallicity between 0.2 and 2 times solar. Since the MAGPHYS code assumes that starlight is the only significant source of dust heating, thus ignoring the presence of a possible AGN component, Berta et al. (2013) have developed a modified version of the MAGPHYS code by adding a torus component to the modelled SED emission, combining the Da Cunha et al. (2008) original code with the Fritz et al. (2006) AGN torus library (see also Feltre et al. 2012). The spectral fitting is performed by comparing the observed SED of our galaxies to every model in the generated library, at the corresponding redshift. A minimisation provides the quality of each fit. We must point out that the mass derivation for unobscured AGN (i.e. AGN1) is a problematic issue, therefore the masses estimated for that class of objects are the most uncertain ones. One source of uncertainty in the mass measurement for AGN1 is due to the fact that, in these objects, the UV part of the SED is likely dominated by the AGN rather than by the host galaxy. This may produce an underestimate of the mass, since, if the AGN contribution is not taken into account, the data can be fit by a bluer, younger and smaller mass object. On the other hand, the mid-IR part of the AGN SED is dominated by dust emission from the dusty torus heated by the central black hole. If a proper decomposition into a stellar and a torus component is not performed, the use of a pure stellar template for estimating the mass from SED-fitting tends to reproduce the mid-IR emission with an older, redder and larger mass object (mass sometimes larger by a factor of 2 than those derived through a decomposition procedure; Santini et al. 2012). These two effects lead to an increase in the uncertainty of the mass derivation, although they might somewhat compensate their effects for a large sample of objects. For this reason, we obtained measurements of the stellar masses of our objects containing an AGN by means of the specific decomposition technique developed by Berta et al. (2013), to separate stellar and nuclear emission components. Examples of the results of this decomposition applied to SF-AGN, AGN2 and AGN1 are shown in Fig. 12. Masses of AGN estimated with the original MAGPHYS and with the Berta et al. (2013) code have been compared, showing very good agreement and small dispersion around the 1–1 relation. Similarly, as further check, we have also computed stellar masses with different code (Hyperz; Bolzonella et al. 2000) and stellar library (BC03, Bruzual & Charlot 2003, instead of the CB07 used as default by MAGPHYS), finding good agreement and no sistematics, too. We have derived the SFRs from the total IR luminosities (estimated from the SED fitting described in Section 2.1) with the standard Kennicutt (1998) relation (converted to Chabrier IMF), after subtracting the AGN contribution to . We note that the total IR luminosity in PEP sources is usually dominated by star formation, even in objects for which an AGN dominates the optical/near-IR/mid-IR part of the spectrum. #### 3.6.2 LFs in different mass bins We compute the total IR LF for galaxies of different stellar masses: 8.5log(/M)10, 10log(/M)11, and 11log(/M)12, by means of the standard 1/V formalism, and we show the results in Figs. 13 (total IR LF in different -bins) and 14 (ratio between the LF in the mass intervals and the total IR LF). We have compared our results with the SFR function (SFR converted to IR luminosity using the Kennicutt (1998) relation) of massive (log(/M10) galaxies derived by Fontanot et al. (2012) from the GOODS-MUSIC sample at redshift 0.41.8. In the common redshift and luminosity range we find an excellent agreement with our total IR LF, which is dominated by sources with 10log(/M)11. At lower luminosities, not sampled by our data, the Fontanot et al. (2012) LFs are characterized by a double-peaked structure, interpreted in terms of the well-known bimodality in the colour(SFR)-Mass diagram. As expected from the SFR-Mass relation, the knee () of our IR LFs in different mass bins moves to higher luminosities with increasing masses (i.e. at 0.00.3, log(/L) changes from 9.5 for log(/M)8.5–10 sources, to 11.3 for sources with log(/M)11). The slope of the total IR LF in each mass bin is always similar to (or flatter than) the “global” LF (total, including all the masses). The lower mass galaxies dominate at lower luminosities (log(/L)9), while the most massive galaxies (log(/M)11) contribute only at higher luminosities, even if they never dominate the LF. At all masses, the LF evolves with redshift, following the evolution of the “global” LF. Fig. 14 shows that the main contribution (50 per cent) to the total IR LF is due to intermediate-mass objects (log(/M)10–11) at all redshifts and luminosities, with their fraction remaining almost the same from 0 to 4, simply shifting to higher luminosities. Lower mass objects (log(/M)8.5–10) contribute significantly only at log(/L)10, with their fraction just shifting to higher luminosities with redshift, but always being below 30 per cent at 0.45 and log(/L)11. The contribution of the most massive objects (log(/M)11–12) increases with IR luminosity and redshift, becoming significant (50 per cent) only at 1.7 and log(/L)12.5. Thus the bulk of the IR luminosity is produced by star-forming galaxies of mass around the characteristic mass M of the Schecter mass function. ### 3.7 Specific-SFR and the main sequence of star-forming galaxies Having computed stellar masses and SFRs for each source, we can check how the PACS selected sources populate the SFR–stellar mass plane and the so called main sequence (MS) of star-forming galaxies, as a function of redshift. This relation (i.e. SFR versus stellar mass) has been shown to be quite tight in the local Universe (Peng et al. 2010, 2011) and well established at redshift 1 (Elbaz et al. 2007) and up to 2 (Daddi et al. 2007, Rodighiero et al. 2011) and 3 (Magdis et al. 2010), with normalisation scaling as (1) out to 2, as shown by Sargent et al. (2012) (see also Elbaz et al. 2007, Rodighiero et al. 2010b, Pannella et al. 2009, Karim et al. 2011). At 2 and 1.5 we assume a slope of 0.79 for the MS in the SFR versus stellar-mass plane (according to Rodighiero et al. 2011 and Sargent et al. 2012), while at 1 we assume a slope of 0.9, as found by Elbaz et al. (2007), and we limit our investigation to the redshift range 0.82.2. By combining UV and far-IR data, Rodighiero et al. (2011) re-evaluated the locus of the MS at 2, showing that objects lying a factor of 4 above the MS (in SFR) can be considered as outliers with respect to the average locus where smoothly star-forming galaxies spend most of their lives in a secular and steady regime. In that work, off-sequence sources (characterized by very high specific-SFRs) are assumed to be in a starburst mode, and are found to contribute only 2 per cent of mass-selected star-forming galaxies and to account for only 10 per cent of the cosmic SFR density at 2 (Rodighiero et al. 2011). In order to check what kind of objects we could classify as on- and off-MS sources in our IR sample compared to previous findings, based either on IR or on optical surveys (e.g. Rodighiero et al. 2011; Sargent et al. 2012), we have splitted our sample into off-MS and on-MS. For consistency with previous studies we have applied the same criterion as Rodighiero et al. (2011) (0.6 dex above the MS) over the whole 0.82.2 redshift range, by using as a reference MS the relation found by Rodighiero et al. (2011) at 2, scaled as described above at 1.5, and the relation found by Elbaz et al. (2007) at 1. In Fig. 15, we show the SFR versus stellar mass distributions in three redshift bins (0.81.25, 1.251.8 and 1.82.2), for the PACS sources included in the computation of the luminosity functions presented in this work. The colour code marks the different SED-classes to which each source belongs. We also report the typical loci of the MS at the various redshifts (scaling as (1), as mentioned above). Details are given in the caption of the Figure. The typical far-IR selection bias (PACS-Herschel in this case) appears as an approximate horizontal SFR cut (Rodighiero et al. 2011, Wuyts et al. 2011), shown as thin dotted line in Fig. 15. We note that the trends of mid/far-IR SEDs with offset from the main sequence observed in Fig.15 (and widely discussed in Section 5) are in good agreement with the results of Elbaz et al. (2011) and Nordon et al. (2012). With the selection based on Rodighiero et al. (2011) and overplotted in Fig. 15 (sources qualify as “off-MS” if they lie more than 0.6 dex above the observed SFR-stellar mass relation) , we can compute the contribution of off-MS (also called “starburst” in the literature) and on-MS (“steady star-formers” in the literature) sources to the total IR LFs. This is presented in Fig. 16, where the total IR LFs of on- and off-MS sources have been computed independently for the three redshift bins. The pink and yellow filled areas correspond to the 1 uncertainty regions of the total IR LFs estimated for the on-MS and off-MS populations, respectively, while the black filled area marks the global population. Our results are compared with the recent estimates by Sargent et al. (2012), a non-parametric approach that is based on three basic observables: the redshift evolution of the stellar mass function for star-forming galaxies; the evolution of the sSFR of MS galaxies; and a double-Gaussian decomposition of the sSFR distribution at fixed stellar mass into a contribution (assumed redshift- and mass-invariant) from MS and off-MS (i.e. starburst) activity. The evolution of the two populations found both in our data and the Sargent et al. (2012) model are very similar. Both data and estimates indicate that the bright-end of the total IR LF is dominated by off-MS sources. However, although consistent within the uncertainties, the relative contribution of off-MS sources seems to be stronger in the Sargent et al. (2012) model than observed in the present computation, where we find that the bright-ends of the PEP IR LFs are more similarly populated by MS and off-MS sources (especially at 2). This difference can be at least partly ascribed to the sharp cut we apply to separate MS from off-MS sources, while Sargent et al. (2012) model the off- and on-MS populations with two continuous log-normal distributions centred at 0.6 dex above the MS and exactly on the MS respectively, of which the one describing the “starburst” population has wings that extend into our on-MS selection region (hence attributing more sources to the starburst category than are selected in our off-MS class). A better agreement between our data and the estimates of Sargent et al. (2012) is found at the faint-end of the LFs that appear to be completely dominated by the “normal” MS galaxies at all redshifts (although the total and relative contributions at log(/L)12 are slightly lower in the data than predicted by Sargent et al. 2012). Good agreement is also found with respect to the evolution of the cross-over luminosity (i.e. where the contributions from on- and off-MS sources are equal); in the model of Sargent et al. (2012) the cross-over luminosity simply shifts to higher luminosities and lower densities (according to the luminosity and density evolution considered). Note that the model assumptions rely on results from different surveys, selected at different wavelengths, complete in mass and with good sampling of the MS. On the other hand, our selection is in SFR and our sources do not follow any clear sequence in stellar mass–SFR plane, because, except at the highest masses, the data are not deep enough to reach well into the main sequence. These different selection effects are likely to lead to some differences between our LFs and the estimates of Sargent et al. (2012). To quantify the relative contribution of the two populations, our observed data have been fitted with a modified Schechter function, in order to integrate them and compute their comoving number and luminosity densities as functions of redshift (see next Section). ## 4 Number Density and IR Luminosity Density We derive the evolution of the comoving number and luminosity density (total, see Fig 18) of the PEP sources, either belonging to the different SED classes (Fig 18, ), to the on- and off-MS categories () and to the different mass intervals (), by integrating the total IR LF in the different redshift bins from 0 to 4. To compute the number (and IR luminosity) density, we integrate the Schechter functions that best reproduce the different populations/mass/sSFR-classes, down to log(/L)8. We note that here we consider lower limits the number and luminosity densities at 3.04.2, since our LF estimate in that redshift bin is likely to be incomplete, as discussed in Section 3.3. We find that the number density of the whole IR population is nearly constant in the 0–1.2 redshift range (slightly increasing from 0 to 0.5), decreasing at 1.2 (see panels of Fig. 18). When decomposing the number density according to the different SED classes, we observe that normal spiral galaxies dominate the local density, with a smaller contribution also from the SF-AGN population and a negligible one from starburst, AGN1 and AGN2. The space density of spiral galaxies decreases rapidly at 0.5, while that of SF-AGN stays nearly constant at 0.52.5, largely dominating in that redshift range. Starburst galaxies never dominate, while the number density of the bright AGN (both AGN1 and AGN2) increases with redshift, from 10 Mpc at 0 to 1–210 Mpc at 3. At higher redshifts the AGN population largely dominates the number density. If the overall contribution to the IR luminosity density () from the AGN components of galaxies is small, can be considered as a proxy of the SFR density (). As a further check, we have therefore studied the evolution of the SF-AGN population (which dominates the distribution of sources) by dividing this class into SF-AGN(SB) and SF-AGN(Spiral) sub-classes and studying their evolution separately. Indeed, we have found different evolutionary paths for the two populations, the former dominating at higher redshifts and showing a behaviour similar to that of AGN-dominated sources (e.g. AGN1 and AGN2), the latter dominating at intermediate redshifts (between 1 and 2), rising sharply from 2 toward the lower redshifts and decreasing, while the spiral population rises at 1. These evolutionary trends, in terms of number and luminosity density, have been reported in Fig. 18 as orange dot-dot-dot-dashed (SF-AGN(SB)) and dark-green dashed (SF-AGN(Spiral)) curves. Galaxies following the SFR–mass relation are always dominant over the off-MS population, at all redshifts (although their space density decreases with increasing , as well as the “global” number density), while the number density of the latter population remains nearly constant between 0.8 and 2.2. In all the mass bins, the trends with redshift of the galaxy number densities are similar to the “global” one, decreasing at higher redshifts, although with slightly different slopes for the different mass intervals. The number densities of low mass galaxies (8.5log(/M)10), reported in the top right panel of Fig. 18, have been computed by integrating the best-fitting modified Schechter function only to 2, since data were not enough to derive reliable fits at higher redshifts. To this redshift, these sources outnumber the higher mass ones, although they fall steeply above 1, when they reach about the same volume density of higher mass galaxies (10log(/M)11). Massive objects (log(/M)11) never dominate (always below 5 per cent) the total number density. The total IR LF allows a direct estimate of the total comoving IR luminosity density () as a function of , which is a crucial tool for understanding galaxy formation and evolution. Although can be converted to a SFR density () under the assumption that the SFR and quantities are connected by the Kennicutt (1998) relation, before doing that we must be sure that the total IR luminosity is produced uniquely by star-formation, without contamination from an AGN. The SED decomposition and separation into AGN and SF contributions show a negligible contribution to (10 per cent) from the AGN in most of the SF-AGN, and a SF component dominating the far-IR even in the majority of more powerful AGN (AGN1 and AGN2). Here we prefer to speak in terms of rather than of , since, especially at high redshift – where the AGN-dominated sources are more numerous – the conversion of could represent only an upper limit to . Note, however, that since this population is never dominant in our IR survey, we do not expect that contamination related to accretion activity occurring in these objects (mainly at high-) can significantly affect the results in terms of .	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9388276934623718, "perplexity": 2262.5881895892926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499890.39/warc/CC-MAIN-20230131190543-20230131220543-00742.warc.gz"}
http://engineerexperiences.com/author/ismail-sarwar/page/2	## Special Types of Energy Meters Special Categories of Energy Meters: In the previous article, we discussed basics types of energy meters. In this article I will continue the discussion on other special types of energy meters. Let’s take this hierarchy diagram again. We already understood about the types of energy meters with respect to technology. Now, let’s talk about category […] ## Basic Types of Energy Meters Basic Categories of Energy Meters There are many basic types of Energy Meters that it is not an easy task to categorize them. Still I will try my best to sort out different types of energy meters in some simple manner. To Study about the Basics of Energy Meters, click here. First, look at this […] ## Objectives of Energy Meters Objectives of Energy Meters With the advancement of technology, objectives of energy meters are not merely to measure energy units. Objectives went far behind from just giving energy readings of some specific consumer. Also, these objectives are not constant, they are increasing day by day with the increase in advancement in energy sector. Let’s discuss […] ## Basics of Energy Meters What is Energy Meter? A device which captures the “units of energy” is called as Energy Meter. This is the basic definition of an Energy Meters. The only difficult part in this definition is “units of energy”. Let’s describe this part in more detail. What are Units of Energy? To understand about the units […] ## Basics of GSM Module Basics of GSM Module If you just started your work on GSM modules and you have no idea where to start then this article is right for you. I will give you step by step details on the basics of GSM modules. But first of all I should build your interest to work on GSM […] ## Smart Energy Meter using Atmel AVR Microcontrollers What is Smart Energy Meter? A smart energy meter is device which can calculate the energy consumption and send it to energy provider through some communication medium. It must be compact, cost effective and able to communicate data by itself with the power control center. I designed a smart energy meter through an ATmega8 microcontroller […] ## 3 Phase Voltage Measurement using Atmel AVR Microcontrollers 3 Phase Voltage Measurement 3 Phase voltage measurement is a little bit tricky task. I will start from the basics and give you details step by step. Specification of this Project Measure voltage of each phase Measure angle of each phase Gives Line to Line voltage as well All results display on 16x2 LCD Less […]	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9032546281814575, "perplexity": 1136.0104261161848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999130.98/warc/CC-MAIN-20190620024754-20190620050754-00370.warc.gz"}
http://www-verimag.imag.fr/Technical-Reports,264.html?lang=fr&number=TR-2012-18	# Technical Reports Ajoy K. Datta, St\'ephane Devismes, Lawrence L. Larmore, S\'ebastien Tixeuil Fast Leader (Full) Recovery despite Dynamic Faults (2012) TR-2012-18.pdf Keywords: self-stabilization, $k$-stabilization, leader election, leader recovery Abstract: In this paper, we give a leader recovery protocol, \lek, that recovers a legitimate configuration where a single leader exists, after at most $k$ memory corruption faults hit the system in an arbitrary manner. That is, if a leader $\ell$ is elected before state corruption, the \emph{same} leader is elected after recovery. Our protocol works for an anonymous bidirectional, yet oriented, ring of size $n$, and does \emph{not} require that processes know $n$, although the knowledge of $k$ is assumed. If $n\ge 18k+1$, our protocol recovers the leader in $O(k^\malytwo)$ rounds using $O(\log k)$ bits per process, assuming unfair scheduling. Our protocol handles \emph{dynamic} faults in the sense that the $k$ memory corruption faults may occur while the network has started recovering the leader. Contact \| Plan du site \| Site réalisé avec SPIP 3.1.11 + AHUNTSIC [CC License] info visites 1350102	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30398330092430115, "perplexity": 7244.315128735095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668765.35/warc/CC-MAIN-20191116204950-20191116232950-00349.warc.gz"}
https://byjus.com/angle-between-two-vectors-formula/	# Angle between Two Vectors Formula If the two vectors are assumed as $\vec{a}$ and $\vec{b}$ then the dot created is articulated as $\vec{a}. \vec{b}$. Let’s suppose these two vectors are separated by angle θ. To know what’s the angle measurement we solve with the below formula we know that the dot product of two product is given as $\vec{a}.\vec{b} =\|\vec{a}\|\|\vec{b}\|cos\theta$ Thus, the angle between two vectors formula is given by $\theta = cos^{-1}\frac{\vec{a}.\vec{b}}{\|\vec{a}\|\|\vec{b}\|}$ where θ is the angle between $\vec{a}$ and $\vec{b}$ ## Angle Between Two Vectors Examples Let’s see some samples on the angle between two vectors: Example 1: Compute the angle between two vectors 3i + 4j – k and 2i – j + k. solution: Let $\vec{a}$ = 3i + 4j – k and $\vec{b}$ = 2i – j + k The dot product is defined as $\vec{a}. \vec{b}$ = (3i + 4j – k).(2i – j + k) = (3)(2) + (4)(-1) + (-1)(1) = 6-4-1 = 1 Thus, $\vec{a}. \vec{b}$ = 1 The Magnitude of vectors is given by $\|\vec{a}\| =\sqrt{(3^{2}+4^{2}+(-1)^{2})} =\sqrt{26}= 5.09$ $\|\vec{b}\| =\sqrt{(2^{2}+(-1)^{2}+1^{2})} =\sqrt{6}= 2.45$ The angle between the two vectors is $\theta = cos^{-1}\frac{\vec{a}.\vec{b}}{\|\vec{a}\|\|\vec{b}\|}$ $\theta = cos^{-1}\frac{1}{(5.09)(2.45)}$ $\theta = cos^{-1}\frac{1}{12.47}$ $\theta = cos^{-1}(0.0802)$ $\theta = 85.39^{\circ}$ Example 2: Find the angle between two vectors 5i – j + k and i + j – k. Solution: Let $\vec{a}$ = 5i – j + k and $\vec{b}$ = i + j – k The dot product is defined as $\vec{a}. \vec{b}$= (5i – j + k)(i + j – k) $\vec{a}. \vec{b}$= (5)(1) + (-1)(1) + (1)(-1) $\vec{a}. \vec{b}$= 5-1-1 $\vec{a}. \vec{b}$= 3 The Magnitude of vectors is given by $\|\vec{a}\| =\sqrt{(5^{2}+(-1)^{2}+1^{2})} =\sqrt{27}= 5.19$ $\|\vec{b}\| =\sqrt{(1^{2}+1^{2}+(-1)^{2})} =\sqrt{3}= 1.73$ The angle between the two vectors is $\theta = cos^{-1}\frac{\vec{a}.\vec{b}}{\|\vec{a}\|\|\vec{b}\|}$ $\theta = cos^{-1}\frac{3}{(5.19)(1.73)}$ $\theta = cos^{-1}\frac{3}{8.97}$ $\theta = cos^{-1}(0.334)$ $\theta =70.48^{\circ}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9976828694343567, "perplexity": 726.9823843757812}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541315293.87/warc/CC-MAIN-20191216013805-20191216041805-00017.warc.gz"}
http://gtx0.com/view.php?post=111965	?> Happy 11th birthday, gtx0! # Department of Science, Math, & Technology E = mc� Reproduction and Sex Posted: Posted June 27th, 2007 by eldin raigmore First, see the following threads in http://listserv.brown.edu/archives/. LISTSERV.BROWN.EDU ( CONLANG: ) Item # Date Time Lines Subject 126275 2005-07-06 14:00 476 THEORY: Language for a Multi-Species Society: Sex-Based Genders Among Neuters, Hermaphrodites, and Sex-Changers. 126325 2005-07-09 17:04 453 Re: THEORY: Language for a Multi-Species Society: Sex-Based Genders Among Neuter ------------------------------------------------------------------------------------- REALISTIC BIOLOGY ------------------------------------------------------------------------------------- There are species on Earth whose reproduction is sexual and which have more than two sexes; but each particular individual just has two parents. It is not always the case among Earth species that an individual's two parents have unequal roles. If the parents' roles are equal, it may be difficult or impossible or unnecessary to decide which parent is its mother and which is its father. When the parents' roles are unequal, on Earth, the following three things tend to go together (but they don't always):* One parent contributes more genetic material; for instance, perhaps both parents contribute equally to the nucleus, but only one contributes any cytoplasmic nucleic acid. One parent contributes the larger gamete and/or the "yolk" material. One parent carries the conceptus in its body, or stays on the nest, or nurses the offspring, or in some other way pays a bigger biological investment.If those three things do in fact go together, that parent is the new individual's "mother" and the other parent is its "father". (There are good reasons to think they'll go together on other planets, too.) It is not always the case among Earth species that some individuals can be mothers but can't be fathers, and other individuals can be fathers but can't be mothers. An individual which, by mating, can become a mother of a new individual, but cannot become a father of a new individual, is called "female"; an individual which, by mating, can become a father of a new individual, but cannot become a mother of a new individual, is called "male"; an individual which, by mating, can become a mother of a new individual, and also, by mating, can become a father of a new individual, is called "hermaphroditic". In many Earth species all individuals are hermaphroditic. In some of these species any individual can fertilize any other individual; in others, even though all individuals are hermaphrodites, the species is divided into classes such that whether or not one individual can fertilize another depends on the classes to which each belongs. In many Earth species it is impossible for any individual to fertilize itself. On Earth, such species are often divided into "total outcrossing classes"; these are the largest groups within the species such that no two members of the same class can fertilize each other. There are often more than two such classes in an Earth species. In case there are exactly two total-outcrossing-classes, and one of them is "all females" and the other is "all males", then we can say this species has sexes. Not all sexually-reproducing Earth species have sexes in that sense. Among Earth species that have sexes, there are several biological strategies by which the sex of an individual becomes determined.* Genetic; the individual's sex is determined at conception.* XY sex chromosome system; a gene that determines maleness is on the Y chromosome; individuals who are XX are female. ZW sex chromosome system. A gene that determines femaleness is on the W chromosome; individuals who are ZZ are male. Diploid/monoploid system: diploid individuals are female, monoploid individuals are male. Reverse diploid/haploid system: monoploid individuals are female, diploid individuals are male. Autosomal genes determine the sex; the species doesn't have sex chromosomes, but there is more than one poly-allelic locus, usually on more than one pair of chromosomes, whose alleles, in various combinations, determine the individual's sex. Incubation/gestation; before birth or hatching, the individual's sex becomes determined by the circumstances of its incubation or gestation (for instance, some crocodilians' sex is determined by the temperature at which they are incubated). A combination of the autosomal chromosomes and the environment of incubation/gestation determines the sex. Following birth or hatching, but before sexual maturity, adulthood, or puberty, the individual's sex is determined. ------------------------------------------------------------------------------------- XENOBIOLOGY ------------------------------------------------------------------------------------- Questions: 1) How likely is it that any species's method of reproduction might require involvement of three or more parents? 2) What if there were two fathers, each of whom contributed half of the nuclear DNA, and one mother, who contributed all of the cytoplasmic DNA, all of the nucleoli, all of the ribosomes, and all of the edit-RNA? 3) Is a three-parent system more, or less, likely among species whose cells have three-stranded DNA instead of just two-stranded? 4) Is a three-stranded DNA even possible at all? If so, is it even compatible with sexual reproduction at all? 5) If there are three parents per individual, how many sexes will there be? * Is "just one sex" a possible answer? Is "two sexes" a possible answer? Is "exactly three sexes" the only possible answer? Could "more than three sexes" be a possible answer? 6) If there are three parents per individual in an intelligent species, how does this affect the society's naming patterns and systems, inheritance patterns and systems, etc.? 7) If every child had three parents, would the three parents be expected to live together to rear the child? ------------------------------------------------------------------------------------- Don't forget to read that thread on CONLANG-L. It's got more stuff that might be interesting. There are 20 Replies Load all posts On page: 1 2 settingsSettings 1) It's less likely than two-parent sexula reproduction, and would require a reason for the added complexity to the system of finding not one but two mates of the right sex(es). Maybe a very quickly mutating parasite or other reason why that much genetic reshuffling would be required. 2) If three-parent reproduction existed, I could see either of your systems working. 3 and 4) I don't think DNA can be three stranded, though there are similar acids that could be. However, you aren't mixing two sides of a DNA strand when animals sexually reproduce, but instead are mixing sets of chromosomes. I would expect a species with this form of reproduction would have one of the following: Three copies of each chromosome (one from each parent) in the neucleus, with one parent contributing any other genetic material, cytoplasm, etc. OR Two of each coming from two of the parents and the rest from the third. 5) Probably one, as that would make things simpler, though it's always possible that there could be two or three sexes. I don't think more than that would be likely. 6) I guess they could take one name from each parent, or a personal name and a family name from one parent, probably their "mother". 7) Possibly. There could be any combination of care-takers: The one who gives birth/lays eggs alone, one of the parents that didn't give birth/lay eggs. both parent that didn't, the one who did and at least one who didn't, or even none of them and the child is just raised by the community. Do what you want with it. Posted June 27th, 2007 by bloodb4roses View Source Quote Report Thank you, BloodB4Roses. 1) It's less likely than two-parent sexula reproduction, and would require a reason for the added complexity to the system of finding not one but two mates of the right sex(es). Maybe a very quickly mutating parasite or other reason why that much genetic reshuffling would be required. Presumably, escaping the parasites' evolved advantages is the selective pressure in favor of sexual reproduction IRL. I wonder what kind of selective pressure would encourage a three-parent system? 2) If three-parent reproduction existed, I could see either of your systems working. Is anyone aware of any conworld that has actually tried that? Or is anyone working on one? 3 and 4) I don't think DNA can be three stranded, though there are similar acids that could be. AIUI and IIRC, it can be; but it requires a different pH. However, you aren't mixing two sides of a DNA strand when animals sexually reproduce, but instead are mixing sets of chromosomes. Yes, that's true. People who play around with three-parent reproduction, and people who play around with 3-stranded genetic material, sometimes forget there's no connection. That's really why I asked questions 3 and 4; to make people think about that. But mightn't a 3-stranded genetic material be much less prone to mutation? When it's copied, one of the new strands has two older strands to be compared against. (OTOH maybe the other copy is even more prone to mutation.) I would expect a species with this form of reproduction would have one of the following: Three copies of each chromosome (one from each parent) in the neucleus, with one parent contributing any other genetic material, cytoplasm, etc. OR Two of each coming from two of the parents and the rest from the third. The latter system is the one I have the easiest time visualizing; two "fathers", each of whom contributes half of the nuclear genes, plus a "mother" who contributes everything else -- all of the cytoplasmic DNA, all of the edit-RNA, all of the ribosomes, all of the nucleoli. Does anyone know of a conworld in which either of those two kinds of three-parent reproduction is the norm for one of the important species? Or is anyone working on one? Who knows of, or is working on, one with all three parents contributing a third each of the nuclear genes? Who knows of, or is working on, one with two parents contributing half of the nuclear genes each, and the third parent contributing everything else? 5) Probably one, as that would make things simpler, though it's always possible that there could be two or three sexes. I don't think more than that would be likely. Well, with just two parents, all kinds of things actually happen IRL here on Earth that just don't seem all that "likely". Why are there total outcrossing classes at all? Given that there are, why can one of them only become fathers and the other only become mothers? OTOH among species which are rare, and the chances of running into a conspecific are slight in the first place, it's advantageous to be hermaphroditic; your date for Saturday night can be the first other individual of your species you run into. Among flatworms, there is then a competition; both would prefer that the other one be the one who becomes pregnant; but both would prefer that the mating take place, more strongly than that the other be the impregnated one. Flatworms can be fertilized on any part of their body; each has two penes, which are sharp-pointed like hypodermic needles. The mating consists of a "dance" or "fencing" in which each attempts to penetrate the other without being penetrated itself. But if an animal species isn't rare, more often than not it's divided into male and female, and each animal, at any particular time, is just male or just female. Why is that? 6) I guess they could take one name from each parent, Kind of what I was thinking of. or a personal name and a family name from one parent, probably their "mother". Seems likeliest. Is anyone working on such a species? 7) Possibly. There could be any combination of care-takers: The one who gives birth/lays eggs alone, one of the parents that didn't give birth/lay eggs. both parent that didn't, the one who did and at least one who didn't, or even none of them and the child is just raised by the community. Do what you want with it. You are right, of course. Among real world species on Earth, often the father puts more time and effort into rearing the young, once they hatch or wean or get born or whatever, than the mother. (OTOH, often not.) Is anyone working on such a thing? Has anyone heard of such a thing in anyone else's work? Posted June 27th, 2007 by eldin raigmore View Source Quote Report The only mention of a three-parent system I've seen is in the kid's books Animorphs. The main villain-race, the Yerks(sp) would combine three individual's genetic material to form many new individuals, but the parents were destroyed in the process. Posted June 28th, 2007 by bloodb4roses View Source Quote Report Thanks! I've never looked at that series. Here's what I found via Google: http://en.wikipedia.org/wiki/Yeerks#Reproduction Reproduction Yeerks reproduce by fusion followed by fission. Three parent Yeerks merge into a single organism, which then breaks apart into hundreds of separate grubs, destroying the parents in the process. Yeerks do not have different sexes; presumably any three random Yeerks can fuse in reproduction. Nevertheless the Yeerks are usually referred to as "he" or "she" in the novels based on their host's sex (usually by a human or Andalite, who do have different sexes). "Their Majesties' Bucketeers" by L. Neil Smith contains another fictional species who have three-parent reproduction. They also have three sexes. But this particular novel doesn't explain anything at the subcellular level; in fact most of Smith's aliens aren't explained much more clearly than Piers Anthony's are. Their Majesties' Bucketeers is the third novel set in the Gallatin Universe. The story is a pastiche of the Sherlock Holmes tales by Arthur Conan Doyle, introducing the Lamviin, a trilaterally symmetrical race of aliens native to the arid planet of Sodde Lydfe. Their Majesties' Bucketeers introduces characters who would later interact with others in the Gallatin Universe. I believe Piers Anthony had a four-sex species with three-parent reproduction. The offspring was of whichever sex none of its parents belonged to. The last of the three parents to join the mating, determined which of the other two became pregnant. Again this was not explained at a cellular or molecular level (nor at any level in between cells and molecules); but Piers Anthony has living, intelligent magnets, and beings who have bells growing from them which are used in mating, and all sorts of other stuff that's very implausible; he doesn't try to be scientific. Posted June 28th, 2007 by eldin raigmore View Source Quote Report In David Gerrold's "Chtorr" there is a species called "bunnymen and libbets". At least I think it's just one species. The bunnymen are the males and the libbets are the females. In that species the males have three parents; two fathers and a mother. The females have just two parents, a mother and one father. The only way I have thought of that this might work is that the males are triploid and the females are diploid. ----------------------------------------- The Chtorr ecology is heavy on parasites; or, rather, on symbiosis. There is a prevalent, versatile parasite, not quite an ectoparasite and barely an endoparasite, that can infest absolutely any animal that's large enough (bigger than a few inches) and has a long enough lifespan. Not only all the Chtorr animals, but any Earth animal that lives in the Chtorr-taken regions long enough, gets covered with a coat of synaesthetic "hair". Most of the bodies of these parasites are outside the bodies of their hosts; but they penetrate the skin with "roots" which then hook into the nervous system. They're actually symbiotic; they allow their hosts to have chemosenses -- taste and smell -- all over their bodies, as well as low-resolution hearing, and even lower-resolution "sight" (or, at least, sensitivity to light). Although by the time the Chtorr ecology invaded the Earth, these parasites had evolved enough restraint that they did not invade the respiratory nor alimentary nor genital nor urinary tracts even of Terrestrial hosts, which had evolved no resistance against them; it's easy to imagine that all living large Chtorran animals are descendants of ancestors which had had to survive infestations by much more virulent, ancient ancestors of these parasites. ------------------------------------------ The triploid organisms -- the bunnymen, the males -- have a 50% greater chance of being heterozygous for any particular trait than any diploid organism would have. As the "sickle cell" trait in RL humans shows, being heterozygous for certain traits can combat certain parasites. A heterozygous individuals red blood cells will not sickle unless infested with the malaria parasite; but if infested, will sickle, killing the parasite (and the red blood cell) before it can reproduce and kill the RBC and go on to infest other RBCs. An individual who is homozygously normal, does not have this protection against malaria. An individual who is homozygous for the sickle-cell trait, unfortunately, has RBCs that will sickle whenever they stay too long in a low-oxygen high-carbon-dioxide environment of the right pH; ordinarily these individuals die before having children (unless treated?). Anyway; suppose a given locus on the bunnymen's genes has three alleles; imagine they are equally common. One out of every nine bunnymen will be homozygous (one out of twenty-seven will be homozygous for each of the three alleles). Two out of every three bunnymen will be heterozygous, having two copies of one allele and one copy of another allele (six different combinations). Two out of every nine bunnymen will be three-way heterozygous, having all three alleles. But for the libbets, one out of every three will be homozygous, and two out of three will be heterozygous; none, of course, will be three-way heterozygous. However there will be greater diversity among the daughters of each given bunnyman/libbet couple than there would be if the bunnymen were diploid instead of triploid; there are 32=6 combinations each can inherit from her parents, instead of just 22=4. So a parasite which had evolved an efficient way to attack the preceding generation would have much less chance that the same method would work on the next generation; and this difference would be greater, even for the libbets, than it would be if the bunnymen were diploid instead of triploid. ----------------------------------------------------- How does that sound for a justification of three-parent reproduction? Posted June 29th, 2007 by eldin raigmore View Source Quote Report I think so. Posted June 29th, 2007 by bloodb4roses View Source Quote Report Flatworms can be fertilized on any part of their body; each has two penes, which are sharp-pointed like hypodermic needles. The mating consists of a "dance" or "fencing" in which each attempts to penetrate the other without being penetrated itself. But if an animal species isn't rare, more often than not it's divided into male and female, and each animal, at any particular time, is just male or just female. Why is that? Maybe the first half answers the second. If a mate is easy to find (e.g. in a herd), then giving an individual the chance to avoid becoming pregnant by mating will cause wasting of their effort. If there are traits that makes individuals either just male or just female, then those individuals will avoid a lot of the bother of both trying to be the father and not the mother. The females won't have to try and the males won't need to. Posted June 29th, 2007 by simon.clarkstone View Source Quote Report Although by the time the Chtorr ecology invaded the Earth, these parasites had evolved enough restraint that they did not invade the respiratory nor alimentary nor genital nor urinary tracts even of Terrestrial hosts, which had evolved no resistance against them; it's easy to imagine that all living large Chtorran animals are descendants of ancestors which had had to survive infestations by much more virulent, ancient ancestors of these parasites. This sounds unrealistic. In the real world, a non-dangerous disease in one population will often turn out to be deadly in a population that has not encountered it before. The hosts' defenses and the parasites' attacking will have moved towards one another to reach an equilibrium, with both being quite powerful. The parasite would ravage the new host population, or would die because it needed part of the hosts' defences to live, or both at once. Evolution exploits anything exploitable you give it, including things that are supposed to hinder rather than help. And obscure bugs in your universe simulator, if simulated. Posted June 29th, 2007 by simon.clarkstone View Source Quote Report This sounds unrealistic. In the real world, a non-dangerous disease in one population will often turn out to be deadly in a population that has not encountered it before. The hosts' defenses and the parasites' attacking will have moved towards one another to reach an equilibrium, with both being quite powerful. The parasite would ravage the new host population, or would die because it needed part of the hosts' defences to live, or both at once. Evolution exploits anything exploitable you give it, including things that are supposed to hinder rather than help. And obscure bugs in your universe simulator, if simulated. I don't know why, but Gerrold had it that these particular parasites didn't kill humans, at least not at all quickly. Furthermore the infestations didn't do a good job of sticking around in case the humans left the Chtorr-dominated zones. Since Gerrold's characters didn't understand the Chtorr ecology, perhaps he didn't think he ought to explain it to his readers yet. (Or just possibly he had no explanation; I don't know.) Posted June 29th, 2007 by eldin raigmore View Source Quote Report Flatworms can be fertilized on any part of their body; each has two penes, which are sharp-pointed like hypodermic needles. The mating consists of a "dance" or "fencing" in which each attempts to penetrate the other without being penetrated itself. But if an animal species isn't rare, more often than not it's divided into male and female, and each animal, at any particular time, is just male or just female. Why is that? Maybe the first half answers the second. If a mate is easy to find (e.g. in a herd), then giving an individual the chance to avoid becoming pregnant by mating will cause wasting of their effort. If there are traits that makes individuals either just male or just female, then those individuals will avoid a lot of the bother of both trying to be the father and not the mother. The females won't have to try and the males won't need to. I don't know. I think that having one sex that is specialized in giving birth also frees up the other sex to specialize in activities where pregnancy would be a hindrance if not an impossible obstacle. Also, IIRC, there was (or is) a theory on sex differentiation that suggested that females would get slighter over time because they can pass through the birth canal more easily that way, while males will get bigger so they can be stronger. I'm not sure I really buy that, and it doesn't say much about egg-laying creatures. Thus, I made Xala females the stronger (and smarter) sex -- and also gave Kesatans very little sex differentiation at all (I'm still debating whether I'll allow them to spontaneously change sex). ________ As for three-parent reproduction: I don't think it's very plausible. I once thought up a three-parent race (though I didn't work out reproductive details) that also had three sexes, but reflecting back on that, it probably wouldn't work to well. Posted July 2nd, 2007 by Fonori View Source Quote Report Next page Load rest of pages On page: /	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37775111198425293, "perplexity": 3214.6810291493066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401643509.96/warc/CC-MAIN-20200929123413-20200929153413-00474.warc.gz"}
https://unapologetic.wordpress.com/2010/12/24/permutations-and-polytabloids/?like=1&source=post_flair&_wpnonce=eb8d9d939c	# The Unapologetic Mathematician ## Permutations and Polytabloids We’ve defined a bunch of objects related to polytabloids. Let’s see how they relate to permutations. First of all, I say that $\displaystyle R_{\pi t}=\pi R_t\pi^{-1}$ Indeed, what does it mean to say that $\sigma\in R_{\pi t}$? It means that $\sigma$ preserves the rows of the tableau $\pi t$. And therefore it acts trivially on the tabloid $\{\pi t\}$. That is: $\sigma\{\pi t\}=\{\pi t\}$. But of course we know that $\{\pi t\}=\pi\{t\}$, and thus we rewrite $\sigma\pi\{t\}=\pi\{t\}$, or equivalently $\pi^{-1}\sigma\pi\{t\}=\{t\}$. This means that $\pi^{-1}\sigma\pi\in R_t$, and thus $\sigma\in\pi R_t\pi^{-1}$, as asserted. Similarly, we can show that $C_{\pi t}=\pi C_t\pi^{-1}$. This is slightly more complicated, since the action of the column-stabilizer on a Young tabloid isn’t as straightforward as the action of the row-stabilizer. But for the moment we can imagine a column-oriented analogue of Young tabloids that lets the same proof go through. From here it should be clear that $\kappa_{\pi t}=\pi\kappa_t\pi^{-1}$. Finally, I say that the polytabloid $e_{\pi t}$ is the same as the polytabloid $\pi e_t$. Indeed, we compute $\displaystyle e_{\pi t}=\kappa_{\pi t}\{\pi t\}=\pi\kappa_t\pi^{-1}\pi\{t\}=\pi\kappa_t\{t\}=\pi e_t$ December 24, 2010 - ## 2 Comments » 1. […] polytabloids is a submodule, we must see that it’s invariant under the action of . We can use our relations to check this. Indeed, if is a polytabloid, then is another polytabloid, so the subspace spanned […] Pingback by Specht Modules « The Unapologetic Mathematician \| December 27, 2010 \| Reply 2. […] use our relations to […] Pingback by Examples of Specht Modules « The Unapologetic Mathematician \| December 28, 2010 \| Reply	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9842222332954407, "perplexity": 526.2386739608728}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988717963.49/warc/CC-MAIN-20161020183837-00191-ip-10-171-6-4.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/111466/upper-bound-on-joint-renyi-entropy	# Upper bound on joint Renyi entropy Renyi entropy of a random pair $(X,Y)$ with probability distribution $p_{X,Y}$ is defined by $$H_\alpha(X,Y) = \frac{1}{1-\alpha}\log\sum_{x,y} p_{X,Y}(x,y)^\alpha.$$ Assume that $X$ and $Y$ have countably infinite alphabets, and observe the case $0\leq\alpha\leq 1$. It is known that this functional is subadditive, i.e., that $H_\alpha(X,Y)\leq H_\alpha(X) + H_\alpha(Y)$, only for $\alpha=0$ (Hartley entropy) and $\alpha=1$ (Shannon entropy). My question is the following: Does there exist some upper bound on the joint entropy for $0<\alpha<1$, in terms of the marginal entropies? In fact, I don't even need an explicit upper bound, answering the following simpler question would suffice: If $H_\alpha(X)<\infty$ and $H_\alpha(Y)<\infty$, does there exist a constant $h$ such that $H_\alpha(X,Y)\leq h$? - – Piotr Migdal May 14 '13 at 15:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9968237280845642, "perplexity": 173.32015390193556}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507452492.48/warc/CC-MAIN-20141017005732-00036-ip-10-16-133-185.ec2.internal.warc.gz"}
https://kerodon.net/tag/01Z1	# Kerodon $\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ Remark 5.5.1.6. Let $X$ and $Y$ be Kan complexes. Then Remark 4.6.7.6 supplies a canonical homotopy equivalence of Kan complexes $\operatorname{Fun}(X,Y) \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{S}}}( X,Y)$. Beware that this homotopy equivalence is generally not an isomorphism.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9630202651023865, "perplexity": 489.2744591609961}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514046.20/warc/CC-MAIN-20210117235743-20210118025743-00433.warc.gz"}
https://samacheerkalvi.guide/samacheer-kalvi-12th-physics-guide-chapter-4/	Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Physics Guide Pdf Chapter 4 Electromagnetic Induction and Alternating Current Text Book Back Questions and Answers, Notes. ## Tamilnadu Samacheer Kalvi 12th Physics Solutions Chapter 4 Electromagnetic Induction and Alternating Current ### 12th Physics Guide Electromagnetic Induction and Alternating Current Text Book Back Questions and Answers Part – I Text Book Evaluation: I. Multiple choice questions: Question 1. An electron moves on a straight line path XY as shown in the figure. The coil abcd is adjacent to the path of the electron. What will be the direction of current, if any, induced in the coil? a) The current will reverse its direction as the electron goes past the coil b) No current will be induced c) abcd a) The current will reverse its direction as the electron goes past the coil Solution: First current develops in direction of abcd but when electron moves away, magnetic field inside loop decreases and current changes its direction. Question 2. A thin semi-circular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. The potential difference developed across the ring when its speed v, is a) Zero b) $$\frac{\mathrm{B} v \pi \mathrm{r}^{2}}{2}$$ and P is at higher potential c) πrBυ and k is at higher potential d) 2rBυ and R is at higher potential d) 2rBυ and R is at higher potential Solution: Motional emt induced in the semi circular ring PQR is equal to the motional emt induced in the imaginary conductor PR. EPQR = EPR = BVl = BV (2r) (l = PR = 2r) ∴ Potential difference developed across the ring is 2r Br with R is at higher potential. Question 3. The flux linked with a coil at any instant t is given by φB= 10t2 – 50t + 250. The induced emf at t = 3s is a) -190 V b) -10 V c) 10 V d) 190 V b) -10V Solution: e = – $$\frac{\mathrm{d} \phi}{\mathrm{dt}}$$ = $$\frac{d}{d t}$$ (10t2 – 50t + 250) e = -20t + 50 e = -10V Question 4. When the current changes from +2A to -2A in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self-induction of the coil is a) 0.2 H b) 0.4 H c) 0.8 H d) 0.1 H d) 0.1 H Solution: Question 5. The current i flowing in a coil varies with time as shown in the figure. The variation of induced emf with time would be Solution: For $$\frac{3 \mathrm{~T}}{4}$$ to T i = 0, $$\frac{d i}{d t}$$ = 0, e = 0 Question 6. A circular coil with a cross-sectional area of 4 cm2 has 10 turns. It is placed at the center of a long solenoid that has 15 turns/cm and a cross-sectional area of 10 cm2. The axis of the coil coincides with the axis of the solenoid. What is their mutual inductance? a) 7.54 μH b) 8.54 μH c) 9.54 μH d) 10.54 μH a) 7.54 μH Solution: M = μ0 N1 N2 A2 =4π × 10-7 × 15 × 102 × 10 × 4 × 10-4 = 4π × 6 × 10-7 = 24 × 3.14 × 10-7 = 75.36 × 10-7 = 7.54 × 10-6 M = 7.54 μH Question 7. In a transformer the number of turns in the primary and the secondary are 410 and 123C respectively. If the current in primary is 6A, then that in the secondary coil is a) 2A b) 18A c) 12A d) 1A a) 2 A Solution: Question 8. A step – down transformer reduces the supply voltage from 220 V to 11 V and increase the current from 6 A to loo A. Then its efficiency is a) 1.2 b) 0.83 c) 0.12 d) 0.9 b) 0.83 Solution: P = VI Input Power = 220 × 6 = 1320 Output Power = 11 × 100 = 1100 η = $$\frac{1100}{1320}$$ = 0.83 Question 9. In an electrical circuit, R, L, C, and AC voltage sources are all connected in series. When L is removed from the circuit, the phase difference between the voltage and current in the circuit is π/3. Instead, if C is removed from the circuit, the phase difference is again π/3. The power factor of the circuit is a) 1/2 b) $$\frac{1}{\sqrt{2}}$$ c) 1 d) $$\frac{\sqrt{3}}{2}$$ c) 1 Solution: It is the condition for resonance therefore phase difference between v and i = 0 Power factor cos Φ = 1 Question 10. In a series RL circuit, the resistance and inductive reactance are the same. Then the phase difference between the voltage and current in the circuit is a) $$\frac{\pi}{4}$$ b) $$\frac{\pi}{2}$$ c) $$\frac{\pi}{6}$$ d) zero a) $$\frac{\pi}{4}$$ Solution: tan Φ = $$=\frac{X_{L}}{R}$$ χL = R tan Φ = 1, Φ = 45° Φ = $$\frac{\pi}{4}$$ Question 11. In a series resonant RLC circuit, the voltage across 100Ω resistor is 40 V. The resonant frequency is 250 rad/s. If the value of C is 4μF, then the voltage across L is a) 600 V b) 4000 V c) 400 V d) 1 V c) 400 V Solution: χc = $$\frac{1}{C \omega}$$ = 1000Ω At resonant χc = χL ∴ I = $$\frac{V}{R}$$ = 0.4 A ∴ VL = IXL = 400 V Question 12. An inductor 20 mH, a capacitor 50 µF, and a resistor 40Ω are connected in series across a source of emf V = 10 sin 340 t. The power loss in the AC circuit is a) 0.76 W b) 0.89 W c) 0.46 W d) 0.67 W c) 0.46 W Solution: Power loss = $$\left(\frac{E_{\mathrm{rms}}}{Z}\right) \mathrm{R}$$ Erms = $$\frac{10}{\sqrt{2}}$$ Z = $$\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$$ χL = 6.82Ω χC = 58.8Ω ∴ Z = 65.6Ω ∴ Power Loss = 0.46 W Question 13. The instantaneous values of alternating current and voltage in a circuit are i = $$\frac{1}{\sqrt{2}}$$ sin(100πt) A and v = $$\frac{1}{\sqrt{2}}$$ sin(100π + π/3) V The average power in watts consumed in the circuit is a) $$\frac{1}{4}$$ b) $$\frac{\sqrt{3}}{4}$$ c) $$\frac{1}{2}$$ d) $$\frac{1}{8}$$ d) $$\frac{1}{8}$$ Solution: Question 14. In an oscillating IC circuit, the maximum charge on the capacitor is Q. The charge on, the capacitor when the energy is stored equally between the electric and magnetic fields is a) $$\frac{Q}{2}$$ b) $$\frac{Q}{\sqrt{3}}$$ c) $$\frac{Q}{\sqrt{2}}$$ d) Q c) $$\frac{Q}{\sqrt{2}}$$ Solution: Question 15. $$\frac{20}{\pi^{2}}$$ H inductor is connected to a capacitor of capacitance C. The value of C in order to impart maximum power at 50 Hz is a) 50 µF b) 0.5 µF c) 500 µF d) 5 µF d) 5 µF Solution: Maximum power at χL = χC L 2πγ = $$\frac{1}{2 \pi \gamma}$$ C = 5 µF Question 1. What is meant by electromagnetic induction? Whenever the magnetic flux linked with a closed coil changes, an emf (electromotive force) is induced and hence an electric current flows in the circuit. Question 2. State Faraday’s laws of electromagnetic induction. First law: Whenever magnetic flux linked with a closed circuit changes, an emf is induced in circuit. Second law: The magnitude of induced emf in a closed circuit is equal to the time rate of change of magnetic flux linked with the circuit $$E=-\frac{\mathrm{d} \theta}{\mathrm{dt}}$$ Question 3. State Lenz’s law. Lenz’s law states that the direction of the induced current is such that it always opposes the cause responsible for its production. Question 4. State Fleming’s right-hand rule. 1. The Thumb, index finger, and middle finger of the right hand are stretched perpendicular to each other. 2. The index finger indicates the direction of the magnetic field. 3. Thumb indicates the direction of motion of the conductor. 4. The middle finger indicates the direction of induced current. Question 5. How is Eddy’s current produced? How do they flow in a conductor? Even for a conductor in the form of a sheet or plate, an emf is induced when magnetic flux linked with it changes. But the difference is that there is no definite loop or path for induced current to flow away. As a result, the induced currents flow in concentric circular paths. As these electric currents resemble eddies of water, these are known as Eddy currents. They are also called Foucault currents. Question 6. Mention the ways of producing induced emf. 1. By changing the magnetic field B. 2. By changing the area A of the coil and 3. By changing the relative orientation of the coil. Question 7. What for an inductor is used? Give some examples. Inductor is a device used to store energy in a magnetic field when an electric current flows through it. The typical examples are coils, solenoids, and toroids. Question 8. What do you mean by self-induction? 1. Its magnetic flux is changed by changing the current in the coil, and induced emf is induced in the same coil. 2. This is known as self-induction. Question 9. What is meant by mutual induction? When an electric current passing through a coil changes with time, an emf is induced in the neighbouring coil. This phenomenon is known as mutual induction. Question 10. Give the principle of AC generator. 1. AC generator works on the principle of electromagnetic induction. 2. The relative motion between a conductor and a magnetic field changes the magnetic flux linked with the conductor which in turn, induces an emf. Question 11. List out the advantages of stationary armature -rotating field system of AC generator. 1. The current is drawn directly from fixed terminals on the stator without the use of brush contacts. 2. The insulation of stationary armature winding is easier. 3. The number of sliding contacts (slip rings) is reduced. Moreover, the sliding contacts are used for low-voltage DC Source. 4. Armature windings can be constructed more rigidly to prevent deformation due to any mechanical stress. Question 12. What are step-up and step-down transformers? 1. A transformer that increases the voltage by decreasing current is known as a step-up transformer. 2. A transformer that decreases the voltage by increasing the current is a step-down transformer. Question 13. Define the average value of an alternating current. The average value of alternating current is defined as the average of all values of current over a positive half-cycle or negative half-cycle. Question 14. How will you define the RMS value of an alternating current? The RMS value of an alternating current is defined as the square root of the mean of the squares of all currents over one cycle. I rms = $$\frac{\mathrm{I}_{\mathrm{m}}}{\sqrt{2}}$$ Question 15. What are phasors? A sinusoidal alternating voltage (or current) can be represented by a vector which rotates about the origin in an anti-clockwise direction at a constant angular velocity ω. Such a rotating vector is called a phasor. Question 16. Define electric resonance. Ans: When frequency of applied alternating source (ωr) is equal to natural frequency $$\left(\frac{1}{\sqrt{L C}}\right)$$ of RLC circuit, the current in the circuit reaches its maximum value. Then the circuit is said to be in electrical resonance. Question 17. What do you mean by resonant frequency? When the frequency of the applied alternating source (ωr) is equal to the natural frequency $$\left[\frac{1}{\sqrt{L C}}\right]$$ of the RLC circuit, the current in the circuit reaches its maximum value. Then the circuit is said to be in electrical resonance. The frequency at which resonance takes place is called resonant frequency. Resonant angular frequency, ωr = $$\frac { 1 }{ \sqrt { LC } }$$ Question 18. How will you define Q-factor? 1. Q factor is defined as the ratio of voltage across L or C to the applied voltage. 2. Q – factor = $$\frac{\text { Voltage across } L \text { or } C}{\text { Applied Voltage }}$$ 3. Q factor = $$\frac{1}{R} \sqrt{\frac{L}{C}}$$ Question 19. What is meant by wattles current? The component of current (IRMS sin φ), which has a phase angle of $$\frac { π }{ 2 }$$ with the voltage is called reactive component. The power consumed is zero. So that it is also known as ‘Wattless’ current. Question 20. Give any one definition of power factor. Power factor is defined as 1. Power factor = cos Φ = cosine of the angle of lead or leg. 2. Power factor = $$\frac{R}{Z}=\frac{\text { Resistance }}{\text { Impedance }}$$ 3. Power factor = $$\frac{\text { True power }}{\text { Apparent power }}$$ Question 21. What are LC oscillations? Whenever energy is given to a LC circuit, the electrical oscillations of definite frequency are generated. These oscillations are called LC oscillations. During LC oscillations, the total energy remains constant. It means that LC oscillations take place in accordance with the law of conservation of energy. Question 1. Establish the fact that the relative motion between the coil and the magnet induces an emf in the coil of a closed circuit. 1. In first experiment when bar magnet is placed close to the coil, magnetic lines pass through coil, the magnetic flux in coil increases and emf is induced hence electric current flows in the circuit. 2. At the same time when they recede away from one another magnetic flux decreases emf is induced in opposite direction. Current flows in opposite direction. So there is a deflection in the galvanometer. 3. In second experiment, when the primary circuit is open, no electric current flows in it, magnetic flux linked with the secondary coil is zero. 4. When primary circuit is closed, increasing current produce magnetic field. So magnetic flux linked with coil increases. This induced current in secondary coil. 5. When primary circuit is broken, decreasing primary current induces current in secondary coil but in opposite direction. So there is a deflection in Galvanorneter. Question 2. Give an illustration of determining direction of induced current by using Lenz’s law. 1. Move the bar magnet towards solenoid with north pole pointing solenoid. 2. When the Magnetic flux increases in the coil, induced current is produced, and the coil becomes magnetic dipole. 3. According to Lenz law, induced current opposes the movement of north pole towards coil. 4. It is possible if end nearer to magnet become north pole, then it repels the north pole of magnet and oppose the movement of magnet. 5. The direction of induced current is found by the right hand thumb rule. 6. When a bar magnet is withdrawn, nearer end becomes south pole which attracts north pole of the bar magnet, opposing the receding motion of magnet. 7. Direction of induced current can be found from Lenz law. Question 3. Show that Lenz’s law is in accordance with the law of conservation of energy. Conservation of energy: The truth of Lenz’s law can be established on the basis of the law of conservation of energy. According to Lenz’s law, when a magnet is moved either towards or away from a coil, the induced current produced opposes its motion. As a result, there will always be a resisting force on the moving magnet. Work has to be done by some external agency to move the magnet against this resisting force. Here the mechanical energy of the moving magnet is converted into electrical energy which in turn, gets converted into Joule heat in the coil i.e., energy is converted from one form to another. Question 4. Obtain an expression for motional emf from Lorentz force. 1. Consider a straight rod AB of length l in uniform magnetic field perpendicularly to plane of paper. 2. Let rod move with constant velocity $$\overrightarrow{\mathrm{v}}$$ towards right side free electrons present in it also move with same $$\overrightarrow{\mathrm{v}}$$ in $$\overrightarrow{\mathrm{B}}$$ 3. The Lorentz force is $$\overrightarrow{\mathrm{F}}_{\mathrm{B}}$$ = -e ($$\overrightarrow{\mathrm{v}}$$ × $$\overrightarrow{\mathrm{B}}$$ ) 4. Due to electric field E , the coulomb force starts acting on free electrons along AB. $$\overrightarrow{\mathrm{F}}_{\mathrm{B}}$$ = -e$$\overrightarrow{\mathrm{E}}$$ 5. Magnitude of $$\overrightarrow{\mathrm{E}}$$ increasing as long as accumulation of electrons at the end A continues $$\overrightarrow{\mathrm{F}}_{\mathrm{E}}$$ increases until equilibrium is reached. 6. At equilibrium, $$\left\|\overrightarrow{\mathrm{F}}_{\mathrm{B}}\right\|=\left\|\overrightarrow{\mathrm{F}}_{\mathrm{E}}\right\|$$ $$\|-e(\vec{v} \times \vec{B})\|=\|-e \quad \overrightarrow{\mathrm{E}}\|$$ vB sin 90° = E vB = E 7. The Potential difference is V = El V = vBl So, ε = Blv 8. An emf is produced due to movement of rod, it is called as motional emf. 9. If A and B are connected by external circuit of resistance R, then the current $$i=\frac{\varepsilon}{R}=\frac{B l V}{R}$$ flows in it. 10. Direction of current is found from right-hand thumb rule. Question 5. Give the uses of Foucault current. Though the production of eddy current is undesirable in some cases, it is useful in some other cases. A few of them are 1. Induction stove 2. Eddy current brake 3. Eddy current testing 4. Electromagnetic damping 1. Induction stove: An induction stove is used to cook the food quickly and safely with less energy consumption. Below the cooking zone, there is a tightly wound coil of insulated wire. The cooking pan made of a suitable material is placed over the cooking zone. When the stove is switched on, an alternating current flowing in the coil produces a high frequency alternating magnetic field which induces very strong eddy currents in the cooking pan. The eddy currents in the pan produce so much of heat due to Joule heating which is used to cook the food. 2. Eddy current brake: This eddy current braking system is generally used in high-speed trains and roller coasters. Strong electromagnets are fixed just above the rails. To stop the train, electromagnets are switched on. The magnetic field of these magnets induces eddy currents in the rails which oppose or resist the movement of the train. This is Eddy’s current linear brake. In some cases, the circular disc, connected to the wheel of the train through a common shaft, is made to rotate in between the poles of an electromagnet. When there is a relative motion between the disc and the magnet, eddy currents are induced in the disc which stop the train. This is Eddy current circular brake. 3. Eddy current testing: It is one of the simple non-destructive testing methods to find defects like surface cracks and air bubbles present in a specimen. A coil of insulated wire is given an alternating electric current so that it produces an alternating magnetic field. When this coil is brought near the test surface, eddy current is induced in the test surface. The presence of defects causes the change in phase and amplitude of the eddy current that can be detected by some other means. In this way, the defects present in the specimen are identified. 4. Electromagnetic damping: The armature of the galvanometer coil is wound on a soft iron cylinder. Once the armature is deflected, the relative motion between the soft iron cylinder and the radial magnetic field induces eddy current in the cylinder. The damping force due to the flow of eddy current brings the armature to rest immediately and then the galvanometer shows a steady deflection. This is called electromagnetic damping. Question 6. Define self – inductance of a coil in terms of (i) magnetic flux and (ii) induced emf. 1. Let be the magnetic flux linked each turn of the coil of N turns, then the total flux linked with the coil NPB is proportional to the current i in the coil B α i B = Li ……………(1) 2. Self-inductance of a coil is defined as the flux linkage of the coil when 1 A current flows through it. L = $$\frac{\mathrm{N} \Phi_{\mathrm{B}}}{i}$$ If i = 1A then L = NφB 3. When the current i changes with time, an emf is induced in it. From Faradys law of electro magnetic induction, this self induced emf is given ε = $$-d \frac{\left(\mathrm{N} \varphi_{\mathrm{B}}\right)}{d t}=-d \frac{(\mathrm{Li})}{d t}$$ Using equation (1) L = $$\frac{-\varepsilon}{d i / d t}$$ If di/dt = 1A.S-1 then L = -ε 4. Self inductance of coil is defined as opposing emf induced in the coil when the rate of change of current through the coil is 1As-1 Question 7. How will you define the unit of inductance? Unit of inductance: Inductance is a scalar and its unit is Wb A-1 or V s A-1. It is also measured in henry (H). 1 H = 1 Wb A-1 = 1 V s A-1 The dimensional formula of inductance is M L2 T-2A-2. If i = 1 A and NΦB = 1 Wb turns, then L = 1 H. Therefore, the inductance of the coil is said to be one henry if a current of 1 A produces unit flux linkage in the coil. If $$\frac { di}{ dt }$$ = 1 As-1 and ε = -1 V, then L = 1 H. Therefore, the inductance of the coil is one henry if a current changing at the rate of 1 A s-1 induces an opposing emf of 1 V in it. Question 8. What do you understand by the self-inductance of a coil? Give its physical significance. Self Inductance of coil: 1. Inductance or simply inductance of a coil is defined as the flux linkage of the coil when I A current flows through it. 2. Inductance of a coil is also defined as opposing emf induced in the coil when the rate of change of current through the is 1 As-1. Physical Significance: 3. In translational motion, mass is measure of inertia, for rotational motion, moment of inertia is a measure of rotational inertia. 4. The inductance plays the same role in circuit as mass and moment of inertia play in mechanical motion. 5. When a circuit is switched on, the increasing current induces on emf which opposes the growth of current in circuit (Figure (a)) 6. Induced emf e opposes the changing current i When circuit is broken, the decreasing current induces an emf in the reverse direction. This emf now opposes the decay of current (Figure (b)) 7. Thus, inductance of the coil opposes any change in current and tries to maintain the original state. Question 9. Assuming that the length of the solenoid is large when compared to its diameter, find the equation for its inductance. 1. Consider a long solenoid of length l and cross-sectional area A. Let n be the number of turns per unit length (1> n). 2. When the current i pass through solenoid, uniform magnetic field B is produced. B = µ0ni 3. The magnetic field passes through each turn is ΦB = $$\int_{A} \vec{B} \cdot d \vec{A}$$ = BA cosθ = BA, Since θ = 0° ΦB = (µ0 ni)A Self inductance of a long solenoid 4. Total magnetic flux of solenoid with N turns (N = nl) B = (nl)(µ0 ni) AB B = (µ0 n2 Al) i 5. we have L = µ0n2Al 6. Inductance depends on geometry of solenoid and medium present inside the solenoid. 7. For dielectric medium of µr L = µn2Al (or) L = µ0 µr n2 Al Question 10. An inductor of inductance L carries an electric current i. How much energy is stored while establishing the current in it? When current is established in circuit, inductance opposes the growth of current. So, work is done against this opposition by external agency. This work done is stored as magnetic potential energy. Induced emf at any instant is ε = -L$$\frac{d i}{d t}$$ Work done dW = -ε dq = -εidt ∴ dq = idt Substituting for ε from first equation ε = -L $$\frac{d i}{d t}$$ dw = -(-L $$\frac{d i}{d t}$$) i dt dw = Li di Total work done W = ∫ dw = $$\int_{0}^{i}$$Li di = L$$\left[\frac{i^{2}}{2}\right]$$ W = $$\frac{1}{2}$$ Li2 This work done is stored as magnetic potential energy ∴ UB = $$\frac{1}{2}$$ Li2 Energy density is the energy stored per unit volume of space UB = $$\frac{\mathrm{U}_{\mathrm{B}}}{\mathrm{Al}}$$ ∴ Volume of solenoid = Al Question 11. Show that the mutual inductance between a pair of coils is same (M12 = M21) Consider two coils placed close to each other, i1 is the electric current sent through coil 1 linked with coil 2. Let Φ21 be the magnetic flux linked with coil 2 of N2 due to coil 1 N2 Φ21 α i1 N2 Φ21 = M21 i1 M21 = $$\frac{\mathrm{N}_{2} \Phi_{21}}{i_{1}}$$ M21 is called mutual inductance of coil 2 with respect to coil 1. It is also called coefficient of mutual inductance. If i1 = 1A then M21 = N2 Φ21 Mutual Inductance M21 is defined as flux linkage of coil 2 when 1 A current flows through coil 1. When i1 changes with time emf ε2 is induced in coil 2. From Faraday’s law of electromagnetic induction Mutual inductance M21 is defined as emf induced in coil 2 when rate of change of current through the coil I is 1 As-1 Similarly, M12 = $$\frac{\mathrm{N}_{1} \Phi_{12}}{i_{2}}$$ and M12 = $$\frac{-\varepsilon_{2}}{d i_{2} / d t}$$ The mutual inductance is same ie M21 = M12 = M The mutual inductance between two coils depends on size, shape, number of turns of the coils, relative orientation and permeability of the medium. Question 12. How will you induce an emf by changing the area enclosed by the coil? 1. Consider a conducting rod of length l moving with velocity v towards left. 2. The whole arrangement is in uniform magnetic field $$\overrightarrow{\mathrm{B}}$$, magnetic lines perpendicular to plane of the paper. 3. As the rod moves from AB to CD in time dt area enclosed by the loop and the magnetic flux through the loop decreases. Induction of emf by changing the area enclosed by the loop Change in magnetic flux in time dt is B = B × change in area = B × Area ABCD = Blv dt (or) $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ = Blv The magnitude of induced emf. ε = $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ ε = Blv The emf is called motional Emf, Direction of induced current is clockwise from Flemings Right hand rule. Question 13. Show mathematically that the rotation of a coil in a magnetic field over one rotation induces an alternating emf of one cycle. 1. Consider a rectangular coil of N turns in a uniform magnetic field $$\overrightarrow{\mathrm{B}}$$ 2. Coil rotates with angular velocity ω about an axis in an anticlockwise direction perpendicular to the field. 3. At t = 0 plane of coil is perpendicular to the field so flux linked with the coil is Φm = BA 4. At t seconds coil is rotated through angle Φ flux is Φm cos ωt, component of Φm normal to the coil. Variation of induced emf as a function ωt According to Faraday’s law the ernf at any instant is ε = –$$\frac{\mathrm{d}}{\mathrm{dt}}$$ (N ΦB) = –$$\frac{\mathrm{d}}{\mathrm{dt}}$$ (N Φm cos ωt) = -NΦm(-sin ωt) ω = NΦm ω sin ωt 5. When the coil is rotated through 90°, sin ωt = 1. 6. The maximum induced emf is εm = NΦm ω εm = NBAω since Φm = BA ∴ Value of induced emf at any instant is ε = εm sin ωt The alternating current is given by i = Im sin ωt Im = maximum value of induced current. Question 14. Elaborate the standard construction details of AC generator. Alternator consists of two major parts namely stator and rotor. i) Stator: 1. The stationary part which has armature windings mounted in it, is called stator. 2. This is outer frame used for holding stator core and armature windings in proper position. It provides best ventilation. Stator core: It is made up of iron or steel alloy. It is hollow cylinder and is laminated to minimize eddy current. Armature winding: 1. It is the coil, wound on slots, provided in the armature core. 2. Two types are single layer winding and double layer winding. ii) Rotor: 1. Rotor contains magnetic field windings. Magnetic poles are magnetized by DC source. 2. Ends of field wings are connected to slip rings attached to rotor rotates. 3. Slip rings rotate along with the rotor. 4. Brushes are used which continuously slide over slip rings to maintain connection between DC source and windings. 5. Two types of rotors are i) salient pole rotor. ii) cylindrical pole rotor. i) Salient pole rotator: It has a number of projecting poles having their bases riveted to the rotor. It is used in low-speed alternators. ii) Cylindrical pole rotor: It consists of a smooth solid cylinder. The slots are cut on the outer surface of the cylinder along its length. It is suitable for very high-speed generator. Question 15. Explain the working of a single-phase AC generator with the necessary diagram. 1. The loop PQRS is stationary and perpendicular to plane, when field windings are excited, magnetic field is produced around it. 2. Let field magnet be rotated in clockwise direction. Assume initial position is horizontal, direction of magnetic field is perpendicular to plane of loop PQRS Induced emf is zero. It is represented by O in the graph. 3. When rotates to 90°, magnetic field is parallel to PQRS, an induced emf becomes maximum. Direction of induced emf is given by Flemming’s right hand rule. The loop PQRS ad field magnet in its initial position Variation of induced emf with respect to time angle 4. When rotates to 180°, field is perpendicular to PQRS, an induced emf is zero. It is represented by point B. 5. When rotates to 270°, field is parallel to PQRS, an induced emf is maximum but in reverse direction. 6. Current flows in SRQP. It is represented by point C. 7. On completion of 360°, field is perpendicular to PQRS, an induced emf is zero and noted by point D. 8. When field magenets complete one rotation, induced emf in PQRS finishes one cycle. 9. Frequency depends on speed of field magnet rotates. Question 16. How are the three different EMFs generated in a three-phase AC generator? Show the graphical representation of these three EMFs. 1. In three-phase AC generator, the armature has 6 slots cut on its inner rim. Each slot is 60° away from one another. Six armature conductors mounted in these slots. 2. The conductors 1 and 4 joined in series to form coil 1. The conductors 3 and 6 form coil 2. The conductors 5 and 2 form coil 3. 3. These coils are rectangular and 120° apart from one another. 4. The initial position of field magnets is horizontal and direction is perpendicular to plane of coil 1. 5. When rotates from clockwise direction alternating emf in coil 1 begins a cycle from 0. 6. The corresponding cycle for in coil 2 starts at A after field magnet rotated through 120°. 7. So phase difference between ε1 and ε2 is 120°. 8. Similarly ε3 in coil 3 would begin its cycle at B after 240° from initial position. 9. Thus emfs produced in three-phase AC generator have 120° phase difference between one another. Construction of three – Phase AC generator Variation of emfs ε1, ε2, and ε3 with time angle Question 17. Explain the construction and working of transformer. 1. The principle of transformer is the mutual induction between two coils. 2. Two coils of high mutual inductance wound over the transformer core. 3. The core is laminated and made up of silicon steel. 4. Coils are insulated but magnetically linked via transformer core. 5. The coil across which alternating voltage is applied is called primary coil P. 6. Core and coil are kept in containers filled with suitable medium for insulation and cooling. Construction of Transformer Working: 1. If primary coil is connected with a.c input voltage the production of alternative magnetic flux linked with primary coil is linked with secondary coil. 2. As a result of flux change emf is induced in both coils. 3. Emf induced in primary coil is νp = εp = -Np $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ ……………(1) 4. Emf induced in secondary coil is εS = -NS $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ 5. Np, NS is a number of turns in primary and secondary coil. 6. If secondary circuit is open εS = νS νS = εS = -NS $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ ………………….(2) 7. From eqn (1) and (2) $$\frac{v_{S}}{v_{p}}=\frac{N_{S}}{N_{P}}=K$$ ………………(3) p is voltage transformer ratio 8. For ideal transformer, Input power vpip = Output power vsis (ip, is are currents in Primary and secondary coil) $$\frac{\mathrm{V}_{\mathrm{S}}}{\mathrm{V}_{\mathrm{P}}}=\frac{\mathrm{N}_{\mathrm{S}}}{\mathrm{N}_{\mathrm{P}}}=\frac{\mathrm{i}_{\mathrm{P}}}{\mathrm{i}_{\mathrm{S}}}$$ ………..(4) $$\frac{\mathrm{V}_{\mathrm{S}}}{\mathrm{V}_{\mathrm{P}}}=\frac{\mathrm{N}_{\mathrm{S}}}{\mathrm{N}_{\mathrm{P}}}=\frac{\mathrm{i}_{\mathrm{P}}}{\mathrm{i}_{\mathrm{S}}}=\mathrm{K}$$ Step up transformer: (i) If Ns > Np or K > I, Vs > Vp and Is < Ip Voltage is increased, the current is decreased. (ii) Step down transformer Ns < Np or K< l, Vs < Vp and Is > Ip Voltage is decreased, the current is increased. Effeciency of a transformer, η = $$\frac{\text { Output power }}{\text { Input power }}$$ × 100% Question 18. Mention the various energy losses in a transformer. i) Core loss or Iron loss: 1. Hysteresis loss and eddy current loss are known as core or Iron loss. 2. When transformer core is magnetized and demagnetized repeatedly by a.c voltage Hysteresis loss takes place. It is minimized by silicon steel core. 3. Alternating magnetic flux in core induce eddy current, due to flow of eddy current energy loss takes place. It is minimized by thin lamination of transformer core. ii) Copper loss: When current flows through core energy is dissipated due to Joule heating. It is a copper loss, it is minimized by using large-diameter wire. iii) Flux leakage: Flux leakage happens, when the magnetic lines of the primary coil are not completely linked with the secondary coil. Energy loss due to flux leakage is minimized by winding coil one over the other. Question 19. Give the advantage of AC in long-distance power transmission with an example. 1. When power is transmitting for long-distance a fraction of power is lost due to joule heating (I2R). 2. This power loss can be tackled either by reducing current i or by reducing resistance R of a transmission line. 3. At the transmitting point, voltage is increased and the current is decreased by a step-up transformer. 4. This reduced current at high voltage reaches the destination without applicable loss. 5. At the receiving point, voltage is decreased and current is increased by step down transformer. Example 1: 2MW power is transmitted at 40Ω with 10 kV voltage I = $$\frac{P}{V}=\frac{2 \times 10^{6}}{10 \times 10^{3}}$$ = 200 A Power loss = I2 R = (200)2 × 40 = 1.6 × 106 W % of Power loss = $$\frac{1.6 \times 10^{6}}{2 \times 10^{6}}$$ × 100% = 80% Example 2: When 2MW power at 40 Q is transmitted with 100 kV voltage. I = $$\frac{P}{V}=\frac{2 \times 10^{3}}{100 \times 10^{3}}$$ = 20 A Power loss = I2 R = (200)2 × 40 = 0.016 × 106 W % of power loss = $$\frac{0.016 \times 10^{6}}{2 \times 10^{6}}$$ × 100% = 0.8 × 100% = 80% Question 20. Find out the phase relationship between voltage and current in a pure inductive circuit. 1. Consider a circuit containing pure inductor L across a.c. voltage source 2. υ = Vm sin ωt Back emf ε = – L $$\frac{d i}{d t}$$ 3. By applying kirchoff’s loop rule ν + ε = 0 Vm sin ωt = L $$\frac{d i}{d t}$$ di = $$\frac{V_{m}}{L}$$ sin ωt dt Integrating both sides. Phasor diagram and wave diagram for AC circuit with L. i = $$\frac{V_{m}}{L}$$ ∫ sin ωt dt i = $$\frac{V_{m}}{L}$$ (- cos ωt) + constant i = $$\frac{V_{m}}{L}$$ sin (ωt – π/2) or i = Im sin (ωt – π/2) where, $$\frac{V_{m}}{\omega L}$$ = Im. The peak value of a.c current lags behind voltage by π/2 in inductive circuit in phasor diagram. In wave diagram current lags voltage by 90°. Im = $$\frac{V_{m}}{\omega L}$$ The quantity ωL is the resistance offered by inductor and called inductive reactance (χL) χL = ωL for ideal inductor χL = 0 Question 21. Derive an expression for phase angle between the applied voltage and current in a series RLC circuit. AC circuit containing R, L and C Phasor diagram for a series RLC – circuit when VL > VC L(VL) leads I by π/2 and voltage across C(VC) lags I by π/2 Phasor diagram is drawn with the current. The length of these phasors are OI = Im, OA = ImR, OB = ImχL; OC = ImχC Vm2 = VR2 + (VL – VC)2 Special cases: i) If χL> χC, (χL – χC) is positive and Φ is also positive. ∴ υ = Vmsin ωt; i = Im(sin(ωt – Φ)) ii) if χL < χC, (χL – χC) is negative and Φ is negative. ∴ υ = Vmsin ωt; i = Im(sin(wt + Φ)) Question 22. Define inductive and capacitive reactance. Give their units. 1. Resistance offered by inductor is called inductive reactance (χL). Its unit is the ohm (Ω) χL = ωL If f = 0. χL = 0. 2. Resistance offered by capacitor is called capacitive reactance (χC). Its unit is also ohm (Ω) χC = $$\frac{1}{\omega C}$$ If f = 0 ; χC = $$\frac{1}{\omega C}$$ = $$\frac{1}{2 \pi f C}=\frac{1}{0}$$ = ∞ Question 23. Obtain an expression for the average power of AC over a cycle. Discuss its special cases. In RLC circuit, υ = Vm sin ωt and i = Im sin (ωt + Φ) where Φ is phase angle between υ and i Instantaneous power is p = υi = Vm Im sin ωt sin (ωt + Φ) = Vm Im sin ωt (sin ωt cos Φ – cos ωt sin Φ) P = Vm Im(cos Φ sin2ωt – sinωt cosωt sin Φ) Average power over a cycle, Pav = Vm Im cos Φ × $$\frac{1}{2}$$ = $$\frac{V_{m}}{\sqrt{2}} \frac{I_{m}}{\sqrt{2}}$$ cos Φ ∴ Pav = VRMS IRMS P cos Φ VRMS IRMS is apparent power cos Φ is power factor Average power of AC circuit is known as the true power of circuit. Special Cases: i) For pure resistive circuit phase angle is zero, cos Φ = 1 ∴ Pav = VRMS IRMS ii) For pure inductive or capacitive circuit cos (± π/2) = 0 ∴ Pav = 0 iii) For RLC circuit Φ = $$\tan ^{-1}\left(\frac{X_{L}-X_{L}}{R}\right)$$ ∴ Pav = VRMS IRMS iv) For RLC circuit at resonance cos Φ = 1 ∴ Pav = VRMS IRMS Question 24. Explain the generation of LC oscillation in a circuit containing an inductor of inductance L and a capacitor of capacitance C. LC Oscillations: Whenever energy is given to a circuit containing a pure inductor of inductance L and a capacitor of capacitance C, the energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor. Thus the electrical oscillations of definite frequency are generated. These oscillations are called LC oscillations. LC Oscillations Generation of LC oscillations: 1. Let us assume that the capacitor is fully charged with maximum charge Qm at the initial stage. So that the energy store in the Qm capacitor is maximum and is given by UE = $$\frac{Q_{m}^{2}}{2 C}$$ 2. As there is no current in the inductor, the energy stored in it is zero i.e., UE = 0. Therefore, the total energy is wholly electrical. (Figure (a)). 3. The capacitor now begins to discharge through the inductor that establishes current i in a clockwise direction. This current produces a magnetic field around the inductor and the energy stored in the inductor is given by UE = $$\frac{\mathrm{Li}^{2}}{2}$$ As the charge in the capacitor decreases, the energy stored in it also decreases and is given by UE = $$\frac{q^{2}}{2 C}$$ total energy is the sum of electrical and magnetic energies. (Figure (b)). 4. When the charges in the capacitor are exhausted, its energy becomes zero i.e., UE = 0. The energy is fully transferred to the magnetic field of the inductor and its energy is maximum. 5. This maximum energy is given by UE = $$\frac{\mathrm{Li}^{2}}{2}$$ where Imis the maximum current flowing in the circuit. The total energy is wholly magnetic (Figure (c)). 6. Even though the charge in the capacitor is zero, the current will continue to flow in the same direction because the inductor will not allow it to stop immediately. 7. As a result of this, the capacitor begins to charge in the opposite direction. A part of the energy is transferred from the inductor back to the capacitor. The total energy is the sum of the electrical and magnetic energies. (Figure (d)). 8. (Fig. e) i = o the capacitor becomes fully charged in the opposite direction. 9. (Fig. f) The state of the circuit is similar to the initial state but the difference is that the capacitor is charged in opposite direction. ∴ Total energy = UE + UB. 10. As already explained, the process repeated in opposite direction (Fig. g and h). Finally alternating current flows in the circuit. 11. This process is repeated again and again to produce LC Oscillations. Question 25. Prove that the total energy is conserved during LC oscillations. 1. LC oscillation takes place in accordance with law of conservation of energy. 2. Total energy U = UE + UB = $$\frac{q^{2}}{2 C}+\frac{1}{2} L i^{2}$$ Case (i): When q = Qm and i = O Total energy is U = $$\frac{\mathrm{Q}_{\mathrm{m}}^{2}}{2 \mathrm{C}}$$ + o = $$\frac{\mathrm{Q}_{\mathrm{m}}^{2}}{2 \mathrm{C}}$$ Total energy is wholly electrical. Case (ii): When q = O i = Im total energy is U = 0 + $$\frac{1}{2} L I^{2}$$ = $$\frac{1}{2} L I^{2}$$ = $$\frac{L}{2} \times\left(\frac{Q^{2} m}{L_{C}}\right)$$ since Im = Qm ω = $$\frac{Q_{m}}{\sqrt{L M}}$$ = $$\frac{Q^{2} m}{2 C}$$ Total energy is wholly magnetic Case (iii): When charge = q, current = i Question 26. Compare the electromagnetic oscillations of the LC circuit with the mechanical oscillations of the block spring system qualitatively to find the expression for the angular frequency of LC oscillators mathematically. i) Qualitative treatment: • Two forms of energy involved in LC oscillations. The’ are 1. electrical energy of capacitor. 2. Magnetic energy of inductor. • Angular frequency of oscillations of spring mass is ω = $$\sqrt{\frac{k}{m}}$$ where k → 1/C and m → L ω = $$\frac{1}{\sqrt{L C}}$$ …………..(1) ii) Quantitative treatment: Mechanical energy of spring mass system, E = $$\frac{1}{2}$$ mv2 + $$\frac{1}{2}$$ kx2 …………(2) m = $$\frac{d^{2} x}{d t^{2}}$$ + kx = 0 ………………..(3) x(t) = Xm cos(ωt + Φ) Electromagnetic energy of LC system is $$\mathrm{U}=\frac{Q_{m}^{2} \cos ^{2} \omega \mathrm{t}}{2 \mathrm{C}}+\frac{L \omega^{2} Q_{m}^{2} \sin ^{2} \omega \mathrm{t}}{2}$$ U = $$\frac{1}{2} L i^{2}+\frac{1}{2}\left(\frac{1}{C}\right) q^{2}$$ = constant ……………(5) Differentiate w.r.t to time $$\frac{d U}{d t}=\frac{1}{2} \mathrm{~L}\left(2 \mathrm{i} \frac{d i}{d t}\right)+\frac{1}{2 C}\left(2 q \frac{d q}{d t}\right)=0$$ $$L \frac{d^{2} q}{d t^{2}}+\frac{1}{C} q=0$$ ………………(6) q(t) = Qm cos(ωt + Φ) ……………..(7) current i(t) i(t) = – Im sin (ωt + Φ) ……………..(8) Angular frequency of LC oscillations $$\frac{d^{2} q}{d t^{2}}$$ = – Qm ω2 cos(ωt + Φ) ……………(9) Substituting (7) and (9) in (6) L[- Qm ω2 cos(ωt + ΦΠ)] + $$\frac{1}{C}$$ Qm cos(ωt + Φ) = 0 Rearranging the terms, angular frequency of LC oscillation is ω = $$\frac{1}{\sqrt{L C}}$$ IV. Numeric Problems: Question 1. A square coil of side 30 cm with 500 turns is kept in a uniform magnetic field of 0.4 T. The plane of the coil is inclined at an angle of 30° to the field. Calculate the magnetic flux through the coil. Given data: Area A = 30 × 30 × 10-4 m2 n = 500 B = 0.4 T Q = 90° – 30° = 60° Φ = nBA cos Φ =500 ×30 × 30 × 10-4 × 0.4 × cos60° = 5 × 10 × 0.4× 9 × $$\frac{1}{2}$$ = 5 × 0.2 × 9 × 10 = 5 × 0.2 × 9 × 10-1 = 1.0 × 9 × 10-1 = 9 wb Φ = 9 wb Question 2. A straight metal wire crosses a magnetic field of flux 4 mWb in a time of 0.4 s. Find the magnitude of the emf induced in the wire. Given data: dΦ = 4 mWb = 4 × 10-3 dt = 0.4 s induced emf ε =? Question 3. The magnetic flux passing through a coil perpendicular to its plane is a function of time and is given by φB = (2t3 + 4t2 + 8t + 8) Wb. If the resistance of the coil is 5Ω, determine the induced current through the coil at a time t = 3 second. Given data : φB = (2t3 + 4t2 + 8t + 8) Wb R = 5Ω t = 3second induced current i = ? i = $$\frac{\varepsilon}{\mathrm{R}}$$ ε = $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ ε = $$\frac{d}{d t}\left(2 t^{3}+4 t^{2}+8 t+8\right)$$ ε = 6t2 + 8t + 8 at t = 3second, ε = 6 × 32 × 8 × 3 + 8 ε = 54 + 24 + 8 ε = 86 V ∴ i = $$\frac{\varepsilon}{R}=\frac{86}{5}$$ = 17.2 A i = 17.2 A Question 4. A closely wound circular coil of radius 0.02 m is placed perpendicular to the magnetic field. When the magnetic field is changed from 8000 T to 2000 T in 6s, an emf of 44 V is induced in it. Calculate, the number of turns in the coil Given data: Q = 90° – 90° = 0° B1 = 8000 T, B2 = 2000 T dt = 68 ε = 68V n = ? ε = nA cos θ $$\frac{\mathrm{dB}}{\mathrm{dt}}$$ Question 5. A rectangular coil of area 6 cm2 having 3500 turns is kept in a uniform magnetic field of 0.4 T. Initially, the plane of the coil is perpendicular to the field and is then rotated through an angle of 180°. If the resistance of the coil of 35Ω, find the amount of charge following through the coil. Given data: Area A = 6 × 10-4 m2 n = 3500 B = 0.4 T Q1 = 180° R = 35Ω amount of charge Q =? Q = di.dt = $$\frac{\varepsilon}{R}$$ dt Question 6. An induced current of 2.5 mA flows through a single conductor of resistance 1ooΩ. Find out the rate at which the magnetic flux is cut by the conductor. Given data: Induced current i = 2.5 mA i= 2.5 × 10-3 A Resistance R = 100Ω ε = $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ where ε = iR ∴ $$\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ = iR = 2.5 × 10-3 × 100 = 250 × 10-3 = 250 mWbs-1 Question 7. A fan of metal blades of length 0.4 m rotates normal to a magnetic field of 4 × 10-3 T. If the induced emf between the center and edge of the blade is 0.02 V, determine the rate of rotation of the blade. Given data: length = 0.4 m B = 4 × 10-3 T ε = 0.02 V The rate of rotation υ =? Question 8. A bicycle wheel with metal spokes of 1m long rotates in Earth’s magnetic field. The plane of the wheel is perpendicular to the horizontal component of Earth’s field of 4 × 10-5 T. If the emf induced across the spokes is 31.4 mV, calculate the rate of revolution of the wheel. length l = 1 m B = 4 × 10-5 T E = 3.14 mV = 3.14 × 10-3 V The rate of revolution = ? Question 9. Determine the self-inductance of 4000 turn air-core solenoid of length 2 m and diameter 0.04 m. Given data: n = 4000 l = 2m diameter d = 0.04 m Self inductance L =? L = µnA2 l L = 4π × 10-7 × 4000 × π × 0.02 × 0.02 × 2 L = 16π × 10-1 × π × 8 × 10-4 L = 1262 × 10-5 L = 12.62 × 10-3 H L = 12.62 mH Question 10. A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 x 10-5 Wb, find the magnetic energy stored in the medium surrounding the coil. Given data: N = 200 turns i = 4A ΦB = 6 × 10-5 Wb Magnetic energy UB =? Question 11. A 50 cm long solenoid has 400 turns per cm. The diameter of the solenoid is 0.04m. Find the, magnetic flux linked turn when it carries a current of IA. Given data: Length of the solenoid, l = 50 cm = 50 × 10-2 m No. of turns / cm = 400 For 50 cm, No. of turns N = 400 × 50 = 20,000 Diameter of the solenoid = 0.04 m ∴ Radius of the solenoid = 0.02 m Current passing through the solenoid = 1 A Area of the solenoid = πr² = 3.14 × 0.02 × 0.02 m2 Formula :- Magnetic flux, φ = µ0 n2 AIl Question 12. A coil of 200 turns carries a current of 0.4 A. If the magnetic flux of 4m Wb is linked with each turn of the coil, find the inductance of the coil. Given data: N = 200 i = 0.4 A ΦB = 4 mWb = 4 × 10-3 Wb L = ? Bi = Li Question 13. Two air core solenoids have the same length of 80 cm and same cross-sectional area 5 cm2. Find the mutual inductance between them if the number of turns in the first coil is 1200 turns and that in the second coil is 400 turns. Given data: l = 80cm A = 52 = 5 × 10-4 m2 = 80 × 10-2 m turns = 1500 turns n1 = $$\frac{1200}{0.8}$$; n1 = 1500turns n2 = $$\frac{400}{0.8}$$; n2 = 500 turns M = ? Mn = μ0 n1 n2 A2 l M = 4π × 10-7 × 1500 × 1500 × 5 × 10-4 × 0.8 M = 4π × 10-7 × 75 × 5 × 0.8 M = 3768 × 10-7 H = 0.3768 × 10-3 H M = 0.38 mH Question 14. A long solenoid having 400 turns per cm carries a current 2A. A 100 turn coil of cross-sectional area 4cm2 is placed co-axially inside the solenoid so that the coil is in the field produced by the solenoid. Find the emf induced in the coil if the current through the solenoid reverses its direction in 0.04 sec. Given data: n1 = 400 turns/cm ∴ n1 = 4000 turns/m n2 = 100 A2 = 4 × 10-4 m2 i = 1 m di = 2-(-2) = 48 dt = 0.04 sec Question 15. A 200 turn circular coil of radius 2 cm is placed co-axially within a long solenoid of 3 cm radius. If the turn density of the solenoid is 90 turns per cm, then calculate mutual inductance of the coil and solenoid. Given data: r2 = 2 cm, n2 = 200 r1 = 3 cm n1 = 90 turns/cm n1 = 9000 turns/m M =? M = μ0 n1 n2 A2 l M = 4π × 10-7 × 280 × 9000 × π × 4 × 10-4 × 1 M = 4π × 10-6 × 18 × 4π M = 2.839.56 × 10-6 H M = 2.839 × 10-3 H M = 2.84 mH Question 16. The solenoids S1 and S2 are wound on an iron-core of relative permeability 900. The area of their cross-section and their lengths are the same and are 4 cm2 and 0.04 m respectively. If the number of turns in S1 is 200 and that in S2 is 800, calculate the mutual inductance between the solenoids. If the current in solenoid 1 is increased from 2A to 8A in 0.04 second. Calculate the induced emf in solenoid 2. Given data: μr = 900 A2 = 4 × 10-4 m2 l = 0.04 m n1 = 5000 n2 = 20,000 i1 =2A to i2 = 8A dt = 0.048 M = ? ε2 = ? Solution: M = μ0 μr n1 n2 A2 l M = 4π × 10-7 × 900 × 5000 × 20000 × 4 × 10-4 ×0.04 M = 4π × 90 × 4 × 4 × 10-4 M = 18086 × 10-4H M = 1.81 H induced emf, ε2 = M $$\frac{d i}{d t}$$ ε2 = 1.81 $$\left(\frac{(8-2)}{0.04}\right)$$ ε2 = $$\frac{1.81 \times 6}{4 \times 10^{-2}}$$ = 2.715 × 10-2 V ε2 = 271.5 V Question 17. A step-down transformer connected to main supply of 220 V is used to operate 11V, 88W lamp. Calculate (i) Transformation ratio and (ii) current in the primary Given data: Vp = 220 V, Ps = 88 W, Vs = 11 V Question 18. A 200 V/ 120 V step down transformer of 90% efficiency is connected to an induction stove of resistance 40Ω. Find the current drawn by the primary of the transformer. Given data: Vp = 200 V Vs = 120 V η = 90% = $$\frac{90}{100}$$ = 0.9 η = $$\frac{\text { output power }}{\text { input power }}$$ Question 19. The 300 turn primary of a transformer has resistance 0.82 Q and the resistance of its secondary of 1200 turns is 6.2 Q. Find the voltage across the primary if the power output from the secondary at 1600 V is 32 kW. Calculate the power losses in both coils when the transformer efficiency is 80%. Given data: NP = 300 NS = 1200 VS = 1600 V, RP = 0.82Ω RS = 6.2Ω PS = 32 KW iv) Power loss in primary = (IP)2 × RP = 100 × 1000 × 0.82 = 0.82 × 1000 = 8.2000 = 8.2 KW v) Power loss in secondary = (IS)2 × RS = 20 × 20 × 6.2 = 400 × 6.2 = 2480W = 2.48 KW Question 20. Calculate the instantaneous value at 60°, average value and RMS value of an alternating current whose peak vaue is 20A. Given data: Im = 20 A Q = 60° i) Instantaneous value of current i = Im sin θ = 20 × Sin 60° = 20 × $$\frac{\sqrt{3}}{2}$$ = 10 × √3 = 10 × 1.732 i = 17.32 A ii) Average value Iav = 0.637 Im Iav = 0.637 × 20 = 6.37 × 2 Iav = 12.74 A iii) Irms = 0.707 Im = 0.707 × 20 = 7.07 × 2 Irms = 14.14 A V. Conceptual Questions: Question 1. A Graph between the magnitude of the magnetic flux linked with a closed-loop and time is given in the figure. Arrange the regions of the graph in ascending order of the magnitude of induced emf in the loop. induced emf ε = $$\frac{-\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}$$ i) Φ – t graph at ab is a straight line ∴ $$\frac{\mathrm{d} \phi}{\mathrm{dt}}$$ = constant ∴ ε = -ve and constant ii) Φ – t graph at bc, Φ is constant ∴ ε = 0 iii) Φ – t graph at cd is a straight line $$\frac{\mathrm{d} \phi}{\mathrm{dt}}$$ = constant ∴ ε = true and constant iv) ab, bc, cd are ascending order of the magnitude of induced emf. Question 2. Using Lenz’s law, predict the direction of induced current in conducting rings 1 and 2 when the current in the wire is steadily decreasing. Current in the wire is steadily decreasing, so the induced current in rings 1 and 2 will flow in such a way that it oppose the decrease of current • ring 1 is clockwise • ring 2 is anti-clockwise Question 3. A flexible metallic loop abcd in the shape of a square is kept in a magnetic field with its plane perpendicular to the field. The magnetic field is directed into the paper normally. Find the direction of the induced current when the square loop is crushed into an irregular shape as shown in the figure. 1. If a wire of irregular shape turns into a square loop then its area increases, so that the magnetic flux linked also increases 2. The induced current is in an anticlockwise direction, along abcd. Question 4. Predict the polarity of the capacitor in a closed circular loop when two bar magnets are moved as shown in the figure. 1. From Lenz’s law, the direction of the induced current is in a clockwise sense. 2. This implies that plate A of the capacitor is at a higher potential than plate B 3. B will be a negative plate while A will be a positive plate. Question 5. In a series LC circuit, the voltages across L and C are 180° out of phase. Is it correct? Explain. 1. Yes, it is correct 2. In a pure inductor, the voltage leads the current by a phase angle of 90°. 3. In a perfect capacitor, the voltage lags behind the current by a phase angle of 90° 4. So, In series LC circuit, the voltage across L and C are 180° out of phase. Question 6. When does the power factor of a series RLC circuit become maximum? 1. Cos Φ is the power factor 2. An RLC series circuit, the phase difference between voltage and current is zero when the circuit is at resonance. 3. The power factor becomes maximum. Part II: ### Physics Guide Electromagnetic Induction and Alternating Current Additional Questions and Answers Question 1. A coil of area of cross section 0.5 m2 with 10 turns is in a plane which is perpendicular to an uniform magnetic field of 0.2 Wb/m2. The flux through the coil is – (a) 100 Wb (b) 10 Wb (c) 1 Wb (d) zero (c) 1 Wb Hint: Φ = NBA cos θ = 10 x 0.2 x 0.5 x cos 0° = 1 Wb Question 2. What happens to the current in a coil while alternating a magnet inside it? a) Increase b) decreases c) Remains constant d) Reverse a) Increases Question 3. A wire of length 1 m moves with a speed of 10 ms-1 perpendiculars to a magnetic field. If the emf induced in the wire is 1 V, the magnitude of the field is- (a) 0.01 T (b) 0.1 T (c) 0.2 T (d) 0.02 T (b) 0.1 T Hint: ε = Blv ⇒ B = $$\frac { ε }{ lv }$$ = $$\frac { 1 }{ 1 × 10 }$$ = 0.02 T Question 4. If a conductor 0.2m long moves with a velocity of 0.3m/s in the magnetic field of 5T. Calculate the emf induced a) 0.3 V b) 0.03 V c) 30 V d) 3 V a) 0.3 V Solution: emf = Blv = 5 × 0.2 × 0.3 = 0.3 V Question 5. A coil of cross-sectional area 400 cm2 having 30 turns is making 1800 rev/min in a magnetic field of IT. The peak value of the induced emf is- (a) 113 V (b) 226 V (c) 339 V (d) 452 V (b) 226 V Hint: εm = NBA ω = 30 x 1 x 400 x 10-4 x 30 x 2π = 226 V Question 6. An electric generator consists of a 10-turn square wire loop of a side 50cm. The loop is turned so as to produce 50 Hz A.C. How strong must the magnetic field be for the peak output voltage to be 300V? a) 2.4 T b) 0.417 T c) 2.62 T d) 0.382 T d) 0.382 T Question 7. By accelerating magnet inside the coil current in it _____ a) increases b) decreases c) remains constant d) reverse a) increases Question 8. When a direct current ‘i’ is passed through an inductance L, the energy stored is- (a) Zero (b) Li (c) $$\frac { 1 }{ 2 }$$ Li2 (d) $$\frac {{ L }^{ 2 }}{2i}$$ (c) $$\frac { 1 }{ 2 }$$ Li2 Question 9. In an LCR series circuit, the voltage across each component L, C, and R is 50V. The voltage across the LC combination will be a) 50 V b) 0 V c) 50 V d) 100 V b) 0 V Solution: V = (ωL – $$\frac{1}{\omega_{C}}$$) Irms = ωLIrms – $$\frac{1}{\omega_{C}}$$Irms = 50 – 50 = 0 Question 10. In AC circuit with inductance and capacitance are joined in series, current is found to be maximum when the value of inductance is 0.5 H and capacitance is 8 μF. The angular frequency of applied alternating voltage will be______ a) 400 Hz b) 5000 Hz c) 2 × 105 Hz d) 300 Hz d) 500 Hz Solution: ω = $$\frac{1}{\sqrt{\mathrm{LC}}}$$ = $$1 / \sqrt{0.5 \times 8 \times 10^{-6}}$$ ω = 500 Hz Question 11. AC supply gives 30V which passes through a 10ω resistance. The power dissipated in it is _______. a) 90√2 W b) 90 W c) 45√2 W d) 45 W b) 90 W Solution: P = $$\frac{V^{2}}{R}=\frac{30^{2}}{10}$$ = 90 W Question 12. In an a.c circuit, an alternating voltage e = 200√2 sin 100t volts is connected to a capacitor of capacity 1 μF. The RMS value of the current in the circuit is a) 10 mA b) 100 mA C) 200 mA d) 20 mA d) 20 mA Solution: Question 13. In an a.c circuit, the emf and current at any instant are e = E0 sin ωt, i = I0 sin ωt – Ø Average power is given by a) E0 I0/2 b) (E0 I0/2) sin Φ c) (E0 I0/2) cos Φ d) E0 I0 c) (E0 I0/2) cos Φ Solution: Question 14. AC power is transmitted from a powerhouse at a high voltage as- (a) the rate of transmission is faster at high voltages (b) it is more economical due to less power loss (c) power cannot be transmitted at low voltages (d) a precaution against theft of transmission lines (b) it is more economical due to less power loss Question 15. What is the maximum value of inductance L for which the current is maximum in LCR circuit with C = 10 μF and ω = 1000 s-1 a) 1 mH b) cannot calculate c) 10 mH d) 100 mH d) 100 mH Solution: Question 16. The primary winding of a transformer has 500 turns, whereas its secondary has 5000 turns. Primary is connected to a.c supply of 20V, 50Hz. The secondary will have an output of a) 2 V, 5 Hz b) 200 V, 500 Hz c) 2 V, 50 Hz d) 200 V, 50 Hz d) 200 V, 50 Hz Solution: Question 17. A step-up transformer operates on a 230 V line and supplied a load of 2A. The ratio of primary and secondary wings is 1:25. The current in primary is_______ a) 25 A b) 50 A c) 15 A d) 12.5 A b) 50 A Solution: Question 18. If N is the number of turns in a coil, the value of self-inductance varies as- (a) N° (b) N (c) N2 (d) N-2 (c) N2 Hint: According to self-inductance of the long solenoid L = $$\frac{\mu_{0} \mathrm{N}^{2} \mathrm{A}}{l}$$ ⇒ L ∝ N2 Question 19. A solenoid has n turns. Its coefficient of an inductance L varies with n as a) L α n b) L α n2 c) L α n-1 d) L α n b) L α n2 Question 20. What is the coefficient of mutual inductance when magnetic flux charges by 2 × 10-2 Wb, one’s change in current is 0.01 A a) 2 H b) 3 H c) 1/2 H d) zero a) 2 H Solution: E = M$$\frac{d I}{d t}$$ = 2 × 10-2 × 0.01 = 2 Question 21. The phase difference between VL and VC in series RLC circuit. a) 2π b) $$\frac{\pi}{2}$$ c) $$\frac{2 \pi}{3}$$ d) π d) π Question 22. The quantity that remains unchanged in a transformer is- (a) voltage (b) current (c) frequency (d) none of these (c) frequency Question 23. The direction of the induced current is such that opposes the very cause that has produced it. This is the law of a) Lenz c) Kirchoff d) Fleming a) Lenz Question 24. Which one is correct? a) Self-inductance is directly proportional to the current flowing through the coil b) Self-inductance is directly proportional to the length c) Self-inductance is directly proportional to its area of cross-section d) Self-inductance is inversely proportional to the area of cross-section c) Self-inductance is directly proportional to its area of cross-section Question 25. A coil has a self-inductance of 0.04 H. The energy required to establish a steady-state current of 5 A in it is- (a) 0.5 J (b) 1.0 J (c) 0.8 J (d) 0.2 J (a) 0.5 J Question 26. A 50 mH coil carries a current of 4 amp. The energy stored in joule is_______ a) 0.4 J b) 4.0 J c) 0.8 J d) 0.04 J a) 0.4J Solution: U = $$\frac{1}{2}$$ Li2 = $$\frac{1}{2}$$ × 50 × 10-3 × 45 × (4)2 Question 27. If the angular speed of rotation of an armature of AC generator is doubled, the induced emf will be _______ a) same b) doubled c) halved b) doubled Question 28. Faraday’s law of electromagnetic induction is related to _______ a) law of conservation of charge b) law of conservation of energy c) Third law of Newton d) law of conservation of angular momentum b) law of conservation of energy Question 29. The rms value of an alternating current, which when passed through a resistor produces heat three times of that produced by a direct current of 2 A in the same resistor, is- (a) 6 A (b) 3 A (c) 2 A (d) 2√3 A (d) 2√3 A Hint: $${ I }_{ rms }^{ 2 }$$R = 3(22R) (or) Irms = 2√3 A Question 30. RMS voltage and frequency of V = 230 sin (314t) A.C. source. a) 162.6 V, 50 Hz b) 230 V, 50 Hz c) 230 V, 60 Hz d) 162.6 V, 25 Hz d) 162.6 V, 25 Hz Question 31. From the reactance and frequency graph value of the inductance of given above the inductor is a) 3.18 × 10-14 H b) 1/100π H c) 50π H d) 6.37 × 10-3 H d) 6.37 × 10-3 H Question 32. The impedance of a circuit consists of 3 Ω resistance and 4 Ω resistance. The power factor of the circuit is (a) 0.4 (b) 0.6 (c) 0.8 (d) 1.0 (b) 0.6 Hint: tan Φ = $$\frac { 4 }{ 3 }$$. Power factor = cos Φ = $$\frac { 3 }{ 5 }$$ = 0.06 Question 33. Calculate the Q factor of RLC circuit if L = 80 µH, C = 2000 pF and R = 50Ω a) 40 b) 400 c) 4 d) 0.4 c) 4 Solution: Q = $$\frac{1}{R} \sqrt{\frac{L}{C}}=\frac{1}{50} \sqrt{\frac{80 \times 10^{-6}}{200 \times 10}}$$ = 4 Question 34. The average power dissipation in pure (Ideal) inductor is a) $$\frac{1}{2}$$ Li2 b) 2 Li2 c) $$\frac{1}{2}$$ Li2 d) zero d) zero Question 35. In an AC circuit, Resonance is obtained when a) Z = R b) Z = ωL – (1/ωC) c) L=R d) None a) Z = R Question 36. Change of current of 1 As-1 causes emf of 1V to be equal to______ a) 1 H b) 1 V m-1 c) 1 Am d) 1 J d) 1 H Question 37. In an AC circuit with voltage V and current I, the power dissipated is- (a) VI (b) $$\frac { 1 }{ 2 }$$ VI (c) $$\frac { 1 }{ √2 }$$ VI (d) depends on the phase difference between I and V (d) depends on the phase difference between I and V Question 38. A metallic ring is attached to wall of room. When north pole of magnet is brought near ring induced current in ring is a) zero b) clockwise c) anticlockwise d) infinite c) anticlockwise Question 39. In a series LCR circuit, R = 10 Ω and the impedance Z = 20 Ω. Then the phase difference between the current and the voltage is- (a) 60° (b) 30° (c) 45° (d) 90° (c) 60° Hint: cos Φ = $$\frac { R }{ Z }$$ = $$\frac { 10 }{ 20 }$$ = $$\frac { 1 }{ 2 }$$ ⇒ Φ = 60° Question 40. Which of the following effects does an alternating current shows a) Chemical effect b) magnetic effect c) heating effect d) all the above c) heating effect Question 41. In the AC circuit the rms value of Irms is related to peak current I0 by the reaction a) Irms = 1 I0 b) Irms = (1/√2) I0 c) Irms = 2 I0 d) Irms = π2I0 b) Irms = (1/√2) I0 Question 42. Match the following: i. Faraday’s law a. conservation of energy ii. Lenz law b. Electromagnetic Induction iii. Transformer c. Right-hand rule iv. Induced current d. ε = – dΦ / dt a) i – a ii – d iii – c iv – b b) i – c ii – a iii – d iv – b c) i – d ii – a iii – b iv – c d) i – a ii – d iii – b iv – c c) i-d, ii-a, iii-b, iv-c Question 43. The wattless circuit is obtained when the phase difference between virtual voltage and virtual current is a) 90° b) 45° c) 80° d) 60° a) 90° II. Choose the Wrong statement: Question 1. Tick out the wrong statement: a) An emf can be induced between the ends of a straight conductor by moving it through a uniform magnetic field. b) The self-induced emf produced by changing the current in a coil always tends to decrease the current. c) inserting an iron core in a coil increases the coefficient of self-inductance. d) According to Lenz’s law direction of induced current oppose the flux change that causes it. Ans : b) The self-induced emf produced by changing the current in a coil always tends to decrease the current. Question 2. Tick out the wrong statement: a) Inductor is used to store energy in a magnetic field when electric current flows through it, b) According to Faraday’s law, an emf is induced in a conductor when magnetic flux passing through it. c) Self-inductance is that current passing through coil changes with time emf is induced in neighbouring coil d) The work done is stored as magnetic potential energy in the inductor. c) Self-inductance is that current passing through coil changes with time emf is induced in neighbouring coil. Question 3. Tick out the wrong one: a) Changing the magnetic field B b) Changing area A c) Changing the orientation of the coil Q d) Changing mass of the rod d) Changing mass of the rod III. Assertion and Reason: Question 1. Assertion (A): Emf is produced due to the movement of the rod it is often called motional emf. Reason (R): When the rod moves, free electrons in it also moves with the same velocity in B a) A and R are correct R is the correct explanation of A b) A and R arc correct But R is not the correct explanation of A c) A is correct R is wrong d) A is the wrong R is correct a) A and R are correct R is the correct explanation of A. Question 2. Assertion (A): Three-phase generator produce higher output than single-phase generator Reason (R): Three-phase transmission is very cheaper. a) A and R are correct R is the correct explanation of A b) A and R are correct But R is not the correct explanation of A c) A is correct R is wrong d) A is the wrong R is correct b) A and R are correct But R is not the correct explanation of A Question 3. Assertion (A): Alternating voltage and current in inductor system is V = Vm sin ωt and i = 1m sin(ωt – π/ 2) Reason (R): Current lags behind applied voltage by π/2 a) A and R are correct R is the correct explanation of A b) A and R are correct But R is not the correct explanation of A c) A is correct R is wrong d) A is the wrong R is correct a) A and R are correct R is the correct explanation of A IV. Fill in the blanks: Question 1. Condition for Resonance in RLC circuit is ______. χL = χC Question 2. Efficiency range of transformer is _______. 96 – 99% Question 3. Energy stored in capacitor is ________. VE = ((Qm)2 / 2C) Question 4. Energy stored in the inductor is ______. VB = Li2/2 Question 5. The magnification of vo1tae at series resonance is _______ Q factor V. Two Mark Questions: Question 1. Define magnetic flux The magnetic flux through an area A in a magnetic field is defined as the number of magnetic field lines passing through that area. ΦB = ∫A $$\overrightarrow{\mathrm{B}}$$ . d $$\overrightarrow{\mathrm{A}}$$ = BA cos θ Question 2. Write down the drawbacks of Eddy currents. When eddy currents flow in the conductor, a large amount of energy is dissipated in the form of heat. The energy loss due to the flow of eddy current is inevitable but it can be reduced to a greater extent with suitable measures. The design of the transformer core and electric motor armature is crucial in order to minimise the eddy current loss. To reduce these losses, the core of the transformer is made up of thin laminas insulated from one another while for electric motor the winding is made up of a group of wires insulated from one another. The insulation used does not allow huge eddy currents to flow and hence losses are minimized. Question 3. What is an inductor? Inductor is a device used to store energy in a magnetic field when an electric current flows through it. Question 4. Define self-inductance in terms of flux. Self-inductance of a coil is defined as the flux linkage of the coil when 1 A current flows through it L = $$\frac{\mathrm{N} \Phi_{\mathrm{B}}}{i}$$ Question 5. Define mutual inductance in terms of emf and current. Mutual inductance M21 is also defined as the opposing emf induced in coil 2 when the rate of change of current through coil 1 is 1 As-1. M12 = $$\frac{-\varepsilon_{1}}{d i_{2} / d t}$$ Question 6. Define Mutual Inductance. Mutual inductance is defined as opposing emf induced in the coil when the rating of change of current through another coil. Question 7. Define the unit of mutual Inductance. The mutual inductance between two coils is said to be one henry if a current of 1A in coil 1 produces unit flux linkage in coil 2. Question 8. Define the principle of Transformer. The principle of transformer is mutual induction between two coils. When electric current passing through a coil changes with time, an emf is induced in neighboring coil. Question 9. Define the Efficiency of Transformer. The ratio of output power to input power is the efficiency of the transformer. η = $$\frac{\text { Output power }}{\text { Input power }}$$ The efficiency range is 96 – 99% Question 10. What is alternating voltage? An alternating voltage is a voltage which changes polarity at regular interval of time and the direction of the resulting alternating current also changes accordingly. Question 11. What is sinusoidal alternating voltage? If the waveform of the alternating voltage is a sine wave, then it is known as sinusoidal alternating voltage. ν = Vm sin ωt. Question 12. Using Lenz’s law, predict the direction of induced current in conducting rings 1 and 2 when the current in the wire is (i) 1f the current is steadily decreasing inducing current will be in a direction so as to oppose the decreasing magnetic flux according to Lenz law. Hence the direction of current is anticlockwise in the ring I and clockwise ring 2. (ii) If the current is steadily increasing the induced current with the flow in such a way the direction of current is clockwise in ring 1 and anticlockwise in ring 2. Question 13. What is meant by sinusoidal alternating voltage? If the waveform of the alternating voltage is a sine wave, then it is known as sinusoidal alternating voltage, which is given by the relation. υ = Vm sin ωt Question 14. Define power in AC circuit Power of a circuit is defined as the rate of consumption of electric energy in that circuit. Question 15. What is ‘wattfull current’? 1. Current component IRMS cos φ is the active component. 2. Power consumed by current is VRMS IRMS cos φ. It is known as a wattful current. Question 16. Write any three definitions of power factor. 1. Power factor = cos φ is = cosine of angle of lead or lag 2. Power factor = $$\frac{R}{Z}=\frac{\text { Resistance }}{\text { Impedance }}$$ 3. Power factor = $$\frac{\mathrm{VI} \cos \phi}{\mathrm{VI}}=\frac{\text { True power }}{\text { Apparent power }}$$ VI. Three Mark Questions: Question 1. List out the importance of Electromagnetic induction. 1. The application of electromagnetic induction is almost everywhere in the present life. 2. Right from home appliances to huge factories, satellite communication all need electricity for their operation. 3. So electric generators and transformers function on electromagnetic induction. 4. Sophisticated human life would not be possible without the discovery of electromagnetic induction. Question 2. What are the drawbacks of eddy current? 1. When an eddy current flows in the conductor, a large amount of heat is dissipated in the form of heat. 2. This can be reduced by suitable measures. 3. The design of the transformer core and the electric motor armature is crucial in order to minimize the eddy current loss. 4. To reduce this loss, the core of the transformer is made up of laminas insulated from one another. 5. Electric motor winding is made up of a group of wires insulated from one another. The insulation does not allow eddy current to flow. Question 3. Write down the applications of the series RLC resonant circuit. RLC circuits have many applications like filter circuits, oscillators, and voltage multipliers, etc. An important use of series RLC resonant circuits is in the tuning circuits of radio and TV systems. The signals from many broadcasting stations at different frequencies are available in the air. To receive the signal of a particular station, tuning is done. Question 4. What are the advantages of the three-phase generator? 1. Three-phase produce a high power output 2. For the same capacity, the three-phase alternator is small in size. 3. It is cheaper. A relatively thinner wire is sufficient for transmission. Question 5. What is the mean or Average value of AC? Derive it. The average value of alternating current is defined as the average of all values of current over the positive or negative half cycle. $$I_{a v}=\frac{\text { Area of }+\text { +ve half cycle }(\text { or }) \text { -ve half cycle }}{\text { Base length of half cycle }}$$ Let i be mid ordinate of that strip Area of elementary strip = i dθ Area of +ve half – cycle = $$\int_{0}^{\pi}$$ idθ = $$\int_{0}^{\pi}$$ Im sinθ dθ = Im $$[-\cos \theta]_{\mathrm{o}}^{\pi}$$ = Im [cos π – cosθ] = 2 Im Average value of AC, Iav = $$\frac{2 \mathrm{I}_{\mathrm{m}}}{\pi}$$ Iav = 0.637 Im For negative half -cycle Iav = – 0.637 Im Question 6. How to draw phasor diagram in AC 1. Length of line segment equals to peak value 2. Vm or Im of alternating voltage. 3. Its angular velocity ω is equal to the angular frequency. 4. The projection of phasor on any vertical axis gives the instantaneous value of alternating voltage or current. 5. The angle between phasor and axis of reference indicates the phase of alternating voltage. Question 7. Write three examples of power factor. 1. Power factor = cos 0° = 1 for pure resistive circuit because the phase angle p between voltage and current is zero. 2. Power factor = cos(±π/2) = 0 for the purely inductive or capacitive circuit, because the phase angle between voltage and current is ±π/2 3. Power factor lies between 0 and I for a circuit having R, L, and C in varying proportions. Question 8. Write the analogies between electrical and mechanical quantities. VII. Five Mark Questions: Question 1. Explain the first illustration of Lenz’s law and find the direction of induced current. 1. Consider a uniform magnetic field, Field lines represented by (x). 2. A rectangular metallic frame ABCD is placed in this magnetic field its plane ⊥ to B. 3. If arm AB slides to our right side, a number of lines passing through ABCD increases and current is induced. 4. By lenz’s law induced current oppose this flux increases and try to reduce it by producing another magnetic field pointing outwards. 5. Magnetic loops of the induced field are represented by circle. Direction of the induced current is found to be anti-clockwise by using right-hand thumb rule. 6. The leftward motion of arm AB decreases magnetic flux. The induced current, this time produce a magnetic field inward direction. Flux decrease is opposed by flow of induced current, it flows in a clockwise direction. Question 2. Explain the simple demonstration of the production of eddy current. 1. Consider a pendulum oscillate between poles of a powerful electromagnet. 2. the First electromagnet is switched off, the pendulum is slightly displaced and released. It begins to oscillate and execute a large number of oscillations before stopping Friction is only damping force. 3. When the electromagnet is switched on, the disc of the pendulum is made to oscillate, eddy currents are produced in it which oppose the oscillation. 4. A heavy damping force of eddy currents will bring the pendulum to rest within few oscillations. 5. If some slots are cut in the disc, eddy currents are reduced. The pendulum now execute several oscillations before coming to rest. 6. This clearly demonstrates the production of eddy current in the disc of the pendulum. Question 3. Derive the equation for mutual inductance between two long co-axial solenoids. Consider two long co-axial solenoids of the same length l, A1 and A2 be an area of two solenoids n1 and n2 be the turn density i1 is current in solenoid 1. B1 = µ0 n1 i1 Magnetic flux Φ21 = $$\int_{A_{2}} \overrightarrow{B_{1}} \cdot \overrightarrow{d A}$$ = B1 A2(0 = 0°) Flux with total turns N2 N2 φ21 = (n2 l) (µ0 n1 i1) A N2 φ21 = (µ0 n1 n2 A2 l) i1 ………………(1) N2 φ21 = M21 i1 Comparing (1) and (2) M21 = µ0 n1 n2 A2 l …………………..(3) Magnetic field produced by solenoid 2 when carrying current i2 B2 = µ0 n2 i2 Φ12 = ∫(A2) B2 → . dA → = B2 A2 = (µ0 n1 n2) A2 N1 Φ12 = (n1 l) (µ0 n2 i2) A2 N1 Φ12 = (µ0 n1 n2 A2 l) i2 N1 Φ12 = M12 i2 M12 i2 = (µ0 n1 n2 A2 l) i2 M12 = µ0 n1 n2 A2 l ………………..(4) Mutual inductance between two long co axial solenoid M = µ0 n1 n2 A2 l ……………(5) For relative permittivity µ M = µn1 n2 A2 l M = µ0 µr n1 n2 A2 l. Question 4. Find the instantaneous current when the AC circuit containing only the capacitor and find the capacitive reactance. 1. Consider a circuit containing a capacitor. 2. The alternating voltage is ν = Vm sin ωt ……………(1) emf a cross capacitor is q/c According to Kirchoff’s loop rule ν = q/C = 0 q = C Vm sin ωt i = $$\frac{\mathrm{dq}}{\mathrm{dt}}$$ = $$\frac{d}{d t}$$ (C Vm sin ωt) = C Vm $$\frac{d}{d t}$$ sin ωt = C Vm ω cos ωt i = $$\frac{\mathrm{V}_{\mathrm{m}}}{\mathrm{I} / \mathrm{C} \omega}$$ sin (ωt + π/2) Instantaneous Current i = I m sin (ωt + π/2) I m = $$\frac{\mathrm{V}_{\mathrm{m}}}{1 / \omega \mathrm{c}}$$ peak value of alternating current. Current leads the voltage by π/2 (or) 90° Capacitive Reactance χC: Resistance offered by capacitor is known as capacitive reactance χC = $$\frac{1}{\mathrm{C} \omega}$$ It varies inversely with frequency, χC = $$\frac{1}{\mathrm{C} = [latex]\frac{1}{2 \pi \mathrm{fC}}=\frac{1}{0}$$ = ∞ Capacitive circuit offers infinite resistance to the steady current. Question 5. Explain the effect of series resonance and draw the Resonance curve. 1. When Series resonance occurs, the impedance of the circuit is minimum and equal to the resistance of the circuit, current in the circuit becomes maximum. 2. This is shown in the Resonance curve drawn between current and frequency. At resonance impedance is Question 6. 1. Generation of AC is cheaper than DC. 2. At high voltage transmission loss is small. 3. We can easily convert AC to DC by rectifiers. 1. We cannot use AC for certain applications like charging of batteries, electroplating, electric traction, etc. 2. At high voltage, it is more dangerous to work with AC than DC. Question 7. Explain energy conservation of loop in the magnetic field and prove that mechanical work done in moving loop appears as thermal energy in the loop. 1. In order to move loop with constant velocity constant $$\overrightarrow{\mathrm{V}}$$ force is equal and opposite to magnetic force applied. Rate of doing work or power is P = $$\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{V}}$$ = F V cos θ, θ = 0° = F V 2. Three deflecting forces $$\overrightarrow{\mathrm{F}}_{1}$$, $$\overrightarrow{\mathrm{F}}_{2}$$, $$\overrightarrow{\mathrm{F}}_{3}$$ acting on three segments of loop, the general equation is $$\overrightarrow{\mathrm{F}_{\mathrm{d}}}=\overrightarrow{\mathrm{il}} \quad \times \overrightarrow{\mathrm{B}}$$ 3. $$\overrightarrow{\mathrm{F}}_{1}$$, $$\overrightarrow{\mathrm{F}}_{2}$$ equal and opposute so cancel each other. 4. When induced current flows in loop Joule heating takes plan Thermal energy is dissipated in the loop. P = i2 R P = $$\left(\frac{B l V}{R}\right)^{2}$$ R ……………..(2) (1) = (2) 5. Thus mechanical work done is moving the loop appears as thermal energy in the loop. Question 1. A series LCR circuit with R = 20Ω L = 1.5 H and c = 35 μF is connected to a variable frequency 200 V ac supply when the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle? R = 20Ω, L = 1.5 H C = 35 μF = 35 × 10-6 F, V = 200 V Impedence of the circuit is $$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$$ At resonance χL = χC Z = R = 20Ω I = $$\frac{V}{Z}=\frac{200}{20}$$ = 10A Average power transferred to the one complete cycle. P = I2 R P = 10 × 10 × 20 = 2000W. Question 2. An ideal transformer has 460 and 40,000 turns in the primary and secondary coils respectively. Find the voltage developed per turn of the secondary coil if the transformer is connected to a 230 V AC main. Np= 460 turns, Ns = 40,000 turns Vp = 230 V Question 3. At a hydroelectric power plant, the water pressure head is at a height of 300m and the water flow available is 100 m3s-1. If the turbine generate efficiency is 60% estimate the electric power available from the plant (g = 9.8 ms-2) Height of water pressure head h = 300 m Volume of water flow per second V = 100 m3 s-1 Efficiency of turbine generator η = 60% = 0.6 Acceleration due to gravity g = 9.8 ms-2 Density of water ρ = 103 kg/m3 Electric Power available from plant = η × hρg = 0.6 × 300 × 103 × 9.8 × 100 = 176.4 × 106 W = 176.4 MW Question 4. A long solenoid with 15 turns per cm has small loops of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid change steadily from 2.0 A to 4.0 A is 0.1 s. What is the induced emf in the loop while the current is changing? Number of turns in solenoid =15 turns/cm = 1500 turns/m No. of turns per unit length n = 1500 turns Small loop Area A = 2.0 cm2 = 2 × 10-4 m2 Change in current di = 4 – 2 = 2 A Change in time dt = 0.1 s induced emf in solenoid e = $$\frac{\mathrm{d} \varphi}{\mathrm{d} t}$$ e = $$\frac{d}{d t} (BA)$$ = Aµ0n $$\frac{d i}{d t}$$ = 2 × 10-4 × 4 × 10-7 × 1500 × $$\frac{2}{0.1}$$ = 7.54 × 10-6 V Induced emf in the loop = 7.54 × 10-6 V. Question 5. A transmitter consists of an LC circuit with an inductance of 1 µH and capacitance of 1 µF. What is the wavelength of the electromagnetic waves it emits?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8700396418571472, "perplexity": 2104.7885147166257}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056856.4/warc/CC-MAIN-20210919095911-20210919125911-00033.warc.gz"}
http://math.stackexchange.com/questions/799519/algebraic-solution-for-the-intersection-points-of-two-parabolas	# Algebraic solution for the intersection point(s) of two parabolas I recently ran through an algebraic solution for the intersection point(s) of two parabolas $ax^2 + bx + c$ and $dx^2 + ex + f$ so that I could write a program that solved for them. The math goes like this: $$ax^2 - dx^2 + bx - ex + c - f = 0 \\ x^2(a - d) + x(b - e) = f - c \\ x^2(a - d) + x(b - e) + \frac{(b - e)^2}{4(a - d)} = f - c + \frac{(b - e)^2}{4(a - d)} \\ (x\sqrt{a - d} + \frac{b - e}{2\sqrt{a - d}})^2 = f - c + \frac{(b - e)^2}{4(a - d)} \\ (a - d)(x + \frac{b - e}{2(a - d)})^2 = f - c + \frac{(b - e)^2}{4(a - d)} \\ x + \frac{b - e}{2(a - d)} = \sqrt{\frac{f - c + \frac{(b - e)^2}{a - d}}{a - d}} \\ x = \pm\sqrt{\frac{f - c + \frac{(b - e)^2}{a - d}}{a - d}} - \frac{b - e}{2(a - d)} \\$$ Then solving for $y$ is as simple as plugging $x$ into one of the equations. $$y = ax^2 + bx + c$$ Is my solution for $x$ and $y$ correct? Is there a better way to solve for the intersection points? - You lost a factor $4$ somewhere. You can simply rewrite your problem as $$(a-d)x^2+(b-e)x+(c-f)=0$$ and use the standard formula for a quadratic equation, i.e. $$x=-\frac{b-e}{2(a-d)}\pm\sqrt{\frac{(b-e)^2}{4(a-d)^2}-\frac{c-f}{a-d}}$$ Before evaluating this equation, you need to check if $a-d=0$, in which case $$x=\frac{f-c}{b-e}$$ In this case you of course need to check if $b-e=0$. - Excellent to spot the exceptions. – Mark Bennet May 17 '14 at 20:58 You should recognise a form of the quadratic formula:$$(a-d)x^2+(b-e)x+(c-f)=0$$ which gives $$x=\frac {-(b-e)\pm \sqrt {(b-e)^2-4(a-d)(c-f)}}{2(a-d)}$$ This is the same as yours except for a missing factor of $\frac 14$ under your square root, which you lost when you took the square root near the end. - All the other answers are fine from a mathematical point of view, but they ignore the fact that using the quadratic formula is a very bad way to solve quadratic equations in computer code (using floating point arithmetic). The problem arises when one of the roots is near zero. In this case, either the "$+$" or the "$-$" formula of the $\pm$ will cause you to subtract two numbers that are nearly equal, and this will result in catastrophic cancellation error. The problem is illustrated here, and the well-known solutions are described. For other interesting examples, see George Forsythe's famous paper "Why a Math Book is not Enough". - Well, you somehow lost the factor of 4, otherwise seems valid. As you are going to write a program for this, you should also write a solution gfor the case $a=d$ and deal with the case the radical is zero or does not exist. Actually, you did not have to write all this, as people usually know the solution of quadratic equation (isn't it school material?). For $ax^2 + bx +c = 0$ usually _the discriminant _$D=b^2 - 4ac$ is calculated, and then $x_{1,2}$ are given as $\frac {-b ±\sqrt D}{2a}$. If D=0 then the only sulution $-\frac b {2a}$ exists, and if $D<0$ there are no real solutions (as $\sqrt D$ is not a real number then or does not exist if we only work with real numbers). Then just use $a-d,b-e$ and $c-f$ as coefficients in the general solution formula. A separate solution for the case $a=d$. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9134387373924255, "perplexity": 230.66033435571623}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701162648.4/warc/CC-MAIN-20160205193922-00116-ip-10-236-182-209.ec2.internal.warc.gz"}
https://arxiv.org/abs/1509.02577	Title:Exact minimum codegree threshold for $K^- _4$-factors Abstract: Given hypergraphs $F$ and $H$, an $F$-factor in $H$ is a set of vertex-disjoint copies of $F$ which cover all the vertices in $H$. Let $K^- _4$ denote the $3$-uniform hypergraph with $4$ vertices and $3$ edges. We show that for sufficiently large $n\in 4 \mathbb N$, every $3$-uniform hypergraph $H$ on $n$ vertices with minimum codegree at least $n/2-1$ contains a $K^- _4$-factor. Our bound on the minimum codegree here is best-possible. It resolves a conjecture of Lo and Markström for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft concerning almost perfect matchings in hypergraphs. Comments: 23 pages Subjects: Combinatorics (math.CO) MSC classes: 05C35, 05C65, 05C70 Cite as: arXiv:1509.02577 [math.CO] (or arXiv:1509.02577v1 [math.CO] for this version) Submission history From: Jie Han [view email] [v1] Tue, 8 Sep 2015 23:16:33 UTC (29 KB)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5417664647102356, "perplexity": 804.9515661320786}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00452.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-9-roots-and-radicals-9-1-roots-and-radicals-problem-set-9-1-page-401/59	## Elementary Algebra $21\sqrt{2}$ Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $7\sqrt{2}+14\sqrt{2} ,$ simplifies to \begin{array}{l}\require{cancel} (7+14)\sqrt{2} \\\\= 21\sqrt{2} .\end{array}	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9956580996513367, "perplexity": 19674.07470012762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578721468.57/warc/CC-MAIN-20190425134058-20190425155220-00012.warc.gz"}
https://efinancemanagement.com/financial-analysis/loan-to-value-ratio	# Loan to Value Ratio ## Concept of Loan to Value Ratio A mortgage is a legal document wherein the lender lends money in exchange for the title of the debtor’s property. Until the payment is received for the entire debt, the lender is the title holder of the property which is mortgaged. There are various types of mortgages. However, despite the type, the lender has to bear significant risk upon lending such large amounts of money. In order to assess the risks, Loan to Value Ratio is used. Let us understand what this ratio does. ## What is Loan to Value Ratio? Loan to Value Ratio is a risk assessment ratio which compares the value of the asset to the amount of the loan given. Based on the ratio, the cost of taking the loan is calculated. It is expressed as a percentage of the loan to the cost or value of the asset. ## Loan to Value Ratio Definition Thus, Loan to Value ratio can be defined as the amount of the mortgage lien divided by the appraised value of the property and expressed as a percentage. Its various uses are as given below. ## Uses of Loan to Value Ratio The Loan to Value ratio is mainly used to determine the value of mortgage costs. The higher the percentage of Loan to Value ratio, the higher is the credit risk. Therefore, the cost of taking the mortgage goes up in terms of interest rates.A high percentage also requires the need to take insurance which in turn increases the cost of borrowing. A lower Loan to Value ratio percentage for the lenders means that they can sell the property at a rate equal to or more than the loan amount in case of a default in repayment. The Loan to Value ratio is also used primarily for the purpose of mortgage underwriting. This is done while purchasing residential property, refinancing a current mortgage into new loans and borrowing against the real value of the property. The real value of the property would be the value minus the mortgages and loans on it. The loan to value ratio is an indicator of the feasibility of such additional lendings. It has a simple formula as shown below. ## Loan to Value Ratio Formula The formula used by the lenders to calculate this ratio is as follows. Loan to Value Ratio = Loan Amount / Appraised Value of Property ## What is a good Loan to Value Ratio? Although there is no set optimal LTV ratio, all lenders prefer a low percentage as it decreases the credit risk. Around 80% is preferred in most of the cases as there is a good chance of recovery. This can be explained with the help of a basic example. ## Loan to Value Ratio Example A borrower wants a loan for purchasing a house worth \$100,000. The amount of the mortgage given by the lender is \$93,500. The Loan to Value Ratio will be \$93,500 / \$100,000 or 93.5%. Thus, this is not a viable ratio for the lender as the percentage is too high. The lender then runs the risk of a loss upon selling the property in case of a default in the repayment. At 93.5% the lender may not even recover the initial principal amount. Conclusion Loan to Value Ratio thus makes it easier for lenders to determine the risk and approve the mortgage. However, it must be noted that this is only one determinant and the approval of a mortgage depends on various other subjective factors and criteria.1,2 Share Knowledge if you liked	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.837161123752594, "perplexity": 1217.2667493178874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991562.85/warc/CC-MAIN-20210519012635-20210519042635-00447.warc.gz"}
https://cs.stackexchange.com/questions/93339/a-fuzzy-string-matching-algorithm-for-finding-all-occurrences-from-a-set-of-stri/93342	# A fuzzy string matching algorithm for finding all occurrences from a set of strings in a large string I have thousands of documents, and a term list with thousands of entries. The entries in the term list range in length from an acronym of two characters to a 14-word phrase with 96 characters. I would like to find every occurrence of any term in the term list in each document in the order that they appear. I have created two test implementations so far: one using the Aho-Corasick algorithm and the other using n-gram matching. I tested them both on a medium-sized document (8 MB). The Aho-Corasick algorithm came up with over 8700 matches in 24 seconds. This would be great, except that I would like to use a fuzzy matching algorithm, and Aho-Corasick only finds exact matches. N-gram matching found 9600 matches, since some of them are approximate, but it took 885 seconds! As such, I would like suggestions on an efficient fuzzy matching algorithm for finding matches from a set of strings. Is there any way to modify the current code I have for the Aho-Corasick algorithm so that it can take into account Levenshtein distance? I have found some other questions on this site that are related, but I didn't feel like they solved my problem. Thanks. One approach: Build a BK tree containing the terms in your term list. Given any word $w$, this lets you efficiently find the term that is closest to $w$ in Levenshtein edit distance.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6764097213745117, "perplexity": 524.1585163800135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371604800.52/warc/CC-MAIN-20200405115129-20200405145629-00541.warc.gz"}
https://tex.stackexchange.com/questions/245143/how-to-draw-a-number-line-with-arrows-inside-it	# How to draw a number line with arrows inside it I am having trouble using TiKz to draw a correct picture. Here is how I started it out: \documentclass{amsart} \usepackage{tikz} \usetikzlibrary{decorations.markings} \usetikzlibrary{arrows} \begin{document} \tikzset{->-/.style={decoration={ markings, mark=at position #1 with {\arrow{<}}},postaction={decorate}}} \begin{tikzpicture} % a straight line segment \draw[latex-] (-2,0) -- (0,0); \draw[->-=.3] (0,0) -- (1,0); \draw[->-=.6] (0,0) -- (1,0); \draw[-latex] (1,0) -- (2,0); % the ticks and their labels \foreach \x in {-1,...,1} \draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt) node[below,fill=white] {\the\numexpr\x +1\relax}; \end{tikzpicture} \end{document} But I want my picture to look like this: How do I make the numbers appear correctly, and also make the curved arrows? Like this? \documentclass[tikz,border=3mm]{standalone} \usepackage{tikz} \usetikzlibrary{decorations.markings} \usetikzlibrary{arrows} \begin{document} \tikzset{->-/.style={decoration={ markings, mark=at position #1 with {\arrow{>}}},postaction={decorate}}} \begin{tikzpicture} % a straight line segment \draw[latex-] (-2,0) -- (0,0); \draw[->-=.3] (0,0) -- (1,0); \draw[->-=.6] (0,0) -- (1,0); \draw[-latex] (1,0) -- (2,0); % the ticks and their labels \foreach \x [count=\i start from 0] in {-1,...,1} \draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt) node[below,fill=white] (\i) {\x}; \draw[->] (2) to [out=-95, in=-85] (0); \draw[<-] (.25mm,1mm) arc(-85:265:3mm); \end{tikzpicture} \end{document} • @ᴇʏᴇs I've updated the answer. You just need {\x} as node contents. \x cannot be used as node names because they are considered real values, and I've used \i which is an integer. But there is no problem using in nodes contents. – Ignasi May 15 '15 at 15:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9280164837837219, "perplexity": 3367.5804498419707}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027330750.45/warc/CC-MAIN-20190825151521-20190825173521-00051.warc.gz"}
https://socratic.org/questions/how-do-you-evaluate-ln-sqrt-e	Precalculus Questions Topics How do you evaluate ln sqrt(e)? Then teach the underlying concepts Don't copy without citing sources preview ? Explanation Explain in detail... Explanation: I want someone to double check my answer 30 Logan Share Apr 10, 2016 $\frac{1}{2}$ Explanation: Recall that: sqrtn=n^(1/2: We can now express your equation as: $\ln \sqrt{e} = \ln {e}^{\frac{1}{2}}$ Recall that: ${\log}_{n} {a}^{m} = m {\log}_{n} a$ We can further simplify the given equation: $\ln {e}^{\frac{1}{2}} = \frac{1}{2} \ln e$ Recall that: $\ln e = {\log}_{e} e = 1$ We can now say that: $\frac{1}{2} \ln e = \frac{1}{2} \left(1\right) = \frac{1}{2}$ Therefore, $\ln \sqrt{e} = \frac{1}{2}$ • 11 minutes ago • 12 minutes ago • 12 minutes ago • 12 minutes ago • 31 seconds ago • A minute ago • A minute ago • A minute ago • 3 minutes ago • 3 minutes ago • 11 minutes ago • 12 minutes ago • 12 minutes ago • 12 minutes ago Impact of this question 5872 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8667062520980835, "perplexity": 20137.174920318324}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863626.14/warc/CC-MAIN-20180520151124-20180520171124-00367.warc.gz"}
http://www.dlyj.ac.cn/CN/10.11821/yj1993010007	• 论文 • ### 三峡水库淹没区农业人口安置问题的几点意见 1. 中国科学院、国家计划委员会地理研究所 • 收稿日期:1992-11-10 修回日期:1992-12-29 出版日期:1993-03-15 发布日期:1993-03-15 ### DEVELOPMENT OF AGRICULTURE IN THE THREE GORGES REGION FOR THE RESETTLEMENT OF FARMING POPULATION IN THE PROJECTED RESERVOIR Huang Bingwei 1. Institute of Geography, Chinese Academy of Sciences and State Planning Commission of the People's Republic of China • Received:1992-11-10 Revised:1992-12-29 Online:1993-03-15 Published:1993-03-15 Abstract: In the projected reservoir of the Three Gorges on the Yangtse River,there are 440000 inhabitants living on tarming.For the resettlement of them, one possibility is the expansion of agriculture in 13 counties and cities in the immediate neighbourhood.This is a mountainous terrain dseply dissected by streams. More than 18% of the load is cultivated, and a 17.6% of the ultivation is distributed on steep slopes>25 °φ Estimated on the agricultural cpopulation alone, the per capita cultivated area is 1.2 mu and per capita tood production 409 kg.Features ot serious water and miss erosion are seldom out of sight.Land deterioration is too obvious to escape the notice of even the lay mind. There is little room for the expansion of conventional agriculture.A proposal under consideration is chiefly the construction of contour terraces with stones on selected sites with slopes up to 25° either cultivated or nonculti vated. According to informatiom available and field observation in a few localities, this seems acceptable in soms cases.Some examples have even experienced unusually heavy storms and severe droughts.However,furrther studies are necessary for assessment with respect to ecological and economic sustainability of terraces in recent years and of the sites for further construction.The search of alternatives for cheaper sustainale utilization of the sloping land is suggested. This includes in the main ths establishment of contour barrier hedgerows composed of woody plants and contourherbaceous strips to shape terraces in between and the use of the litter for plant. production to meet the demands of the local population and accessible markets. On the terraces contour planting contour tillage, minimum tillageand soil surfae mulch are called to provide additional protection against water eeosion and proper selection of plants, appropriats planting patterns aad and rotation for the replenishment of nutrients and the maintaince and improvement of soil physical properties Cost-effeetivensss analysis should be included in the design of hedgerows and herbaceous strips, waereas extended cost-benefit analysis plays the role in planning the terrace utilization. Since the terraces result from hedgerows and herbaceous strips, the whole slope beginning from the water-divide down to the foot should be taken as a unit for cost-benefit analysis. To evalue the off-site benefits, it is more practical to encompass a watershed composed of several slopes.There are tracts of land not amenable for terrace making terraces with hedgerovs and herbaceous strips because of slopss too steep or soils too thin For much of these, utilization and amelioration are still possible provided that the local demands for fuel, fertilizer and other products are satisfied otherwise. Some plants commonly found in the region are adaptable to such adverse habitats as stony soils and rocky surface with cracks and does not fail to supply some useful products and help to control water and mass erosion.More will be found in further investigations. Key words: Agriculture, Three Gorges Region	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16312164068222046, "perplexity": 6800.24034731577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104672585.89/warc/CC-MAIN-20220706121103-20220706151103-00259.warc.gz"}
https://matheducators.stackexchange.com/users/262/benjamin-dickman?tab=answers&sort=activity	Benjamin Dickman • Member for 7 years, 10 months • Last seen this week I recall an undergraduate thesis presentation on grade inflation at a particular liberal arts college in the United States (completed for the Department of Economics). The thesis can be found here; it ... One place to look is in the following source: National Research Council. Evaluating and Improving Undergraduate Teaching in Science, Technology, Engineering, and Mathematics. Washington, DC: The ... With regard to Math Education literature on proofs: a person to look to is Eric Knuth (Google Scholar). However, it may be more fruitful to shift from talking about writing (formal) mathematical ... Here I broach only the case in which students have consistent internet access; the more general case is clearly much more difficult. Moreover, this answer is written for the present context, i.e., a ... Update for JMM 2020: See the potentially relevant blogpost here. The post begins: I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often ... I do not believe that this is a concern that would surface, or be worth surfacing, in the courses named by this question's title. In my reading, the question is analogous to worrying about whether you ... I wrote to a professor of mathematics at a liberal arts college that has, in recent years, found great success in attracting more math majors. Here are lightly edited excerpts from the two emails I ... I suggest reading the AMS blog posts about active learning [which I think can serve as a suitable substitute$^{\star}$ for what you refer to as "student-centered"] for which the 2015 series ... I appreciate Ben Orlin's "Math with Bad Drawings" post about Andrew Wiles, for which the theme is not mistakes but rather being stuck. I have the sense that it contains some relevant content ... The various journals listed in the MSE question here can help with the university portion. These include, but are not limited to, the journals: The American Mathematical Monthly (AMM) College ... I disagree with the notion that the unit circle approach preceding the triangle approach should be, if it is contextualized historically, "baffling." To this end, I suggest two pieces if you are ... I gave an earlier answer [to a rather different question] in which I pointed to the Regents Exam Archives. One approach that you could take would be to look over a few tests from the 1990s as compared ... The Common Core State Standards for Mathematics (CCSSM) provides a list of standards that should be covered; the inference that a topic not mentioned in the algebra strand should, therefore, be ... I am writing this based on pure observation (e.g., entering year four of teaching this topic to secondary school students, and having co-taught a minicourse for teachers on absolute value functions$^\... View answer 4 votes Have you looked into Desmos for possible resources? In particular: How about the Marbleslides activities? I'm not sure whether this satisfies the criteria in your case (specifically: I do not know ... View answer 4 votes Edit (June 2019): I used this final project with minor tweaks again this year. You can find links to some of the output for Spring 2019 - both students' graphs and write-ups - here and here. I used a ... View answer 26 votes Re-Re-Edit (May 2019): Found in a selection of tweets here but pasted as images to preserve. Credit for the first one goes to @lizardbill and to the rest to @GeneticJen: Re-Edit (Jan 2016): Perhaps ... View answer Accepted answer 23 votes Edit 2: This story continues to reappear periodically in mainstream media; this month (April 2019) it was featured in a BBC Feature story here. The article title is: The violent attack that turned a ... View answer 3 votes With regard to this question: Any ... books I can buy which can help me to explain this? Here is a specific book recommendation, which is a source that I have personally found helpful: National ... View answer 12 votes At the moment, I can answer bullet point two: Are there any high school textbooks that explicitly acknowledge that the methods included in the text are not adequate to solve all 3rd and 4th degree ... View answer Accepted answer 5 votes The linear function component is covered early(ish) in Algebra 1, and quadratic functions are covered towards the end of Algebra 1; so, the former by 7th/8th grade and the latter - if at all - by 8th ... View answer Accepted answer 40 votes I'm slightly concerned that Is there a mathematical reason (like a proof) of why this happens? is a purely mathematical question, but since you write "we just warn students" I will assume that ... View answer 3 votes Here is the course description I wrote for a (high school) class on Statistics and Probability. I think you could modify it ever so slightly if you are covering Statistics, specifically, and that it ... View answer Accepted answer 11 votes Edit: See also the PDF linked here: Wikipedia has a list of mathematics education journals; I happen to prefer the list of mathematics education journals compiled here, as they are provided along ... View answer Accepted answer 9 votes You can find some further studies that cited the original writing on google scholar: link Mahajan (PDF) remarks that: Etta Berman, one of the teachers in the program, studied it for ... View answer 0 votes The book that I used was Applied Combinatorics by Alan Tucker. There is a preview available for free on google books, link. Here is part of the table of contents: [FWIW: I mentioned this same book ... View answer Accepted answer 8 votes I've heard very good reviews of the 2017 book, "An Illustrated Theory of Numbers" by MH Weissman. The book's main site is here; a write-up, along with some reviews, by the American ... View answer 2 votes One certain source can be found by looking through winners of the Morgan Prize, which is awarded for mathematical research by undergraduate students. Besides the wikipage linked above, there is also ... View answer 8 votes I wrote an article for NCTM's grades 8-14 journal, The Mathematics Teacher, which is about building towards${\rm F}\ell{\rm T}\$ by thinking through ways in which the following statement can be ...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43526312708854675, "perplexity": 1335.982442092802}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302723.60/warc/CC-MAIN-20220121040956-20220121070956-00309.warc.gz"}
http://teaching.shelswell.org.uk/a-level/d1/prims-complexity/	## Prim’s Complexity Prim’s algorithm starts by selecting the least weight edge from one node. In a complete network there are $(n - 1)$ edges from each node. At step 1 this means that there are $(n - 1) - 1$ comparisons to make. Having made the first comparison and selection there are $(n - 2)$ unconnected nodes, with a edges joining from each of the two nodes already selected. This means that there are $(n - 2) - 1$ comparisons that need to be made. Carrying on this argument results in the following expression for the number of comparisons that need to be made to complete the minimum spanning tree: $((n - 1) - 1) + (2(n - 2) - 1) + (3(n - 3) - 1) + \dotsc + ((n - 1)(n - (n - 1)) - 1)$ The result is that Prim’s algorithm has cubic complexity.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6973081231117249, "perplexity": 354.87486274973884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171043.28/warc/CC-MAIN-20170219104611-00004-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.cheenta.com/well-ordering-principle-and-bezout-theorem/	Select Page Get motivated Consider the following set of numbers: $$\displaystyle {M = \{ \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, … \} }$$ Does this set have a least number? Can you rigorously prove your answer? Concept – Well ordering principle, Bezout Theorem The well-ordering principle states that every non-empty set of positive integers contains a least element. Counter Example: The set of rational numbers does not have this property Bezout Theorem: Let a and b be integers with greatest common divisor d. Then, there exist integers x and y such that ax + by = d. More generally, the integers of the form ax + by are exactly the multiples of d.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7913681864738464, "perplexity": 206.06779684357397}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506121.24/warc/CC-MAIN-20200401192839-20200401222839-00187.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2021182	# American Institute of Mathematical Sciences doi: 10.3934/dcds.2021182 Online First Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible. Readers can access Online First articles via the “Online First” tab for the selected journal. ## Crystalline flow starting from a general polygon 1 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan 2 Department of Indian Philosophy and Buddhist Studies, Humanities, Faculty of Letters, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 3 Airitech Co., Ltd., Masonic 39MT Building, 2-4-5 Azabudai, Minato-ku, Tokyo 106-0041, Japan * Corresponding author: Yoshikazu Giga Received March 2021 Revised September 2021 Early access November 2021 Fund Project: The work of the second author was partly supported by the Japan Society for the Promotion of Science (JSPS) through the grants KAKENHI No. 19H00639, No. 18H05323, No. 17H01091 and by Arithmer Inc. through collaborative grant This paper solves a singular initial value problem for a system of ordinary differential equations describing a polygonal flow called a crystalline flow. Such a problem corresponds to a crystalline flow starting from a general polygon not necessarily admissible in the sense that the corresponding initial value problem is singular. To solve the problem, a self-similar expanding solution constructed by the first two authors with H. Hontani (2006) is effectively used. Citation: Mi-Ho Giga, Yoshikazu Giga, Ryo Kuroda, Yusuke Ochiai. Crystalline flow starting from a general polygon. Discrete & Continuous Dynamical Systems, doi: 10.3934/dcds.2021182 ##### References: [1] B. Andrews, Singularities in crystalline curvature flows, Asian J. Math., 6 (2002), 101-121. doi: 10.4310/AJM.2002.v6.n1.a6. Google Scholar [2] S. Angenent and M. E. Gurtin, Multiphase thermomechanics with interfacial structure. II. Evolution of an isothermal interface, Arch. Rational Mech. Anal., 108 (1989), 323-391. doi: 10.1007/BF01041068. Google Scholar [3] G. Bellettini, M. Novaga and M. 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Rates of convergence towards the boundary of a self-similar set. Discrete & Continuous Dynamical Systems, 2007, 19 (4) : 799-811. doi: 10.3934/dcds.2007.19.799 [19] Marek Fila, Michael Winkler, Eiji Yanagida. Convergence to self-similar solutions for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 703-716. doi: 10.3934/dcds.2008.21.703 [20] Hyungjin Huh. Self-similar solutions to nonlinear Dirac equations and an application to nonuniqueness. 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https://en.wikipedia.org/wiki/Cardinal_utility	# Cardinal utility A simple example of two cardinal utility functions u (first column) and v (second column) whose values in all circumstances are related by v=2u+3 In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations.[1][2] Two utility indices are related by an affine transformation if for the value $u(x_i)$ of one index u, occurring at any quantity $x_i$ of the goods bundle being evaluated, the corresponding value $v(x_i)$ of the other index v satisfies a relationship of the form $v(x_i) = au(x_i) + b\!$, for fixed constants a and b. Thus the utility functions themselves are related by $v(x) = au(x) + b.$ The two indices differ only with respect to scale and origin.[1] Thus if one is concave, so is the other, in which case there is said to be diminishing marginal utility. Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction exist, so that the magnitudes of increments to satisfaction can be compared across different situations. This contrasts with ordinal utility, in which concavity or convexity of the utility function has no economic relevance. The idea of cardinal utility is considered outdated except for specific contexts such as decision making under risk, utilitarian welfare evaluations, and discounted utilities for intertemporal evaluations where it is still applied.[3] Elsewhere, such as in general consumer theory, ordinal utility with its weaker assumptions Is preferred because results that are just as strong can be derived. ## History The first one to theorize about the marginal value of money was Apurva Chaurasia in 1738. He assumed that the value of an additional amount is inversely proportional to the pecuniary possessions which a person already owns. Since Bernoulli tacitly assumed that an interpersonal measure for the utility reaction of different persons can be discovered, he was then inadvertedly using an early conception of cardinality.[4] Bernoulli's imaginary logarithmic utility function and Gabriel Cramer's U=W1/2 function were conceived at the time not for a theory of demand but to solve the St. Petersburg's game. Bernoulli assumed that "a poor man generally obtains more utility than a rich man from an equal gain"[5] an approach that is more profound that the simple mathematical expectation of money as it involves a law of moral expectation. Early theorists of utility considered that it had physically quantifiable attributes. They thought that utility behaved like the magnitudes of distance or time, in which the simple use of a ruler or stopwatch resulted in a distinguishable measure. "Utils" was the name actually given to the units in a utility scale. In the Victorian era many aspects of life were succumbing to quantification.[6] The theory of utility soon began to be applied to moral-philosophy discussions. The essential idea in utilitarianism is to judge people's decisions by looking at their change in utils and measure whether they are better off. The main forerunner of the utilitarian principles since the end of the 18th century was Jeremy Bentham, who believed utility could be measured by some complex introspective examination and that it should guide the design of social policies and laws. For Bentham a scale of pleasure has as a unit of intensity "the degree of intensity possessed by that pleasure which is the faintest of any that can be distinguished to be pleasure";[7] he also stated that, as these pleasures increase in intensity higher and higher numbers could represent them.[7] In the 18th and 19th centuries utility's measurability received plenty of attention from European schools of political economy, most notably through the work of marginalists (e.g. William Stanley Jevons,[8] Léon Walras, Alfred Marshall). However, neither of them offered solid arguments to backup up the assumption of measurability. In Jevon's case he added to the later editions of his work a note on the difficulty of estimating utility with accuracy.[7] Walras, too, struggled for many years before he could even attempt to formalize the assumption of measurability.[9] Marshall was ambiguous about the measurability of hedonism because he adhered to its psychological-hedonistic properties but he also argued that it was "unrealistical" to do so.[10] Supporters of cardinal utility theory in the 19th century suggested market prices reflected utility, although they did not say much about them being incompatible (i.e. prices are objective measures but utility is subjective). Accurately measuring subjective pleasure (or pain) seemed awkward, as the thinkers of the time were surely aware. They renamed utility in imaginative ways such as subjective wealth, overall happiness, moral worth, psychic satisfaction, or ophélimité. During the second half of the 19th century, many studies related to this fictional magnitude -utility- were conducted, but the conclusion was always the same: it proved impossible to definitively say whether a good is worth 50, 75, or 125 utils to a person, or to two different people. Moreover, the mere dependence of utility on notions of hedonism, led academic circles to be skeptical of this theory.[11] Francis Edgeworth was also aware of the need to ground the theory of utility into the real world. He discussed the quantitative estimates that a person can make of his own pleasure or the pleasure of others, borrowing methods developed in psychology to study hedonic measurement: psychophysics. This field of psychology was built on work by Ernst H. Weber, but around the time of World War I, psychologists grew discouraged of it.[12][13] In the late 19th century, Carl Menger and his followers from the Austrian school of economics undertook the first successful departure from measurable utility, in the clever form of a theory of ranked uses. Despite abandoning the thought of quantifiable utility (i.e. psychological satisfaction mapped into the set of real numbers) Menger managed to establish a body of hypothesis about decision-making, resting solely on a few axioms of ranked preferences over the possible uses of goods and services. His numerical examples are "illustrative of ordinal, not cardinal, relationships".[14] Around the turn of the 19th century neoclassical economists started to embrace alternative ways to deal with the measurability issue. By 1900, Pareto was hesitant about accurately measuring pleasure or pain because he thought that such a self-reported subjective magnitude lacked scientific validity. He wanted to find an alternative way to treat utility that did not rely on erratic perceptions of the senses.[15] Pareto's main contribution to ordinal utility was to assume that higher indifference curves have greater utility, but how much greater does not need to be specified to obtain the result of increasing marginal rates of substitution. The works and manuals of Vilfredo Pareto, Francis Edgeworth, Irving Fischer, and Eugene Slutsky departed from cardinal utility and served as pivots for others to continue the trend on ordinality. According to Viner,[16] these economic thinkers came up with a theory that explained the negative slopes of demand curves. Their method avoided the measurability of utility by constructing some abstract indifference curve map. During the first three decades of the 20th century, economists from Italy and Russia became familiar with the Paretian idea that utility does not need to be cardinal. According to Schultz,[17] by 1931 the idea of ordinal utility was not yet embraced by American economists. The breakthrough occurred when a theory of ordinal utility was put together by John Hicks and Roy Allen in 1934.[18] In fact pages 54–55 from this paper contain the first use ever of the term 'cardinal utility'.[19] The first treatment of a class of utility functions preserved by affine transformations, though, was made in 1934 by Oskar Lange.[20] In 1944 Frank Knight argued extensively for cardinal utility. In the decade of 1960 Parducci studied human judgements of magnitudes and suggested a range-frequency theory.[21] Since the late 20th century economists are having a renewed interest in the measurement issues of happiness.[22][23] This field has been developing methods, surveys and indices to measure happiness. Several properties of Cardinal utility functions can be derived using tools from measure theory and set theory. ### Measurability A utility function is considered to be measurable, if the strength of preference or intensity of liking of a good or service is determined with precision by the use of some objective criteria. For example, suppose that eating an apple gives to a person exactly half the pleasure of that of eating an orange. This would be a measurable utility if and only if the test employed for its direct measurement is based on an objective criterion that could let any external observer repeat the results accurately.[24] One hypothetical way to achieve this would be by the use of an hedonometer, which was the instrument suggested by Edgeworth to be capable of registering the height of pleasure experienced by people, diverging according to a law of errors.[12] Before the 1930s, the measurability of utility functions was erroneously labeled as cardinality by economists. A different meaning of cardinality was used by economists who followed the formulation of Hicks-Allen. Under this usage, the cardinality of a utility function is simply the mathematical property of uniqueness up to a linear transformation. Around the end of the 1940s, some economists even rushed to argue that von Neumann-Morgenstern axiomatization of expected utility had resurrected measurability.[15] The confusion between cardinality and measurability was not to be solved until the works of Armen Alchian,[25] William Baumol,[26] and John Chipman.[27] The title of Baumol's paper, "The cardinal utility which is ordinal", expressed well the semantic mess of the literature at the time. It is helpful to consider the same problem as it appears in the construction of scales of measurement in the natural sciences.[28] In the case of temperature there are two degrees of freedom for its measurement - the choice of unit and the zero. Different temperature scales map its intensity in different ways. In the celsius scale the zero is chosen to be the point where water freezes, and likewise, in cardinal utility theory one would be tempted to think that the choice of zero would correspond to a good or service that brings exactly 0 utils. However this is not necessarily true. The mathematical index remains cardinal, even if the zero gets moved arbitrarily to another point, or if the choice of scale is changed, or if both the scale and the zero are changed. Every measurable entity maps into a cardinal function but not every cardinal function is the result of the mapping of a measurable entity. The point of this example was used to prove that (as with temperature) it is still possible to predict something about the combination of two values of some utility function, even if the utils get transformed into entirely different numbers, as long as it remains a linear transformation. Von Neumann and Morgenstern stated that the question of measurability of physical quantities was dynamic. For instance, temperature was originally a number only up to any monotone transformation, but the development of the ideal-gas-thermometry led to transformations in which the absolute zero and absolute unit were missing. Subsequent developments of thermodynamics even fixed the absolute zero so that the transformation system in thermodynamics consists only of the multiplication by constants. According to Von Neumann and Morgenstern (1944, p. 23) "For utility the situation seems to be of a similar nature [to temperature]". The following quote from Alchian served to clarify once and for all the real nature of utility functions, emphasizing that they no longer need to be measurable: Can we assign a set of numbers (measures) to the various entities and predict that the entity with the largest assigned number (measure) will be chosen? If so, we could christen this measure "utility" and then assert that choices are made so as to maximize utility. It is an easy step to the statement that "you are maximizing your utility", which says no more than that your choice is predictable according to the size of some assigned numbers. For analytical convenience it is customary to postulate that an individual seeks to maximize something subject to some constraints. The thing -or numerical measure of the "thing"- which he seeks to maximize is called "utility". Whether or not utility is of some kind glow or warmth, or happiness, is here irrelevant; all that counts is that we can assign numbers to entities or conditions which a person can strive to realize. Then we say the individual seeks to maximize some function of those numbers. Unfortunately, the term "utility" has by now acquired so many connotations, that it is difficult to realize that for present purposes utility has no more meaning than this. Armen Alchian, The meaning of utility measurement[25] ### Order of preference For more details on this topic, see Preference (economics). In 1955 Patrick Suppes and Muriel Winet solved the issue of the representability of preferences by a cardinal utility function, and derived the set of axioms and primitive characteristics required for this utility index to work.[29] Suppose an agent is asked to rank his preferences of A relative to B and his preferences of B relative to C. If he finds that he can state, for example, that his degree of preference of A to B exceeds his degree of preference of B to C, we could summarize this information by any triplet of numbers satisfying the two inequalities: UA > UB > UC and UA - UB > UB - UC. If A and B were sums of money, the agent could vary the sum of money represented by B until he could tell us that he found his degree of preference of A over the revised amount B' equal to his degree of preference of B' over C. If he finds such a B', then the results of this last operation would be expressed by any triplet of numbers satisfying the relationships: (a) UA > UB' > UC , and (b) UA - UB' = UB' - UC. Any two triplets obeying these relationships must be related by a linear transformation; they represent utility indices differing only by scale and origin. In this case, "cardinality" means nothing more being able to give consistent answers to these particular questions. Note that this experiment does not require measurability of utility. Itzhak Gilboa gives a sound explanation of why measurability can never be attained solely by introspection: It might have happened to you that you were carrying a pile of papers, or clothes, and didn't notice that you dropped a few. The decrease in the total weight you were carrying was probably not large enough for you to notice. Two objects may be too close in terms of weight for us to notice the difference between them. This problem is common to perception in all our senses. If I ask whether two rods are of the same length or not, there are differences that will be too small for you to notice. The same would apply to your perception of sound (volume, pitch), light, temperature, and so forth... —Itzhak Gilboa, Theory of decision under uncertainty[30] According to this view, those situations where a person just cannot tell the difference between A and B will lead to indifference not because of a consistency of preferences, but because of a misperception of the senses. Moreover, human senses adapt to a given level of stimulation and then register changes from that baseline.[31] ## Construction Suppose a certain agent has a preference ordering over random outcomes (lotteries). If the agent can be queried about his preferences, it is possible to construct a cardinal utility function that represents these preferences. This is the core of the Von Neumann–Morgenstern utility theorem. ## Applications ### Welfare economics Among welfare economists of the utilitarist school it has been the general tendency to take satisfaction (in some cases, pleasure) as the unit of welfare. If the function of welfare economics is to contribute data which will serve the social philosopher or the statesman in the making of welfare judgements, this tendency leads perhaps, to a hedonistic ethics.[32] Under this framework, actions (including production of goods and provision of services) are judged by their contributions to the subjective wealth of people. In other words, it provides a way of judging the "greatest good to the greatest number of persons". An act that reduces one person's utility by 75 utils while increasing two others' by 50 utils each has increased overall utility by 25 utils and is thus a positive contribution; one that costs the first person 125 utils while giving the same 50 each to two other people has resulted in a net loss of 25 utils. If a class of utility functions is cardinal, intrapersonal comparisons of utility differences are allowed. If, in addition, some comparisons of utility are meaningful interpersonally, the linear transformations used to produce the class of utility functions must be restricted across people. An example is cardinal unit comparability. In that information environment, admissible transformations are increasing affine functions and, in addition, the scaling factor must be the same for everyone. This information assumption allows for interpersonal comparisons of utility differences, but utility levels cannot be compared interpersonally because the intercept of the affine transformations may differ across people.[33] ### Marginalism For more details on this topic, see Marginal utility. • Under cardinal utility theory, the sign of the marginal utility of a good is the same for all the numerical representations of a particular preference structure. • The magnitude of the marginal utility is not the same for all cardinal utility indices representing the same specific preference structure. • The sign of the second derivative of a differentiable utility function that is cardinal, is the same for all the numerical representations of a particular preference structure. Given that this is usually a negative sign, there is room for a law of diminishing marginal utility in cardinal utility theory. • The magnitude of the second derivative of a differentiable utility function is not the same for all cardinal utility indices representing the same specific preference structure. ### Expected utility theory For more details on this topic, see Expected utility theory. This type of indices involves choices under risk. In this case, A, B, and C, are lotteries associated with outcomes. Unlike cardinal utility theory under certainty, in which the possibility of moving from preferences to quantified utility was almost trivial, here it is paramount to be able to map preferences into the set of real numbers, so that the operation of mathematical expectation can be executed. Once the mapping is done, the introduction of additional assumptions would result in a consistent behavior of people regarding fair bets. But fair bets are, by definition, the result of comparing a gamble with an expected value of zero to some other gamble. Although it is impossible to model attitudes toward risk if one doesn't quantify utility, the theory should not be interpreted as measuring strength of preference under certainty.[34] ### Construction of the utility function Suppose that certain outcomes are associated with three states of nature, so that x3 is preferred over x2 which in turn is preferred over x1; this set of outcomes, X, can be assumed to be a calculable money-prize in a controlled game of chance, unique up to one positive proportionality factor depending on the currency unit. Let L1 and L2 be two lotteries with probabilities p1, p2, and p3 of x1, x2, and x3 respectively being $L_1 =(0.6, 0, 0.4),$ $L_2 =(0,1,0)\ .$ Assume that someone has the following preference structure under risk: $L_{1} \succ L_{2},$ meaning that L1 is preferred over L2. By modifying the values of p1 and p3 in L1, eventually there will be some appropriate values (L1') for which she is found to be indifferent between it and L2—for example $L_{1}' =(0.5, 0, 0.5).$ Expected utility theory tells us that $EU(L_{1}') = EU(L_2)\!$ and so $(0.5)u(x_1)+(0.5)u(x_{3})=1u(x_{2}).$ In this example from Majumdar[35] fixing the zero value of the utility index such that the utility of x1 is 0, and by choosing the scale so that the utility of x2 equals 1, gives $(0.5)u(x_{3})=1.$ $u(x_{3}) = 2.$ ### Intertemporal utility For more details on this topic, see Intertemporal choice. Models of utility with several periods, in which people discount future values of utility, need to employ cardinalism in order to have well-behaved utility functions. According to Paul Samuelson the maximization of the discounted sum of future utilities implies that a person can rank utility differences.[19] ## Controversies Some authors have commented on the misleading nature of the terms "cardinal utility" and "ordinal utility", as used in economic jargon: These terms, which seem to have been introduced by Hicks and Allen (1934), bear scant if any relation to the mathematicians' concept of ordinal and cardinal numbers; rather they are euphemisms for the concepts of order-homomorphism to the real numbers and group-homomorphism to the real numbers —John Chipman, The foundations of utility[27] There remain economists who believe that utility, if it cannot be measured, at least can be approximated somewhat to provide some form of measurement, similar to how prices, which have no uniform unit to provide an actual price level, could still be indexed to provide an "inflation rate" (which is actually a level of change in the prices of weighted indexed products). These measures are not perfect but can act as a proxy for the utility. Lancaster's[36] characteristics approach to consumer demand illustrates this point. ## Comparison between ordinal and cardinal utility functions The following table compares the two types of utility functions common in economics: Level of measurement Represents preferences on - Unique up to - Existence proved by- Mostly used in - Ordinal utility Ordinal scale - sure outcomes - Increasing monotone transformation - Debreu (1954) Consumer theory Cardinal utility Interval scale - random outcomes (lotteries) - Increasing monotone linear transformation - Von Neumann-Morgenstern (1947) Game theory ## References 1. ^ a b Ellsberg, Daniel (1954). "Classic and current notions of 'Measurable utility'". Economic Journal 64 (255): 528–556. doi:10.2307/2227744. 2. ^ Strotz, Robert. (1953). "Cardinal utility". American economic review Vol. 43, No. 2, pp. 384–397 3. ^ Köbberling, Veronika. (2006). "Strength of preference and cardinal utility". Economic theory, No. 27, p. 375 4. ^ Kauder, Emil (1953). "Genesis of the Marginal Utility Theory: From Aristotle to the End of the Eightteenth Century". Economic Journal 63 (251): 648. Retrieved 29 April 2015. 5. ^ Samuelson, Paul (1977). "St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described". Journal of Economic Literature 15 (1): 38. Retrieved 11 May 2015. 6. ^ Bernstein, Peter. (1996). Against the gods. The remarkable story of risk. New York: John Wiley and Sons, p. 191 7. ^ a b c Stigler, George. (1950). "The development of utility theory. I". Journal of political economy Vol. 58, No. 4, pp. 307–327 8. ^ Jevons, William Stanley (1862). "Brief account of a general mathematical theory of political economy". Journal of the Royal Statistical Society 29: 282–287. 9. ^ Jaffé, William (1977). "The Walras-Poincaré Correspondence on the Cardinal Measurability of Utility". Canadian Journal of Economics 10 (2): 300. Retrieved 19 May 2015. 10. ^ Martinoia, Rozenn (2003). "That which is desired, which pleases, and which satisfies: Utility according to Alfred Marshall" (PDF). Journal of the History of Economic Thought 25 (3): 350. Retrieved 21 May 2015. 11. ^ Stigler, George. (1950). "The development of utility theory. II". Journal of political economy Vol. 58, No. 5, pp. 373–396 12. ^ a b Colander, David. (2007). "Retrospectives: Edgeworth's hedonimeter and the quest to measure utility". Journal of economic perspectives, Vol. 21, No. 2, pp. 215–226. 13. ^ McCloskey, Deirdre N. "Happyism". New Republic. Retrieved 11 March 2013. 14. ^ Stigler, George (1937). "The Economics of Carl Menger". Journal of Political Economy 45 (2): 240. Retrieved 21 May 2015. 15. ^ a b Lewin, Shira. (1996). "Economics and psychology: lessons for our own day from the early twentieth century". Journal of economic literature 34 (3), 1293–1323. 16. ^ Viner, Jacob. (1925a). "The utility concept in value theory and its critics". Journal of political economy Vol. 33, No. 4, pp. 369–387 17. ^ Schultz, Henry (1931). "The Italian School of Mathematical Economics". Journal of Political Economy 39 (1): 77. Retrieved 3 June 2015. 18. ^ Hicks, John and Roy Allen. (1934). "A reconsideration of the theory of value". Economica Vol. 1, No. 1, pp. 52–76 19. ^ a b Moscati, Ivan. "How cardinal utility entered economic analysis during the Ordinal Revolution" (PDF). Working Paper. Universita Dell'Insubria Facolta di Economia. Retrieved 9 February 2013. 20. ^ Lange, Oskar (1934). "The Determinateness of the Utility Function". Review of Economic Studies 1 (3): 218–225. Retrieved 10 June 2015. 21. ^ Kornienko, T. (2004). A cognitive bases for cardinal utility. Retrieved November 4, 2012 from the website of the University of Stirling: http://staff.stir.ac.uk/tatiana.kornienko/tape.pdf, p. 3 22. ^ Kahneman, Daniel., Peter Wakker, and Rakesh Sarin. (1997). "Back to Bentham? Explorations of experienced utility?". Quarterly journal of economics Vol. 112, No. 2, pp. 375–405. 23. ^ Kahneman, Daniel., Ed Diener and Norbert Schwarz. (1999). Well-being: the foundations of hedonic psychology. New York: Rusell Sage Foundation 24. ^ Bernadelli, H. (1938). "The end of the marginal utility theory". Economica, Vol. 5, No. 18, p. 196 25. ^ a b Alchian, Armen. (1953). "The meaning of utility measurement". American economic review Vol. 43, No. 1, pp. 26–50. 26. ^ Baumol, William. (1958). "The cardinal utility which is ordinal". Economic journal Vol. 68, No. 272, pp. 665–672 27. ^ a b Chipman, John. (1960). "The foundations of utility". Econometrica Vol. 28, No. 2, pp. 215–216 28. ^ Allen, Roy. (1935). "A note on the determinateness of the utility function". Review of economic studies, Vol. 2, No. 2, pp. 155–158 29. ^ Suppes, Patrick and Muriel Winet. (1955). "An axiomatization of utility based on the notion of utility differences". Management science No. 1, pp. 259–270 30. ^ Gilboa, Itzhak. (2008). Theory of Decision under uncertainty. Cambridge University Press. 31. ^ Poundstone, William. (2010). Priceless. The myth of fair value (and how to take advantage of it). New York: Hill and Wang, p. 39 32. ^ Viner, Jacob. (1925b). "The utility concept in value theory and its critics. II. The utility concept in welfare economics". Journal of political economy Vol. 33, No. 6, pp. 638–659. 33. ^ Blackorby, Charles; Bossert, Walter; Donaldson, David (2002). "Utilitarianism and the theory of justice". In Arrow, Kenneth; Sen, Amartya; Suzumura, Kotaru. Handbook of social choice and welfare. Elsevier. p. 552. ISBN 978-0-444-82914-6. 34. ^ Shoemaker, Paul. (1982). "The expected utility model: its variants, purposes, evidence and limitations". Journal of economic literature, Vol. 20, No. 2, pp. 529–563 35. ^ Majumdar, Tapas. (1958). "Behaviourist cardinalism in utility theory". Economica, Vol. 25, No. 97, pp. 26–33 36. ^ Lancaster, Kelvin. (1966). "A new approach to consumer theory". Journal of political economy Vol. 74, No. 2, pp. 132–157	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8525060415267944, "perplexity": 1714.5622195409658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443738095178.99/warc/CC-MAIN-20151001222135-00195-ip-10-137-6-227.ec2.internal.warc.gz"}
http://mathhelpforum.com/differential-geometry/179775-continuous-metric-spaces.html	# Math Help - continuous metric spaces 1. ## continuous metric spaces Show that 1. the projection map p : R^2 → R given by p(x; y) := x is continuous. . My proofs: We want to show that $\forall$ $\epsilon$ > 0, $\exists$ $\delta$>0 such that: d(x,y)< $\delta$ $\Rightarrow$ d(f(x),f(y)) < $\epsilon$ (x1,y1) (x2,y2) are points in R^2 1) d(x1,x2) < $\epsilon$ \|x1-x2\| < $\epsilon$ We can define $\delta$ = the square root of ( $\epsilon$^2 - (y2-y1)^2) Since there exists a delta for any epsilon we choose, implies that p is continuous. Is this correct... 2. Looks quite correct to me.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9871405959129333, "perplexity": 2738.9904881174793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927104.48/warc/CC-MAIN-20150521113207-00187-ip-10-180-206-219.ec2.internal.warc.gz"}
https://www.licor.com/env/applications/c4photosynthesis.html	# CO2 Response in C4 Plants Understanding the CO2-concentrating mechanism of C4 plants is becoming increasingly important as scientists strive to meet global needs for fuel and food. As in C3 photosynthesis, C4 plants use ribulose 1,5-bisphophate carboxylase/oxygenase (Rubisco) as the carboxylation enzyme for the formation of metabolic carbon. However, the initial reaction in C4 plants occurs in the mesophyll cells, where CO2 is fixed to pyruvate by phosphoenolpyruvate carboxylase (PEPc). The phosphoenolpyruvate formed in this initial reaction is converted to malate which is transferred from the mesophyll cells to the bundle sheath cells (Kanai and Edwards, 1999). This carboxylation reaction functions to increase Rubisco's efficiency by increasing the CO2 concentration ([CO2]) around Rubisco in the bundle sheath (Kanai and Edwards, 1999). The increased [CO2] inhibits the competitive photorespiratory reaction, thereby increasing the net carbon assimilation (von Caemmerer, 2000). C4 plants decrease the rate of photorespiration from approximately 50% in C3 plants (Björkman, 1966; Sharkey, 1988) to about 2% in C4 plants (Dai et al., 1993) at current atmospheric concentrations of CO2 and O2. In measured assimilation rates at different intercellular CO2 concentrations (Ci), the greater efficiency of the C4 is evident in the Ci that corresponds to a net positive rate as carbon assimilation or CO2-compensation point (Γ). Typically, C4 plants' Γ occurs at <10 µmolCO2 molair-1 whereas C3 plants' Γ often ranges from 40 - 50 µmolCO2 molair-1 (Lambers et al., 2006) Biochemical limitations of different enzymes control the assimilation rates at different Ci. At low Ci, the photosynthetic rate is limited by the initial carboxylation of PEPc and can be given by: $A=\frac{{C}_{m}{V}_{\mathrm{pmax}}}{{C}_{m}+{K}_{p}}-{R}_{m}+{g}_{s}{C}_{m}$ where Cm is the [CO2] in the mesophyll cells, Vpmax is the maximum rate of carboxylation of PEPc, Kp is the Michaelis-Menton constant of PEPc for CO2, Rm is the mesophyll dark respiration rate, and gsCm is the inward CO2 diffusion to the bundle sheath (von Caemmerer, 2000). At saturating light, the assimilation rate is linearly related to the maximum PEPc activity (von Caemmerer and Furbank, 1999). Empirical gas-exchange measurements of the assimilation rate at very low Ci can be accomplished either by decreasing the [CO2] outside the leaf (Ca) to low levels or by driving stomatal conductance down, thereby decreasing the CO2 diffusion into the leaf. The first method is preferable since it will drive the Ci down, while other conditions within the leaf chamber can be optimized for measured gas exchange including high stomatal conductance. Errors in leaf stomatal conductance to water (gs) measurements are carried through when calculating Ci (see LI-COR, 2008). As the gs approaches 0, the uncertainty in the calculated Ci increases significantly. Conversely, greater gs decreases the uncertainty in the calculated Ci. Additionally, the greater gs will allow more CO2 to diffuse into the leaf for utilization in assimilation decreasing stomatal limitation (l). Björkman, O. (1966) The effect of oxygen concentration on photosynthesis in higher plants. Physiologia Plantarum, 19, 618-633. Dai, Z., Ku, M. & Edwards, G. E. (1993) C4 Photosynthesis (The CO2-Concentrating Mechanism and Photorespiration). Plant Physiology, 103, 83-90. Kanai, R. & Edwards, G. E. (1999) The biochemistry of C4 photosynthesis. C4 Plant Biology (eds R. F. Sage & R. K. Monson). Academic Press, San Diego. Lambers, H., Chapin III, F. S. & Pons, T. L. (2006) Plant Physiological Ecology. Springer Science+Business Media, LLC, New York. LI-COR, Inc. (2008) Using the LI-6400/LI-6400XT portable photosynthesis system. LI-COR, Inc., Lincoln, NE, USA. Sharkey, T. D. (1988) Estimating the rate of photorespiration in leaves. Physiologia Plantarum, 73, 147-152. von Caemmerer, S. (2000) Biochemical Models of Leaf Photosynthesis. Techniques in Plant Science. CSIRO Publishing, Collingwood, VIC, Australia. von Caemmerer, S. & Furbank, R. T. (1999) Modeling C4 photosynthesis. C4 Plant Biology (eds R. F. Sage & R. K. Monson). Academic Press, San Diego. ### LI-COR Instruments for Measuring C4 Photosynthesis: The LI-6400XT and LI-6800 Portable Photosynthesis Systems are compact, rugged, field portable instruments able to provide researchers with detailed information on plant responses, including the ability to measure fluorescence and gas exchange simultaneously. The LI-6800 is our newest system, featuring a touch-screen interface, improved fluorometer, better gas analyzer precision, better control over chamber conditions, and more. Scroll to Top	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7411730885505676, "perplexity": 14832.195111442445}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221214691.99/warc/CC-MAIN-20180819031801-20180819051801-00294.warc.gz"}
https://www.sarthaks.com/9826/define-1-j-of-work	# Define 1 J of work. 43 views in Physics Define 1 J of work. by (127k points) 1 J is the amount of work done by a force of 1 N on an object that displaces it through a distance of 1 m in the direction of the applied force. 80	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9464606642723083, "perplexity": 521.5902584842074}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141745780.85/warc/CC-MAIN-20201204223450-20201205013450-00190.warc.gz"}
https://kwkelly.com/blog/the-most-important-stations-for-capital-bikeshare/	In my previous two blog posts I've explored some of the data provided by DC's Capital Bikeshare. I've looked at usage trends broken down by group and time and visualized the most traversed routes using Google Maps and Bokeh. Looking back at the map post, it's pretty clear that the Bikeshare dock pair with the most usage is Lincoln Memorial and Jefferson Dr & 14th St SW. They look like they link very heavily to each other, with only tenuous links to other locations. On the other hand, Columbus Circle / Union Station has several heavily trafficked station pair routes emanating from it. Certainly these locations seem very important to Capital Bikeshare, but does that mean they are the most important? This depends, of course, upon exactly what is meant by "most important." # Networks Look again at that map from the previous post. This sort of structure is known as a graph The stations are nodes (or vertices) and the links between them are edges. Graphs are very common in mathematics and computer science; they are used to represent social networks, Markov chains, links on the internet, map routes, and more. The graphs that I've used to display relative bikeshare station pair utilization are called weighted undirected graphs. Undirected implies that the graph does not distinguish between trip directions, so that trips from, for example, New Hampshire Ave & T St NW to Massachusettes Ave & Dupont Cir NW and the reverse trip are the same. Weighted means that there is a number, called (unsurprisingly) a weight, associated to each edge whose meaning depends on context. In our case edge weights indicate the number of trips from one station to another; on a map the weights could be distances between vertices. In a social network the edges may be unweighted with with each edge weight set to 1, indicating that two people are connected. In a Markov chain the edge weights represent transition probabilities. The actual data provided by Capital Bikeshare does yield a directed graph, i.e. one where the direction matters, but I did not have a convenient way of displaying that data on top of a map. In this blog post I am going to attempt to determine the nodes (stations) of the graph that are most important, or most central, to Capital Bikeshare. ## Example Here is an example of a simple graph which represents a two state Markov chain that I took from wikipedia: There are two nodes and four edges. The direction of the edge is given as an arrow and the weight of that edge is given by the number next to it. We can also represent this graph by a matrix. $$G=\begin{bmatrix} 0.3 & 0.4\\ 0.7 & 0.6 \end{bmatrix}$$ The first row gives the probabilities of transitioning from node A to another node -- in this case either itself or node E, respctively. The second row gives those probabilities for node E, again in the same order. This is actually a very special type of matrix called a left stochastic matrix with some neat properties. NB: This is not necessarily the most common matrix representation for the graph. I chose to represent the incoming edges for a node along each row and the outgoing down each column. Representing it the opposite way is also perfectly valid and perhaps more common, but the only difference is that the matrix is transposed. I chose this representation because I prefer to multiply using column vectors, which will come up some time later. # Centrality In graph theory, a question that comes up somewhat regularly is "what is the most important node in my graph?" Measures of graph centrality provide an answer to this question, but the answer is not necessarily unique. On this issue of nonuniqueness, wikipedia says: The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed. "Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternately be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness. Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category. So centrality can give us a way of determining which nodes in a graph are most important, but there are many different ways of ranking centrality! So which one should we use? Let's explore different measures of centrality applied to the graph given by Capital Bikeshare usage to see if we can figure it out. ## Degree centrality Degree centrality is perhaps the simplest method of determining the importance of a vertex. For a directed graph like the one we have, we can compute both indegree and outdegree centrality. In our simple example above, the out degree is given by the column sums and the in degree is given by the row sums. Using this knowledge, or by inspecting the picture, we can see that node A has the largest in degree, with a value of 1.3. However, each node has out degree 1! This is one of those special properties of the stochastic matrix. In the bikeshare example we can do the same thing. We take our graph and turn it into a matrix with starting locations (nodes) running down the columns and ending stations running across the rows. End station number 31000 31001 31002 31003 31004 31005 31006 31007 ... Start station number 31000 21 1 6 5 1 25 1 2 31001 4 28 1 1 14 19 46 3 31002 3 1 41 33 5 29 38 3 31003 4 0 20 55 5 63 50 5 31004 1 17 37 16 14 321 46 15 . . . Our data here is in a pandas dataframe so computing the maximum in and out degree is easy. max_out = grouped.sum(axis=0).argmax() max_in = grouped.sum(axis=1).argmax() Computing this we learn that Columbus Circle / Union Station has both the maximum in degree and out degree at 13120 and 13879. This means that in the first quarter of 2016 over 26000 bikes went through that station. Incredible! The corresponding degrees for the Lincoln Memorial station are 9419 and 9388. So even though we see that incredibly strong link coming from the Lincoln Memorial it's not the most important station, at least by this metric. This should make some sense since there are several relatively large links surrounding Columbus Circle / Union Station, but only one large one coming from the Lincoln Memorial. Let's look at another way of measuring centrality. ## Eigenvector centrality Eigenvector centrality uses the principal eigenvector of the graph to assign a measure of centrality. "It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes." Note how this is different from degree centrality. It doesn't only matter that a given node has many connections, but also if what it is connected to has many connections. This should be better because a node that has very strong connections to one other node, but then both are barely connected to any others should not be central. Let's do an example. First, let's compute the eignvalue centrality for our network. Exactly how this is done isn't important for this example and we'll get to the details later. Our computation indicates that the central vertex is the Jefferson Dr & 14th St SW. This is different from what degree centrality yields, but this seems like a reasonable choice since it is clearly strongly connected. Now let's mess with the data a little bit to show why eigenvector centrality differs from degree centrality in another way. We are going to take or data from before, but replace G(31000,31001) with 100,000. End station number 31000 31001 31002 31003 31004 31005 31006 31007 ... Start station number 31000 21 100000 6 5 1 25 1 2 31001 4 28 1 1 14 19 46 3 31002 3 1 41 33 5 29 38 3 31003 4 0 20 55 5 63 50 5 31004 1 17 37 16 14 321 46 15 . . . Previously, Eads St & 15th St S had an in degree of 299, and now it has 100,298 and while 18th & Eads St had an out degree 330 and now has an out degree of 100,329. This is a huge change and of course now these two rank highest in degree centrality (we saw before that the maxima were only around 13,000). However, the eigenvalue centrality still indicates that Jefferson Dr & 14th St SW is the most central node. The eigenvalue centrality is unaffected by strongly connected nodes that are weakly connected to the rest of the graph. ### What is an eigenvector anyway? And how do we compute it? A casual reader may skip this section if he or she is uninterested in the mathemetics. Given a square matrix (or linear operator) $G$, a vector $v\ne0$ is an eigenvector of $G$ if and only if there exists a $\lambda$ such that $Gv = \lambda v$. Notice that if $v$ is an eigenvector, then so too is any scalar multiple $av$, so we can assume for the rest of this discussion that our eigenvectors are scaled so that $\sum_{i=1}^n v_i = 1$, without loss of generality. So why is the principal eigenvector of a graph a good measure of the centrality? Consider the following example: $$G=\begin{bmatrix} 1 & 3 & 5\\ 4 & 2 & 1\\ 4 & 1 & 0 \end{bmatrix}$$ We have a weighted digraph (directed graph) with some self loops. We are going to do a random walk on this graph, starting with each node being equiprobable. So at each node we assign a probability of $1/3$. Now, we move from node to node, multiplying the probability at each node by the wight to an adjacent node. Consider only the edges going into node A for a moment. A to A gives us $1/3 \times 1 = 1/3$. B to A gives us $1/3 \times 3 = 1$ and C to A gives us $1/3 \times 5 = 5/3$. Do that with the other two nodes. A to B gives us $1/3 \times 4 = 4/3$, B to B $1/3 \times 2 = 2/3$, C to B $1/3 \times 1 = 1/3$ And finally for C we get A to C gives us $1/3 \times 4 = 4/3$, B to C $1/3 \times 1 = 1/3$, C to C $1/3 \times 0 = 0$ Sum the values going into each node and we get A=$9/3$, B=$7/3$, C=$5/3$ Normalize (i.e. ensure everything still sums to 1) and we get A=$9/21$, B=$7/21$, C=$5/21$. We can iterate this process until the probabilities associated to each node cease to move appreciably. Putting the probabilities through the network again, really doesn't change it. The process we just went through to find this fixed point is essentially power iteration (though we used a different normalization). This pdf does a good job showing the connetion between power iteration and a fixed point method. Running those probabilities through the network was exactly multiplication of the probability vector by the link matrix. Repeating that process gets us the power method. Here's a short example in python import numpy as np # initialize the data G = np.matrix('1 3 5; 4 2 1; 4 1 0') v = np.array([1,1,1])/3 v.shape = (3,1) print("G: {}".format(G)) print("v: {}".format(v)) # loop through multiplying each time for i in range(10): v = (Gv)/sum(Gv) print("v: {}".format(v)) G: [[1 3 5] [4 2 1] [4 1 0]] v: [[ 0.33333333] [ 0.33333333] [ 0.33333333]] v: [[ 0.42857143] [ 0.33333333] [ 0.23809524]] v: [[ 0.35947712] [ 0.35947712] [ 0.28104575]] v: [[ 0.40166205] [ 0.34441367] [ 0.25392428]] v: [[ 0.37536845] [ 0.35383827] [ 0.27079328]] v: [[ 0.39163744] [ 0.34800827] [ 0.26035428]] v: [[ 0.38152852] [ 0.35163086] [ 0.26684062]] v: [[ 0.38779355] [ 0.34938576] [ 0.26282069]] v: [[ 0.38390453] [ 0.35077941] [ 0.26531606]] v: [[ 0.38631623] [ 0.34991516] [ 0.26376861]] v: [[ 0.38481974] [ 0.35045144] [ 0.26472883]] ### Back to why As per the example, we see that the principal eigenvector indicates where random walks end up in the graph. This means that the natural flow of information through the network ends up in a proportion according to the values in the principal eigenvector. Since the first value in the principal eigenvector in our example above was the largest, it is the most central node in our graph, according to eigenvector centrality. It should make sense then why we use the principal eigenvector for measuring which nodes in a graph are important. ## PageRank PageRank is the famed algorithm by Larry Page and Sergey Brin that Google's search engine was originally based on. This algorithm ranks web pages, represented as a graph of hyperlinks, by means of graph centrality. There's a good, gentle introduction to PageRank here, a good article on it from the AMS here, and a good blog post with some mathematical rigor practical considerations here. PageRank is very similar to eigenvalue centrality, with a few key adjustemnts made. There's some more math incoming, but only a little linear algebra is needed to understand it. If you wish to skip it, just know that PageRank adjusts the matrix so that a most central node always exists and is always unqiue. ### Mathematical diversion First we take $G$ and ensure that it is column stochastic by normalizing each column by the sum of its entries. Specifically, let $B$ be a matrix, the same size as $G$ whose entries are all $1/n$, where $n$ is the size of $G$. Note that $B$ is both column and row stochastic. Define $p \in [0,1]$ as the probability of randomly jumping from one node to another. Finally we can define the PageRank matrix $$C = pB + (1-p)G.$$ Finally, we just compute the principal eigenvector of this new matrix, just like we did before. That's it. Pretty simple, huh? def page_rank(A, p=0.15, num=1): """Compute the page rank of a given graph A and return the num largest values""" m,n = A.shape assert(m == n) A = A/A.sum(axis=0)[None, :] # normalize columns B = np.full((m, n), 1/m, dtype=A.dtype) C = pB + (1-p)A w, v = eigs(C, k=1, which='LM') return v This matrix is still column stochastic since it is a convex combination of two column stochastic matrices. For $p>0$ the graph $C$ is strongly connected (and is in fact a complete digraph) and the matrix is actually a positive matrix in the sense that each entry is positive. Positiivity is important because it ensures that the matrix satisifies the hypotheses of the Perron-Frobenius theorem, which guarantees that the matrix C has a unique principal eigenvector with all positive components. It also ensures that the algorithm to compute the eigenvector will converge. The stochasticity property ensures that the principal eigenvalue is 1. All of these changes seem reasonable and all of these properties are nice, but what's the point? It seemed like eigenvector centrality was doing just fine, right? ### Back on track On the issue of graph completeness and what could happen if this property is not satisfied, Sergey and Brin in their original PageRank paper (pdf) offer: Consider two web pages that point to each other but to no other page. And suppose there is some web page which points to one of them. Then, during iteration, this loop will accumulate rank but never distribute any rank (since there are no outedges). The loop forms a sort of trap which we call a rank sink. So if the graph is not complete, the flow of information through the graph can get trapped and give some misleading answers. So when we run PageRank, we find that the most important node is Columbus Circle / Union Station. This seems reasonable given its high degree of incoming nodes (it is the most node with highest in degree and out degree), but is it necesarily the correct answer? Surely if Google uses this algorithm it must be the best, right? It does work incredibly well for link networks, but does that make it the correct choice for other types of networks? PageRank emphasizes incoming links more than outgoing while in a bikeshare network it would seem that both of these should be important. Caution: What we did here was not strictly PageRank since PageRank uses unweighted graphs to begin with. Another paper from a few years later (pdf) creates a new algorithm called TextRank which uses weighted graphs, but is exactly the same thing. In writing this post I created that algorithm by accident. ### HITS HITS is an algorithm that predates PageRank and is pretty similar to eigenvalue centrality as well. Instead of just looking at the graph we've been using which is directed, HITS turns it into an undirected graph emphasizing incoming or outgoing edges, alternately. To do this (more linear algebra) HITS computes the left and right singular vectors of the graph, as opposed to the eigenvectors. It does not include the normalization and irreducibility adjustments that PageRank has, but a matrix always has a singular value decomposition though uniqueness is not guaranteed unless all the singular values are distinct. I'm curious what similar adjustments could do for HITS, but that will have to be left for a different time. Because we get two vectors (the left and right singular vectors) from the HITS algorithm, we get two different answers for centrality. The left singular vectors are called the "hubs" of the graph and the right singular vectors are the "authorities." The hubs are nodes in the graph that link to a lot of other nodes; they are important outlinking nodes. The authorities are the opposite, many other nodes point to them, referring to them as one might expect many people to refer to an authority. The algorithm for this is also pretty simple: def hits(A): m, n = A.shape Hu = np.dot(A.T, A) Au = np.dot(A, A.T) w, authorities = eigs(Au, k=1, which='LM') w, hubs = eigs(Hu, k=1, which='LM') return authorities, hubs You'll notice (perhaps you already knew) that the singular vectors that I referred to are exactly the eigenvectors of the matrices $A^TA$ and $AA^T$. This algorithm gives that the authority is Jefferson Dr & 14th St SW and that the hub is Lincoln Memorial. This shouldn't be too surprising since there are very strong links to this nodes from each other ## Summary Here is a table that shows the top 6 most important Capital Bikshare docks for each of the centrality measures considered here. Algorithms Ranks In Degree Centrality Out Degree Centrality Eigenvector Centrality PageRank HITS Hubs HITS Authorities 1 Columbus Circle / Union Station Columbus Circle / Union Station Jefferson Dr & 14th St SW Columbus Circle / Union Station Lincoln Memorial Jefferson Dr & 14th St SW 2 Massachusetts Ave & Dupont Circle NW Massachusetts Ave & Dupont Circle NW Lincoln Memorial Lincoln Memorial Jefferson Dr & 14th St SW Lincoln Memorial 3 Lincoln Memorial Lincoln Memorial Columbus Circle / Union Station Massachusetts Ave & Dupont Circle NW Columbus Circle / Union Station Massachusetts Ave & Dupont Circle NW 4 Jefferson Dr & 14th St SW Jefferson Dr & 14th St SW Massachusetts Ave & Dupont Circle NW Jefferson Dr & 14th St SW Massachusetts Ave & Dupont Circle NW Columbus Circle / Union Station 5 15th & P St NW Thomas Circle 15th & P St NW 15th & P St NW 15th & P St NW 15th & P St NW 6 14th & V St NW 15th & P St NW Jefferson Memorial Jefferson Memorial New Hampshire Ave & T St NW 14th & V St NW Looking at this we can see that for the graph considered here, the various different measures do not produce super different results. Regardless of the centrality measure that we used, the top several most important nodes in the graph appear over and over again. I don't mean to imply that it doesn't matter which one you use, just that for some graphs it may not matter too much. The Wikipedia page on graph centrality has the following figure showing how the most central nodes can be very different depending on the measure chosen for a particular example graph. Clearly these are all different, so which is the best method for ranking nodes in a bikeshare network? I really don't know. If anyone does, you can find my email on my About or message me on twitter. The code I used to comptute all the ranks can be found on my github.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7023695111274719, "perplexity": 705.2853165827114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826968.71/warc/CC-MAIN-20181215174802-20181215200802-00195.warc.gz"}
http://math.stackexchange.com/questions/375299/calculating-circle-properties	# Calculating circle properties. How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle. I have 127 segments each with 5 points in a segment. This is 635 in circumference. The closest radius to this is 102. - The question isn't terribly clear. Could you try to clarify? What, e.g. is the center (it's coordinates), and what is the radius? I'm not sure what you mean when you say you have the radius, but end your post with "the closest radius to 'this' [what this] is 102"? – amWhy Apr 28 '13 at 15:34 I have 127 segments that I need to render points for, each segment has 5 points. This gives me 635. So I need a circle with the circumference of 635, each point in the circumference can be mapped by a point in a segment. Calculating the radius of this causes a flooring of a floating point number to an integer of 102. I would like to calculate each point in the circumference, each point in each segment. So e.g. for each angle in the circle, 360 is used, incremented by 1 each time, how can I determine the (x, y) coordinate of each point in the circumference path, (going clockwise)? – Helium3 Apr 28 '13 at 15:42 If you have 635 points, and want them evenly dispersed along a circle, you can increment the angle by $\dfrac{360}{635}^\circ$. – amWhy Apr 28 '13 at 15:59 $$x = r\cos\theta, \quad y = r\sin\theta, \quad\text{for circle radius r centered at origin}$$ With an arbitrary center $(x_c, y_c)$, then $$(x - x_c) = r\cos\theta, \quad (y - y_c) = r\sin\theta$$ $$x = r\cos\theta + x_c, \quad y = r\sin\theta + y_c$$ $$\tan\theta = \dfrac{y - y_c}{x - x_c} \iff \theta = \arctan\left(\frac{y - y_c}{x - x_c}\right)$$ - Thank you for your time on helping me. :) – Helium3 Apr 28 '13 at 17:22 You're welcome, Helium3! – amWhy Apr 28 '13 at 17:25 Nice, clean answer +1 – Amzoti Apr 29 '13 at 0:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8752407431602478, "perplexity": 706.3327907496237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042986625.58/warc/CC-MAIN-20150728002306-00256-ip-10-236-191-2.ec2.internal.warc.gz"}
https://practice-questions.wizako.com/gmat/quant/permutation-combination-probability/specific-sequence-probability-rearrangement-3.shtml	# GMAT® Quant Practice : Probability Concept: Rearranging letters of a word. Basics of probability. This GMAT quant practice question is a problem solving question in probability. The concept tested in this question is to find the probability that a specific sequence occurs when letters of a word are rearranged. #### Question: What is the probability that the position in which the consonants appear remain unchanged when the letters of the word Math are re-arranged? 1. $\frac{1}{4}\\$ 2. $\frac{1}{6}\\$ 3. $\frac{1}{3}\\$ 4. $\frac{1}{24}\\$ 5. $\frac{1}{12}\\$ Video explanation will be added soon #### Compute denominator In any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes. The total number of ways in which the letters of the word MATH can be re-arranged = 4! = 432*1 = 24 ways. #### Compute numerator and the probability If the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position. The consonants M, T and H can be re-arranged in the first, third and fourth positions in 3! = 6 ways so that the positions in which the consonants appear remain unchanged. Therefore, the required probability $\frac{6}{24} = \frac{1}{4}\\$ Choice A is the correct answer. ### Are you targeting Q-51 in GMAT Quant? Make it a reality! Comprehensive Online classes for GMAT Math. 20 topics. Focused preparation for the hard-to-crack eggs in the GMAT basket!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9508455991744995, "perplexity": 711.6996946023011}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806736.55/warc/CC-MAIN-20171123050243-20171123070243-00767.warc.gz"}
https://questionpaper.org/reasoning-aptitude-model-test-paper-2/	# Model Test Paper - 2 Question 1: Sushil was thrice as old as Snehal 6 years back. Sushil will be times as old as Snehal 6 years hence. How old is Snehal today? [Bank P.O. 1992] Options (a) 18 years (b) 12 years (c) 22 years (d) 24 years Answer: Let Snehals age 6 years back = x. Then, Sushils age 6 years back = 3x. $\left ( \frac{5}{3} \right )$ Χ (x + 6 + 6) = (3x + 6 + 6) hence 5(x+ 12) = 3(3x+ 12) so x=6. Snehal today = (x+ 6) years = 12 years. Question 2: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? Options (a) 230 m (b) 260 m (c) 240 m (d) 270 m Answer: Relative speed = (120 + 80) km/hr $\left ( 200\times \frac{5}{18} \right )m/sec$ $\left (\frac{500}{9}\right )m/sec$ Let the length of the other train be x metres. Then, $\frac{x+270}{9}=\frac{500}{9}$ x+ 270 = 500 x = 230. Question 3: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%? Options (a) Rs. 21,000 (b) Rs. 22,500 (c) Rs. 25,300 (d) Rs. 25,800 Answer: 85 : 18700 = 115 : x x = 18700 x 115 = 25300. Hence, S.P. = Rs. 25,300 Question 4: The discount on a bill due 9 months hence a 16% per annum is Rs.189 The amount of the bill is : Options (a) Rs.1468 (b) Rs.1764 (c) Rs.1575 (d) Rs.2356 Answer: Let P.W. be RS. x. Then,S.I. on Rs. x at 16% for 9 months=Rs.189. $\therefore$ x$\times 16\times \frac{9}{12}\times \frac{1}{100}=189 or x =1575$ $\therefore$ P.W.=Rs.1575. $\therefore$ Sum due = P.W.+T.D==Rs.(1575+189)=Rs.1764 . Question 5: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? (S.B.I. 2000) Options (a) $\frac{3}{4}$ (b) $\frac{2}{4}$ (c) $\frac{3}{2}$ (d) None of these Answer: n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} n(E) = 27. $\therefore p(E)=\frac{N(E)}{N(S)}=\frac{27}{36}=\frac{3}{4}$ Question 6: The third proportional to 0.36 and 0.48 is : Options (a) 0.64 (b) 0.1728 (c) 0.42 (d) 0.94 Answer: Let the third proportional to 0.36 and 0.48 be x Then, 0.36 : 0.48 : 0.48 : x $\Rightarrow \left ( \frac{0.48\times 0.48}{0.36} \right )=0.64$ Question 7: The cost of 15 Bags of salt, each weighing 915 grams is Rs. 18. What will be the cost of 25 Bags, if each bag weight is 1 kg? Options (a) 32.78 (b) 46.64 (c) 53.3 (d) 34.23 More weight, More cost Bags 15 : 25 } :: 18 : z Weighing 915 : 1000 Therefore, (15 x 915 x z) = (25 x 1000 x 18) So, the Rs. is 32.78. Question 8: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: (bank p.o 2002) Options (a) 145.50 (b) 165.70 (c) 175.50 (d) None of these Answer: Since first and second varieties are mixed in equal proportions. So, their average price = Rs.$(\frac{126+135}{2})$ So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: $\therefore \frac{x-153}{22.50}=\: 1\Rightarrow x - 153 = 22.50$ x = 175.50 Question 9: Which of the following number divides the product of 8 consecutive integers? Options (a) 4! (b) 8! (c) 6! (d) 7! Answer: 8! = $8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$ so 8! is divisible by 8 consecutive number Question 10: From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is: (bank p.o 1999) Options (a) 100 m (b) 150 m (c) 173 m (d) 200 m Answer: Let AB be the tower. Then , $\angle APB=30^{\circ}$ and AB = 100 m $\Rightarrow AP=(AB\times \sqrt{3})m$ = $100\sqrt{3}m$ = (100 x 1.73) m = 173 m. Question 11: He was sleeping(1)/in his room when a thief(2)/entered into his house (3)/ and took away a lot of things. (4) No Error (5) Options (a) He was sleeping (b) in his room when a thief (c) entered into his house (d) and took away a lot of things. (e) No Error Question 12: The car in which the minister was traveling ...... with an accident. (bank 2000) Options (a) met (b) crashed (c) hit (d) drove Question 13: Find the correctly spelt words. Options (a) Treachrous (b) Trecherous (c) Trechearous (d) Treacherous Answer: Treacherous means guilty of or involving betrayal or deception. Question 14: More than one person was killed in accident. Options (a) were killed (b) are killed (c) have been killed (d) No improvement Question 15: The man who has committed such a serious crime must get the mostly severe punishment. Options (a) be getting the mostly severely (b) get the most severe (c) have got the most severely (d) have been getting the severe most (e) No correction required Question 16: The employer appeared to be in such an affable mood that Rohit _______. Options (a) felt very guilty for his inadvertent slip (b) decided to ask for a raise in his salary (c) promised him that he would not commit mistake again (d) was pained to press his demand for a new flat. Question 17: Rearrange the following six sentences in proper sequence to form a meaningful paragraph, then answer the questions given below. 1.A case in point is the programme involving the Sardar Sarovar Dam which would displace about 2, 00, 000 people 2. Critics decry the fact that a major development institution appears to absorb more capital than it distributes to borrowers. 3. For all its faults critics however, concede that the bank remains a relatively efficient instrument for distribution of development-aid money. 4. One of the key complaint focuses on this non-profit bank's recent "profitability" 5. Although the lives of millions of people around the globe have been improved by the bank's activities, it is now under fire. 6 .The bank is also being blamed for large-scale involuntary resettlement to make way for dams and other construction projects. Which sentence should come sixth in the paragraph? Options (a) 3 (b) 4 (c) 1 (d) None of these Question 18: As a rule of thumb, a manned mission costs from fifty to a hundred times more than a comparable unmanned mission. Thus, for scientific exploration alone, ...(1)... missions, employing machine intelligence, are ...(2)... However, there may well be ...(3)... other than scientific for exploring ...(4)... social, economic, political, cultural or ...(5)... (solve as per the direction given above) Options (a) manned (b) unmanned (c) space (d) lunar Question 19: I felt the wall of the tunnel shiver. The master alarm squealed through my earphones. Almost simultaneously, Jack yelled down to me that there was a warning light on. Fleeting but spectacular sights snapped into ans out of view, the snow, the shower of debris, the moon, looming close and big, the dazzling sunshine for once unfiltered by layers of air. The last twelve hours before re-entry were particular bone-chilling. During this period, I had to go up in to command module. Even after the fiery re-entry splashing down in 81° water in south pacific, we could still see our frosty breath inside the command module. The word 'Command Module' used twice in the given passage indicates perhaps that it deals with Options (a) an alarming journey (b) a commanding situation (c) a journey into outer space (d) a frightful battle Answer: A journey into outer space. Question 20: Each question consist of two words which have a certain relationship to each other followed by four pairs of related words, Select the pair which has the same relationship. TEN:DECIMAL Options (a) seven:septet (b) four:quartet (c) two:binary (d) five:quince Question 21: 6 42 294 2058 14406? Options (a) 100842 (b) 72030 (c) 86436 (d) 115248 (e) 129654 Question 22: In these series, you will be looking at both the letter pattern and the number pattern. Fill the blank in the middle of the series or end of the series. SCD, TEF, UGH, _______, WKL Options (a) CMN (b) UJI (c) IJT (d) VIJ Answer: There are two alphabetical series here. The first series is with the first letters only: STUVW. The second series involves the remaining letters: CD, EF, GH, IJ, KL. Question 23: Each question has an underlined word followed by four answer choices. You will choose the word that is a necessary part of the following word. shoe Options (a) laces (b) walking (c) sole (d) leather Answer: All shoes have a sole of some sort.Not all shoes are made of leather (choice b); nor do they all have laces (choice c). Walking (choice d) is not essential to a shoe. Question 24: A good way to figure out the relationship in a given question is to make up a sentence that describes the relationship between the first two words. Then, try to use the same sentence to find out which of the answer choices completes the same relationship with the third word. Careful is to cautious as boastful is to Options (a) arrogant (b) humble (c) joyful (d) suspicious Answer: Careful and cautious are synonyms (they mean the same thing). Boastful and arrogant are also synonyms. The answer is not (choice b) because humble means the opposite of boastful. The answer is not choice c or d because neither means the same as boastful. Question 25: First, you will be given a list of three "nonsense" words and their English word meanings. The question(s) that follow will ask you to reverse the process and translate an English word into the artificial language. Here are some words translated from an artificial language. godabim means kidney stones romzbim means kidney beans romzbako means wax beans Which word could mean "wax statue"? Options (a) godaromz (b) lazbim (c) wasibako (d) romzpeo Answer: In this language, the adjective follows the noun. From godabim and romzbim, you can determine that bim means kidney. From romzbim and romzbako, you can determine that romz means beans. Therefore, bako means wax. Because the adjective wax must come after the noun in this language, wasibako is the only choice. Question 26: Each question presents a situation and asks you to make a judgment regarding that particular circumstance. Answer each one solely on the basis of the information given. Mark is working with a Realtor to find a location for the toy store he plans to open in his town. He is looking for a place that is either in, or not too far from, the center of town and one that would attract the right kind of foot traffic. Which of the following locations should Mark's Realtor call to his attention? Options (a) a little shop three blocks away from the town's main street, located across the street from an elementary school and next door to an ice cream store (b) a stand-alone storefront on a quiet residential street ten blocks away from the town's center (c) a storefront in a new high-rise building near the train station in the center of town whose occupants are mainly young, childless professionals who use the train to commute to their offices each day. (d) a storefront in a small strip mall located on the outskirts of town that is also occupied by a pharmacy and a dry cleaner. Answer: This option is both near the center of town and in a location (near a school and an ice cream store) where children and their parents are sure to be around. This is the only option that meets both of Mark's requirements. Question 27: Read the below passage carefully and answer the following questions: At a small company, parking spaces are reserved for the top executives: CEO, president, vice president, secretary, and treasurer with the spaces lined up in that order. The parking lot guard can tell at a glance if the cars are parked correctly by looking at the color of the cars. The cars are yellow, green, purple, red, and blue, and the executives names are Alice, Bert, Cheryl, David, and Enid. # The car in the first space is red. # A blue car is parked between the red car and the green car. # The car in the last space is purple. #The secretary drives a yellow car. # Alice's car is parked next to David's. # Enid drives a green car # Bert's car is parked between Cheryl's and Enid's. # David's car is parked in the last space. Who is the secretary? Options (a) David (b) Alice (c) Bert (d) Cheryl (e) Enid Answer: Cheryl cannot be the secretary, since she's the CEO, nor can Enid, because she drives a green car, and the secretary drives a yellow car. David's, the purple car, is in the last space. Alice is the secretary, because her car is parked next to David's, which is where the secretary's car is parked. Question 28: In each question below is given a statement followed by two assumptions numbered I and II. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement. Assumptions: 2. The people want to know the criterion of an excellent suit. Options (a) Only assumption 1 is implicit (b) Only assumption 2 is implicit (c) Either 1 or 2is implicit (d) Neither 1nor 2 is implicit (e) Both 1and 2 are implicit Answer: The statement mentions that if the people ask about the tailor, your suit is good. This means that people ask only in the situation when the thing is good. So, I is implicit. The criteria of an excellent suit is not mentioned. So, II is not implicit. Question 29: In each question below is given a statement followed by two courses of action numbered 1 and 2 . You have to assume everything in the statement to be true and on the basis of the information given in the statement, decide which of the suggested courses of action logically follow(s) for pursuing. Statement: A large number of people in ward X of the city are diagnosed to be suffering from a fatal malaria type. Courses of Action: The city municipal authority should take immediate steps to carry out extensive fumigation in ward X. The people in the area should be advised to take steps to avoid mosquito bites. Options (a) Only 1 follows (b) Only 2 follows (c) Either 1 or 2 follows (d) Neither 1 nor 2 follows (e) Both 1 and 2 follow Answer: Clearly, prevention from mosquitoes and elimination of mosquitoes are two ways to prevent malaria. So, both the courses follow. Question 30: If, in a code, MIND becomes KGLB and ARGUE becomes YPESC, then what will DIAGRAM be in that code? Options (a) BGYPYEK (b) LKBGYPK (c) GLPEYKB (d) BGYEPYK Answer: Each letter in the word is moved two steps backward to obtain the corresponding letter of the code. Question31: What does the && operator do in a program code? Answer: The && is also referred to as AND operator. When using this operator, all conditions specified must be TRUE before the next action can be performed. If you have 10 conditions and all but 1 fails to evaluate as TRUE, the entire condition statement is already evaluated as FALSE. Question 32: What is syntax error? Answer :Syntax errors are associated with mistakes in the use of a programming language. It maybe a command that was misspelled or a command that must was entered in lowercase mode but was instead entered with an upper case character. A misplaced symbol, or lack of symbol, somewhere within a line of code can also lead to syntax error. Question 33: What is the difference between the expression “++a” and “a++”? Answer :In the first expression, the increment would happen first on variable a, and the resulting value will be the one to be used. This is also known as a prefix increment. In the second expression, the current value of variable a would the one to be used in an operation, before the value of a itself is incremented. This is also known as postfix increment. Question 34: What would happen to X in this expression: X += 10; (assuming the value of X is 5) Answer :X +=10 is a short method of writing X = X + 10, so if the initial value of X is 5, then 5 + 10 = 15. Question 35: What are header files and what are its uses in C programming? Answer :Header files are also known as library files. They contain two essential things: the definitions and prototypes of functions being used in a program. Simply put, commands that you use in C programming are actually functions that are defined from within each header files. Each header file contains a set of functions. For example: stdio.h is a header file that contains definition and prototypes of commands like printf and scanf. ### Institute Management Software Start Teaching – Start Earning Please comment on Model Test Paper - 2	{"extraction_info": {"found_math": true, "script_math_tex": 19, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49412810802459717, "perplexity": 2494.6301124201113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585204.68/warc/CC-MAIN-20211018155442-20211018185442-00576.warc.gz"}
https://galoisrepresentations.wordpress.com/2015/10/17/hilbert-modular-forms-of-partial-weight-one-part-iii/	Hilbert Modular Forms of Partial Weight One, Part III My student Richard Moy is graduating! Richard’s work has already appeared on this blog before, where we discussed his joint work with Joel Specter showing that there existed non-CM Hilbert modular forms of partial weight one. Today I want to discuss a sequel of sorts to that paper, which also forms part of Richard’s thesis (I should note that he already has five publications and will have 7 or 8 papers by the time he graduates.) The starting observation is as follows. Fix a real quadratic field F. From the perspective of Galois representations, the Hilbert modular forms of partial weight one fall under the case $\ell_0 = 1$ in the notation of my paper with David Geraghty (this is in the context of coherent cohomology). To orient the reader, let us discuss three classes of such forms: 1. Hilbert modular forms of weight $[2k+1,1]$ for a real quadratic field $F.$ 2. Regular algebraic cuspidal automorphic forms for $\mathrm{GL}(3)/\mathbf{Q}.$ 3. Regular algebraic cuspidal automorphic forms for $\mathrm{GL}(2)/F$ for an imaginary quadratic field $F.$ Suppose one fixes a tame level $N$ and then looks at the space of such forms as the weights vary. In both of the latter cases, the problem has been raised (or even conjectured, for $N = 1$ and $\mathrm{GL}(3)$ by Ash and Pollack here), of whether all but finitely many such forms arise via functoriality from a smaller group. More explicitly, one can ask whether: 1. If $G = \mathrm{GL}(2)/F,$ then all but finitely many cuspidal regular algebraic forms of conductor $N$ either arise (up to twist) via base change from $\mathrm{GL}(2)/\mathbf{Q},$ or are induced from a quadratic CM extension $E/F.$ 2. If $G = \mathrm{GL}(3)/\mathbf{Q},$ then all but finitely many cuspidal regular algebraic forms of conductor $N$ arise up to twist as the symmetric square of a form from $\mathrm{GL}(2)/\mathbf{Q}.$ Naturally enough, one can make the same conjecture whenever $\ell_0 > 0,$ appropriately formulated. There does not seem to be any case of this conjecture which is known, although there are analogous results (where one fixes the weight and varies the level) in both weight one (where it is almost trivial) and for imaginary quadratic fields (in the work of Calegari-Dunfield and Boston-Ellenberg). Still, the conjectures in varying weight seem pretty hard even for $N = 1.$ In that context, Richard proves the following nice complementary pair of theorems below. Let $F = \mathbf{Q}(\sqrt{7}).$ The field $F$ has narrow class number $2$ and there is a unique odd everywhere unramified quadratic character $\chi$ of $G_F$ with fixed field $E = F(\sqrt{-1}).$ Theorem I (Moy) Let $F$ and $\chi$ be as above. Every Hilbert modular form over $F$ of weight $[2k+1,1]$ and level $N = 1$ is CM, and in particular is induced from $E.$ Theorem II (Moy) Let $F$ and $\chi$ be as above. Let $M$ be a strongly compatible family of two dimensional Galois representations of $F$ with determinant $\chi,$ level $N = 1,$ and Hodge–Tate weights $[0,0]$ and $[k,-k].$ Then $M$ is induced from $E.$ Theorem I is almost an immediate consequence of Theorem II, with the caveat that one doesn’t quite have complete local-global compatibility for partial weight one modular forms (though results and methods of Luu, Jorza, and Newton get close). Theorem II on the other hand is a consequence of the following: Theorem III (Moy) Let $F$ and $\chi$ be as above. Let $\rho: G_F \rightarrow \mathrm{GL}_2(\overline{\mathbf{Q}}_3)$ be a continuous irreducible representation with determinant $\chi$ that is unramified at all finite places except for one prime $v\|3.$ Then $\rho$ is induced from a character of $G_E.$ The argument in this case is (roughly) the following. Using a Tate-style argument (with discriminant bounds), one proves that the residual representation $\overline{\rho}$ must have semi-simplification $\chi \oplus 1.$ The restriction of $\rho$ to $G_E$ then has the property that its image is pro-3 and unramified outside the fixed prime $v\|3.$ Yet one shows by a class field theory computation that the largest abelian 3-extension unramified outside $v\|3$ is cyclic, which (by consideration of the Frattini quotient) immediately implies that the image of $\rho$ restricted to $G_E$ factors through a cyclic quotient as well, and one is done. Note that to deduce Theorem I, one first has to prove (using a congruence argument) that at the other prime $w\|3,$ either: 1. The representation $\rho$ is unramified at $w,$ 2. The representation $\rho$ restricted to $D_w$ has unramified semi-simplification. In particular, the generalized eigenvalues of $\mathrm{Frob}_w$ for $\overline{\rho}$ are both the same. To finish, one rules out the second possibility by computing all the modular residual representations explicitly by doing computations in low weight (this can ultimately be reduced to a computation on the definite quaternion side, although Richard had to write his own programs to do this since the current magma implementation required trivial character for non-parallel weight.) It is true that these arguments will not suffice for the more general conjecture, but then, I haven’t seen a viable strategy to prove those conjectures either! This entry was posted in Mathematics and tagged , , , , , , , , , , . Bookmark the permalink. One Response to Hilbert Modular Forms of Partial Weight One, Part III 1. 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http://math.stackexchange.com/users/5282/fuzxxl?tab=questions	FUZxxl Reputation 2,075 Next privilege 2,500 Rep. Create tag synonyms 2 11 27 Impact ~62k people reached • 3 helpful flags • 235 votes cast # 39 Questions 55 140 14 19k views 8 20 5 1k views 3 19 1 404 views 4 13 3 2k views 3 12 1 685 views 2 11 1 517 views 6 9 3 4k views 5 9 5 9k views 5 7 4 463 views 4 5 1 192 views 3 5 4 299 views 1 4 1 55 views 2 4 2 423 views 3 4 3 388 views 3 5 142 views 1 3 2 110 views 1 3 4 173 views 1 3 3 645 views 2 1 109 views 2 2 3 66 views 2 2 2 494 views 1 2 0 43 views ### An equivalent statement for convergence [duplicate] jun 21 '12 at 12:15 Martin Sleziak 32.6k 2 2 1 473 views 1 2 2 414 views 2 2 3 208 views 1 2 1 65 views 1 2 2 917 views 1 1 vote 2 71 views 1 0 0 68 views ### Can we express every partial order with these two combinators? oct 19 at 13:25 lisyarus 1,933 1 0	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5843569040298462, "perplexity": 24731.257231013322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398450715.63/warc/CC-MAIN-20151124205410-00336-ip-10-71-132-137.ec2.internal.warc.gz"}
https://onepetro.org/SNAMETOS/proceedings-abstract/TOS15/1-TOS15/D013S003R002/3712	The determining of aerodynamic coefficients is one of the essential steps in the design of an offshore structure such as an FPSO (Floating Production Storage and Offloading). It is extremely important as they are one of the dimensioning criteria for the mooring design. Nowadays, these loads are mainly assessed through wind tunnel tests performed at model scale. Estimating realistic wind loads however, remains a big challenge. The complexity and associated simplification level of FPSO topside structures, the scale effects and the establishment of the atmospheric boundary layer imply that many simplifications are to be made. Nowadays with the evolution of CFD (Computational Fluid Dynamics) software, and the increase of the meshing capacity, new scopes open to CFD. Aerodynamic simulations on complex FPSO structures are therefore now possible, but need specific developments and validations that are presented in this paper. The first steps for setting up a procedure for computing these coefficients are thus presented. The main objective of the work presented here is to investigate the ability of CFD for evaluating wind loads on complex FPSOs topsides. In a first stage, the first elements of the numerical model used as a numerical wind tunnel are presented and studied. Then, some specific effects such as the blockage effects, the atmospheric boundary layer and their numerical modelling are studied. The geometric model used corresponds to the one used in wind tunnel. The same Atmospheric Boundary Layer is simulated and a thorough effort is performed to ensure the mesh convergence. Then, the accuracy of the blockage effect correction is evaluated by performing computations with and without blockage, and results are compared with classical corrections applied in wind tunnel tests. In the last step, a relevant comparison between wind tunnel tests and simulations on different geometries with grids density up to 50 million cells is presented. The ability for CFD to evaluate aerodynamic coefficients is then discussed. This content is only available via PDF.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9250544309616089, "perplexity": 956.5110210097383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00263.warc.gz"}
http://www.sciencemadness.org/talk/viewthread.php?tid=29&page=4#pid117316	Sciencemadness Discussion Board » Special topics » Energetic Materials » Trinitrotoluene preparation Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Responsible Practices » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues Pages: 1 2 4 6 .. 11 Author: Subject: Trinitrotoluene preparation CD-ROM-LAUFWERK Harmless Posts: 30 Registered: 23-4-2005 Member Is Offline Mood: No Mood i cant open both of it... quicksilver International Hazard Posts: 1820 Registered: 7-9-2005 Location: Inches from the keyboard.... Member Is Offline Mood: ~-=SWINGS=-~ I was very curious about something related to TNT and didn't want to start another thread so I thought I would reserect this one. I have two questions that I was wondering about : 1.) TNT appears to crystalize in needles and in platlets. What contributing factors allow TNT to crystalize in needle form? 2.) Has anyone developed a solid nitrate synth for TNT? It appears that those who have attempted same have not had success. I have put together what looks like a good experiment for a solid nitrate / nitrafication of toluene but wanted to know if there are circumstances that inhibit the synth of TNT using soolid nitrates. Superficially it appears to solve the higher nitration issue in the "German" single pot nitration. nitro-genes International Hazard Posts: 1029 Registered: 5-4-2005 Member Is Offline IIRC, higher concentration solutions of TNT favor plattlets while lower concentrations favor needles... YT2095 International Hazard Posts: 1091 Registered: 31-5-2003 Location: Just left of Europe and down a bit. Member Is Offline Mood: within Nominal Parameters I made a few milligrams of TNT many moons ago following an A level text book, my Nitric acid wasnt all that strong though and so my crystalisation took place in the fridge to leave waxy needle like crystals growing off the walls in the test tube under the soln. they were an off white color and washed up very nicely. so a Not so strong nitrating mix and fridge cooling over a few days seemed to work for me. other than quantity of the reaction mix being less that outlined thats the only deviation I made from the text book. \"In a world full of wonders mankind has managed to invent boredom\" - Death Twinkies don\'t have a shelf life. They have a half-life! -Caine (a friend of mine) quicksilver International Hazard Posts: 1820 Registered: 7-9-2005 Location: Inches from the keyboard.... Member Is Offline Mood: ~-=SWINGS=-~ From what I had seen temp and nitration concentration had direct effects on crystal structure but I would not quantify the results. I had two observations of two nitrations; both equal. One went to needles (nice ones) the other platlets... it was infuriating. I am convinced that TNT is one of the easiest energetic materials to synth aside from NG and I love crystal structue in general so it has been a favorite of mine for many years to study. However there seems no reason not to be able to utilize a solid nitrate to this end and that would put it in the realm of hobbiest material. There was someone who attempted it awhile back and said that it appeared that the nitration went too fast! -That the high concentation of acids didn't allow for the control needed to maintain temp, etc. This seemed too much for me. Higher concentrations have always been just as easy to control if the temp was controlable. This is the same issue as tetryl. Dimethylaniline (also a benzene) nitrates much too vigorously in streight HNO3 so the use of sulfonation (via H2SO4 in a prior solution) controls that issue. But most of the original material calls for a higher concentration than 70% HN03. So why not use a mixed acid in addition to the sulfonated solution? It works with no problem so long as the original H2SO4 is accounted for in the nitration (no by products). -Extrapolating this and attempting it with toluene would seem even easier. Toluene is easy to nitrate. But the original material calls for 75% HNO3 and indeed, if the level IS higher the yield should be better and product purer. With 68-70 % it's easy to get an 80% yield. I believe that with using a solid nitrate the yield should be vastly higher and the product purer due to lack of water in the nitration. But I have not heard of it being done. This is something that if successful, would produce a workable secondary of consistent quality. TNT may be a gateway to a heck of a lot of fun stuff. Found some answers. (Friends at the local university are great) Notes on trinitrotoluene 1/14/07 TNT has isomers in its production as a crude product. These produce differing crystal: needles palettes, rhomboids, etc. The isomers are alpha, beta, gamma, delta, epsilon, & zeta. Alpha produces needles. Beta –thin platelet’s, gamma –rhomboids & zeta possibly plates of a differing type. The MP of the differing isomers are : alpha – 80C beta- 112, gamma 104, delta-137, epsilon- 97, & zeta-79.5 Gamma isomer crystallizes first from recrystalized material dissolved in hot (boil level) ethanol. This is a crude separation from fractional crystallization. Alpha isomer is separated by fractional precipitation from warm etoh: Alpha being slightly more soluble than the others. Alpha, beta, & gamma will react with aniline (or dimethylanaline but it will or course be a dimethyl isomer) and this gives distinctive products – nice crystals. Alpha crystallizes in long glinting VIOLET needles! (the same as trinitrobenzene – mp 83C) Beta – deep red plates, Gamma – reacts w/ hot alcoholic aniline to give orange rhomboids. Super Sensitizing Idea; Beta & Gamma Isomers react w/ NaOH to sensitize powerfully. But NaOH is not the only salt that will sensitize TNT thus the care in which anti acid wash should be chosen. Even carbonates of the alkali metals will sensitize (barium carbonate used in Japan?) Sodium carbonate (alcoholic solution – 1% in reaction) precipitates a dark blue substance in the solution being treated w/ acid. – Turns out this substance is dinitrocresol! However 1% sodium carbonate in alcoholic solution also produces dinitrotolyloxides. When they are formed salts of this complex are very explosive (primaries?) Ammonium sulfide in reaction w/ TNT isomers yield interesting color variations. Alpha – deep red. Beta –greenish yellow Gamma – blue! Epsilon –rose red (light). Zeta – orange TNT dets from heat! There is something called “Goettig’s Mixture”. Heat from platinum wire causes explosion! Actual detonation as in primary is yet to be proven. Data from German text book (1907). TNT - 22.22% Barium Nitrate - 9.83% Nitro Cellulous (smokeless powder nitrate level - 67.96% Intimate mixture via whetting, etc. So why does a batch have one isomer greater or another?? Well I have a collection of isomers in each batch. So the primacy of one, let's say alpha is more determined by getting rid of the rest via either recrystalization or happenstance when a batch is finished. Since hobbiest lab conditioons vary no matter what due to small batch size and lack of automation I don't think I can do much about it other than "weed-out" the unwanted isomers rather than the other way.... [Edited on 15-2-2007 by quicksilver] quicksilver International Hazard Posts: 1820 Registered: 7-9-2005 Location: Inches from the keyboard.... Member Is Offline Mood: ~-=SWINGS=-~ Interesting crystal growth pictures utilizing differing re-crystalization methods.... Using acetone and ethanol differing crystals may be obtained. Rhomboids (acetone) are unusually dense while needles (ethanol) can be grown up to one inch in size. MP on both 80 C. [Edited on 25-2-2007 by quicksilver] Attachment: pics.rar (806kB) Rosco Bodine Banned Posts: 6370 Registered: 29-9-2004 Member Is Offline Mood: analytical Hey quicksilver . Could you please edit that image size downward to about half what it is .....so that it doesn't mess up the text page width formatting ? quicksilver International Hazard Posts: 1820 Registered: 7-9-2005 Location: Inches from the keyboard.... Member Is Offline Mood: ~-=SWINGS=-~ Sorry about that. I thought it was a querk of FireFox and would be compensated for in a relaod of the page. Rosco Bodine Banned Posts: 6370 Registered: 29-9-2004 Member Is Offline Mood: analytical optimum nitrating acid composition This short article provides some insight concerning the optimum yield nitrating acid composition for nitration of a mononitrotoluene precursor to the trinitrated TNT . As the article states , this data is not pertinent to the disclosure of the most economical proportions or stepwise process , but only studies the composition and quantity of acid in order to identify the optimum conditions in terms of yield for the complete nitration of a mononitrotoluene precursor , to develop good data which is relevant to further process modeling . The most pertinent data is the perhaps surprising result concerning the beginning and final water content of the nitration acids , where the result is that some water content actually provides a higher yield than anhydrous nitration acid mixtures which are attained by use of fuming sulfuric acid , as oleum . This result has also been reported for nitration mixtures for nitroesters , where some small water content in the nitrating acids also results in a higher yield than absolutely anhydrous nitrating acids . Anyway , the charted nitrating acid data should be useful in projecting and calculating what may also be a useful acid composition for a more typical nitration which is applied to a dinitrotoluene precursor . For example something a bit over half the quantity and composition of acid reported optimum for the conversion of mononitrotoluene to TNT should be applicable for conversion of dinitrotoluene to TNT , resulting in a similar spent acid composition . I believe this is also good news with respect to the possible usefulness of dehydrating salts which might be an included part of nitrating acid mixtures , as an alternative strategy to the use of oleum to reduce the water content of nitration acids for TNT . I have long had the idea that a respectably efficient nitration mixture for TNT could be attained by use of dehydrating salts , and perhaps added nitration catalysts also , if indeed the dehydrating salt did not serve that function also , without the need for nitration mixtures made up from oleum . Attachment: Nitration of Toluene to TNT.pdf (308kB) tito-o-mac Hazard to Others Posts: 117 Registered: 30-6-2007 Member Is Offline Mood: No Mood You can find TNT preparation here with many other explosives: http://www.roguesci.org/megalomania/explo/trinitrotoluene.ht... Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood When I make MNT I will not convert it to DNT right after I make it. I will store it for around 1 week. Can I just remove it from the spent acid or do I also have to neutralize and wash it? quicksilver International Hazard Posts: 1820 Registered: 7-9-2005 Location: Inches from the keyboard.... Member Is Offline Mood: ~-=SWINGS=-~ In order to complete a synthesis you should do your best to clean the product from it's lab components and clean your equipment as well. Things should not be haphazard in any of your work. YES, clean the product; that way you'll know that you have that material, not many others in that container. Additionally it will keep better and be less reactive. Just like doing homework for school, you wouldn't do a half-job there / so why do that in your lab? Be thorough and complete; reach for exacting standards. Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood To 60 ml of conc. H2SO4 (made by boiling down the acid extracted from a old car battery) I added 45 g of NaNO3. When the NaNO3 dissolved I added 30 ml of toluene in 4 portions). The toluene first turned in a red liquid, then orange and then again to red. After around 45 min it looked like this: Then I added it to water, then to a sodium bicarbonate solution and then in a saturated salt solution. Final yield is around 26 ml of non-clear orange MNT (it has a very nice smell) Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood Does anyone know in what ratio should I add MNT to a H2SO4/NaNO3 mixture to nitrate it to DNT? You know there is an edit button for your previous post, so you should have edited and added this to that post as opposed to making a new post. Next time it gets deleted. -Davster [Edited on 3-2-2008 by The_Davster] quicksilver International Hazard Posts: 1820 Registered: 7-9-2005 Location: Inches from the keyboard.... Member Is Offline Mood: ~-=SWINGS=-~ How do you know you did something "wrong" or "right"? What mechanism are you using for verification of success? Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood Quote: Originally posted by quicksilver How do you know you did something "wrong" or "right"? If I did something right the product is what it must be. If I did something wrong the product is not what it must be. Quote: Originally posted by quicksilver What mechanism are you using for verification of success? By the color, smell, and does it float or sink in water. Sobrero Harmless Posts: 21 Registered: 20-5-2006 Location: Belgium Member Is Offline Mood: Lifting my skinny fists like antennas to heaven I've made TNT a few times, by first nitrating toluene to DNT and then to TNT. I like this path a lot since it contains only two steps and proceeds just as fine! Toluene can be easily nitrated to dinitrotoluene by adding , for example, 10ml of toluene to a cooled nitrating mixture comprising 18g of ammonium nitrate (130% of theory) and 32ml sulfuric acid, and heating this for 2 hours at 60Â°C, with stirring. Then, after drowning, washing and neutralising, DNT is obtained in 95% yield, as a light yellow, slightly waxy solid . So, @ Zinc, for the preparation of DNT from MNT, a nitrating mixture containing a slight (~5-10% excess) molar excess of (in your case) sodium nitrate and sulfuric acid should be entirely adequate (with reaction conditions mentioned above). "There exists a world. In terms of probability, this borders on the impossible." (Jostein Gaarder) Fashist Hazard to Self Posts: 73 Registered: 19-7-2007 Member Is Offline Mood: Powerful I made tnt very easy by reflux system(see below picture) First i made Dnt and then made tnt in the reflux system(100-105c, 2hour) Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood I have tried the method that Sobrero posted only a little upscaled and used sodium nitrate instead ammonium nitrate. I heated the mix for two hours (sometimes even hotter than 60 C). At the begging I had a runaway but I cooled it fast and then again put it on a hotplate to heat it. After two hours there is an orange oil on top of the acid. As DNT is solid I think that the reaction failed. What did I do wrong? At least I got some MNT Fascist what ratios of chemicals did you use to make your DNT and how long did you heat it? Sobrero Harmless Posts: 21 Registered: 20-5-2006 Location: Belgium Member Is Offline Mood: Lifting my skinny fists like antennas to heaven You mean liquid at elevated (60-70Â°C) or at room temperature (after 'drowning')? Dinitrotouene melts quite easily (around 50-60Â°C IIRC, for a mixture of isomers). [Edite le 8-2-2008 par Sobrero] "There exists a world. In terms of probability, this borders on the impossible." (Jostein Gaarder) Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood It was liquid at the elevated temperature. Fashist Hazard to Self Posts: 73 Registered: 19-7-2007 Member Is Offline Mood: Powerful I used this book Ratio http://rapidshare.com/files/90231545/fmx.zip.html Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood Thank you! Very interesting book. Zinc National Hazard Posts: 472 Registered: 10-5-2006 Member Is Offline Mood: No Mood Today I made more MNT. Now i have 132 g I want to make DNT from it using a mixture of sodium or ammonium nitrate and H2SO4. So how much of NO3/AN should I use? As far as I know I need one mol of NO2 anions per one mol of MNT to make DNT. 132 g of MNT is around one mol. So for that I need one mol of NH4NO3 (or NaNO3) and that is around 80 g (or 85 g of NaNO3) as one mol of NaNO3 or NH4NO3 gives one mol of NO2 anions. So how much of H2SO4 should I add to the nitrate (I think one mol as the nitrates turn to bisulfates and how much more to absorb the water?)? And how much excess of nitrate and sulfuric acid should I use? And under what conditions should the reactants to be to react (heat how long and that things)? And are the things I wrote above correct? Sorry for too much questions but I don't know a lot of theoretical chemistry. Fashist Hazard to Self Posts: 73 Registered: 19-7-2007 Member Is Offline Mood: Powerful My Suggestion is Using Con.Nitric Acid I Made it Using Dry Mg(NO3)2 + HNO3(57%) and then Distil. Pages: 1 2 4 6 .. 11 Sciencemadness Discussion Board » Special topics » Energetic Materials » Trinitrotoluene preparation Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Responsible Practices » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5297443866729736, "perplexity": 8210.233428123149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572215.27/warc/CC-MAIN-20220815235954-20220816025954-00591.warc.gz"}
https://www.arxiv-vanity.com/papers/cond-mat/0109042/	# Statistical properties of contact vectors A. Kabakçıoğlu, I. Kanter, M. Vendruscolo, and E. Domany Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel Department of Physics, Bar Ilan University, 52900 Ramat Gan,Israel Oxford Centre for Molecular Sciences, Central Chemistry Laboratory University of Oxford, South Parks Road, OX1 3QH Oxford UK ###### Abstract We study the statistical properties of contact vectors, a construct to characterize a protein’s structure. The contact vector of an -residue protein is a list of integers , representing the number of residues in contact with residue . We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of is only less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction. I. Introduction The protein folding problem has been the subject of extensive research in the last decade and although much has been learned a satisfactory understanding of the phenomenon has not been reached yet [1, 2, 3]. The physical approach to the problem is to consider the native state of a protein as the ground-state of a Hamiltonian which acts on sequence space and summarizes the inter-residue and residue-solvent interactions [1, 2, 4]. Recently it was shown that there are several cases for which there is no possible choice of pairwise contact interactions between residues that suffices to pin down the native state even for a single protein [5, 6]. This conclusion is supported by molecular dynamics studies [7] and lattice models [8] on residue-solvent interactions, where many-body forces are shown, or can be deduced to be, as relevant as two-body forces. To get around this failure of the two-body Hamiltonian approach while retaining a coarse-grained description (as opposed to, say, an all-atom one, including water [9]), we need to introduce new terms at the residue level, to bias the optimization procedure towards the true minima. It is widely accepted that hydrophobicity is the force driving the folding process [10]. At the individual residue level, hydrophobicity is correlated with the solvent-exposed surface area in the native state [11]. In addition, as reported below, a statistical analysis of the native structures deposited in the Protein Data Bank (PDB) [12]) reveals a good correlation (coefficient of correlation 0.8) between the solvent-hidden surface area per residue and the number of inter-residue contacts per residue in the native state. We therefore propose the following two-step procedure for predicting the native state of a protein. First, a reasonably accurate prediction of the exposed surface area in the native fold is made on the basis of sequence information [11]. Second, this information is translated into a prediction of the number of native contacts of each residue, e.g. to a predicted native contact vector. Even if this scheme will turn out to be insufficient to perform a successful prediction, it opens the possibility to confine the search for the native fold to a small portion of the conformational space. The question then becomes “How many folded configurations are there, consistent with a given set of contact numbers ?” And, for that matter, “Is such a contact-number representation of the protein structure degenerate at all ?” The rest of this paper addresses these questions. II. Contact maps versus contact vectors The contact map (CM) [13] of a protein of amino-acids is a symmetric binary matrix of size , such that when the and the amino-acids of the sequence are neighbors, with some suitable definition of “neighborhoodness” (e.g., a common construct is to threshold the pairwise distance matrix for the C atoms [5]). The CM has proven to be a convenient encoding of the 3-dimensional native fold: 1. The native backbone conformation can be reproduced to within 1.5 Å average uncertainty (the same as most X-ray data) [14], 2. It allows for an efficient search of the configuration space, since large conformational changes can be obtained by minor modifications of the CM [15]. Within such minimalistic framework one hopes to gain new insight to the protein-folding problem since it is amenable to different physical and mathematical tools. For instance, the following Hamiltonian acting on the contact map space has been extensively used in the past [16, 17, 18, 19] : H=∑ijw(ai,aj)Cij , (1) where is one of the 210 energy parameters representing the contact energy between the amino-acid types and . Unfortunately, this formulation has limited predictive power. For example, given a large enough set of sequences and decoys (obtained by threading) from the PDB, no set of exists, for which has its ground-states at the native-folds [6]. This is in accordance with the recent studies on the nature of the hydrophobic interaction [7, 8], whose conclusion is that many-body interactions are of the same order of magnitude as two-body interactions. One possible way to improve the Hamiltonian in Eq. (1) is to include an energy penalty for deviations from the native-contacts: H=(1−λ)∑ijw(ai,aj)Cij+λ∑i(ni−nnati)2 (2) where we define a “contact vector” (CV) of rank , which is the sum of the entries of the CM on each row (or column) (see Fig.(1)) : ni=∑jCij . (3) Contact vectors have already been studied in the context of protein folding [20, 21, 22, 23, 24, 25, 26, 27, 28]. We note in particular that the second term in Eq. (2) resembles a hydrophobic term introduced previously [29] and studied in Ref. [30], with the difference that there the desired number of contacts of residue is determined by its species. Here instead we assume the knowledge of , the correct number of contacts of residue in the native structure. Hence the second term in Eq. (2) carries the same spirit as the Go model [31]. In this work we are interested in studying the statistical properties of contact vectors. For our more general purpose, it would seem inconsistent to use Eq. (2) to predict the native structure of a protein, as we bias the Hamiltonian towards the minimum by using information which is not accessible to us before we actually solve the problem. However, unlike in the Go model, the information required here about the native state (the number of contacts for each residue) is modest, and, most crucially, can be predicted. Learning algorithms have been recently developed, which are trained on known structures to predict the surface exposure of the amino-acids in the native fold [11, 32]. Since the hydrophobic effect is driving the folding process [10], it is natural to expect that an accurate prediction of the solvent exposed surface of each residue in the folded state may lead to prediction of the correct native structure. To bridge the gap between the exposed-surface information and the CV defined above, we performed an analysis on a representative set of proteins from the PDB database. We found a linear correlation with a coefficient of correlation of 0.8 between the solvent hidden surface area of a residue and the number of amino-acids it is in contact with (see Fig.(2)). Therefore, in future work we expect to replace the term in Eq. (2) by , thereby breaking the causality loop which is a characteristic of Go-like models. Another reason to study the model of Eq. (2) is that a related kind of Hamiltonian has been recently proved to be useful to determine the structure of nearly-native protein conformations [33]. In that study, represent the number of native contacts formed by residue in the contact map . Also in that case, it was found that a large variance in (see below) implies a low degeneracy in mapping between contact vectors and three-dimensional conformations. In studying Eq. (2), first we tried to use a set of contact energy parameters , found earlier by an optimization process, using Eq. (2) with . This attempt failed to assign the minimal energy to the native state for any choice of . However, an optimization of over the known structures by using the Hamiltonian in Eq. (2) with may, perhaps, successfully identify the native state. We will investigate this possibility in the future. The Hamiltonian (2), with , fails to identify the native fold. This statement means that it is possible to find conformations which on the one hand are very different from the native one and, on the other, each amino-acid has exactly the correct number of neighbors, that is the same number of neighbors as in the native state. This result was first found by Ejtehadi et al. [22] by exact enumeration of all the compact conformations on a cubic lattice. For actual proteins, an example is given in Fig. 3 in the case of protein CI2 (PDB code 2ci2), where the CMs of the native fold and of another conformation are superimposed. These two conformations have identical CVs. At first glance, it would seem unlikely to find two compact configurations where each residue has exactly the same number of neighboring residues in contact. On the other hand, the cautious reader will attribute this degeneracy to the loss of information (from binary variables to integers of size ) associated with going from a given CM to its corresponding CV via Eq. (3). Quantifying the resulting degeneracy is a non-trivial problem. The next section is an analytical attempt in this direction. III. An analytical approach We ask the following question: “How many contact maps exist for a given contact vector ?”. In fact, we should be counting, for a given , only the physical CM that are consistent with it. A physical CM [29, 14] is one for which a perfectly matching chain configuration can be found. There is, however, no known analytical selection rule for the physical CMs among all symmetric and traceless matrices; therefore in our analytic study we will consider all binary symmetric matrices. This is essentially the mean-field treatment of the problem, since in the limit of infinite dimensions, all the constraints on the CM, except being symmetric with zero trace, will be relaxed. For any finite dimension we overestimate the degeneracy - the number of physical CMs scales exponentially, as , whereas the number of possible CMs scales as [13]. The formal expression for the number of symmetric, traceless binary matrices consistent with a given vector, , is d(→n)=i>j∑{xij} N∏i=1δ(∑jxij),ni . (4) The sum over represents a trace over all binary matrices, and the constraint ensures symmetry and zero trace. In order to perform the summation, we rewrite the Kronecker as a discrete Fourier sum: d(→n) = i>j∑{cij} N∏i=1[1NN−1∑k=0ei2πkN(∑jxij−ni)] (5) = 1NNN−1∑k1=0N−1∑k2=0⋯N−1∑kN=0⎛⎜⎝i>j∑{xij}ei2πN∑iki(∑jxij−ni)⎞⎟⎠. Scaling by , approximate the sums by integrals. Then, evaluate the trace over the matrix elements, paying special attention to and : d(→n) = ∫10dk1dk2...dkN⎛⎜⎝i>j∑{xij}ei2π∑iki(∑jxij−ni)⎞⎟⎠ (6) = 2N(N−1)/2∫10dk1dk2...dkNe−i2π∑iki[(N−1)/2−ni]∏i>jcos[π(ki+kj)] . The integral can now be evaluated around its saddle points, and , which contribute equally. After we set and assume is divisible by 4, we obtain ≃ 2N(N−1)/22∫1/2−1/2dq1dq2...dqNe−i2π∑iqi[(N−1)/2−ni]−(π2/2)[N∑iq2i+(∑iqi)2] . (7) The last square term in the exponent can be eliminated by a Hubbard- transformation after rescaling by and defining : d(→n) ≃ 2N(N−1)/2√2π∫1/2−1/2dq1dq2...dqN∫∞−∞dye−y2/2+iπy∑iqi+i2π∑iηiqi−Nπ2/2∑iq2i , which finally simplifies to yield d(→n) ≃ 2N2/2(N/π)N/2√Ne−2σ2η−¯η2 , (8) where and are the average and the standard deviation of . This is a mean-field estimate of how the degeneracy of a CV scales with respect to the statistical properties of the CV. The leading behavior is clearly far from being realistic, since the degeneracy should scale at most as for some ( is in 2d [13] and 1.32 in 3d as calculated here). Eq. (8) further suggests that the maximally degenerate CV with a fixed average number of contacts has , i.e., all the amino-acids have equal number of contacts, whereas an unbiased sample of CVs will be dominated by those vectors with a typical standard deviation of . The mean-field message is that the degeneracy is a decreasing function of , i.e., variation in contact number is desirable for low degeneracy. In the next section, we argue that this is true away from the saddle point as well. IV. Finite connectivity : Graph counting In the previous section, we allowed for the number of contacts to take any value between and . In reality, and also in lattice models, the number of contacts is of order unity. Therefore, it is desirable to have an estimate of the degeneracy of such CVs. Once again, we consider all traceless, symmetric, binary matrices. We first observe that every such matrix encodes a unique graph with N vertices, a vertex pair being connected if the corresponding matrix element is 1. Symmetry ensures that the graph is undirected. We can ensure chain connectivity (but not the graph being physical!) by freezing connections on the first off-diagonal; if we choose to relax these “backbone connections”, the remaining graph need not be connected. The degeneracy of a CV, can then be approximated by the number of graphs with N vertices and given connectivities. We imagine the vertices from 1 to N with corresponding number of legs sticking out of each and we ask in how many ways these legs can be connected such that none will be left out (the total number of legs is an even number). Eq. (9) follows immediately if one imagines connecting pairs of legs sequentially (the numerator) and remembering that legs coming out of the same vertex are interchangeable (denominator). Let’s assume we allow the entries of the CV to be one of , , and the composition given by , being the number of amino acids with contacts. The average number of contacts is . The corresponding number of graphs reads d(N,{pi})=(cN−1)!!(0!)N0(1!)N1...(n!)Nn . (9) (The only difference with the usual Feynman diagram counting is the missing in the denominator: our vertices are distinguishable since they correspond to the amino-acids labelled by their sequence number.) Note that this expression is an approximation to the number of symmetric traceless CMs, since diagrams with small loops involving one vertex, as well as with more than one line connecting the same two vertices are counted in Eq. (9), even though they do not correspond to any CMs. However, corrections due to excluding such diagrams do not change the scaling with . Applying Stirling’s formula to Eq. (9), d(N,{pi})≃exp[cN2lnN+N(c2lnc−1−∑pnln(n!))] . (10) The leading order is now with . Better estimations require taking into consideration the spatial correlations in the contact numbers due to the underlying one-dimensional chain. Our next task is to find the compositions with the minimum and maximum degeneracy. The leading order in Eq. (10) depends only on the total number of contacts, so it is sensible to confine the search into the subspace of CVs with a fixed average connectivity. We then extremize the next order term with respect to , subject to the constraints and to find which distribution of contacts allows for the better “designability” (i.e., less degeneracy). Fig.(4) shows the choice of with maximum/minimum degeneracy obtained numerically, as a function of the average contact number, (maximum number of non-backbone contacts, , is chosen to be 4 as for the cubic lattice). As read from the graphs, the highly degenerate scenario is when the number of contacts for each residue is minimally away from the average, and vice versa for the low degeneracy. Even though here we deal with low connectivity , whereas in the previous section we had , the result obtained here is the same as there - low degeneracy goes in parallel with maximal variation in contact number. One application of this principle is an order of magnitude estimation for the “optimal” length for a protein. Consider a necklace model of the protein, each residue represented by a sphere of fixed radius, and the necklace itself folded into a large compact sphere, where compactness is imposed as a necessary condition for stability. Then, maximal contact number fluctuation is attained when the number of buried residues equals the number of residues on the surface. From this purely geometric construction, one can estimate an “ideal” chain size: Let the radii of the individual residues be unity, and the radius of the protein be . Assuming hcp-like packing, each residue occupies a volume of , and those on the surface cover, roughly, of surface area. Then, if is the number of residues, we have and , which yields . V. Numerical results To compare the analytical findings presented above with numerical simulations, we performed several exact enumeration studies on the square and the cubic lattices. Therefore, in this section, we deal with physical CMs and contact vectors, i.e., those generated by self-avoiding walks in two and three dimensions. In each analysis, we kept a record of the distinct CMs we encountered and the corresponding CVs. Our first observation is that, the number of distinct CVs for a given size scales exponentially with : Ncv∼eacvN . For given , the number of CVs, CMs, and self-avoiding walks increase in the given order. Yet, it is interesting that the growth rate is only about less than the corresponding rate for the CMs in three dimensions (see Fig.(5), and also [13]). The discrepancy between the mean-field analytical calculations and the exact enumeration results points to the fact that the finite dimensionality and the correlations between contacts due to the underlying one-dimensional chain (i.e. working with physical CMs and CVs) are crucial. The almost identical growth rates is in accordance with our next analysis on the compact configurations on a square lattice (see [34]): Considering all the Hamiltonian walks inside a square, we identified the number of walks that correspond to each CV and found that the number of CVs with degeneracy drops more or less exponentially with (see Fig.(6)). In fact, more than of all the contact vectors have degeneracy , although it is possible to find a vector with 69 Hamiltonian walks mapped on it (not shown in Fig.(6)). The degeneracy gets even smaller in the case of a compact but less than perfect packing , in our case when the square is mostly filled with a 32-residue chain: introduced vacancies (especially when in the core) “label” some of the residues with otherwise identical contact number. Rearrangement of the core, where all the residues have identical number of contacts, is the dominant mechanism of degeneracy. Hence, it gets more difficult to find conformations with the same CV, once this degeneracy is lifted by the vacancies. In this case, for practically all the CVs we have . In three dimensions, for the system sizes within reach, practically all the residues are on the surface. Therefore, we have not extended this analysis to such case. VI. Conclusion Existing and future prediction methods for the accessible surface area of individual residues can be adopted to predict the number of native contacts of each amino acid of a given protein. This prediction can then be used for an efficient search of the native contact map (and the corresponding conformation) in a dramatically reduced configuration space. The prerequisite of such a program is to be able to identify different folds consistent with a given set of contact numbers for each residue. We investigated at the mean-field level the partition of the configuration space (or rather the contact map space) into degeneracy classes labelled by the CVs. The average degeneracy predicted by the analytical calculations disagrees with the numerical findings, indicating that the finite dimensionality and the correlations induced by the underlying one-dimensional chain are crucial even for a qualitatively satisfactory result. We did find, already at the mean-field level, that the increasing the fluctuations in the native contact-numbers reduces the contact vectors’ degeneracy. This finding is also supported by another analytical calculation, valid in a different regime, where the average contact number is . We further investigated by exact enumeration the degeneracy spectrum of CVs for self-avoiding walks on the square and the cubic lattice. We found that for compact self-avoiding walks the CM and the CV representations carry nearly the same amount of information. This is an encouraging result, for an accurate enough prediction of solvent exposed surface areas in the native state may then be used to reduce the search space sufficiently, so that within the limited set of remaining candidate CMs a simple pairwise interaction potential may suffice to single out the native fold of the protein. In addition, we performed exact enumeration over all SAWs of steps in three dimension, and found that the number of CVs grows exponentially with the protein length, with a prefactor only a few percent smaller than that for the CMs. The slow exponential growth of the average degeneracy of the CVs is largely overestimated by our mean-field calculations. Further analytical and numerical research is certainly called for. We also observed that for compact configurations, CV CM mapping is practically one-to-few. The Hamiltonian in Eq. (1), therefore, may still be promising if the pairwise interactions are optimized within the context of a (even roughly) predicted CV. A. K. acknowledges many useful discussions with G. Getz and A. Punnose and is also grateful to the Bilkent University Physics Department for their hospitality during his visit. This work was partially supported by grants from the US-Israel Binational Science Foundation (BSF) and the Minerva Foundation. I. Kanter thanks the Einstein Center for Theoretical Physics for partial support. Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8937209844589233, "perplexity": 563.4028896935762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381989.92/warc/CC-MAIN-20210308052217-20210308082217-00462.warc.gz"}
https://www.nature.com/articles/s41561-019-0305-y?error=cookies_not_supported&code=402bc4cf-5637-4eff-8f0e-998ce64aff34	# Reply to: No evidence for equatorial Pacific dust fertilization replying to A. W. Jacobel et al. Nature Geoscience https://doi.org/10.1038/s41561-019-0304-z (2019) We disagree with the arguments put forth by Jacobel et al.1 and stand by our original interpretations2. Jacobel et al.1 assert that no evidence of Fe fertilization by dust is provided by Loveley et al.2 and claim the same for their dataset from nearby Ocean Drilling Program (ODP) Site 1240. However, we interpret their dataset differently: there is a moderate, statistically strong positive correlation between the excess Ba (xsBa) and 232Th fluxes (coefficient of correlation, r = + 0.49, P < 0.01; fig. 1a in ref. 1). The relationship between their 232Th and Fe fluxes is even stronger (r = + 0.62, P < 0.01; Fig. 1b in ref. 1), indicating a significant influence of dust on Fe availability. Fluxes of xsBa scale nonlinearly with dust flux at site MV1014-02-17JC. We stated that, and noted a clear relationship between xsBa and dust “during or near Heinrich Stadials (HS) 1, 2, 5, 6 and 7”2. For HS6 and 7 there are statistically significant positive correlations between xsBa and dust fluxes (r = + 0.47, P < 0.05 and r = + 0.96, P < 0.01, respectively). For HS1, 2 and 5, xsBa is likely affected by bottom-water hypoxia, defined by authigenic U values that are the highest in the entire record (>10 ppm)2. The low-O2 bottom waters probably released Ba3, which diffused downwards slightly and re-precipitated, causing the xsBa flux to lead the dust flux signal by only ~1 kyr. We see no evidence in Jacobel et al.1 in support of their claim that upwelling of equatorial undercurrent waters provides all of the Fe and is the sole cause of fertilization in the easternmost eastern equatorial Pacific (EEP). During past cold events, similar to boreal winter conditions today, a southward-shifted intertropical convergence zone probably reduced equatorial upwelling4. Regardless, Fe concentrations in the eastward-flowing equatorial undercurrent, sourced from continental inputs in the western Pacific, are nearly zero by 110° W due to scavenging and the short residence time of Fe (0.8–1.0 nM at 140° W to ≤0.09 nM at 110° W)5. Even farther east, the Galapagos Islands obstruct, deflect and weaken the equatorial undercurrent6, making the role it plays in supplying Fe to our site at 86° W even less likely. It is apparent that our site would be more sensitive to dust fertilization due to continental proximity, which leads to dust fluxes that are about 5–10 times greater than those at all 11 locations considered by Jacobel and colleagues1. In fact, east of the Galapagos Islands2,7,8,9,10,11,12, changes in aeolian delivery and its role in export production and the global CO2 cycle cannot be ruled out. We therefore find the assertions1 that there is unquestionably no dust fertilization at our site or theirs to be unwarranted. The EEP is the greatest oceanic source of CO2 to the atmosphere today13, yet an abundance of data show that the easternmost EEP may have been a net sink of CO2 at times during the last deglacial and glacial periods7,9,10,11,12. The argument1 against net changes in biological pump efficiency and atmospheric $$p_{{\mathrm {CO}}_2}$$ drawdown relies on nutrients sourced from equatorial upwelling, resulting in surface waters with elevated CO2 concentrations. This assumption fails to consider that Fe fertilization from dust can increase the efficiency of the biological pump and carbon sequestration in a high nutrient–low chlorophyll region, even with no net changes in upwelling. ## References 1. 1. Jacobel, A. W. et al. No evidence for equatorial Pacific dust fertilization. Nat. Geosci. https://doi.org/10.1038/s41561-019-0304-z (2018). 2. 2. Loveley, M. R. et al. Millennial-scale iron fertilization of the eastern equatorial Pacific over the past 100,000 years. Nat. Geosci. 10, 760–764 (2017). 3. 3. McManus, J. et al. Geochemistry of barium in marine sediments: implications for its use as a paleoproxy. Geochim. Cosmochim. Acta 62, 3453–3473 (1998). 4. 4. Fiedler, P. C. & Talley, L. D. Hydrography in the eastern tropical Pacific: a review. Progr. Oceanogr. 69, 143–180 (2006). 5. 5. Kaupp, L. J. et al. The distribution of dissolved Fe and Al in the upper waters of the eastern equatorial Pacific. Deep Sea Res. Part II 58, 296–310 (2011). 6. 6. Lukas, R. The termination of the equatorial undercurrent in the eastern Pacific. Progr. Oceanogr. 16, 63–90 (1986). 7. 7. de la Fuente, M. et al. The evolution of deep ocean chemistry and respired carbon in the eastern equatorial Pacific over the last deglaciation. Paleoceanography 32, 1371–1385 (2017). 8. 8. Costa, K. M. et al. Productivity patterns in the equatorial Pacific over the last 30,000 years. Glob. Biogeochem. Cycles 31, 850–865 (2017). 9. 9. Martínez-Botí, M. A. et al. Boron isotope evidence for oceanic carbon dioxide leakage during the last deglaciation. Nature 518, 219–222 (2015). 10. 10. Doss, W. & Marchitto, T. M. Glacial deep ocean sequestration of CO2 driven by the eastern equatorial Pacific biologic pump. Earth Planet. Sci. Lett. 377–378, 43–54 (2013). 11. 11. Robinson, R. S., Martinez, P., Pena, L. D. & Cacho, I. Nitrogen isotopic evidence for deglacial changes in nutrient supply in the eastern equatorial Pacific. Paleoceanography 24, PA4213 (2009). 12. 12. Pichevin, L. E. et al. Enhanced carbon pump inferred from relaxation of nutrient limitation in the glacial ocean. Nature 459, 1114–1117 (2009). 13. 13. Takahashi, T. et al. Global sea-air CO2 flux based on climatological surface ocean pCO2, and seasonal biological and temperature effects. Deep Sea Res. Part II 49, 1601–1622 (2002). ## Author information Authors ### Contributions F.M., M.R.L., M.W.S. and J.E.H. each contributed to the discussion, writing and editing of the manuscript. ### Corresponding author Correspondence to F. Marcantonio. ## Ethics declarations ### Competing interests The authors declare no competing interests. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Rights and permissions Reprints and Permissions Marcantonio, F., Loveley, M.R., Schmidt, M.W. et al. Reply to: No evidence for equatorial Pacific dust fertilization. Nat. Geosci. 12, 156 (2019). https://doi.org/10.1038/s41561-019-0305-y • Accepted: • Published: • Issue Date: • ### Controls on Primary Productivity in the Eastern Equatorial Pacific, East of the Galapagos Islands, During the Penultimate Deglaciation • Lucía Quirós‐Collazos • , Eva Calvo • , Stefan Schouten • , Marcel T. J. Meer • , Marta Rodrigo‐Gámiz • , Leopoldo D. Pena • , Isabel Cacho • & Carles Pelejero Paleoceanography and Paleoclimatology (2020) • ### Orbital and sea-level changes regulate the iron-associated sediment supplies from Papua New Guinea to the equatorial Pacific • Haowen Dang • , Jiawang Wu • , Zhifang Xiong • , Peijun Qiao • , Tiegang Li • & Zhimin Jian Quaternary Science Reviews (2020) • ### Deep Equatorial Pacific Ocean Oxygenation and Atmospheric CO2 Over The Last Ice Age • Franco Marcantonio • , Ryan Hostak • , Jennifer E. Hertzberg • & Matthew W. Schmidt Scientific Reports (2020) • ### Marine nitrogen fixers mediate a low latitude pathway for atmospheric CO2 drawdown • Pearse J. Buchanan • , Zanna Chase • , Richard J. Matear • , Steven J. Phipps • & Nathaniel L. Bindoff Nature Communications (2019)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6262714862823486, "perplexity": 15269.144031190937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402124756.81/warc/CC-MAIN-20201001062039-20201001092039-00141.warc.gz"}
https://mitpress.mit.edu/index.php?q=books/masters-truth-archaic-greece	Hardcover \| $36.95 Trade \| £25.95 \| ISBN: 9780942299854 \| 232 pp. \| 6 x 9 in \| July 1996 Paperback \|$19.95 Trade \| £13.95 \| ISBN: 9780942299861 \| 232 pp. \| 6 x 9 in \| October 1999 # The Masters of Truth in Archaic Greece ## Overview foreword by Pierre Vidal-Naquet The Masters of Truth in Archaic Greece, the acclaimed French classicist Marcel Detienne's first book, traces the odyssey of "truth," aletheia, from mytho-religious concept to philosophical thought in archaic Greece. Detienne's starting point is a simple observation: in archaic Greece, three figures - the diviner, the bard, and the king - all share the privilege of dispensing truth by virtue of the religious power of divine memory, which provides them with knowledge, both oracular and inspired, of the present, past, and future. Beginning with this definition of the prerational meaning of truth, Detienne examines how truth in Greek literature, especially in the poetic tradition, first emerges as an enigma, a paradox defined neither by its opposition to nor its contradiction with falsehood or with lethe (oblivion and forgetfulness), but by its association with ambiguity and ambivalence. Detienne then explains how sophists and orators alike figure into the lineage of these pre-Platonic masters of truth. Still distinct from the logic of correspondence and of noncontradiction that comes to characterize the mode of argumentation of the first Western rationalist philosophers, these masters' truth appears through their maneuvering of apate, deceit, and cunning. In following this artful understanding and use of speech - its effect, techniques, and relation to the world and other people - Detienne identifies, particularly in the work of Simonides, a movement from a religious to a secular thought about truth. The study culminates with an original reinterpretation of Parmenides' poem on Being. ## Endorsements "A penetrating study of the meaning of 'truth' in archaic Greece." Parabola "Richly suggestive and written with verve and wit. . . " Choice	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.381897509098053, "perplexity": 9126.84880643009}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644060103.8/warc/CC-MAIN-20150827025420-00074-ip-10-171-96-226.ec2.internal.warc.gz"}
https://worldwidescience.org/topicpages/p/prima+facie+reason.html	#### Sample records for prima facie reason 1. Obligaciones prima facie y derrotabilidad OpenAIRE Oller, Carlos A. 2006-01-01 Este artículo examina algunos de los problemas que presenta el tratamiento lógico de las obligaciones prima facie en la obra de Carlos Alchourrón. Por una parte, señalaremos que su sistema para los condicionales derrotables DFT no formaliza adecuadamente la noción intuitiva de condición contribuyente que Alchourrón utiliza para elucidar la de condicional derrotable. Por otra parte, argumentaremos que la noción de deber prima facie de David Ross no queda adecuadamente formalizada en el sistema... 2. Prima facie questions in quantum gravity Science.gov (United States) Isham, C. J. The long history of the study of quantum gravity has thrown up a complex web of ideas and approaches. The aim of this article is to unravel this web a little by analysing some of the {\\em prima facie\\/} questions that can be asked of almost any approach to quantum gravity and whose answers assist in classifying the different schemes. Particular emphasis is placed on (i) the role of background conceptual and technical structure; (ii) the role of spacetime diffeomorphisms; and (iii) the problem of time. 3. Statistics and Title VII Proof: Prima Facie Case and Rebuttal. Science.gov (United States) Whitten, David 1978-01-01 The method and means by which statistics can raise a prima facie case of Title VII violation are analyzed. A standard is identified that can be applied to determine whether a statistical disparity is sufficient to shift the burden to the employer to rebut a prima facie case of discrimination. (LBH) 4. The Burger Court and the Prima Facie Case in Employment Discrimination Litigation: A Critique. Science.gov (United States) Friedman, Joel William 1979-01-01 The unprincipled and contrived reasoning running through these opinions manifests an intentional effort by the Court to impede litigants' ability to secure their rights to equal employment opportunity by raising the requirements of the prima facie case. Available from Fred B. Rothman & Co., 10368 West Centennial Road, Littleton, CO 80123; sc… 5. Prima facie evidence against spin-two Higgs impostors OpenAIRE Ellis, John; Sanz, Veronica; You, Tevong 2013-01-01 The new particle X recently discovered by the ATLAS and CMS Collaborations is widely expected to have spin zero, but this remains to be determined. The leading alternative is that X has spin two, presumably with graviton-like couplings. We show that measurements of the X particle to pairs of vector bosons constrain such scenarios. In particular, a graviton-like Higgs impostor in scenarios with a warped extra dimension of AdS type is prima facie excluded, principally because they predict too s... 6. Prima facie evidence against spin-two Higgs impostors Science.gov (United States) Ellis, John; Sanz, Verónica; You, Tevong 2013-10-01 The new particle X recently discovered by the ATLAS and CMS Collaborations is widely expected to have spin zero, but this remains to be determined. The leading alternative is that X has spin two, presumably with graviton-like couplings. We show that measurements of the X particle to pairs of vector bosons constrain such scenarios. In particular, a graviton-like Higgs impostor in scenarios with a warped extra dimension of AdS type is prima facie excluded, principally because they predict too small a ratio between the X couplings to WW and ZZ, compared with that to photons. The data also disfavour universal couplings to pairs of photons and gluons, which would be predicted in a large class of graviton-like models. 7. Prima Facie Evidence against Spin-Two Higgs Impostors CERN Document Server Ellis, John; You, Tevong 2013-01-01 The new particle X recently discovered by the ATLAS and CMS Collaborations is widely expected to have spin zero, but this remains to be determined. The leading alternative is that X has spin two, presumably with graviton-like couplings. We show that measurements of the X particle to pairs of vector bosons constrain such scenarios. In particular, a graviton-like Higgs impostor in scenarios with a warped extra dimension of AdS type is prima facie excluded, principally because they predict too small a ratio between the X couplings to WW and ZZ, compared with that to photons. The data also disfavour universal couplings to pairs of photons and gluons, which would be predicted in a large class of graviton-like models. 8. Prima facie evidence against spin-two Higgs impostors International Nuclear Information System (INIS) Ellis, John; Sanz, Verónica; You, Tevong 2013-01-01 The new particle X recently discovered by the ATLAS and CMS Collaborations is widely expected to have spin zero, but this remains to be determined. The leading alternative is that X has spin two, presumably with graviton-like couplings. We show that measurements of the X particle to pairs of vector bosons constrain such scenarios. In particular, a graviton-like Higgs impostor in scenarios with a warped extra dimension of AdS type is prima facie excluded, principally because they predict too small a ratio between the X couplings to WW and ZZ, compared with that to photons. The data also disfavour universal couplings to pairs of photons and gluons, which would be predicted in a large class of graviton-like models 9. Prima facie evidence against spin-two Higgs impostors Energy Technology Data Exchange (ETDEWEB) Ellis, John [Theoretical Particle Physics and Cosmology Group, Physics Department, King' s College London, London WC2R 2LS (United Kingdom); TH Division, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Sanz, Verónica, E-mail: [email protected] [TH Division, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Department of Physics and Astronomy, York University, Toronto, ON, M3J 1P3 (Canada); You, Tevong [Theoretical Particle Physics and Cosmology Group, Physics Department, King' s College London, London WC2R 2LS (United Kingdom) 2013-10-07 The new particle X recently discovered by the ATLAS and CMS Collaborations is widely expected to have spin zero, but this remains to be determined. The leading alternative is that X has spin two, presumably with graviton-like couplings. We show that measurements of the X particle to pairs of vector bosons constrain such scenarios. In particular, a graviton-like Higgs impostor in scenarios with a warped extra dimension of AdS type is prima facie excluded, principally because they predict too small a ratio between the X couplings to WW and ZZ, compared with that to photons. The data also disfavour universal couplings to pairs of photons and gluons, which would be predicted in a large class of graviton-like models. 10. 17 CFR 270.3a-1 - Certain prima facie investment companies. Science.gov (United States) 2010-04-01 ... 17 Commodity and Securities Exchanges 3 2010-04-01 2010-04-01 false Certain prima facie investment companies. 270.3a-1 Section 270.3a-1 Commodity and Securities Exchanges SECURITIES AND EXCHANGE COMMISSION (CONTINUED) RULES AND REGULATIONS, INVESTMENT COMPANY ACT OF 1940 § 270.3a-1 Certain prima facie investment... 11. [Burden of proof in medical cases--presumption of fact and prima facie evidence. II. Presumption of fact and prima facie evidence]. Science.gov (United States) Sliwka, Marcin 2004-01-01 The aim of this paper was to present the main rules concerning the burden of proof in polish civil trials, including medical cases. The standard rules were presented with all the important exclusions such as presumption of law and fact or prima facie evidence. The author analyses the effect of these institutions on burden of proof in medical cases. The difference between presumptions of fact and prima facie evidence was analysed and explained. This paper also describes the importance of the res ipsa loquitur rule in United Kingdom and USA. This paper includes numerous High Court sentences on evidential and medical issues. 12. Getting to First Base: Prima Facie Arguments for Propositions of Value. Science.gov (United States) Tuman, Joseph S. 1987-01-01 Argues that few clear standards exist for value debate. Defines values as instrumental or terminal, and identifies four prima facie burdens necessary for affirming a value resolution: value identification; value criteria; value hierarchy; and topicality through relevance. Examines the role of presumption and burden of proof in value debate. (MM) 13. In defence of moral imperialism: four equal and universal prima facie principles. Science.gov (United States) Dawson, A; Garrard, E 2006-04-01 Raanan Gillon is a noted defender of the four principles approach to healthcare ethics. His general position has always been that these principles are to be considered to be both universal and prima facie in nature. In recent work, however, he has made two claims that seem to present difficulties for this view. His first claim is that one of these four principles, respect for autonomy, has a special position in relation to the others: he holds that it is first among equals. We argue that this claim makes little sense if the principles are to retain their prima facie nature. His second claim is that cultural variation can play an independent normative role in the construction of our moral judgments. This, he argues, enables us to occupy a middle ground between what he sees as the twin pitfalls of moral relativism and (what he calls) moral imperialism. We argue that there is no such middle ground, and while Gillon ultimately seems committed to relativism, it is some form of moral imperialism (in the form of moral objectivism) that will provide the only satisfactory construal of the four principles as prima facie universal moral principles. 14. LA VALIDEZ PRIMA FACIE Y EL PRINCIPIO DE DERROTABILIDAD DE LAS NORMAS JURÍDICAS OpenAIRE GARCÍA-YZAGUIRRE, JOSÉ VÍCTOR 2012-01-01 El presente artículo pretende explorar las implicancias teóricas del concepto prima facie y como este se relaciona con el principio de derrotabilidad, el cual es aplicable para justificar el incumplimiento de un deber jurídico a causa del acatamiento de otro en un contexto en el que ambos son incompatibles entre sí. Partiremos desde su sustento conceptual analizando cuál es el rol y la importancia del contexto en el razonamiento jurídico hasta arribar a pautas concretas de cómo opera en la pr... 15. [First trimester screening for Down syndrome at Prima facie. A 6-year survey]. Science.gov (United States) Roth, P; Bernard, J-P; Meyer, V; Beaujard, M-P; Salomon, L-J; Ville, Y 2016-02-01 To evaluate the results of screening for trisomy 21 by the combined risk of first trimester (as defined by the decree of June 23, 2009) in the Prima facie structure. Single center study involving all patients that were seen for first trimester screening at Prima facie with singleton living pregnancy, not obtained by embryo donation, between 1 January 2009 and 31 December 2014. Eighteen thousand two hundred and fifty-one patients were included, of which underwent screening for trisomy 21 by the combined risk. One thousand and forty-six (6.1%) had a calculated risk higher than 1/250. Seventy-five were affected by trisomy 21, of whom 65 in the high risk group. The sensitivity and specificity of screening are 86.7% and 94.4%. The median nuchal translucency was 0.98 MoM. Screening for trisomy 21 by calculating the combined risk of first trimester enabled to detect 86.7% of trisomy 21 with a false positive rate of 5.6%. Copyright © 2015 Elsevier Masson SAS. All rights reserved. 16. HIV status: the prima facie right not to know the result. Science.gov (United States) Chan, Tak Kwong 2016-02-01 When a patient regains consciousness from Cryptococcus meningitis, the clinician may offer an HIV test (in case it has not already been done) (scenario 1) or offer to tell the patient his HIV status (in case the test has already been performed with a positive result while the patient was unconscious) (scenario 2). Youngs and Simmonds proposed that the patient has the prima facie right to refuse an HIV test in scenario 1 but not the prima facie right not to be told the HIV status in scenario 2. I submit that the claims to the right of refusal in both scenarios are similarly strong as they should both be grounded in privacy, self determination or dignity. But a conscientious agent should bear in mind that members of the public also have the right not to be harmed. When the circumstance allows, a proper balance of the potential benefits and harm for all the competing parties should guide the clinical decision as to whose right should finally prevail. Where a full ethical analysis is not possible, the presumption should favour respecting the patient's right of refusal in both scenarios. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/ 17. La validez prima facie y el principio de derrotabilidad de Las normas jurídicas Directory of Open Access Journals (Sweden) José Víctor García-Yzaguirre 2012-01-01 Full Text Available El presente artículo pretende explorar las implicancias teóricas del concepto prima facie y como este se relaciona con el principio de derrotabilidad, el cual es aplicable para justificar el incumplimiento de un deber jurídico a causa del acatamiento de otro en un contexto en el que ambos son incom- patibles entre sí. Partiremos desde su sustento conceptual analizando cuál es el rol y la importancia del contexto en el razonamiento jurídico hasta arribar a pautas concretas de cómo opera en la práctica judicial ofreciendo algunos ejemplos hipotéticos y jurisprudenciales. 18. Objective justification and Prima Facie anti-competitive unilateral conduct : an exploration of EU Law and beyond NARCIS (Netherlands) Vijver, Tjarda Desiderius Oscar van der 2014-01-01 The prohibition of anti-competitive unilateral conduct by firms with market power is not absolute, but allows for derogation. For the purposes of EU law, the ECJ has accepted that a so-called ‘objective justification’ plea may be invoked in the case of a prima facie abuse of dominance. Even though 19. The Student-Athlete and the National Collegiate Athletic Association: The Need for a Prima Facie Tort Doctrine Science.gov (United States) Duckworth, Roy D., III 1975-01-01 In examining whether courts have jurisdiction to hear student-athlete grievances against the National Collegiate Athletic Association (NCAA) the author rejects the position that the NCAA's activities are under cover of state law, and instead proposes that the student-athlete's remedy lies in an action against the NCAA for a prima facie tort. (JT) 20. Autoantibodies to neuronal antigens in children with focal epilepsy and no prima facie signs of encephalitis. Science.gov (United States) Borusiak, Peter; Bettendorf, Ulrich; Wiegand, Gert; Bast, Thomas; Kluger, Gerhard; Philippi, Heike; Münstermann, Dieter; Bien, Christian G 2016-07-01 There is increasing awareness of neuronal autoantibodies and their impact on the pathogenesis of epilepsy. We investigated children with focal epilepsy in order to provide an estimate of autoantibody frequency within a pediatric population without prima facie evidence of encephalitis using a broad panel of autoantibodies. This was done to assess the specificity of antibodies and to see whether antibodies might be of modifying influence on the course of focal epilepsies. We searched for autoantibodies in 124 patients with focal epilepsy (1-18 years; mean 10; 6 years). Sera were tested using a broad panel of surface and intracellular antigens. We found autoantibodies in 5/124 patients (4%): high-positive GAD65 antibodies (n = 1), low-positive GAD65 antibodies (N = 1), VGKC complex antibodies not reactive with LGI1 or CASPR2 (n = 3). We did not find any distinctive features distinguishing antibody positive patients from those without antibodies. The antibodies found in this cohort are probably neither disease-specific nor pathogenic. This has been suggested before for these antigenic targets. Moreover, they do not seem to modify disease severity in the antibody-positive epilepsy patients. Copyright © 2016 European Paediatric Neurology Society. Published by Elsevier Ltd. All rights reserved. 1. The Adversarial Principle in Prima Facie Judgments of the Legal Thesis Firmed in the Trial of Repetitive Cases Directory of Open Access Journals (Sweden) Juliana Provedel Cardoso 2016-10-01 Full Text Available The present articles objective is to analyse the highly effective adversarial principle from the Constitutional Democratic State of Law and the cooperative process structure. In this sense, an analysis of the repetitive cases model is made with special relevance to the Civil Procedure Codice 2015, put in evidence the preliminary injunction, the repetitive appeals and the resolution incident repetitive demands. With the establishment of the premises, an analysis of the adversarial principle is made on prima facie judgments of the legal thesis firmed in the trial of repetitive cases, in view of the motivation of the court decision (speech of the case and law (speech of the precedents. 2. Tort recovery of acid rain damages in the United States--observations on plaintiff's prima facie case Energy Technology Data Exchange (ETDEWEB) Honabach, D.R. 1982-01-01 Common law tort doctrine has long supplied a judicially administered vehicle for dealing with harms suffered by one party as a result of the activities of another. As such, it might be used to address the problem of acid rain. Before tort law may be used, however, a would-be plaintiff must make out a prima facie case. While traditional applications of tort doctrine might effectively prevent plaintiff from doing so, recent court decisions suggest that plaintiff might nevertheless be successful in obtaining at least partial recovery. 3. Dowód prima facie w postępowaniu cywilnym dotyczącym szkód powstałych w związku z leczeniem OpenAIRE Białkowski, Michał 2014-01-01 The objective of this paper is to present main perspectives expressed by representatives of Polish legal doctrine as well as several examples of applications of prima facie evidence in legal cases submitted to Polish Supreme Court. Although not codified in Polish civil procedure prima facie evidence is applied in cases concerning claims for compensation for damages such as those occurred during medical treatment or inflicted by employees. The paper tries to answer whether prima facie evidence... 4. Intent v. Impact: The Standard of Proof Necessary to Establish a Prima Facie Case of Race Discrimination under 42 U.S.C. Section 1981. Science.gov (United States) Heiser, Walter 1979-01-01 Considers action's impact and intent as proof; analyzes language, purpose, and legislative history of civil rights statutes; and concludes that the Supreme Court will likely require proof of intent to sustain a prima facie case of discrimination. Available from San Diego Law Review Association, University of San Diego School of Law, San Diego,… 5. The Dsu Article 3.8 Presumption that an Infringement Constitutes a Prima Facie Case of Nullification or Impairment: When Does it Operate and Why? OpenAIRE Arwel Davies 2010-01-01 This article considers the origin, meaning and current relevance of the Dispute Settlement Understanding (DSU) Article 3.8 presumption that a government measure which infringes World Trade Organization (WTO) obligations constitutes a prima facie case of nullification or impairment. It is argued that the prevailing interpretation of this provision is inconsistent with its plain language and may have contributed to the tendency of respondent states to invoke the presumption in order to undermin... 6. Evidence for new resonances in the K-barN system: A prima facie case for the even-wave harmonic-oscillator model International Nuclear Information System (INIS) Kamath, S.G. 1978-01-01 Arguments are presented to show that the new resonance parameters obtained by Alston-Garnjost et al. in a recent analysis of the K-barN system from 365 to 1320 MeV/c provide a prima facie case for the even-wave harmonic-oscillator theory of baryonic states in the framework of SU(6)/sub W/ x O(3). A new quantum classification of the Λ states belonging to the (70,1 - ) is also proposed 7. Scaling-Up Ionic Liquid-Based Technologies: How Much Do We Care About Their Toxicity? Prima Facie Information on 1-Ethyl-3-Methylimidazolium Acetate. Science.gov (United States) Ostadjoo, Shaghayegh; Berton, Paula; Shamshina, Julia L; Rogers, Robin D 2018-02-01 The potential of the ionic liquid (IL) 1-ethyl-3-methylimidazolium acetate ([C2mim][OAc]) to dissolve a variety of biopolymers such as cellulose and chitin, makes it an attractive candidate for scaled-up industrial utilization. In fact, the first steps towards its use at industrial scale have been taken. This increases the urgency to fill the knowledge gaps in its toxicity and environmental impact in order to predict and control its environmental fate. In this mini-review, we discuss the available literature surrounding this key IL. The literature (through the analysis of toxicity of the anion and the cation separately) suggests that [C2mim][OAc] is a relatively safe choice for industrial applications. However, because the IL should be considered as a compound, with unique properties arising from the interactions between the ions, comprehensive toxicity information for this particular IL is still required. To decide, prima facie, if this IL is toxic or not, evaluation of its influence on human health and ecotoxicity is needed prior to its large scale utilization. We chose in this mini-review to focus on toxicity surrounding this IL and evaluate what is known and what is not. Here with all the information in hand, we hope that the urgent need for [C2mim][OAc] toxicological assessment before it can be used in numerous technologies is highlighted. In the near future, we expect that the assessment of toxicity and environmental fate and impact can be integrated directly into any research into the industrial utilization of this IL and any others contemplated for industrial application. © The Author 2017. Published by Oxford University Press on behalf of the Society of Toxicology. All rights reserved. For Permissions, please e-mail: [email protected]. 8. A liberdade de expressão como direito fundamental preferencial prima facie (análise crítica e proposta de revisão ao padrão jurisprudencial brasileiro) OpenAIRE Cláudio Márcio de Carvalho Chequer 2010-01-01 Em um Estado Democrático de Direito, o direito fundamental à liberdade de expressão deve ser tratado de forma heterogênea, sendo capaz de gozar de um status de direito fundamental preferencial prima facie nas hipóteses em que estiver relacionado a um tema de interesse público, tendo em vista a ocorrência de duas premisssas existentes nesses casos: a do direito que a sociedade tem de saber a respeito dos assuntos de interesse público e a do dever que a imprensa tem de informar a respeito desse... 9. Prima facie reasons to question enclosed intellectual property regimes and favor open-source regimes for germplasm. Science.gov (United States) 2017-01-01 In principle, intellectual property protections (IPPs) promote and protect important but costly investment in research and development. However, the empirical reality of IPPs has often gone without critical evaluation, and the potential of alternative approaches to lend equal or greater support for useful innovation is rarely considered. In this paper, we review the mounting evidence that the global intellectual property regime (IPR) for germplasm has been neither necessary nor sufficient to generate socially beneficial improvements in crop plants and maintain agrobiodiversity. Instead, based on our analysis, the dominant global IPR appears to have contributed to consolidation in the seed industry while failing to genuinely engage with the potential of alternatives to support social goods such as food security, adaptability, and resilience. The dominant IPR also constrains collaborative and cumulative plant breeding processes that are built upon the work of countless farmers past and present. Given the likely limits of current IPR, we propose that social goods in agriculture may be better supported by alternative approaches, warranting a rapid move away from the dominant single-dimensional focus on encouraging innovation through ensuring monopoly profits to IPP holders. 10. Seismic facies; Facies sismicas Energy Technology Data Exchange (ETDEWEB) Johann, Paulo Roberto Schroeder [PETROBRAS, Rio de Janeiro, RJ (Brazil). Exploracao e Producao Corporativo. Gerencia de Reservas e Reservatorios]. E-mail: [email protected] 2004-11-01 The method presented herein describes the seismic facies as representations of curves and vertical matrixes of the lithotypes proportions. The seismic facies are greatly interested in capturing the spatial distributions (3D) of regionalized variables, as for example, lithotypes, sedimentary facies groups and/ or porosity and/or other properties of the reservoirs and integrate them into the 3D geological modeling (Johann, 1997). Thus when interpreted as curves or vertical matrixes of proportions, seismic facies allow us to build a very important tool for structural analysis of regionalized variables. The matrixes have an important application in geostatistical modeling. In addition, this approach provides results about the depth and scale of the wells profiles, that is, seismic data is integrated to the characterization of reservoirs in depth maps and in high resolution maps. The link between the different necessary technical phases involved in the classification of the segments of seismic traces is described herein in groups of predefined traces of two approaches: a) not supervised and b) supervised by the geological knowledge available on the studied reservoir. The multivariate statistical methods used to obtain the maps of the seismic facies units are interesting tools to be used to provide a lithostratigraphic and petrophysical understanding of a petroleum reservoir. In the case studied these seismic facies units are interpreted as representative of the depositional system as a part of the Namorado Turbiditic System, Namorado Field, Campos Basin.Within the scope of PRAVAP 19 (Programa Estrategico de Recuperacao Avancada de Petroleo - Strategic Program of Advanced Petroleum Recovery) some research work on algorithms is underway to select new optimized attributes to apply seismic facies. One example is the extraction of attributes based on the wavelet transformation and on the time-frequency analysis methodology. PRAVAP is also carrying out research work on an 11. Prima Vista toob pargiraamatukogu Index Scriptorium Estoniae 2005-01-01 5. ja 6. mail 2005 toimub teine Tartu kirjandusfestival "Prima Vista". Avatakse pargiraamatukogu, kus esinevad 5. mail Jürgen Rooste, Merca, Aapo Ilves, Peep Ilmet, Marko Martinson, Jüri Kaldmaa, Jaan Pehk Index Scriptorium Estoniae 2008-01-01 Kirjandusfestivalist Prima Vista 8.-11. maini Tartus ja laulvate kirjanike kontsertidest: 9. mail Tõnu Trubetsky kontsert ansambliga The Flovers of Romance, 10. mail Villu Tamme, Mathura, Lauri Sommer, Kaarel B. Väljamäe, Andreas Kalkuni, Kauksi Ülle, Merca ja Aapo Ilves 13. Antinatalism, Asymmetry, and an Ethic of Prima Facie Duties ... African Journals Online (AJOL) Benatar's central argument for antinatalism develops an asymmetry between the pain and pleasure in a potential life. I am going to present an alternative route to the antinatalist conclusion. I argue that duties require victims and that as a result there is no duty to create the pleasures contained within a prospective life but a ... NARCIS (Netherlands) Douven, Igor Bayesians understand the notion of evidential support in terms of probability raising. Little is known about the logic of the evidential support relation, thus understood. We investigate a number of prima facie plausible candidate logical principles for the evidential support relation and show which 15. Eclogite facies rocks National Research Council Canada - National Science Library Carswell, D. A 1990-01-01 .... This is the first volume to provide a coherent and comprehensive review of the conditions necessary for the formation of eclogites and eclogite facies rocks and assemblages, and a detailed account... 16. Facies and facies architecture and depositional environments of the ... African Journals Online (AJOL) Facies and facies architecture and depositional environments of the ... PROMOTING ACCESS TO AFRICAN RESEARCH ... Depositional environments of the Yolde Formation were studied based on the analysis of facies and facies architecture. ... Senegal (6); Sierra Leone (1); South Africa (96); South Sudan (1); Sudan (3) ... 17. The best-interests standard as threshold, ideal, and standard of reasonableness. Science.gov (United States) Kopelman, L M 1997-06-01 The best-interests standard is a widely used ethical, legal, and social basis for policy and decision-making involving children and other incompetent persons. It is under attack, however, as self-defeating, individualistic, unknowable, vague, dangerous, and open to abuse. The author defends this standard by identifying its employment, first, as a threshold for intervention and judgment (as in child abuse and neglect rulings), second, as an ideal to establish policies or prima facie duties, and, third, as a standard of reasonableness. Criticisms of the best-interests standard are reconsidered after clarifying these different meanings. 18. PRIMA-X Final Report Energy Technology Data Exchange (ETDEWEB) Lorenz, Daniel [German Research School for Simulation Sciences GmbH, Aachen (Germany); Wolf, Felix [German Research School for Simulation Sciences GmbH, Aachen (Germany) 2016-02-17 The PRIMA-X (Performance Retargeting of Instrumentation, Measurement, and Analysis Technologies for Exascale Computing) project is the successor of the DOE PRIMA (Performance Refactoring of Instrumentation, Measurement, and Analysis Technologies for Petascale Computing) project, which addressed the challenge of creating a core measurement infrastructure that would serve as a common platform for both integrating leading parallel performance systems (notably TAU and Scalasca) and developing next-generation scalable performance tools. The PRIMA-X project shifts the focus away from refactorization of robust performance tools towards a re-targeting of the parallel performance measurement and analysis architecture for extreme scales. The massive concurrency, asynchronous execution dynamics, hardware heterogeneity, and multi-objective prerequisites (performance, power, resilience) that identify exascale systems introduce fundamental constraints on the ability to carry forward existing performance methodologies. In particular, there must be a deemphasis of per-thread observation techniques to significantly reduce the otherwise unsustainable flood of redundant performance data. Instead, it will be necessary to assimilate multi-level resource observations into macroscopic performance views, from which resilient performance metrics can be attributed to the computational features of the application. This requires a scalable framework for node-level and system-wide monitoring and runtime analyses of dynamic performance information. Also, the interest in optimizing parallelism parameters with respect to performance and energy drives the integration of tool capabilities in the exascale environment further. Initially, PRIMA-X was a collaborative project between the University of Oregon (lead institution) and the German Research School for Simulation Sciences (GRS). Because Prof. Wolf, the PI at GRS, accepted a position as full professor at Technische Universität Darmstadt (TU 19. PACMAN: PRIMA astrometric instrument software Science.gov (United States) Abuter, Roberto; Sahlmann, Johannes; Pozna, Eszter 2010-07-01 The dual feed astrometric instrument software of PRIMA (PACMAN) that is currently being integrated at the VLTI will use two spatially modulated fringe sensor units and a laser metrology system to carry out differential astrometry. Its software and hardware compromises a distributed system involving many real time computers and workstations operating in a synchronized manner. Its architecture has been designed to allow the construction of efficient and flexible calibration and observation procedures. In parallel, a novel scheme of integrating M-code (MATLAB/OCTAVE) with standard VLT (Very Large Telescope) control software applications had to be devised in order to support numerically intensive operations and to have the capacity of adapting to fast varying strategies and algorithms. This paper presents the instrument software, including the current operational sequences for the laboratory calibration and sky calibration. Finally, a detailed description of the algorithms with their implementation, both under M and C code, are shown together with a comparative analysis of their performance and maintainability. 20. Attentional Bias in Patients with Decompensated Tinnitus: Prima Facie Evidence from Event-Related Potentials. Science.gov (United States) Li, Zhicheng; Gu, Ruolei; Zeng, Xiangli; Zhong, Weifang; Qi, Min; Cen, Jintian 2016-01-01 Tinnitus refers to the auditory perception of sound in the absence of external sound or electric stimuli. The influence of tinnitus on cognitive processing is at the cutting edge of ongoing tinnitus research. In this study, we adopted an objective indicator of attentional processing, i.e. the mismatch negativity (MMN), to assess the attentional bias in patients with decompensated tinnitus. Three kinds of pure tones, D1 (8,000 Hz), S (8,500 Hz) and D2 (9,000 Hz), were used to induce event-related potentials (ERPs) in the normal ear. Employing the oddball paradigm, the task was divided into two blocks in which D1 and D2 were set as deviation stimuli, respectively. Only D2 induced a significant MMN in the tinnitus group, while neither D1 nor D2 was able to induce MMN in the control group. In addition, the ERPs in the left hemisphere, which were recorded within the time window of 90-150 ms (ERP 90-150 ms), were significantly higher than those in the right hemisphere in the tinnitus group, while no significant difference was observed in the control group. Lastly, the amplitude of ERP 90-150 ms in the tinnitus group was significantly higher than that in the control group. These findings suggest that patients with decompensated tinnitus showed automatic processing of acoustic stimuli, thereby indicating that these patients allocated more cognitive resources to acoustic stimulus processing. We suggest that the difficulty in disengaging or facilitated attention of patients might underlie this phenomenon. The limitations of the current study are discussed. © 2016 S. Karger AG, Basel. 1. Justificação epistêmica: prima e ultima facie OpenAIRE Fusari, Lionara 2010-01-01 A investigação e a análise relativa ao problema da justificação epistêmica são realizadas desde a Antiga Grécia, sendo a justificação um dos assuntos bem centrais no estudo da epistemologia contemporânea. Nesse sentido, este trabalho aborda inicialmente o conceito de justificação, algumas fontes de justificação para as crenças e algumas teorias da justificação epistêmica. Um pressuposto que deve ser levado em conta é que sempre a ideia de “justificação”, sobre a qual se trabalha aqui, é a de ... 2. Level System Use in Special Education: Classroom Intervention with Prima Facie Appeal. Science.gov (United States) Smith, Stephen W.; Farrell, Daniel T. 1993-01-01 This article chronicles the development of level systems designed for students with significant behavior problems, to foster student improvement through self-management and positive reinforcement. The article examines assumptions underlying level systems' concepts and components and offers recommendations to guide future research into the design… 3. Presentation and information management server PRIMAS International Nuclear Information System (INIS) Gibbert, R. 1998-01-01 An advanced computerized information system, PRIMAS, is presented. Its tasks include legal demands by the Federal government and the EU, environmental data model solutions, multi-sectorial analysis etc. Its structure, an open system architecture makes possible to be integrated and connected to existing standard systems. Its main use is the provision and processing of environmental information. (R.P.) 4. Neural net generated seismic facies map and attribute facies map International Nuclear Information System (INIS) 1998-01-01 The usefulness of 'seismic facies maps' in the analysis of an Upper Wilcox channel system in a 3-D survey shot by CGG in 1995 in Lavaca county in south Texas was discussed. A neural net-generated seismic facies map is a quick hydrocarbon exploration tool that can be applied regionally as well as on a prospect scale. The new technology is used to classify a constant interval parallel to a horizon in a 3-D seismic volume based on the shape of the wiggle traces using a neural network technology. The tool makes it possible to interpret sedimentary features of a petroleum deposit. The same technology can be used in regional mapping by making 'attribute facies maps' in which various forms of amplitude attributes, phase attributes or frequency attributes can be used 5. Sustaining Competitive Advantage in Prima Sakti Directory of Open Access Journals (Sweden) Kristin Handoyo 2016-06-01 Full Text Available Didirikan pada tahun 1993, Prima Sakti adalah sebuah perusahaan metal stamping dan plastic injection parts. Setelah lebih dari dua dekade, perusahaan ini telah berkembang menjadi sebuah perusahaan yang kompleks dalam hal ukuran, pasar dan produk. Penelitian kualitatif ini dipandu oleh sejumlah teori sebagai landasan dan menggunakan triangulasi data. Hasil dan pembahasan menunjukkan adanya perkembangan perusahaan dari sistem made-to-order menjadi sistem hybrid antara sistem made-to-order dan made-to-stock untuk memaksimalkan kapasitas dalam menerapkan cost leadership. Target pasar juga meluas dalam hal melanjutkan penetrasi pasar, pengembangan pasar dan pengembangan produk. Hasil dan pembahasan juga mengindikasi bahwa untuk mendapatkan keunggulan kompetitif, perusahaan mengintegrasi strategi cost leadership dan differentiation. Sebagai penutup, peneliti mengusulkan sebuah teori-mini yang didasarkan pada sejumlah variabel antara lain reputasi perusahaan, kualitas produk, pelayanan, learning effect, economies of scale, economies of scope dan capacity utilization yang mungkin memengaruhi keunggulan kompetitif untuk diuji secara kuantitatif. 6. ESPRI: Astrometric planet search with PRIMA at the VLTI Directory of Open Access Journals (Sweden) Ségransan D. 2011-07-01 Full Text Available The ESPRI consortium will conduct an astrometric survey for extrasolar planets, using the PRIMA facility at the Very Large Telescope Interferometer. Our scientific goals include determining orbital inclinations and masses for planets already known from radial-velocity surveys, searches for planets around nearby stars of all masses, and around young stars. The consortium has built the PRIMA differential delay lines, developed an astrometric operation and calibration plan, and will deliver astrometric data reduction software. 7. Gene alterations at Drosophila inversion breakpoints provide prima facie evidence for natural selection as an explanation for rapid chromosomal evolution Science.gov (United States) 2012-01-01 Background Chromosomal inversions have been pervasive during the evolution of the genus Drosophila, but there is significant variation between lineages in the rate of rearrangement fixation. D. mojavensis, an ecological specialist adapted to a cactophilic niche under extreme desert conditions, is a chromosomally derived species with ten fixed inversions, five of them not present in any other species. Results In order to explore the causes of the rapid chromosomal evolution in D. mojavensis, we identified and characterized all breakpoints of seven inversions fixed in chromosome 2, the most dynamic one. One of the inversions presents unequivocal evidence for its generation by ectopic recombination between transposon copies and another two harbor inverted duplications of non-repetitive DNA at the two breakpoints and were likely generated by staggered single-strand breaks and repair by non-homologous end joining. Four out of 14 breakpoints lay in the intergenic region between preexisting duplicated genes, suggesting an adaptive advantage of separating previously tightly linked duplicates. Four out of 14 breakpoints are associated with transposed genes, suggesting these breakpoints are fragile regions. Finally two inversions contain novel genes at their breakpoints and another three show alterations of genes at breakpoints with potential adaptive significance. Conclusions D. mojavensis chromosomal inversions were generated by multiple mechanisms, an observation that does not provide support for increased mutation rate as explanation for rapid chromosomal evolution. On the other hand, we have found a number of gene alterations at the breakpoints with putative adaptive consequences that directly point to natural selection as the cause of D. mojavensis rapid chromosomal evolution. PMID:22296923 8. Gene alterations at Drosophila inversion breakpoints provide prima facie evidence for natural selection as an explanation for rapid chromosomal evolution. Science.gov (United States) Guillén, Yolanda; Ruiz, Alfredo 2012-02-01 Chromosomal inversions have been pervasive during the evolution of the genus Drosophila, but there is significant variation between lineages in the rate of rearrangement fixation. D. mojavensis, an ecological specialist adapted to a cactophilic niche under extreme desert conditions, is a chromosomally derived species with ten fixed inversions, five of them not present in any other species. In order to explore the causes of the rapid chromosomal evolution in D. mojavensis, we identified and characterized all breakpoints of seven inversions fixed in chromosome 2, the most dynamic one. One of the inversions presents unequivocal evidence for its generation by ectopic recombination between transposon copies and another two harbor inverted duplications of non-repetitive DNA at the two breakpoints and were likely generated by staggered single-strand breaks and repair by non-homologous end joining. Four out of 14 breakpoints lay in the intergenic region between preexisting duplicated genes, suggesting an adaptive advantage of separating previously tightly linked duplicates. Four out of 14 breakpoints are associated with transposed genes, suggesting these breakpoints are fragile regions. Finally two inversions contain novel genes at their breakpoints and another three show alterations of genes at breakpoints with potential adaptive significance. D. mojavensis chromosomal inversions were generated by multiple mechanisms, an observation that does not provide support for increased mutation rate as explanation for rapid chromosomal evolution. On the other hand, we have found a number of gene alterations at the breakpoints with putative adaptive consequences that directly point to natural selection as the cause of D. mojavensis rapid chromosomal evolution. 9. [Burden of proof in medical cases--presumption of fact and prima facie evidence. 1. Burden of proof]. Science.gov (United States) Sliwka, Marcin 2004-01-01 The aim of this paper was to present the main rules concerning the burden of proof in polish civil trials, including medical cases. This paper also describes the subject of evidence were presented and explained. The court influence on evidence procedure was also analysed. The effect of the institution of informed consent on burden of proof in polish civil law is also described. This paper includes numerous High Court sentences on evidential and medical issues. 10. Gene alterations at Drosophila inversion breakpoints provide prima facie evidence for natural selection as an explanation for rapid chromosomal evolution Directory of Open Access Journals (Sweden) Guillén Yolanda 2012-02-01 Full Text Available Abstract Background Chromosomal inversions have been pervasive during the evolution of the genus Drosophila, but there is significant variation between lineages in the rate of rearrangement fixation. D. mojavensis, an ecological specialist adapted to a cactophilic niche under extreme desert conditions, is a chromosomally derived species with ten fixed inversions, five of them not present in any other species. Results In order to explore the causes of the rapid chromosomal evolution in D. mojavensis, we identified and characterized all breakpoints of seven inversions fixed in chromosome 2, the most dynamic one. One of the inversions presents unequivocal evidence for its generation by ectopic recombination between transposon copies and another two harbor inverted duplications of non-repetitive DNA at the two breakpoints and were likely generated by staggered single-strand breaks and repair by non-homologous end joining. Four out of 14 breakpoints lay in the intergenic region between preexisting duplicated genes, suggesting an adaptive advantage of separating previously tightly linked duplicates. Four out of 14 breakpoints are associated with transposed genes, suggesting these breakpoints are fragile regions. Finally two inversions contain novel genes at their breakpoints and another three show alterations of genes at breakpoints with potential adaptive significance. Conclusions D. mojavensis chromosomal inversions were generated by multiple mechanisms, an observation that does not provide support for increased mutation rate as explanation for rapid chromosomal evolution. On the other hand, we have found a number of gene alterations at the breakpoints with putative adaptive consequences that directly point to natural selection as the cause of D. mojavensis rapid chromosomal evolution. 11. From chemistry to consciousness the legacy of Hans Primas CERN Document Server Müller-Herold, Ulrich 2016-01-01 This book reflects on the significant and highly original scientific contributions of Hans Primas. A professor of chemistry at ETH Zurich from 1962 to 1995, Primas continued his research activities until his death in 2014. Over these 50 years and more, he worked on the foundations of nuclear magnetic resonance spectroscopy, contributed to a number of significant issues in theoretical chemistry, helped to clarify central topics in quantum theory and the philosophy of physics, suggested innovative ways of addressing interlevel relations in the philosophy of science, and introduced cutting-edge approaches in the flourishing young field of scientific studies of consciousness. His work in these areas of research and its continuing impact is described by noted experts, colleagues, and collaborators of Primas. All authors contextualize their contributions to facilitate the mutual dialog between these fields. 12. Prima Vistale tuleb tuntud kirjanikke mitmest Euroopa riigist / Kaarel Kressa Index Scriptorium Estoniae Kressa, Kaarel, 1983- 2010-01-01 Prima Vista kirjandusfestivali külalisi: Leonie Swann, Attila Bartis, Dmitri Bõkov, Zinaida Lindén, Mihhail Šiškin, Fay Weldon, Jason Goodwin, Rosa Maria Rodríguez Magda, Inga Gaile, Juris Kronbergs, Guntars Godinš, Liana Langa 13. Al CERN prima fase sistema gestione dati LHC CERN Multimedia 2003-01-01 "Al via la prima fase per la realizzazione del sistema Lhc computing Grid (LCG), progettato per elaborare le quantita' di dati senza precedenti che, a partire dal 2007, saranno prodotte dagli esperimenti eseguiti con il nuovo grande acceleratore Large Hadron Collider (LHC), presso il Cern di Ginevra" 1 page 14. Facies Constrained Elastic Full Waveform Inversion KAUST Repository Zhang, Z. 2017-05-26 Current efforts to utilize full waveform inversion (FWI) as a tool beyond acoustic imaging applications, for example for reservoir analysis, face inherent limitations on resolution and also on the potential trade-off between elastic model parameters. Adding rock physics constraints does help to mitigate these issues. However, current approaches to add such constraints are based on averaged type rock physics regularization terms. Since the true earth model consists of different facies, averaging over those facies naturally leads to smoothed models. To overcome this, we propose a novel way to utilize facies based constraints in elastic FWI. A so-called confidence map is calculated and updated at each iteration of the inversion using both the inverted models and the prior information. The numerical example shows that the proposed method can reduce the cross-talks and also can improve the resolution of inverted elastic properties. 15. Facies Constrained Elastic Full Waveform Inversion KAUST Repository Zhang, Z.; Zabihi Naeini, E.; Alkhalifah, Tariq Ali 2017-01-01 Current efforts to utilize full waveform inversion (FWI) as a tool beyond acoustic imaging applications, for example for reservoir analysis, face inherent limitations on resolution and also on the potential trade-off between elastic model parameters. Adding rock physics constraints does help to mitigate these issues. However, current approaches to add such constraints are based on averaged type rock physics regularization terms. Since the true earth model consists of different facies, averaging over those facies naturally leads to smoothed models. To overcome this, we propose a novel way to utilize facies based constraints in elastic FWI. A so-called confidence map is calculated and updated at each iteration of the inversion using both the inverted models and the prior information. The numerical example shows that the proposed method can reduce the cross-talks and also can improve the resolution of inverted elastic properties. 16. Barrier island facies models and recognition criteria Science.gov (United States) Mulhern, J.; Johnson, C. L. 2017-12-01 Barrier island outcrops record transgressive shoreline motion at geologic timescales, providing integral clues to understanding how coastlines respond to rising sea levels. However, barrier island deposits are difficult to recognize. While significant progress has been made in understanding the modern coastal morphodynamics, this insight is not fully leveraged in existing barrier island facies models. Excellent outcrop exposures of the paralic Upper Cretaceous Straight Cliffs Formation of southern Utah provide an opportunity to revise facies models and recognition criteria for barrier island deposits. Preserved barrier islands are composed of three main architectural elements (shorefaces, tidal inlets, and tidal channels) which occur independently or in combination to create larger-scale barrier island deposits. Barrier island shorefaces record progradation, while barrier island tidal inlets record lateral migration, and barrier island tidal channels record aggradation within the tidal inlet. Four facies associations are used to describe and characterize these barrier island architectural elements. Barrier islands occur in association with backarrier fill and internally contain lower and upper shoreface, high-energy upper shoreface, and tidal channel facies. Barrier islands bound lagoons or estuaries, and are distinguished from other shoreface deposits by their internal facies and geometry, association with backbarrier facies, and position within transgressive successions. Tidal processes, in particular tidal inlet migration and reworking of the upper shoreface, also distinguish barrier island deposits. Existing barrier island models highlight the short term heterogeneous and dynamic nature of barrier island systems, yet overlook processes tied to geologic time scales, such as multi-directional motion, erosion, and reworking, and their expressions in preserved barrier island strata. This study uses characteristic outcrop expressions of barrier island successions to 17. Applications in Foreign Currency Prima CV Ellindo Money Changer OpenAIRE Wisnu Sutrisno; Ire Puspa Wardhani, Skom, MMSI 2004-01-01 This explains the scientific writing about the design of application programs forforeign currency transactions by using Visual Basic 6.0 programming language.In scientific writing database is also used by Visual Data Manager (VisData)integrated in Visual Basic 6.0 program itself. Consists of three tables namelyCurrency,Customer and Transaction.In the end application program for foreign currency transactions will be applied to theCV. Prima Ellindo Money Changer for ease in performing activitie... 18. A Facies Model for Temperate Continental Glaciers. Science.gov (United States) Ashley, Gail Mowry 1987-01-01 Discusses the presence and dynamics of continental glaciers in the domination of the physical processes of erosion and deposition in the mid-latitudes during the Pleistocene period. Describes the use of a sedimentary facies model as a guide to recognizing ancient temperate continental glacial deposits. (TW) Directory of Open Access Journals (Sweden) Yugowati Praharsi 2015-06-01 Full Text Available PT. Artha Prima Sukses Makmur memiliki lima mesin dalam menjalankan kegiatan produksi sol sepatu yang berlangsung 24 jam setiap hari, sehingga kegiatan perawatan dan pemeliharaan perlu dilakukan dengan baik dan dijadwalkan agar tidak mengganggu kegiatan produksi yang sedang berlangsung. Kerusakan mesin saat ini masih terhitung tinggi dan memerlukan waktu perbaikan yang cukup lama. Perancangan penjadwalan maintenancediperlukan untuk mengurangi downtime pada mesin, sehingga tidak menghambat dan mengganggu jadwal produksi. Penjadwalan yang diusulkan adalah preventive maintenance dengan metode age replacement. Berdasarkan prinsip Pareto terdapat dua mesin kritis dari lima mesin yang ada.Hasil perhitungan dari data kerusakan mesin sebelumnya diketahui, jika dilakukan preventive maintenance downtime akan berkurang sebanyak 2.85%, dan terjadi penghematan sebesar 38%. Directory of Open Access Journals (Sweden) Yugowati Praharsi 2015-06-01 Full Text Available PT. Artha Prima Sukses Makmur memiliki lima mesin dalam menjalankan kegiatan produksi sol sepatu yang berlangsung 24 jam setiap hari, sehingga kegiatan perawatan dan pemeliharaan perlu dilakukan dengan baik dan dijadwalkan agar tidak mengganggu kegiatan produksi yang sedang berlangsung. Kerusakan mesin saat ini masih terhitung tinggi dan memerlukan waktu perbaikan yang cukup lama. Perancangan penjadwalan maintenancediperlukan untuk mengurangi downtime pada mesin, sehingga tidak menghambat dan mengganggu jadwal produksi. Penjadwalan yang diusulkan adalah preventive maintenance dengan metode age replacement. Berdasarkan prinsip Pareto terdapat dua mesin kritis dari lima mesin yang ada.Hasil perhitungan dari data kerusakan mesin sebelumnya diketahui, jika dilakukan preventive maintenance downtime akan berkurang sebanyak 2.85%, dan terjadi penghematan sebesar 38%. 1. Variations in vitrinite reflectance with organic facies - examples from Pennsylvanian cyclothems of the Midcontinent, USA Energy Technology Data Exchange (ETDEWEB) Wenger, L M; Baker, D R 1987-01-01 Significant variations in vitrinite reflectance (% R/sub o/) with organic facies have been demonstrated from Pennsylvanian -aged cyclothems of the Midcontinent, USA. Thermal alteration index (TAI) and Rock-Eval T/sub m/ax values remain relatively constant through these thin lithologic successions, regardless of facies, and are in reasonable agreement with R/sub o/ measurements on interbedded coal. Organic-rich black and phosphatic black-shales, which contain significant component of liptinitic organic matter of presumed marine algal derivation, display R/sub o/ values which are suppressed relative to the coal benchmark. A distinct correlation between increased hydrogen index (HI) and liptinite content with suppressed reflectivities is apparent. More oxic facies (e.g. calcareous and fossiliferous gray shales and limestones) often display R/sub o/'s that are considerably higher than for coal. Soxhlet extraction prior to maceration yielded no variation in reflectance compared to non-extracted kerogens suggesting bitumen adsorption was not the cause of the apparent suppression in the organic-rich black-shales. Lower total organic carbon (TOC)-normalized bitumen contents and Rock-Eval transformations ratios in liptinite-rich facies suggest differential reaction kinetics for kerogen types, with terrestrial organic matter 'maturing' at an earlier stage than hydrogen-rich marine-derived organic matter. 8 refs., 6 figs., 1 tab. 2. Pengembangan Aplikasi E-Crm pada PT Trafoindo Prima Perkasa Directory of Open Access Journals (Sweden) Honni Honni 2008-10-01 Full Text Available Various surveys show that the key to corporate success lies not only on the product or service being offered but how far the company’s efforts to satisfy the needs of its customers. Companies have to provide products or services that match customer needs and wants, and then maintain close relations with customers. Customer loyalty will be the key to success, not only in the short term but sustainable competitive advantage. This is because customer loyalty has strategic value for the company. One way that proved effective and successful to meet and satisfy customer needs is through the CRM (Customer Relationship Management. CRM is not new in the business world. Customer Relationship has long been applied by traditional businessmen. Technology in the form of a web can be utilized as a catalyst in improving the quality of CRM. Combining Technology and CRM in a business called E-CRM. E-CRM application development web based on PT Trafoindo Prima Perkasa aims to analyze and design company and customer needs. The research method used in this writing is descriptive survey method primarily associated with the customer. The analysis tool used is the model porter five forces and industry analysis: CPM Matrix, the External Factor Evaluation Matrix (EFE, the Internal Factor Evaluation Matrix (IFE, SWOT Matrix, IE Matrix, SPACE Matrix, and Grand Strategy Matrix to identify alternative strategies can be applied. Alternative strategy is then measured with a Matrix QSP charm, coupled with the approach of Object Oriented Analysis and Design as the basis for the development of E-CRM application based on web. Conclusions obtained are E-CRM applications have produced work as expected.Keywords: development, application of E-CRM, Trafoindo Prima Perkasa 3. The earthing system of the PRIMA Neutral Beam Test Facility based on the Mesh Common Bonding Network topology International Nuclear Information System (INIS) Pomaro, Nicola; Boldrin, Marco; Lazzaro, Gabriele 2015-01-01 Highlights: • We designed a high performance earthing system for the ITER Neutral Beam Test Facility. • The system is based on the Mesh Common Bonded Network topology. • Careful bonding of all metallic structures allowed to obtain a well meshed system. • Special care was dedicated to improve EMC performance of critical areas like control rooms. • The facility experimental results will be representative also of the ITER situation. - Abstract: PRIMA is a large experimental facility under realization in Padova, aimed at developing and testing the Neutral Beam Injectors for ITER. The operation of these devices involves high RF power and voltage up to 1 MV. Frequent and high voltage electrical breakdowns inside the beam sources occur regularly. The presence of a distributed carefully optimized earthing system is of paramount importance to achieve a satisfying disturbances immunity for equipment and diagnostics. The paper describes the design and the realization of the earthing system of the PRIMA facility, which is based on the MESH-Common Bonding Network (MESH-CBN) topology, as recommended by IEC and IEEE standards for installations with high levels of Electromagnetic Interferences (EMI). The principles of the MESH-CBN approach were adapted to the PRIMA layout, which is composed by several buildings, that are independent for seismic and architectural reasons, but are linked by many electrical conduits and hydraulic pipelines. The availability of huge foundations, with a large number of poles and pillars, was taken into account; building parts dedicated to host control rooms and sensitive equipment were treated with particular care. Moreover, the lightning protection system was integrated and harmonized with the earthing system. 4. The earthing system of the PRIMA Neutral Beam Test Facility based on the Mesh Common Bonding Network topology Energy Technology Data Exchange (ETDEWEB) Pomaro, Nicola, E-mail: [email protected]; Boldrin, Marco; Lazzaro, Gabriele 2015-10-15 Highlights: • We designed a high performance earthing system for the ITER Neutral Beam Test Facility. • The system is based on the Mesh Common Bonded Network topology. • Careful bonding of all metallic structures allowed to obtain a well meshed system. • Special care was dedicated to improve EMC performance of critical areas like control rooms. • The facility experimental results will be representative also of the ITER situation. - Abstract: PRIMA is a large experimental facility under realization in Padova, aimed at developing and testing the Neutral Beam Injectors for ITER. The operation of these devices involves high RF power and voltage up to 1 MV. Frequent and high voltage electrical breakdowns inside the beam sources occur regularly. The presence of a distributed carefully optimized earthing system is of paramount importance to achieve a satisfying disturbances immunity for equipment and diagnostics. The paper describes the design and the realization of the earthing system of the PRIMA facility, which is based on the MESH-Common Bonding Network (MESH-CBN) topology, as recommended by IEC and IEEE standards for installations with high levels of Electromagnetic Interferences (EMI). The principles of the MESH-CBN approach were adapted to the PRIMA layout, which is composed by several buildings, that are independent for seismic and architectural reasons, but are linked by many electrical conduits and hydraulic pipelines. The availability of huge foundations, with a large number of poles and pillars, was taken into account; building parts dedicated to host control rooms and sensitive equipment were treated with particular care. Moreover, the lightning protection system was integrated and harmonized with the earthing system. 5. Sasaran Strategis Perusahaan Perkebunan Kelapa Sawit Teladan Prima Group Directory of Open Access Journals (Sweden) Sali Subakti 2017-09-01 Full Text Available Teladan Prima Group (TPG as one of the palm oil plantations company have a strategic objectives in perspective of financial, customer, internal business processes, and learning and growth with the implementation of the Balanced Scorecard (BSC. The efforts to improve of high productivity of all resources that owned, are effectiveness managed with cost efficiency is the ultimate goal of company performance measurement. The problems occurred, management is confronted on the issues of the achievement of company performance targets that are not optimal and the strategic objectives of the company have not been cascaded down in a balanced way. The purpose of this research is to analyze of the strategic objectives and the implementation of BSC by using the technique of analysis of fourteen strategic objectives of the company in the four BSC perspectives with the integration of analytic network process (ANP. Results from the processing of primary data obtained through in-depth interviews and pairwise comparison of 7 respondents on the company executive level shows the results: financial perspective has the biggest weighting 42.21%, internal business process perspective 27.45%, customer perspective 16.29% growth and learning perspective 14.04% with consistency ratio (CR 2.14% which means the respondent opinion is acceptable and consistent.Keywords: strategic objectives, balanced scorecard, ANP, oil palmAbstrak: Teladan Prima Group (TPG sebagai salah satu perusahaan perkebunan kelapa sawit memiliki sasaran strategi dalam perspektif kinerja keuangan, pelanggan, proses bisnis internal dan pembelajaran dan pertumbuhan dengan penerapan Balanced Scorecard (BSC. Upaya peningkatan produktivitas sumberdaya yang dimiliki, dengan efektivitas pengelolaan dan efisiensi biaya merupakan tujuan akhir dari pengukuran kinerja perusahaan. Permasalahan yang terjadi, manajemen dihadapkan pada isu pencapaian target kinerja perusahaan yang belum optimum dan sasaran strategis 6. Pengaruh Komunikasi Interpersonal dan Iklim Organisasi terhadap Kinerja Karyawan PT. Selatan Prima Sejahtera Jaya Pekanbaru OpenAIRE Restu, Restu; Indarti, Sri; Johanes, Johanes 2015-01-01 The purpose of this study was to determine the effect of partial and simultaneous interpersonal communication and organizational climate simultaneously on the performance of employees of PT. South Prima Sejahtera Jaya Pekanbaru. The sample in this study were all employees of PT. South PrimaSejahtera Jaya Pekanbaru totaling 35 people. The technique of collecting data using questionnaires. Data analysis technique is quantitative descriptive method and regression.The results showed that interper... 7. Las facies Keuper al SW de la provincia de Soria Directory of Open Access Journals (Sweden) Hernando, S. 1988-08-01 Full Text Available This paper deals with the sedimentological analysis of the materials that correspond to the Keuper facies in the area situated between the Iberian Ranges and the Central System. Acording to the obtained data, two main aspects are emphasized: - During the Upper Triassic, a c1ear retreat of the roast line towards the East took place, since this area constituted the litoral zone during the sedimentation of the Rot and Muschelkalk. - Facies change lateraly from West to East as proximal alluvial Can sediments pass into facies interpreted as distal alluvial fans and continental sabkha environment.Se analizan, desde el punto de vista sedimentológico, unos materiales correspondientes a las facies Keuper entre la Cordillera Ibérica y el Sistema Central. Dos aspectos resaltan tras este análisis: - Desplazamiento de la línea de costa (que durante la sedimentación del Rot y del Muschelkalk estaba situada en esta zona hacia el Este. - Marcado cambio lateral de facies desde el Oeste hacia el Este, pasando de unas facies proximales-medias de abanico aluvial a unas facies distales y ambiente de sabkha continental. 8. Prima facie evidence that a phytocystatin for transgenic plant resistance to nematodes is not a toxic risk in the human diet. Science.gov (United States) Atkinson, Howard J; Johnston, Katherine A; Robbins, Mark 2004-02-01 A protein-engineered rice cystatin (OcIDeltaD86) provides transgenic, partial crop resistance to plant nematodes. This study determined whether its oral uptake has adverse effects on male Sprague-Dawley rats when they are administered by oral gavage 0.1-10 mg OcIDeltaD86/kg body weight daily for 28 d. Body weight and water and food intakes were unaltered for most of the study. The only significant changes in fresh weight of nine organs were for the liver (4% decrease; P 95% loss of such inhibition after 15 s in simulated gastric fluid. The results suggest that the no effect level (NOEL) for OcIDeltaD86 is >10 mg/(kg. d). This provides a range of dietary exposure >200-2000 fold depending upon the promoter used to control its expression in potato. 9. A Systems Approach for Ameliorating Possible Prima Facie Denial of Hispanic/Black Students' Rights Through Disproportionate Enrollment in Special Education. Science.gov (United States) McDonnell, James R. The paper discusses the issue of educational equity, principles of systems analysis, systems approaches in the educational milieu, the evaluation aspect of the systems approach, and application of the systems approach to preventing disproportionate enrollment of Hispanics and Blacks in special education classes in Holyoke, Massachusetts. The… 10. Elastic properties of granulite facies rocks of Mahabalipuram, Tamil ... the granulite facies rocks have helped us to under- stand the metamorphic ... imperative need to make new and accurate lab- .... the driving side and a digital storage oscilloscope ..... propagation in rocks and other lossy media: An experi-. 11. PROBLEMS AND METHODOLOGY OF THE PETROLOGIC ANALYSIS OF COAL FACIES. Science.gov (United States) Chao, Edward C.T. 1983-01-01 This condensed synthesis gives a broad outline of the methodology of coal facies analysis, procedures for constructing sedimentation and geochemical formation curves, and micro- and macrostratigraphic analysis. The hypothetical coal bed profile has a 3-fold cycle of material characteristics. Based on studies of other similar profiles of the same coal bed, and on field studies of the sedimentary rock types and their facies interpretation, one can assume that the 3-fold subdivision is of regional significance. 12. CONFLICTING REASONS OpenAIRE Parfit, Derek 2016-01-01 Sidgwick believed that, when impartial reasons conflict with self-interested reasons, there are no truths about their relative strength. There are such truths, I claim, but these truths are imprecise. Many self-interested reasons are decisively outweighed by conflicting impar-tial moral reasons. But we often have sufficient self-interested reasons to do what would make things go worse, and we sometimes have sufficient self-interested reasons to act wrongly. If we reject Act Consequentialism, ... 13. Fine-Grained Turbidites: Facies, Attributes and Process Implications Science.gov (United States) Stow, Dorrik; Omoniyi, Bayonle 2016-04-01 Within turbidite systems, fine-grained sediments are still the poor relation and sport several contrasting facies models linked to process of deposition. These are volumetrically the dominant facies in deepwater and, from a resource perspective, they form important marginal and tight reservoirs, and have great potential for unconventional shale gas, source rocks and seals. They are also significant hosts of metals and rare earth elements. Based on a large number of studies of modern, ancient and subsurface systems, including 1000s of metres of section logging, we define the principal genetic elements of fine-grained deepwater facies, present a new synthesis of facies models and their sedimentary attributes. The principal architectural elements include: non-channelised slope-aprons, channel-fill, channel levee and overbank, turbidite lobes, mass-transport deposits, contourite drifts, basin sheets and drapes. These comprise a variable intercalation of fine-grained facies - thin-bedded and very thin-bedded turbidites, contourites, hemipelagites and pelagites - and associated coarse-grained facies. Characteristic attributes used to discriminate between these different elements are: facies and facies associations; sand-shale ratio, sand and shale geometry and dimensions, sand connectivity; sediment texture and small-scale sedimentary structures; sediment fabric and microfabric; and small-scale vertical sequences of bed thickness. To some extent, we can relate facies and attribute characteristics to different depositional environments. We identify four distinct facies models: (a) silt-laminated mud turbidites, (b) siliciclastic mud turbidites, (c) carbonate mud turbidites, (d) disorganized silty-mud turbidites, and (e) hemiturbidites. Within the grainsize-velocity matrix turbidite plot, these all fall within the region of mean size < 0.063mm, maximum grainsize (one percentile) <0.2mm, and depositional velocity 0.1-0.5 m/s. Silt-laminated turbidites and many mud 14. Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints Science.gov (United States) Zhang, Zhen-dong; Alkhalifah, Tariq; Naeini, Ehsan Zabihi; Sun, Bingbing 2018-03-01 Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method. 15. Multiparameter elastic full waveform inversion with facies-based constraints Science.gov (United States) Zhang, Zhen-dong; Alkhalifah, Tariq; Naeini, Ehsan Zabihi; Sun, Bingbing 2018-06-01 Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize FWI beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a priori information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method. 16. Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints KAUST Repository Zhang, Zhendong 2018-03-20 Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method. 17. Tectonic controls on preservation of Middle Triassic Halfway reservoir facies, Peejay Field, northeastern British Columbia: a new hydrocarbon exploration model Energy Technology Data Exchange (ETDEWEB) Caplan, M. L. [British Columbia Univ., Vancouver, BC (Canada). Dept. of Geological Sciences; Moslow, T. F. [Calgary Univ., AB (Canada). Dept. of Geology and Geophysics 1997-12-01 The Peejay Field in northeastern British Columbia was chosen as the site of a detailed study to establish the paleogeography, geological history and genesis of reservoir facies of Middle Triassic strata. A total of 132 cores and well logs from 345 wells were examined to establish the depositional model, to identify the origin of all reservoir facies and to construct an exploration model to improve the prediction of reservoir facies. Results show that the Middle Triassic Halfway Formation of northeastern British Columbia is comprised of at least four west-southwest prograding paleoshorelines. The Lithofacies Succession One quartz-arenites paleoshore faces have less porosity and permeability and are laterally discontinuous. For these reasons shoreface facies have minimal reservoir quality. The tidal inlet fill successions were found to have the greatest observed porosity, permeability and lateral continuity in the Peejay Field. The geometry and orientation of these tidal inlet fill deposits are controlled by tectonic processes. It was suggested that the success of hydrocarbon exploration in this structurally complex area of northeastern British Columbia and west-central Alberta depends on further stratigraphic and sedimentological examination of Middle Triassic strata on a regional scale to obtain a complete understanding of the geological history of the area. 39 refs., 13 refs. 18. Delineation of geological facies from poorly differentiated data Energy Technology Data Exchange (ETDEWEB) Wohlberg, Brendt [Los Alamos National Laboratory; Tartakovsky, Daniel [UCSC 2008-01-01 The ability to delineate geologic facies and to estima.te their properties from sparse data is essential for modeling physical and biochemical processes occurring in the 'ubsurface. If such data are poorly differentiated, this challcnrring task is complicated further by the absence of a clear distinction between different hydrofacies even at locations where data. are available. vVe consider three alt mative approaches for analysis of poorly differentiated data: a k-means clU!:iterinrr algorithm, an expectation-maximization algorithm, and a minimum-variance algorithm. Two distinct synthetically generated geological settings are used to r:tnalyze the ability of these algorithmti to as ign accurately the membership of such data in a given geologic facies. On average, the minimum-variance algorithm provides a more robust p rformance than its two counterparts and when combined with a nearest-neighbor algorithm, it also yields the most accurate reconstruction of the boundaries between the facies. 19. Fluvial to Lacustrine Facies Transitions in Gale Crater, Mars Science.gov (United States) Sumner, Dawn Y.; Williams, Rebecca M. E.; Schieber, Juergen; Palucis, Marisa C.; Oehler, Dorothy Z.; Mangold, Nicolas; Kah, Linda C.; Gupta, Sanjeev; Grotzinger, John P.; Grant, John A., III; 2015-01-01 NASA's Curiosity rover has documented predominantly fluvial sedimentary rocks along its path from the landing site to the toe of the Peace Vallis alluvial fan (0.5 km to the east) and then along its 8 km traverse across Aeolis Palus to the base of Aeolis Mons (Mount Sharp). Lacustrine facies have been identified at the toe of the Peace Vallis fan and in the lowermost geological unit exposed on Aeolis Mons. These two depositional systems provide end members for martian fluvial/alluvial-lacustrine facies models. The Peace Vallis system consisted of an 80 square kilometers alluvial fan with decimeter-thick, laterally continuous fluvial sandstones with few sedimentary structures. The thin lacustrine unit associated with the fan is interpreted as deposited in a small lake associated with fan runoff. In contrast, fluvial facies exposed over most of Curiosity's traverse to Aeolis Mons consist of sandstones with common dune-scale cross stratification (including trough cross stratification), interbedded conglomerates, and rare paleochannels. Along the southwest portion of the traverse, sandstone facies include south-dipping meter-scale clinoforms that are interbedded with finer-grained mudstone facies, interpreted as lacustrine. Sedimentary structures in these deposits are consistent with deltaic deposits. Deltaic deposition is also suggested by the scale of fluvial to lacustrine facies transitions, which occur over greater than 100 m laterally and greater than 10 m vertically. The large scale of the transitions and the predicted thickness of lacustrine deposits based on orbital mapping require deposition in a substantial river-lake system over an extended interval of time. Thus, the lowermost, and oldest, sedimentary rocks in Gale Crater suggest the presence of substantial fluvial flow into a long-lived lake. In contrast, the Peace Vallis alluvial fan onlaps these older deposits and overlies a major unconformity. It is one of the youngest deposits in the crater, and 20. OpenAIRE Ruiz, Sebastián Martín 2002-01-01 Un libro para los amantes de los números: La función de Smarandache aplicada a los números perfectos, congruencias. También, las funciones prima y coprima de Smarandache en conexión con expresiones de los números primos. 1. Una community emergente tra progettazione territorio e infrastrutture La prima conferenza Autodesk degli utenti italiani Directory of Open Access Journals (Sweden) Redazione Redazione 2005-10-01 Full Text Available La prima edizione dell’Autodesk User Conference dedicata aiSistemi Informativi Territoriali ed alla progettazione delle infrastrutture, tenutasi a Roma il 29 settembre 2005, diventerà l’appuntamento fisso sulla convergenza tra tecnologie CAD e GISche molti reclamavano da tempo. 2. The investigation of sedimentary facies and stacking pattern in the Mulid River (Southeastern Qayen Directory of Open Access Journals (Sweden) Marzieh Fayazi Borujeni 2017-03-01 recognized based on geometry and boundary surfaces and are used for depositional interpretation. These elements are included channel sediment fills (CH, gravel bars and bedforms (GB, sediment gravity flow deposits (SG, sandy bedforms (SB and overbank fines (FF. The wide range of sedimentary processes are controlled the fluvial style. Therefore the river channel morphology usually vary from upstream to downstream that these variations are due to change of some factors such as valley slope, sediment supply, climate and tectonic of the studied area. According to recognized sedimentary facies and architectural elements in the Mulid River channel walls and based on provided models of Miall (2006 two sedimentary models are proposed for this river: a The gravel- bed braided river with sediment gravity flow deposits and b the shallow gravel- bed braided river. The difference of a and b models is in frequency of various architectural elements and abundance of sedimentary facies. The first sedimentary model is formed in the proximal and high relief area where the slope, the discharge rate and sediment supply are high and the sediment transported currents are gravity flows. In this reason, the abundance of architectural elements and sandy and fine sedimentary facies that are results of traction currents, are low. In the second sedimentary model, away from the source area, the slope of longitudinal profile of river decreases and therefore the discharge rate of flow and sediment supply decrease. The abundance of debris flows are very low and the sediment gravity flow deposits are not observed in the end parts of rivers. The most important flow that is transported the sediments, is the traction current in this model. In due to decreasing sediment supply and increasing the accommodation space, frequency of sandy and muddy facies are increased with respect to previous model. The paleohydraulic parameters are estimated with facies variations for three gravely terraces with suitable exposures 3. Uranium, rare metals, and granulite-facies metamorphism Directory of Open Access Journals (Sweden) Michel Cuney 2014-09-01 The Tranomaro metasomatized marbles recrystallizing under granulite-facies conditions represent a demonstrative example of fluid transfer from granulite-facies supracrustals to traps represented by regional scale skarns. Such fluids may be at the origin of the incompatible element enrichment detected in leucosomes of migmatites from St Malo in Brittany (France and Black Hills in South Dakota. The northern French Massif Central provides us with an example of a potential association between incompatible element enrichment of granitic melts and granulite-facies metamorphism. U- and F-enriched fine-grained granites are emplaced along a crustal scale shear zone active during the emplacement within the St Sylvestre peraluminous leucogranitic complex. We propose that during granulite-facies metamorphism dominated by carbonic waves in a deep segment of the continental crust, these shear zones control: (i the percolation of F-, LILE-, rare metal-rich fluids liberated primarily by the breakdown of biotite; (ii the enhancement of partial melting by F-rich fluids at intermediate crustal levels with the generation of F-, LILE-, rare metal-rich granitic melts; (iii their transfer through the crust with protracted fractionation facilitated by their low viscosity due to high F-Li contents; and finally (iv their emplacement as rare metal intrusions at shallow crust levels. 4. Late Permian (Zechstein) carbonate-facies maps, the Netherlands NARCIS (Netherlands) Geluk, M.C. 2000-01-01 The Late Permian Zechstein carbonates in the Southern Permian Basin were deposited under marine conditions. The carbonates form part of a largely progradational infill, with a gradual northward facies shift. The paleogeography of the Zechstein carbonate deposits has been reviewed recently on the 5. Facies analysis and paleoenvironments of the upper cretaceous ... African Journals Online (AJOL) The Bida Basin is located in central Nigeria and it is perpendicular to the main axis of the Benue Trough. Due to its large areal extent and facies variation, the basin is often geographically divided into northern and southern Bida Basins. Whereas, aspects of the mineral resource and sedimentation history of the sediments in ... 6. Level-set techniques for facies identification in reservoir modeling Science.gov (United States) Iglesias, Marco A.; McLaughlin, Dennis 2011-03-01 In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil-water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301-29 2004 Inverse Problems 20 259-82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg-Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush-Kuhn-Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies. 7. Level-set techniques for facies identification in reservoir modeling International Nuclear Information System (INIS) Iglesias, Marco A; McLaughlin, Dennis 2011-01-01 In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil–water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301–29; 2004 Inverse Problems 20 259–82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg–Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush–Kuhn–Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies 8. Pertinent reasoning CSIR Research Space (South Africa) Britz, K 2010-05-01 Full Text Available In this paper the authors venture beyond one of the fundamental assumptions in the non-monotonic reasoning community, namely that non-monotonic entailment is supra-classical. They investigate reasoning which uses an infra-classical entailment... 9. Sedimentary facies and lithologic characters as main factors controlling hydrocarbon accumulations and their critical conditions Directory of Open Access Journals (Sweden) Jun-Qing Chen 2015-10-01 Full Text Available Taking more than 1000 clastic hydrocarbon reservoirs of Bohai Bay Basin, Tarim Basin and Junggar Basin, China as examples, the paper has studied the main controlling factors of hydrocarbon reservoirs and their critical conditions to reveal the hydrocarbon distribution and to optimize the search for favorable targets. The results indicated that the various sedimentary facies and lithologic characters control the critical conditions of hydrocarbon accumulations, which shows that hydrocarbon is distributed mainly in sedimentary facies formed under conditions of a long-lived and relatively strong hydrodynamic environment; 95% of the hydrocarbon reservoirs and reserves in the three basins is distributed in siltstones, fine sandstones, lithified gravels and pebble-bearing sandstones; moreover, the probability of discovering conventional hydrocarbon reservoirs decreases with the grain size of the clastic rock. The main reason is that the low relative porosity and permeability of fine-grained reservoirs lead to small differences in capillary force compared with surrounding rocks small and insufficiency of dynamic force for hydrocarbon accumulation; the critical condition for hydrocarbon entering reservoir is that the interfacial potential in the surrounding rock (Φn must be more than twice of that in the reservoir (Φs; the probability of hydrocarbon reservoirs distribution decreases in cases where the hydrodynamic force is too high or too low and when the rocks have too coarse or too fine grains. 10. Depositional facies mosaics and their time lines in Lower Ordovician carbonates of central Appalachians Energy Technology Data Exchange (ETDEWEB) Nguyen, C.T.; Goldhammer, R.K.; Hardie, L.A. 1985-02-01 A comparative sedimentology and facies stratigraphy study of the Lower Ordovician carbonate of the central Appalachians (Beekmantown Group and equivalents) has been carried out. Our approach used subfacies (rock record of subenvironments) as the basin units of section measurement. The authors differentiated related sets of subfacies into larger facies units (rock record of environments). Facies were then correlated from section to section using fossils and lithostratigraphy to make a 3-dimensional facies mosaic. Within this mosaic, time lines were constructed using onlap-offlap tongues and cyclic sequences. These time lines cut across facies boundaries. Using this approach, the authors have established that the lower 600 m of the Lower Ordovician carbonate sequence is made up of 4 main facies: (1) cyclic laminite facies composed of a package of shoaling-upward shelf lagoon-peritidal cycles, (2) thin-bedded grainstone facies deposited in a shelf lagoon, (3) Renalcis bioherm facies recording a shelf lagoon patch-reef environment, and (4) Epiphyton bioherm facies recording a shelf-edge reef system. The distribution of these facies along time lines across the strike of the central Appalachians is markedly zoned. Epiphyton bioherm facies dominate the eastern margin while cyclic laminite facies dominate the western margin, with thin-bedded grainstone and Renalcis bioherm facies making up the central belt. This zonation of facies is a typical shallow carbonate shelf system with fringing reefs along the eastern, seaward margin and tidal flats along the western, landward margin. Vertical distribution of these facies across strike records 3 major sea level changes during deposition of the lower 600 m of this extensive Lower Ordovician carbonate shelf. 11. PRIMA Platform capability for satellite missions in LEO and MEO (SAR, Optical, GNSS, TLC, etc.) Science.gov (United States) Logue, T.; L'Abbate, M. 2016-12-01 PRIMA (Piattaforma Riconfigurabile Italiana Multi Applicativa) is a multi-mission 3-axis stabilized Platform developed by Thales Alenia Space Italia under ASI contract.PRIMA is designed to operate for a wide variety of applications from LEO, MEO up to GEO and for different classes of satellites Platform Family. It has an extensive heritage in flight heritage (LEO and MEO Satellites already fully operational) in which it has successfully demonstrated the flexibility of use, low management costs and the ability to adapt to changing operational conditions.The flexibility and modularity of PRIMA provides unique capability to satisfy different Payload design and mission requirements, thanks to the utilization of recurrent adaptable modules (Service Module-SVM, Propulsion Module-PPM, Payload Module-PLM) to obtain mission dependent configuration. PRIMA product line development is continuously progressing, and is based on state of art technology, modular architecture and an Integrated Avionics. The aim is to maintain and extent multi-mission capabilities to operate in different environments (LEO to GEO) with different payloads (SAR, Optical, GNSS, TLC, etc.). The design is compatible with a wide range of European and US equipment suppliers, thus maximising cooperation opportunity. Evolution activities are mainly focused on the following areas: Structure: to enable Spacecraft configurations for multiple launch; Thermal Control: to guarantee thermal limits for new missions, more demanding in terms of environment and payload; Electrical: to cope with higher power demand (e.g. electrical propulsion, wide range of payloads, etc.) considering orbital environment (e.g. lighting condition); Avionics : AOCS solutions optimized on mission (LEO observation driven by agility and pointing, agility not a driver for GEO). Use of sensors and actuators tailored for specific mission and related environments. Optimised Propulsion control. Data Handling, SW and FDIR mission customization 12. Analisis Pengaruh Keterlibatan Kerja dan Kepuasan Kerja terhadap Organizational Citizenship Behavior di PT Prima Graphia Digital Directory of Open Access Journals (Sweden) 2013-11-01 Full Text Available PT Prima Graphia Digital is a company engaged in the area of digital printing, locates at Kalibaru Timur Street IV No 5-7, Senen, Central Jakarta, Indonesia, 10460. The purpose of this research is to analyze the effect of job involvement and work satisfaction towards Organizational Citizenship Behavior in PT. Prima Graphia Digital. Research used associative method. Data used were primary and secondary data obtained through observation, interview and questionnaire distribution to 86 staffs of the company as respondents. After obtaining the data, then data were processed using Pearson correlation, simple and multiple regression. Results showed that job involvement has positive effect and is significant towards Organizational Citizenship Behavior. Similarly, work satisfaction does also have a positive effect and is significant towards Organizational Citizenship Behavior. Furthermore, job involvement and work satisfaction simultaneously have a significant effect towards Organizational Citizenship Behavior. 13. Characterizing Geological Facies using Seismic Waveform Classification in Sarawak Basin Science.gov (United States) 2017-10-01 Numerous effort have been made to build relationship between geology and geophysics using different techniques throughout the years. The integration of these two most important data in oil and gas industry can be used to reduce uncertainty in exploration and production especially for reservoir productivity enhancement and stratigraphic identification. This paper is focusing on seismic waveform classification to different classes using neural network and to link them according to the geological facies which are established using the knowledge on lithology and log motif of well data. Seismic inversion is used as the input for the neural network to act as the direct lithology indicator reducing dependency on well calibration. The interpretation of seismic facies classification map provides a better understanding towards the lithology distribution, depositional environment and help to identify significant reservoir rock 14. Petrology of blueschist facies metamorphic rocks of the Meliata Unit Directory of Open Access Journals (Sweden) 1997-06-01 Full Text Available Meliata blueschists originated from basalts, limestones, pelites, psammitic and amphibolite facies basement rocks. Compositionally, the metabasalts have a geochemical signature mostly indicative of a transitional arc-MORB origin, but some mafic rocks having affinity with within plate basalts also present. The mafic blueschists consist of blue amphibole, epidote and albite, rarely also garnet, Na-pyroxene and chloritoid. Apart from phengite and quartz the metapelites and metapsammites contain one or more of the minerals: chloritoid, paragonite, glaucophane, albite, chlorite, occasionally also Na-pyroxene and garnet. Amphibolite facies rocks contain relic garnet, plagioclase and hornblende, the latter two replaced by albite and blue amphibole, respectively. The zoning patterns of blue amphibole, garnet and chloritoid suggest their formation during prograde stage of metamorphism. P-T conditions of meta-morphism are estimated to be about 350-460 oC and 10-12 kbar. 15. JESTIANALYSIS OF CICERO'S ORATIO IN CATILINAM PRIMA FROM THE ASPECT OF PHONOSTYLISTICS AND LEXICOSTYLISTICS Directory of Open Access Journals (Sweden) Sanja Merzić 2013-05-01 Full Text Available This work represents an analysis of Cicero's speech Oratio in Catilinam Prima on two levels: phonostylistic and lexicostylistic with the goal to represent expressive voice function and figures of speech on phonostylistic level and to represent lexic with additional meaning, relations between words and lexico-syntactic figures on lexicostylistic level. Also, the purpose of the speech is to show what makes Cicero's speeches specific and successful. 16. Additional aspects of facies determination of the Souza Formation International Nuclear Information System (INIS) Vasconcelos, E.C.; Mabesoone, J.M. 1984-01-01 By means of geochemical analysis of total sample and trace elements, x-ray and DTA investigation of the clay fractions, and microfanes study, obtained by the facies determination of the Souza Formation, some additional aspects giving evidence of the sequence of events responsable by origin, deposition and formation of sediments of this middle unit of the Rio do Peixe group were established. (Author) [pt 17. Comparison of four approaches to a rock facies classification problem Science.gov (United States) Dubois, M.K.; Bohling, Geoffrey C.; Chakrabarti, S. 2007-01-01 In this study, seven classifiers based on four different approaches were tested in a rock facies classification problem: classical parametric methods using Bayes' rule, and non-parametric methods using fuzzy logic, k-nearest neighbor, and feed forward-back propagating artificial neural network. Determining the most effective classifier for geologic facies prediction in wells without cores in the Panoma gas field, in Southwest Kansas, was the objective. Study data include 3600 samples with known rock facies class (from core) with each sample having either four or five measured properties (wire-line log curves), and two derived geologic properties (geologic constraining variables). The sample set was divided into two subsets, one for training and one for testing the ability of the trained classifier to correctly assign classes. Artificial neural networks clearly outperformed all other classifiers and are effective tools for this particular classification problem. Classical parametric models were inadequate due to the nature of the predictor variables (high dimensional and not linearly correlated), and feature space of the classes (overlapping). The other non-parametric methods tested, k-nearest neighbor and fuzzy logic, would need considerable improvement to match the neural network effectiveness, but further work, possibly combining certain aspects of the three non-parametric methods, may be justified. ?? 2006 Elsevier Ltd. All rights reserved. 18. Multiparameter Elastic Full Waveform Inversion With Facies Constraints KAUST Repository Zhang, Zhendong 2017-08-17 Full waveform inversion (FWI) aims fully benefit from all the data characteristics to estimate the parameters describing the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion as a tool beyond acoustic imaging applications, for example in reservoir analysis, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Adding rock physics constraints does help to mitigate these issues, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a boundary condition for the whole area. Since certain rock formations inside the Earth admit consistent elastic properties and relative values of elastic and anisotropic parameters (facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel confidence map based approach to utilize the facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such a confidence map using Bayesian theory, in which the confidence map is updated at each iteration of the inversion using both the inverted models and a prior information. The numerical examples show that the proposed method can reduce the trade-offs and also can improve the resolution of the inverted elastic and anisotropic properties. 19. STOCHASTIC FRACTURED ROCK FACIES FOR GROUNDWATER FLOW MODELING Directory of Open Access Journals (Sweden) DANIELA BLESSENT 2013-01-01 Full Text Available Este artículo presenta los resultados de una simulación de flujo de agua subterránea en rocas fracturadas. Se emplea un enfoque estocástico (modelo estocástico equivalente en medio poroso fracturado para construir el modelo conceptual y para usar este último en la roca de baja permeabilidad encontrada en el sitio elegido como caso de estudio (Olkiluoto, Finlandia. La roca que se investiga se encuentra localizada alrededor de un grupo de pozos de sondeo y cubre un área de algunas hectáreas. Las mediciones de campo de pruebas de interferencia hidráulica se utilizan para calibrar el modelo de flujo de agua subterránea. Múltiples combinaciones de facies estocásticos se consideran para evaluar el impacto de la distribución y del número de facies en las cargas hidráulicas y en los caudales. Este estudio cuantifica la variabilidad de los resultados numéricos, lo cual es importante para el análisis de la incertidumbre en los sistemas hidrogeológicos. Por otra parte, este estudio muestra que el modelo conceptual de facies estocásticos es una alternativa adecuada a los modelos conceptuales de redes de fracturas discretas. 20. Proteomics Characterization of the Molecular Mechanisms of Mutant P53 Reactivation with PRIMA-1 in Breast Cancer Cells National Research Council Canada - National Science Library Daoud, Sayed S 2006-01-01 The main purpose of the study is to identify novel protein-protein interactions in various locations of cells to establish the molecular mechanisms of mutant p53 reactivation with PRIMA-1 in breast cancer cells... 1. Pengkajian Rakitan Teknologi Budidaya Kentang dan Strategi Pengembangannya : Studi Kasus di Wilayah Prima Tani Lahan Kering Dataran Tinggi Kabupaten Magetan OpenAIRE Santoso, Pudji; Yuniarti; Purnomo, Sudarmadi; Subandi 2009-01-01 Pengkajian Rakitan Teknologi Budidaya Kentang dan Strategi Pengembangannya : Studi Kasus di Wilayah Prima Tani Lahan Kering Dataran Tinggi Kabupaten Magetan. The assessment on improving the cultivation technology of potato as demonstration plot in farmer's land was done in Prima Tani area of Magetan regency in Genilangit village, during dry season on June – September 2007. Collecting data was done using farm record keeping method on the application of improving cultivation technology of potat... 2. Proportional reasoning DEFF Research Database (Denmark) Dole, Shelley; Hilton, Annette; Hilton, Geoff 2015-01-01 Proportional reasoning is widely acknowledged as a key to success in school mathematics, yet students’ continual difficulties with proportion-related tasks are well documented. This paper draws on a large research study that aimed to support 4th to 9th grade teachers to design and implement tasks... 3. Verbal Reasoning Science.gov (United States) 1992-08-31 Psicologia , 4(3), 183-198. 94 Guyote, M.J. and Sternberg, R.J. (1981). A transitive-chain theory of syllogistic reasoning. Cognitive Psychology, 13(4), 461...personal connections. Journal of Social Psychology, 20, 39-59. Newell, A. (1990). Unified Theories of Cognition. Cambridge, Massachusetts: Harvard 4. Diagrammatic Reasoning DEFF Research Database (Denmark) Tylén, Kristian; Fusaroli, Riccardo; Stege Bjørndahl, Johanne 2015-01-01 of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds of diagram manipulation: Sometimes diagrams... 5. 8 CFR 1245.8 - Adjustment of status as a special immigrant under section 101(a)(27)(K) of the Act. Science.gov (United States) 2010-01-01 ... a prima facie determination regarding eligibility for naturalization benefits if the applicant is to... residence fails to complete his or her total active duty service obligation for reasons other than an... 6. 8 CFR 245.8 - Adjustment of status as a special immigrant under section 101(a)(27)(K) of the Act. Science.gov (United States) 2010-01-01 ... a prima facie determination regarding eligibility for naturalization benefits if the applicant is to... residence fails to complete his or her total active duty service obligation for reasons other than an... 7. Zeolite facies and regional rank of bituminous coals Energy Technology Data Exchange (ETDEWEB) Kisch, H J 1966-01-01 The author has correlated diagnostic analcime-, heulandite-, and laumontite-bearing mineral assemblages from four areas in the Upper Carboniferous and the Permian of New South Wales with the rank of the associated coals, represented by the carbon content of vitrinite. The results show that lowest-grade regional metamorphism of the zeolite facies reflects at least in part the same physical conditions of metamorphism as the increase in degree of coalification (rank) in the bituminous coal range. Degree of coalification is probably independent of partial pressures of H/sub 2/O and CO/sub 2/: it is controlled mainly by maximum depth of burial, its duration, and the geothermal gradient. 8. Facies architecture and diagenesis of Belgian Late Frasnian carbonate mounds OpenAIRE Boulvain, Frédéric 2001-01-01 Late Frasnian Petit-Mont Member carbonate mounds occur in the southern pail of the Dinant Synclinorium and in the Philippeville Anticline (SW Belgium). These mounds are 30 to 80 m thick and 100 to 250 m in diameter. They are embedded in shale, nodular shale and argillaceous limestone. Based on facies mapping of 14 buildups and related off-mound sediments, these mounds typically started from below the photic and storm wave base zones and builtup into shallow water environments. Above an argill... 9. Trace fossil analysis of lacustrine facies and basins Science.gov (United States) Buatois, L.A.; Mangano, M.G. 1998-01-01 Two ichnofacies are typical of lacustrine depositional systems. The Scoyenia ichnofacies characterizes transitional terrestrial/nonmarine aquatic substrates, periodically inundated or desiccated, and therefore is commonly present in lake margin facies. The Mermia ichnofacies is associated with well oxygenated, permanent subaqueous, fine-grained substrates of hydrologically open, perennial lakes. Bathymetric zonations within the Mermia ichnofacies are complicated by the wide variability of lacustrine systems. Detected proximal-distal trends are useful within particular lake basins, but commonly difficult to extrapolate to other lakes. Other potential ichnofacies include the typically marine Skolithos ichnofacies for high-energy zones of lakes and substrate-controlled, still unnamed ichnofacies, associated to lake margin deposits. Trace fossils are useful for sedimentologic analysis of event beds. Lacustrine turbidites are characterized by low-diversity suites, reflecting colonization by opportunistic organisms after the turbidite event. Underflow current beds record animal activity contemporaneous with nearly continuous sedimentation. Ichnologic studies may also help to distinguish between marine and lacustrine turbidites. Deep-marine turbidites host the Nereites ichnofacies that consists of high diversity of ornate grazing traces and graphoglyptids, recording highly specialized feeding strategies developed to solve the problem of the scarcity of food in the deep sea. Deep lacustrine environments contain the Mermia ichnofacies, which is dominated by unspecialized grazing and feeding traces probably related to the abundance and accessibility of food in lacustrine systems. The lower diversity of lacustrine ichnofaunas in comparison with deep-sea assemblages more likely reflects lower species diversity as a consequence of less stable conditions. Increase of depth and extent of bioturbation through geologic time produced a clear signature in the ichnofabric record of 10. Plant integration of MITICA and SPIDER experiments with auxiliary plants and buildings on PRIMA site Energy Technology Data Exchange (ETDEWEB) Fellin, Francesco, E-mail: [email protected]; Boldrin, Marco; Zaccaria, Pierluigi; Agostinetti, Piero; Battistella, Manuela; Bigi, Marco; Palma, Samuele Dal Bello Mauro Dalla; Fiorentin, Aldo; Luchetta, Adriano; Maistrello, Alberto; Marcuzzi, Diego; Ocello, Edoardo; Pasqualotto, Roberto; Pavei, Mauro; Pomaro, Nicola; Rizzolo, Andrea; Toigo, Vanni; Valente, Matteo; Zanotto, Loris; Calore, Luca; and others 2015-10-15 Highlights: • Focus on plant integration work supporting the realization of SPIDER and MITICA fusion experiments hosted in PRIMA buildings complex in Padova, Italy. • Huge effort of coordination and integration among many stakeholders, taking into account several constrains coming from experiments requirements (on-going) and precise time schedule and budget on buildings construction. • The paper also deals of interfaces management, coordination and integration of many competences, problems solving to find best solution also considering other aspects like safety and maintenance. - Abstract: This paper presents a description of the PRIMA (Padova Research on ITER Megavolt Accelerator) Plant Integration work, aimed at the construction of PRIMA Buildings, which will host two nuclear fusion test facilities named SPIDER and MITICA, finalized to test and optimize the neutral beam injectors for ITER experiment. These activities are very complex: inputs coming from the experiments design are changing time to time, while the buildings construction shall fulfill precise time schedule and budget. Moreover the decision process is often very long due to the high number of stakeholders (RFX, IO, third parties, suppliers, domestic agencies from different countries). The huge effort includes: forecasting what will be necessary for the integration of many experimental plants; collecting requirements and translating into inputs; interfaces management; coordination meetings with hundreds of people with various and different competences in construction and operation of fusion facilities, thermomechanics, electrical and control, buildings design and construction (civil plants plus architectural and structural aspects), safety, maintenance and management. The paper describes these activities and also the tools created to check and to validate the building design, to manage the interfaces and the organization put in place to achieve the required targets. 11. Plant integration of MITICA and SPIDER experiments with auxiliary plants and buildings on PRIMA site International Nuclear Information System (INIS) Fellin, Francesco; Boldrin, Marco; Zaccaria, Pierluigi; Agostinetti, Piero; Battistella, Manuela; Bigi, Marco; Palma, Samuele Dal Bello Mauro Dalla; Fiorentin, Aldo; Luchetta, Adriano; Maistrello, Alberto; Marcuzzi, Diego; Ocello, Edoardo; Pasqualotto, Roberto; Pavei, Mauro; Pomaro, Nicola; Rizzolo, Andrea; Toigo, Vanni; Valente, Matteo; Zanotto, Loris; Calore, Luca 2015-01-01 Highlights: • Focus on plant integration work supporting the realization of SPIDER and MITICA fusion experiments hosted in PRIMA buildings complex in Padova, Italy. • Huge effort of coordination and integration among many stakeholders, taking into account several constrains coming from experiments requirements (on-going) and precise time schedule and budget on buildings construction. • The paper also deals of interfaces management, coordination and integration of many competences, problems solving to find best solution also considering other aspects like safety and maintenance. - Abstract: This paper presents a description of the PRIMA (Padova Research on ITER Megavolt Accelerator) Plant Integration work, aimed at the construction of PRIMA Buildings, which will host two nuclear fusion test facilities named SPIDER and MITICA, finalized to test and optimize the neutral beam injectors for ITER experiment. These activities are very complex: inputs coming from the experiments design are changing time to time, while the buildings construction shall fulfill precise time schedule and budget. Moreover the decision process is often very long due to the high number of stakeholders (RFX, IO, third parties, suppliers, domestic agencies from different countries). The huge effort includes: forecasting what will be necessary for the integration of many experimental plants; collecting requirements and translating into inputs; interfaces management; coordination meetings with hundreds of people with various and different competences in construction and operation of fusion facilities, thermomechanics, electrical and control, buildings design and construction (civil plants plus architectural and structural aspects), safety, maintenance and management. The paper describes these activities and also the tools created to check and to validate the building design, to manage the interfaces and the organization put in place to achieve the required targets. 12. Analysis of the effect on growth kinetics of gamma prima phase in Inconel 713C alloys International Nuclear Information System (INIS) Thorp, S.I.; Versaci, R.A.; Ges, A.; Palacio, H.A. 1993-01-01 This work shows the analysis of the effect on growth kinetics of gamma prima phase in Inconel 713C alloy of two thermic treatments. In this study, SEM are used and the results are analyzed by means of the theory developed by Lifshitz, Slyozov and Wagner (LSW theory). The findings have revealed that with such theory it is not possible to determine if the process of growth is controlled either through diffusion or through diffusion in the interface as to the time employed in the experiment (2600 hours); the time required is approximately 10000 hours. (Author) 13. Producción de biodiesel a partir de materias primas no convencionales OpenAIRE Aguilar Sánchez, Rocío 2011-01-01 Proyecto Fin de Carrera leído en la Universidad Rey Juan Carlos en el curso académico 2010/2011. Directores del Proyecto: Gabriel Morales Sánchez y Rebeca Sánchez Vázquez Actualmente, para la producción industrial de biodiesel se emplean aceites vegetales de alta calidad como materia prima, y se utilizan catalizadores básicos homogéneos, KOH o NaOH. Los productos de reacción son FAME y glicerina. Sin embargo, debido a los problemas derivados del uso de aceites vegetales comestible... 14. Inductive reasoning. Science.gov (United States) Hayes, Brett K; Heit, Evan; Swendsen, Haruka 2010-03-01 Inductive reasoning entails using existing knowledge or observations to make predictions about novel cases. We review recent findings in research on category-based induction as well as theoretical models of these results, including similarity-based models, connectionist networks, an account based on relevance theory, Bayesian models, and other mathematical models. A number of touchstone empirical phenomena that involve taxonomic similarity are described. We also examine phenomena involving more complex background knowledge about premises and conclusions of inductive arguments and the properties referenced. Earlier models are shown to give a good account of similarity-based phenomena but not knowledge-based phenomena. Recent models that aim to account for both similarity-based and knowledge-based phenomena are reviewed and evaluated. Among the most important new directions in induction research are a focus on induction with uncertain premise categories, the modeling of the relationship between inductive and deductive reasoning, and examination of the neural substrates of induction. A common theme in both the well-established and emerging lines of induction research is the need to develop well-articulated and empirically testable formal models of induction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd. 15. Analisis Faktor-Faktor Penempatan Karyawan Terhadap Kepuasan Kerja Karyawan Di PT Yuniko Asia Prima Di Kota Bandung Directory of Open Access Journals (Sweden) Darwis Agustriyana 2015-10-01 Full Text Available The research objective is to be achieved (1 To know how the placement of employees and job satisfaction in a textile factory Yuniko Asia Prima (2 To determine the effect of the placement of employees on the level of job satisfaction in a textile factory Yuniko Asia Prima. The study populations were employees at a textile factory Yuniko Asia Prima and the sample is taken as many as 83 employees by the simple technique of sampling with multiple regression analysis. The results showed that the placement of employees at PT Asia Prima Yuniko already well underway. Employees of the company were placed in accordance with academic achievement as well as its experience, and in accordance with the physical and mental health. Also according to the employees, the company delivers wages in accordance with the number of dependents received, and promotion according to the marital status of an employee owned. Employee satisfaction gets a positive response from employees. It can be seen that the needs of the wages, the work itself, promotion, co-workers and supervisors and supervisor monitoring can fulfill the wishes of employees. Influence simultaneously, variable placement of employees has a significant influence with employee job satisfaction, and the results of the analysis of the coefficient of determination, the variable placement of employees by 69% has an influence on the formation of employee satisfaction. However partially, variable marital status and age did not have influence on job satisfaction of employees at PT Yuniko Asia Prima. 16. Morphological redescription and DNA barcoding of Linevitshia prima Makarchenko, 1987 (Diptera: Chironomidae: Diamesinae) from Amur River basin (Russian Far East), with notes on systematics of the genus. Science.gov (United States) Makarchenko, Eugenyi A; Semenchenko, Alexander A 2014-10-10 Additions and corrections to the diagnosis of the genus Linevitshia for male adult, pupa and larva are given, and systematic position of the genus is discussed. Illustrated redescription of adult male and first description of 4th instar larva of L. prima Makarchenko from Amur River basin are provided. Comparison of data based on a new material with those of L. yezoensis Endo showed that the latter name is a junior synonym of L. prima. The species-specificity of L. prima COI sequences is analyzed and the sequences are presented as diagnostic characters-molecular markers of L. prima. 17. Heuristic reasoning CERN Document Server 2015-01-01 How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the ‘method’ of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences. 18. Progress in the realization of the PRIMA neutral beam test facility Science.gov (United States) Toigo, V.; Boilson, D.; Bonicelli, T.; Piovan, R.; Hanada, M.; Chakraborty, A.; Agarici, G.; Antoni, V.; Baruah, U.; Bigi, M.; Chitarin, G.; Dal Bello, S.; Decamps, H.; Graceffa, J.; Kashiwagi, M.; Hemsworth, R.; Luchetta, A.; Marcuzzi, D.; Masiello, A.; Paolucci, F.; Pasqualotto, R.; Patel, H.; Pomaro, N.; Rotti, C.; Serianni, G.; Simon, M.; Singh, M.; Singh, N. P.; Svensson, L.; Tobari, H.; Watanabe, K.; Zaccaria, P.; Agostinetti, P.; Agostini, M.; Andreani, R.; Aprile, D.; Bandyopadhyay, M.; Barbisan, M.; Battistella, M.; Bettini, P.; Blatchford, P.; Boldrin, M.; Bonomo, F.; Bragulat, E.; Brombin, M.; Cavenago, M.; Chuilon, B.; Coniglio, A.; Croci, G.; Dalla Palma, M.; D'Arienzo, M.; Dave, R.; De Esch, H. P. L.; De Lorenzi, A.; De Muri, M.; Delogu, R.; Dhola, H.; Fantz, U.; Fellin, F.; Fellin, L.; Ferro, A.; Fiorentin, A.; Fonnesu, N.; Franzen, P.; Fröschle, M.; Gaio, E.; Gambetta, G.; Gomez, G.; Gnesotto, F.; Gorini, G.; Grando, L.; Gupta, V.; Gutierrez, D.; Hanke, S.; Hardie, C.; Heinemann, B.; Kojima, A.; Kraus, W.; Maeshima, T.; Maistrello, A.; Manduchi, G.; Marconato, N.; Mico, G.; Moreno, J. F.; Moresco, M.; Muraro, A.; Muvvala, V.; Nocentini, R.; Ocello, E.; Ochoa, S.; Parmar, D.; Patel, A.; Pavei, M.; Peruzzo, S.; Pilan, N.; Pilard, V.; Recchia, M.; Riedl, R.; Rizzolo, A.; Roopesh, G.; Rostagni, G.; Sandri, S.; Sartori, E.; Sonato, P.; Sottocornola, A.; Spagnolo, S.; Spolaore, M.; Taliercio, C.; Tardocchi, M.; Thakkar, A.; Umeda, N.; Valente, M.; Veltri, P.; Yadav, A.; Yamanaka, H.; Zamengo, A.; Zaniol, B.; Zanotto, L.; Zaupa, M. 2015-08-01 The ITER project requires additional heating by two neutral beam injectors, each accelerating to 1 MV a 40 A beam of negative deuterium ions, to deliver to the plasma a power of about 17 MW for one hour. As these requirements have never been experimentally met, it was recognized as necessary to setup a test facility, PRIMA (Padova Research on ITER Megavolt Accelerator), in Italy, including a full-size negative ion source, SPIDER, and a prototype of the whole ITER injector, MITICA, aiming to develop the heating injectors to be installed in ITER. This realization is made with the main contribution of the European Union, through the Joint Undertaking for ITER (F4E), the ITER Organization and Consorzio RFX which hosts the Test Facility. The Japanese and the Indian ITER Domestic Agencies (JADA and INDA) participate in the PRIMA enterprise; European laboratories, such as IPP-Garching, KIT-Karlsruhe, CCFE-Culham, CEA-Cadarache and others are also cooperating. Presently, the assembly of SPIDER is on-going and the MITICA design is being completed. The paper gives a general overview of the test facility and of the status of development of the MITICA and SPIDER main components at this important stage of the overall development; then it focuses on the latest and most critical issues, regarding both physics and technology, describing the identified solutions. 19. The PRIMA Test Facility: SPIDER and MITICA test-beds for ITER neutral beam injectors Science.gov (United States) Toigo, V.; Piovan, R.; Dal Bello, S.; Gaio, E.; Luchetta, A.; Pasqualotto, R.; Zaccaria, P.; Bigi, M.; Chitarin, G.; Marcuzzi, D.; Pomaro, N.; Serianni, G.; Agostinetti, P.; Agostini, M.; Antoni, V.; Aprile, D.; Baltador, C.; Barbisan, M.; Battistella, M.; Boldrin, M.; Brombin, M.; Dalla Palma, M.; De Lorenzi, A.; Delogu, R.; De Muri, M.; Fellin, F.; Ferro, A.; Fiorentin, A.; Gambetta, G.; Gnesotto, F.; Grando, L.; Jain, P.; Maistrello, A.; Manduchi, G.; Marconato, N.; Moresco, M.; Ocello, E.; Pavei, M.; Peruzzo, S.; Pilan, N.; Pimazzoni, A.; Recchia, M.; Rizzolo, A.; Rostagni, G.; Sartori, E.; Siragusa, M.; Sonato, P.; Sottocornola, A.; Spada, E.; Spagnolo, S.; Spolaore, M.; Taliercio, C.; Valente, M.; Veltri, P.; Zamengo, A.; Zaniol, B.; Zanotto, L.; Zaupa, M.; Boilson, D.; Graceffa, J.; Svensson, L.; Schunke, B.; Decamps, H.; Urbani, M.; Kushwah, M.; Chareyre, J.; Singh, M.; Bonicelli, T.; Agarici, G.; Garbuglia, A.; Masiello, A.; Paolucci, F.; Simon, M.; Bailly-Maitre, L.; Bragulat, E.; Gomez, G.; Gutierrez, D.; Mico, G.; Moreno, J.-F.; Pilard, V.; Kashiwagi, M.; Hanada, M.; Tobari, H.; Watanabe, K.; Maejima, T.; Kojima, A.; Umeda, N.; Yamanaka, H.; Chakraborty, A.; Baruah, U.; Rotti, C.; Patel, H.; Nagaraju, M. V.; Singh, N. P.; Patel, A.; Dhola, H.; Raval, B.; Fantz, U.; Heinemann, B.; Kraus, W.; Hanke, S.; Hauer, V.; Ochoa, S.; Blatchford, P.; Chuilon, B.; Xue, Y.; De Esch, H. P. L.; Hemsworth, R.; Croci, G.; Gorini, G.; Rebai, M.; Muraro, A.; Tardocchi, M.; Cavenago, M.; D'Arienzo, M.; Sandri, S.; Tonti, A. 2017-08-01 The ITER Neutral Beam Test Facility (NBTF), called PRIMA (Padova Research on ITER Megavolt Accelerator), is hosted in Padova, Italy and includes two experiments: MITICA, the full-scale prototype of the ITER heating neutral beam injector, and SPIDER, the full-size radio frequency negative-ions source. The NBTF realization and the exploitation of SPIDER and MITICA have been recognized as necessary to make the future operation of the ITER heating neutral beam injectors efficient and reliable, fundamental to the achievement of thermonuclear-relevant plasma parameters in ITER. This paper reports on design and R&D carried out to construct PRIMA, SPIDER and MITICA, and highlights the huge progress made in just a few years, from the signature of the agreement for the NBTF realization in 2011, up to now—when the buildings and relevant infrastructures have been completed, SPIDER is entering the integrated commissioning phase and the procurements of several MITICA components are at a well advanced stage. 20. Penerapan Best Practice IT Service Management dalam Perbaikan IT Service Desk: Studi Kasus PT. Matahari Putra Prima Directory of Open Access Journals (Sweden) Hendra Hendra 2011-06-01 Full Text Available Information Technology (IT grows very rapidly and affects every aspect of business life to support competition with other companies that have the same field. PT. Matahari Putra Prima has implemented a computerized system as one of its business strategy in achieving the company's business objectives. With the implementation of IT in the company, the role of Service Desk is indispensable in providing services to users. This study aims to identify and analyze the implementation of IT Service Desk of PT. Matahari Putra Prima to the users. This research is expected to increase and improve the quality of IT Service Desk PT. Matahari Putra Prima based on the IT Service Management (ITSM. 1. Detailed facies analyses within the Bluell and Sherwood Members, Mission Canyon Formation, North Dakota, USA - Facies stacking patterns, sequence stratigraphy and porosity relationship, consequences for reservoir distribution OpenAIRE Sjöstedt, Tony 2017-01-01 Detailed core analysis from seven wells with cores cut within the overall carbonate succession that makes up the Bluell and Sherwood Members of the Mission Canyon Formation located in Renville County, North Dakota, resulted in the identification of eleven depositional facies. These facies that reflect a range in depositional conditions from inner to back ramp, that is shallow fair-weather to uppermost intertidal and supratidal conditions. Systematic core analysis using a highly detailed digit... 2. Acoustic Impedance Inversion To Identify Oligo-Miocene Carbonate Facies As Reservoir At Kangean Offshore Area Science.gov (United States) Zuli Purnama, Arif; Ariyani Machmud, Pritta; Eka Nurcahya, Budi; Yusro, Miftahul; Gunawan, Agung; Rahmadi, Dicky 2018-03-01 Model based inversion was applied to inversion process of 2D seismic data in Kangean Offshore Area. Integration acoustic impedance from wells and seismic data was expected showing physical property, facies separation and reservoir quality of carbonate rock, particularly in Kangean Offshore Area. Quantitative and qualitative analysis has been conducted on the inversion results to characterize the carbonate reservoir part of Kujung and correlate it to depositional facies type. Main target exploration in Kangean Offshore Area is Kujung Formation (Oligo-Miocene Carbonate). The type of reservoir in this area generate from reef growing on the platform. Carbonate rock is a reservoir which has various type and scale of porosity. Facies determination is required to to predict reservoir quality, because each facies has its own porosity value. Acoustic impedance is used to identify and characterize Kujung carbonate facies, also could be used to predict the distribution of porosity. Low acoustic impedance correlated with packstone facies that has acoustic impedance value below 7400 gr/ccm/s. In other situation, high acoustic impedance characterized by wackestone facies above 7400 gr/ccm/s. The interpretation result indicated that Kujung carbonate rock dominated by packstone facies in the upper part of build-up and it has ideal porosity for hydrocarbon reservoir. 3. Pilot points method for conditioning multiple-point statistical facies simulation on flow data Science.gov (United States) Ma, Wei; Jafarpour, Behnam 2018-05-01 We propose a new pilot points method for conditioning discrete multiple-point statistical (MPS) facies simulation on dynamic flow data. While conditioning MPS simulation on static hard data is straightforward, their calibration against nonlinear flow data is nontrivial. The proposed method generates conditional models from a conceptual model of geologic connectivity, known as a training image (TI), by strategically placing and estimating pilot points. To place pilot points, a score map is generated based on three sources of information: (i) the uncertainty in facies distribution, (ii) the model response sensitivity information, and (iii) the observed flow data. Once the pilot points are placed, the facies values at these points are inferred from production data and then are used, along with available hard data at well locations, to simulate a new set of conditional facies realizations. While facies estimation at the pilot points can be performed using different inversion algorithms, in this study the ensemble smoother (ES) is adopted to update permeability maps from production data, which are then used to statistically infer facies types at the pilot point locations. The developed method combines the information in the flow data and the TI by using the former to infer facies values at selected locations away from the wells and the latter to ensure consistent facies structure and connectivity where away from measurement locations. Several numerical experiments are used to evaluate the performance of the developed method and to discuss its important properties. 4. Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics with Level Set Transformation. Energy Technology Data Exchange (ETDEWEB) Hammond, Glenn Edward; Song, Xuehang; Ye, Ming; Dai, Zhenxue; Zachara, John; Chen, Xingyuan 2017-03-01 A new approach is developed to delineate the spatial distribution of discrete facies (geological units that have unique distributions of hydraulic, physical, and/or chemical properties) conditioned not only on direct data (measurements directly related to facies properties, e.g., grain size distribution obtained from borehole samples) but also on indirect data (observations indirectly related to facies distribution, e.g., hydraulic head and tracer concentration). Our method integrates for the first time ensemble data assimilation with traditional transition probability-based geostatistics. The concept of level set is introduced to build shape parameterization that allows transformation between discrete facies indicators and continuous random variables. The spatial structure of different facies is simulated by indicator models using conditioning points selected adaptively during the iterative process of data assimilation. To evaluate the new method, a two-dimensional semi-synthetic example is designed to estimate the spatial distribution and permeability of two distinct facies from transient head data induced by pumping tests. The example demonstrates that our new method adequately captures the spatial pattern of facies distribution by imposing spatial continuity through conditioning points. The new method also reproduces the overall response in hydraulic head field with better accuracy compared to data assimilation with no constraints on spatial continuity on facies. 5. Sedimentary environment and facies of St Lucia Estuary Mouth, Zululand, South Africa Science.gov (United States) Wright, C. I.; Mason, T. R. The St. Lucia Estuary is situated on the subtropical, predominantly microtidal Zululand coast. Modern sedimentary environments within the estuary fall into three categories: (1) barrier environments; (2) abandoned channel environments; and (3) estuarine/lagoonal environments. The barrier-associated environment includes tidal inlet channel, inlet beach face, flood-tidal delta, ebb-tidal delta, spit, backspit and aeolian dune facies. The abandoned channel environment comprises washover fan, tidal creek tidal creek delta and back-barrier lagoon facies. The estuarine/lagoonal environment includes subtidal estuarine channel, side-attached bar, channel margin, mangrove fringe and channel island facies. Each sedimentary facies is characterised by sedimentary and biogenic structures, grain-size and sedimentary processes. Vertical facies sequences produced by inlet channel migration and lagoonal infilling are sufficiently distinct to be recognized in the geological record and are typical of a prograding shoreline. 6. Study of fuel element characteristic of SM and SMP (SM-PRIMA) fuel assemblies International Nuclear Information System (INIS) Klinov, A.V.; Kuprienko, V.A.; Lebedev, V.A.; Makhin, V.M.; Tuchnin, L.M.; Tsykanov, V.A. 1999-01-01 The paper discusses the techniques and results of reactor tests and post-reactor investigations of the SM reactor fuel elements and fuel elements developed in the process of designing the specialized PRIMA test reactor with the SM reactor fuel elements used as a prototype and which are referred to as the SMP fuel elements. The behavior of fuel elements under normal operating conditions and under deviation from normal operating conditions was studied to verify the calculation techniques, to check the calculation results during preparation of the SM reactor safety substantiation report and to estimate the possibility of using such fuel elements in other projects. During tests of fuel rods under deviation from normal operating conditions their advantages were shown over fuel elements, the components of which were produced using the Al-based alloys. (author) 7. Perancangan Sistem Informasi Penjualan dan Persediaan pada PT Selatan Jaya Prima Perkasa Directory of Open Access Journals (Sweden) Stephanie Surja 2013-12-01 Full Text Available This study aims to analyze the organization needs in sales and stock company process that related with the current business process at PT Selatan Jaya Prima Perkasa. The result will be used for developing an integrated system that can be the solution for the company needs in running their sales and to control theirinventory stock status as the main business of the company. The analyzed result in the company needs will be documented using unified modeling language. This information system is expected to simplify ease the company’s activitis in sales process and inventory stock control. This system will also minimize the data lost and human error usually caused by manual process of transactional data storage. 8. La memoria alla barocca ne L’isola del giorno prima di Umberto Eco Directory of Open Access Journals (Sweden) Agnieszka Piwowarska 2012-12-01 Full Text Available In his third novel The Island of the Day Before (L’isola del giorno prima Umberto Eco narrates a story of an unusual castaway named Roberto who – instead of being on a desert island – finishes up on an abandoned (but only at first sight ship. The article aims to analyze how the book’s main character, during his loneliness, reminisces about events from his past. And because the novel is set in the Baroque, Roberto´s memories respect the spirit of that time : numerous flashbacks are evoked by unexpected metaphors that link very distant things. The ship, which is for a young man a cumbersome prison, becomes a real Theatre of Memory, according to Giulio Camillo’s idea. 9. Uso de rejeitos de granitos como matérias-primas cerâmicas Directory of Open Access Journals (Sweden) Menezes R. R. 2002-01-01 Full Text Available A indústria do beneficiamento de granito gera uma enorme quantidade de rejeitos, que poluem e degradam o meio ambiente. Assim este trabalho tem por objetivo caracterizar e avaliar as possibilidades de utilização dos rejeitos da serragem de granitos gerados pelas indústrias de beneficiamento da Região Nordeste, como matéria-prima cerâmica alternativa na produção de blocos e revestimentos cerâmicos. Foram coletadas amostras de resíduos da serragem de granito em empresas da Paraíba, Ceará e Pernambuco, em seguida foi realizada sua caracterização através da determinação da distribuição granulométrica, massa específica real e área específica (BET e de análise química, ATD, ATG, DRX, MEV. Após caracterização foram conduzidos ensaios tecnológicos com composições cerâmicas a fim de avaliar a possibilidade de adição dos resíduos em massas cerâmicas para confecção de blocos e revestimentos cerâmicos. Com base nos resultados verificou-se que os resíduos apresentam características físicas e mineralógicas semelhantes as das matérias-primas cerâmicas convencionais e que corpos cerâmicos formulados com resíduos apresentam características dentro das especificações da normalização brasileira tanto para blocos como para revestimentos cerâmicos. Science.gov (United States) Shapiro, R. S.; Jameson, S.; Rutter, A.; McCarthy, K.; Planavsky, N. J.; Severson, M. 2013-12-01 The discovery of richly microfossiliferous cherty stromatolites near Schreiber and Kakabeka Falls, Ontario, in the 1.9 Ga Gunflint Iron Formation, firmly established the field of pre-Cambrian paleontology. In the half-century since this discovery, paradigm shifts in the ecology of the microfossils as well as the utility of stromatolites as biological markers has caused a re-evaluation of our understanding of the pre-Cambrian fossil record. This research summarizes facies evaluation of the two stromatolite marker beds in the Gunflint-correlative Biwabik Iron Formation of Minnesota. The centimeter-scale microstratigraphy of cores drilled through the central and eastern Mesabi Iron Range was coupled with field descriptions of outcrops and mines in both the Biwabik and Gunflint iron formations. Eight lithologic facies associated with the stromatolites are identified: A) Pebble conglomerate clasts ranging in size of 0.5-3 cm, syneresis cracks, and septarian nodules with medium to coarse grain matrix; B) siltstone with subparallel sub-mm to 5 cm magnetitic and non-magnetic bands; C) stromatolitic boundstone comprising stratiform, pseudocolumnar, domal, undulatory, flat-laminated, dendritic, columnar, and mico-digitate forms and oncoids 0.5 to 2 cm diameter; D) grainstone with medium to coarse siliceous and carbonate ooids and peloids; E) massive green crystalline beds with bands of magnetite, quartz, calcite, disseminated pyrite and localized ankerite; F) autobreccicated fabric of 0.3 to 10 mm clasts; G) medium to coarse sandstone; H) quartzite. Correlation between 11 cores near Hoyt Lakes and 9 cores through the basal stromatolite layer at the MinnTac Mine near Virginia revealed that stromatolites formed both on conglomerate and medium quartz sandstone. Multiple forms of stromatolite may occur in a vertical succession (flat-laminated to undulatory to psuedocolumnar to columnar) or a core may be dominated by one type, typically columnar-stratiform. Where stromatolites do 11. Joint inversion of geophysical data using petrophysical clustering and facies deformation wth the level set technique Science.gov (United States) Revil, A. 2015-12-01 Geological expertise and petrophysical relationships can be brought together to provide prior information while inverting multiple geophysical datasets. The merging of such information can result in more realistic solution in the distribution of the model parameters, reducing ipse facto the non-uniqueness of the inverse problem. We consider two level of heterogeneities: facies, described by facies boundaries and heteroegenities inside each facies determined by a correlogram. In this presentation, we pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion of the geophysical data is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case for which we perform a joint inversion of gravity and galvanometric resistivity data with the stations located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to perform such deformation preserving prior topological properties of the facies throughout the inversion. With the help of prior facies petrophysical relationships and topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The method is applied to a second synthetic case showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries using the 2D joint inversion of 12. Middle Eocene seagrass facies from Apennine carbonate platforms (Italy) Science.gov (United States) Tomassetti, Laura; Benedetti, Andrea; Brandano, Marco 2016-04-01 Two stratigraphic sections located in the Latium-Abruzzi (Monte Porchio, Central Apennines, Central Italy) and in the Apulian carbonate platform (S. Cesarea-Torre Tiggiano, Salento, Southern Italy) were measured and sampled to document the sedimentological characteristic and the faunistic assemblages of Middle Eocene seagrass deposits. The faunistic assemblages are dominated by porcellaneous foraminifera Orbitolites, Alveolina, Idalina, Spiroloculina, Quinqueloculina, Triloculina and abundant hooked-shaped gypsinids, associated with hooked red algae and green algae Halimeda. Fabiania, rotaliids and textulariids as well as nummulitids are subordinated. The samples were assigned to Lutetian (SBZ13-16) according to the occurrence of Nummulites cf. lehneri, Alveolina ex. gr. elliptica, Idalina berthelini, Orbitolites complanatus, Slovenites decastroi and Medocia blayensis. At Santa Cesarea reticulate nummulites occur in association with Alveolina spp. and Halkyardia minima marking the lower Bartonian (SBZ17). Three main facies associations have been recognised: I) larger porcellaneous foraminiferal grainstones with orbitolitids and alveolinids deposited into high-energy shallow-water settings influenced by wave processes that reworked the sediments associated with a seagrass; II) grainstone to packstone with small porcellaneous foraminifera and abundant permanently-attached gypsinids deposited in a more protected (e.g., small embayment) in situ vegetated environment; III) bioclastic packstone with parautochthonous material reworked from the seagrass by rip currents and accumulated into rip channels in a slightly deeper environment. The biotic assemblages suggest that the depositional environment is consistent with tropical to subtropical vegetated environments within oligotrophic conditions. 13. Dating Metasomatism: Monazite and Zircon Growth during Amphibolite Facies Albitization Directory of Open Access Journals (Sweden) Cailey B. Condit 2018-04-01 Full Text Available We present coupled textural observations and trace element and geochronological data from metasomatic monazite and zircon, to constrain the timing of high-grade Na-metasomatism (albitization of an Archean orthogneiss in southwest Montana, USA. Field, mineral textures, and geochemical evidence indicate albitization occurred as a rind along the margin of a ~3.2 Ga granodioritic orthogneiss (Pl + Hbl + Kfs + Qz + Bt + Zrn exposed in the Northern Madison range. The metasomatic product is a weakly deformed albitite (Ab + Bt + OAm + Zrn + Mnz + Ap + Rt. Orthoamphibole and biotite grew synkinematically with the regional foliation fabric, which developed during metamorphism that locally peaked at upper amphibolite-facies during the 1800–1710 Ma Big Sky orogeny. Metasomatism resulted in an increase in Na, a decrease in Ca, K, Ba, Fe, and Sr, a complete transformation of plagioclase and K-feldspar into albite, and loss of quartz. In situ geochronology on zoned monazite and zircon indicate growth by dissolution–precipitation in both phases at ~1750–1735 Ma. Trace element geochemistry of rim domains in these phases are best explained by dissolution–reprecipitation in equilibrium with Na-rich fluid. Together, these data temporally and mechanistically link metasomatism with high-grade tectonism and prograde metamorphism during the Big Sky orogeny. 14. Combined tide and storm influence on facies sedimentation of miocene Miri Formation, Sarawak International Nuclear Information System (INIS) Yuniarta Ulfa; Nasiman Sapari; Zuhar Zahir Tuan Harith 2011-01-01 This study was conducted on the sedimentary rocks belonging to the Miri Formation (Middle - Late Miocene). The primary objective of the present study is to provide additional interpretation on the stratigraphy of the Miri Formation in the Miri Field based on the new information gathered from new outcrops in the area. Five outcrops were examined in detail on sedimentology and stratigraphy. Based on lithology, sedimentary structures, bedding geometry and traces fossil, the sediments of the Miri Formation were grouped into fourteen lithofacies. Influence of tide and storm during the depositional processes of the formation were indicated by the group of two main facies associations which are: (i) tide-dominated estuary; and (ii) wave-and-storm dominated facies associations. The tide-dominated estuary system of the Miri Formation are includes variety of sub environments: estuary mouth or tidal channel and sand bars (characterized by trough cross-stratified sandstone with mud drapes facies), estuary channel or upper flow regime of sand flat (characterized by parallel stratified sandstone with mud-laminas facies), mixed-tidal flat (characterized by wavy and flaser bedded sandstone facies), and mud-tidal flat (characterized by rhythmic stratified sandstone-mudstone and lenticular bedding facies). The wave-and-storm dominated varied from lower to middle shore face (characterized by hummocky cross-stratified sandstone and rhythmic parallel stratified sandstone and laminated siltstone facies), upper shore face (characterized by swaley cross-stratified sandstone), lower shore face inter bedded to bioturbated sandstone and siltstone facies), and offshore transitional (characterized by bioturbated sandstone and mudstone inter bedding with parallel to hummocky cross-stratified sandstone facies). (author) 15. Modeling Oligo-Miocence channel sands (Dezful Embayment, SW Iran): an integrated facies classification workflow International Nuclear Information System (INIS) 2014-01-01 This study has been conducted on Mansuri onshore oilfield located in Dezful Embayment, south-west Iran. One of the hydrocarbon-bearing formations is a Oligo-Miocene Asmari formation—the most prolific Iranian reservoir rock. Like many other oilfields in the area, the trap in this field is deemed structural (anticline), formed during the collision of the Arabian plate with the Iranian plate and the folding of Neotethys deposits with a NW–SE trend. This study integrates three different quantitative studies from geology, geophysics and petrophysics disciplines to quantitate ‘the qualitative study of seismic facies analysis based on trace shapes and 3D multi-attribute clustering’. First, stratigraphic sequences and seismic detectable facies were derived at one well location using the available high resolution core facies analysis and depositional environment assessment reports. Paleo and petrophysical logs from other wells were subsequently used for the extrapolation of stratigraphic sequences interpreted at the first well. Utilizing lithology discrimination obtained by wire-line log interpretation, facies were extrapolated to all wells in the area. Seismic 3D attribute analysis and seismic facies classification established a 3D facies volume accordingly, which was finally calibrated to geological facies at well locations. The ultimate extracted facies-guided geobody shows that good reservoir-quality channel sands have accumulated with NW/SE elongation at the ridge of the structure. As a result, this type of geometry has created a stratigraphic/structural hydrocarbon trap in this oilfield. Moreover, seismic facies analysis shows that buried channels do not parallel the predominant Arabian plate-originated channels (with SW–NE trends) in SW Zagros and are locally swerved in this area. (paper) 16. Lithofacies-paleo-geography and uranium sedimentary facies in Hailar basin International Nuclear Information System (INIS) Qi Fucheng 1992-01-01 Cretaceous-Tertiary sedimentary paleo-structure and lithofacies-paleo-geography in Hailar Basin are described. Taking Chenqi coal field as an example, the sedimentary facies pattern of coal-bearing series characterized by alternating sedimentation of fluviatile and lacustrine-swampy facies is reconstructed. It is pointed out that this sedimentary facies not only controls the sedimentation and distribution of syngenetic uranium mineralization, but also is a favourable place that converges uranium-bearing solution and reduces and precipitates uranium for the second time in epigenetic mineralization 17. Upper Cretaceous chalk facies and depositional history recorded in the Mona-1 core, Mona Ridge DEFF Research Database (Denmark) Anderskouv, Kresten; Surlyk, Finn 2011-01-01 , including mudflow, debris flow, and slumping. Pelagic deposits vary mainly in terms of the concentration of siliciclastic material, the trace-fossil assemblage, and the presence or absence of primary sedimentary structures. Pelagic sedimentation was probably punctuated by the deposition of thin turbidites...... slump packages (14–18 in total) are interpreted, forming over 40% of the succession; debrites appear to be the most common precursor facies involved in slumping. The vertical succession of facies records an earliest Cenomanian facies shift from dominantly siliciclastic to chalk deposition... 18. Gres porcelánico esmaltado producido por vía seca: materias primas fundentes Directory of Open Access Journals (Sweden) Boschi, A. O. 2012-04-01 densificación y, por consiguiente, determinan la temperatura de cocción y la deformación piroplástica. Los agentes fundentes que se usan habitualmente en las composiciones de gres porcelánico son: feldespatos, filitas (usadas en Brasil y nefelinas. Estas materias primas no son solubles al agua, lo que las hace particularmente adecuadas para las composiciones de gres porcelánico tradicional producido por vía húmeda. Sin embargo, existe un gran grupo de materias primas solubles que también tienen un gran potencial como fundentes y que podrían utilizarse en los procesos de vía seca. En este contexto, el objetivo de este trabajo ha sido determinar el potencial fundente de las materias primas solubles al agua, o parcialmente solubles al agua, en una composición de gres porcelánico. La efectividad de varios boratos, es decir, la colemanita, la ulexita, la hidroboracita, así como el carbonato sódico, fueron ensayados en un estudio de tipo comparativo. Los resultados de este estudio indican que la incorporación de pequeñas cantidades de estos fundentes es suficiente para reducir la temperatura de cocción de forma importante, sin causar una alta deformación piroplástica de los soportes. Los mejores resultados se obtuvieron con las composiciones que contenían hidroboracita. Este resultado es especialmente relevante para la creación de composiciones alternativas de piezas de gres porcelánico producidas por vía seca. El proceso de vía seca es, en la actualidad, un tema de especial interés, debido a las cuestiones medioambientales y económicas. 19. EFEKTIVITAS METODE ROLE PLAYING PADA MENDESKRIPSIKAN PELAYANAN PRIMA UNTUK MENINGKATKAN HASIL BELAJAR Directory of Open Access Journals (Sweden) Indah Tri Lestari 2013-02-01 Full Text Available Tujuan dari penelitian ini adalah untuk mengetahui efektivitas metode pembelajaran role playing pada pokok bahasan mendeskripsikan pelayanan prima untuk meningkatkan hasil belajar siswa kelas X Administrasi Perkantoran SMK Hidayah Semarang. Subjek penelitian ini adalah siswa kelas X AP SMK Hidayah Semarang Tahun Ajaran 2011/2012. Prosedur penelitian ini merupakan siklus kegiatan pembelajaran yang terdiri dari dua siklus, dimana setiap siklus meliputi perencanaan, pelaksanaan tindakan, pengamatan dan refleksi. Instrumen pengumpulan data dalam penelitian ini adalah tes evaluasi yang berupa tes objektif pada tiap akhir siklus dan lembar observasi untuk aktivitas siswa dan kinerja guru. Hasil belajar kognitif siswa pada siklus I sebesar 74,5 dengan ketuntasan klasikal 66,7%. Rata-rata hasil belajar siklus II sebesar 82,5 dengan ketuntasan klasikal 96,7%. Adapun sikap siswa terhadap pembelajaran pada siklus I sebesar 55% dan pada siklus II mencapai peningkatan sebesar 87,5%. Sedangkan kinerja guru pada siklus I mencapai 58,3% dan pada siklus II meningkat menjadi 93,1%. Penerapan metode pembelajaran role playing pada pokok bahasan mendeskripsikan pelayanan prima efektif untuk meningkatkan hasil belajar siswa kelas X Administrasi Perkantoran SMK Hidayah Semarang. Abstract ___________________________________________________________________ The purpose from this research was to determine effectiveness of role playing in describing excellent service to improve students� result class X AP Hidayah Vocational School of Semarang year 2011/2012. The subject of this research is the class X AP of Hidayah Vocational School of Semarang year 2011/2012. The procedure of this research is a cycle of learning activities that consists of two cycles, in which each cycle includes planning, implementation of the action, observation and reflection. Instrument of data collection is the evaluation tests in the form of objective tests at each end of the cycle and observation 20. Anthropogenic effects on sedimentary facies in Lake Baldeney, West Germany Science.gov (United States) Neumann-Mahlkau, Peter; Niehaus, Heinz Theo 1983-12-01 Analysis of well logs of Lake Baldeney, a reservoir of the Ruhr River, yields four facies factors that reflect the effect of anthropogenic processes on the sediment. First, the sedimentation rate is directly related to the subsidence caused by mining. The extent of the subsidence was such that the sediment load of the river could not compensate for the sinking of the lake bottom. Discharged sediment filled about one-fifth of the basin within 40 years. In certain areas of the basin the sedimentation rate reached up to 10 cm per year. Second, the grain-size distribution of the sediment was influenced by long-term and short-term events. During the subsidence, grain-size distribution remained relatively constant. The destruction of the Möhne River dam during World War II resulted in the presence of an extremely large grain size as evidenced by the so-called Möhnelage. The filling of the lake after 1961 was accompanied by a continual increase in medium grain size. Third, until 1975, the mode of the lake sediment reflects the effect of mining in the vicinity of the lake. High coal content can be traced to its origin. The introduction of modern production processes, modernization of coal dressing, and hydraulic hauling is documented in the sediment. Finally, the heavy metal content of the sediment corresponds to the industrial development in the drainage area the Ruhr River. The accumulation of Cd reached an extreme concentration, exceeding the natural content by a thousand times. Variation in concentration reflects an increase in industrial production, as well as measures undertaken to restore water quality. 1. PRIMA-1 and PRIMA-1Met (APR-246: From Mutant/Wild Type p53 Reactivation to Unexpected Mechanisms Underlying Their Potent Anti-Tumor Effect in Combinatorial Therapies Directory of Open Access Journals (Sweden) Anne Perdrix 2017-12-01 Full Text Available p53 protects cells from genetic assaults by triggering cell-cycle arrest and apoptosis. Inactivation of p53 pathway is found in the vast majority of human cancers often due to somatic missense mutations in TP53 or to an excessive degradation of the protein. Accordingly, reactivation of p53 appears as a quite promising pharmacological approach and, effectively, several attempts have been made in that sense. The most widely investigated compounds for this purpose are PRIMA-1 (p53 reactivation and induction of massive apoptosis and PRIMA-1Met (APR-246, that are at an advanced stage of development, with several clinical trials in progress. Based on publications referenced in PubMed since 2002, here we review the reported effects of these compounds on cancer cells, with a specific focus on their ability of p53 reactivation, an overview of their unexpected anti-cancer effects, and a presentation of the investigated drug combinations. 2. Fluvial facies reservoir productivity prediction method based on principal component analysis and artificial neural network Directory of Open Access Journals (Sweden) Pengyu Gao 2016-03-01 Full Text Available It is difficult to forecast the well productivity because of the complexity of vertical and horizontal developments in fluvial facies reservoir. This paper proposes a method based on Principal Component Analysis and Artificial Neural Network to predict well productivity of fluvial facies reservoir. The method summarizes the statistical reservoir factors and engineering factors that affect the well productivity, extracts information by applying the principal component analysis method and approximates arbitrary functions of the neural network to realize an accurate and efficient prediction on the fluvial facies reservoir well productivity. This method provides an effective way for forecasting the productivity of fluvial facies reservoir which is affected by multi-factors and complex mechanism. The study result shows that this method is a practical, effective, accurate and indirect productivity forecast method and is suitable for field application. 3. Sedimentary Facies of the West Crocker Formation North Kota Kinabalu-Tuaran Area, Sabah, Malaysia Science.gov (United States) Mohamed, Azfar; Hadi Abd Rahman, Abdul; Suhaili Ismail, Mohd 2016-02-01 Newly outcrops exposed in the West Crocker Formation have led to the detail sedimentolgical analysis of the formation. Eight sedimentary facies have been recognised in which it was divided into three main groups: (1) sand-dominated facies (F1-F2), (2) poorly- sorted unit mixed sand and mud-dominated facies (F3), and (3) mud-dominated facies (F4-F5). These are: F1- graded sandstone (massive to planar laminated), F2-ripple-cross laminated, wavy and convolute lamination sandstone, F3-chaotic beds of mixed sandstone and mudstone blocks and clasts, F4-lenticular bedded of sandstone, and F5-shale. The studies of the formation has come out that it was deposited in a sand-rich submarine fan with specific location located at (1) inner fan channel-levee complex; (2) mid-fan channelised lobes, and (3) outer fan. 4. Distinguishing fluvio-deltaic facies by bulk geochemistry and heavy minerals: an example from the Miocene of Denmark DEFF Research Database (Denmark) Olivarius, Mette; Rasmussen, Erik S.; Siersma, Volkert Dirk 2011-01-01 Interpretations of seismic profiles, gamma-ray logs and sediment descriptions were used to classify seven facies in Miocene fluvio-deltaic deposits ofDenmark. An impartial approach was adopted by not including analytical data in the facies definition. This approach allowed identification of signi......Interpretations of seismic profiles, gamma-ray logs and sediment descriptions were used to classify seven facies in Miocene fluvio-deltaic deposits ofDenmark. An impartial approach was adopted by not including analytical data in the facies definition. This approach allowed identification...... grain size of quartz and heavy minerals from the channel facies towards the delta shoreface facies and further along the coast to the spit shoreface facies is associated with an increase in sorting and textural maturity. This trend is related to longshore drift. Increasing heavy mineral grain size...... is found from the delta slope facies offshore to the delta toe and shelf facies. This trend is interpreted as a result of sorting by turbidity currents. The mixed origin of the transgressive lag facies is shown by the poorer sorting in this facies. By indicating the amount of alteration the sediments have... 5. Polymetamorphic evolution of the granulite-facies Paleoproterozoic basement of the Kabul Block, Afghanistan Science.gov (United States) 2015-08-01 The Kabul Block is an elongate crustal fragment which cuts across the Afghan Central Blocks, adjoining the Indian and Eurasian continents. Bounded by major strike slip faults and ophiolitic material thrust onto either side, the block contains a strongly metamorphosed basement consisting of some of the only quantifiably Proterozoic rocks south of the Herat-Panjshir Suture Zone. The basement rocks crop-out extensively in the vicinity of Kabul City and consist predominantly of migmatites, gneisses, schists and small amounts of higher-grade granulite-facies rocks. Granulite-facies assemblages were identified in felsic and mafic siliceous rocks as well as impure carbonates. Granulite-facies conditions are recorded by the presence of orthopyroxene overgrowing biotite in felsic rocks; by orthopyroxene overgrowing amphibole in mafic rocks and by the presence of olivine and clinohumite in the marbles. The granulite-facies assemblages are overprinted by a younger amphibolite-facies event that is characterized by the growth of garnet at the expense of the granulite-facies phases. Pressure-temperature (P-T) conditions for the granulite-facies event of around 850 °C and up to 7 kbar were calculated through conventional thermobarometry and phase equilibria modeling. The younger, amphibolite-facies event shows moderately higher pressures of up to 8.5 kbar at around 600 °C. This metamorphism likely corresponds to the dominant metamorphic event within the basement of the Kabul Block. The results of this work are combined with the litho-stratigraphic relations and recent geochronological dating to analyze envisaged Paleoproterozoic and Neoproterozoic metamorphic events in the Kabul Block. 6. Estimasi Nilai Pasar Wajar Ekuitas PT Prima Layanan Nasional Enjiniring Dalam Persiapan Initial Public Offering (IPO Directory of Open Access Journals (Sweden) 2015-11-01 Full Text Available PT Prima Layanan Nasional Enjiniring (PT PLN Enjiniring plans to conduct an initial public offering in 2012 that is intended for business development. Purpose of this research was to estimate the fair market value of equity of PT PLN Enjiniring in the framework of an initial public offering. Fair market value of equity of PT PLN Enjiniring is acquired by using discounted cash flow-free cash flow to equity method. Information used for this research come from two secondary data from financial reports and other information contained in the annual report 2008-2010 PT PLN Enjiniring years audited by public accountants, comperative financial reports, and company’s stock data comparison. The estimated fair market value of equity of PT PLN Enjiniring per December 31st 2011 by using the method of discounted cash flow-free cash flow to equity is obtained indication the fair market value of equity amounting to Rp2.583.155.716.515. 7. L'universo prima del Big Bang cosmologia e teoria delle stringhe CERN Document Server Gasperini, Maurizio 2002-01-01 Termini come "universo in espansione", "big bang", "singolarità iniziale" sono ormai entrati a far parte del linguaggio comune. L'idea che l'universo che oggi osserviamo abbia avuto origine da una grossa esplosione (big bang) è ormai ampiamente diffusa e accettata nella moderna cultura popolare, a tutti i libelli. Ma cosa c'era prima del big bang? E ha senso porsi questo interrogativo in un contesto scientifico? I recenti progressi della fisica teoria, e in particolare della cosiddetta teoria delle stringhe, suggeriscono una risposta a questa domanda, fornendo degli strumenti matematici capaci, in linea di principio, di ricostruire la storia dell'universo spingendosi anche oltre l'istante del big bang. Ne emerge un possibile scenario cosmologico nel quale l'universo, anzichè essere "appena nato" al momento del big bang, era piuttosto nel punto di mezzo della sua evoluzione, di durata probabilmente infinita. In questo libro si cerca di illustrare tale scenario usando un linguaggio non troppo tecnico, rivolt... 8. IMPACTO DEL MATERIAL RECICLADO EN LOS INVENTARIOS DE MATERIAS PRIMAS DE UNA EMPRESA MANUFACTURERA Directory of Open Access Journals (Sweden) Guillermo Antonio Salinas López Full Text Available En el presente trabajo, se diseña un modelo de dinámica de sistemas, que junto con algunos indicadores de gestión, se usan para dimensionar el impacto del uso del material reciclado en una industria. Lo anterior, con el fin de proveer mejores elementos en la toma de decisiones sobre la gestión de las existencias de materias primas. Para esto se hace una revisión de los principales elementos que inciden en el esquema productivo de una empresa caso de estudio, con la cual se obtiene, una caracterización de la industria y posterior configuración de la estructura y las relaciones del sistema, para modelar y simular utilizando el software Vensim DSS. A partir de dichas simulaciones, se revisa el comportamiento del sistema, así como las variaciones que presenta, ante diferentes escenarios y cambios en sus parámetros más relevantes. Al final, se obtiene un modelo que ilustra el comportamiento de los niveles de inventario de distintos tipos de materiales, así como los valores de algunos indicadores logísticos y energéticos, que revelan el importante trabajo por realizar, en materia de reciclaje en la región del Valle del Cauca y Colombia en general. 9. Sedimentary facies and Holocene depositional processes of Laura Island, Majuro Atoll Science.gov (United States) Yasukochi, Toru; Kayanne, Hajime; Yamaguchi, Toru; Yamano, Hiroya 2014-10-01 The depositional processes that formed Laura Island, Majuro Atoll, Marshall Islands, were reconstructed based on a facies analysis of island sediments and spine ratios, and radiocarbon ages of foraminifera. Sedimentary facies were analyzed from trenches and drill cores excavated on the island and its adjacent reef flat. Depositional ages were obtained using benthic foraminifera (Calcarina) whose spines had not been abraded. The facies were classified into two types: gravelly and sandy. The initial sediments of these sites consisted of gravelly facies in the lower horizon and sandy facies in the upper horizon. Their ages were approximately 2000 cal BP and coincident with the onset of a 1.1-m decline in regional relative sea level, which enabled deposition of the gravelly facies. Half of the sand fraction of the sediment was composed of larger benthic foraminifera. The spine ratio showed that their supply source on the reef flat was located oceanside of the island. The supply source appears to have been caused by the relative sea-level fall. This indicates that the studied island was formed by a relative reduction in wave energy and enhanced foraminiferal supply, both of which were triggered by the late Holocene relative sea-level fall. 10. El tratamiento actuarial de los periodos de carencia y el contraseguro de primas en el seguro de dependencia. Directory of Open Access Journals (Sweden) Ricote Gil, Fernando. 2003-01-01 Full Text Available La dependencia es un estado en el que se encuentran las personas que por razones ligadas a la falta o la pérdida de autonomía física, psíquica o intelectual tienen necesidad de asistencia y/o atención significativa para la realización los actos corrientes de la vida diaria. Dentro de la iniciativa privada, el sector asegurador juega un importante papel para la prestación de garantías derivadas de esta cobertura. Un aspecto fundamental en el estudio de esta cobertura es la consideración de los periodos de carencia y el tratamiento del contraseguro de primas durante los mismo. Se analiza el riesgo actuarial y su tratamiento en esta cobertura y la incidencia en la valoración actuarial de las primas por prestaciones de dependencia. 11. EVALUACIÓN AMBIENTAL PARA PROCESOS QUE USAN RESIDUOS DE LA INDUSTRIA DE LOS BIOCOMBUSTIBLES COMO MATERIAS PRIMAS Directory of Open Access Journals (Sweden) Mónica Julieth Valencia Botero Full Text Available La industria creciente de los biocombustibles genera grandes cantidades de residuos que tienen alto potencial para la obtención de productos con alto valor agregado. En el presente documento se lleva a cabo el análisis de ciclo de vida (ACV para el glicerol y el bagazo de caña de azúcar durante su producción y para su uso como materia prima en cuatro procesos diferentes. El objetivo fue determinar el impacto ambiental de los cuatro procesos, por medio de la cuantificación de gases de efecto invernadero (GEI asociados al ciclo de vida. Los resultados indican que las emisiones de GEI asociadas a los procesos que utilizan el glicerol como materia prima son mayores que las emisiones de GEI para los procesos que involucran bagazo de caña de azúcar, pero que el aprovechamiento del glicerol podría considerarse más eficiente, ya que las emisiones por unidad de masa en el uso del glicerol son 75% inferiores a las emisiones calculadas para los procedimientos utilizando bagazo de caña como materia prima. 12. Relations between Inductive Reasoning and Deductive Reasoning Science.gov (United States) Heit, Evan; Rotello, Caren M. 2010-01-01 One of the most important open questions in reasoning research is how inductive reasoning and deductive reasoning are related. In an effort to address this question, we applied methods and concepts from memory research. We used 2 experiments to examine the effects of logical validity and premise-conclusion similarity on evaluation of arguments.… 13. Stratigraphy and Facies Analysis of a 122 M Long Lacustrine Sequence from Chalco Lake, Central Mexico Science.gov (United States) Herrera, D. A.; Ortega, B.; Caballero, M.; Lozano, S.; Pi, T.; Brown, E. T. 2010-12-01 Chalco lake is located SE of the outskirts of Mexico City, at the central part of the Trans Mexican Volcanic Belt. Previous studies show the importance of this lacustrine sequence as an archive of paleoenvironmental and paleoclimatic changes. A set of five cores up to 122 m depth were drilled in the basin, in order to analyze the sedimentary record and to extent the previous knowledge of past environmental changes in central Mexico. As an initial step, in this work we present the identification and classification of sedimentary facies. Preliminary paleomagnetism analyses recognize the possible record of the Blake Event (ca. 120 kyr BP), and suggest that the sequence might span the last 240 kyr. In this case, variations in sedimentary facies could reflect the conditions of the MIS 1-7. The facies are mostly diatom ooze, carbonate mud, organic rich silt and volcaniclastic, both massive and laminated, and massive dark gray to reddish brown silt. From 1 to 8 m depth dominates the organic rich silt facies, which correlates with the MIS 1. Intercalations of reddish brown and grayish brown silt facies, between 8 to 60 m depth, indicate changes occurred during MIS 2 to 5d. Between 60-75 m depth the sequence is characterized by dark grayish silty clay facies, which possibly coincide with the MIS 5e. At 79 m depth (ca. 130 kyr BP) we found struvite (MgNH4PO4.6H2O), which may be related to dry conditions. The laminated diatom ooze facies dominates between 90 to 122 m depth and indicates rhythmic changes in the sediment deposition of the basin. The volcaniclastic facies is represented by lapilli and ash deposits in more than 100 individual tephra layers of both mafic and felsic composition. Some of them correspond to main volcanic eruptions, as the Upper Toluca Pumice (13,500 cal yr BP), from the Nevado de Toluca volcano and the Pómez con Andesita (17,700 cal yr BP) from the Popocatépetl volcano. The carbonate mud facies is composed of calcite and siderite, with frequent 14. Petrographic changes induced by artificial coalification of peat: comparison of two planar facies (Rhizophora and Cladium) from the Everglades-mangrove complex of Florida and a domed facies (Cyrilla) from the Okefenokee Swamp of Georgia Energy Technology Data Exchange (ETDEWEB) Cohen, A.D.; Bailey, A.M. [University of South Carolina, Columbia, SC (United States). Dept. of Geological Sciences 1997-12-01 Petrographic changes during coalification of three peat samples were investigated by artificial coalification experiments using a semi-open reactor system. Compressions of from 83 to 88% produced dark brown to black, shiny, flattened pellets exhibiting microscopic banding. Overall amounts of compression inversely correlated with the framework to matrix ratios (F/M) although certain tissue fragments remained relatively uncompressed due to the presence of tanniferous cell fillings. The most distinct microscopic banding (longest and widest bands) developed in samples of the dome-formed peat facies. The planar, root-dominated, Rhizophora facies showed the greatest change in microbanding character during coalification, with greater compressions roots having disappeared. This could explain why roots are significant components of many modern peats (and ancient coal ball concretions) but are difficult to recognize in bituminous coals. Similarly, separation of cuticles from leaves in modern peat-forming environments partially explains why leaf remains are also difficult to recognize in most coals, even those with abundant cutinites. Macerals were also affected. These petrographic results, along with previously reported chemical results, all suggest that the methods used in these experiments have produced changes that might reasonably be expected to occur during natural coalification (despite speeding up). Although more work needs to be done to verify and refine these results and to establish a correlation between these artificial coalification steps and true coalification, the new observations and conclusions from these studies might still be helpful in constructing models to predict or interpret coal seam characteristics and to establish the timing and release-potential of gaseous or liquid hydrocarbons from coals. 69 refs., 28 figs., 5 tabs. 15. Mineralogical Characterization of The Alteration Facies at Gabal El-Missikat Area, Central Eastern Desert, Egypt International Nuclear Information System (INIS) El-Sherif, A.M. 2013-01-01 The present study deals with the petrographical, mineralogical and geochemical characteristics of the alteration facies zones recognized around the shear zone at Gabal El-Missikat area, Central Eastern Desert, Egypt. Petrographically, the fresh granitic samples are composed mainly of quartz, K-feldspars (microcline and microcline perthite), plagioclase, biotite. The secondary minerals are sericite, kaolinite, muscovite, chlorite and epidote as well as zircon, apatite, fluorite, titanite and iron oxides as accessory minerals. Two alteration facies zones are recognized and namely as propylitic and advanced argillic. The propylitic facies zone is composed mainly of sericite with minor kaolinite, muscovite, quartz, relics of plagioclases, chlorite and rare epidote as well as zircon, hematite, goethite, magnetite, ilmenite, ilmenorutile, rutile, titanite, apatite, columbite and fluorite and secondary uranium minerals, the advanced argillic facies zone is composed mainly of kaolinite with minor sericite, quartz, muscovite, chlorite and rare epidote as well as zircon, hematite, goethite, magnetite, ilmenite, ilmenorutile, rutile, titanite, apatite and garnet of spessartine type as accessory minerals. The identified minerals in the studied two alteration facies zones can be grouped into three mineral groups which are: the primary minerals (pyrite, magnetite, galena, columbite and gold), the secondary minerals (uranophane, kasolite and wulfenite) and the gangue minerals (anhydrite, barite, celestine, hematite, goethite and fluorite). The identified mineral assemblage of the studied propylitic alteration facies zone may be attributed to strongly alkaline hydrothermal solutions at ph value of more than 7 with temperature varying between 350 and 450°C, while the advanced argillic alteration facies zone is essentially associated with strongly acidic hydrothermal solutions at ph value less than 7 with temperature varying between 150 and 400°C 16. Mineralogical and Micro-fabric investigation of the Sandy Facies of Opalinus Clay (Mont Terri) International Nuclear Information System (INIS) Kaufhold, Annette; Siegesmund, Siegfried; Dohrmann, Reiner; Graesle, Werner; Plischke, Ingo 2013-01-01 In the field of geological disposal of radioactive waste in many countries argillaceous formations are considered as potential host rock. For the understanding of the long-term behaviour of clay host rock, it is important to understand the interaction between mechanical behaviour, micro-fabric, and mineral composition. Previous publications showed that particularly the carbonate content and the arrangement of the carbonate grains (as cement in the matrix or as shells) determines the mechanical strength of Opalinus Clay and Callovo-Oxfordian Clay specimens, respectively. Klinkenberg et al. (2009) studied the shaly facies of Opalinus Clay, however, the actual deposit is planned to be built in the sandy facies of Opalinus Clay. The aim of the present study is to investigate the relation between micro-fabric, mineral composition, and mechanical properties of different samples derived from the sandy facies (BLT-A2). Image analysis showed that the carbonates in the sandy facies mainly occur as 1) matrix which in turn acts as cement. Carbonates also occur 2) in the fine sand fraction and 3) biogenic carbonates as traces. The carbonates of the sandy facies, therefore, appear to be similar to the carbonates of the Callovo-Oxfordian Clay with respect to their possible influence on failure strength. The mechanical testing showed that the shear strength increases with increasing carbonate content. This phenomenon was also observed for the samples of the Callovo-Oxfordian Clay, while the opposite relation was found for the shaly facies of the Opalinus Clay. Preliminary results presented here, indicate that the sandy facies (drilling BLT-A2) and Callovo-Oxfordian Clay show similar mechanical properties - in detail: 1) Micro-fabric: carbonates predominate in the matrix, 2) Mineralogy: high carbonate content and 3) Mechanical testing: shear strength increases with increasing carbonate content, where the type of carbonates which controls the increase of strength has to be 17. The relationship between hydrogeologic properties and sedimentary facies: an example from Pennsylvanian bedrock aquifers, southwestern Indiana International Nuclear Information System (INIS) Fisher, A.T.; Barnhill, M.; Revenaugh, J. 1998-01-01 The relationship between the hydrogeologic properties and sedimentary facies of shallow Pennsylvanian bedrock aquifers was examined using detailed sedimentologic descriptions, aquifer (slug) tests, and gamma ray logs. The main goal of the study was to determine if it was possible to reliably estimate near-well hydraulic conductivities using core descriptions and logging data at a complex field site, based on assignment of consistent conductivity indicators to individual facies. Lithologic information was gathered from three sources: core descriptions, simplified lithologic columns derived from the core descriptions, and drillers' logs. Gamma ray data were collected with a conventional logging instrument. Slug tests were conducted in all wells containing screened zones entirely within the Pennsylvanian facies of interest. Simplified subsets of sedimentologic facies were assembled for classification of subsurface geology, and all rocks within the screened intervals of test wells were assigned to individual facies based on visual descriptions. Slug tests were conducted to determine the bulk hydraulic conductivity (a spatial average within the screened interval) in the immediate vicinity of the wells, with measured values varying from 10 -4 m/s to 10 -8 m/s. Gamma ray logs from these wells revealed variations in raw counts above about 1.5 orders of magnitude. Data were combined using simple linear and nonlinear inverse techniques to derive relations between sedimentologic facies, gamma ray signals, and bulk hydraulic conductivities. The analyses suggest that facies data alone, even those derived from detailed core descriptions, are insufficient for estimating hydraulic conductivity in this setting to better than an order of magnitude. The addition of gamma ray data improved the estimates, as did selective filtering of several extreme values from the full data set. Better estimates might be obtained through more careful field measurements and reduction of 18. Age and duration of eclogite-facies metamorphism, North Qaidam HP/UHP terrane, Western China Science.gov (United States) Mattinson, C.G.; Wooden, J.L.; Liou, J.G.; Bird, D.K.; Wu, C.L. 2006-01-01 Amphibolite-facies para-and orthogneisses near Dulan, at the southeast end of the North Qaidam terrane, enclose minor eclogite and peridotite which record ultra-high pressure (UHP) metamorphism associated with the Early Paleozoic continental collision of the Qilian and Qaidam microplates. Field relations and coesite inclusions in zircons from paragneiss suggest that felsic, mafic, and ultramafic rocks all experienced UHP metamorphism and a common amphibolite-facies retrogression. SHRIMP-RG U-Pb and REE analyses of zircons from four eclogites yield weighted mean ages of 449 to 422 Ma, and REE patterns (flat HREE, no Eu anomaly) and inclusions of garnet, omphacite, and rutile indicate these ages record eclogite-facies metamorphism. The coherent field relations of these samples, and the similar range of individual ages in each sample suggests that the ???25 m.y. age range reflects the duration of eclogite-facies conditions in the studied samples. Analyses from zircon cores in one sample yield scattered 433 to 474 Ma ages, reflecting partial overlap on rims, and constrain the minimum age of eclogite protolith crystallization. Inclusions of Th + REE-rich epidote, and zircon REE patterns are consistent with prograde metamorphic growth. In the Lu??liang Shan, approximately 350 km northwest in the North Qaidam terrane, ages interpreted to record eclogite-facies metamorphism of eclogite and garnet peridotite are as old as 495 Ma and as young as 414 Ma, which suggests that processes responsible for extended high-pressure residence are not restricted to the Dulan region. Evidence of prolonged eclogite-facies metamorphism in HP/UHP localities in the Northeast Greenland eclogite province, the Western Gneiss Region of Norway, and the western Alps suggests that long eclogite-facies residence may be globally significant in continental subduction/collision zones. 19. APR-246/PRIMA-1Met Inhibits and Reverses Squamous Metaplasia in Human Conjunctival Epithelium. Science.gov (United States) Li, Jing; Li, Cheng; Wang, Guoliang; Liu, Zhen; Chen, Pei; Yang, Qichen; Dong, Nuo; Wu, Huping; Liu, Zuguo; Li, Wei 2016-02-01 Squamous metaplasia is a common pathologic condition in ocular surface diseases for which there is no therapeutic medication in clinic. In this study, we investigated the effect of a small molecule, APR-246/PRIMA-1(Met), on squamous metaplasia in human conjunctival epithelium. Human conjunctival explants were cultured for up to 12 days under airlifting conditions. Epithelial cell differentiation and proliferation were assessed by Cytokeratin 10 (K10), K14, K19, Pax6, MUC5AC, and p63 immunostaining patterns. β-catenin and TCF-4 immunofluorescent staining and real-time PCR characterized Wnt signaling pathway involvement. Pterygium clinical samples were cultured under airlifting conditions with or without APR-246 for 4 days. p63, K10, β-catenin, and TCF-4 expression in pterygial epithelium was determined by immunofluorescent staining and real-time PCR. Airlift conjunctival explants resulted in increased stratification and intrastromal epithelial invagination. Such pathology was accompanied by increases in K10, K14, and p63 expression, whereas K19 and Pax6 levels declined when compared to those in freshly isolated tissue. On the other hand, APR-246 reversed all of these declines in K10, K14, and p63 expression. Furthermore, K19 and Pax6 increased along with rises in goblet cell density. These effects of APR-246 were accompanied by near restoration of normal conjunctival epithelial histology. APR-246 also reversed squamous metaplasia in pterygial epithelium that had developed after 4 days in ex vivo culture. Reductions in squamous metaplasia induced by APR-246 suggest it may provide a novel therapeutic approach in different squamous metaplasia-associated ocular surface diseases. 20. KANDUNGAN KARBON DI HUTAN RAWA GAMBUT KAWASAN KONSERVASI PT NATIONAL SAGO PRIMA, KEPULAUAN MERANTI, RIAU Directory of Open Access Journals (Sweden) Yusi Rosalina 2013-07-01 Full Text Available This study was conducted to collect information regarding carbon storage, particularly the carbon stored in the aboveground biomass as well as in the peat soil. The study site was in a conservation area of the PT National Sago Prima belonging to the PT Sampoerna Agro Tbk. Group. The work was undertaken in January-February 2012. The total aboveground biomass and carbon storage in the research site indicates that the conservation area is a secondary peat swamp forest, with the biomass of 149.18 ton/ha and carbon stock of 70.12 ton C/ha. The aboveground biomass and carbon consisted of biomass and carbon of tree (83.97 ton/ha containing 39.47 ton C/ha, respectively, saplings (20.69 ton/ha containing 9.72 ton C/ha and seedlings and undergrowth plants (0.03 ton/ha containing 0.01 ton C/ha, wood necromass (24.06 ton/ha containing 11.31 ton C/ha, and litter (20.44 ton/ha containing 9.61 ton C/ha. An allometric equation was developed for Pandanus atrocarpus Griff. providing an estimated total biomass and carbon of 5.16 ton/ha containing 2.42 ton C/ha. The underground C with the mean peat depth of 5.5 m, mean bulk density of 0.18 g/cm3, and the mean organic C of 46.6 % was 464.895,94 ton C/ha. In the entire conservation forest area of 541 ha the total aboveground biomassa and carbon storage was estimated to be 80,708.64 ton and 37,934.00 ton C, while the total underground carbon was 238,96 million MT C. 1. Defeasibility in Legal Reasoning OpenAIRE SARTOR, Giovanni 2009-01-01 I shall first introduce the idea of reasoning, and of defeasible reasoning in particular. I shall then argue that cognitive agents need to engage in defeasible reasoning for coping with a complex and changing environment. Consequently, defeasibility is needed in practical reasoning, and in particular in legal reasoning 2. Sedimentology, eruptive mechanism and facies architecture of basaltic scoria cones from the Auckland Volcanic Field (New Zealand) Science.gov (United States) Kereszturi, Gábor; Németh, Károly 2016-09-01 Scoria cones are a common type of basaltic to andesitic small-volume volcanoes (e.g. 10- 1-10- 5 km3) that results from gas-bubble driven explosive eruptive styles. Although they are small in volume, they can produce complex eruptions, involving multiple eruptive styles. Eight scoria cones from the Quaternary Auckland Volcanic Field in New Zealand were selected to define the eruptive style variability from their volcanic facies architecture. The reconstruction of their eruptive and pyroclastic transport mechanisms was established on the basis of study of their volcanic sedimentology, stratigraphy, and measurement of their pyroclast density, porosity, Scanning Electron Microscopy, 2D particle morphology analysis and Visible and Near Visible Infrared Spectroscopy. Collection of these data allowed defining three end-member types of scoria cones inferred to be constructed from lava-fountaining, transitional fountaining and Strombolian type, and explosive Strombolian type. Using the physical and field-based characteristics of scoriaceous samples a simple generalised facies model of basaltic scoria cones for the AVF is developed that can be extended to other scoria cones elsewhere. The typical AVF scoria cone has an initial phreatomagmatic phases that might reduce the volume of magma available for subsequent scoria cone forming eruptions. This inferred to have the main reason to have decreased cone volumes recognised from Auckland in comparison to other volcanic fields evolved dominantly in dry eruptive condition (e.g. no external water influence). It suggests that such subtle eruptive style variations through a scoria cone evolution need to be integrated into the hazard assessment of a potentially active volcanic field such as that in Auckland. 3. Non-marine carbonate facies, facies models and palaeogeographies of the Purbeck Formation (Late Jurassic to Early Cretaceous) of Dorset (Southern England). Science.gov (United States) Gallois, Arnaud; Bosence, Dan; Burgess, Peter 2015-04-01 Non-marine carbonates are relatively poorly understood compared with their more abundant marine counterparts. Sedimentary facies and basin architecture are controlled by a range of environmental parameters such as climate, hydrology and tectonic setting but facies models are few and limited in their predictive value. Following the discovery of extensive Early Cretaceous, non-marine carbonate hydrocarbon reservoirs in the South Atlantic, the interest of understanding such complex deposits has increased during recent years. This study is developing a new depositional model for non-marine carbonates in a semi-arid climate setting in an extensional basin; the Purbeck Formation (Upper Jurassic - Lower Cretaceous) in Dorset (Southern England). Outcrop study coupled with subsurface data analysis and petrographic study (sedimentology and early diagenesis) aims to constrain and improve published models of depositional settings. Facies models for brackish water and hypersaline water conditions of these lacustrine to palustrine carbonates deposited in the syn-rift phase of the Wessex Basin will be presented. Particular attention focusses on the factors that control the accumulation of in-situ microbialite mounds that occur within bedded inter-mound packstones-grainstones in the lower Purbeck. The microbialite mounds are located in three units (locally known as the Skull Cap, the Hard Cap and the Soft Cap) separated by three fossil soils (locally known as the Basal, the Lower and the Great Dirt Beds) respectively within three shallowing upward lacustrine sequences. These complex microbialite mounds (up to 4m high), are composed of tabular small-scale mounds (flat and long, up to 50cm high) divided into four subfacies. Many of these small-scale mounds developed around trees and branches which are preserved as moulds (or silicified wood) which are surrounded by a burrowed mudstone-wackestone collar. Subsequently a thrombolite framework developed on the upper part only within 4. Facies discrimination in a mixed fluvio-eolian setting using elemental whole rock geochemistry DEFF Research Database (Denmark) Svendsen, Johan; Friis, Henrik; Stollhofen, Harald 2007-01-01 -eolian successions. The method is developed on the modern fluvio-eolian sediments from the Skeleton Coast dune field, Namibia. The examined sediments comprise eight different facies types; eolian dune sands, inter dune fluvial channel sands, intra erg mass flow deposits, intra erg hyperconcentrated flow deposits......, fluvial channel sands, fluvial mud, lacustrine heterolithic sand and lacustrine heterolithic mud. The contrasting provenance of the fluvial and eolian sediments results in a distinct source fingerprint which can be discriminated using elemental whole rock geochemistry. Multivariate statistical technique...... performed on the geochemical data has enabled discrimination of seven of the eight facies types. Furthermore, the facies discrimination method allowed a quantitative estimate of the degree of fluvial reworking of eolian sand. We believe that the method presented here, when calibrated to a reference well... 5. The influence of facies heterogeneity on the doublet performance in low-enthalpy geothermal sedimentary reservoirs DEFF Research Database (Denmark) Crooijmans, R. A.; Willems, C. J L; Nick, Hamid 2016-01-01 A three-dimensional model is used to study the influence of facies heterogeneity on energy production under different operational conditions of low-enthalpy geothermal doublet systems. Process-based facies modelling is utilised for the Nieuwerkerk sedimentary formation in the West Netherlands Basin...... and the energy recovery rate for different discharge rates and the production temperature (Tmin) above which the doublet is working. With respect to the results, we propose a design model to estimate the life time and energy recovery rate of the geothermal doublet. The life time is estimated as a function of N....../G, Tmin and discharge rate, while the design model for the energy recovery rate is only a function of N/G and Tmin. Both life time and recovery show a positive relation with an increasing N/G. Further our results suggest that neglecting details of process-based facies modelling may lead to significant... 6. Relations between inductive reasoning and deductive reasoning. Science.gov (United States) Heit, Evan; Rotello, Caren M 2010-05-01 One of the most important open questions in reasoning research is how inductive reasoning and deductive reasoning are related. In an effort to address this question, we applied methods and concepts from memory research. We used 2 experiments to examine the effects of logical validity and premise-conclusion similarity on evaluation of arguments. Experiment 1 showed 2 dissociations: For a common set of arguments, deduction judgments were more affected by validity, and induction judgments were more affected by similarity. Moreover, Experiment 2 showed that fast deduction judgments were like induction judgments-in terms of being more influenced by similarity and less influenced by validity, compared with slow deduction judgments. These novel results pose challenges for a 1-process account of reasoning and are interpreted in terms of a 2-process account of reasoning, which was implemented as a multidimensional signal detection model and applied to receiver operating characteristic data. PsycINFO Database Record (c) 2010 APA, all rights reserved. 7. Facies analysis of tuffaceous volcaniclastics and felsic volcanics of Tadpatri Formation, Cuddapah basin, Andhra Pradesh, India Science.gov (United States) Goswami, Sukanta; Dey, Sukanta 2018-05-01 The felsic volcanics, tuff and volcaniclastic rocks within the Tadpatri Formation of Proterozoic Cuddapah basin are not extensively studied so far. It is necessary to evaluate the extrusive environment of felsic lavas with associated ash fall tuffs and define the resedimented volcaniclastic components. The spatial and temporal bimodal association were addressed, but geochemical and petrographic studies of mafic volcanics are paid more attention so far. The limited exposures of eroded felsic volcanics and tuffaceous volcaniclastic components in this terrain are highly altered and that is the challenge of the present facies analysis. Based on field observation and mapping of different lithounits a number of facies are categorized. Unbiased lithogeochemical sampling have provided major and selective trace element data to characterize facies types. Thin-section studies are also carried out to interpret different syn- and post- volcanic features. The facies analysis are used to prepare a representative facies model to visualize the entire phenomenon with reference to the basin evolution. Different devitrification features and other textural as well as structural attributes typical of flow, surge and ash fall deposits are manifested in the middle, lower and upper stratigraphic levels. Spatial and temporal correlation of lithologs are also supportive of bimodal volcanism. Felsic and mafic lavas are interpreted to have erupted through the N-S trending rift-associated fissures due to lithospheric stretching during late Palaeoproterozoic. It is also established from the facies model that the volcaniclastics were deposited in the deeper part of the basin in the east. The rifting and associated pressure release must have provided suitable condition of decompression melting at shallow depth with high geothermal gradient and this partial melting of mantle derived material at lower crust must have produced mafic magmas. Such upwelling into cold crust also caused partial heat 8. Performance Refactoring of Instrumentation, Measurement, and Analysis Technologies for Petascale Computing. The PRIMA Project Energy Technology Data Exchange (ETDEWEB) Malony, Allen D. [Univ. of Oregon, Eugene, OR (United States). Dept. of Computer and Information Science; Wolf, Felix G. [Wilhelm-Johnen-Strasse, Julich (Germany). Forschungszentrum Julich GmbH 2014-01-31 The growing number of cores provided by today’s high-end computing systems present substantial challenges to application developers in their pursuit of parallel efficiency. To find the most effective optimization strategy, application developers need insight into the runtime behavior of their code. The University of Oregon (UO) and the Juelich Supercomputing Centre of Forschungszentrum Juelich (FZJ) develop the performance analysis tools TAU and Scalasca, respectively, which allow high-performance computing (HPC) users to collect and analyze relevant performance data – even at very large scales. TAU and Scalasca are considered among the most advanced parallel performance systems available, and are used extensively across HPC centers in the U.S., Germany, and around the world. The TAU and Scalasca groups share a heritage of parallel performance tool research and partnership throughout the past fifteen years. Indeed, the close interactions of the two groups resulted in a cross-fertilization of tool ideas and technologies that pushed TAU and Scalasca to what they are today. It also produced two performance systems with an increasing degree of functional overlap. While each tool has its specific analysis focus, the tools were implementing measurement infrastructures that were substantially similar. Because each tool provides complementary performance analysis, sharing of measurement results is valuable to provide the user with more facets to understand performance behavior. However, each measurement system was producing performance data in different formats, requiring data interoperability tools to be created. A common measurement and instrumentation system was needed to more closely integrate TAU and Scalasca and to avoid the duplication of development and maintenance effort. The PRIMA (Performance Refactoring of Instrumentation, Measurement, and Analysis) project was proposed over three years ago as a joint international effort between UO and FZJ to 9. Performance Refactoring of Instrumentation, Measurement, and Analysis Technologies for Petascale Computing: the PRIMA Project Energy Technology Data Exchange (ETDEWEB) Malony, Allen D. [Department of Computer and Information Science, University of Oregon; Wolf, Felix G. [Juelich Supercomputing Centre, Forschungszentrum Juelich 2014-01-31 The growing number of cores provided by today’s high-end computing systems present substantial challenges to application developers in their pursuit of parallel efficiency. To find the most effective optimization strategy, application developers need insight into the runtime behavior of their code. The University of Oregon (UO) and the Juelich Supercomputing Centre of Forschungszentrum Juelich (FZJ) develop the performance analysis tools TAU and Scalasca, respectively, which allow high-performance computing (HPC) users to collect and analyze relevant performance data – even at very large scales. TAU and Scalasca are considered among the most advanced parallel performance systems available, and are used extensively across HPC centers in the U.S., Germany, and around the world. The TAU and Scalasca groups share a heritage of parallel performance tool research and partnership throughout the past fifteen years. Indeed, the close interactions of the two groups resulted in a cross-fertilization of tool ideas and technologies that pushed TAU and Scalasca to what they are today. It also produced two performance systems with an increasing degree of functional overlap. While each tool has its specific analysis focus, the tools were implementing measurement infrastructures that were substantially similar. Because each tool provides complementary performance analysis, sharing of measurement results is valuable to provide the user with more facets to understand performance behavior. However, each measurement system was producing performance data in different formats, requiring data interoperability tools to be created. A common measurement and instrumentation system was needed to more closely integrate TAU and Scalasca and to avoid the duplication of development and maintenance effort. The PRIMA (Performance Refactoring of Instrumentation, Measurement, and Analysis) project was proposed over three years ago as a joint international effort between UO and FZJ to accomplish 10. Materias primas no tradicionales en la industria cerámica Directory of Open Access Journals (Sweden) Caligaris, R. 2000-10-01 cerámicos con el fin de mejorar sus propiedades finales. Todos los compactos, obtenidos por prensado uniaxial de estos polvos, recibieron tratamientos térmicos adecuados a sus composiciones, para luego ser caracterizados por diversas técnicas entre las que se pueden mencionar: dilatometría, difracción de rayos X, porosidad, microdureza, microscopías óptica y electrónica de barrido y análisis por dispersión de energías. Del análisis de los resultados obtenidos en estos estudios, se concluyó que los materiales ensayados constituyen una potencial fuente de materia prima para la industria cerámica. 11. Determinación de sílice libre en materias primas para la industria del cemento Directory of Open Access Journals (Sweden) Calleja, J. 1965-12-01 Full Text Available Not availableLa existencia de sílice libre en las materias primas y, por lo tanto, en los crudos empleados en la fabricación de cemento Portland es desventajosa por la escasa reactividad de esta sílice, sobre todo si no posee una finura suficiente. La determinación de sílice cuarzosa en tales materiales es decisiva para la buena marcha de la clinkerización en fábricas cuyas materias primas adolecen de la desventaja de contenerla. Los métodos propugnados suelen ser poco reproducibles y precisos, y dan resultados bastante erráticos. En el presente trabajo, y después de haber ensayado diversos métodos citados en la bibliografía, se describe y recomienda un procedimiento, basado en el ataque del material por ácido pirofosfórico. Las variables que juegan en el proceso descrito son el tamaño de grano de la muestra, en particular el de la sílice libre, la temperatura y el tiempo de ataque. En las condiciones que se especifican se consigue una disolución prácticamente total de los silicatos, sin que apenas se· disuelvan las partículas más finas de cuarzo. Con ello se consigue una exactitud y una precisión tal como pone de manifiesto el análisis estadístico de los resultados obtenidos al determinar sílice libre en diversas materias primas y crudos para cemento. 12. Studiare i prezzi dei libri nell'Europa della prima età moderna: questioni e fonti Directory of Open Access Journals (Sweden) Angela Nuovo 2017-09-01 Full Text Available Il contributo presenta in modo sintetico il quadro concettuale all'interno del quale uno studio dei prezzi dei libri nella prima età moderna dovrebbe muoversi, così come i problemi metodologici da affrontare. Nonostante la natura di manufatto semi-industriale ponga il libro a stampa in una classe merceologica del tutto particolare nell'economia pre-industriale, è possibile utilizzare le categorie generali di domanda e offerta per identificare alcuni fattori atti ad impostare specifici percorsi di ricerca basati sull'analisi storico-economica. La storia del libro può essere quindi messa in relazione con alcuni temi classici della storia economica, allo scopo di inserire il problema del commercio librario e dei prezzi dei libri in un dibattito storiografico più ampio. Tra le fonti disponibili per lo studio dei prezzi dei libri nella prima età moderna, l'inventario di bottega di Bernardo Giunti (Department of Special Collections, UCLA, Collection 170/622 è una chiara testimonianza del fiorente mercato librario allora esistente a Venezia. Le quasi 12.000 registrazioni incluse nella lista dei libri in vendita riflettono gli scopi e gli obiettivi dell’azienda. La struttura di questo documento è decisamente complessa, frutto di più di venti anni di uso continuo (1600-1620 c.. Lungo questo periodo di tempo, il documento sembra essere evoluto da un semplice elenco o catalogo ad uso del personale interno a un importante strumento per la gestione della bottega e del suo magazzino. Quasi ogni titolo presenta un prezzo, e ciò rende questo inventario una delle fonti più ampie e significative per lo studio dei prezzi dei libri nella prima età moderna.This project has received funding from the European Research Council (ERC under the European Union's Horizon 2020 research and innovation programme (Grant Agreement n° 694476. 13. Importance of separating sedimentation facies in prospecting for oil and gas pools confined to sloping structures Energy Technology Data Exchange (ETDEWEB) Zhang, B 1984-01-01 The Shuantotszi field which is in the southeast part of the Sunlyalo oil and gas basin was discovered in 1962. For a long time the correlation of the main factors controlling the oil and gas distribution remained obscure. It has been established in recent years that the main volume of oil and gas is confined to facies in the channels of the second order, arranged between the facies of the main channel and the perlite deposits of the delta. It was established that formation of the accumulation is associated with redistribution and secondary migration of hydrocarbons. 14. Coupling of Oceanic and Continental Crust During Eocene Eclogite-Facies Metamorphism: Evidence From the Monte Rosa Nappe, Western Alps, Italy Science.gov (United States) Lapen, T. J.; Johnson, C. M.; Baumgartner, L. P.; Skora, S.; Mahlen, N. J.; Beard, B. L. 2006-12-01 Subduction of continental crust to HP-UHP metamorphic conditions requires overcoming density contrasts that are unfavorable to deep burial, whereas exhumation of these rocks can be reasonably explained through buoyancy-assisted transport in the subduction channel to more shallow depths. In the western Alps, both continental and oceanic lithosphere has been subducted to eclogite-facies metamorphic conditions. The burial and exhumation histories of these sections of lithosphere bear directly on the dynamics of subduction and the stacking of units within the subduction channel. We address the burial history of the continental crust with high precision U-Pb rutile and Lu-Hf garnet geochronology of the eclogite-facies Monte Rosa nappe (MR), western Alps, Italy. U-Pb rutile ages from quartz-carbonate-white mica-rutile veins that are hosted within eclogite and schist of the MR, Gressoney Valley, Italy, indicate that it was at eclogite-facies metamorphic conditions at 42.6 +/- 0.6 Ma. The sample area (Indren glacier, Furgg zone; Dal Piaz, 2001) consists of eclogite boudins that are surrounded by micaceous schist. Associated with the eclogite and schist are quartz-carbonate-white mica-rutile veins that formed in tension cracks in the eclogite and along the contact between eclogite and surrounding schist. Intrusion of the veins occurred at eclogite-facies metamorphic conditions (480-570°C, >1.3-1.4 GPa) based on textural relations, oxygen isotope thermometry, and geothermobarometry. Lu-Hf geochronology of garnet from a chloritoid-talc-garnet-phengite-quartz-calcite-pyrite - chalcopyrite bearing boudin within talc-chloritoid whiteschists of the MR, Val d'Ayas, Italy (Chopin and Monie, 1984; Pawlig, 2001) yields an age of 40.54 +/- 0.36 Ma. The talc-chloritoid whiteschists from the area record pressures and temperatures of 1.6-2.4 GPa and 500-530°C (Chopin and Monie, 1984; Le Bayon et al., 2006) indicating near UHP metamorphic conditions. Based on the age, P-T, and textural 15. Stereotypical Reasoning: Logical Properties OpenAIRE Lehmann, Daniel 2002-01-01 Stereotypical reasoning assumes that the situation at hand is one of a kind and that it enjoys the properties generally associated with that kind of situation. It is one of the most basic forms of nonmonotonic reasoning. A formal model for stereotypical reasoning is proposed and the logical properties of this form of reasoning are studied. Stereotypical reasoning is shown to be cumulative under weak assumptions. 16. Facies analysis and paleoenvironmental reconstruction of Upper Cretaceous sequences in the eastern Para-Tethys Basin, NW Iran Energy Technology Data Exchange (ETDEWEB) Omidvar, M.; Safari, A.; Vaziri-Moghaddam, H.; Ghalavand, H. 2016-07-01 Upper Cretaceous mixed carbonate-siliciclastic sequences are among the most important targets for hydrocarbon exploration in the Moghan area, located in the eastern Para-Tethys Basin. Despite of their significance, little is known about their facies characteristics and depositional environments. Detailed facies analysis and paleoenvironmental reconstruction of these sequences have been carried out in eight surface sections. Accordingly, four siliciclastic facies, eight carbonate facies and one volcanic facies have been recognized. Detailed facies descriptions and interpretations, together with the results of facies frequency analysis, standard facies models and Upper Cretaceous depositional models of Para-Tethys Basin, have been integrated and a non-rimmed carbonate platform is presented. This platform was affected by siliciclastic influx, in the form of coastal fan delta and submarine fans in the shallow- to deep-marine parts, respectively. This model is interpreted to be shallower in the central and northeastern parts of the Moghan area. Toward the southeast and southwest, this shallow platform turns into deep marine settings along steep slopes without remarkable marginal barriers. (Author) 17. Optimum and robust 3D facies interpolation strategies in a heterogeneous coal zone (Tertiary As Pontes basin, NW Spain) Energy Technology Data Exchange (ETDEWEB) Falivene, Oriol; Cabrera, Lluis; Saez, Alberto [Geomodels Institute, Group of Geodynamics and Basin Analysis, Department of Stratigraphy, Paleontology and Marine Geosciences, Universitat de Barcelona, c/ Marti i Franques s/n, Facultat de Geologia, 08028 Barcelona (Spain) 2007-07-02 Coal exploration and mining in extensively drilled and sampled coal zones can benefit from 3D statistical facies interpolation. Starting from closely spaced core descriptions, and using interpolation methods, a 3D optimum and robust facies distribution model was obtained for a thick, heterogeneous coal zone deposited in the non-marine As Pontes basin (Oligocene-Early Miocene, NW Spain). Several grid layering styles, interpolation methods (truncated inverse squared distance weighting, truncated kriging, truncated kriging with an areal trend, indicator inverse squared distance weighting, indicator kriging, and indicator kriging with an areal trend) and searching conditions were compared. Facies interpolation strategies were evaluated using visual comparison and cross validation. Moreover, robustness of the resultant facies distribution with respect to variations in interpolation method input parameters was verified by taking into account several scenarios of uncertainty. The resultant 3D facies reconstruction improves the understanding of the distribution and geometry of the coal facies. Furthermore, since some coal quality properties (e.g. calorific value or sulphur percentage) display a good statistical correspondence with facies, predicting the distribution of these properties using the reconstructed facies distribution as a template proved to be a powerful approach, yielding more accurate and realistic reconstructions of these properties in the coal zone. (author) 18. Unsupervised seismic facies analysis with spatial constraints using regularized fuzzy c-means Science.gov (United States) Song, Chengyun; Liu, Zhining; Cai, Hanpeng; Wang, Yaojun; Li, Xingming; Hu, Guangmin 2017-12-01 Seismic facies analysis techniques combine classification algorithms and seismic attributes to generate a map that describes main reservoir heterogeneities. However, most of the current classification algorithms only view the seismic attributes as isolated data regardless of their spatial locations, and the resulting map is generally sensitive to noise. In this paper, a regularized fuzzy c-means (RegFCM) algorithm is used for unsupervised seismic facies analysis. Due to the regularized term of the RegFCM algorithm, the data whose adjacent locations belong to same classification will play a more important role in the iterative process than other data. Therefore, this method can reduce the effect of seismic data noise presented in discontinuous regions. The synthetic data with different signal/noise values are used to demonstrate the noise tolerance ability of the RegFCM algorithm. Meanwhile, the fuzzy factor, the neighbour window size and the regularized weight are tested using various values, to provide a reference of how to set these parameters. The new approach is also applied to a real seismic data set from the F3 block of the Netherlands. The results show improved spatial continuity, with clear facies boundaries and channel morphology, which reveals that the method is an effective seismic facies analysis tool. 19. Spectral properties and ASTER-based alteration mapping of Masahim volcano facies, SE Iran Science.gov (United States) Tayebi, Mohammad H.; Tangestani, Majid H.; Vincent, Robert K.; Neal, Devin 2014-10-01 This study applies Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data and the Mixture Tuned Matched Filtering (MTMF) algorithm to map the sub-pixel distribution of alteration minerals associated with the Masahim volcano, SE Iran for understanding the spatial relationship between alteration minerals and volcano facies. Investigations of the alteration mineralogy were conducted using field-spectroscopy, X-ray diffraction (XRD) analysis and ASTER Short Wave Infrared (SWIR) spectral data. In order to spectrally characterize the stratovolcano deposits, lithological units and alteration minerals, the volcano was divided into three facies: the Central, Proximal, and Medial-distal facies. The reflectance spectra of rock samples show absorption features of a number of minerals including white mica, kaolinite, montmorillonite, illite, goethite, hematite, jarosite, opal, and chlorite. The end-members of key alteration minerals including sericite (phyllic zone), kaolinite (argillic zone) and chlorite (propylitic zone) were extracted from imagery using the Pixel Purity Index (PPI) method and were used to map alteration minerals. Accuracy assessment through field observations was used to verify the fraction maps. The results showed that most prominent altered rocks situated at the central facies of volcano. The alteration minerals were discriminated with the coefficient of determination (R2) of 0.74, 0.81, and 0.68 for kaolinite, sericite, and chlorite, respectively. The results of this study have the potential to refine the map of alteration zones in the Masahim volcano. 20. Hierarchy of facies of pyroclastic flow deposits generated by Laacher See type eruptions Science.gov (United States) Freundt, A.; Schmincke, H.-U. 1985-04-01 The upper Quaternary pyroclastic flow deposits of Laacher See volcano show compositional and structural facies variations on four different scales: (1) eruptive units of pyroclastic flows, composed of many flow units; (2) depositional cycles of as many as five flow units; flow units containing (3) regional intraflow-unit facies; and (4) local intraflow-unit subfacies. These facies can be explained by successively overlapping processes beginning in the magma column and ending with final deposition. The pyroclastic flow deposits thus reflect major aspects of the eruptive history of Laacher See volcano: (a) drastic changes in eruptive mechanism due to increasing access of water to the magma chamber and (b) change in chemical composition and crystal and gas content as evacuation of a compositionally zoned magma column progressed. The four scales of facies result from four successive sets of processes: (1) differentiation in the magma column and external factors governing the mechanism of eruption; (2) temporal variations of factors inducing eruption column collapse; (3) physical conditions in the eruption column and the way in which its collapse proceeds; and (4) interplay of flow-inherent and morphology-induced transport mechanics. 1. Facies architecture of heterolithic tidal deposits : The Holocene Holland Tidal Basin NARCIS (Netherlands) Donselaar, M.E.; Geel, C.R. 2007-01-01 The size, shape and spatial position of lithofacies types (or facies architecture) in a tidal estuarine basin are complex and therefore difficult to model. The tidal currents in the basin concentrate sand-sized sediment in a branching pattern of tidal channels and fringing tidal flats. Away from the 2. Cataplectic facies: clinical marker in the diagnosis of childhood narcolepsy-report of two cases. Science.gov (United States) Prasad, Manish; Setty, Gururaj; Ponnusamy, Athi; Hussain, Nahin; Desurkar, Archana 2014-05-01 Narcolepsy is a chronic disease and is commonly diagnosed in adulthood. However, more than half of the patients have onset of symptoms in childhood and/or adolescence. The full spectrum of clinical manifestations, namely excessive daytime sleepiness, cataplexy, hypnagogic hallucinations, and sleep paralysis, is usually not present at disease onset, delaying diagnosis during childhood. Mean delay in diagnosis since symptom onset is known to be several years. Initial manifestations can sometimes be as subtle as only partial drooping of eyelids leading to confusion with a myasthenic condition. We present two children who presented with "cataplectic facies," an unusual facial feature only recently described in children with narcolepsy with cataplexy. The diagnosis of narcolepsy was confirmed by multiple sleep latency test along with human leukocyte antigen typing and cerebrospinal fluid hypocretin assay. The diagnosis of narcolepsy with cataplexy at onset can be challenging in young children. With more awareness of subtle signs such as cataplectic facies, earlier diagnosis is possible. To date, only 11 children between 6 and 18 years of age presenting with typical cataplectic facies have been reported in the literature. We present two patients, one of whom is the youngest individual (4 years old) yet described with the typical cataplectic facies. Copyright © 2014 Elsevier Inc. All rights reserved. 3. The intrusive complexof the Island of Giglio: geomagnetic characteristics of plutonic facies with low susceptibility contrast Directory of Open Access Journals (Sweden) R. Cavallini 1998-06-01 Full Text Available Two main plutonic facies characterize the intrusive complex of the Island of Giglio, and the trend of their contact at depth has been modelled using a 2D½ analysis based on a detailed geomagnetic survey in order to verify the geological hypothesis of the subsurface geometry of this contact. The magnetic anomaly connected with the discontinuity is quite low, due to the small difference between the magnetic susceptibilities of the two granitic facies. Development of this model of inversion of the magnetic field, which is in good agreement with the geological interpretation, was made possible by: 1 accurate control of the geomagnetic time variations and consequent temporal reduction, 2 a very low level of the artificial magnetic noise, 3 high density of the magnetic survey, 4 detailed knowledge of the mapped geologic contact between facies and of their petrologic characteristics, and 5 direct local measurements of the magnetic susceptibilities of the key lithologies. The model shows the trends of the geological contact, as projected in three E-W sections, that dips eastward in the range between 210 and 540, supporting the geologic hypothesis that the Pietrabona facies represents an external shell of the shallowly emplaced Giglio monzogranite intrusion. 4. Multinomial Logistic Regression & Bootstrapping for Bayesian Estimation of Vertical Facies Prediction in Heterogeneous Sandstone Reservoirs Science.gov (United States) Al-Mudhafar, W. J. 2013-12-01 Precisely prediction of rock facies leads to adequate reservoir characterization by improving the porosity-permeability relationships to estimate the properties in non-cored intervals. It also helps to accurately identify the spatial facies distribution to perform an accurate reservoir model for optimal future reservoir performance. In this paper, the facies estimation has been done through Multinomial logistic regression (MLR) with respect to the well logs and core data in a well in upper sandstone formation of South Rumaila oil field. The entire independent variables are gamma rays, formation density, water saturation, shale volume, log porosity, core porosity, and core permeability. Firstly, Robust Sequential Imputation Algorithm has been considered to impute the missing data. This algorithm starts from a complete subset of the dataset and estimates sequentially the missing values in an incomplete observation by minimizing the determinant of the covariance of the augmented data matrix. Then, the observation is added to the complete data matrix and the algorithm continues with the next observation with missing values. The MLR has been chosen to estimate the maximum likelihood and minimize the standard error for the nonlinear relationships between facies & core and log data. The MLR is used to predict the probabilities of the different possible facies given each independent variable by constructing a linear predictor function having a set of weights that are linearly combined with the independent variables by using a dot product. Beta distribution of facies has been considered as prior knowledge and the resulted predicted probability (posterior) has been estimated from MLR based on Baye's theorem that represents the relationship between predicted probability (posterior) with the conditional probability and the prior knowledge. To assess the statistical accuracy of the model, the bootstrap should be carried out to estimate extra-sample prediction error by randomly 5. Modern foraminiferal facies in a subtropical estuarine channel, Bertioga, São Paulo, Brazil Science.gov (United States) Eichler, P.P.B.; Eichler, B.B.; De Miranda, L. B.; Rodrigues, A.R. 2007-01-01 Numerical analyses of modern foraminiferal abundance and environmental data from the Bertioga Channel (Sa??o Paulo, Brazil) reveal multiple biofacies within an overall paralic setting. Despite its fisheries, mariculture and attraction to tourists, the environmental state of Bertioga Channel remains poorly studied. The present investigation is an attempt to partly fill this gap; the parameters examined include depth, salinity, temperature, organic carbon, sulfur content and bottom sediment type. Muddy sediments with high organic carbon content derived from land drainage are found in the inner parts of the channel, whereas sandy sediment dominates the areas adjacent to the Atlantic Ocean. In the eastern entrance to the channel, sandy sediment contain species of Rotaliida from Facies 1 (including Elphidium discoidale, Elphidium poeyanum, Hanzawaia boueana, Pararotalia cananeiaensis and Nonionella atlantica), reflecting normal marine salinity. Sediments with high percentages of silt and clay in polyhaline and eurybaline environments of the eastern part and Itapanhau?? River contain Facies 2, which includes Ammonia beccarii and Pararotalia cananeiaensis. In the western entrance and central, western and eastern parts, where salinities vary from 18 to 30 psu and the sediments contain both low and high organic carbon, the foraminifera from Facies 3 are dominated by Quinqueloculina milletti, Arenoparrella mexicana, Pararotalia cananeiaensis, Ammonia beccarii, Buliminella elegantissima, Elphidium sp., Elphidium excavatum, Elphidium gunteri and Elphidium poeyanum. In mesohaline and polyhaline waters of the central part, the organic-carbon-rich silt and clay contain Facies 4, which includes Ammonia beccarii, Pararotalia cananeiaensis, Elphidium excavatum and Elphidium sp. Most of organic-carbon-enriched, silty-clay substrates that are subject to the highest fresh-water discharge and high bottom temperatures support two different assemblages: one of mostly Rotaliina and the 6. Mapping Depositional Facies on Great Bahama Bank: An Integration of Groundtruthing and Remote Sensing Methods Science.gov (United States) Hariss, M.; Purkis, S.; Ellis, J. M.; Swart, P. K.; Reijmer, J. 2013-12-01 Great Bahama Bank (GBB) has been used in many models to illustrate depositional facies variation across flat-topped, isolated carbonate platforms. Such models have served as subsurface analogs at a variety of scales. In this presentation we have integrated Landsat TM imagery, a refined bathymetric digital elevation model, and seafloor sample data compiled into ArcGIS and analyzed with eCognition to develop a depositional facies map that is more robust than previous versions. For the portion of the GBB lying to the west of Andros Island, the facies map was generated by pairing an extensive set of GPS-constrained field observations and samples (n=275) (Reijmer et al., 2009, IAS Spec Pub 41) with computer and manual interpretation of the Landsat imagery. For the remainder of the platform, which lacked such rigorous ground-control, the Landsat imagery was segmented into lithotopes - interpreted to be distinct bodies of uniform sediment - using a combination of edge detection, spectral and textural analysis, and manual editing. A map was then developed by assigning lithotopes to facies classes on the basis of lessons derived from the portion of the platform for which we had rigorous conditioning. The new analysis reveals that GBB is essentially a very grainy platform with muddier accumulations only in the lee of substantial island barriers; in this regard Andros Island, which is the largest island on GBB, exerts a direct control over the muddiest portion of GBB. Mudstones, wackestones, and mud-rich packstones cover 7%, 6%, and 15%, respectively, of the GBB platform top. By contrast, mud-poor packstones, grainstones, and rudstones account for 19%, 44%, and 3%, respectively. Of the 44% of the platform-top classified as grainstone, only 4% is composed of 'high-energy' deposits characterized by the development of sandbar complexes. The diversity and size of facies bodies is broadly the same on the eastern and western limb of the GBB platform, though the narrower eastern 7. PET/CT assessment in follicular lymphoma using standardized criteria: central review in the PRIMA study Energy Technology Data Exchange (ETDEWEB) Tychyj-Pinel, Christelle [Service de Medecine Nucleaire, Hospices Civils de Lyon, Centre Hospitalier Lyon Sud, Pierre-Benite (France); Ricard, Fabien [Service de Medecine Nucleaire, Hospices Civils de Lyon, Centre Hospitalier Lyon Sud, Pierre-Benite (France); Universite de Lyon, Faculte de Medecine, UCB Lyon 1, Lyon (France); Fulham, Michael [Royal Prince Alfred Hospital, Department of PET and Nuclear Medicine, Sydney (Australia); University of Sydney, Sydney Medical School, Sydney (Australia); Fournier, Marion [Centre Hospitalier Lyon Sud, The Lymphoma Academic Research Organisation (LYSARC), Pierre-Benite (France); Meignan, Michel [CHU Henri Mondor, Medicine Nucleaire, Creteil (France); Lamy, Thierry [Service d' Hematologie, CHU, Rennes (France); Vera, Pierre [Centre Henri Becquerel, Service de Medecine Nucleaire, Rouen (France); Rouen University, QuantIF (Litis EA4108), Rouen (France); Salles, Gilles [Universite de Lyon, Faculte de Medecine, UCB Lyon 1, Lyon (France); Service d' Hematologie, Hospices Civils de Lyon, Centre Hospitalier Lyon Sud, Pierre-Benite (France); Trotman, Judith [University of Sydney, Sydney Medical School, Sydney (Australia); Concord Hospital, Department of Haematology, Concord, NSW (Australia) 2014-03-15 We aimed to compare the standardized central review of {sup 18}F-fluorodeoxyglucose (FDG) positron emission tomography (PET)/CT scans performed after induction therapy for follicular lymphoma (FL) in the PRIMA study (Salles et al., Lancet 377:42-51, 2011; Trotman et al., J Clin Oncol 29:3194-3200, 2011) to scan review at local centres. PET/CT scans were independently evaluated by two nuclear medicine physicians using the 2007 International Harmonization Project (IHP) criteria (Cheson et al., J Clin Oncol 25:579-586, 2007; Juweid et al., J Clin Oncol 25:571-578, 2007; Shankar et al., J Nucl Med 47:1059-1066, 2006) and Deauville 5-point scale (5PS) criteria (Meignan et al., Leuk Lymphoma 50:1257-1260, 2009; Meignan et al., Leuk Lymphoma 51:2171-2180, 2010; Barrington et al., Eur J Nucl Med Mol Imaging 37:1824-1833, 2010). PET/CT status was compared with prospectively recorded patient outcomes. Central evaluation was performed on 119 scans. At diagnosis, 58 of 59 were recorded as positive, with a mean maximum standardized uptake value (SUV{sub max}) of 11.7 (range 4.6-35.6). There was no significant association between baseline SUV{sub max} and progression-free survival (PFS). Sixty post-induction scans were interpreted using both the IHP criteria and 5PS. Post-induction PET-positive status failed to predict progression when applying the IHP criteria [p = 0.14; hazard ratio (HR) 1.9; 95 % confidence interval (CI) 0.8-4.6] or 5PS with a cut-off ≥3 (p = 0.12; HR 2.0; 95 % CI 0.8-4.7). However, when applying the 5PS with a cut-off ≥4, there was a significantly inferior 42-month PFS in PET-positive patients of 25.0 % (95 % CI 3.7-55.8 %) versus 61.4 % (95 % CI 45.4-74.1 %) in PET-negative patients (p = 0.01; HR 3.1; 95 % CI 1.2-7.8). The positive predictive value (PPV) of post-induction PET with this liver cut-off was 75 %. The 42-month PFS for patients remaining PET-positive by local assessment was 31.1 % (95 % CI 10.2-55.0 %) vs 64.6 % (95 % CI 47.0-77.6 %) for PET 8. Sobre producción de la materia prima (leche en el altiplano de Bolivia Directory of Open Access Journals (Sweden) Apaza-Huallpa Yesenia 2017-07-01 Full Text Available Por la falta de mercados para acomodar la producción nacional de leche, muchos productores locales están reduciendo significativamente el número de sus vacas lecheras, que están siendo comercializadas como vacuno corriente en ferias o mataderos a un tercio del precio que tenían pocos años atrás. Actualmente existe una sobreproducción de leche en el departamento de La Paz y cada vez se reduce la demanda de la población, así los agricultores se quedan con el producto teniendo que darle otra finalidad, pero en muchos casos se vuelve inevitable por las grandes cantidades de materia prima, para regular esta crisis, que se ha visto agudizada, por los bajos precios internacionales de este alimento de primera necesidad, situación que estaría impulsando el ingreso de leche y productos procedentes de las países vecinos, de ahí que, es necesario realizar esfuerzos e inversiones para innovar y producir nuevas variedades de artículos lácteos, pue permitan ampliar el mercado, y así competir en mejores condiciones respecto a los productos foráneos. Sería iniciativas que necesitan apoyo del Estado para su materialización, por ejemplo con dotación de infraestructura industrial, fuentes de energía, exenciones impositivas a la importación de tecnología, mayor flexibilidad fiscal y laboral, facilidades de financiamiento, medidas orientadas a fomentar la producción láctea del país en particular y la industria nacional en general. El mercado de la leche se ve afectado por la presencia de leche en polvo de contrabando o legalmente importada, situación que un paquete de leche importada en polvo cuesta hasta 20 Bs., mientras que la Planta Industrializadora de Leche (PIL-Andina comercializa en 41.70 Bs. La leche es un nutrimento fundamental para la salud humana, su aporte en proteínas, calcio y vitaminas es absolutamente importante, sin embargo hay una tendencia muy arraigada, que la leche no le gusta a la población. Esta es una posici 9. Parts-based geophysical inversion with application to water flooding interface detection and geological facies detection Science.gov (United States) Zhang, Junwei I built parts-based and manifold based mathematical learning model for the geophysical inverse problem and I applied this approach to two problems. One is related to the detection of the oil-water encroachment front during the water flooding of an oil reservoir. In this application, I propose a new 4D inversion approach based on the Gauss-Newton approach to invert time-lapse cross-well resistance data. The goal of this study is to image the position of the oil-water encroachment front in a heterogeneous clayey sand reservoir. This approach is based on explicitly connecting the change of resistivity to the petrophysical properties controlling the position of the front (porosity and permeability) and to the saturation of the water phase through a petrophysical resistivity model accounting for bulk and surface conductivity contributions and saturation. The distributions of the permeability and porosity are also inverted using the time-lapse resistivity data in order to better reconstruct the position of the oil water encroachment front. In our synthetic test case, we get a better position of the front with the by-products of porosity and permeability inferences near the flow trajectory and close to the wells. The numerical simulations show that the position of the front is recovered well but the distribution of the recovered porosity and permeability is only fair. A comparison with a commercial code based on a classical Gauss-Newton approach with no information provided by the two-phase flow model fails to recover the position of the front. The new approach could be also used for the time-lapse monitoring of various processes in both geothermal fields and oil and gas reservoirs using a combination of geophysical methods. A paper has been published in Geophysical Journal International on this topic and I am the first author of this paper. The second application is related to the detection of geological facies boundaries and their deforation to satisfy to geophysica 10. Calculo y comparacion de la prima de un reaseguro de salud usando el modelo de opciones de Black-Scholes y el modelo actuarial Directory of Open Access Journals (Sweden) Luis Eduardo Giron 2015-12-01 Full Text Available La presente investigación pretende calcular y comparar la prima de un reaseguro usando el modelo de opciones de Black-Scholes y el modelo clásico actuarial tradicional. El período de análisis va desde enero de 2011 hasta diciembre de 2012. Los resultados obtenidos muestran que el modelo de Black-Scholes, que se utiliza normalmente para valorar opciones financieras, puede ser también usado para la estimación de primas de reaseguros de salud; y que la prima neta estimada a partir de este modelo se aproxima a las establecidas por el método actuarial, excepto cuando el deducible del reaseguro es muy alto (por encima de \$200.000.000. 11. Sedimentary Facies Mapping Based on Tidal Channel Network and Topographic Features Science.gov (United States) Ryu, J. H.; Lee, Y. K.; Kim, K.; Kim, B. 2015-12-01 Tidal flats on the west coast of Korea suffer intensive changes in their surface sedimentary facies as a result of the influence of natural and artificial changes. Spatial relationships between surface sedimentary facies distribution and benthic environments were estimated for the open-type Ganghwa tidal flat and semi closed-type Hwangdo tidal flat, Korea. In this study, we standardized the surface sedimentary facies and tidal channel index of the channel density, distance, thickness and order. To extract tidal channel information, we used remotely sensed data, such as those from the Korea Multi-Purpose Satellite (KOMPSAT)-2, KOMPSAT-3, and aerial photographs. Surface sedimentary facies maps were generated based on field data using an interpolation method.The tidal channels in each sediment facies had relatively constant meandering patterns, but the density and complexity were distinguishable. The second fractal dimension was 1.7-1.8 in the mud flat, about 1.4 in the mixed flat, and about 1.3 in the sand flat. The channel density was 0.03-0.06 m/m2 in the mud flat and less than 0.02 m/m2 in the mixed and sand flat areas of the two test areas. Low values of the tidal channel index, which indicated a simple pattern of tidal channel distribution, were identified at areas having low elevation and coarse-grained sediments. By contrast, high values of the tidal channel index, which indicated a dendritic pattern of tidal channel distribution, were identified at areas having high elevation and fine-grained sediments. Surface sediment classification based on remotely sensed data must circumspectly consider an effective critical grain size, water content, local topography, and intertidal structures. 12. Teaching for Ethical Reasoning Science.gov (United States) Sternberg, Robert J. 2012-01-01 This article argues for the importance of teaching for ethical reasoning. Much of our teaching is in vain if it is not applied to life in an ethical manner. The article reviews lapses in ethical reasoning and the great costs they have had for society. It proposes that ethical reasoning can be taught across the curriculum. It presents an eight-step… 13. Inductive Reasoning and Writing Science.gov (United States) Rooks, Clay; Boyd, Robert 2003-01-01 Induction, properly understood, is not merely a game, nor is it a gimmick, nor is it an artificial way of explaining an element of reasoning. Proper understanding of inductive reasoning--and the various types of reasoning that the authors term inductive--enables the student to evaluate critically other people's writing and enhances the composition… 14. PRIMA-1Met/APR-246 induces apoptosis and tumor growth delay in small cell lung cancer expressing mutant p53 DEFF Research Database (Denmark) Zandi, Roza; Selivanova, Galina; Christensen, Camilla Laulund 2011-01-01 Small cell lung cancer (SCLC) is a highly malignant disease with poor prognosis, necessitating the need to develop new and efficient treatment modalities. PRIMA-1(Met) (p53-dependent reactivation of massive apoptosis), also known as APR-246, is a small molecule, which restores tumor suppressor...... function to mutant p53 and induces cancer cell death in various cancer types. Since p53 is mutated in more than 90% of SCLC, we investigated the ability of PRIMA-1(Met) to induce apoptosis and inhibit tumor growth in SCLC with different p53 mutations.... 15. Pengaruh Jenis Nasabah dan Frekuensi Pencairan Pembiayaan terhadap Profit Margin di Bank Pembiayaan Rakyat Syariah (BPRS Sarana Prima Mandiri Pamekasan Directory of Open Access Journals (Sweden) Sundari Aniga 2016-06-01 Full Text Available Bank is a financial institution whose main activities to collect funds and distribute funds to the community. Factors that very influence in the bank's success in obtaining profit is by increasing the disbursement frequency of financing and client’s types as one of the factors that influence the amount of profit margin obtained bank. Based on that, then there are two problems who became a study principal in this research as follows: first: Is there any influence of customer type and financing liquefaction frequency towards Profit Margin in BPRS Sarana Prima Mandiri Pamekasan; second, which is the most influential variable on the Profit Margin in BPRS Sarana Prima Mandiri Pamekasan. This Research uses a quantitative approach with research type is multiple linear regression. The amount of data used in this research as many as 20 data taken from published reports of Quarterly Bank Indonesia and published reports BPRS Sarana Prima Mandiri in January 2011 until December 2015. The research results of T Test of the respective T count X1 amounted to 3.184 and variable X2 amounted to 2.475 and T table amounted to 2.101, (X1 = 3.184> 2.101 and X2 = 2.475> 2.101, it can be concluded the results of the partial test (T test shows that all variables X (Customer type and financing liquefaction frequency effect on variable Y (Profit Margin partially significantly ≤ 0.05 X1 (Customer type greater influence than X2 (financing liquefaction frequency T count X1 greater exceeds X2. Equation Y = ( -16.387 0.399X1 + 0186 + X2 + e, based on multiple regression analysis, the regression coefficient obtained shows, customer type (b1 = 0.399 become the largest independent variables that influence Profit Margin (Y. While base testing the determinant coefficient using the program SPSS acquired adjusted R2 amounted to 0.732 or 73.2% means variable of Customer Type Financing and financing liquefaction frequency affect toward the profit margin amounted to 73.2% while the 16. MAPPING OF RESERVOIR PROPERTIES AND FACIES THROUGH INTEGRATION OF STATIC AND DYNAMIC DATA Energy Technology Data Exchange (ETDEWEB) Albert C. Reynolds; Dean S. Oliver; Fengjun Zhang; Yannong Dong; Jan Arild Skjervheim; Ning Liu 2003-01-01 Knowledge of the distribution of permeability and porosity in a reservoir is necessary for the prediction of future oil production, estimation of the location of bypassed oil, and optimization of reservoir management. But while the volume of data that can potentially provide information on reservoir architecture and fluid distributions has increased enormously in the past decade, it is not yet possible to make use of all the available data in an integrated fashion. While it is relatively easy to generate plausible reservoir models that honor static data such as core, log, and seismic data, it is far more difficult to generate plausible reservoir models that honor dynamic data such as transient pressures, saturations, and flow rates. As a result, the uncertainty in reservoir properties is higher than it could be and reservoir management can not be optimized. The goal of this project is to develop computationally efficient automatic history matching techniques for generating geologically plausible reservoir models which honor both static and dynamic data. Solution of this problem is necessary for the quantification of uncertainty in future reservoir performance predictions and for the optimization of reservoir management. Facies (defined here as regions of relatively uniform petrophysical properties) are common features of all reservoirs. Because the flow properties of the various facies can vary greatly, knowledge of the location of facies boundaries is of utmost importance for the prediction of reservoir performance and for the optimization of reservoir management. When the boundaries between facies are fairly well known, but flow properties are poorly known, the average properties for all facies can be determined using traditional techniques. Traditional history matching honors dynamic data by adjusting petrophysical properties in large areas, but in the process of adjusting the reservoir model ignores the static data and often results in implausible reservoir 17. Biostratigraphy, facies and sequence stratigraphy of the Sarvak Formation in the Ahwaz Oil Field, North Dezful Embayment Zone Directory of Open Access Journals (Sweden) 2016-08-01 Full Text Available Paleontological studies lead to recognition of 21 genera and 16 species of benthic foraminifera, 5 genera and 6 species of planktonic foraminifera and 3 genera and 3 species of oligosteginids. The vertical distribution of fauna lead to identification of 5 biozones including: Favusella washitensis Range Zone, Oligostegina Assemblage Zone, Rudist debris Zone, Nezzazata-Alveolinids Assemblage Zone, Nezzazatinella-Dicyclina Assemblage Zone. Based on the indicated biozones, the age of the Sarvak Formation is Late Albian to Early Turonian in the study area. Eleven carbonate facies belonging to four environments including tidal flat, restricted and semi-restricted lagoon, shoal and open marine are recognized. The identified facies are deposited on the homoclinal ramp setting. Based on the vertical changes of facies and recognized depositional environments, four third-order depositional sequences are represented. The transgressive systems tracts mainly comprises of open marine facies including sponge spicule, oligosteginid, echinoid and benthic foraminifera, while the highstand systems tracts mainly consists of shoal facies rich in bioclast, and restricted and semi-restricted lagoon facies rich in porcellaneous and hyaline benthic foraminifera and peloid. The maximum flooding surface represented by open marine facies including echinoid and planktonic foraminifera 18. Late Pleistocene dune-sourced alluvial fans in coastal settings: Sedimentary facies and related processes (Mallorca, Western Mediterranean) Science.gov (United States) Pomar, F.; del Valle, L.; Fornós, J. J.; Gómez-Pujol, L. 2018-05-01 Aeolian-alluvial sedimentary interaction results in the formation of deposits characterized by typical alluvial sedimentary structures, but is composed of conspicuous amounts of aeolian sediments. The literature on this topic is limited and most works relate more with continental aeolian dunes or fluvial dune interference with fan bodies. Furthermore, there is a lack of examples of aeolian-alluvial sedimentary interference in coastal settings. In the western Mediterranean, there are many Pleistocene alluvial fan deposits built up partly by sediment originating from coastal dunes dismantled by alluvial streams. Very often, these deposits show a continuous sedimentary sequence through which we can derive the contribution and predominance of coastal, alluvial-colluvial and aeolian processes and their controls on landscape formation. This is an outstanding feature within coastal systems since it shows marine sediments reworked and integrated within coastal dune fields by aeolian transport, and the latter built up into alluvial fan bodies. In this sense, aeolian-alluvial interaction is the geomorphic-sedimentary expression of the coexistence and overlapping of alluvial and aeolian environments resulting in deposits sharing sedimentary features from both environments. The aim of this paper is to unravel the contribution of coastal dunes in the construction of alluvial fans bodies and identify the main sedimentary facies that constitute these deposits, as well as their climatic controls. For this reason, Es Caló fan (northern Mallorca) has been selected due to its well-exposed deposits exhibiting the alternation of aeolian, alluvial and colluvial deposits. Sedimentological and stratigraphic analyses based on 33 logs and complementary analyses demonstrate that most of the facies constituting the fan body are made up completely of marine bioclastic sands. These deposits record an alluvial fan sedimentary environment characterized by sediments inputs that do not proceed 19. Public Reason Renaturalized DEFF Research Database (Denmark) Tønder, Lars 2014-01-01 . The article develops this argument via a sensorial orientation to politics that not only re-frames existing critiques of neo-Kantianism but also includes an alternative, renaturalized conception of public reason, one that allows us to overcome the disconnect between the account we give of reason and the way......This article takes up recent discussions of nature and the sensorium in order to rethink public reason in deeply divided societies. The aim is not to reject the role of reason-giving but rather to infuse it with new meaning, bringing the reasonable back to its sensorially inflected circumstances...... it is mobilized in a world of deep pluralism. The article concludes with a discussion of how a renaturalized conception of public reason might change the positioning of contemporary democratic theory vis-a-vis the struggle for empowerment and pluralization in an age of neo-liberalism and state-surveillance.... 20. Learning clinical reasoning. Science.gov (United States) Pinnock, Ralph; Welch, Paul 2014-04-01 Errors in clinical reasoning continue to account for significant morbidity and mortality, despite evidence-based guidelines and improved technology. Experts in clinical reasoning often use unconscious cognitive processes that they are not aware of unless they explain how they are thinking. Understanding the intuitive and analytical thinking processes provides a guide for instruction. How knowledge is stored is critical to expertise in clinical reasoning. Curricula should be designed so that trainees store knowledge in a way that is clinically relevant. Competence in clinical reasoning is acquired by supervised practice with effective feedback. Clinicians must recognise the common errors in clinical reasoning and how to avoid them. Trainees can learn clinical reasoning effectively in everyday practice if teachers provide guidance on the cognitive processes involved in making diagnostic decisions. © 2013 The Authors. Journal of Paediatrics and Child Health © 2013 Paediatrics and Child Health Division (Royal Australasian College of Physicians). 1. On quanta, mind, and matter: Hans Primas in Context. H. Atmanspacher, A. Amann, U. Müller-Herold (Eds), Kluwer, Boston, 1999, pp. 398 + viii, US192.00 £133.56 (hardback), ISBN 0-7923-5696-9 Science.gov (United States) Halvorson, Hans This book consists of a collection of 18 articles by students, colleagues, and friends of the theoretical chemist/philosopher of science, Hans Primas. Although the articles are written in honor of Primas, the editors state that the collection is not a Festschrift, but that it simply 'takes up some of the discussions that Primas has initiated or inspired' (p. 2). Due to the breadth of Primas' intellectual interests, the result is a highly eclectic collection of articles, whose topics range through (i) the historical development of experimental NMR spectroscopy, (ii) Jungian psychology, (iii) a defense of determinism in the rationalistic tradition of Leibniz, to (iv) a mathematical exposition of 'operator trigonometry.' However, since our space-and my expertise-is limited, the following comments will be restricted to those articles that deal with the mathematical and conceptual foundations of physics, a subject to which Primas has made a large contribution. 2. Metacognition and reasoning Science.gov (United States) Fletcher, Logan; Carruthers, Peter 2012-01-01 This article considers the cognitive architecture of human meta-reasoning: that is, metacognition concerning one's own reasoning and decision-making. The view we defend is that meta-reasoning is a cobbled-together skill comprising diverse self-management strategies acquired through individual and cultural learning. These approximate the monitoring-and-control functions of a postulated adaptive system for metacognition by recruiting mechanisms that were designed for quite other purposes. PMID:22492753 3. Felsic granulite with layers of eclogite facies rocks in the Bohemian Massif; did they share a common metamorphic history? Science.gov (United States) 2017-08-01 High pressure granulite and granulite gneiss from the Rychleby Mountains in the East Sudetes form an approximately 7 km long and 0.8 km wide body, which is enclosed by amphibolite facies orthogneiss with a steep foliation. Well preserved felsic granulite is located in the central part of the body, where several small bodies of mafic granulite are also present. In comparison to other high pressure granulites in the Bohemian Massif, which show strong mineral and textural re-equilibration under granulite facies conditions, the mafic granulite samples preserve eclogite facies minerals (garnet, omphacite, kyanite, rutile and phengite) and their field and textural relations indicate that both mafic and felsic granulites shared common metamorphic history during prograde eclogite facies and subsequent granulite facies events. Garnet from both granulite varieties shows prograde compositional zoning and contains inclusions of phengite. Yttrium and REEs in garnet show typical bell-shaped distributions with no annular peaks near the grain rims. Investigation of major and trace elements zoning, including REEs distribution in garnet, was combined with thermodynamic modelling to constrain the early eclogite facies metamorphism and to estimate pressure-temperature conditions of the subsequent granulite facies overprint. The first (U)HP metamorphism occurred along a low geothermal gradient in a subduction-related environment from its initial stage at 0.8 GPa/460 °C and reached pressures up to 2.5 GPa at 550 °C. The subsequent granulite facies overprint (1.6-1.8 GPa/800-880 °C) affected the rocks only partially; by replacement of omphacite into diopside + plagioclase symplectite and by compositional modification of garnet rims. The mineral textures and the preservation of the eclogite facies prograde compositional zoning in garnet cores confirm that the granulite facies overprint was either too short or too faint to cause recrystallisation and homogenisation of the eclogite 4. Mid amphibolite facies metamorphism of harzburgites in the Neoproterozoic Cerro Mantiqueiras Ophiolite, southernmost Brazil Directory of Open Access Journals (Sweden) HARTMANN LÉO A. 2003-01-01 Full Text Available Valuable information is retrieved from the integrated investigation of the field relationships, microstructure and mineral compositions of harzburgites from the Neoproterozoic Cerro Mantiqueiras Ophiolite. This important tectonic marker of the geological evolution of southernmost Brazilian Shield was thoroughly serpentinized during progressive metamorphism, because the oldest mineral assemblage is: olivine + orthopyroxene + tremolite + chlorite + chromite. This M1 was stabilized in mid amphibolite facies - 550-600ºC as calculated from mineral equilibria. No microstructural (e.g. ductile deformation of olivine or chromite or compositional (e.g. mantle spinel remnant of mantle history was identified. A metamorphic event M2 occurred in the low amphibolite facies along 100 m-wide shear zones, followed by intense serpentinization (M3 and narrow 1-3 m-wide shear zones (M4 containing asbestos. 5. Zircon ages in granulite facies rocks: decoupling from geochemistry above 850 °C? Science.gov (United States) Kunz, Barbara E.; Regis, Daniele; Engi, Martin 2018-03-01 Granulite facies rocks frequently show a large spread in their zircon ages, the interpretation of which raises questions: Has the isotopic system been disturbed? By what process(es) and conditions did the alteration occur? Can the dates be regarded as real ages, reflecting several growth episodes? Furthermore, under some circumstances of (ultra-)high-temperature metamorphism, decoupling of zircon U-Pb dates from their trace element geochemistry has been reported. Understanding these processes is crucial to help interpret such dates in the context of the P-T history. Our study presents evidence for decoupling in zircon from the highest grade metapelites (> 850 °C) taken along a continuous high-temperature metamorphic field gradient in the Ivrea Zone (NW Italy). These rocks represent a well-characterised segment of Permian lower continental crust with a protracted high-temperature history. Cathodoluminescence images reveal that zircons in the mid-amphibolite facies preserve mainly detrital cores with narrow overgrowths. In the upper amphibolite and granulite facies, preserved detrital cores decrease and metamorphic zircon increases in quantity. Across all samples we document a sequence of four rim generations based on textures. U-Pb dates, Th/U ratios and Ti-in-zircon concentrations show an essentially continuous evolution with increasing metamorphic grade, except in the samples from the granulite facies, which display significant scatter in age and chemistry. We associate the observed decoupling of zircon systematics in high-grade non-metamict zircon with disturbance processes related to differences in behaviour of non-formula elements (i.e. Pb, Th, U, Ti) at high-temperature conditions, notably differences in compatibility within the crystal structure. 6. Regional facies variations in the Vempalle formation of Cuddapah Basin: implications on uranium exploration International Nuclear Information System (INIS) Rajaraman, H.S.; Mukundhan, A.R.; Ramesh Kumar, K.; Achar, K.K.; Umamaheswar, K. 2012-01-01 Strata-bound large tonnage uranium deposit hosted by the Grey-impure-dolostone of Vempalle Formation of Cuddapah Basin is known in Tummalapalle-Rachakuntapalle sector. Deposition of rocks of Cuddapah Basin commenced with Papaghni Group, which comprises Clastic - Gulcheru Formation and Chemogenic - Vempalle Formation. The Vempalle Formation is developed over 280 km stretch from south to north along the western margin of Cuddapah Basin with maximum thickness of about 2.1 km. Recent studies helped in classifying the Vempalle Formation into five major lithofacies viz. Massive Dolostone, Conglomerate, Grey-impure-dolostone (host rock for uranium mineralization), Purple shale and Cherty Dolostone. The lithofacies studies along selected traverses from Tummalapalle in south to Dhone in north revealed the development of all five facies upto Narpala near Chitravati River whereas towards its north, the Grey-impure-dolostone and Cherty Dolostone dominate. The study also revealed over lapping nature of Cherty Dolostone in North of Nossam-Peddapaya lineament; where it directly rests above the Gulcheru Formation. Environment of deposition for these facies of Vempalle Formation place this in a Shallowing-upward carbonate depositional system with characteristic tidal flat environment. The Grey-impure-dolostone facies hosting uranium is interpreted to be developed in Supratidal environment with a narrow pH range of 7.0 - 7.5 in a reducing environment along with precipitation of phosphate. Since the tidal flats have later extension over several kilometers, favorable environment of Grey-impure-dolostone may exist over wide area in northern part also. The search for Grey-impure-dolostone hosted uranium, therefore has a bearing an understanding the regional facies variations in Vempalle Formation. The paper presents the studies carried out in this direction and results thereof. (author) 7. Facies and sedimentary series in the La Camocha Carboniferous, (Gijon, NW Spain) Energy Technology Data Exchange (ETDEWEB) Corrales, I; Flor, G; Pello, J; Peon, A 1985-01-01 The Carboniferous of La Camocha Mine consists mainly of terrigenous facies belonging to a fluvial-dominated delta system. Occasionally, as a consequence of avulsion, the area is abandoned by the distributary channels; it gives occasion for some quick marine transgression, the sediments of which being of carbonate character. This situation occurs in the lower part of the studied succession; the upper one is characterised only by sediments of the delta plain environments. 12 references. 8. The use of anion geochemistry in mapping groundwater facies in the ... African Journals Online (AJOL) The groundwater system of the Port Harcourt area is home to three anion facies, the Cl – SO4, the Cl – SO4 – HCO3 and the HCO3 – Cl – SO4. The first two types exist in both shallow – and deep – groundwater environments while the third is restricted to the deep environment. Although there are natural intermittent and, ... 9. Hypoxic resistance of KRAS mutant tumor cells to 3-Bromopyruvate is counteracted by Prima-1 and reversed by N-acetylcysteine. Science.gov (United States) Orue, Andrea; Chavez, Valery; Strasberg-Rieber, Mary; Rieber, Manuel 2016-11-18 The metabolic inhibitor 3-bromopyruvate (3-BrPA) is a promising anti-cancer alkylating agent, shown to inhibit growth of some colorectal carcinoma with KRAS mutation. Recently, we demonstrated increased resistance to 3-BrPA in wt p53 tumor cells compared to those with p53 silencing or mutation. Since hypoxic microenvironments select for tumor cells with diminished therapeutic response, we investigated whether hypoxia unequally increases resistance to 3-BrPA in wt p53 MelJuso melanoma harbouring (Q61L)-mutant NRAS and wt BRAF, C8161 melanoma with (G12D)-mutant KRAS (G464E)-mutant BRAF, and A549 lung carcinoma with a KRAS (G12S)-mutation. Since hypoxia increases the toxicity of the p53 activator, Prima-1 against breast cancer cells irrespective of their p53 status, we also investigated whether Prima-1 reversed hypoxic resistance to 3-BrPA. In contrast to the high susceptibility of hypoxic mutant NRAS MelJuso cells to 3-BrPA or Prima-1, KRAS mutant C8161 and A549 cells revealed hypoxic resistance to 3-BrPA counteracted by Prima-1. In A549 cells, Prima-1 increased p21CDKN1mRNA, and reciprocally inhibited mRNA expression of the SLC2A1-GLUT1 glucose transporter-1 and ALDH1A1, gene linked to detoxification and stem cell properties. 3-BrPA lowered CAIX and VEGF mRNA expression. Death from joint Prima-1 and 3-BrPA treatment in KRAS mutant A549 and C8161 cells seemed mediated by potentiating oxidative stress, since it was antagonized by the anti-oxidant and glutathione precursor N-acetylcysteine. This report is the first to show that Prima-1 kills hypoxic wt p53 KRAS-mutant cells resistant to 3-BrPA, partly by decreasing GLUT-1 expression and exacerbating pro-oxidant stress. 10. Hydrothermal dolomite reservoir facies in the Sinian Dengying Fm, central Sichuan Basin Directory of Open Access Journals (Sweden) Yuqiang Jiang 2017-07-01 Full Text Available The Upper Sinian Dengying Fm is the focus of natural gas exploration in the central part of the Sichuan Basin (central Sichuan Basin in recent years. Especially, epigenic karstification and its resulted reservoir-seepage spaces have always been the focal points in researches. Based on the petrographic characteristics of drilling cuttings and core samples, and through experimental analysis by using trace elements, isotopes, and cathodoluminescence, the Dengying Fm dolomite was demonstrated to have matrix recrystallized dolomite (MRD, filled saddle dolomite (FSD (the mean homogenization temperature of inclusion: 178.5 °C, high concentrations of Fe & Mn, slightly positive 87Sr/86Sr value and hydrothermal minerals combination (including sphalerite, galena, pyrite, and quartz, etc.. Thus, it was proposed that hydrothermal dolomite reservoir facies (HDRF exist in the Dengying Fm dolomite, in other words, the dolomite reservoir is composed of hydrothermal dissolved pores, intercrystalline pores of hydrothermal origin, hydrothermal caverns and expanded fractures, and was formed due to the reworking of hydrothermal fluid on tight matrix dolomite. Identification marks are presented in terms of petrography and geochemistry so that hydrothermal dolomite reservoir facies can be effectively recognized and identified. It is concluded that the development of hydrothermal dolomite reservoir facies in this area are preliminary controlled by deep and large basement faults and the strength of hydrothermal fluids. 11. Tacuari formation (Nov. Nom.): Lithostratigraphy, facies, environment, age and geological significance (Cerro Largo - Uruguay) International Nuclear Information System (INIS) Veroslavsky, G.; De Santa Ana, H.; Daners, G. 2006-01-01 The definition of the Tacuari formation is proposed to group a set of glacial and fossiliferous siliciclastic rock deposited during the Upper proterozoic in the northeast of Uruguay. Up to this paper these lithologies were included in the San Gregorio formation (Carboniferous - Permian - Norte Basin). However, Leiosphaeridia tenuissima, L, minutissima, Myxcocooides distola, M, siderophila, Soldadophycus bossil and S. major were recorded in these rocks.This finded motivated the accomplishment of geological surveys that allowed to ferify the glacial origin of the Tacuari formation, to define its stratigraphic relationships and to corroborate its affectation by the Sierra Ballena shear zone. Two association of facies were recognized in the Tacuari formation: the base is represented by facies association A (outwash plains), characterized diamictites, sandostones and pelites; at the top, the facies association B (glaciomarine) includes a package of rhythmites with dropstones. On account of the tectonic setting, nature of sedimentation, age, and fossils, the definition of Tacuari formation constitutes a novel contribution to the regional evolutionary model of the Upper proterozoic. discussion of posible stratigraphc correlations with other neoproterozoic units of Western wondwana is also attempted 12. Intuition, Reason, and Metacognition Science.gov (United States) Thompson, Valerie A.; Prowse Turner, Jamie A.; Pennycook, Gordon 2011-01-01 Dual Process Theories (DPT) of reasoning posit that judgments are mediated by both fast, automatic processes and more deliberate, analytic ones. A critical, but unanswered question concerns the issue of monitoring and control: When do reasoners rely on the first, intuitive output and when do they engage more effortful thinking? We hypothesised… OpenAIRE Meyer, J.-J. 2004-01-01 In this paper we discuss the role of emotions in artificial agent design, and the use of logic in reasoning about the emotional or affective states an agent can reside in. We do so by extending the KARO framework for reasoning about rational agents appropriately. In particular we formalize in this framework how emotions are related to the action monitoring capabilities of an agent. 14. Clinical reasoning: concept analysis. Science.gov (United States) Simmons, Barbara 2010-05-01 This paper is a report of a concept analysis of clinical reasoning in nursing. Clinical reasoning is an ambiguous term that is often used synonymously with decision-making and clinical judgment. Clinical reasoning has not been clearly defined in the literature. Healthcare settings are increasingly filled with uncertainty, risk and complexity due to increased patient acuity, multiple comorbidities, and enhanced use of technology, all of which require clinical reasoning. Data sources. Literature for this concept analysis was retrieved from several databases, including CINAHL, PubMed, PsycINFO, ERIC and OvidMEDLINE, for the years 1980 to 2008. Rodgers's evolutionary method of concept analysis was used because of its applicability to concepts that are still evolving. Multiple terms have been used synonymously to describe the thinking skills that nurses use. Research in the past 20 years has elucidated differences among these terms and identified the cognitive processes that precede judgment and decision-making. Our concept analysis defines one of these terms, 'clinical reasoning,' as a complex process that uses cognition, metacognition, and discipline-specific knowledge to gather and analyse patient information, evaluate its significance, and weigh alternative actions. This concept analysis provides a middle-range descriptive theory of clinical reasoning in nursing that helps clarify meaning and gives direction for future research. Appropriate instruments to operationalize the concept need to be developed. Research is needed to identify additional variables that have an impact on clinical reasoning and what are the consequences of clinical reasoning in specific situations. 15. Specification of Nonmonotonic Reasoning. NARCIS (Netherlands) Engelfriet, J.; Treur, J. 2000-01-01 Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first Level is defined semantically by the notion of belief state frame, the second Level by the notion of reasoning frame. We introduce two specification languages to 16. Specification of Nonmonotonic Reasoning NARCIS (Netherlands) Engelfriet, J.; Treur, J. 1996-01-01 Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first level is defined semantically by the notion of belief state frame, the second level by the notion of reasoning frame. We introduce two specification languages to 17. Measuring Relational Reasoning Science.gov (United States) Alexander, Patricia A.; Dumas, Denis; Grossnickle, Emily M.; List, Alexandra; Firetto, Carla M. 2016-01-01 Relational reasoning is the foundational cognitive ability to discern meaningful patterns within an informational stream, but its reliable and valid measurement remains problematic. In this investigation, the measurement of relational reasoning unfolded in three stages. Stage 1 entailed the establishment of a research-based conceptualization of… 18. Predicting Reasoning from Memory Science.gov (United States) Heit, Evan; Hayes, Brett K. 2011-01-01 In an effort to assess the relations between reasoning and memory, in 8 experiments, the authors examined how well responses on an inductive reasoning task are predicted from responses on a recognition memory task for the same picture stimuli. Across several experimental manipulations, such as varying study time, presentation frequency, and the… 19. A reasonable Semantic Web NARCIS (Netherlands) Hitzler, Pascal; Van Harmelen, Frank 2010-01-01 The realization of Semantic Web reasoning is central to substantiating the Semantic Web vision. However, current mainstream research on this topic faces serious challenges, which forces us to question established lines of research and to rethink the underlying approaches. We argue that reasoning for 20. Model-Based Reasoning Science.gov (United States) Ifenthaler, Dirk; Seel, Norbert M. 2013-01-01 In this paper, there will be a particular focus on mental models and their application to inductive reasoning within the realm of instruction. A basic assumption of this study is the observation that the construction of mental models and related reasoning is a slowly developing capability of cognitive systems that emerges effectively with proper… NARCIS (Netherlands) Meyer, J.-J. In this paper we discuss the role of emotions in artificial agent design, and the use of logic in reasoning about the emotional or affective states an agent can reside in. We do so by extending the KARO framework for reasoning about rational agents appropriately. In particular we formalize in 2. Sedimentary facies and evolution of the upper member of cretaceou Sunjiawan formation in Heishui area of western Liaoning International Nuclear Information System (INIS) Zhao Zhonghua; Xi Haiyin; Chen Debing; Wang Liming; Rao Minghui 2010-01-01 The upper member of Sunjiawan formation in Heishui area is mainly alluvial fan facies. From the macroscopic view, alluvial fan facies can be divided into three sub-facies of proximal end gravel braided plain, distal end gravel braided plain and pre-fan flood-plain and further into some micro-facies of debris flow, gravel braided channel, gravel dam, flood-fine and peat bog etc. The upper member of Sunjiawan formation could be divided into three sub-members. The first sub-member is retrograding dry land type fan sediment under drought-humid climate. The second sub-member is retrograding wet land type fan deposit under humid climate. Third sub-member is progradational wetland type fan sediments under humid climate. Sunjiawan formation in Heishui area experienced three evolutionary stages: the early retrograding dryland type fan deposition, the medium term retrograding wet land type fan deposition and the later progradational wetland type fan. (authors) 3. The identification of provenance-controlled facies by geochemical methods on a portion of the Vaal Reef, Klerksdorp Goldfield International Nuclear Information System (INIS) Henckel, J.; Schweitzer, J.K.; Horsch, H. 1990-01-01 The use of geochemical methods for identifying provenance controlled facies in Witwatersrand reefs is considered. Three methods - whole rock geochemistry, zircon analysis, and chromite analysis - have been evaluated in order to establish the feasibility of using these geochemical techniques. An area of Vaal Reef where two sedimentological facies with distinct gold distributions had previously been identified was investigated. The studies reported here gave evidence of differences in the source areas for these two facies. Accordingly, it is concluded that the application of geochemistry to identify provenance-controlled facies is a useful technique which can help geologists arrive at a better interpretation of depositional systems within Witwatersrand reefs and thereby assist in the understanding of gold distribution patterns. 26 refs., 11 figs., 4 tabs 4. Clay mineral facies and lateritization in basalts of the southeastern Parana Basin, Brazil International Nuclear Information System (INIS) Oliveira, M.T.G. de; Formoso, M.L.L.; Trescases, J.J.; Meunier, A. 1998-01-01 Seventeen samples from two lateritic profiles, each with five facies, were studied. These profiles occur on the old planation surface of the plateau basalts of the southern part of ParanáBasin, Brazil. Optical microscopy, X-ray diffraction, electron microprobe, Mössbauer spectroscopy and Fourier Transform Infrared Spectra were used to obtain information about the nature and chemical composition of each weathering facies. In addition, scanning electron microscopy and analyses of clay minerals were performed to detect microcrystalline environmental changes. Both profiles have two major parts: a loose red-clay latosol separated from an underlying mottled clay and an alterite facies; a stone line may or may not be present between the latosol and the underlying units. In both profiles the latosol consists principally of kaolinite, hematite and goethite. Two alterite facies, shaped by differential weathering, are also present in the lower profile: a halloysite–nontronite clayey matrix with a well developed fissure system occurs in the argillaceous alterite and a network of Al–goethite aggregates is typical of the highly porous cortex of the boulder alterite that is found in the stone line and below it. Gibbsite has crystallized in the large pores of porphyritic boulder alterite but is absent in the small pores of the subaphyric boulder alterite. Clay minerals observed in fissures include halloysite associated with goethite and manganese oxides. The basalt has hydrothermal green-clays (mixed layers and trioctahedral smectites) that formed between primary plagioclase, pyroxene and Ti–magnetite crystals while fresh corestones of the boulder alterite have cryptocrystalline iron-rich material. The study of these profiles shows one principal evolutionary trend for clay minerals. This trend is from smectite and mixed layers that form green clays in altered bedrock at the base of the profile to an intermediate association of nontronite and halloysite in the argillaceous 5. Facies analysis of an Upper Jurassic carbonate platform for geothermal reservoir characterization Science.gov (United States) von Hartmann, Hartwig; Buness, Hermann; Dussel, Michael 2017-04-01 The Upper Jurassic Carbonate platform in Southern Germany is an important aquifer for the production of geothermal energy. Several successful projects were realized during the last years. 3D-seismic surveying has been established as a standard method for reservoir analysis and the definition of well paths. A project funded by the federal ministry of economic affairs and energy (BMWi) started in 2015 is a milestone for an exclusively regenerative heat energy supply of Munich. A 3D-seismic survey of 170 square kilometer was acquired and a scientific program was established to analyze the facies distribution within the area (http://www.liag-hannover.de/en/fsp/ge/geoparamol.html). Targets are primarily fault zones where one expect higher flow rates than within the undisturbed carbonate sediments. However, since a dense net of geothermal plants and wells will not always find appropriate fault areas, the reservoir properties should be analyzed in more detail, e.g. changing the viewpoint to karst features and facies distribution. Actual facies interpretation concepts are based on the alternation of massif and layered carbonates. Because of successive erosion of the ancient land surfaces, the interpretation of reefs, being an important target, is often difficult. We found that seismic sequence stratigraphy can explain the distribution of seismic pattern and improves the analysis of different facies. We supported this method by applying wavelet transformation of seismic data. The splitting of the seismic signal into successive parts of different bandwidths, especially the frequency content of the seismic signal, changed by tuning or dispersion, is extracted. The combination of different frequencies reveals a partition of the platform laterally as well as vertically. A cluster analysis of the wavelet coefficients further improves this picture. The interpretation shows a division into ramp, inner platform and trough, which were shifted locally and overprinted in time by other 6. The potential role of fluids during regional granulite-facies dehydration in the lower crust Directory of Open Access Journals (Sweden) Daniel E. Harlov 2012-11-01 Full Text Available High-grade dehydration of amphibolite-facies rocks to granulite-facies is a process that can involve partial melting, fluid-aided solid-state dehydration, or varying degrees of both. On the localized meter scale, solid-state dehydration, due to CO2-rich fluids traveling along some fissure or crack and subsequently outwards along the mineral grain boundaries of the surrounding rock, normally is the means by which the breakdown of biotite and amphibole to orthopyroxene and clinopyroxene occur. Various mineral textures and changes in mineral chemistry seen in these rocks are also seen in more regional orthopyroxene-clinopyroxene-bearing rocks which, along with accompanying amphibolite-facies rocks, form traverses of lower crust. This suggests that solid-state dehydration during high-grade metamorphism could occur on a more regional scale. The more prominent of these fluid-induced textures in the granulite-facies portion of the traverse take the form of micro-veins of K-feldspar along quartz grain boundaries and the formation of monazite inclusions in fluorapatite. The fluids believed responsible take the form of concentrated NaCl- and KCl- brines from a basement ultramafic magma heat source traveling upwards along grain boundaries. Additional experimental work involving CaSO4 dissolution in NaCl-brines, coupled with natural observation of oxide and sulfide mineral associations in granulite-facies rocks, have demonstrated the possibility that NaCl-brines, with a CaSO4 component, could impose the oxygen fugacity on these rocks as opposed to the oxygen fugacity being inherent in their protoliths. These results, taken together, lend credence to the idea that regional chemical modification of the lower crust is an evolutionary process controlled by fluids migrating upwards from the lithospheric mantle along grain boundaries into and through the lower crust where they both modify the rock and are modified by it. Their presence allows for rapid mass and 7. 27 CFR 70.206 - Discharge of liens; redemption by United States. Science.gov (United States) 2010-04-01 ... this section, shall constitute prima facie evidence of the regularity of the redemption. When a... include the amount of the obligation secured by such lien to the extent legally satisfied by reason of the... obligation secured by such lien to the extent legally satisfied by reason of the sale and (B) Any additional... 8. Facies and depositional model of Almada Canyon, Almada Basin, Bahia, Brazil; Facies e modelo deposicional do Canyon de Almada, Bacia de Almada, Bahia Energy Technology Data Exchange (ETDEWEB) D' Avila, Roberto Salvador Francisco; Souza Cruz, Carlos Emanoel de; Oliveira Filho, Jose Souto; Jesus, Candida Menezes de; Cesero, Pedro de; Dias Filho, Dorval Carvalho; Lima, Claudio Coelho de; Queiroz, Claudia Lima de; Santos, Saulo Ferreira; Ferreira, Eduardo Araripe [PETROBRAS, Santos, SP (Brazil). Unidade de Negocio de Exploracao]. E-mail: [email protected] 2004-11-01 In the continental portion of the Almada Basin outcrops of canyon filling deposits are represented by turbidite channels and associated facies from Urucutuca Formation. The canyon - semi-exhumated - eroded basement and pre-Cenomanian sedimentary rocks. The field study of the outcrops and cores obtained in adjacent perforations lead to the understanding of the facies and processes that controlled the deposition of these channeled turbidite that can be compared to the reservoirs of many oil fields in Brazil. The Almada canyon is a submarine conduct of tectonic origin that was enlarged by the repeated passing of turbidity currents. During the rift phase and the Albian period, compressive events reactivated old N E and N W faults in the basement as trans current fault systems. The continuation of these stresses, from the Cenomanian to the Maastrichtian, developed normal faults that controlled a submarine canyon that connected the continent, where an estuary was formed between the mountains, to the deep marine region of the basin. The canyon has received sediments brought by catastrophic fluvial floods coming from the surrounding mountains, which formed hyperpicnal flows that have evolved as turbidity currents, thus causing erosion of the substrate and carrying a huge volume of sediments to the basin. A part of that load was deposited in the canyon and formed turbidite channels filled by conglomerates, sandstones and shales. These moderately to highly efficient turbidite are intercalated to pro delta pelites and low density turbid plumes deposits, which have mostly been re mobilized as slump and debris flows (chaotic deposits). Pelites were accumulated mainly in the normal fluvial sedimentation phases, when the sandy sediment was retained next to the canyon head and were reworked by the tides on the upper part of the estuary. (author) 9. Figuraciones de la escritura de un a opera prima en la obra de César Aira Directory of Open Access Journals (Sweden) Graciela Villanueva 2012-10-01 Full Text Available Una de las formas que adopta la reflexión sobre los comienzos en la obra de César Aira es la figuración de la escritura de una opera prima. Los escritores noveles aparecen ya en la ficción airiana de los años 90 (en El volante, por ejemplo, pero su frecuencia aumenta en las novelas de la década siguiente (Varamo, El mago, Parménides, La vida nueva. Por muy distintos que sean los protagonistas de todas estas novelas, los planteos que surgen al narrar cómo cada uno de ellos se convierte en escritor guardan una estrecha relación con la poética del propio César Aira. La figuración de la escritura de una opera prima prolonga y completa una reflexión ya iniciada anteriormente, por ejemplo en el diálogo que las primeras novelas de Aira entablan con los textos fundadores de la literatura argentina, en el diálogo con el Génesis bíblico propuesto por El congreso de literatura y en las páginas que El vestido rosa consagra a la cuestión del comienzo de la ficción, páginas que Diario de la hepatitis y Fragmento de un diario en los Alpes desarrollan y enriquecen en las décadas siguientes.La figuration de l’écriture d’une opera prima est une des formes adoptées par la réflexion sur le commencement dans la fiction de de César Aira. Les écrivains débutants apparaissent déjà dans les romans des années 90 (dans Le prospectus, par exemple, mais leur fréquence augmente dans les romans des années 2000 (Varamo, Le magicien, Parménide, La vie nouvelle. Les héros de tous ces romans ont beau être très différents, les idées qui naissent du récit de la manière dont ils ont commencé à écrire sont étroitement liées à la poétique de César Aira. La figuration de l’écriture d’une première œuvre prolonge et complète une réflexion que Aira avait entamée à travers le dialogue que ses premiers romans établissent avec les textes fondateurs de la littérature argentine, à travers le dialogue entre le Livre biblique de 10. Upper Cretaceous chalk facies and depositional history recorded in the Mona-1 core, Mona Ridge, Danish North Sea Directory of Open Access Journals (Sweden) Finn Surlyk 2011-12-01 Full Text Available The 331 m long core from the Mona-1 well in the Danish North Sea spans almost the entire Upper Cretaceous Chalk Group but only about 10% of Late Cretaceous time is represented. The succession comprises 14 facies representing pelagic deposition, turbidity flow, and mass-transport processes, including mudflow, debris flow, and slumping. Pelagic deposits vary mainly in terms of the concentration of siliciclastic material, the trace-fossil assemblage, and the presence or ab¬sence of primary sedimentary structures. Pelagic sedimentation was probably punctuated by the deposition of thin turbidites, and the resultant deposits were thoroughly bioturbated if deposited during normal oxygenation at the sea floor. Periodic benthic dysoxia resulted in the preservation of primary structures, as represented by laminated chalk which consists of thin pelagic laminae alternating with thin turbidites. In addition to the thin turbidites in the laminated chalk, four dif¬ferent turbidite facies are interpreted as representing high- to low-energy flows. Clast-supported chalk conglomerates have previously not been differentiated from other turbidites, but are here interpreted to be directly related to the down-slope evolution of debris flows. Debris flows are rep¬resented by matrix-supported conglomerates, which form one of the most common facies in the succession. High-concentration, gravity-driven suspension flows passed into dilute visco-plastic flows during the final stages of deposition and resulted in the deposition of structureless chalks. Limited shear deformation produced distinct quasi-facies from which the precursor facies can be deduced, whereas intense or continued shear deformation produced a shear-banded quasi-facies from which the precursor facies cannot be deduced in all cases. A series of major slump packages (14–18 in total are interpreted, forming over 40% of the succession; debrites appear to be the most common precursor facies involved in 11. Upper Cretaceous chalk facies and depositional history recorded in the Mona-1 core, Mona Ridge, Danish North Sea: Plate 1 Directory of Open Access Journals (Sweden) Surlyk, Finn 2011-12-01 Full Text Available The 331 m long core from the Mona-1 well in the Danish North Sea spans almost the entire Upper Cretaceous Chalk Group but only about 10% of Late Cretaceous time is represented. The succession comprises 14 facies representing pelagic deposition, turbidity flow, and mass-transport processes, including mudflow, debris flow, and slumping. Pelagic deposits vary mainly in terms of the concentration of siliciclastic material, the trace-fossil assemblage, and the presence or ab¬sence of primary sedimentary structures. Pelagic sedimentation was probably punctuated by the deposition of thin turbidites, and the resultant deposits were thoroughly bioturbated if deposited during normal oxygenation at the sea floor. Periodic benthic dysoxia resulted in the preservation of primary structures, as represented by laminated chalk which consists of thin pelagic laminae alternating with thin turbidites. In addition to the thin turbidites in the laminated chalk, four dif¬ferent turbidite facies are interpreted as representing high- to low-energy flows. Clast-supported chalk conglomerates have previously not been differentiated from other turbidites, but are here interpreted to be directly related to the down-slope evolution of debris flows. Debris flows are rep¬resented by matrix-supported conglomerates, which form one of the most common facies in the succession. High-concentration, gravity-driven suspension flows passed into dilute visco-plastic flows during the final stages of deposition and resulted in the deposition of structureless chalks. Limited shear deformation produced distinct quasi-facies from which the precursor facies can be deduced, whereas intense or continued shear deformation produced a shear-banded quasi-facies from which the precursor facies cannot be deduced in all cases. A series of major slump packages (14–18 in total are interpreted, forming over 40% of the succession; debrites appear to be the most common precursor facies involved in 12. Recent benthic foraminifera and sedimentary facies distribution of the Abu Dhabi (United Arab Emirates) coastline Science.gov (United States) Fiorini, Flavia; Lokier, Stephen W. 2014-05-01 The distribution of benthic foraminifera and sedimentary facies from Recent coastline environments adjacent to the coastline of Abu Dhabi (UAE) was studied in detail with the aim to: 1) provide reliable analogs for understanding and interpreting the depositional environment of ancient shallow-marine sediments from the UAE; 2) assess any modifications in the distribution of benthic environments and sedimentary facies in an area affected by significant anthropogenic activities - particular construction and land reclamation. A total of 100 sea-floor sediment samples were collected in different shallow-marine sedimentary environments (nearshore shelf, beach-front, channels, ooid shoals, lagoon and mangals) close to the coastline of Abu Dhabi Island. Where possible, we revisited the sampling sites used in several studies conducted in the middle of last century (prior to any significant anthropogenic activities) to assess temporal changes in Recent benthic foraminifera and sedimentary facies distribution during the last 50 years. Five foraminiferal assemblages were recognized in the studied area. Species with a porcellaneous test mainly belonging to the genera Quinqueloculina, Triloculina, Spiroloculina, Sigmoilinita are common in all studied areas. Larger benthic foraminifera Peneroplis and Spirolina are particularly abundant in samples collected on seaweed. Hyaline foraminifera mostly belonging to the genera Elphidium, Ammonia, Bolivina and Rosalina are also common together with Miliolidae in the nearshore shelf and beach front. Agglutinated foraminifera (Clavulina, Textularia, Ammobaculites and Reophax) are present in low percentages. The species belonging to the genera Ammobaculites and Reophax are present only in the finest grain samples particularly in lagoons and mangal environments and have not been reported previously in the studied area. The majority of the ooid shoal sediments, the coarser sediments of the beach-front and samples collected in dredged channels 13. The Archaen volcanic facies in the Migori segment, Nyanza greenstone belt, Kenya: stratigraphy, geochemistry and mineralisation Science.gov (United States) Ichang'l, D. W.; MacLean, W. H. The Migori segment is an 80 by 20 km portion of the Nyanza greenstone belt which forms the northern part of the Archean Tanzanian Craton in western Kenya, northern Tanzania and southeastern Uganda. It consists of two volcanic centres, each with central, proximal and distal volcanic facies, comprising the Migori Group, the Macalder and Lolgorien Subgroups, and eleven volcano-sedimentary formations. The centres are separated by a basin of tuffs and greywacke turbidites. The volcanics are bimodal mafic basalt and dolerite ( Zr/Y = 3.8 - 6.5, La N/Yb N = 1.0 - 2.4) , and felsic calc-alkaline dacite-rhyolite ( Zr/Y = 10 - 21, La N/Yb N = 19 - 42 ) and high-K dacite ( Zr/Y = 9 - 16, La N/Yb N = 21 - 22 ). Felsic units form approximately three-fourths of the volcanic stratigraphy. Basalts, calc-alkaline dacites and rhyolites were deposited in a submarine environment, but the voluminous high-K dacites were erupted subaerially. The turbidites contain units of iron-formations. Granitic intrusions are chemically continuous with the high-K dacites. The felsic volcanics are anologous to those found at modern volcanic arc subduction settings involving continental crust. The Macalder ZnCuAuAg volcanogenic massive sulphide deposits is in central facies basalts-greywacke-rhyolite. Gold mineralisation occurs in proximal facies tuffs and iron formation, and in oblique and semi-conformable quartz veins. Greenstones in the Nyanza belt are dominated by calc-alkaline felsic volcanics in constrast to the komatiite-tholeiitic basalt volcanism in the Kaapvaal Craton of South Africa, and a mixture of the two types in the Zimbabwe Craton. 14. Science Teachers' Analogical Reasoning Science.gov (United States) Mozzer, Nilmara Braga; Justi, Rosária 2013-08-01 Analogies can play a relevant role in students' learning. However, for the effective use of analogies, teachers should not only have a well-prepared repertoire of validated analogies, which could serve as bridges between the students' prior knowledge and the scientific knowledge they desire them to understand, but also know how to introduce analogies in their lessons. Both aspects have been discussed in the literature in the last few decades. However, almost nothing is known about how teachers draw their own analogies for instructional purposes or, in other words, about how they reason analogically when planning and conducting teaching. This is the focus of this paper. Six secondary teachers were individually interviewed; the aim was to characterize how they perform each of the analogical reasoning subprocesses, as well as to identify their views on analogies and their use in science teaching. The results were analyzed by considering elements of both theories about analogical reasoning: the structural mapping proposed by Gentner and the analogical mechanism described by Vosniadou. A comprehensive discussion of our results makes it evident that teachers' content knowledge on scientific topics and on analogies as well as their pedagogical content knowledge on the use of analogies influence all their analogical reasoning subprocesses. Our results also point to the need for improving teachers' knowledge about analogies and their ability to perform analogical reasoning. 15. Calvin on Human Reason Directory of Open Access Journals (Sweden) Nicolaas Vorster 2014-10-01 Full Text Available In his recent book The Unintended Reformation, Brad Gregory makes the statement that the Reformation replaced the teleological social ethics of Roman Catholicism based on virtue with formal social ethics based on rules and enforced by magistrates, because they regarded human reason as too depraved to acquire virtue. The result, according to Gregory, is that the relation between internalised values and rules were undermined. This article asks whether this accusation is true with regard to Calvin. The first section discusses the intellectual environment of Calvin’s day – something that inevitably influenced his theory on reason, whilst the second part analyses Calvin’s view on the created nature of reason. The third section investigates Calvin’s view on the effects of sin on reason; and the fourth section discusses Calvin’s perspective on the relation between grace and reason. The article concludes that Gregory’s accusation against the Reformation is not applicable to Calvin. Gregory fails to take into account Calvin’s modified position that the imago Dei was not totally destroyed by sin as well as his teaching on common grace that maintains that even non-believers are able to acquire virtue through the common grace of God. 16. Coralgal facies of the Upper Eocene-Lower Oligocene limestones in Letca-Rastoci area Directory of Open Access Journals (Sweden) Ioana Prica 2001-09-01 Full Text Available In this paper are described the coralgal facies identified in the Upper Eocene-Lower Oligocene limestone succession (Cozla Formation outcropping in two quarries at Letca and Rastoci (Sălaj district, Romania. In the studied profiles the coral and algae limestones are interlayered with bioclastic limestones with foraminifera. On the top of relatively deep water deposits, coral and algae crusts and dendritic corals coated by algae were deposited. The environment registered a gradual deepening, the deposits being completely immersed, while bioclastic limestones with foraminifera were recurrently formed. This cycle is repeated, the whole succession being caracterized by several such “parasequences”. 17. Fluid heterogeneity during granulite facies metamorphism in the Adirondacks: stable isotope evidence Science.gov (United States) Valley, J.W.; O'Neil, J.R. 1984-01-01 The preservation of premetamorphic, whole-rock oxygen isotope ratios in Adirondack metasediments shows that neither these rocks nor adjacent anorthosites and gneisses have been penetrated by large amounts of externally derived, hot CO2-H2O fluids during granulite facies metamorphism. This conclusion is supported by calculations of the effect of fluid volatilization and exchange and is also independently supported by petrologic and phase equilibria considerations. The data suggest that these rocks were not an open system during metamorphism; that fluid/rock ratios were in many instances between 0.0 and 0.1; that externally derived fluids, as well as fluids derived by metamorphic volatilization, rose along localized channels and were not pervasive; and thus that no single generalization can be applied to metamorphic fluid conditions in the Adirondacks. Analyses of 3 to 4 coexisting minerals from Adirondack marbles show that isotopic equilibrium was attained at the peak of granulite and upper amphibolite facies metamorphism. Thus the isotopic compositions of metamorphic fluids can be inferred from analyses of carbonates and fluid budgets can be constructed. Carbonates from the granulite facies are on average, isotopically similar to those from lower grade or unmetamorphosed limestones of the same age showing that no large isotopic shifts accompanied high grade metamorphism. Equilibrium calculations indicate that small decreases in ??18O, averaging 1 permil, result from volatilization reactions for Adirondack rock compositions. Additional small differences between amphibolite and granulite facies marbles are due to systematic lithologie differences. The range of Adirondack carbonate ??18O values (12.3 to 27.2) can be explained by the highly variable isotopic compositions of unmetamorphosed limestones in conjunction with minor 18O and 13C depletions caused by metamorphic volatilization suggesting that many (and possibly most) marbles have closely preserved their 18. Verdine and glaucony facies from surficial sediments of the eastern continental margin of India Digital Repository Service at National Institute of Oceanography (India) Rao, V.P.; Thamban, M.; Lamboy, M. -trioctahedral Fe-rich 1:l clay mineral. Clay Miner., 23: 237-247. Murthy, K.S.R., 1989. Seismic stratigraphy of Ongole-Paradip continental shelf East coast of India. Indian J. Mar. Sci., 16: 47-58. Murthy, K.S.R., Rao, T.C.S., Subramanyam, AS., Rao, M... at the continent- ocean boundary: the verdine facies. Clay Miner. 25: 477-483. Rao, K.M. and Rao, T.C.S., 1994. Holocene sea levels of Visakhapatnam shelf, East Coast of India. J. Geol. Sot. India, 44: 685-689. Rao, V.P., 1991. Clay mineral distribution... 19. Reasons Internalism and the function of normative reasons OpenAIRE Sinclair, Neil 2017-01-01 What is the connection between reasons and motives? According to Reasons Internalism there is a non-trivial conceptual connection between normative reasons and the possibility of rationally accessing relevant motivation. Reasons Internalism is attractive insofar as it captures the thought that reasons are for reasoning with and repulsive insofar as it fails to generate sufficient critical distance between reasons and motives. Rather than directly adjudicate this dispute, I extract from it two... 20. Causal reasoning in physics CERN Document Server Frisch, Mathias 2014-01-01 Much has been written on the role of causal notions and causal reasoning in the so-called 'special sciences' and in common sense. But does causal reasoning also play a role in physics? Mathias Frisch argues that, contrary to what influential philosophical arguments purport to show, the answer is yes. Time-asymmetric causal structures are as integral a part of the representational toolkit of physics as a theory's dynamical equations. Frisch develops his argument partly through a critique of anti-causal arguments and partly through a detailed examination of actual examples of causal notions in physics, including causal principles invoked in linear response theory and in representations of radiation phenomena. Offering a new perspective on the nature of scientific theories and causal reasoning, this book will be of interest to professional philosophers, graduate students, and anyone interested in the role of causal thinking in science. 1. Training propositional reasoning. Science.gov (United States) Klauer, K C; Meiser, T; Naumer, B 2000-08-01 Two experiments compared the effects of four training conditions on propositional reasoning. A syntactic training demonstrated formal derivations, in an abstract semantic training the standard truth-table definitions of logical connectives were explained, and a domain-specific semantic training provided thematic contexts for the premises of the reasoning task. In a control training, an inductive reasoning task was practised. In line with the account by mental models, both kinds of semantic training were significantly more effective than the control and the syntactic training, whereas there were no significant differences between the control and the syntactic training, nor between the two kinds of semantic training. Experiment 2 replicated this pattern of effects using a different set of syntactic and domain-specific training conditions. 2. Utilización de cenizas volantes y mineralizadores como materia prima en la fabricación de cemento Directory of Open Access Journals (Sweden) Palomo Sánchez, Ángel 1983-03-01 Full Text Available In this research the process of formation of a low energy clinker is studied, when fly-ashes (rich in sulphates and lime and fluorspar are used as raw materials (fly-ashes replaces to the tradicional raw mix partially. The availability of those fly-ashes is shown since clinker at 1.340 °C is obtained. The mineralogical composition, mineralizer capacity and temperature of formation of the new liquid phase is studied. En el presente trabajo se estudia el proceso de formación de un clínker de bajo consumo energético, empleando como materia prima cenizas volantes sulfocálcicas (en sustitución parcial del crudo tradicional y fluorita. Se demuestra la validez de dichas cenizas volantes, obteniendo clínker a 1.340 °C. Se estudia la composición mineralógica, capacidad de mineralización y temperatura de formación de la nueva fase líquida. 3. Exploração de subprodutos de maçã como matérias-primas alternativas em formulações para Columba livia OpenAIRE Ferreira, João Manuel Silva Loureiro Alves 2015-01-01 O crescimento da população humana deverá continuar até 2050. Por este motivo, a competição por matérias-primas entre a nossa alimentação e a alimentação animal será inevitável, tornando importante o recurso a matérias-primas alternativas, provenientes dos excedentes da indústria alimentar, como o bagaço de maçã e o resíduo da filtração do sumo concentrado denominado por retentato de maçã. Dentro das gamas de produtos fabricados pela indústria da alimentação animal, temos as rações para pom... 4. Case-based reasoning CERN Document Server Kolodner, Janet 1993-01-01 Case-based reasoning is one of the fastest growing areas in the field of knowledge-based systems and this book, authored by a leader in the field, is the first comprehensive text on the subject. Case-based reasoning systems are systems that store information about situations in their memory. As new problems arise, similar situations are searched out to help solve these problems. Problems are understood and inferences are made by finding the closest cases in memory, comparing and contrasting the problem with those cases, making inferences based on those comparisons, and asking questions whe 5. Design for reasoning DEFF Research Database (Denmark) Christiansen, Ellen Tove 2009-01-01 The aim of this paper is to position interaction design and information architecture in relation to design of interfaces to ICT applications meant to serve the goal of supporting users’ reasoning, be it learning applications or self-service applications such as citizen self-service. Interaction...... with such applications comprises three forms of reasoning: deduction, induction and abduction. Based on the work of Gregory Bateson, it is suggested that the disciplines of interaction design and information architecture are complementary parts of information processes. To show that abduction, induction and deduction... 6. Properties of inductive reasoning. Science.gov (United States) Heit, E 2000-12-01 This paper reviews the main psychological phenomena of inductive reasoning, covering 25 years of experimental and model-based research, in particular addressing four questions. First, what makes a case or event generalizable to other cases? Second, what makes a set of cases generalizable? Third, what makes a property or predicate projectable? Fourth, how do psychological models of induction address these results? The key results in inductive reasoning are outlined, and several recent models, including a new Bayesian account, are evaluated with respect to these results. In addition, future directions for experimental and model-based work are proposed. 7. Teater : Tänavused balletipreemiad. "Prima la Donna". Kontsertetendus "Sina ja mina". Rahvakultuur : Laste murdelaulu ja -luulepäevad tänavu Hageris / Vesta Uuetoa Index Scriptorium Estoniae Uuetoa, Vesta 2002-01-01 Rahvusooperis laulab "Boheemis" külaline Soomest - Ari Grönthal. Kadrioru lossis antakse üle traditsioonilised balletiauhinnad. 20.-26. V toimub rahvusooperis Estonia ooperi ja balletifestival "Prima la Donna", mille teemaks on saatuslikud, tähelepanuväärsed ja jõulised naised. Kurt Weilli ja Lotte Lenya elu draamas ja muusikas on lavastanud Mart Kampus. 18. ja 19. mail saavad Hageris kokku murdelaulu ja -luulega tegelevad lapsed 8. Speed of reasoning and its relation to reasoning ability NARCIS (Netherlands) Goldhammer, F.; Klein Entink, R.H. 2011-01-01 The study investigates empirical properties of reasoning speed which is conceived as the fluency of solving reasoning problems. Responses and response times in reasoning tasks are modeled jointly to clarify the covariance structure of reasoning speed and reasoning ability. To determine underlying 9. The reason project International Nuclear Information System (INIS) Atwood, W.; Blankenbecler, R.; Kunz, P.F.; Mours, B.; Weir, A.; Word, G. 1990-01-01 Reason is a software package to allow one to do physics analysis with the look and feel of the Apple Macintosh. It was implemented on a NeXT computer which does not yet support the standard HEP packages for graphics and histogramming. This paper will review our experiences and the program 10. Reason destroys itself CERN Multimedia Penrose, Roger 2008-01-01 "Do we know for certain that 2 lus 2 equals 4? Of course we don't. Maybe every time everybody in the whole world has ever done that calculation and reasoned it through, they've made a mistake." (1 page0 11. Reasoning=working Memoryattention Science.gov (United States) Buehner, M.; Krumm, S.; Pick, M. 2005-01-01 The purpose of this study was to clarify the relationship between attention, components of working memory, and reasoning. Therefore, twenty working memory tests, two attention tests, and nine intelligence subtests were administered to 135 students. Using structural equation modeling, we were able to replicate a functional model of working memory… DEFF Research Database (Denmark) Nielsen, Mogens 1998-01-01 In this extended abstract, we briefly recall the abstract (categorical) notion of bisimulation from open morphisms, as introduced by Joyal, Nielsen and Winskel. The approach is applicable across a wide range of models of computation, and any such bisimulation comes automatically with characterist...... of reasoning about the past.... 13. Diagnostic reasoning in action DEFF Research Database (Denmark) Rasmussen, Jens 1993-01-01 of system failures; and in medicine, diagnosis is the basis for any patient treatment. The paper presents a discussion of the basic nature of causal reasoning as applied for diagnosis and the mental strategies applied when diagnosis is viewed as an integrated part of ''natural decision making... 14. Reason and Less Directory of Open Access Journals (Sweden) Vinod eGoel 2014-08-01 Full Text Available We consider ourselves to be rational beings. We feel that our choices, decisions, and actions are selected from a flexible array of possibilities, based upon reasons. When we vote for a political candidate, it is because they share our views on certain critical issues. When we hire an individual for a job, it is be-cause they are the best qualified. However, if this is true, why does an analysis of the direction of shift in the timbre of the voice of political candidates during an exchange or debate, predict the winner of American presidential elections? Why is it that while only 3% of the American population consists of white men over 6'4 tall, 30% of the CEOs of Fortune 500 companies are white men over 6'4 tall? These are examples of instinctual biases affecting or modulating rational thought processes. I argue that existing theories of reasoning cannot substantively accommodate these ubiquitous, real-world phe-nomena. Failure to recognize and incorporate these types of phenomena into the study of human reasoning results in a distorted understanding of rationality. The goal of the article is to draw attention to these types of phenomena and propose an adulterated rationality account of reasoning to explain them. 15. One reason, several logics Directory of Open Access Journals (Sweden) Evandro Agazzi 2011-06-01 Full Text Available Humans have used arguments for defending or refuting statements long before the creation of logic as a specialized discipline. This can be interpreted as the fact that an intuitive notion of "logical consequence" or a psychic disposition to articulate reasoning according to this pattern is present in common sense, and logic simply aims at describing and codifying the features of this spontaneous capacity of human reason. It is well known, however, that several arguments easily accepted by common sense are actually "logical fallacies", and this indicates that logic is not just a descriptive, but also a prescriptive or normative enterprise, in which the notion of logical consequence is defined in a precise way and then certain rules are established in order to maintain the discourse in keeping with this notion. Yet in the justification of the correctness and adequacy of these rules commonsense reasoning must necessarily be used, and in such a way its foundational role is recognized. Moreover, it remains also true that several branches and forms of logic have been elaborated precisely in order to reflect the structural features of correct argument used in different fields of human reasoning and yet insufficiently mirrored by the most familiar logical formalisms. 16. Reasoning with Causal Cycles Science.gov (United States) Rehder, Bob 2017-01-01 This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new… 17. Varieties of clinical reasoning. Science.gov (United States) Bolton, Jonathan W 2015-06-01 Clinical reasoning comprises a variety of different modes of inference. The modes that are practiced will be influenced by the sociological characteristics of the clinical settings and the tasks to be performed by the clinician. This article presents C.S. Peirce's typology of modes of inference: deduction, induction and abduction. It describes their differences and their roles as stages in scientific argument. The article applies the typology to reasoning in clinical settings. The article describes their differences, and their roles as stages in scientific argument. It then applies the typology to reasoning in typical clinical settings. Abduction is less commonly taught or discussed than induction and deduction. However, it is a common mode of inference in clinical settings, especially when the clinician must try to make sense of a surprising phenomenon. Whether abduction is followed up with deductive and inductive verification is strongly influenced by situational constraints and the cognitive and psychological stamina of the clinician. Recognizing the inevitability of abduction in clinical practice and its value to discovery is important to an accurate understanding of clinical reasoning. © 2015 John Wiley & Sons, Ltd. 18. Observing Reasonable Consumers. Science.gov (United States) Silber, Norman I. 1991-01-01 Although courts and legislators usually set legal standards that correspond to empirical knowledge of human behavior, recent developments in behavioral psychology have led courts to appreciate the limits and errors in consumer decision making. "Reasonable consumer" standards that are congruent with cognitive reality should be developed.… 19. Reason and less. Science.gov (United States) Goel, Vinod 2014-01-01 We consider ourselves to be rational beings. We feel that our choices, decisions, and actions are selected from a flexible array of possibilities, based upon reasons. When we vote for a political candidate, it is because they share our views on certain critical issues. When we hire an individual for a job, it is because they are the best qualified. However, if this is true, why does an analysis of the direction of shift in the timbre of the voice of political candidates during an exchange or debate, predict the winner of American presidential elections? Why is it that while only 3% of the American population consists of white men over 6'4″ tall, 30% of the CEOs of Fortune 500 companies are white men over 6'4″ tall? These are examples of "instinctual biases" affecting or modulating rational thought processes. I argue that existing theories of reasoning cannot substantively accommodate these ubiquitous, real-world phenomena. Failure to recognize and incorporate these types of phenomena into the study of human reasoning results in a distorted understanding of rationality. The goal of this article is to draw attention to these types of phenomena and propose an "adulterated rationality" account of reasoning as a first step in trying to explain them. 20. Identificación de dos formas polimórficas cristalinas de clopidogrel bisulfato en materia prima farmacéutica Directory of Open Access Journals (Sweden) Full Text Available Introducción: el clopidogrel bisulfato existe en numerosas formas cristalinas, que varían en su estabilidad fisicoquímica, por lo que algunas de estas formas, patentadas o no, son útiles en la fabricación de medicamentos. Objetivo: identificar las formas cristalinas existentes en dos muestras de clopidogrel bisulfato materia prima comercializadas para la fabricación de medicamentos y el estado de pureza de ambas muestras. Métodos: las muestras de materia prima se obtuvieron de una industria nacional. Se examinaron mediante técnicas analíticas avanzadas como difracción de rayos X, calorimetría diferencial de barrido, termogravimetría y espectroscopia infrarroja. Se compararon los valores encontrados con los del estado del arte reconocidos en la literatura revisada para el clopidogrel bisulfato materias primas y tomados como referencia. Resultados: se obtuvieron los difractogramas, termogramas y espectros de absorción correspondientes a las muestras analizadas. Se utilizó el software TA Universal Analysis para obtener el porcentaje de descomposición, punto de fusión y picos identificadores en las muestras. Conclusiones: la muestra 1 contiene la forma cristalina I del bisulfato de clopidogrel, que no es pura ya que existe una banda característica de la presencia de contaminación con la forma cristalina II. La muestra 2 corresponde a la forma cristalina II del producto en forma pura. 1. Application of probabilistic facies prediction and estimation of rock physics parameters in a carbonate reservoir from Iran International Nuclear Information System (INIS) Karimpouli, Sadegh; Hassani, Hossein; Nabi-Bidhendi, Majid; Khoshdel, Hossein; Malehmir, Alireza 2013-01-01 In this study, a carbonate field from Iran was studied. Estimation of rock properties such as porosity and permeability is much more challenging in carbonate rocks than sandstone rocks because of their strong heterogeneity. The frame flexibility factor (γ) is a rock physics parameter which is related not only to pore structure variation but also to solid/pore connectivity and rock texture in carbonate reservoirs. We used porosity, frame flexibility factor and bulk modulus of fluid as the proper parameters to study this gas carbonate reservoir. According to rock physics parameters, three facies were defined: favourable and unfavourable facies and then a transition facies located between these two end members. To capture both the inversion solution and associated uncertainty, a complete implementation of the Bayesian inversion of the facies from pre-stack seismic data was applied to well data and validated with data from another well. Finally, this method was applied on a 2D seismic section and, in addition to inversion of petrophysical parameters, the high probability distribution of favorable facies was also obtained. (paper) 2. Stratigraphy and facies development of the marine Late Devonian near the Boulongour Reservoir, northwest Xinjiang, China Science.gov (United States) Suttner, Thomas J.; Kido, Erika; Chen, Xiuqin; Mawson, Ruth; Waters, Johnny A.; Frýda, Jiří; Mathieson, David; Molloy, Peter D.; Pickett, John; Webster, Gary D.; Frýdová, Barbora 2014-02-01 Late Devonian to Early Carboniferous stratigraphic units within the 'Zhulumute' Formation, Hongguleleng Formation (stratotype), 'Hebukehe' Formation and the Heishantou Formation near the Boulongour Reservoir in northwestern Xinjiang are fossil-rich. The Hongguleleng and 'Hebukehe' formations are biostratigraphically well constrained by microfossils from the latest Frasnian linguiformis to mid-Famennian trachytera conodont biozones. The Hongguleleng Formation (96.8 m) is characterized by bioclastic argillaceous limestones and marls (the dominant facies) intercalated with green spiculitic calcareous shales. It yields abundant and highly diverse faunas of bryozoans, brachiopods and crinoids with subordinate solitary rugose corals, ostracods, trilobites, conodonts and other fish teeth. The succeeding 'Hebukehe' Formation (95.7 m) consists of siltstones, mudstones, arenites and intervals of bioclastic limestone (e.g. 'Blastoid Hill') and cherts with radiolarians. A diverse ichnofauna, phacopid trilobites, echinoderms (crinoids and blastoids) together with brachiopods, ostracods, bryozoans and rare cephalopods have been collected from this interval. Analysis of geochemical data, microfacies and especially the distribution of marine organisms, which are not described in detail here, but used for facies analysis, indicate a deepening of the depositional environment at the Boulongour Reservoir section. Results presented here concern mainly the sedimentological and stratigraphical context of the investigated section. Additionally, one Late Devonian palaeo-oceanic and biotic event, the Upper Kellwasser Event is recognized near the section base. 3. Seismic facies analysis from pre-stack data using self-organizing maps International Nuclear Information System (INIS) 2014-01-01 In facies analysis, seismic data are clustered in different groups. Each group represents subsurface points with similar physical properties. Different groups can be related to differences in lithology, physical properties of rocks and fluid changes in the rocks. The supervised and unsupervised data clustering are known as two types of clustering architecture. In supervised clustering, the number of clusters is predefined, while in unsupervised clustering, a collection of patterns partitions into groups without predefined clusters. In this study, the pre-stack data clustering is used for seismic facies analysis. In this way, a horizon was selected from pre-stack data, followed by sorting of data using offset. A trace associated with each CDP is constructed, for which the first and second samples are related to the first and second offsets, respectively. The created trace is called consolidated trace which is characteristic of subsurface points. These consolidated traces are clustered by using self-organizing maps (SOM). In proposed pre-stack seismic data clustering, points with similar physical properties are placed in one cluster. Seismic data associated with hydrocarbon reservoirs have very different characteristics that are easily recognized. The efficiency of the proposed method was tested on both synthetic and real seismic data. The results showed that the algorithm improves the data classification and the points of different properties are noticeable in final maps. (paper) 4. Facies-related fracturing in turbidites: insights from the Marnoso-Arenacea Fm. (Northern Apennines, Italy) Science.gov (United States) Ogata, Kei; Storti, Fabrizio; Balsamo, Fabrizio; Bedogni, Enrico; Tinterri, Roberto; Fetter, Marcos; Gomes, Leonardo; Hatushika, Raphael 2016-04-01 Natural fractures deeply influence subsurface fluid flow, exerting a primary control on resources like aquifers, hydrocarbons and geothermal reservoirs, and on environmental issues like CO2 storage and nuclear waste disposal. In layered sedimentary rocks, depositional processes-imprinted rock rheology favours the development of both mechanical anisotropy and heterogeneity on a wide range of scales, and are thus expected to strongly influence location and frequency of fractures. To better constrain the contribution of stratigraphic, sedimentological and petrophysical attributes, we performed a high-resolution, multidisciplinary study on a selected stratigraphic interval of jointed foredeep turbidites in the Miocene Marnoso-arenacea Formation (Northern Apennines, Italy), which are characterised by a great lateral and vertical variability of grain-size and depositional structures. Statistical relationships among field and laboratory data significantly improve when the single facies scale is considered, and, for similar facies recording different evolutionary stages of the parent turbidity currents, we observed a direct correlation between the three-dimensional anisotropies of rock hardness tensors and the normalized fracture frequencies, testifying for the primary sedimentary flow-related control on fracture distributions. 5. Facies analysis, sedimentology and paleocurrent of the quaternary nenering formation, Pengkalan Hulu, Malaysia International Nuclear Information System (INIS) Yuniarti Ulfa; Evonne Hooi Rong Yu; Ooi Cheng Kit 2014-01-01 Nenering Formation is essentially made up of semi-consolidated sediments, which are divided into basal conglomerate beds, conglomeratic sandstone, cross-bedded sandstone, and siltstone to muddy layers facies. It is overlie unconformable to the Berapit Formation, but conformable to the Kroh and Grik Formations. The stratigraphy of Nenering Formation is a fining upwards sequence where the thickness of conglomerate beds become thinner upwards and become thicker for conglomeratic sandstone. The thickness varies from 0.5 m to tenths of meters. The more sandy in the upper portion (cross-bedded sandstone) overlie with thin siltstone and mud stone facies. The clast and grain composition suggested that the material making up the sedimentary sequence were derived predominantly from the erosion of granitoid rocks and sedimentary and metamorphic rocks constitute a minor provenance. Imbrications and the trend sizes of clasts indicate that the paleo-current flow toward northeast. Cross bedding that was found in conglomerate and sandstone indicates the main channel depositional environment. The sequence stratigraphy of this area match with the Saskatchewan fluvial braided channel model. (author) 6. 76 FR 37813 - Agency Information Collection Activities: Submission for OMB Review; Comment Request Science.gov (United States) 2011-06-28 ... are being included with this revised PRA submission, and with completing the Prima Facie Evidence... completing the Prima Facie Evidence cover sheet, was included in the burden estimate for submitting a... 7. 25 CFR 249.3 - Identification cards. Science.gov (United States) 2010-04-01 ... the issuance of an appropriate identification card to any Indian entitled thereto as prima facie... any Federal, State, or tribal enforcement officer shall be prima facie evidence that the person is not... 8. 33 CFR 1.07-10 - Reporting and investigation. Science.gov (United States) 2010-07-01 ... evidence to establish a prima facie case. If there is insufficient evidence, the case is either returned... prima facie case does exist, a case file is prepared and forwarded to the Hearing Officer, with a... 9. 37 CFR 2.41 - Proof of distinctiveness under section 2(f). Science.gov (United States) 2010-07-01 ... mark may be accepted as prima facie evidence of distinctiveness. Also, if the mark is said to have... with § 2.20, in the application may, in appropriate cases, be accepted as prima facie evidence of... 10. 42 CFR 1003.133 - Statistical sampling. Science.gov (United States) 2010-10-01 ... constitute prima facie evidence of the number and amount of claims or requests for payment as described in § 1003.102. (b) Once the Inspector General has made a prima facie case as described in paragraph (a) of... 11. 45 CFR 150.443 - Standard of proof. Science.gov (United States) 2010-10-01 ... establish a prima facie case; (2) The respondent has the burden of coming forward with evidence in response, once CMS has established a prima facie case; and (3) CMS has the burden of persuasion regarding facts... 12. 46 CFR 221.63 - Investigation. Science.gov (United States) 2010-10-01 ... investigate the matter and decide whether there is sufficient evidence to establish a prima facie case that a violation occurred. (b) If that Officer decides there is a prima facie case, then that Officer may enter... 13. 47 CFR 1.54 - Petitions for forbearance must be complete as filed. Science.gov (United States) 2010-10-01 ... requested relief. (b) Prima facie case. Petitions for forbearance must contain facts and arguments which, if... statement of the petitioner's prima facie case for relief. (3) Appendices that list: (i) The scope of relief... 14. 45 CFR 160.536 - Statistical sampling. Science.gov (United States) 2010-10-01 ..., constitutes prima facie evidence of the number of violations and the existence of factors material to the... prima facie case, as described in paragraph (a) of this section, the burden of going forward shifts to... 15. 77 FR 28570 - Pure Magnesium From the People's Republic of China: Notice of Court Decision Not in Harmony With... Science.gov (United States) 2012-05-15 ... its discretion when it declines to remand to an agency when evidence sufficient to make a prima facie... Department determined there was clear and convincing evidence sufficient to make a prima facie case that the... 16. 16 CFR 703.4 - Qualification of members. Science.gov (United States) 2010-01-01 ... acquisition or ownership of an interest which is offered to the general public shall be prima facie evidence... acquisition or ownership of an interest which is offered to the general public shall be prima facie evidence... 17. Sedimentary facies and depositional environments of early Mesozoic Newark Supergroup basins, eastern North America Science.gov (United States) Smoot, J.P. 1991-01-01 The early Mesozoic Newark Supergroup consists of continental sedimentary rocks and basalt flows that occupy a NE-trending belt of elongate basins exposed in eastern North America. The basins were filled over a period of 30-40 m.y. spanning the Late Triassic to Early Jurassic, prior to the opening of the north Atlantic Ocean. The sedimentary rocks are here divided into four principal lithofacies. The alluvial-fan facies includes deposits dominated by: (1) debris flows; (2) shallow braided streams; (3) deeper braided streams (with trough crossbeds); or (4) intense bioturbation or hyperconcentrated flows (tabular, unstratified muddy sandstone). The fluvial facies include deposits of: (1) shallow, ephemeral braided streams; (2) deeper, flashflooding, braided streams (with poor sorting and crossbeds); (3) perennial braided rivers; (4) meandering rivers; (5) meandering streams (with high suspended loads); (6) overbank areas or local flood-plain lakes; or (7) local streams and/or colluvium. The lacustrine facies includes deposits of: (1) deep perennial lakes; (2) shallow perennial lakes; (3) shallow ephemeral lakes; (4) playa dry mudflats; (5) salt-encrusted saline mudflats; or (6) vegetated mudflats. The lake margin clastic facies includes deposits of: (1) birdfoot deltas; (2) stacked Gilbert-type deltas; (3) sheet deltas; (4) wave-reworked alluvial fans; or (5) wave-sorted sand sheets. Coal deposits are present in the lake margin clastic and the lacustrine facies of Carnian age (Late Triassic) only in basins of south-central Virginia and North and South Carolina. Eolian deposits are known only from the basins in Nova Scotia and Connecticut. Evaporites (and their pseudomorphs) occur mainly in the northern basins as deposits of saline soils and less commonly of saline lakes, and some evaporite and alkaline minerals present in the Mesozoic rocks may be a result of later diagenesis. These relationships suggest climatic variations across paleolatitudes, more humid to the 18. Investigation of Facies Types and Associations of Kuhlan Red Bed Formation in NW Yemen: A New Hypothesis for Origin and Depositional Environment Directory of Open Access Journals (Sweden) Mohammed A. Al-Wosabi 2006-06-01 Full Text Available Varieties of thirteen facies types were recognized in the Kuhlan Formation represented by red bed siliciclastic sequences of argillaceous sediments. Examination of the Kuhlan stratigraphic column included sequence relationships, lithology, sedimentary characters, structures and petrography of the dominant rock types. These facies types are grouped in three distinct associations of facies. The lower unit A comprises association of facies (Distal turbidites represented by alternates of turbidity sequences including sandstone, siltstone and thick shale beds. These facies types confirm a regressive depositional environment in deep marine shelf conditions. There are three facies types which are identified as massive sandstone, cross-bedded sandstone and pebbly sandstone facies. The middle unit B association of facies (Proximal turbedites represents glaciomarine sequences displaying high lateral and vertical facies changes of glacioturbidite sediment alternates with diamictites and tillite beds. The sequences are affected by eustatic and eustatism of the glacial advance and retreat. This unit B includes eight types of facies. These are identified as; tillite, massive diamictites, stratified diamictites, laminated siltstone/shale, deformed siltstone/mudstone, graded rhythmic siltstone, massive conglomerate and cross-stratified sandy conglomerate facies. The upper unit C association of facies is represented by shallow marine shelf sequences displaying very thick massive and locally cross-bedded sand bar sandstone overlying the laminated siltstone/shale interbeds. The upward gradual changes in mineralogical composition and color confirms the start of marine transgression and later deposited platform Amran Group. Mineralogical composition of Kuhlan sandstone displays impure dirty rocks consisting of more than 30% of argillaceous matrix, 50% of cristobalite and quartz grains, more than 10% of ferruginous cement and 10% of detrital iron oxide grains, potash 19. Analysis of students’ mathematical reasoning Science.gov (United States) Sukirwan; Darhim; Herman, T. 2018-01-01 The reasoning is one of the mathematical abilities that have very complex implications. This complexity causes reasoning including abilities that are not easily attainable by students. Similarly, studies dealing with reason are quite diverse, primarily concerned with the quality of mathematical reasoning. The objective of this study was to determine the quality of mathematical reasoning based perspective Lithner. Lithner looked at how the environment affects the mathematical reasoning. In this regard, Lithner made two perspectives, namely imitative reasoning and creative reasoning. Imitative reasoning can be memorized and algorithmic reasoning. The Result study shows that although the students generally still have problems in reasoning. Students tend to be on imitative reasoning which means that students tend to use a routine procedure when dealing with reasoning. It is also shown that the traditional approach still dominates on the situation of students’ daily learning. Science.gov (United States) Hinze, Ralf Programmers happily use induction to prove properties of recursive programs. To show properties of corecursive programs they employ coinduction, but perhaps less enthusiastically. Coinduction is often considered a rather low-level proof method, in particular, as it departs quite radically from equational reasoning. Corecursive programs are conveniently defined using recursion equations. Suitably restricted, these equations possess unique solutions. Uniqueness gives rise to a simple and attractive proof technique, which essentially brings equational reasoning to the coworld. We illustrate the approach using two major examples: streams and infinite binary trees. Both coinductive types exhibit a rich structure: they are applicative functors or idioms, and they can be seen as memo-tables or tabulations. We show that definitions and calculations benefit immensely from this additional structure. 1. How reasonable is ALARA? International Nuclear Information System (INIS) Kiefer, H. 1991-01-01 The linear extrapolation of the established dose-effect relation at higher doses was accepted as a simple working hypothesis to determine dose limits for professional radiation personnel. It has been misused, however, for calculations of population risks in the very low dose region. This lead to an overestimation of radiation hazards by the public, followed by an overregulation of radiation protection. The ALARA recommendations of ICRP - justification of radiation application, optimisation of protection, and protection of the individual, - was aimed at counterpoising this trend and elucidate the aims of radiation protection. But even the ALARA principle will only be successful if it is applied with reason. The lend more weight to reason in radiation protection, an award for FS members is proposed, as well as an anti-award for the most nonsensical action in radiation protection. (orig.) [de 2. The Upper Permian sandstones of Mountains Mecsek: form elements of uranium ore mineralization and facies relations Pt. 2 International Nuclear Information System (INIS) Vincze, Janos; Somogyi, Janos 1984-01-01 The ore mineralization in the Upper Permian sandstones of Mountais Mecsek, Hungary, was brought about at the oxidation-reduction front between the grey and red sandstones; the predominant rock colour here is green. The sandstones of different colour are oxidation-reduction species. The formation is a megacycle containing in its core grey sandstones of reduced state with coalified plant remains and in its mantle oxidized red sandstones. Uranium accumulates mainly in the transitional green facies. Uranium content gets enriched to a commercial concentration only if the difference in potential of neighbouring beds is in the range of 400-480 mV. The relationship between organic matter and uranium content in the individual facies is shown. The principles of oxidation-reduction processes in the formation of boundary facies are discussed. (V.N.) 3. Developing geometrical reasoning OpenAIRE Brown, Margaret; Jones, Keith; Taylor, Ron; Hirst, Ann 2004-01-01 This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current requirements of the UK National Curriculum and the Key Stage 3 strategy, and to consider the whole atta... 4. Tactical Diagrammatic Reasoning Directory of Open Access Journals (Sweden) 2017-01-01 Full Text Available Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction in the construction of proofs and of providing explanations of solutions expressed in the proofs remain to be addressed. In this paper we take an interactive proof assistant for Euler diagrams, Speedith, and add tactics to its reasoning engine, providing a level of automation in the construction of proofs. By adding tactics to Speedith's repertoire of inferences, we ease the interaction between the user and the system and capture a higher level explanation of the essence of the proof. We analysed the design options for tactics by using metrics which relate to human readability, such as the number of inferences and the amount of clutter present in diagrams. Thus, in contrast to the normal case with sentential tactics, our tactics are designed to not only prove the theorem, but also to support explanation. 5. REASON for Europa Science.gov (United States) Moussessian, A.; Blankenship, D. D.; Plaut, J. J.; Patterson, G. W.; Gim, Y.; Schroeder, D. M.; Soderlund, K. M.; Grima, C.; Young, D. A.; Chapin, E. 2015-12-01 The science goal of the Europa multiple flyby mission is to "explore Europa to investigate its habitability". One of the primary instruments selected for the scientific payload is a multi-frequency, multi-channel ice penetrating radar system. This "Radar for Europa Assessment and Sounding: Ocean to Near-surface (REASON)" would revolutionize our understanding of Europa's ice shell by providing the first direct measurements of its surface character and subsurface structure. REASON addresses key questions regarding Europa's habitability, including the existence of any liquid water, through the innovative use of radar sounding, altimetry, reflectometry, and plasma/particles analyses. These investigations require a dual-frequency radar (HF and VHF frequencies) instrument with concurrent shallow and deep sounding that is designed for performance robustness in the challenging environment of Europa. The flyby-centric mission configuration is an opportunity to collect and transmit minimally processed data back to Earth and exploit advanced processing approaches developed for terrestrial airborne data sets. The observation and characterization of subsurface features beneath Europa's chaotic surface require discriminating abundant surface clutter from a relatively weak subsurface signal. Finally, the mission plan also includes using REASON as a nadir altimeter capable of measuring tides to test ice shell and ocean hypotheses as well as characterizing roughness across the surface statistically to identify potential follow-on landing sites. We will present a variety of measurement concepts for addressing these challenges. 6. Increasing cocoa productivity and farmer capacity in surrounding area of PT Kaltim Prima Coal and PT Berau Coal Directory of Open Access Journals (Sweden) J.B.Baon 2014-01-01 Full Text Available Based on agro-climate factors, most of surrounding area of coal mining sites in Indonesia is suitable for cocoa cultivation. However, most of cocoa farmers in the environs of coal mining sites have little access both to new technology of cocoa cultivation and to market of their cocoa products. Therefore, productivity of cocoa farms and the income of cocoa farmers are low, which may disturb social responsibility of the coal mining companies present in their surroundings. These are the consequences of poor interaction between the government, private sector and research sector. The aim of this study is to transfer and to implement good agricultural practices of cocoa in surrounding area of mining sites of Kaltim Prima Coal (KPC and Berau Coal (BC, East Kalimantan, in order to increase farmer capacity and cocoa productivity. Indonesian Coffee and Cocoa Research Institute as the developing agent of cocoa technology has established collaboration with corporate social responsibility program of KPC (already 7 years and BC (already 2 years to improve productivity and farmer capacity of cocoa farms surroundings the two cocoa mining companies. This paper discusses the aspects of natural, economic and human resources; baseline study; technology transfers; marketing partnership; cocoa productivity; farmer income after technology implementing; study of cocoa growth on post-coal-mining. It is concluded that improvement of the cocoa productivity and farmer capacity surroundings the two mining sites associated with high adoption of technology by farmers, better access to availability of knowledge for good agricultural practices, extension officers, demonstration plots, cocoa price, and length of market chains, partnership, and competition with oil palm plantations. 7. Long-term results of aortic valve replacement with Edwards Prima Plus stentless bioprosthesis: eleven years' follow up. Science.gov (United States) Auriemma, Stefano; D'Onofrio, Augusto; Brunelli, Massimo; Magagna, Paolo; Paccanaro, Mariemma; Rulfo, Fanny; Fabbri, Alessandro 2006-09-01 The Edwards Lifesciences Prima Plus stentless valve (ELSV) is a bioprosthesis manufactured from a porcine aortic root. The study aim was to evaluate late clinical outcomes after aortic valve replacement (AVR) with ELSV implanted as a miniroot in patients with aortic valve disease. Between 1993 and 2004, 318 patients (232 males, 86 females; mean age 69 +/- 9 years; range: 37-83 years) underwent AVR with the ELSV. Preoperatively, 102 patients (32%), 162 (51%) and 54 (17%) were in NYHA classes I/II, III and IV, respectively. Aortic stenosis, aortic regurgitation and combined lesions were present in 124 patients (39%), 114 (36%) and 41 (13%), respectively. Twenty patients (6%) were referred for an acute aortic dissection, 20 (6%) for an aortic root aneurysm, and 139 (44%) had an associated aneurysmal dilatation of the ascending aorta. The ascending aorta was replaced in 159 patients (50%); aortic arch replacement was required in 10 (3%). Coronary artery bypass graft was performed in 86 patients (27%). The follow up was based on clinical data. Operative mortality was 5% (n = 17). There were 49 late deaths (5.2%/pt-yr). Valve-related mortality occurred in 10 patients (1%/pt-yr). Actuarial survival at five and 10 years was 78% and 33%, respectively. Actuarial freedom from valve reoperation and structural valve deterioration at 10 years were 100% and 64%. Actuarial freedom from embolic events and endocarditis at 10 years were 84% and 81%, respectively. The ELSV, when implanted as a miniroot, provided good early and long-term results in terms of survival and freedom from major complications. 8. Lacustrine sedimentation and facies model for the last 45,000 yr in Chalco basin. Central Mexico Science.gov (United States) Ortega, B.; Lozano, S.; Caballero, M.; Herrera, D. 2013-05-01 Chalco basin in central Mexico (19° 15' N, 98° 58' W, 2200 m asl) is one of the most detailed lake sediment sequence analyzed in Mexico for paleoclimatic and paleoenvironmental studies. In this former lake, five drill cores up to 27 m depth were recovered in 1987-1989 by the UNAM team, and three cores covering most of the former sequence were obtained in 2008 and 2011. The upper 27 m of the Chalco lacustrine sequence contains the record of the last 45 kyr climate history in the northern American tropics. The active tectonic and volcanic setting of Chalco Lake in the Trans-Mexican Volcanic Belt, provides an opportunity to evaluate environmental (volcanic + tectonic vs. climatic) controls on lacustrine sedimentation. The establishment of a detailed time scale by 14C in pollen extracts provides an accurate chronological control. The stratigraphical and sedimentological analyses presented here provided the recognition of depositional environments and the architecture of the upper lacustrine succession. Sedimentary facies were defined on the basis of sedimentological descriptions, microscopic observation and compositional analyses. According to compositional criteria, facies were identified and groped into two main categories according to compositional criteria: 1) detrital and volcaniclastic, and 2) biogenic facies. The clastic facies includes massive to laminated, silty and clayey sediments composed of clay minerals, feldspars, amphiboles with minor amounts of quartz, opaque minerals and calcite. Diatoms are the most common biological remains in all the clastic facies. Most of the volcaniclastic deposits correspond to fall-out deposits, some of them of well documented eruptions of the nearby large stratovolcanoes Popocatepetl and Nevado de Toluca, which in turn serve as stratigraphical markers. The biogenic facies are massive to finely laminated diatom ooze and ostracod ooze layers. The sedimentary architecture of the lacustrine succession has been controlled by 9. Calvin on Human Reason Directory of Open Access Journals (Sweden) Nicolaas Vorster 2014-10-01 Full Text Available In his recent book The Unintended Reformation, Brad Gregory makes the statement that the Reformation replaced the teleological social ethics of Roman Catholicism based on virtue with formal social ethics based on rules and enforced by magistrates, because they regarded human reason as too depraved to acquire virtue. The result, according to Gregory, is that the relation between internalised values and rules were undermined. This article asks whether this accusation is true with regard to Calvin. The first section discusses the intellectual environment of Calvin’s day – something that inevitably influenced his theory on reason, whilst the second part analyses Calvin’s view on the created nature of reason. The third section investigates Calvin’s view on the effects of sin on reason; and the fourth section discusses Calvin’s perspective on the relation between grace and reason. The article concludes that Gregory’s accusation against the Reformation is not applicable to Calvin. Gregory fails to take into account Calvin’s modified position that the imago Dei was not totally destroyed by sin as well as his teaching on common grace that maintains that even non-believers are able to acquire virtue through the common grace of God. Calvyn oor Menslike Rede. In sy onlangse boek, The Unintended Reformation, maak Brad Gregory die stelling dat die Reformasie die substantiewe teleologiese deugde-etiek van die Rooms-Katolisisme vervang het met ‘n formele etiek gebaseer op reëls wat deur magistrate afgedwing moet word. Die Reformasie was, volgens Gregory, van mening dat die menslike rede sodanig deur sonde geskend is dat die mens nie langer deugde kan beoefen nie. Dit het tot ‘n skadelike skeiding tussen waardes en reëls gelei. Hierdie artikel ondersoek die vraag of Gregory se stelling op Calvyn van toepassing is. Die eerste afdeling bespreek die intellektuele omgewing waarin Calvyn gewerk het. Tweedens word Gregory se siening van die geskape 10. Reasonable Accommodation Information Tracking System Data.gov (United States) U.S. Environmental Protection Agency — The Reasonable Accommodation Information Tracking System (RAITS) is a case management system that allows the National Reasonable Accommodation Coordinator (NRAC) and... 11. Model Based Temporal Reasoning Science.gov (United States) Rabin, Marla J.; Spinrad, Paul R.; Fall, Thomas C. 1988-03-01 Systems that assess the real world must cope with evidence that is uncertain, ambiguous, and spread over time. Typically, the most important function of an assessment system is to identify when activities are occurring that are unusual or unanticipated. Model based temporal reasoning addresses both of these requirements. The differences among temporal reasoning schemes lies in the methods used to avoid computational intractability. If we had n pieces of data and we wanted to examine how they were related, the worst case would be where we had to examine every subset of these points to see if that subset satisfied the relations. This would be 2n, which is intractable. Models compress this; if several data points are all compatible with a model, then that model represents all those data points. Data points are then considered related if they lie within the same model or if they lie in models that are related. Models thus address the intractability problem. They also address the problem of determining unusual activities if the data do not agree with models that are indicated by earlier data then something out of the norm is taking place. The models can summarize what we know up to that time, so when they are not predicting correctly, either something unusual is happening or we need to revise our models. The model based reasoner developed at Advanced Decision Systems is thus both intuitive and powerful. It is currently being used on one operational system and several prototype systems. It has enough power to be used in domains spanning the spectrum from manufacturing engineering and project management to low-intensity conflict and strategic assessment. Science.gov (United States) Friedman, A; Brown, N R 2000-06-01 To understand the nature and etiology of biases in geographical judgments, the authors asked people to estimate latitudes (Experiments 1 and 2) and longitudes (Experiments 3 and 4) of cities throughout the Old and New Worlds. They also examined how people's biased geographical judgments change after they receive accurate information ("seeds") about actual locations. Location profiles constructed from the pre- and postseeding location estimates conveyed detailed information about the representations underlying geography knowledge, including the subjective positioning and subregionalization of regions within continents; differential seeding effects revealed between-region dependencies. The findings implicate an important role for conceptual knowledge and plausible-reasoning processes in tasks that use subjective geographical information. CERN Document Server Allen, James; Pelavin, Richard; Tenenberg, Josh 1991-01-01 This book presents four contributions to planning research within an integrated framework. James Allen offers a survey of his research in the field of temporal reasoning, and then describes a planning system formalized and implemented directly as an inference process in the temporal logic. Starting from the same logic, Henry Kautz develops the first formal specification of the plan recognition process and develops a powerful family of algorithms for plan recognition in complex situations. Richard Pelavin then extends the temporal logic with model operators that allow the representation to 14. Quantitative Algebraic Reasoning DEFF Research Database (Denmark) 2016-01-01 We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We deﬁne an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...... equational theory whose free algebras correspond to well known structures. In each case we have ﬁnitary and continuous versions. The four cases are: Hausdorﬀ metrics from quantitive semilattices; pWasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed... 15. "Critique of intuitive reason" Directory of Open Access Journals (Sweden) Dobrijević Aleksandar 2005-01-01 Full Text Available The author displays and reexamines Hare’s "two-level theory" of normative moral thinking ("intuitive" level and "critical" level, including goals that are intended by its establishing. Given Hare’s holism, the met ethical level, considered as fundamental or the "third" level, has notable effect on process of normative reasoning, especially if it is taken as one of the determinant of the critical moral thin king. Central part of the analysis is examination of utilitarian character of the theory. 16. Charisma and Moral Reasoning Directory of Open Access Journals (Sweden) Jessica Flanigan 2013-04-01 Full Text Available Charisma is morally problematic insofar as it replaces followers’ capacity to engage in genuine moral reasoning. When followers defer to charismatic leaders and act in ways that are morally wrong they are not only blameworthy for wrongdoing but for failing in their deliberative obligations. Even when followers defer to charismatic leaders and do the right thing, their action is less praiseworthy to the extent that it was the result of charisma rather than moral deliberation. Therefore, effective charismatic leadership reliably undermines the praiseworthiness and amplifies the blameworthiness of follower’s actions. 17. Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling International Nuclear Information System (INIS) Li Yupeng; Deutsch, Clayton V. 2012-01-01 In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example. 18. Lower Tertiary Sedimentary Turbidite Facies at the Chicontepec Basin, East-Central Mexico Directory of Open Access Journals (Sweden) Santillán-Piña N. 2011-07-01 Full Text Available The study area comprises the northwestern portion of the Chicontepec Basin at southeastern San Luis Potosí and northeastern Hidalgo States. At the stratigraphy sequences of the Chicontepec Formation from Lower Paleocene in isolated outocrops, were herein interpreted two major sedimentary sub-environments into the fan model: the middle and the external sedimentary settings; the applied criteria for their identification were: (a lithostratigraphic (thickness, geometry and distribution; (b internal and external primary sedimentary structures, and (c intra-formational deformation structures. The sedimentary facies are composed of siliciclastic and calcareous particles sourced from the Sierra Madre Oriental, western; the Tuxpan paleo-island, eastern; and from the Teziutlan Massif, southern; the sediments were massively transported by slideing, slumping, flow debris and turbidity currents, then deposited as massive, tabular, lenticular and lobely in shape at the slope foot and on the sea marine floor. 19. Automatic interpretation of seismic micro facies using the fuzzy mathematics method Energy Technology Data Exchange (ETDEWEB) Dongrun, G.; Gardner, G.H.F. 1988-01-01 The interpretation of seismic micro facies concentrates on changes involving single reflection or several reflections, and endeavors to explain the relations between these changes and stratigraphic variation or hydrocarbon accumulation. In most cases, one can not determine the geological significance of reflection character anomalies on single or several seismic sections. But when one maps them on a plane, their distribution may on the whole indicate the geological significance. It is stated how the fuzzy method is used on a VAX computer to automatically construct a plane map of the reflection character changes in a time window. What an interpreter needs to do for whole interpretation is only to provide some parameters, such as time window, threshold, weight coefficients etc. 20. Pennsylvanian coniferopsid forests in sabkha facies reveal the nature of seasonal tropical biome Science.gov (United States) Falcon-Lang, H. J.; Jud, N.A.; John, Nelson W.; DiMichele, W.A.; Chaney, D.S.; Lucas, S.G. 2011-01-01 Pennsylvanian fossil forests are known from hundreds of sites across tropical Pangea, but nearly all comprise remains of humid Coal Forests. Here we report a unique occurrence of seasonally dry vegetation, preserved in growth position along >5 km of strike, in the Pennsylvanian (early Kasimovian, Missourian) of New Mexico (United States). Analyses of stump anatomy, diameter, and spatial density, coupled with observations of vascular traces and associated megaflora, show that this was a deciduous, mixed-age, coniferopsid woodland (~100 trees per hectare) with an open canopy. The coniferopsids colonized coastal sabkha facies and show tree rings, confirming growth under seasonally dry conditions. Such woodlands probably served as the source of coniferopsids that replaced Coal Forests farther east in central Pangea during drier climate phases. Thus, the newly discovered woodland helps unravel biome-scale vegetation dynamics and allows calibration of climate models. ?? 2011 Geological Society of America. 1. 76 FR 71375 - Scott D. Fedosky, M.D.; Denial of Application Science.gov (United States) 2011-11-17 ... statement of position and supporting letter, I conclude that the Government has made out a prima facie case... inconsistent with the public interest. However, where the Government makes out a prima facie case to deny an... the public interest. In this matter, I conclude that the Government has established a prima facie case... 2. 77 FR 2011 - Reorganization of Regulations on the Adjudication of Department of Homeland Security Practitioner... Science.gov (United States) 2012-01-13 ..., fails to make a prima facie showing that there is a material issue of fact in dispute. A practitioner is... practitioner has made a prima facie showing that there is a material issue of fact in dispute. See 8 CFR 1003... Discipline, makes a prima facie showing that there is a material issue of fact in dispute, regardless of... 3. 29 CFR 24.104 - Investigation. Science.gov (United States) 2010-07-01 ... be dismissed unless the complainant has made a prima facie showing that protected activity was a... to make a prima facie showing as follows: (i) The employee engaged in a protected activity; (ii) The... be dismissed unless the complainant has made a prima facie showing that protected activity was a... 4. 47 CFR 1.1409 - Commission consideration of the complaint. Science.gov (United States) 2010-10-01 ... available to it, or both. (b) The complainant shall have the burden of establishing a prima facie case that... denial was lawful, once a prima facie case is established by the complainant. (c) The Commission shall... complaint if it determines that the complainant has not established a prima facie case, or that the rate... 5. 49 CFR 1037.1 - Weights and weighing. Science.gov (United States) 2010-10-01 ... on supervised scales, establishes prima facie that the loss occurred in transit and that the railroad... in combination with a supervised weight establishes prima facie that the loss occurred in transit and... the above exception, a prima facie case of railroad liability for loss in transit has not been... 6. 76 FR 13937 - Rules of Practice in Proceedings Relative to False Representation and Lottery Orders Science.gov (United States) 2011-03-15 ... Officer shall review the complaint and any supporting information and determine whether a prima facie... by 39 U.S.C. 3005(a). Where the Judicial Officer concludes that a prima facie showing has not been made the complaint shall be dismissed. Where the Judicial Officer concludes that a prima facie showing... 7. 8 CFR 245a.13 - During pendency of application. Science.gov (United States) 2010-01-01 ... States submits a prima facie application for adjustment of status under LIFE Legalization during the... inadmissibility, an application for adjustment of status shall be treated as a prima facie application during the... eligible alien who submits a prima facie application for adjustment of status under this Subpart B shall be... 8. 75 FR 420 - Receipt of Domestic Interested Party Petition Concerning the Tariff Classification of Wickless... Science.gov (United States) 2010-01-05 ... application of GRI 2(a). In the alternative, the petitioner argues that the wax objects are prima facie... alternative argument offered by NCA is that the wax objects are prima facie classifiable in both heading 3406... application of GRI 3(a) is inappropriate because the wax objects are not prima facie classifiable in two or... 9. 39 CFR 952.7 - Notice of answer and hearing. Science.gov (United States) 2010-07-01 ... supporting information and determine whether a prima facie showing has been made that Respondent is engaged... civil penalties authorized by 39 U.S.C. 3012. Where he concludes that a prima facie showing has not been made he shall dismiss the complaint. Where he concludes that a prima facie showing has been made, he... 10. 76 FR 52561 - Timely Mailing Treated as Timely Filing Science.gov (United States) 2011-08-23 ... to the only ways to establish prima facie evidence of delivery of documents that have a filing... (PDS) designated under criteria established by the IRS, will constitute prima facie evidence of... taxpayers to be able to establish the postmark date and prima facie evidence of delivery when using... 11. Facies volcánicas del depósito de avalancha de detritos del volcán Tata Sabaya, Andes Centrales Volcanic facies of the debris avalanche deposit of Tata Sabaya Volcano, Central Andes Directory of Open Access Journals (Sweden) Benigno Godoy 2012-09-01 Full Text Available Las avalanchas de detritos, asociadas a colapsos parciales de edificios volcánicos, son fenómenos comunes en la evolución de un volcán. Este tipo de flujos son por inestabilidades, que pueden deberse a factores tales como la existencia de zonas afectadas por alteración hidrotermal, cambios climáticos, terremotos, intrusión de magmas en zonas superficiales (criptodomos y/o diques y/o movimiento de fallas bajo el edificio volcánico o cercanas a él. El producto final de estos flujos -denominado depósito de avalancha de detritos (DAD- presenta morfologías típicas de cerrillos y drenajes cerrados. En los Andes Centrales se han reconocido, al menos, 14 centros volcánicos con depósitos de avalancha asociados, entre los que está el volcán Tata Sabaya (Bolivia. El colapso que ha dado origen a este depósito podría haberse generado por una combinación de actividad sísmica y magmática en el volcán. El depósito asociado al colapso parcial de este volcán se distribuye sobre la parte baja del flanco sur del volcán y sobre la parte noroccidental de la cuenca del salar de Coipasa. Cubre una superficie de más de 230 km² y tiene un volumen estimado de 6±1 km³. Sobre la base de las composiciones litológicas, se ha establecido que el depósito está constituido por 6 tipos distintos de cerrillos, los cuales son: lávicos, piroclásticos, sedimentarios mixtos, brecha piroclástica y andesítico-basálticos. Considerando el tipo predominante de cerrillos y su distribución espacial dentro del depósito, se ha definido 6 facies diferentes (Facies de Bloques Toreva, Facies de Cerrillos Volcánicos, Facies Central, Facies de Cerrillos Sedimentarios, Facies Mixta y Facies de Cerrillos de Brecha Piroclástica. Tomando en cuenta la distribución espacial de estas facies, se propone la estructura del paleovolcán previa a su colapso parcial.Debris avalanches associated with partial sector collapse of volcanic edifices are common phenomena in the 12. 3D modeling of stratigraphic units and simulation of seismic facies in the Lion gulf margin; Modelisation 3D des unites stratigraphiques et simulation des facies sismiques dans la marge du golfe du Lion Energy Technology Data Exchange (ETDEWEB) Chihi, H. 1997-05-12 This work aims at providing a contribution to the studies carried out on reservoir characterization by use of seismic data. The study mainly consisted in the use of geostatistical methods in order to model the geometry of stratigraphic units of the Golfe du Lion margin and to simulate the seismic facies from high resolution seismic data. We propose, for the geometric modelling, a methodology based on the estimation of the surfaces and calculation afterwards of the thicknesses, if the modelling of the depth is possible. On the other hand the method consists in estimating the thickness variable directly and in deducing the boundary surfaces afterwards. In order to simulate the distribution of seismic facies within the units of the western domain, we used the truncated Gaussian method. The used approach gave a satisfactory results, when the seismic facies present slightly dipping reflectors with respect to the reference level. Otherwise the method reaches its limits because of the problems of definition of a reference level which allows to follow the clino-forms. In spite of these difficulties, this simulation allows us to estimate the distribution of seismic facies within the units and then to deduce their probable extension. (author) 150 refs. 13. Upper Carboniferous retroarc volcanism with submarine and subaerial facies at the western Gondwana margin of Argentina Science.gov (United States) Koukharsky, M.; Kleiman, L.; Etcheverría, M.; Quenardelle, S.; Bercowski, F. 2009-04-01 During Late Carboniferous times a continental magmatic arc developed at the western margin of Gondwana in South America, as several marine sedimentary basins were formed at the same time in the retroarc region. North of 33°S, at Cordón Agua del Jagüel, Precordillera of Mendoza, Argentina, a volcanic sequence crops out which was emplaced in a submarine environment with some subaerial exposures, and it is intercalated in marine sediments of Agua del Jagüel Formation, which fills of one of these retroarc basins. This paper presents, for the first time, a facies analyses together with geochemical and isotopic data of this volcanic suite, suggesting its deposition in an ensialic retroarc marine basin. The volcanic succession comprises debris flows with either sedimentary or volcanic fragments, base surge, resedimented massive and laminated dacitic-andesitic hyaloclastite, pillow lava, basic hyaloclastite and dacitic-andesitic lavas and hyaloclastite facies. Its composition is bimodal, either basaltic or dacitic-andesitic. The geochemistry data indicate a subalkaline, low K calk-alkaline and metaluminous affinity. The geochemistry of the basalts points to an origin of the magmas from a depleted mantle source with some crustal contamination. Conversely, the geochemistry of the dacites-andesites shows an important participation of both crustal components and subduction related fluids. A different magmatic source for the basalts than for the dacites-andesites is also supported by Sr and Nd isotopic initial ratios and Nd model ages. The characteristics of this magmatic suite suggest its emplacement in an extensional setting probably associated with the presence of a steepened subduction zone at this latitude during Upper Carboniferous times. 14. Coastal dune facies, Permian Cutler Formation (White Rim Sandstone), Capitol Reef National Park area, southern Utah Science.gov (United States) Kamola, Diane L.; Chan, Marjorie A. 1988-04-01 The Permian Cutler Formation (White Rim Sandstone) in the Capitol Reef National Park area in southern Utah is an excellent example of a coastal dune complex subjected to periodic flooding by marine waters. Wind-ripple, grainfall and grainflow laminae compose the cross-sets deposited by eolian dunes. However, wave-reworked structures such as oscillation ripples, the occurrence of the characteristically marine trace fossils Thalassinoides and Chondrites, and interfingering marine carbonate beds of the Kaibab Formation collectively indicate marine interaction with the eolian environment. Four facies are distinguished: cross-stratified sandstone, burrowed to bioturbated sandstone, brecciated and deformed sandstone, and ripple-laminated sandstone and thin carbonate beds. One unusual aspect of the cross-stratified sandstone facies is the abundance of coarse-grained sand. Coarse-grained sand is atypical in many ancient eolian slipface deposits, but occurs here in large slipface foresets as both grainflow and wind-ripple deposits. No water-laid structures are found in these slipface deposits. Coarse-grained sand was probably transported to the Cutler shoreline by fluvial systems draining the Uncompahgre Uplift to the east, and then concentrated as coarse-grained ripples in interdune areas. Some of these coarse-grained ripples migrated up the stoss side of the dunes and accumulations of coarse-grained sand avalanched down the crest to form grainflow deposits. An extensive amount of soft-sediment deformation is indicated by the presence of convolute bedding and brecciation. These features occur near the zone of interfingering with marine carbonate beds of the Kaibab Formation. The water-saturated and moist conditions required for extensive deformation may have been controlled by the proximity of these sandstones to the shoreline, and fluctuations in the associated groundwater table. 15. Beaulieu-Boycott-Innes syndrome: an intellectual disability syndrome with characteristic facies. Science.gov (United States) Casey, Jillian; Jenkinson, Allan; Magee, Alex; Ennis, Sean; Monavari, Ahmad; Green, Andrew; Lynch, Sally A; Crushell, Ellen; Hughes, Joanne 2016-10-01 We report a female child from an Irish Traveller family presenting with severe intellectual disability, dysmorphic features, renal anomalies, dental caries and cyclical vomiting. Current health issues include global developmental delay, mild concentric left ventricular hypertrophy, dental malocclusion and caries and a single duplex left kidney. The proband and her mother also have multiple epiphyseal dysplasia. Whole-exome sequencing was performed to identify the underlying genetic cause. DNA from the proband was enriched with the Agilent Sure Select v5 Exon array and sequenced on an Illumina HiSeq. Rare homozygous variants were prioritized. Whole-exome sequencing identified three linked homozygous missense variants in THOC6 (c.298T>A, p.Trp100Arg; c.700G>C, p.Val234Leu; c.824G>A, p.Gly275Asp) as the likely cause of this child's intellectual disability syndrome, resulting in a molecular diagnosis of Beaulieu-Boycott-Innes syndrome (BBIS). This is the first report of BBIS in Europe. BBIS has been reported previously in two Hutterite families and one Saudi family. A review of all patients to date shows a relatively homogenous phenotype. Core clinical features include low birth weight with subsequent growth failure, short stature, intellectual disability with language delay, characteristic facies, renal anomalies and dental malocclusion with caries. Some patients also have cardiac defects. All patients show characteristic dysmorphic facial features including a tall forehead with high anterior hairline and deep-set eyes with upslanting palpebral fissures. The coexistence of intellectual disability together with these characteristic facies should provide a diagnostic clue for BBIS during patient evaluation. 16. 26 CFR 400.5-1 - Redemption by United States. Science.gov (United States) 2010-04-01 ... subparagraph (1) of this paragraph (d), shall constitute prima facie evidence of the regularity of the... of the obligation secured by such lien to the extent legally satisfied by reason of the sale); (ii.... Subsequently, A defaults on the mortgage and B forecloses on the mortgage which has an outstanding obligation... 17. The Harm Principle as a Mid-level Principle? Three Problems from the Context of Infectious Disease Control NARCIS (Netherlands) Krom, A. 2011-01-01 Effective infectious disease control may require states to restrict the liberty of individuals. Since preventing harm to others is almost universally accepted as a legitimate (prima facie) reason for restricting the liberty of individuals, it seems plausible to employ a mid-level harm principle in 18. Oxygenation in carbonate microbialites and associated facies after the end-Permian mass extinction: Problems and potential solutions Directory of Open Access Journals (Sweden) Stephen Kershaw 2018-01-01 The oxygenation state of post-end-Permian extinction shallow marine facies continues to present a challenge of interpretation, and requires high-resolution sampling and careful attention to small-scale changes, as well as loss of rock through pressure solution, as the next step to resolve the issue. 19. Heuristic reasoning and relative incompleteness OpenAIRE Treur, J. 1993-01-01 In this paper an approach is presented in which heuristic reasoning is interpreted as strategic reasoning. This type of reasoning enables one to derive which hypothesis to investigate, and which observable information to acquire next (to be able to verify the chosen hypothesis). A compositional architecture for reasoning systems that perform such heuristic reasoning is introduced, called SIX (for Strategic Interactive eXpert systems). This compositional architecture enables user interaction a... 20. The Christological Ontology of Reason DEFF Research Database (Denmark) Nissen, Ulrik Becker 2006-01-01 Taking the startingpoint in an assertion of an ambiguity in the Lutheran tradition’s assessment of reason, the essay argues that the Kantian unreserved confidence in reason is criticised in Bonhoeffer. Based upon a Christological understanding of reason, Bonhoeffer endorses a view of reason which...... is treated in the essay. Here it is argued that Bonhoeffer may be appropriated in attempting to outline a Christological ontology of reason holding essential implications for the sources and conditions of public discourse.... 1. Two kinds of reasoning. Science.gov (United States) Rips, L J 2001-03-01 According to one view of reasoning, people can evaluate arguments in at least two qualitatively different ways: in terms of their deductive correctness and in terms of their inductive strength. According to a second view, assessments of both correctness and strength are a function of an argument's position on a single psychological continuum (e.g., subjective conditional probability). A deductively correct argument is one with the maximum value on this continuum; a strong argument is one with a high value. The present experiment tested these theories by asking participants to evaluate the same set of arguments for correctness and strength. The results produced an interaction between type of argument and instructions: In some conditions, participants judged one argument deductively correct more often than a second, but judged the second argument inductively strong more often than the first. This finding supports the view that people have distinct ways to evaluate arguments. 2. IPP (INNOVACIÓN EN PRODUCTOS Y PROCESOS PARA EL SECTOR DE LAS MATERIAS PRIMAS MINERALES Y ENERGÉTICAS Directory of Open Access Journals (Sweden) CORREA ESPINAL ALEXANDER 2010-05-01 Full Text Available Este articulo proscrita los resultados del proyecto ce Investigación IPP (Innovación ce Procesos y Productos que plantea un análisis profundo y sistémico de las cadenas productivas, basado en el estudio de la productividad y los procesos. Este proyecto se trabajo en 4 fases: Inteligencia, Experimentación. Innovación y Apropiación tecnológica. Estas etapas están dirigidas al mejoramiento continuo ce los procesos, de los productos ce la organización y de las interacciones entre los actores de la cadena productiva de las materias primas minerales y energéticas. En la fase de inteligencia, se estudiaron las características, las ecesidades. el mercado y el entorno de la cadena productiva que son el resultado del aprovechamiento de los recursos naturales y del ambiente En la segunda fase, se caracterizó la formulación, diseño c implantación ce prototipos de procesos y productos que emulen el comportamiento del proceso en un sistema real y sean amigables con el medio ambiente. Teniendo en cuenta las dos primeras fases, la tercera se caracterizó por la formulación y el diseño ce nuevos procesos y productos que mejoren la eficiencia y la productividad. En la última fase del proyecto, se planteó el servicio de apropiación tecnológica que busca transferir innovación y conocimiento de punta a la cadena. Finalmente el resultado ce IPP es la propuesta de un centro de innovación y tecnología en la Universidad Nacional de Colombia, que garantizará la apropiación y adecuación de las soluciones a las cadenas productivas, siendo una innovación para el sector de la minería, los materiales y la energía, y teniendo como principios, productos y procesos amigables con el ambiente. 3. Materias primas para pavimentos y revestimientos cerámicos en la región de Murcia Directory of Open Access Journals (Sweden) Fernández, C. 2001-10-01 Full Text Available The clay industry of the Murcia Region has never had a relevant industrial importance, with only around ten brick operations in the last few years. Today only only two brid factories are operative having certain size. The extraordinary industrial development currently experienced by the Region has leaded to the development of new initiatives which need institutional backing. In this framework and under the sponsoring of the Council of Technologies, Industry and Commerce of the Autonomic Community, the Spanish Geological Survey (ITGE has carried out a general survey for raw materials for the ceramic industry in the region, mainly aimed to find clays for ceramic gres and glazed tiles, whose results are discussed in this paper. Murcia has a very complicated geology, being carbonated marine sediments the most important lithologies. Due to it, it is difficult to find no-carbonated shales or clays to produce gres tiles. We have found six zones containing different clay types, that reach a few hundreds million tons of resources. With that clays we have produce in the laboratory gres tiles and glazed tiles of commercial quality. La industria cerámica de la Región de Murcia no ha tenido gran importancia industrial, limitándose a una decena de fábricas de ladrillos. Hoy en día sólo operan en la región 2 fábricas de ladrillos de cierta entidad. El extraordinario desarrollo industrial que experimenta actualmente la Región suscita nuevas iniciativas empresariales, que precisan del apoyo institucional. En este marco y bajo el auspicio y con la financiación parcial de la Consejería Tecnologías, Industria y Comercio de la Comunidad Autónoma, el Instituto Tecnológico Geominero de España ha realizado en los tres últimos años una investigación general de materias primas para la industria cerámica en la región, especialmente dirigida a localizar arcillas para pavimentos y revestimientos cerámicos, cuyos resultados se exponen en este 4. Facies analysis, depositional environments and paleoclimate of the Cretaceous Bima Formation in the Gongola Sub - Basin, Northern Benue Trough, NE Nigeria Science.gov (United States) Shettima, B.; Abubakar, M. B.; Kuku, A.; Haruna, A. I. 2018-01-01 Facies analysis of the Cretaceous Bima Formation in the Gongola Sub -basin of the Northern Benue Trough northeastern Nigeria indicated that the Lower Bima Member is composed of alluvial fan and braided river facies associations. The alluvial fan depositional environment dominantly consists of debris flow facies that commonly occur as matrix supported conglomerate. This facies is locally associated with grain supported conglomerate and mudstone facies, representing sieve channel and mud flow deposits respectively, and these deposits may account for the proximal alluvial fan region of the Lower Bima Member. The distal fan facies were represented by gravel-bed braided river system of probably Scot - type model. This grade into sandy braided river systems with well developed floodplains facies, forming probably at the lowermost portion of the alluvial fan depositional gradient, where it inter-fingers with basinal facies. In the Middle Bima Member, the facies architecture is dominantly suggestive of deep perennial sand-bed braided river system with thickly developed amalgamated trough crossbedded sandstone facies fining to mudstone. Couplets of shallow channels are also locally common, attesting to the varying topography of the basin. The Upper Bima Member is characterized by shallow perennial sand-bed braided river system composed of successive succession of planar and trough crossbedded sandstone facies associations, and shallower channels of the flashy ephemeral sheetflood sand - bed river systems defined by interbedded succession of small scale trough crossbedded sandstone facies and parallel laminated sandstone facies. The overall stacking pattern of the facies succession of the Bima Formation in the Gongola Sub - basin is generally thinning and fining upwards cycles, indicating scarp retreat and deposition in a relatively passive margin setting. Dominance of kaolinite in the clay mineral fraction of the Bima Formation points to predominance of humid sub - tropical 5. Mechanical properties, mineralogical composition, and micro fabric of Opalinus Clay. Sandy and shaly facies (Mont Terri, Switzerland) International Nuclear Information System (INIS) Kaufhold, Annette; Graesle, Werner; Plischke, Ingo 2015-01-01 For the safe disposal of high-level radioactive waste, different host rocks are currently considered. The favorable properties of claystone are low permeability, retention capacity for some radionuclides, and the ability to self-seal cracks, e.g. by swelling or time-dependent compaction creep. For the understanding of the long-term behavior of clay host rocks, the interaction between mechanical behavior, micro fabric, and mineral composition has to be understood (Bock et al., 2010). In the international research project Mont Terri (Switzerland) the Opalinus Clay (Jurassic Formation) is investigated in an underground rock laboratory (URL). In the present study the relationship between mechanical, mineralogical and micro fabric properties were studied on representative samples of the sandy and shaly facies of the Opalinus Clay (OPA) from Mont Terri. The mineral composition of all samples was analysed by using a complex mineral phase analysis. Therefore, the results of the X-ray diffraction, X-ray fluoreszence, organic and inorganic carbonate analysis (LECO) were adjusted with each other. In the case of the sandy facies (OPA) the mechanical strength inrcreases with increasing carbonate content. Here small carbonate particles form the matrix and act as stabilisator. The carbonates of the shaly facies (OPA), on the other hand, are mainly fossil fragments (e.g. shells) aligned parallel to bedding. These large carbonate particles are acting as predetermined breaking surfaces. Hence, in the case of shaly facies (OPA) the mechanical strength decreases with increasing carbonate content. Image Analyses (Fiji registered ) of scattering electron microscope images of polished sections proved the determined microstructural differences. Besides, carbonate particles in the sandy facies are mostly isometric, in contrast carbonates of the shaly facies show different shapes. This is explained further in terms of the aspect ratio. The mechanical tests were carried out as triaxial 6. Mechanical properties, mineralogical composition, and micro fabric of Opalinus Clay. Sandy and shaly facies (Mont Terri, Switzerland) Energy Technology Data Exchange (ETDEWEB) Kaufhold, Annette; Graesle, Werner [BGR Hannover (Germany); Plischke, Ingo 2015-07-01 For the safe disposal of high-level radioactive waste, different host rocks are currently considered. The favorable properties of claystone are low permeability, retention capacity for some radionuclides, and the ability to self-seal cracks, e.g. by swelling or time-dependent compaction creep. For the understanding of the long-term behavior of clay host rocks, the interaction between mechanical behavior, micro fabric, and mineral composition has to be understood (Bock et al., 2010). In the international research project Mont Terri (Switzerland) the Opalinus Clay (Jurassic Formation) is investigated in an underground rock laboratory (URL). In the present study the relationship between mechanical, mineralogical and micro fabric properties were studied on representative samples of the sandy and shaly facies of the Opalinus Clay (OPA) from Mont Terri. The mineral composition of all samples was analysed by using a complex mineral phase analysis. Therefore, the results of the X-ray diffraction, X-ray fluoreszence, organic and inorganic carbonate analysis (LECO) were adjusted with each other. In the case of the sandy facies (OPA) the mechanical strength inrcreases with increasing carbonate content. Here small carbonate particles form the matrix and act as stabilisator. The carbonates of the shaly facies (OPA), on the other hand, are mainly fossil fragments (e.g. shells) aligned parallel to bedding. These large carbonate particles are acting as predetermined breaking surfaces. Hence, in the case of shaly facies (OPA) the mechanical strength decreases with increasing carbonate content. Image Analyses (Fiji {sup registered}) of scattering electron microscope images of polished sections proved the determined microstructural differences. Besides, carbonate particles in the sandy facies are mostly isometric, in contrast carbonates of the shaly facies show different shapes. This is explained further in terms of the aspect ratio. The mechanical tests were carried out as triaxial 7. Chemopreventive Effects of the p53-Modulating Agents CP-31398 and Prima-1 in Tobacco Carcinogen-Induced Lung Tumorigenesis in A/J Mice Directory of Open Access Journals (Sweden) Chinthalapally V. Rao 2013-09-01 Full Text Available Lung cancer is the leading cause of cancer deaths worldwide. Expression of the p53 tumor suppressor protein is frequently altered in tobacco-associated lung cancers. We studied chemopreventive effects of p53-modulating agents, namely, CP-31398 and Prima-1, on 4-(methylnitrosamino-1-(3-pyridyl-1-butanone (NNK-induced lung adenoma and adenocarcinoma formation in female A/J mice. Seven-week-old mice were treated with a single dose of NNK (10 µmol/mouse by intraperitoneal injection and, 3 weeks later, were randomized to mice fed a control diet or experimental diets containing 50 or 100 ppm CP-31398 or 150 or 300 ppm Prima-1 for either 17 weeks (10 mice/group or 34 weeks (15 mice/group to assess the efficacy against lung adenoma and adenocarcinoma. Dietary feeding of 50 or 100 ppm CP-31398 significantly suppressed (P < .0001 lung adenocarcinoma by 64% and 73%, respectively, after 17 weeks and by 47% and 56%, respectively, after 34 weeks. Similarly, 150 or 300 ppm Prima-1 significantly suppressed (P < .0001 lung adenocarcinoma formation by 56% and 62%, respectively, after 17 weeks and 39% and 56%, respectively, after 34 weeks. Importantly, these results suggest that both p53 modulators cause a delay in the progression of adenoma to adenocarcinoma. Immunohistochemical analysis of lung tumors from mice exposed to p53-modulating agents showed a significantly reduced tumor cell proliferation and increased accumulation of wild-type p53 in the nucleus. An increase in p21- and apoptotic-positive cells was also observed in lung tumors of mice exposed to p53-modulating agents. These results support a chemopreventive role of p53-modulating agents in tobacco carcinogen-induced lung adenocarcinoma formation. 8. Nueva materia prima borácica como componente de esmaltes cerámicos. Estudio de su solubilidad en suspensiones acuosas concentradas Directory of Open Access Journals (Sweden) Galindo, M. 2009-02-01 Full Text Available This paper presents an alternative to the use of conventional ceramic frits as raw materials that contribute boron to glaze compositions: a new semi-processed borate (patent pending (WO 2007/148101. The solubility of this new raw material is analysed and compared with that exhibited by conventional ceramic frits and other, natural and processed borates. This comparative analysis has been performed by determining the boron percentage present in the liquid phase of several glaze compositions prepared with each of these raw materials, modifying the type of deflocculant used and the solid/liquid contact time. The results of this study demonstrate the low solubility of the new semi-processed borate and its suitability for use in ceramic glaze formulation. En el presente trabajo se presenta una alternativa a la utilización de fritas cerámicas convencionales como materias primas que aportan boro a las composiciones de esmalte: un nuevo borato sintético (patente pendiente WO2007/148101. Se ha estudiado y comparado la solubilidad de esta nueva materia prima con la que exhiben las fritas cerámicas convencionales y otros boratos, tanto naturales como sintéticos. Para ello, se ha determinado el porcentaje de boro presente en la fase líquida de varios esmaltes preparados con cada una de dichas materias primas, modificando el tipo de desfloculante utilizado y el tiempo de contacto sólido/líquido. El resultado de este trabajo ha puesto de manifiesto la baja solubilidad que presenta el nuevo borato sintético y su aptitud para ser usado en la formulación de esmaltes cerámicos. 9. Mejoramiento de la gestión de compras e inventario de materia prima en la empresa Cepeda Cía. Ltda. OpenAIRE Villacís Mayorga, Grace Silvana 2015-01-01 En los resultados obtenidos en el proyecto "Diagnóstico de la Gestión de Compras y Control de Inventarios en la Empresa Cepeda Cía. Ltda.", se determinaron problemas de excesos y desabastecimientos de materia prima, procedimientos no actualizados del sistema de gestión; falta de un control formal o técnico en la gestión de los procesos de compra y control de inventarios evidenciándose que se requiere de planificación y orden. Para el mejoramiento del Proceso de Compras e Inventarios de Materi... 10. Le Visage de la Victoire di Henry De Groux: la riscoperta di un’opera antimilitarista del tempo della Prima guerra mondiale Directory of Open Access Journals (Sweden) Carol Morganti 2014-03-01 Full Text Available Il presente intervento è dedicato a un’importante raccolta di incisioni, oggi riscoperta: Le Visage de la Victoire, eseguita dall’artista belga Henry De Groux. Costituita da oltre 40 incisioni (acqueforti e vernici molli, è stata realizzata nel corso della Prima Guerra Mondiale al fine di denunciare l’inutile massacro in corso. Si tratta di opere di ispirazione visionaria, che rivelano significati universali, mettendo il maestro belga in rapporto di affinità con artisti quali Goya e Otto Dix. 11. Avaliação da qualidade de matérias-primas de ruibarbo utilizadas em formulações farmacêuticas Directory of Open Access Journals (Sweden) O.V. Sousa Full Text Available As plantas denominadas de ruibarbo sintetizam antraquinonas e taninos, que são responsáveis pelos efeitos laxante e adstringente, respectivamente. Análises da qualidade de cinco matérias-primas de ruibarbo foram realizadas a fim de detectar adulterações. As reações para antraquinonas e taninos foram positivas. Os constituintes rapônticos foram observados na amostra de Rheum palmatum (2. As medidas de cinzas totais para Rheum palmatum (2 e Ferraria cathartica estão acima do esperado. Conforme resultados, as amostras de Rheum palmatum (2 e Ferraria cathartica devem estar adulteradas. 12. PROCESO ENZIMATICO PARA LA PRODUCCION DE METIL ESTERES DE ACIDOS GRASOS UTILIZANDO ACEITES RESIDUALES DE FRITURA EN MEZCLA CON ACEITE DE RAPS COMO MATERIA PRIMA OpenAIRE AZOCAR ULLOA; LAURA HAYDEE; AZOCAR ULLOA; LAURA HAYDEE 2010-01-01 Los procesos catalizados por lipasas han sido ampliamente investigados como alternativa para la producción de metil ésteres de ácidos grasos (fatty acid methyl ester, FAME) o biodiesel. El interés en este proceso radica en que a diferencia de los procesos convencionales catalizados con sales alcalinas, los procesos catalizados con lipasas permiten el uso de materias primas alternativas y de menor costo, tales como el aceite residual de fritura (waste frying oil, WFO). Pese a los l... 13. Evaluación de distintas materias primas para la producción de almácigo de tomate OpenAIRE Fernando Richmond 2010-01-01 Se evaluaron mezclas de materias primas naturales en diferentes proporciones y en el siguiente orden: fibra de coco (Cocos nucifera), aserrín de melina (Gmelina arborea) y abono orgánico Coope Victoria, para utilizarlos como sustrato en la etapa de almácigo de tomate híbrido FBM-17. Se hicieron mezclas entre sí de fibra de coco y aserrín de melina en diferentes proporciones (30%, 40% y 50% de cada material), para un total de 9 tratamientos; el abono orgánico se agregó para completar el 100%. ... 14. The sedimentary facies characteristics and lithofacies palaeogeography during Middle-Late Cambrian, Sichuan Basin and adjacent area Directory of Open Access Journals (Sweden) Feifan Lu 2017-06-01 Full Text Available Combined with the regional strata filling characteristics of Middle-Upper Cambrian, the present paper conducts a systematic research on sedimentary facies in the basin and its peripheral area by utilizing 164 field outcrops and drilling and coring data. Further, the method of “multi-factor comprehensive synthesis based on single-factor analysis” was employed to investigate the sedimentary facies and palaeogeography of the study area and establish the sedimentary facies model. Stratigraphic reveals that the study area represents the pattern of thin-northwest and thick-southeast by stretching northeast-southwest. Within the present basin, the pattern of “one thin and two thick” predominates, while outside the basin “four thin and three thick” filling feature was found. Sedimentary facies shows that the study area was featured by rimmed carbonate platform. Specifically, carbonate platform, slope and northeastern corner Qinling paleooceanic Basin and southeastern corner Jiangnan Bain was identified from the west to the east. The carbonate platform contains restricted platform, evaporation-restricted platform, semi-restricted platform and the platform margin. Single factor analysis and lithofacies palaeogeographic characteristics manifests that during Middle-Late Cambrian, the western Old land evolved into peneplain stage, and that the eastern and southwestern sub-sags remained connected to the open-sea to some extent. At the time, the shllow seawater circulation was relatively restricted, while the ancient seabed tended to be flat and evaporation characteristics significantly diminished. Secondary sea-level fluctuation intensively influenced the development of scaled grain beach. It is suggested that tide marginal beach, intraplatform shoal subfacies zone, along with Shiqian-SangZhi in southeast and Zhenba-Xinshan in northeast platform-margin beach subfacies zone to be preferable targets for the favorable reservoir facies zone and 15. Using Relational Reasoning Strategies to Help Improve Clinical Reasoning Practice. Science.gov (United States) Dumas, Denis; Torre, Dario M; Durning, Steven J 2018-05-01 Clinical reasoning-the steps up to and including establishing a diagnosis and/or therapy-is a fundamentally important mental process for physicians. Unfortunately, mounting evidence suggests that errors in clinical reasoning lead to substantial problems for medical professionals and patients alike, including suboptimal care, malpractice claims, and rising health care costs. For this reason, cognitive strategies by which clinical reasoning may be improved-and that many expert clinicians are already using-are highly relevant for all medical professionals, educators, and learners.In this Perspective, the authors introduce one group of cognitive strategies-termed relational reasoning strategies-that have been empirically shown, through limited educational and psychological research, to improve the accuracy of learners' reasoning both within and outside of the medical disciplines. The authors contend that relational reasoning strategies may help clinicians to be metacognitive about their own clinical reasoning; such strategies may also be particularly well suited for explicitly organizing clinical reasoning instruction for learners. Because the particular curricular efforts that may improve the relational reasoning of medical students are not known at this point, the authors describe the nature of previous research on relational reasoning strategies to encourage the future design, implementation, and evaluation of instructional interventions for relational reasoning within the medical education literature. The authors also call for continued research on using relational reasoning strategies and their role in clinical practice and medical education, with the long-term goal of improving diagnostic accuracy. 16. Reason with me : 'Confabulation' and interpersonal moral reasoning NARCIS (Netherlands) Nyholm, S.R. 2015-01-01 According to Haidt’s ‘social intuitionist model’, empirical moral psychology supports the following conclusion: intuition comes first, strategic reasoning second. Critics have responded by arguing that intuitions can depend on non-conscious reasons, that not being able to articulate one’s reasons 17. Resultados preliminares sôbre o estudo do quenafe como matéria-prima para papel Preliminary results on the study of kenaf as a raw-material for the pulp and paper industry Directory of Open Access Journals (Sweden) Dirceu Ciaramello 1971-01-01 Full Text Available Variedades de quenafe, plantadas em diferentes espaçamentos, foram estudadas em ensaio instalado em 1968 no Centro Experimental de Campinas, do Instituto Agronômico, visando à produção de matéria-prima para celulose e papel. Produções da ordem de 29,4 t/ha de massa verde renderam 6,7 t/ha de caules secos, que foram estudados, sob diversos processos de cozimento, na produção de pasta para papel. Os processos sulfato e sulfito neutro de sódio revelaram-se apropriados para a obtenção de pasta celulósica de quenafe, dando papéis com boas características físico-mecânicas.The production of pulping raw material for the paper industry of four varieties of kenaf (Hibiscus cannabinus L. sown at three spacings (30, 40 and 50 cm was compared in a field trial made at the Experimental Center, Campinas, SP. The analysis of variance of obtained data showed no differences between production of varieties or/and spacings. As an average, the yield was 29.4 metric ton of green stems which corresponded to 6.7 ton of dried weight per hectare. Determinations of physical properties indicated that basic density of stems is only 0.13 g/cm³ and that bast fibers are identical to those of softwood. Wood fibers, however, are shorter and with a larger lumen. Coockings by the sodium sulfate and neutral sodium sulfite processes gave pulp of reasonable quality in bursting, folding and tensile strengths but weak in the tearing and with low porosity. 18. Argumentation in Legal Reasoning Science.gov (United States) Bench-Capon, Trevor; Prakken, Henry; Sartor, Giovanni A popular view of what Artificial Intelligence can do for lawyers is that it can do no more than deduce the consequences from a precisely stated set of facts and legal rules. This immediately makes many lawyers sceptical about the usefulness of such systems: this mechanical approach seems to leave out most of what is important in legal reasoning. A case does not appear as a set of facts, but rather as a story told by a client. For example, a man may come to his lawyer saying that he had developed an innovative product while working for Company A. Now Company B has made him an offer of a job, to develop a similar product for them. Can he do this? The lawyer firstly must interpret this story, in the context, so that it can be made to fit the framework of applicable law. Several interpretations may be possible. In our example it could be seen as being governed by his contract of employment, or as an issue in Trade Secrets law. 19. Motivated reasoning during recruitment. Science.gov (United States) Kappes, Heather Barry; Balcetis, Emily; De Cremer, David 2018-03-01 This research shows how job postings can lead job candidates to see themselves as particularly deserving of hiring and high salary. We propose that these entitlement beliefs entail both personal motivations to see oneself as deserving and the ability to justify those motivated judgments. Accordingly, we predict that people feel more deserving when qualifications for a job are vague and thus amenable to motivated reasoning, whereby people use information selectively to reach a desired conclusion. We tested this hypothesis with a 2-phase experiment (N = 892) using materials drawn from real online job postings. In the first phase of the experiment, participants believed themselves to be more deserving of hiring and deserving of higher pay after reading postings composed of vaguer types of qualifications. In the second phase, yoked observers believed that participants were less entitled overall, but did not selectively discount endorsement of vaguer qualifications, suggesting they were unaware of this effect. A follow-up preregistered experiment (N = 905) using postings with mixed qualification types replicated the effect of including more vague qualifications on participants' entitlement beliefs. Entitlement beliefs are widely seen as problematic for recruitment and retention, and these results suggest that reducing the inclusion of vague qualifications in job postings would dampen the emergence of these beliefs in applicants, albeit at the cost of decreasing application rates and lowering applicants' confidence. (PsycINFO Database Record (c) 2018 APA, all rights reserved). 20. Component Processes in Analogical Reasoning Science.gov (United States) Sternberg, Robert J. 1977-01-01 Describes alternative theoretical positions regarding (a) the component information processes used in analogical reasoning and (b) strategies for combining these processes. Also presents results from three experiments on analogical reasoning. (Author/RK) 1. Preferential reasoning for modal logics CSIR Research Space (South Africa) Britz, K 2011-11-01 Full Text Available Modal logic is the foundation for a versatile and well-established class of knowledge representation formalisms in artificial intelligence. Enriching modal logics with non-monotonic reasoning capabilities such as preferential reasoning as developed... 2. EVALUACIÓN DE MATERIAS PRIMAS EN UNA PLANTA DE BENEFICIO DE ARENA DE SILICE PARA AUMENTAR LA EFICIENCIA ENERGÉTICA DEL PROCESO DE MOLIENDA Directory of Open Access Journals (Sweden) BEATRIZ ÁLVAREZ-RODRÍGUEZ 2013-01-01 Full Text Available El presente trabajo tiene por objetivo primordial optimizar el consumo energético y reducir la contaminación ambiental asociada, por la liberación de CO2, en una planta de micronización de sílice. La metodología empleada consiste en aplicar la teoría de Bond para la selección de materias primas a tratar en la mencionada planta, la cual dependiendo de las necesidades actuales opera con dos tamaños de molienda d100, 50 y 75μm. Los ensayos experimentales se llevaron a cabo sobre muestras tomadas en la planta, teniendo en cuenta que las tres materias primas son de distinta procedencia y de similares características químicas y mineralógicas. Del análisis de los resultados obtenidos se concluye que el consumo energético de la planta puede reducirse hasta algo más de un 30% en ambos tamaños y evitando las emisiones de CO2 en 293,83 kg y 128,86 kg por hora de funcionamiento respectivamente. 3. Analogical Reasoning in Geometry Education Science.gov (United States) Magdas, Ioana 2015-01-01 The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a… 4. Heuristic reasoning and relative incompleteness NARCIS (Netherlands) Treur, J. 1993-01-01 In this paper an approach is presented in which heuristic reasoning is interpreted as strategic reasoning. This type of reasoning enables one to derive which hypothesis to investigate, and which observable information to acquire next (to be able to verify the chosen hypothesis). A compositional 5. Heuristic Elements of Plausible Reasoning. Science.gov (United States) Dudczak, Craig A. At least some of the reasoning processes involved in argumentation rely on inferences which do not fit within the traditional categories of inductive or deductive reasoning. The reasoning processes involved in plausibility judgments have neither the formal certainty of deduction nor the imputed statistical probability of induction. When utilizing… 6. Analogical Reasoning and Computer Programming. Science.gov (United States) Clement, Catherine A.; And Others 1986-01-01 A study of correlations between analogical reasoning and Logo programming mastery among female high school students related the results of pretests of analogical reasoning to posttests of programming mastery. A significant correlation was found between analogical reasoning and the ability to write subprocedures for use in several different… 7. Tectonic and climatic controls on continental depositional facies in the Karoo Basin of northern Natal, South Africa Science.gov (United States) Turner, Brian R. 1986-02-01 The eastern Karoo Basin, South Africa, contains a thick sequence of terrigenous clastic sediments comprising a meanderbelt facies, braided channel facies divided into coarse and fine subfacies, fluviolacustrine facies and aeolian facies. Depositional trends and changes in fluvial style reflect a progressive increase in aridity of the climate under stable tectonic conditions, interrupted by two phases of source area tectonism and the development of fine and coarse clastic wedges of the braided channel subfacies; the latter signifying a short interlude of cool, wet conditions. The fine braided channel subfacies occurs in the upper part of the meanderbelt facies, which was deposited by ephemeral, meandering mixed-load streams of variable discharge and sinuosity, under dry, semi-arid climatic conditions. These deposited complex, internally discordant channel sands and well-developed levee deposits. Following deposition of the coarse braided channel subfacies semi-arid conditions returned and fluvial deposition was dominated by ephemeral, straight to slightly sinuous mixed load streams characterised by simple channel sand bodies. As the aridity of the climate increased, the streams became more localised and carried an increasing proportion of fines. Interbedded with and overlying the fluvial deposits is a mudstone-dominated lacustrine sequence grading up into aeolian sands suggesting a playa lake-type situation. The general absence of evaporites from these sediments is attributed to the fresh nature of the lake waters, as evidenced by the freshwater aquatic organisms and clay-mineral suite, the lack of adequate inflow for solute accumulation and the removal of dust impregnated by salts from the surface of the dry lake bed during the dry season by superheated, upward-spiralling columns of air. Broadly similar environments to the fluvio-lacustrine and aeolian facies sequence are to be found in the Lake Eyre Basin of central Australia and the Okavango "delta" of northern 8. Mesozoic Alpine facies deposition as a result of past latitudinal plate motion. Science.gov (United States) Muttoni, Giovanni; Erba, Elisabetta; Kent, Dennis V; Bachtadse, Valerian 2005-03-03 The fragmentation of Pangaea as a consequence of the opening of the Atlantic Ocean is documented in the Alpine-Mediterranean region by the onset of widespread pelagic sedimentation. Shallow-water sediments were replaced by mainly pelagic limestones in the Early Jurassic period, radiolarian cherts in the Middle-Late Jurassic period, and again pelagic limestones in the Late Jurassic-Cretaceous period. During initial extension, basin subsidence below the carbonate compensation depth (CCD) is thought to have triggered the transition from Early Jurassic limestones to Middle-Late Jurassic radiolarites. It has been proposed that the transition from radiolarites to limestones in the Late Jurassic period was due to an increase in calcareous nannoplankton abundance when the CCD was depressed below the ocean floor. But in modern oceans, sediments below the CCD are not necessarily radiolaritic. Here we present palaeomagnetic samples from the Jurassic-Cretaceous pelagic succession exposed in the Lombardian basin, Italy. On the basis of an analysis of our palaeolatitudinal data in a broader palaeogeographic context, we propose an alternative explanation for the above facies tripartition. We suggest that the Lombardian basin drifted initially towards, and subsequently away from, a near-equatorial upwelling zone of high biosiliceous productivity. Our tectonic model for the genesis of radiolarites adds an essential horizontal plate motion component to explanations involving only vertical variations of CCD relative to the ocean floor. It may explain the deposition of radiolarites throughout the Mediterranean and Middle Eastern region during the Jurassic period. 9. Prograding coastal facies associations in the Vryheid formation (Permian) at Effingham quarries near Durban, South Africa Science.gov (United States) Tavener-Smith, R. 1982-05-01 This paper describes and interprets a flat-lying, sandstone—siltstone sequence 70 m thick in three disused quarries. The beds comprise the lowest part of the Vryheid Formation (middle Ecca) in the Durban vicinity. The sequence is conveniently divisible into two parts: the Lower Division constitutes a prograding beach barrier association, while the upper one represents a back barrier lagoonal complex. Fourteen sedimentary facies are described and interpreted to represent a range of depositional environments including open water shelf silts, sandy shoreface and littoral deposits, organic-rich muds and peats of lagoonal origin, a tidal inlet, washover fans and a fluvial channel sand. Among the conclusions reached are that the local middle Ecca coastline extended in a northwest to southeast direction and that progradation was towards the southwest; that the coastline was microtidal and that stormy conditions were common with prevalent palaeowinds from the northwest. The absence of invertebrate body fossils in these strata is attributed to penecontemporaneous solution of shelly remains. This is the first time that a coastal sequence has been identified on the southeast margin of the Main Karoo Basin of South Africa 10. Towards the definition of AMS facies in the deposits of pyroclastic density currents Science.gov (United States) Ort, M.H.; Newkirk, T.T.; Vilas, J.F.; Vazquez, J.A.; Ort, M.H.; Porreca, Massimiliano; Geissman, J.W. 2014-01-01 Anisotropy of magnetic susceptibility (AMS) provides a statistically robust technique to characterize the fabrics of deposits of pyroclastic density currents (PDCs). AMS fabrics in two types of pyroclastic deposits (small-volume phreatomagmatic currents in the Hopi Buttes volcanic field, Arizona, USA, and large-volume caldera-forming currents, Caviahue Caldera, Neuquén, Argentina) show similar patterns. Near the vent and in areas of high topographical roughness, AMS depositional fabrics are poorly grouped, with weak lineations and foliations. In a densely welded proximal ignimbrite, this fabric is overprinted by a foliation formed as the rock compacted and deformed. Medial deposits have moderate–strong AMS lineations and foliations. The most distal deposits have strong foliations but weak lineations. Based on these facies and existing models for pyroclastic density currents, deposition in the medial areas occurs from the strongly sheared, high-particle-concentration base of a density-stratified current. In proximal areas and where topography mixes this denser base upwards into the current, deposition occurs rapidly from a current with little uniformity to the shear, in which particles fall and collide in a chaotic fashion. Distal deposits are emplaced by a slowing or stalled current so that the dominant particle motion is vertical, leading to weak lineation and strong foliation. 11. MAPPING OF RESERVOIR PROPERTIES AND FACIES THROUGH INTEGRATION OF STATIC AND DYNAMIC DATA Energy Technology Data Exchange (ETDEWEB) Albert C. Reynolds; Dean S. Oliver; Yannong Dong; Ning Liu; Guohua Gao; Fengjun Zhang; Ruijian Li 2004-12-01 Knowledge of the distribution of permeability and porosity in a reservoir is necessary for the prediction of future oil production, estimation of the location of bypassed oil, and optimization of reservoir management. The volume of data that can potentially provide information on reservoir architecture and fluid distributions has increased enormously in the past decade. The techniques developed in this research will make it easier to use all the available data in an integrated fashion. While it is relatively easy to generate plausible reservoir models that honor static data such as core, log, and seismic data, it is far more difficult to generate plausible reservoir models that honor dynamic data such as transient pressures, saturations, and flow rates. As a result, the uncertainty in reservoir properties is higher than it could be and reservoir management can not be optimized. In this project, we have developed computationally efficient automatic history matching techniques for generating geologically plausible reservoir models which honor both static and dynamic data. Specifically, we have developed methods for adjusting porosity and permeability fields to match both production and time-lapse seismic data and have also developed a procedure to adjust the locations of boundaries between facies to match production data. In all cases, the history matched rock property fields are consistent with a prior model based on static data and geologic information. Our work also indicates that it is possible to adjust relative permeability curves when history matching production data. 12. Late Neogene organic-rich facies from the Mediterranean region: the role of productivity and anoxia Energy Technology Data Exchange (ETDEWEB) Howell, M.W.; Thunell, R.C.; Tappa, E. 1985-01-01 Various factors influence the deposition of organic-rich facies in the marine environment, including: bulk sedimentation rate, water depth, primary productivity and oxygen content of bottom waters. Organic-rich sediments have been periodically deposited during the Neogene within both the deep basins and the marginal areas of the Mediterranean, and have been attributed to either the development of bottom water anoxia or greatly increased surface productivity. In order to evaluate the relative importance of each of these factors, organic-rich sediments from both the deep eastern Mediterranean and an uplifted sequence at Vrica (Calabria, Italy) have been studied. The deep sea sapropels examined were deposited during the last full interglacial (approx. 125,000 YBP) and preceeding glacial (approx. 160,000 YBP), while the laminites from Vrica are late Pliocene and early Pleistocene in age. The sapropels have maximum organic carbon contents of 10%, with C/N ratios typically between 15-20. In contrast, the maximum organic carbon content of the laminites if approx. 1%, and the C/N ratios are between 5-10. The C/N ratios, particularly those for the sapropels, are indicative of a multiple source, and may reflect some terrestrial organic matter input. The oxygen isotopic composition of calcareous plankton associated with both laminite and sapropel deposition is suggestive of reduced surface water salinities, while the carbon isotopic composition is suggestive of a change in source of surface waters which maybe responsible for increased productivity. 13. Application of Musical Information Retrieval (MIR Techniques to Seismic Facies Classification. Examples in Hydrocarbon Exploration Directory of Open Access Journals (Sweden) Paolo Dell’Aversana 2016-12-01 Full Text Available In this paper, we introduce a novel approach for automatic pattern recognition and classification of geophysical data based on digital music technology. We import and apply in the geophysical domain the same approaches commonly used for Musical Information Retrieval (MIR. After accurate conversion from geophysical formats (example: SEG-Y to musical formats (example: Musical Instrument Digital Interface, or briefly MIDI, we extract musical features from the converted data. These can be single-valued attributes, such as pitch and sound intensity, or multi-valued attributes, such as pitch histograms, melodic, harmonic and rhythmic paths. Using a real data set, we show that these musical features can be diagnostic for seismic facies classification in a complex exploration area. They can be complementary with respect to “conventional” seismic attributes. Using a supervised machine learning approach based on the k-Nearest Neighbors algorithm and on Automatic Neural Networks, we classify three gas-bearing channels. The good performance of our classification approach is confirmed by borehole data available in the same area. 14. Stepped fans and facies-equivalent phyllosilicates in Coprates Catena, Mars Science.gov (United States) Grindrod, P. M.; Warner, N. H.; Hobley, D. E. J.; Schwartz, C.; Gupta, S. 2018-06-01 Stepped fan deposits and phyllosilicate mineralogies are relatively common features on Mars but have not previously been found in association with each other. Both of these features are widely accepted to be the result of aqueous processes, but the assumed role and nature of any water varies. In this study we have investigated two stepped fan deposits in Coprates Catena, Mars, which have a genetic link to light-toned material that is rich in Fe-Mg phyllosilicate phases. Although of different sizes and in separate, but adjacent, trough-like depressions, we identify similar features at these stepped fans and phyllosilicates that are indicative of similar formation conditions and processes. Our observations of the overall geomorphology, mineralogy and chronology of these features are consistent with a two stage formation process, whereby deposition in the troughs first occurs into shallow standing water or playas, forming fluvial or alluvial fans that terminate in delta deposits and interfinger with interpreted lacustrine facies, with a later period of deposition under sub-aerial conditions, forming alluvial fan deposits. We suggest that the distinctive stepped appearance of these fans is the result of aeolian erosion, and is not a primary depositional feature. This combined formation framework for stepped fans and phyllosilicates can also explain other similar features on Mars, and adds to the growing evidence of fluvial activity in the equatorial region of Mars during the Hesperian and Amazonian. 15. Phosphate-rich sedimentary rocks: significance for organic facies and petroleum exploration Energy Technology Data Exchange (ETDEWEB) Waples, D W 1982-03-01 Phosphorus-bearing rocks and sediments can be divided into two genetically distinct classes: phosphatic shales or limestones and phosphorites. Phosphatic shales are primary sediments in which phosphate nodules or micronodules have formed diagenetically by precipitation of calcium phosphates derived mainly from organic phosphorus. The nodules form in reducing environments at shallow depths within the sediments, where loss of phosphate by diffusion to the overlying water column is minimized. Highly biogenic sediments containing large amounts of organic matter and some fine clastic debris provide ideal environments for the formation of phosphate nodules. Phosphorites, in contrast, represent concentrated accumulations of reworked phosphate nodules which originated in phosphatic shales or limestones. Currents, wave action, recrystallization, and erosion and resedimentation are important mechanisms in the concentration process. Phosphatic shales and limestones may become excellent oil source rocks if thermal maturity is achieved. They are useful facies indicators for anoxic or nearly anoxic depositional environments, and are often associated with restricted basins, or, during certain geologic periods, with broad shelves developed during transgressions. Phosphorites, in contrast, are often correlated with sea-level regressions or uplifts. They are modest source rocks because of their low organic carbon contents and the fact that they were reworked under oxidizing conditions. Nevertheless, because phosphorites are derived from, and often grade into, phosphatic shales, they also are of potential utility in the search for oil source beds. 16. Facies associations, depositional environments and stratigraphic framework of the Early Miocene-Pleistocene successions of the Mukah-Balingian Area, Sarawak, Malaysia Science.gov (United States) 2018-02-01 Thirty-five stratigraphic section exposed along the Mukah-Selangau road in the Mukah-Balingian area have been studied. Sedimentological and palynological data have been integrated to gain a better insight into the depositional architecture of the area. Broadly, the Mukah-Balingian area is dominated by fluvial, floodplain and estuarine related coal-bearing deposits. The Balingian, Begrih and Liang formations have been described and interpreted in terms of seven facies association. These are: FA1 - Fluvial-dominated channel facies association; FA2 - Tide-influenced channel facies association; FA3 - Tide-dominated channel facies association; FA4 - Floodplain facies association; FA5 - Estuarine central basin-mud flats facies association; FA6 - Tidal flat facies association and FA7 - Coastal swamps and marshes facies association. The Balingian Formation is characterised by the transgressive phase in the base, followed by a regressive phase in the upper part. On the basis of the occurrence of Florscheutzia trilobata with Florscheutzia levipoli, the Early to Middle Miocene age has been assigned to the Balingian Formation. The distinct facies pattern and foraminifera species found from the samples taken from the Begrih outcrop imply deposition in the intertidal flats having pronounced fluvio-tidal interactions along the paleo-margin. Foraminiferal data combined with the pronounced occurrence of Stenochlaena laurifolia suggest at least the Late Miocene age for the Begrih Formation. The internal stratigraphic architecture of the Liang Formation is a function of a combination of sea level, stable tectonic and autogenic control. Based on stratigraphic position, the Middle Pliocene to Pleistocene age for the Liang Formation is probable. The Balingian, Begrih and Liang formations display deposits of multiple regressive-transgressive cycles while the sediments were derived from the uplifted Penian high and Rajang group. 17. The Christological Ontology of Reason DEFF Research Database (Denmark) Nissen, Ulrik Becker 2006-01-01 Taking the startingpoint in an assertion of an ambiguity in the Lutheran tradition’s assessment of reason, the essay argues that the Kantian unreserved confidence in reason is criticised in Bonhoeffer. Based upon a Christological understanding of reason, Bonhoeffer endorses a view of reason which...... is specifically Christian and yet maintains a universality. With a focus on Bonhoeffer’s »Ethik« as the hermeneutical key to his theology, Bonhoeffer’s notion is also discussed in the light of contemporary Christian ethics. In this part it is particularly the role of reason within a public dis-course which... 18. A new ‘superassemblage’ model explaining proximal-to-distal and lateral facies changes in fluvial environments, based on the Proterozoic Sanjauli Formation (Lesser Himalaya, India Directory of Open Access Journals (Sweden) 2016-09-01 Full Text Available Facies analysis of fluvial deposits of the Proterozoic Sanjauli Formation in the Lesser Himalaya was combined with an architectural analysis. On this basis, a model was developed that may be applied to other fluvial systems as well, whether old or recent. The new model, which might be considered as an assemblage of previous models, explains lateral variations in architecture and facies but is not in all respects consistent with the standard fluvial models. The Sanjauli fluvial model is unique in that it deals with lateral facies variations due to shifts of the base-level along with fluctuations in accommodation space owing to changes in palaeoclimate. 19. Critique of historical reason Directory of Open Access Journals (Sweden) David B. Richardson 2009-03-01 Full Text Available El enfoque aquí desarrollado presupone una nueva visión del mundo civilizado (Weltanschauungen. La idea del historiador de los hechos históricos presupone una visión global del mundo, a excepción de las sociedades que carecen de un lenguaje escrito. Por eso, la razón histórica discutida aquí se limita al tipo de historia que trata de civilizaciones más elevadas. El análisis de visiones del mundo aquí utilizado presupone que los símbolos son muy importantes y que pierden su poder simbólico si se cristalizan en un único sentido. Como en la teoría de Jung, un símbolo tiene la capacidad de estar activo en la mente como un transformador de la conciencia, libre de asociarse con nuevas experiencias y pensamientos. Esta teoría presta especial atención al problema de Dilthey: es decir, el problema de la calidad racional de los hechos históricos. Las visiones del mundo, que dan un significado profundo a muchos hechos históricos, se componen de símbolos y metáforas, incluyendo ideas, imágenes, valores y emociones. Estos tipos de visiones son casi todos instintivos. Es cierto que los historiadores pueden haber formulado, consciente definiciones de estos tipos de visiones del mundo así como ocurrió por las civilizaciones griega y china. Dado que la actual Weltbilt es mucho más compleja e inconsciente, se necesita algo más que una definición lógica para entenderla. Este artículo indica la forma en que puede ser alcanzada una comprensión racional de estas visiones del mundo._____________ABSTRACT:The approach here entertained presupposes a fresh theory of world pictures (Weltanschauungen of higher civilizations. For the historian's idea of historical facts presupposes a world picture, except for societies which lack a written language. That is why the historical reason discussed here is limited to the kind of history which deals with higher civilizations. The analysis of world pictures used here itself presupposes that symbols are 20. Information processing systems, reasoning modules, and reasoning system design methods Science.gov (United States) Hohimer, Ryan E; Greitzer, Frank L; Hampton, Shawn D 2014-03-04 Information processing systems, reasoning modules, and reasoning system design methods are described. According to one aspect, an information processing system includes working memory comprising a semantic graph which comprises a plurality of abstractions, wherein the abstractions individually include an individual which is defined according to an ontology and a reasoning system comprising a plurality of reasoning modules which are configured to process different abstractions of the semantic graph, wherein a first of the reasoning modules is configured to process a plurality of abstractions which include individuals of a first classification type of the ontology and a second of the reasoning modules is configured to process a plurality of abstractions which include individuals of a second classification type of the ontology, wherein the first and second classification types are different. 1. Information processing systems, reasoning modules, and reasoning system design methods Energy Technology Data Exchange (ETDEWEB) Hohimer, Ryan E.; Greitzer, Frank L.; Hampton, Shawn D. 2016-08-23 Information processing systems, reasoning modules, and reasoning system design methods are described. According to one aspect, an information processing system includes working memory comprising a semantic graph which comprises a plurality of abstractions, wherein the abstractions individually include an individual which is defined according to an ontology and a reasoning system comprising a plurality of reasoning modules which are configured to process different abstractions of the semantic graph, wherein a first of the reasoning modules is configured to process a plurality of abstractions which include individuals of a first classification type of the ontology and a second of the reasoning modules is configured to process a plurality of abstractions which include individuals of a second classification type of the ontology, wherein the first and second classification types are different. 2. Information processing systems, reasoning modules, and reasoning system design methods Energy Technology Data Exchange (ETDEWEB) Hohimer, Ryan E.; Greitzer, Frank L.; Hampton, Shawn D. 2015-08-18 Information processing systems, reasoning modules, and reasoning system design methods are described. According to one aspect, an information processing system includes working memory comprising a semantic graph which comprises a plurality of abstractions, wherein the abstractions individually include an individual which is defined according to an ontology and a reasoning system comprising a plurality of reasoning modules which are configured to process different abstractions of the semantic graph, wherein a first of the reasoning modules is configured to process a plurality of abstractions which include individuals of a first classification type of the ontology and a second of the reasoning modules is configured to process a plurality of abstractions which include individuals of a second classification type of the ontology, wherein the first and second classification types are different. 3. Calcareous nannofossils and sedimentary facies in the Upper Cretaceous Bozeş Formation (Southern Apuseni Mountains, Romania Directory of Open Access Journals (Sweden) Ramona Balc 2012-02-01 Full Text Available The lithology, sedimentology and biostratigraphy of the Bozes Formation, which crop out in the SE Metaliferi Mountains (Apuseni Mts. have been investigated in order to establish the age of the deposits and the depositional environment. The sedimentary structures and facies are interpreted as indicating a deep-water depositional environment, representing part of a submarine fan lobe. Three facies assemblages have been identified and described. Calcareous nannofossils were used to determine the age of the investigated deposits. The presence of Lucianorhabdus cayeuxii and Calculites obscurus indicates the CC17 biozone, while UC13 Zone is pointed out by the continuous occurrence of Arkhangelskiella cymbiformis and the absence of Broinsonia parca parca. Thus, the age of the studied deposits is Late Santonian -?Early Campanian. 4. ) Organic Facies Variations in the Middle Cretaceous Black Shales of the Abakaliki Fold Belt, South-East, Nigeria International Nuclear Information System (INIS) 2003-01-01 An assessment, based on organic facies characteristics, have been carried out on the middle Cretaceous black shales, in order to determine their hydrocarbon source potential, thermal maturity, and depositional environments. The methods employed include evaluation of organic carbon content, rockeval pyrolysis, extractable organic matter, maceral composition and biomarker distributions.Organic facies criteria such as TOC, HI, Tmax, liptinite content, SOMIFOC and SHC/AHC indicate that Albian to middle Cenomanian shales are could only generate gas. The late Cenomanian to early Turonian shales are characterized by Type I/II kerogen, mature and could generate both oil and characterized by Type III kerogen, immature and could generate gas with little oil. The biomarker distributions indicate immature to mature source rock, moderately biodegraded and with reduced marine environment prevailing during the deposition of the lack shales. The late Cenomanian to early Turonian black shales show the highest source-rock potential 5. Facies and sedimentary environments of the Abu Qada Formation at Gabal El-Gunna, Southeastern Sinai, Egypt Directory of Open Access Journals (Sweden) Tarek Y.M.A. El-Hariri 2012-06-01 Full Text Available The biostratigraphy, microfacies association, mineralogical interferences, depositional environments and geochemical properties of the Abu Qada Formation, which exposed at Gabal El-Gunna Southeastern Sinai, Egypt were delineated. It belongs to the planktonic foraminiferal Whiteinella archaeocretacea Zone of the Late Cenomanian-Early Turonian and consists of calcareous shale and limestone. The calcareous shale facies is characterized by chlorite, smectite and illite with high concentration of P2O5, Zn, Ni, V, and Cr. The carbonate rocks are characterized by foraminiferal wakestone and bioclastic grainstone. These microfacies associations are characterized by barite with high content of Sr. The facies types with faunal contents, geochemical and mineralogical studies suggest a restricted to shelf lagoon open circulation environment. 6. Emotional reasoning and parent-based reasoning in normal children. OpenAIRE Morren, M.; Muris, P.; Kindt, M. 2004-01-01 A previous study by Muris, Merckelbach, and Van Spauwen demonstrated that children display emotional reasoning irrepective of their anxiety levels. That is when estimating whether a situation is dangerous, childen not only rely on objective danger information but also on their own anciety-response. The present study further examined emotional reasoning in childeren aged 7-13 years (N=508). In addition, it was investigated whether children also show parent-based reasoning, which can be defined... 7. Preliminary Facies Reconstruction of a Late Pleistocene Cypress Forest Discovered on the Northern Gulf of Mexico Continental Shelf Science.gov (United States) Gonzalez Rodriguez, S. M.; Bentley, S. J.; DeLong, K. L.; Xu, K.; Caporaso, A.; Obelcz, J. B.; Harley, G. L.; Reese, C. A.; Truong, J. T. 2016-12-01 We are investigating the origin and preservation of an ancient bald cypress forest (Taxodium distichum) discovered on the continental shelf seafloor, offshore of Gulf Shores, Alabama, USA, in 20 m water depth. The forest was likely buried in the late Pleistocene, possibly exhumed by Hurricane Ivan in 2004, and is now exposed as stumps in life position with little evidence of decay before recent marine exposure. Radiocarbon analyses show that the forest age is near (and in some cases beyond) the limits of 14C dating, at least 41-45 ky BP. In August 2015 and July 2016, submersible vibracores (up to 5 m in length) were collected. Ongoing core analyses include: organic content (loss on ignition), granulometry, and core logging using a Geotek Multi Sensor Core Logger to generate imagery, bulk density, and x-ray fluorescence data. To bolster 14C analyses, cores collected in 2016 are presently being dated using optically stimulated luminescence. Local stratigraphy consists of a surface facies of Holocene transgressive sands, underlain by possible estuarine sediments of interbedded sand and mud (potentially Holocene or Pleistocene), overlying a swamp or delta plain facies (likely Pleistocene) containing woody debris and mud. Deeper woody facies are thought to include the soil horizons of the ancient cypress forest. Cores collected in 2016 revealed a Pleistocene paleosol beneath Holocene sands in a nearby trough. Elevation differences between swamp and paleosol horizons will be evaluated from bathymetric and subbottom data, to help characterize the preserved ancient landscape. Initial interpretation based on close proximity of Pleistocene swamp and oxidized paleosol sediments, and regional geomorphic gradients suggest that this relatively diverse assemblage of facies developed up to tens of km from the glacial-age coastline, and relatively rapid burial prevented erosion by coastal processes during the Holocene transgression thus preserving the tree stumps and wood debris. 8. Optical-televiewer-based identification and characterization of material facies associated with an Antarctic ice-shelf rift OpenAIRE Hubbard, B.; Tison, J.-L.; Pattyn, F.; Dierckx, M.; Boereboom, T.; Samyn, D. 2012-01-01 We have drilled 13 boreholes within and around a through-cutting rift on the (unofficially named) Roi Baudouin Ice Shelf, East Antarctica. Logging by optical televiewer (OPTV) combined with core inspection has resulted in the identification and characterization of several material facies. Outside the rift, OPTV-imaged annual layering indicates ~150 years of accumulation over the 66m length of one of the boreholes. Luminosity analysis of this image also reveals the presence of numerous dark me... 9. Multiscale heterogeneity characterization of tidal channel, tidal delta and foreshore facies, Almond Formation outcrops, Rock Springs uplift, Wyoming Energy Technology Data Exchange (ETDEWEB) Schatzinger, R.A.; Tomutsa, L. [BDM Petroleum Technologies, Bartlesville, OK (United States) 1997-08-01 In order to accurately predict fluid flow within a reservoir, variability in the rock properties at all scales relevant to the specific depositional environment needs to be taken into account. The present work describes rock variability at scales from hundreds of meters (facies level) to millimeters (laminae) based on outcrop studies of the Almond Formation. Tidal channel, tidal delta and foreshore facies were sampled on the eastern flank of the Rock Springs uplift, southeast of Rock Springs, Wyoming. The Almond Fm. was deposited as part of a mesotidal Upper Cretaceous transgressive systems tract within the greater Green River Basin. Bedding style, lithology, lateral extent of beds of bedsets, bed thickness, amount and distribution of depositional clay matrix, bioturbation and grain sorting provide controls on sandstone properties that may vary more than an order of magnitude within and between depositional facies in outcrops of the Almond Formation. These features can be mapped on the scale of an outcrop. The products of diagenesis such as the relative timing of carbonate cement, scale of cemented zones, continuity of cemented zones, selectively leached framework grains, lateral variability of compaction of sedimentary rock fragments, and the resultant pore structure play an equally important, although less predictable role in determining rock property heterogeneity. A knowledge of the spatial distribution of the products of diagenesis such as calcite cement or compaction is critical to modeling variation even within a single facies in the Almond Fin. because diagenesis can enhance or reduce primary (depositional) rock property heterogeneity. Application of outcrop heterogeneity models to the subsurface is greatly hindered by differences in diagenesis between the two settings. The measurements upon which this study is based were performed both on drilled outcrop plugs and on blocks. 10. Reaction softening by dissolution–precipitation creep in a retrograde greenschist facies ductile shear zone, New Hampshire, USA Science.gov (United States) McAleer, Ryan J.; Bish, David L.; Kunk, Michael J.; Sicard, Karri R.; Valley, Peter M.; Walsh, Gregory J.; Wathen, Bryan A.; Wintsch, R.P. 2016-01-01 We describe strain localization by a mixed process of reaction and microstructural softening in a lower greenschist facies ductile fault zone that transposes and replaces middle to upper amphibolite facies fabrics and mineral assemblages in the host schist of the Littleton Formation near Claremont, New Hampshire. Here, Na-poor muscovite and chlorite progressively replace first staurolite, then garnet, and finally biotite porphyroblasts as the core of the fault zone is approached. Across the transect, higher grade fabric-forming Na-rich muscovite is also progressively replaced by fabric-forming Na-poor muscovite. The mineralogy of the new phyllonitic fault-rock produced is dominated by Na-poor muscovite and chlorite together with late albite porphyroblasts. The replacement of the amphibolite facies porphyroblasts by muscovite and chlorite is pseudomorphic in some samples and shows that the chemical metastability of the porphyroblasts is sufficient to drive replacement. In contrast, element mapping shows that fabric-forming Na-rich muscovite is selectively replaced at high-strain microstructural sites, indicating that strain energy played an important role in activating the dissolution of the compositionally metastable muscovite. The replacement of strong, high-grade porphyroblasts by weaker Na-poor muscovite and chlorite constitutes reaction softening. The crystallization of parallel and contiguous mica in the retrograde foliation at the expense of the earlier and locally crenulated Na-rich muscovite-defined foliation destroys not only the metastable high-grade mineralogy, but also its stronger geometry. This process constitutes both reaction and microstructural softening. The deformation mechanism here was thus one of dissolution–precipitation creep, activated at considerably lower stresses than might be predicted in quartzofeldspathic rocks at the same lower greenschist facies conditions. 11. CARBONATE FACIES ZONATION OF THE UPPER JURASSIC-LOWER CRETACEOUS APULIA PLATFORM MARGIN (GARGANO PROMONTORY, SOUTHERN ITALY Directory of Open Access Journals (Sweden) MICHELE MORSILLI 1997-07-01 Full Text Available The Late Jurassic-Early Cretaceous Apulia platform margin and the transition to adjacent basinal deposits (inner platform to basin are well exposed in the Gargano Promontory. Detailed field work has allowed to recognize eight main facies associations which reflect various depositional environments, and which document a differentiated zonation, from the inner platform to the basin. A shallow lagoon existed in the internal part of the Gargano Promontory with a transition to tidal flat areas (F1. Oolitic shoals (F2 bordered this internal peritidal area passing seaward to a reef-flat with abundant corals (F3. A reef-front, associated with a coral rubble zone, has been found in some areas (F4. In the external margin zone, massive wackestones with Ellipsactinia occur (F5 and pass gradually to a rudstone facies on the proximal slope (F6. The base-of-slope facies association consists of pelagic sediments interbedded with gravity-displaced deposits (F7 and F8. The depositional profile of the Apulia Platform is typical of the Tethyan Jurassic-Early Cretaceous platforms, with slope declivities in the order of 25°-28°. The remarkable progradation of the platform in the northern tract of the Gargano (Lesina and Varano lakes area and its substantial stability east- and southwards (Mattinata area suggest a possible windward position of the margin in this latter portion and, in contrast, a leeward position of the northern portion. 12. Preliminary investigation on the sedimentary facies of the middle silurian uraniferous rock formations in western Qinling Region International Nuclear Information System (INIS) Mao Yunian; Min Yongming. 1987-01-01 The Middle Silurian stratabound uranium deposits in Western Qinling were formed due to hydrothermal modification of ground water and reconcentration of uranium from the sedimentary source rocks. The Silurian system consists of the sediments deposited in the marginal sea of the passive continent, to the south of which is the Ruoergai palaeocontinent. The Middle Silurian is divided into three formations. The lower members of each formation are composed of fine-grained clastic rocks with bay-lagoon facies, while the upper members of each formation are uraniferous rock formations consisted of carbonaceous-siliceous-limestone-argillaceous rocks. During the Middle Silurian period there occurred an island chain barrier which is roughly parallel to the palaeocoast and was formed by undersea uplifts. The uraniferous rock formations belong to the assemblage of lagoon-reef-back tidal flat-reef beach facies. Nearshore shallow water environment, abundant terrestrial fine detritus, local reduction facies and zones are three cardinal conditions for the formation of uranium-rich sediments. Uranium deposition mainly took place in the environments of the inner part of reef beach and reef-back tidal flat, which are characterized by having medium to slightly lower energy, the terrestrial fine detritus involved, and local reduction field resulting from the decomposition of organism after their massive death. Furing the process of relative slow deposition, UO 2 2+ in the sea water was formed by means of infiltration, diffusion and alternative absorption of water at the bottom into organic matter and clay 13. Paragenetic evolution of reservoir facies, Middle Triassic Halfway Formation, PeeJay Field, northeastern British Columbia: controls on reservoir quality Energy Technology Data Exchange (ETDEWEB) Caplan, M. L. [Alberta Univ., Dept. of Earth and Atmospheric Sciences, Edmonton, AB (Canada); Moslow, T. F. [Ulster Petroleum Ltd., Calgary, AB (Canada) 1998-09-01 Because of the obvious importance of reservoir quality to reservoir performance, diagenetic controls on reservoir quality of Middle Triassic reservoir facies are investigated by comparing two reservoir lithofacies. The implications of porosity structure on the efficiency of primary and secondary hydrocarbon recovery are also assessed. Halfway reservoir facies are composed of bioclastic grainstones (lithofacies G) and litharenites/sublitharenites (lithofacies H), both of which are interpreted as tidal inlet fills. Although paragenetic evolution was similar for the two reservoir facies, subtle differences in reservoir quality are discernible. These are controlled by sedimentary structures, porosity type, grain constituents, and degree of cementation. Reservoir quality in lithofacies G is a function of connectivity of the pore network. In lithofacies H, secondary granular porosity creates a more homogeneous interconnected pore system, wide pore throats and low aspect ratios. The high porosity and low permeability values of the bioclastic grainstones are suspected to cause inefficient flushing of hydrocarbons during waterflooding. However, it is suggested that recovery may be enhanced by induced hydraulic fracturing and acidization of lower permeability calcareous cemented zones. 52 refs., 15 figs. 14. Zircon (Hf, O isotopes) as melt indicator: Melt infiltration and abundant new zircon growth within melt rich layers of granulite-facies lenses versus solid-state recrystallization in hosting amphibolite-facies gneisses (central Erzgebirge, Bohemian Massif) Science.gov (United States) Tichomirowa, Marion; Whitehouse, Martin; Gerdes, Axel; Schulz, Bernhard 2018-03-01 In the central Erzgebirge within the Bohemian Massif, lenses of high pressure and ultrahigh pressure felsic granulites occur within meta-sedimentary and meta-igneous amphibolite-facies felsic rocks. In the felsic granulite, melt rich parts and restite form alternating layers, and were identified by petrology and bulk rock geochemistry. Mineral assemblages representing the peak P-T conditions were best preserved in melanocratic restite layers. In contrast, in the melt rich leucocratic layers, garnet and related HP minerals as kyanite are almost completely resorbed. Both layers display differences in accessory minerals: melanosomes have frequent and large monazite and Fe-Ti-minerals but lack xenotime and apatite; leucosomes have abundant apatite and xenotime while monazite is rare. Here we present a detailed petrographic study of zircon grains (abundance, size, morphology, inclusions) in granulite-facies and amphibolite-facies felsic gneisses, along with their oxygen and hafnium isotope compositions. Our data complement earlier Usbnd Pb ages and trace element data (REE, Y, Hf, U) on zircons from the same rocks (Tichomirowa et al., 2005). Our results show that the degree of melting determines the behaviour of zircon in different layers of the granulites and associated amphibolite-facies rocks. In restite layers of the granulite lenses, small, inherited, and resorbed zircon grains are preserved and new zircon formation is very limited. In contrast, new zircons abundantly grew in the melt rich leucocratic layers. In these layers, the new zircons (Usbnd Pb age, trace elements, Hf, O isotopes) best preserve the information on peak metamorphic conditions due to intense corrosion of other metamorphic minerals. The new zircons often contain inherited cores. Compared to cores, the new zircons and rims show similar or slightly lower Hf isotope values, slightly higher Hf model ages, and decreased oxygen isotope ratios. The isotope compositions (Hf, O) of new zircons indicate 15. DNA hypermethylation and decreased mRNA expression of MAL, PRIMA1, PTGDR and SFRP1 in colorectal adenoma and cancer International Nuclear Information System (INIS) Kalmár, Alexandra; Péterfia, Bálint; Hollósi, Péter; Galamb, Orsolya; Spisák, Sándor; Wichmann, Barnabás; Bodor, András; Tóth, Kinga; Patai, Árpád V.; Valcz, Gábor; Nagy, Zsófia Brigitta; Kubák, Vivien; Tulassay, Zsolt; Kovalszky, Ilona; Molnár, Béla 2015-01-01 Colorectal cancer (CRC) development is accompanied by changes in expression for several genes; but the details of the underlying regulatory procesess remain unknown. Our aims were to assess the role of epigenetic processes in tumour formation and to identify characteristic DNA methylation and miRNA alterations in the colorectal adenoma-carcinoma sequence. Whole genome expression profiling was performed on colonic biopsy samples (49 healthy normal, 49 colorectal adenoma (AD), 49 CRC); on laser capture microdissected (LCM) epithelial and stromal cells from 6 CRC-normal adjacent tissue (NAT) samples pairs, and on demethylated human CRC cell lines using HGU133 Plus 2.0 microarrays (Affymetrix). Methylation status of genes with gradually altering expression along the AD-CRC sequence was further analysed on 10–10 macrodissected and 5–5 LCM samples from healthy colon, from adenoma and from CRC biopsy samples using bisulfite-sequencing PCR (BS-PCR) followed by pyrosequencing. In silico miRNA prediction for the selected genes was performed with miRWALK algorithm, miRNA expression was analysed on 3 CRC-NAT sample pairs and 3 adenoma tissue samples using the Human Panel I + II (Exiqon). SFRP1 immunohistochemistry experiments were performed. A set of transcripts (18 genes including MAL, SFRP1, SULT1A1, PRIMA1, PTGDR) showed decreasing expression (p < 0.01) in the biopsy samples along the adenoma-carcinoma sequence. Three of those (COL1A2, SFRP2, SOCS3) showed hypermethylation and THBS2 showed hypomethylation both in AD and in CRC samples compared to NAT, while BCL2, PRIMA1 and PTGDR showed hypermethylation only in the CRC group. miR-21 was found to be significantly (p < 0.01) upregulated in adenoma and tumour samples compared to the healthy colonic tissue controls and could explain the altered expression of genes for which DNA methylation changes do not appear to play role (e.g. BCL2, MAL, PTGS2). Demethylation treatment could upregulate gene expression of genes that were 16. Tracing Young Children's Scientific Reasoning Science.gov (United States) Tytler, Russell; Peterson, Suzanne 2003-08-01 This paper explores the scientific reasoning of 14 children across their first two years of primary school. Children's view of experimentation, their approach to exploration, and their negotiation of competing knowledge claims, are interpreted in terms of categories of epistemological reasoning. Children's epistemological reasoning is distinguished from their ability to control variables. While individual children differ substantially, they show a relatively steady growth in their reasoning, with some contextual variation. A number of these children are reasoning at a level well in advance of curriculum expectations, and it is argued that current recommended practice in primary science needs to be rethought. The data is used to explore the relationship between reasoning and knowledge, and to argue that the generation and exploration of ideas must be the key driver of scientific activity in the primary school. 17. Seismo-turbidite Sedimentology: Implications for Active Tectonic Margin Stratigraphy and Sediment Facies Patterns Science.gov (United States) Nelson, C. H.; Goldfinger, C.; Gutierrez Pastor, J.; Polonia, A.; Van Daele, M. E. 2014-12-01 Earthquakes generate mass transport deposits (MTDs); megaturbidites (MTD overlain by coeval turbidite); multi-pulsed, stacked, and mud homogenite seismo-turbidites; tsunamites; and seiche deposits. The strongest (Mw 9) earthquake shaking signatures appear to create multi-pulsed individual turbidites, where the number and character of multiple coarse-grained pulses for correlative turbidites generally remain constant both upstream and downstream in different channel systems. Multiple turbidite pulses, that correlate with multiple ruptures shown in seismograms of historic earthquakes (e.g. Chile 1960, Sumatra 2004 and Japan 2011), support this hypothesis. The weaker (Mw = or turbidity currents that deposit in channels below confluences of the tributaries. Proven tsunamites, which result from tsunami waves sweeping onshore and shallow water debris into deeper water, are a fine-grained turbidite cap over other seismo-turbidites. In contrast, MTDs and seismo-turbidites result from slope failures. Multiple great earthquakes cause seismic strengthening of slope sediment, which results in minor MTDs in basin floor turbidite system deposits (e.g. maximum run-out distances of MTDs across basin floors along active margins are up to an order of magnitude less than on passive margins). In contrast, the MTDs and turbidites are equally intermixed in turbidite systems of passive margins (e.g. Gulf of Mexico). In confined basin settings, earthquake triggering results in a common facies pattern of coeval megaturbidites in proximal settings, thick stacked turbidites downstream, and ponded muddy homogenite turbidites in basin or sub-basin centers, sometimes with a cap of seiche deposits showing bi-directional flow patterns. 18. First direct observations linking confined supercritical turbidity currents to their depositional architecture and facies characteristics Science.gov (United States) Hage, S.; Cartigny, M.; Hughes Clarke, J. E.; Clare, M. A.; Sumner, E.; Hubbard, S. M.; Talling, P.; Lintern, G.; Stacey, C.; Vardy, M. E.; Hunt, J.; Vendettuoli, D.; Yokokawa, M.; Hizzett, J. L.; Vellinga, A. J.; Azpiroz, M. 2017-12-01 Turbidity currents transfer globally significant amounts of sediment via submarine channels from the continental margin to deep submarine fans. Submarine channel inception is thought to result from erosive, supercritical turbidity currents that are common in proximal settings of the marine realm. Recent monitoring of submarine processes have provided the first measurements of supercritical turbidity currents (Hughes Clarke, 2016), demonstrating that they drive the upstream migration of crescentic bedforms in confined submarine channels. Although upstream-migrating bedforms are common in confined channels across the world's oceans, there is considerable debate over the type of deposits that they produce. It is important to understand what types of deposit record these supercritical bedforms to potentially identify them from geological archives. For the first time, we combine direct measurements from supercritical field-scale turbidity currents with the facies and depositional architecture resulting from such flows. We show how the subsurface architecture evolves in a highly active channel at Squamish submarine delta, British Columbia, Canada. Repeated upstream migration of bedforms is found to create two main deposit geometries. First, regular back-stepping beds result from flow deceleration on the slightly-inclined sides of the bedforms. Second, lens-shaped scour fills composed of massive deposits result from erosion of the back-stepping beds by subsequent turbidity currents. We relate our findings to a range of ancient outcrop studies to demonstrate that supercritical flows are common in proximal settings through the geological record. This study provides the first direct observation-based model to identify confined supercritical turbidity currents and their associated upslope-migrating bedforms in the sedimentary record. This is important for correctly identifying the proximal sites of ancient submarine channels that served as past conduits for globally 19. Pb and O isotope systematics in granulite facies xenoliths, French Massif Central: Implications for crustal processes International Nuclear Information System (INIS) Downes, H.; Kempton, P.D.; Harmon, R.S.; Briot, D.; Leyreloup, A.F. 1991-01-01 Pb and O isotope data are represented for a suite of granulite facies xenoliths found within Tertiary alkaline volcanic rocks of the Massif Central, France. The suite consists of ultramafic and mafic cumulates, metagabbros which are considered to represent basic liquids, felsic meta-igneous lithologies (charnockites) and metasediments. Ranges of δ 18 O values are +6.9 to +9.8per mille for mafic xenoliths, +9.3 to +10.2per mille for felsic meta-igneous samples and +6.1 to +11.8per mille for the metasediments. By comparison, δ 18 O values for mantle peridotites from the same region range from +5.1 to +6.9per mille, whilst local Hercynian granitoids vary from +8.6 to +12.0per mille. The 206 Pb/ 204 Pb ratios of the granulite xenoliths are between 17.77 and 19.19, 207 Pb/ 204 Pb ratios vary from 15.51 to 15.69, and 208 Pb/ 204 Pb ratios range from 38.07 to 40.07. In general, metasedimentary granulites have the more radiogenic Pb isotope compositions, whereas mafic meta-igneous samples are less radiogenic. These isotopic characteristics can be explained as the result of the interaction of mafic magmas with the metasedimentary crust into which they intruded. The release of heat also provoked melting of the more fusible parts of the lower crust and led to the formation of late-orogenic Hercynian granitoids. However, an additional component which provides less radiogenic Pb is also needed in the source of the granitoids; this may be the felsic meta-igneous xenoliths or middle/upper crustal gneisses. (orig.) 20. Learning in Order to Reason OpenAIRE Roth, Dan 1995-01-01 Any theory aimed at understanding commonsense reasoning, the process that humans use to cope with the mundane but complex aspects of the world in evaluating everyday situations, should account for its flexibility, its adaptability, and the speed with which it is performed. In this thesis we analyze current theories of reasoning and argue that they do not satisfy those requirements. We then proceed to develop a new framework for the study of reasoning, in which a learning component has a princ... 1. Logical Reasoning and Decision Making OpenAIRE Ong, D; Khaddaj, Souheil; Bashroush, Rabih 2011-01-01 Most intelligent systems have some form of \\ud decision making mechanisms built into their \\ud organisations. These normally include a logical \\ud reasoning element into their design. This paper reviews \\ud and compares the different logical reasoning strategies, \\ud and tries to address the accuracy and precision of \\ud decision making by formulating a tolerance to \\ud imprecision view which can be used in conjunction with \\ud the various reasoning strategies. 2. Clinical reasoning and critical thinking. Science.gov (United States) da Silva Bastos Cerullo, Josinete Aparecida; de Almeida Lopes Monteiro da Cruz, Diná 2010-01-01 This study identifies and analyzes nursing literature on clinical reasoning and critical thinking. A bibliographical search was performed in LILACS, SCIELO, PUBMED and CINAHL databases, followed by selection of abstracts and the reading of full texts. Through the review we verified that clinical reasoning develops from scientific and professional knowledge, is permeated by ethical decisions and nurses values and also that there are different personal and institutional strategies that might improve the critical thinking and clinical reasoning of nurses. Further research and evaluation of educational programs on clinical reasoning that integrate psychosocial responses to physiological responses of people cared by nurses is needed. 3. Public policy, rationality and reason Directory of Open Access Journals (Sweden) Rodolfo Canto Sáenz 2015-07-01 Full Text Available This work suggests the incorporation of practical reason in the design, implementation and evaluation of public policies, alongside instrumental rationality. It takes two proposals that today point in this direction: Rawls distinction between reasonable (practical reason and rational (instrumental reason and what this author calls the CI Procedure (categorical imperative procedure and Habermas model of deliberative democracy. The main conclusion is that the analysis of public policies can not be limited to rather narrow limits of science, but requires the contribution of political and moral philosophy. 4. Facies interpretations and lateral variability based on correlation of conventional core in the Logan canyon and Mississauga formations of the Scotian Basin Energy Technology Data Exchange (ETDEWEB) 2011-07-01 In the Lower Cretaceous of the Scotian Basin in Canada, sediment facies have been interpreted mostly using vertical successions of rock. However, other studies show that the lateral extent and variability of sediment facies must be understood to assess reservoir extent and connectivity. The aim of this paper is to present the investigation of two areas of the Scotian Basin. In each area, a regional correlation was performed using gamma ray well logs and the lithology, sedimentary and biogenic structures were determined for 67 different cores. It was found that the determination of facies and vertical successions was useful for comparing and correlating across multiple wells. In addition it was shown that gamma logs are effective for regional correlation but can only correlate major changes. This paper demonstrated that gamma logs are useful for performing facies interpretations and determining lateral variability. 5. Syn-sedimentary tectonics and facies analysis in a rift setting: Cretaceous Dalmiapuram Formation, Cauvery Basin, SE India Directory of Open Access Journals (Sweden) Nivedita Chakraborty 2018-04-01 Full Text Available The Cretaceous (Albian–Cenomanian Dalmiapuram Formation is one of the economically significant constituents in the hydrocarbon-producing Cauvery rift basin, SE India that opened up during the Late Jurassic–Early Cretaceous Gondwanaland fragmentation. The fossil-rich Dalmiapuram Formation, exposed at Ariyalur within the Pondicherry sub-basin of Cauvery Basin, rests in most places directly on the Archean basement and locally on the Lower Cretaceous (Barremian–Aptian Basal Siliciclastic Formation. In the Dalmiapuram Formation, a facies association of tectonically-disturbed phase is sandwiched between two drastically quieter phases. The early syn-rift facies association (FA 1, records the first carbonate marine transgression within the basin, comprising a bar–lagoon system with occasionally storms affecting along the shore and a sheet-like non-recurrent biomicritic limestone bed on the shallow shelf that laterally grades into pyrite–glauconite-bearing dark-colored shale in the deeper shelf. Spectacular breccias together with varied kinds of mass-flow products comprise the syn-rift facies association (FA 2. While the breccias occur at the basin margin area, the latter extend in the deeper inland sea. Clast composition of the coarse clastics includes large, even block-sized limestone fragments and small fragments of granite and sandstone from the basement. Marl beds of quieter intervals between tectonic pulses occur in alternation with them. Faulted basal contact of the formation, and small grabens filled by multiple mass-flow packages bear the clear signature of the syntectonic activity localized contortions, slump folds, and pillow beds associated with mega slump/slide planes and joints, which corroborates this contention further. This phase of tectonic intervention is followed by another relatively quieter phase and accommodates the late syn-rift facies association (FA 3. A tidal bar–interbar shelf depositional system allowed a 6. Controls on facies and sequence stratigraphy of an upper Miocene carbonate ramp and platform, Melilla basin, NE Morocco Science.gov (United States) Cunningham, K.J.; Collins, Luke S. 2002-01-01 Upwelling of cool seawater, paleoceanographic circulation, paleoclimate, local tectonics and relative sea-level change controlled the lithofacies and sequence stratigraphy of a carbonate ramp and overlying platform that are part of a temporally well constrained carbonate complex in the Melilla basin, northeastern Morocco. At Melilla, from oldest to youngest, a third-order depositional sequence within the carbonate complex contains (1) a retrogradational, transgressive, warm temperate-type rhodalgal ramp; (2) an early highstand, progradational, bioclastic platform composed mainly of a temperate-type, bivalve-rich molechfor facies; and (3) late highstand, progradational to downstepping, subtropical/tropical-type chlorozoan fringing Porites reefs. The change from rhodalgal ramp to molechfor platform occurred at 7.0??0.14 Ma near the Tortonian/Messinian boundary. During a late stage in the development of the bioclastic platform a transition from temperate-type molechfor facies to subtropical/tropical-type chlorozoan facies occurred and is bracketed by chron 3An.2n (??? 6.3-6.6 Ma). Comparison to a well-dated carbonate complex in southeastern Spain at Cabo de Gata suggests that upwelling of cool seawater influenced production of temperate-type limestone within the ramp and platform at Melilla during postulated late Tortonian-early Messinian subtropical/tropical paleoclimatic conditions in the western Paleo-Mediterranean region. The upwelling of cool seawater across the bioclastic platform at Melilla could be related to the beginning of 'siphoning' of deep, cold Atlantic waters into the Paleo-Mediterranean Sea at 7.17 Ma. The facies change within the bioclastic platform from molechfor to chlorozoan facies may be coincident with a reduction of the siphoning of Atlantic waters and the end of upwelling at Melilla during chron 3An.2n. The ramp contains one retrogradational parasequence and the bioclastic platform three progradational parasequences. Minor erosional surfaces 7. Geomorphology, facies architecture, and high-resolution, non-marine sequence stratigraphy in avulsion deposits, Cumberland Marshes, Saskatchewan Science.gov (United States) Farrell, K. M. 2001-02-01 This paper demonstrates field relationships between landforms, facies, and high-resolution sequences in avulsion deposits. It defines the building blocks of a prograding avulsion sequence from a high-resolution sequence stratigraphy perspective, proposes concepts in non-marine sequence stratigraphy and flood basin evolution, and defines the continental equivalent to a parasequence. The geomorphic features investigated include a distributary channel and its levee, the Stage I crevasse splay of Smith et al. (Sedimentology, vol. 36 (1989) 1), and the local backswamp. Levees and splays have been poorly studied in the past, and three-dimensional (3D) studies are rare. In this study, stratigraphy is defined from the finest scale upward and facies are mapped in 3D. Genetically related successions are identified by defining a hierarchy of bounding surfaces. The genesis, architecture, geometry, and connectivity of facies are explored in 3D. The approach used here reveals that avulsion deposits are comparable in process, landform, facies, bounding surfaces, and scale to interdistributary bayfill, i.e. delta lobe deposits. Even a simple Stage I splay is a complex landform, composed of several geomorphic components, several facies and many depositional events. As in bayfill, an alluvial ridge forms as the feeder crevasse and its levees advance basinward through their own distributary mouth bar deposits to form a Stage I splay. This produces a shoestring-shaped concentration of disconnected sandbodies that is flanked by wings of heterolithic strata, that join beneath the terminal mouth bar. The proposed results challenge current paradigms. Defining a crevasse splay as a discrete sandbody potentially ignores 70% of the landform's volume. An individual sandbody is likely only a small part of a crevasse splay complex. The thickest sandbody is a terminal, channel associated feature, not a sheet that thins in the direction of propagation. The three stage model of splay evolution 8. Facies distribution, depositional environment, and petrophysical features of the Sharawra Formation, Old Qusaiba Village, Central Saudi Arabia Science.gov (United States) Abbas, Muhammad Asif; Kaminski, Michael; Umran Dogan, A. 2016-04-01 moderate-scale transgressive episodes, while the thin shale interbeds in the middle and upper part of the Sharawra Formation represent small-scale transgressions. Overall, the Sharawra Formation contains a series of repetitive transgressive and regressive events and has been interpreted as a pro-deltaic deposit in previous studies. In the present study, the lowermost sandstone thickly bedded facies lie within the transition zone environment. The siltstone facies and the horizontally stratified facies show a middle shore face environment. The middle shore face environment is present locally. The bioturbation in the uppermost facies is indicative of the upper shore face environment. The porosity values do not vary much, as the average porosity for the sandstone facies is about 15%, for the siltstones it ranges about 7%. The permeability is variable throughout the formation, the values range from 50 to 300 md. Although sandstone has a good porosity and permeability, the siltstone facies exhibit poor petrophysical characteristics. In terms of reservoir characterization, the mineralogical mature, moderately well sorted top most sandstone facies, with appreciable porosity and permeability can be considered as a potential reservoir rock. This study has provided a base for future quantitative studies in this important formation in the area. 9. Tradução Oral à Prima Vista na formação do intérprete: considerações pedagógicas OpenAIRE Gloria Regina Loreto Sampaio 2017-01-01 A Tradução Oral à Prima Vista (TrPV) é um elemento de relevância para a formação do intérprete e um componente essencial para o desempenho do futuro profissional em muitos ambientes de atuação. Consequentemente, a prática da TrPV se faz presente em cursos de formação bem estruturados. Neste escrito, após uma breve referência à natureza, complexidade e desafios impostos pela TrPV, e tendo como base uma vivência docente extensa da autora, será apresentada uma possível abordagem pedagógica, volt... 10. Utilización de una nueva materia prima borácica para la formulación de esmaltes Directory of Open Access Journals (Sweden) Gómez-Tena, M. P. 2010-10-01 contenido en B2O3 entre un 10-11 % en peso. Es en gran parte amorfo, siendo el cuarzo la fase cristalina presente de forma mayoritaria. Características tales, como presentar una baja solubilidad y formar fácilmente fase vítrea, hace que sea posible utilizar el nuevo borato, como materia prima en composiciones de esmalte. Su aptitud para la formulación de esmaltes, ha sido el resultado de varios años de investigación en colaboración con el Instituto de Tecnología Cerámica. En este trabajo se ha estudiado la viabilidad de fabricar esmaltes cerámicos haciendo uso de una nueva materia prima borácica sintética, la cual permite aportar boro a la composición de los esmaltes sin necesidad de hacerlo en forma fritada. Se ha podido obtener vidriados con similares características técnicas y estéticas que los obtenidos a partir de esmaltes de uso industrial que contienen fritas típicas en su composición, por lo que resulta posible formular esmaltes mediante el empleo de la nueva materia prima de boro sintética. De los resultados se deriva, que la utilización de esta nueva materia prima (E-4972 es especialmente adecuada para la obtención de vidriados de bajo brillo a elevada temperatura. 11. Análise do posicionamento da empresa Baldo S/A na obtenção da matéria-prima erva-mate OpenAIRE Gurski, Clóvis Roberto 2003-01-01 Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Sócio-Econômico. Programa de Pós-Graduação em Economia. Esse trabalho teve como objetivo identificar e analisar a forma de obtenção de matéria-prima erva-mate pela empresa BALDO S/A, filial 16, sediada no município de São Mateus do Sul, no estado do Paraná, a partir dos conceitos da Teoria dos Custos de Transação. Para tanto, esta pesquisa, de natureza exploratória, utilizou como instrumento para coleta de dados, um qu... 12. CONDIÇÕES DE ARMAZENAGEM E QUALIDADE DA MATÉRIA PRIMA: ESTUDO DE CASO EM UMA DERIVADORA DE ALIMENTOS A BASE DE MILHO Directory of Open Access Journals (Sweden) Samara Pereira Dias 2017-12-01 Full Text Available O processo de armazenagem, de alguma forma, tem influência direta na produção e no status do produto final derivado. Foi possível constatar neste estudo de caso, que o sistema de armazenagem da empresa está deficitário, necessitando de melhorias, principalmente quando da entrada da matéria prima para produção. Tais problemas, como impurezas, grãos quebrados e ardidos, são gerados no próprio armazém, por falta de prudência e coordenação. Constatações que contrariam o objetivo do armazenamento que é a conservação das particularidades dos grãos e que podem desmerecer os atributos do produto fim, em termos de sabor, características físico químicas e condições visuais. Entre as possíveis causas dos distúrbios, estão a falta de manutenção das máquinas, as ineficientes aeração e aferição da termometria. Como sugestão, além das melhorias sobre os problemas citados, a implantação de gestão e estratégia de estoques, de programas e controle de qualidade, desenvolvimento dos agentes produtores, planejamento e métodos de solução de problemas. O declínio da qualidade da matéria prima, o milho, pode resultar em efeito cadeia, prejudicando o produto final, logo, lesando os resultados financeiros da organização. 13. Heuristics Reasoning in Diagnostic Judgment. Science.gov (United States) O'Neill, Eileen S. 1995-01-01 Describes three heuristics--short-cut mental strategies that streamline information--relevant to diagnostic reasoning: accessibility, similarity, and anchoring and adjustment. Analyzes factors thought to influence heuristic reasoning and presents interventions to be tested for nursing practice and education. (JOW) 14. Hurrah for the Reasonable Woman. Science.gov (United States) Leland, Dorothy 1994-01-01 Recent court cases on sexual harassment, and the outcomes, were reviewed in terms of how the court viewed a "reasonable" woman. Rulings in such cases can vary because of different interpretations of the "reasonable" concept. Also discusses how recent rulings will affect sexual harassment policymakers in the workplace and educational institutions.… 15. Competent Reasoning with Rational Numbers. Science.gov (United States) Smith, John P. III 1995-01-01 Analyzed students' reasoning with fractions. Found that skilled students applied strategies specifically tailored to restricted classes of fractions and produced reliable solutions with a minimum of computation effort. Results suggest that competent reasoning depends on a knowledge base that includes numerically specific and invented strategies,… 16. Moral Reasoning in Genetics Education Science.gov (United States) van der Zande, Paul; Brekelmans, Mieke; Vermunt, Jan D.; Waarlo, Arend Jan 2009-01-01 Recent neuropsychological research suggests that intuition and emotion play a role in our reasoning when we are confronted with moral dilemmas. Incorporating intuition and emotion into moral reflection is a rather new idea in the educational world, where rational reasoning is preferred. To develop a teaching and learning strategy to address this… 17. Logic, reasoning, and verbal behavior OpenAIRE Terrell, Dudley J.; Johnston, J. M. 1989-01-01 This paper analyzes the traditional concepts of logic and reasoning from the perspective of radical behaviorism and in the terms of Skinner's treatment of verbal behavior. The topics covered in this analysis include the proposition, premises and conclusions, logicality and rules, and deductive and inductive reasoning. 18. Cultural Differences in Justificatory Reasoning Science.gov (United States) Soong, Hannah; Lee, Richard; John, George 2012-01-01 Justificatory reasoning, the ability to justify one's beliefs and actions, is an important goal of education. We develop a scale to measure the three forms of justificatory reasoning--absolutism, relativism, and evaluativism--before validating the scale across two cultures and domains. The results show that the scale possessed validity and… 19. Human reasoning and cognitive science NARCIS (Netherlands) Stenning, K.; van Lambalgen, M. 2008-01-01 In Human Reasoning and Cognitive Science, Keith Stenning and Michiel van Lambalgen—a cognitive scientist and a logician—argue for the indispensability of modern mathematical logic to the study of human reasoning. Logic and cognition were once closely connected, they write, but were "divorced" in the 20. Archivists Killed for Political Reasons NARCIS (Netherlands) de Baets, Antoon 2015-01-01 This essay, Archivists Killed for Political Reasons, offers an overview of archivists who were killed for political reasons through the ages. After determining the criteria for inclusion, sixteen such political murders of archivists are briefly discussed. These cases were distributed over six 1. Learning to reason from samples NARCIS (Netherlands) Ben-Zvi, Dani; Bakker, Arthur; Makar, Katie 2015-01-01 The goal of this article is to introduce the topic of learning to reason from samples, which is the focus of this special issue of Educational Studies in Mathematics on statistical reasoning. Samples are data sets, taken from some wider universe (e.g., a population or a process) using a particular 2. Inductive Reasoning: A Training Approach Science.gov (United States) Klauer, Karl Josef; Phye, Gary D. 2008-01-01 Researchers have examined inductive reasoning to identify different cognitive processes when participants deal with inductive problems. This article presents a prescriptive theory of inductive reasoning that identifies cognitive processing using a procedural strategy for making comparisons. It is hypothesized that training in the use of the… 3. From Inductive Reasoning to Proof Science.gov (United States) Yopp, David A. 2009-01-01 Mathematical proof is an expression of deductive reasoning (drawing conclusions from previous assertions). However, it is often inductive reasoning (conclusions drawn on the basis of examples) that helps learners form their deductive arguments, or proof. In addition, not all inductive arguments generate more formal arguments. This article draws a… 4. Adversarial reasoning: challenges and approaches Science.gov (United States) Kott, Alexander; Ownby, Michael 2005-05-01 This paper defines adversarial reasoning as computational approaches to inferring and anticipating an enemy's perceptions, intents and actions. It argues that adversarial reasoning transcends the boundaries of game theory and must also leverage such disciplines as cognitive modeling, control theory, AI planning and others. To illustrate the challenges of applying adversarial reasoning to real-world problems, the paper explores the lessons learned in the CADET -- a battle planning system that focuses on brigade-level ground operations and involves adversarial reasoning. From this example of current capabilities, the paper proceeds to describe RAID -- a DARPA program that aims to build capabilities in adversarial reasoning, and how such capabilities would address practical requirements in Defense and other application areas. 5. Meta-Reasoning: Monitoring and Control of Thinking and Reasoning. Science.gov (United States) Ackerman, Rakefet; Thompson, Valerie A 2017-08-01 Meta-Reasoning refers to the processes that monitor the progress of our reasoning and problem-solving activities and regulate the time and effort devoted to them. Monitoring processes are usually experienced as feelings of certainty or uncertainty about how well a process has, or will, unfold. These feelings are based on heuristic cues, which are not necessarily reliable. Nevertheless, we rely on these feelings of (un)certainty to regulate our mental effort. Most metacognitive research has focused on memorization and knowledge retrieval, with little attention paid to more complex processes, such as reasoning and problem solving. In that context, we recently developed a Meta-Reasoning framework, used here to review existing findings, consider their consequences, and frame questions for future research. Copyright © 2017 Elsevier Ltd. All rights reserved. 6. Petrogenesis of the crater-facies Tokapal kimberlite pipe, Indrāvati Basin, Central India Directory of Open Access Journals (Sweden) N.V. Chalapathi Rao 2014-11-01 Full Text Available New geochemical data of the crater-facies Tokapal kimberlite system sandwiched between the lower and upper stratigraphic horizons of the Mesoproterozoic Indrāvati Basin are presented. The kimberlite has been subjected to extensive and pervasive low-temperature alteration. Spinel is the only primary phase identifiable, while olivine macrocrysts and juvenile lapilli are largely pseudomorphed (talc-serpentine-carbonate alteration. However, with the exception of the alkalies, major element oxides display systematic fractionation trends; likewise, HFSE patterns are well correlated and allow petrogenetic interpretation. Various crustal contamination indices such as (SiO2 + Al2O3 + Na2O/(MgO + K2O and Si/Mg are close to those of uncontaminated kimberlites. Similar La/Yb (79–109 of the Tokapal samples with those from the kimberlites of Wajrakarur (73–145 and Narayanpet (72–156, Eastern Dharwar craton, southern India implies a similarity in their genesis. In the discriminant plots involving HFSE the Tokapal samples display strong affinities to Group II kimberlites from southern Africa and central India as well as to ‘transitional kimberlites’ from the Eastern Dharwar craton, southern India, and those from the Prieska and Kuruman provinces of southern Africa. There is a striking similarity in the depleted-mantle (TDM Nd model ages of the Tokapal kimberlite system, Bastar craton, the kimberlites from NKF and WKF, Eastern Dharwar craton, and the Majhgawan diatreme, Bundelkhand craton, with the emplacement age of some of the lamproites from within and around the Palaeo-Mesoproterozoic Cuddapah basin, southern India. These similar ages imply a major tectonomagmatic event, possibly related to the break-up of the supercontinent of Columbia, at 1.3–1.5 Ga across the three cratons. The ‘transitional’ geochemical features displayed by many of the Mesoproterozoic potassic-ultrapotassic rocks, across these Indian cratons are inferred to be 7. Sulfur Isotope Trends in Archean Microbialite Facies Record Early Oxygen Production and Consumption Science.gov (United States) Zerkle, A.; Meyer, N.; Izon, G.; Poulton, S.; Farquhar, J.; Claire, M. 2014-12-01 The major and minor sulfur isotope composition (δ34S and Δ33S) of pyrites preserved in ~2.65-2.5 billion-year-old (Ga) microbialites record localized oxygen production and consumption near the mat surface. These trends are preserved in two separate drill cores (GKF01 and BH1-Sacha) transecting the Campbellrand-Malmani carbonate platform (Ghaap Group, Transvaal Supergroup, South Africa; Zerkle et al., 2012; Izon et al., in review). Microbialite pyrites possess positive Δ33S values, plotting parallel to typical Archean trends (with a Δ33S/δ34S slope of ~0.9) but enriched in 34S by ~3 to 7‰. We propose that these 34S-enriched pyrites were formed from a residual pool of sulfide that was partially oxidized via molecular oxygen produced by surface mat-dwelling cyanobacteria. Sulfide, carrying the range of Archean Δ33S values, could have been produced deeper within the microbial mat by the reduction of sulfate and elemental sulfur, then fractionated upon reaction with O2 produced by oxygenic photosynthesis. Preservation of this positive 34S offset requires that: 1) sulfide was only partially (50-80%) consumed by oxidation, meaning H2S was locally more abundant (or more rapidly produced) than O2, and 2) the majority of the sulfate produced via oxidation was not immediately reduced to sulfide, implying either that the sulfate pool was much larger than the sulfide pool, or that the sulfate formed near the mat surface was transported and reduced in another part of the system. Contrastingly, older microbialite facies (> 2.7 Ga; Thomazo et al., 2013) appear to lack these observed 34S enrichments. Consequently, the onset of 34S enrichments could mark a shift in mat ecology, from communities dominated by anoxygenic photosynthesizers to cyanobacteria. Here, we test these hypotheses with new spatially resolved mm-scale trends in sulfur isotope measurements from pyritized stromatolites of the Vryburg Formation, sampled in the lower part of the BH1-Sacha core. Millimeter 8. La Prima guerra mondiale e l'uso pubblico della storia in Lituania: i nuovi Cavalieri teutonici Directory of Open Access Journals (Sweden) Andrea Griffante 2014-10-01 Full Text Available At the outburst of the First World War, the mobilization of masses represented, even if for different reasons, an unavoidable goal for both the Imperial powers and national intellectual groups operating in the Tsarist Empire. Symbols and elements of national mythology were often used as cultural mobilization instruments. Lithuanian intellectuals based their mobilization work mainly on the memory of the Battle of Grünwald (1410. When the German occupation began, the Lithuanians used the category of “Teutonic bestiality” to make sense of their experience. 9. To Reason or Not to Reason: Is Autobiographical Reasoning Always Beneficial? Science.gov (United States) McLean, Kate C.; Mansfield, Cade D. 2011-01-01 Autobiographical reasoning has been found to be a critical process in identity development; however, the authors suggest that existing research shows that such reasoning may not always be critical to another important outcome: well-being. The authors describe characteristics of people such as personality and age, contexts such as conversations,… 10. Approximate reasoning in physical systems International Nuclear Information System (INIS) Mutihac, R. 1991-01-01 The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author) 11. Tufa in Northern England: depositional facies, carbonate mineral fabrics, and role of biomineralization Science.gov (United States) Manzo, E.; Mawson, M.; Perri, E.; Tucker, M. E. 2009-04-01 Tufas are widely scattered in northern England, being concentrated in areas of limestone (Carboniferous and Permian), where there are springs, seepages, streams and waterfalls with waters supersatured in respect of calcite. Some deposits are clearly related to faults. Tufas have been examined in Gordale and Malham (SW Yorkshire), Teesdale and Weardale (Co. Durham), Sunderland (Tyne & Wear) and Great Asby Fell (Cumbria). A variety of tufa types are developed: spring-related pisoids and moss tufa, fluviatile barrage and waterfall tufa, and seepage and spring tufa with microbial oncoids in a paludal setting. We present preliminary data and observations on tufa in the Teesdale area, which forms along the valley-side adjacent to the River Tees. Locally here, a tiny stream draining agricultural land runs over a sandstone outcrop at the top of a 30 metre high slope; water descends the 30-60 degrees slope, creating tiny waterfalls and pools across an area reaching 10 metres wide, on the way down towards the river. Three main facies are recognizable in the tufa deposits: carbonate crusts, moss tufa and pisoids. In the upper part of the slope tufa occurs as sub-vertical 0.5-5 cm thick carbonate crusts forming "sheets" with a bulbous external surface covered by a green biofilm, with some insect larvae. Encrustations form upon surfaces of rock exposures and pebbles, and coat plant fragments (leaves, twigs, pine cones). Tufa precipitation, particularly on mosses, liverworts and leaves (moss tufa), creates a series of rimmed pools, a few decimetres across and centimetres deep. Apart from the presence of moss, which gives the tufa has a vacuolar texture, the main constituents are cyanobacteria and diatoms. The moss tufa deposit may reach a metre or more in height and several metres in width, notably towards the base of the slope, adjacent to the river. Within the small pools on the slope, pisoids and partially calcified plant remains accumulate. They also occur abundantly in the 12. Facies-controlled reservoir properties in ramp-fan and slope-apron deposits, Miocene Puente Formation, Los Angeles basin Energy Technology Data Exchange (ETDEWEB) Lyons, K.T.; Geving, R.L.; Suchecki, R.K. 1989-03-01 The Miocene Puente Formation in outcrops of the eastern Los Angeles basin is interpreted as a succession of slope-apron and ramp-fan deposits that accumulated in a prism-rise wedge. The principal depositional components of this dominantly base-of-slope and ramp system are ramp-fan channels and lobes, and slope-channel and slope-apron channel/interchannel deposits. Facies-specific textural, compositional, and diagenetic attributes observed in thin section assist in the classification of depositional facies. Specifically, occurrence of carbonate cement, clay mineralogy, and abundance of organic material vary as a function of component facies architecture of the depositional system. Slope and ramp-fan channel-fill sandstones are characterized by pervasive carbonate cements, including poikilotopic and fine-grained calcite, fine-grained and baroque dolomite, and minor siderite. Diagenetic clays predate carbonate cements, and dolomite predates coarser, void-filling calcite. Ramp-fan lobe and interchannel deposits are carbonate free but are rich in detrital clay and organic matter. Diagenetic clays include mixed-layer illite/smectite and kaolinite. Sediments deposited in slope-apron channel fill are virtually cement free except for small amounts of authigenic illite/smectite. Slope-apron interchannel deposits are characterized by high content of organic matter and clay-rich matrix. Potential reservoir characteristics, such as grain size, sorting, and abundance of depositional clay matrix, are related to the primary sedimentary properties of depositional architectural components in the ramp-fan and slope-apron system. Additional diagenetic modifications, without consideration of compaction, were controlled by precipitation reactions associated with fluid flow along pathways related to the depositional architectural framework. 13. Artificial intelligence: Deep neural reasoning Science.gov (United States) Jaeger, Herbert 2016-10-01 The human brain can solve highly abstract reasoning problems using a neural network that is entirely physical. The underlying mechanisms are only partially understood, but an artificial network provides valuable insight. See Article p.471 14. Logic, Probability, and Human Reasoning Science.gov (United States) 2015-01-01 accordingly suggest a way to integrate probability and deduction. The nature of deductive reasoning To be rational is to be able to make deductions...3–6] and they underlie mathematics, science, and tech- nology [7–10]. Plato claimed that emotions upset reason- ing. However, individuals in the grip...fundamental to human rationality . So, if counterexamples to its principal predictions occur, the theory will at least explain its own refutation 15. Fuzzy reasoning on Horn Set International Nuclear Information System (INIS) Liu, X.; Fang, K. 1986-01-01 A theoretical study in fuzzy reasoning on Horn Set is presented in this paper. The authors first introduce the concepts of λ-Horn Set of clauses and λ-Input Half Lock deduction. They then use the λ-resolution method to discuss fuzzy reasoning on λ-Horn set of clauses. It is proved that the proposed λ-Input Half Lock resolution method is complete with the rules in certain format 16. Improving practical reasoning and argumentation OpenAIRE Baumtrog, Michael David 2015-01-01 This thesis justifies the need for and develops a new integrated model of practical reasoning and argumentation. After framing the work in terms of what is reasonable rather than what is rational (chapter 1), I apply the model for practical argumentation analysis and evaluation provided by Fairclough and Fairclough (2012) to a paradigm case of unreasonable individual practical argumentation provided by mass murderer Anders Behring Breivik (chapter 2). The application shows that by following t... 17. Petrological and zircon evidence for the Early Cretaceous granulite-facies metamorphism in the Dabie orogen, China Science.gov (United States) Gao, Xiao-Ying; Zhang, Qiang-Qiang; Zheng, Yong-Fei; Chen, Yi-Xiang 2017-07-01 An integrated study of petrology, mineralogy, geochemistry, and geochronology was carried out for contemporaneous mafic granulite and diorite from the Dabie orogen. The results provide evidence for granulite-facies reworking of the ultrahigh-pressure (UHP) metamorphic rock in the collisional orogen. Most zircons from the granulite are new growth, and their U-Pb ages are clearly categorized into two groups at 122-127 Ma and 188 ± 2 Ma. Although these two groups of zircons show similarly steep HREE patterns and variably negative Eu anomalies, the younger group has much higher U, Th and REE contents and Th/U ratios, much lower εHf(t) values than the older group. This suggests their growth is associated with different types of dehydration reactions. The older zircon domains contain mineral inclusions of garnet + clinopyroxene ± quartz, indicating their growth through metamorphic reactions at high pressures. In contrast, the young zircon domains only contain a few quartz inclusions and the garnet-clinopyroxene-plagioclase-quartz barometry yields pressures of 4.9 to 12.5 kb. In addition, the clinopyroxene-garnet Fe-Mg exchange thermometry gives temperatures of 738-951 °C. Therefore, the young zircon domains would have grown through peritectic reaction at low to medium pressures. The younger granulite-facies metamorphic age is in agreement not only with the adjacent diorite at 125 ± 1 Ma in this study but also the voluminous emplacement of coeval mafic and felsic magmas in the Dabie orogen. Mineral separates from both mafic granulite and its adjacent diorite show uniformly lower δ18O values than normal mantle, similar to those for UHP eclogite-facies metaigneous rocks in the Dabie orogen. In combination with major-trace elements and zircon Lu-Hf isotope compositions, it is inferred that the protolith of mafic granulites shares with the source rock of diorites, both being a kind of mafic metasomatites at the slab-mantle interface in the continental subduction channel 18. Las almas indisciplinadas: comentario crítico y estilístico de Plut., De facie 945B Directory of Open Access Journals (Sweden) Luisa Lesage Gárriga 2016-12-01 Full Text Available El mito escatológico que aparece al final del tratado de Plutarco De facie in orbe lunae todavía a día de hoy presenta problemas textuales y de interpretación que deben ser estudiados. Con este análisis del texto, que parte de estudios de crítica textual y crítica literaria y estilística, intento arrojar algo de luz sobre un pasaje que versa sobre el destino de las almas licenciosas. 19. Ichnofabrics and Facies in the Paleocene of Chicxulub: A Record of the Recovery of Life Post-Impact Science.gov (United States) Whalen, M. T.; O'Malley, K.; Lowery, C. M.; Rodriguez-Tovar, F. J.; Gulick, S. P. S.; Morgan, J. V. 2017-12-01 IODP/ICDP Expedition 364 recovered 829 m of core at Site M0077 including 110 m of post-impact, (hemi)pelagic Paleogene sedimentary rocks overlying the Chicxulub impact crater peak ring formed from suevite, melt rock, and granitic basement. The transition between suevite and Paleocene limestone (Unit 1F) is a remarkable fining upward package of gravel to sand-sized suevite (Unit 2A) overlain by the laminated carbonate-rich Unit 1G that records deposition of fine-grained material post-impact and contains a mix of Late Cretaceous and earliest Danian taxa. This study concentrates on the overlying Unit 1F. The ichnofabric index (ii, 1-6 indicating no bioturbation to complete homogenization), provides a semiquantitative estimate of burrow density to help assess the return of life to the crater. Unit 1F is 10 m thick with a sharp contact at the base of a green claystone (ii 2) that overlies Unit 1G. It consists of cm-dm interbedded blue-gray marlstone (ii 2) grading upward into gray to blue-gray wacke/packstone (ii 3-5). Contacts between facies are mostly gradational due to burrowing. The upper 3 m of the unit is a yellow-brown burrowed packstone (ii 4) intercalated with gray marlstone (ii 2). The uppermost 7.5 cm is calcite cemented with 1 cm wide burrows (ii 3-4) and fine to coarse sand size clasts including foraminifera. The upper surface of the unit is a hardground with an 2 Myr unconformity overlain by Eocene rocks. The first well-defined burrows occur in the upper 30 cm of Unit 1G. Unequivocal burrows (ii 2) that disturb sedimentary facies occur in overlying Unit 1F with values of 3-5 recorded in the overlying 10 cm indicating significant disruption of primary sedimentary structures. The iis in Unit 1F vary between 2 and 5 with rare laminated intervals without bioturbation (ii 1). Values of ii correlate well with facies changes, i.e. marlstones display lower iis than more carbonate-rich facies, implying a depth and/or redox control on burrower distribution. The ii 20. Facies and depositional environments for the coquinas of the Morro do Chaves Formation, Sergipe-Alagoas Basin, defined by taphonomic and compositional criteria Directory of Open Access Journals (Sweden) Ana Carolina Tavares Full Text Available Lacustrine carbonate rocks form important hydrocarbon accumulations along the Brazilian continental margin, some of which are contained in oil fields in which coquinas are one of the main reservoirs (viz. Campos Basin. The complexity and heterogeneity of these deposits make them a challenge in terms of reservoir description. For the necessary classification and paleoenvironmental interpretation of the coquinas, it is essential to evaluate many aspects including biological (such as carbonate productivity, sedimentological (energy regime in the depositional environment, transport of bioclasts, terrigenous supply, taphonomic (fragmentation of shells, abrasion and diagenetic processes. The facies analysis applied in this study is considered a more appropriate classification approach to understand these coquinas, since it is more flexible and comprehensive than the existing classifications for carbonate rocks. The material investigated here consists of rock samples of the coquinas from the Atol Quarry of the Morro do Chaves Formation (Barremian/Aptian, Sergipe-Alagoas Basin. These rocks that crop out in the Atol quarry complex can be considered as a case study for similar coquinas reservoirs found in the Brazilian continental margin basins. Six sedimentary facies were described, using the main taphonomic (fragmentation of shells and compositional (presence of micrite and siliciclastic matrix features as a diagnostic criteria. Two carbonate facies, two mixed carbonate-siliciclastic facies and two siliciclastic facies (mudstones were identified. From the facies succession, combined with a review of the literature on the subject, the following depositional paleoenvironments were defined: high-energy lake platform, lacustrine delta in a high-energy lake platform and lake-centre. In this paper, a new facies model for the studied coquinas succession is proposed. 1. Conditional Reasoning in Schizophrenic Patients. Science.gov (United States) Kornreich, Charles; Delle-Vigne, Dyna; Brevers, Damien; Tecco, Juan; Campanella, Salvatore; Noël, Xavier; Verbanck, Paul; Ermer, Elsa 2017-01-01 Conditional reasoning (if p then q) is used very frequently in everyday situations. Conditional reasoning is impaired in brain-lesion patients, psychopathy, alcoholism, and polydrug dependence. Many neurocognitive deficits have also been described in schizophrenia. We assessed conditional reasoning in 25 patients with schizophrenia, 25 depressive patients, and 25 controls, using the Wason selection task in three different domains: social contracts, precautionary rules, and descriptive rules. Control measures included depression, anxiety, and severity of schizophrenia measures as a Verbal Intelligence Scale. Patients with schizophrenia were significantly impaired on all conditional reasoning tasks compared to depressives and controls. However, the social contract and precautions tasks yielded better results than the descriptive tasks. Differences between groups disappeared for social contract but remained for precautions and descriptive tasks when verbal intelligence was used as a covariate. These results suggest that domain-specific reasoning mechanisms, proposed by evolutionary psychologists, are relatively resilient in the face of brain network disruptions that impair more general reasoning abilities. Nevertheless, patients with schizophrenia could encounter difficulties understanding precaution rules and social contracts in real-life situations resulting in unwise risk-taking and misunderstandings in the social world. 2. Nódulos opalinos en facies marginales del salar Olaroz (Puna Argentina Directory of Open Access Journals (Sweden) Alonso, R. 1989-04-01 Full Text Available This article reports the results of a petrological and geochemical study of silica nodules from Quaternary alluvial fallS of the Olaroz Salar. The nodules are mainly constituted by C-T opal, d. (101 spacing to 4,11 A, implying a high-disorder; this is commonly observed in opa! rocks formed in near surface environments, without burial and heating. The chemical composition of the nodules is anomalous when compared with other typical silica-rocks formed in arid continental closed basin, without any eruptive environments (for instance the Cuenca del Tajo in Spain. The siliceous nodules do not have the characteristics of the silcretes and are not associated to the evaporitic facies of the salar. Their genesis is probably related to contamination of groundwater of the alluvial fan with high-silica thermal water. The C-T opal would thus precipitate by either displacing tbe terrigenous host-rock or replacing previous ulexite nodules.Se realiza un estudio petrológico y geoquímico de los nódulos silíceos que se encuentran incluidos en sedimentos terrígenos cuaternarios de la Cuenca de Olaroz (La Puna, Argentina. Estos nódulos se localizan en abanicos aluviales que aparecen encajados, debido a los cambios en el nivel de base que se produce desde el Pleistoceno a la actualidad, durante la evolución de los cuerpos lacustres a salares. Un estudio mediante DRX revela que son rocas constituidas por ópalo C-T, con un espaciado (101 a 4,11 A, que implica un grado de desorden alto, típico de las rocas silíceas formadas en superficie y que no han sufrido enterramiento ni influencia térmica. Su composición química es anómala si se compara con rocas silíceas continentales formadas en ambiente endorreico y fuera de un marco volcánico (Mioceno de la Cuenca del Tajo. No poseyendo características de silcretas y no estando asociadas a la sedimentación evaporítica de los salares, se considera la influencia de aguas termales. La contaminación local y en 3. Oceanographic controls on sedimentary and geochemical facies on the Peru outer shelf and upper slope Science.gov (United States) Arthur, Michael A.; Dean, Walter E. 2013-01-01 Concentrations and characteristics of organic matter in surface sediments deposited under an intense oxygen-minimum zone (OMZ) on the Peru margin were mapped and studied in samples from deck-deployed box cores and push cores acquired by submersible on two east-west transects spanning depths of 75 to 1,000 meters (m) at 12°S and 13.5°S. On the basis of sampling and analyses of the top 1–2 centimeters (cm) of available cores, three main belts of sediments were identified on each transect with increasing depth: (1) muds rich in organic carbon (OC); (2) authigenic phosphatic mineral crusts and pavements; and (3) glaucony facies.Sediments rich in OC on the 12°S transect were mainly located on the outer shelf and upper slope (150–350 m), but they occurred in much shallower water (approximately 100 m) on the 13.5°S transect. The organic matter is almost entirely marine as confirmed by Rock-Eval pyrolysis and isotopic composition of OC. Concentrations of OC are highest (up to 18 percent) in sediments within the OMZ where dissolved oxygen (DO) concentrations are Peru margin can only become buried and incorporated into the geologic record once bottom currents slacken sufficiently to allow fine-grained sediment to accumulate.Glaucony-rich surface sediments, relatively undiluted by other components, were found mainly in deeper water on the 13.5°S transect (750 m to at least 1,067 m). These sediments consist almost entirely of sand-size glaucony pellets. These widespread glaucony sands formed in place and were then concentrated and reworked by strong currents that winnowed away the fine-grained matrix. Although the glaucony occurs in sand-size pellets, the pellets are made up of aggregates of authigenic, platy, micaceous clay minerals. Glaucony is predominantly a potassium (K), sodium (Na), iron (Fe), magnesium (Mg) aluminosilicate with an approximate formula of (K,Na)(Fe3+,Al,Mg)2(Si,Al)4O10(OH)2. The glaucony on the 13.5°S transect forms by alteration of one or more 4. 34 CFR 81.34 - Notice of a disallowance decision. Science.gov (United States) 2010-07-01 ... requested, or other means that ensure proof of receipt. (b)(1) The notice must establish a prima facie case... records constitutes a prima facie case for the recovery of the funds affected. (i) If the recipient failed... obtained in a determination of harm to the Federal interest. (2) For the purpose of this section, a prima... 5. 42 CFR 402.109 - Statistical sampling. Science.gov (United States) 2010-10-01 ... or caused to be presented. (b) Prima facie evidence. The results of the statistical sampling study, if based upon an appropriate sampling and computed by valid statistical methods, constitute prima... § 402.1. (c) Burden of proof. Once CMS or OIG has made a prima facie case, the burden is on the... 6. Analogical reasoning in schizophrenic delusions. Science.gov (United States) Simpson, Jane; Done, D John 2004-09-01 Reasoning ability has often been argued to be impaired in people with schizophrenic delusions, although evidence for this is far from convincing. This experiment examined the analogical reasoning abilities of several groups of patients, including non-deluded and deluded schizophrenics, to test the hypothesis that performance by the deluded schizophrenic group would be impaired. Eleven deluded schizophrenics, 10 depressed subjects, seven non-deluded schizophrenics and 16 matched non-psychiatric controls, who were matched on a number of key variables, were asked to solve an analogical reasoning task. Performance by the deluded schizophrenic group was certainly impaired when compared with the depressed and non-psychiatric control groups though less convincingly so when compared with the non-deluded schizophrenic group. The impairment shown by the deluded schizophrenic group seemed to occur at the initial stage of the reasoning task. The particular type of impairment shown by the deluded subjects was assessed in relation to other cognitive problems already researched and the implications of these problems on reasoning tasks and theories of delusions was discussed. 7. Pore facies analysis: incorporation of rock properties into pore geometry based classes in a Permo-Triassic carbonate reservoir in the Persian Gulf International Nuclear Information System (INIS) Rahimpour-Bonab, H; Aliakbardoust, E 2014-01-01 Pore facies analysis is a useful method for the classification of reservoir rocks according to pore geometry characteristics. The importance of this method is related to the dependence of the dynamic behaviour of the reservoir rock on the pore geometry. In this study, pore facies analysis was performed by the quantification and classification of the mercury injection capillary pressure (MICP) curves applying the multi-resolution graph-based clustering (MRGC) method. Each pore facies includes a limited variety of rock samples with different depositional fabrics and diagenetic histories, which are representative of one type of pore geometry. The present pore geometry is the result of the interaction between the primary rock fabric and its diagenetic overprint. Thus the variations in petrographic properties can be correlated with the pore geometry characteristics. Accordingly, the controlling parameters in the pore geometry characteristics were revealed by detailed petrographic analysis in each pore facies. The reservoir rock samples were then classified using the determined petrographic properties which control the pore system quality. This method is proposed for the classification of reservoir rocks in complicated carbonate reservoirs, in order to reduce the incompatibility of traditional facies analysis with pore system characteristics. The method is applicable where enough capillary pressure data is not available. (papers) 8. Halite depositional facies in a solar salt pond: A key to interpreting physical energy and water depth in ancient deposits? Science.gov (United States) Robertson Handford, C. 1990-08-01 Subaqueous deposits of aragonite, gypsum, and halite are accumulating in shallow solar salt ponds constructed in the Pekelmeer, a sea-level sauna on Bonaire, Netherlands Antilles. Several halite facies are deposited in the crystallizer ponds in response to differences in water depth and wave energy. Cumulate halite, which originates as floating rafts, is present only along the protected, upwind margins of ponds where low-energy conditions foster their formation and preservation. Cornet crystals with peculiar mushroom- and mortarboard-shaped caps precipitate in centimetre-deep brine sheets within a couple of metres of the upwind or low-energy margins. Downwind from these margins, cornet and chevron halite precipitate on the pond floors in water depths ranging from a few centimetres to ˜60 cm. Halite pisoids with radial-concentric structure are precipitated in the swash zone along downwind high-energy shorelines where they form pebbly beaches. This study suggests that primary halite facies are energy and/or depth dependent and that some primary features, if preserved in ancient halite deposits, can be used to infer physical energy conditions, subenvironments such as low- to high-energy shorelines, and extremely shallow water depths in ancient evaporite basins. 9. Applying and improving a sedimentary facies model for exploration of stratigraphic traps in the Austrian Molasse basin Energy Technology Data Exchange (ETDEWEB) Hinsch, R.; Kofler, N. [Rohoel-Aufsuchungs AG (RAG), Vienna (Austria); Hubbard, S. [Calgary Univ., Calgary (Canada). Dept. of Geology and Geophysics 2007-09-13 In the Molasse foreland basin of Upper Austria gas is produced from deep-water sandstones and conglomerates of the Puchkirchen and basal Hall formations (Oligocene-Lower Miocene). The basin is mature, with >750 wells drilled by RAG to date. An extensive 3-D seismic reflection dataset that covers much of the paleo-basin foredeep has been acquired in the study area over the last 15 years. Seismic stratigraphic analysis has revealed that deepwater sedimentation in the basin was dominated by a channel belt up to 5 km wide that transported sediment derived from the Central and Eastern Alps eastward along the basin axis (Linzer, 2001; de Ruig, 2003). Based on these findings, a detailed sedimentary facies model has been developed, outlining several distinct depositional elements that reveal numerous possible stratigraphic trap types (de Ruig and Hubbard, 2006). This depositional model is currently being applied and tested in exploration and refined by ongoing research. Channel abandonment and migration are important processes that resulted in stratigraphic configurations consisting of coarse-grained sandstones and conglomerates overlain by channel and overbank mudstones. This represents ideal reservoir architecture, including porous reservoir facies sealed by impermeable deposits. Additional stratigraphic trapping conditions can result from special spatial arrangements of depositional elements, for example a sandstone-filled tributary channel that is sealed by an overlying mudstone-filled abandonment channel. Recognizing and further improving such stratigraphic trapping configurations are important for future exploration in Upper Austria, where most of the structural traps have been drilled. (orig.) 10. Resolving Carbonate Platform Geometries on the Island of Bonaire, Caribbean Netherlands through Semi-Automatic GPR Facies Classification Science.gov (United States) Bowling, R. D.; Laya, J. C.; Everett, M. E. 2018-05-01 The study of exposed carbonate platforms provides observational constraints on regional tectonics and sea-level history. In this work Miocene-aged carbonate platform units of the Seroe Domi Formation are investigated, on the island of Bonaire, located in the Southern Caribbean. Ground penetrating radar (GPR) was used to probe near-surface structural geometries associated with these lithologies. The single cross-island transect described herein allowed for continuous mapping of geologic structures on kilometer length scales. Numerical analysis was applied to the data in the form of k-means clustering of structure-parallel vectors derived from image structure tensors. This methodology enables radar facies along the survey transect to be semi-automatically mapped. The results provide subsurface evidence to support previous surficial and outcrop observations, and reveal complex stratigraphy within the platform. From the GPR data analysis, progradational clinoform geometries were observed on the northeast side of the island which supports the tectonics and depositional trends of the region. Furthermore, several leeward-side radar facies are identified which correlate to environments of deposition conducive to dolomitization via reflux mechanisms. 11. Características generales, propiedades, yacimientos y aplicaciones de pirofilita. II. Yacimientos, aplicaciones y utilización como materia prima cerámica Directory of Open Access Journals (Sweden) Sánchez Soto, P. J. 1998-10-01 Full Text Available In this work, the main world deposits of pyrophyllite are indicated according to the literature, showing the available production data. It is emphasized the research focusing on mining and characterization of raw materials containing pyrophyllite, which shows a marked applied interest. It is described and reviewed the most relevant applications of pyrophyllite and pyrophyllite raw materials, in especial refractories and ceramics, fillers, building materials, catalysts and as a high-pressure medium for synthesis of materials. Finally, it is also described and reviewed its use as raw material for the preparation of advanced materials, such as sialon, emphasizing the possibilities of application of pyrophyllite raw materials in our country as a result of distinct investigations of relevant interest performed by several Research Institutes and University Departments. It is deduced that pyrophyllite and pyrophyllite raw materials are increasing in relative importance in many applied fields, as compared with other layer silicates, such as talc and kaolinite. En este trabajo se indican los principales yacimientos mundiales de pirofilita según la bibliografía, los datos de producción disponibles, además de revisar las investigaciones más destacadas sobre prospección y caracterización de materias primas que contienen pirofilita y que presentan un marcado interés aplicado. Se realiza una amplia revisión de las principales aplicaciones a las que se destinan dichas materias primas, en especial para la preparación de materiales cerámicos y refractarios, su uso como carga, en la construcción, obtención de catalizadores y síntesis de materiales a alta presión debido a sus propiedades. Por último, se describen y revisan sus aplicaciones en la preparación de nuevos materiales y materiales avanzados, como son los sialones, destacando su potencial de utilización en nuestro país como resultado de diversas investigaciones de inter 12. La Génesis de los Universales en Prasastapada y la Génesis de Los Principia Prima y los Universales en Aristóteles Directory of Open Access Journals (Sweden) Fernando Tola 2015-03-01 Full Text Available En este artículo los autores ofrecen un nuevo caso en soporte de su tesis concerniente a las frecuentes coincidencias temáticas en las Filosofías de la India y de Occidente, que ellos han desarrolladoen especial en sus libros On the Myth of the Opposition between Indian Thought and Western Philosophy, Hildesheim: Olms Verlag, 2004, reseñado por Ernst Steinkellner en Wiener Zeitschrift fürdie Kunde Südasiens Band XLVIII 2004, 224-225, y Yoga. Un Camino Místico Universal, Barcelona: Editorial Kairós, 2006. Dicha tesis apunta a lo que podríamos llamar una suerte de globalidad intrínseca del pensar filosófico, más allá de la cultura de que se trate. Prasastapada (circa segunda mitad del siglo VII d.C., en Prasastapadabhasya (llamado también Padarthadharmasngraha, Libro V: Samanyapadarthanirupana, da dos descripciones de la génesis de los universales. Describe primeramente de una manera abstracta y concisa el proceso de surgimiento de todo samanya, «universal», y después explica de una manera más concreta el surgimiento del universal inferior y del superior (satta, «la existencia», a través de la reiteración de la percepción de objetos que presentan similares atributos y de la intervención del recuerdo de percepciones similares pasadas. Aristóteles (siglo IV a.C., en Analytica Posteriora, Libro II, Capítulo XIX, y Temistio (circa 317-circa387, en su comentario, explican a su vez el modo en que son aprehendidos los principios universales o premisas de la demostración (principia prima. Los autores de este artículo muestran cómo la descripción de Aristóteles y Temistio de la génesis de los principia prima y los universales concuerda de manera sorprendente con la de Prasastapada concerniente a los universales. 13. Race, Reason and Reasonableness: Toward an "Unreasonable" Pedagogy Science.gov (United States) De Lissovoy, Noah 2016-01-01 Starting from the contemporary critical-theoretical notion of an "objective violence" that organizes social reality in capitalism, including processes of systemic racism, as well as from phenomenological inquiries into processes of race and identity, this article explores the relationship between racism and reasonableness in education… 14. Emotional Reasoning and Parent-Based Reasoning in Normal Children Science.gov (United States) Morren, Mattijn; Muris, Peter; Kindt, Merel 2004-01-01 A previous study by Muris, Merckelbach, and Van Spauwen [1] demonstrated that children display emotional reasoning irrespective of their anxiety levels. That is, when estimating whether a situation is dangerous, children not only rely on objective danger information but also on their "own" anxiety-response. The present study further examined… 15. Emotional reasoning and parent-based reasoning in normal children. NARCIS (Netherlands) Morren, M.; Muris, P.; Kindt, M. 2004-01-01 A previous study by Muris, Merckelbach, and Van Spauwen demonstrated that children display emotional reasoning irrepective of their anxiety levels. That is when estimating whether a situation is dangerous, childen not only rely on objective danger information but also on their own anciety-response. 16. Emotional reasoning and parent-based reasoning in normal children NARCIS (Netherlands) Morren, M.; Muris, P.; Kindt, M. 2004-01-01 A previous study by Muris, Merckelbach, and Van Spauwen demonstrated that children display emotional reasoning irrespective of their anxiety levels. That is, when estimating whether a situation is dangerous, children not only rely on objective danger information but also on their own 17. Logic, probability, and human reasoning. Science.gov (United States) Johnson-Laird, P N; Khemlani, Sangeet S; Goodwin, Geoffrey P 2015-04-01 This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn - not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction. Copyright © 2015 Elsevier Ltd. All rights reserved. 18. Uncertain deduction and conditional reasoning. Science.gov (United States) Evans, Jonathan St B T; Thompson, Valerie A; Over, David E 2015-01-01 There has been a paradigm shift in the psychology of deductive reasoning. Many researchers no longer think it is appropriate to ask people to assume premises and decide what necessarily follows, with the results evaluated by binary extensional logic. Most every day and scientific inference is made from more or less confidently held beliefs and not assumptions, and the relevant normative standard is Bayesian probability theory. We argue that the study of "uncertain deduction" should directly ask people to assign probabilities to both premises and conclusions, and report an experiment using this method. We assess this reasoning by two Bayesian metrics: probabilistic validity and coherence according to probability theory. On both measures, participants perform above chance in conditional reasoning, but they do much better when statements are grouped as inferences, rather than evaluated in separate tasks. 19. Inductive reasoning 2.0. Science.gov (United States) Hayes, Brett K; Heit, Evan 2018-05-01 Inductive reasoning entails using existing knowledge to make predictions about novel cases. The first part of this review summarizes key inductive phenomena and critically evaluates theories of induction. We highlight recent theoretical advances, with a special emphasis on the structured statistical approach, the importance of sampling assumptions in Bayesian models, and connectionist modeling. A number of new research directions in this field are identified including comparisons of inductive and deductive reasoning, the identification of common core processes in induction and memory tasks and induction involving category uncertainty. The implications of induction research for areas as diverse as complex decision-making and fear generalization are discussed. This article is categorized under: Psychology > Reasoning and Decision Making Psychology > Learning. © 2017 Wiley Periodicals, Inc. 20. Il sistema di accoglienza dei migranti in Italia. Riflessioni a partire da una esperienza di prima accoglienza allo sbarco Directory of Open Access Journals (Sweden) Concetta Chiara Cannella 2014-03-01 Full Text Available After the description of the main migration routes toward Italian territory, the article provides an overview of the laws and administrative policy instruments that characterize the system of reception and detention of migrants in Italy. This type of information can help psychosocial workers supporting migrants to better cope with various psychosocial issues, such as the landing in a foreign country. Following a report on the first reception intervention carried out in Palermo, Sicily, by Psicologi per i Popoli – Sicilia, some reflections about the strengths and weaknesses identified as well as the potential for a greater involvement of psychosocial teams in immigrants reception and detention processes are presented. In fact, psychological science may improve the quality and effectiveness of the emergency services provided to migrants and be useful both in the training of workers and in crisis and emergency risk communication, with particular reference to risk perception about infectious diseases. However, the “added value” of psychological intervention might remain concealed and its usefulness may appear unimpressive. For this reason the papers suggests some principles through which psychology can contribute to processes of inclusiveness within a multicultural society and promote the acknowledgement of its own role in the field of humanitarian intervention. 1. Darwin's "strange inversion of reasoning". Science.gov (United States) Dennett, Daniel 2009-06-16 Darwin's theory of evolution by natural selection unifies the world of physics with the world of meaning and purpose by proposing a deeply counterintuitive "inversion of reasoning" (according to a 19th century critic): "to make a perfect and beautiful machine, it is not requisite to know how to make it" [MacKenzie RB (1868) (Nisbet & Co., London)]. Turing proposed a similar inversion: to be a perfect and beautiful computing machine, it is not requisite to know what arithmetic is. Together, these ideas help to explain how we human intelligences came to be able to discern the reasons for all of the adaptations of life, including our own. 2. Sequential development of platform to off-platform facies of the great American carbonate bank in the central Appalachians: chapter 15 Science.gov (United States) Brezinski, David K.; Taylor, John F.; Repetski, John E. 2012-01-01 In the central Appalachians, carbonate deposition of the great American carbonate bank began during the Early Cambrian with the creation of initial ramp facies of the Vintage Formation and lower members of the Tomstown Formation. Vertical stacking of bioturbated subtidal ramp deposits (Bolivar Heights Member) and dolomitized microbial boundtsone (Fort Duncan Member) preceded the initiation of platform sedimentation and creation of sand shoal facies (Benevola Member) that was followed by the development of peritidal cyclicity (Daragan Member). Initiation of peritidal deposition coincided with the development of a rimmed platform that would persist throughout much of the Cambrian and Early Odrovician. At the end of deposition of the Waynesboro Formation, the platform became subaerially exposed because of the Hawke Bay regression, bringing the Sauk I supersequence to and end. In the Conestoga Valley of eastern Pennsylvania, Early Cambrian ramp deposition was succeeded by deposition of platform-margin and periplatfrom facies of the Kinzers Formation. 3. Field-trip guide to subaqueous volcaniclastic facies in the Ancestral Cascades arc in southern Washington State—The Ohanapecosh Formation and Wildcat Creek beds Science.gov (United States) Jutzeler, Martin; McPhie, Jocelyn 2017-06-27 Partly situated in the idyllic Mount Rainier National Park, this field trip visits exceptional examples of Oligocene subaqueous volcaniclastic successions in continental basins adjacent to the Ancestral Cascades arc. The >800-m-thick Ohanapecosh Formation (32–26 Ma) and the >300-m-thick Wildcat Creek (27 Ma) beds record similar sedimentation processes from various volcanic sources. Both show evidence of below-wave-base deposition, and voluminous accumulation of volcaniclastic facies from subaqueous density currents and suspension settling. Eruption-fed facies include deposits from pyroclastic flows that crossed the shoreline, from tephra fallout over water, and from probable Surtseyan eruptions, whereas re-sedimented facies comprise subaqueous density currents and debris flow deposits. 4. Expert Causal Reasoning and Explanation. Science.gov (United States) Kuipers, Benjamin The relationship between cognitive psychologists and researchers in artificial intelligence carries substantial benefits for both. An ongoing investigation in causal reasoning in medical problem solving systems illustrates this interaction. This paper traces a dialectic of sorts in which three different types of causal resaoning for medical… 5. Heuristic Biases in Mathematical Reasoning Science.gov (United States) 2005-01-01 In this paper we briefly describe the dual process account of reasoning, and explain the role of heuristic biases in human thought. Concentrating on the so-called matching bias effect, we describe a piece of research that indicates a correlation between success at advanced level mathematics and an ability to override innate and misleading… 6. Children Reason about Shared Preferences Science.gov (United States) Fawcett, Christine A.; Markson, Lori 2010-01-01 Two-year-old children's reasoning about the relation between their own and others' preferences was investigated across two studies. In Experiment 1, children first observed 2 actors display their individual preferences for various toys. Children were then asked to make inferences about new, visually inaccessible toys and books that were described… 7. Saving Money Using Proportional Reasoning Science.gov (United States) de la Cruz, Jessica A.; Garney, Sandra 2016-01-01 It is beneficial for students to discover intuitive strategies, as opposed to the teacher presenting strategies to them. Certain proportional reasoning tasks are more likely to elicit intuitive strategies than other tasks. The strategies that students are apt to use when approaching a task, as well as the likelihood of a student's success or… 8. Dual Coding, Reasoning and Fallacies. Science.gov (United States) Hample, Dale 1982-01-01 Develops the theory that a fallacy is not a comparison of a rhetorical text to a set of definitions but a comparison of one person's cognition with another's. Reviews Paivio's dual coding theory, relates nonverbal coding to reasoning processes, and generates a limited fallacy theory based on dual coding theory. (PD) 9. #FakeNobelDelayReasons CERN Multimedia 2013-01-01 Tuesday’s hour-long delay of the Nobel Prize in Physics announcement was (and still is) quite the cause for speculation. But on the Twittersphere, it was simply the catalyst for some fantastic puns, so-bad-they're-good physics jokes and other shenanigans. Here are some of our favourite #FakeNobelDelayReasons. 10. Conceptual Knowledge Representation and Reasoning DEFF Research Database (Denmark) Oldager, Steen Nikolaj 2003-01-01 One of the main areas in knowledge representation and logic-based artificial intelligence concerns logical formalisms that can be used for representing and reasoning with concepts. For almost 30 years, since research in this area began, the issue of intensionality has had a special status... 11. Clinical reasoning as social deliberation DEFF Research Database (Denmark) Thorgård, Keld 2014-01-01 In this paper I will challenge the individualistic model of clinical reasoning. I will argue that sometimes clinical practice is rather machine-like, and information is called to mind and weighed, but the clinician is not just calculating how to use particular means to reach fixed ends. Often... 12. A Chemistry Concept Reasoning Test Science.gov (United States) Cloonan, Carrie A.; Hutchinson, John S. 2011-01-01 A Chemistry Concept Reasoning Test was created and validated providing an easy-to-use tool for measuring conceptual understanding and critical scientific thinking of general chemistry models and theories. The test is designed to measure concept understanding comparable to that found in free-response questions requiring explanations over… 13. Fukushima accident - reasons and impacts International Nuclear Information System (INIS) Slugen, V. 2011-01-01 The Fukushima accident influenced dramatically the current view on safety of nuclear facilities. Consideration about possible impacts of natural catastrophe in design of nuclear facilities seems to be much more important than before. European commission is focused on the stress-tests at nuclear power plants. His paper will go more in details having in mind reasons and impacts of Fukushima accident (Author) 14. Negligent Rape and Reasonable Beliefs DEFF Research Database (Denmark) Hansen, Pelle Guldborg 2008-01-01 practice such defences are often acknowledged if the belief is reasonable by some general standard, even when this standard does not pertain to the rules currently governing the practice of intercourse in Denmark. As a result it has often been argued that the notion of negligent rape should be introduced... 15. Quantitative Reasoning in Problem Solving Science.gov (United States) Ramful, Ajay; Ho, Siew Yin 2015-01-01 In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions. 16. Sensitizing Reasons by Emulating Exemplars Directory of Open Access Journals (Sweden) Kunimasa Sato 2015-05-01 Full Text Available The fostering of rationality has long been endorsed as an educational ideal by some philosophers; in recent years, whereas some have argued for this ideal, others have challenged it, particularly within debates relevant to the study of critical thinking. Harvey Siegel, who has spelled out the philosophical theory of educating for rationality, not only has defended his view from such challenges but also has been deepening his thoughts regarding how rationality can be fostered. This paper centers on the cultivating of sensitivity to reasons in the fostering of rationality by critically examining and extending Siegel’s arguments concerning the notion of what he calls “felt reasons.” By clarifying the notion of felt reasons, I will argue for two ideas: first, teachers, parents, and fictional characters in media such as novels and films can be seen as exemplars that manifest rationality; second, the emotion of admiring exemplars may act as a motivating force for children—including small children who are still not sensitive to reasons and thus are not moved by reasons—to be critical thinkers. 17. AAAI Workshop on Nonmonotonic Reasoning OpenAIRE Etherington, David 1985-01-01 On October 17-19 1984 a workshop on non-monotonic reasoning was held at Mohonk Mountain House, outside New Paltz, New York. The workshop was organized by Raymond Reiter and Bonnie Webber, and was sponsored by the Association for the Advancement of Artificial Intelligence. 18. Team reasoning and group identification NARCIS (Netherlands) Hindriks, Frank The team reasoning approach explains cooperation in terms of group identification, which in turn is explicated in terms of agency transformation and payoff transformation. Empirical research in social psychology is consistent with the significance of agency and payoff transformation. However, it 19. Teaching Inductive Reasoning with Puzzles Science.gov (United States) Wanko, Jeffrey J. 2017-01-01 Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra… 20. Approximate reasoning in decision analysis Energy Technology Data Exchange (ETDEWEB) Gupta, M M; Sanchez, E 1982-01-01 The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms. 1. Impaired epithelial differentiation of induced pluripotent stem cells from ectodermal dysplasia-related patients is rescued by the small compound APR-246/PRIMA-1MET. Science.gov (United States) Shalom-Feuerstein, Ruby; Serror, Laura; Aberdam, Edith; Müller, Franz-Josef; van Bokhoven, Hans; Wiman, Klas G; Zhou, Huiqing; Aberdam, Daniel; Petit, Isabelle 2013-02-05 Ectodermal dysplasia is a group of congenital syndromes affecting a variety of ectodermal derivatives. Among them, ectrodactyly, ectodermal dysplasia, and cleft lip/palate (EEC) syndrome is caused by single point mutations in the p63 gene, which controls epidermal development and homeostasis. Phenotypic defects of the EEC syndrome include skin defects and limbal stem-cell deficiency. In this study, we designed a unique cellular model that recapitulated major embryonic defects related to EEC. Fibroblasts from healthy donors and EEC patients carrying two different point mutations in the DNA binding domain of p63 were reprogrammed into induced pluripotent stem cell (iPSC) lines. EEC-iPSC from both patients showed early ectodermal commitment into K18(+) cells but failed to further differentiate into K14(+) cells (epidermis/limbus) or K3/K12(+) cells (corneal epithelium). APR-246 (PRIMA-1(MET)), a small compound that restores functionality of mutant p53 in human tumor cells, could revert corneal epithelial lineage commitment and reinstate a normal p63-related signaling pathway. This study illustrates the relevance of iPSC for p63 related disorders and paves the way for future therapy of EEC. 2. Tradução Oral à Prima Vista na formação do intérprete: considerações pedagógicas Directory of Open Access Journals (Sweden) Gloria Regina Loreto Sampaio 2017-12-01 Full Text Available A Tradução Oral à Prima Vista (TrPV é um elemento de relevância para a formação do intérprete e um componente essencial para o desempenho do futuro profissional em muitos ambientes de atuação. Consequentemente, a prática da TrPV se faz presente em cursos de formação bem estruturados. Neste escrito, após uma breve referência à natureza, complexidade e desafios impostos pela TrPV, e tendo como base uma vivência docente extensa da autora, será apresentada uma possível abordagem pedagógica, voltada à aquisição da competência em TrPV e a um desempenho de qualidade nessa modalidade híbrida, situada no espaço fronteiriço tradução escrita e tradução oral. 3. Composición quimicomineralógica de las materias primas y ahorro de energía en la industria del cemento Directory of Open Access Journals (Sweden) Soria Santamaría, Francisco 1982-06-01 Full Text Available In the field of energy saving, mainly thermic, in the cement industry, not only should we consider the possibilities in the technological process or the finished product, but also the influence of the chemical-mineral composition of the raw materials. The distinct parameters which fall into the reactivity of the crudes are analyzed, such as the size of the grain (fineness, chemical and mineral composition of the principal components. There follows an exposition of the importance of the minority components as smelting and mineralizers, finally emphasizing the interest and practical behaviour of some of them. En el campo del ahorro de energía, principalmente térmica, en la industria cementera, no sólo deben contemplarse las posibilidades en cuanto al proceso tecnológico o el producto acabado, sino también la influencia de la composición quimicomineralógica de las materias primas. Se analizan los distintos parámetros que inciden en la reactividad de los crudos, tales como tamaño de grano (finura, composición química y mineralogía de los componentes principales. A continuación se hace una exposición de la importancia de los componentes minoritarios como fundentes y mineralizadores, destacando finalmente el interés y comportamiento práctico de alguno de ellos. 4. Determinación espectrofotométrica de un producto activo zeolítico en materia prima y tabletas vaginales Directory of Open Access Journals (Sweden) Mercedes Machuá Veitía 1999-12-01 Full Text Available El empleo de productos activos zeolíticos como fármacos de acción específica requiere el desarrollo de técnicas analíticas para el control de la calidad de las formas terminadas. Se desarrolló y validó un método espectrofotométrico de análisis para una zeolita activada con cinc (PAZ-ZZ a partir de la reacción con zincón. Se evaluó la linealidad, precisión, exactitud y especificidad del método propuesto. La técnica se aplicó posteriormente al análisis de materia prima PAZ-ZZ y tabletas vaginales que contienen este principio activo; los resultados se compararon con los obtenidos para espectroscopia de absorción atómica.The use of active zeolitic products as drugs of specific action requires the development of analytical techniques to control the quality of the finished product. A spectrophotometric method of analysis was validated for a zinc?activated zeolite (PAZ-ZZ, starting from the reaction with zincum. The lineality, precision, exactitude and specificity of the proposed method were evaluated. This technique was later applied to the analysis of PAZ-ZZ raw material and vaginal tablets containing this active principle. The results were compared with those obtained for atomic absortion spectroscopy. 5. Avaliação da aplicação do processo de hidroesterificação na produção de biodiesel a partir de matérias-primas de baixa qualidade OpenAIRE Santos, Letícia Karen dos [UNESP 2016-01-01 A produção de biodiesel a partir de Óleos e Gorduras Residuais (OGR), óleos brutos e outras matérias-primas com acidez elevada e alto teor de umidade, tem se tornado um desafio para a cadeia produtiva de biodiesel. Neste cenário surge como alternativa a hidroesterificação, processo que envolve duas etapas consecutivas: a hidrólise térmica seguida de esterificação o que permite o uso de qualquer matéria-prima graxa. Neste estudo foi avaliada a produção de biodiesel por hidroesterificação de ól... 6. Depositional facies and aqueous-solid geochemistry of travertine-depositing hot springs (Angel Terrace, Mammoth Hot Springs, Yellowstone National Park, USA) Energy Technology Data Exchange (ETDEWEB) Fouke, B.W.; Farmer, J.D.; Des Marais, D.J.; Pratt, L.; Sturchio, N.C.; Burns, P.C.; Discipulo, M.K. 2000-05-01 Petrographic and geochemical analyses of travertine-depositing hot springs at Angel Terrace, Mammoth Hot Springs, Yellowstone National Park, have been used to define five depositional facies along the spring drainage system. Spring waters are expelled in the vent facies at 71 to 73 C and precipitate mounded travertine composed of aragonite needle botryoids. The apron and channel facies (43--72 C) is floored by hollow tubes composed of aragonite needle botryoids that encrust sulfide-oxidizing Aquificales bacteria. The travertine of the pond facies (30--62 C) varies in composition from aragonite needle shrubs formed at higher temperatures to ridged networks of calcite and aragonite at lower temperatures. Calcite ice sheets, calcified bubbles, and aggregates of aragonite needles (fuzzy dumbbells) precipitate at the air-water interface and settle to pond floors. The proximal-slope facies (28--54 C), which forms the margins of terracette pools, is composed of arcuate aragonite needle shrubs that create small microterracettes on the steep slope face. Finally, the distal-slope facies (28--30 C) is composed of calcite spherules and calcite feather crystals. Despite the presence of abundant microbial mat communities and their observed role in providing substrates for mineralization, the compositions of spring-water and travertine predominantly reflect abiotic physical and chemical processes. Vigorous CO{sub 2} degassing causes a +2 unit increase in spring water pH, as well as Rayleigh-type covariations between the concentration of dissolved inorganic carbon and corresponding {delta}{sup 13}C. Travertine {delta}{sup 13}C and {delta}{sup 18}O are nearly equivalent to aragonite and calcite equilibrium values calculated from spring water in the higher-temperature ({approximately}50--73 C) depositional facies. Conversely, travertine precipitating in the lower-temperature (<{approximately}50 C) depositional facies exhibits {delta}{sup 13}C and {delta}{sup 18}O values that are as 7. Supercritical flows and their control on the architecture and facies of small-radius sand-rich fan lobes Science.gov (United States) Postma, George; Kleverlaan, Kick 2018-02-01 New insights into flow characteristics of supercritical, high-density turbidity currents initiated renewed interest in a sand-rich lobe complex near the hamlet of Mizala in the Sorbas Basin (Tortonian, SE Spain). The field study was done using drone-made images taken along bed strike in combination with physical tracing of bounding surfaces and section logging. The studied lobe systems show a consistent built-up of lobe elements of 1.5-2.0 m thick, which form the building 'blocks' of the lobe system. The stacking of lobe elements shows lateral shift and compensational relief infill. The new model outlined in this paper highlights three stages of fan lobe development: I. an early aggradational stage with lobe elements characterized by antidune and traction-carpet bedforms and burrowed mud intervals (here called 'distal fan' deposits); II. a progradational stage, where the distal fan deposits are truncated by lobe elements of amalgamated sandy to gravelly units characterized by cyclic step bedform facies (designated as 'supra fan' deposits). The supra fan is much more channelized and scoured and of higher flow energy than the distal-fan. Aggradation of the supra-fan is terminated by a 'pappy' pebbly sandstone and by substrate liquefaction, 'pappy' referring to a typical, porridge-like texture indicating rapid deposition under conditions of little-to-no shear. The facies-bounded termination of the supra-fan is here related to its maximum elevation, causing the lobe-feeding supercritical flow to choke and to expand upwards by a strong hydraulic jump at the channel outlet; III. a backfilling stage, characterized by backfilling of the remaining relief with progressively thinning and fining of turbidite beds and eventually with mud. The three-stage development for fan-lobe building is deducted from reoccurring architectural and facies characteristics in three successive fan-lobes. The validity of using experimental, supercritical-flow fan studies for understanding the 8. Exploring students' patterns of reasoning Science.gov (United States) Matloob Haghanikar, Mojgan As part of a collaborative study of the science preparation of elementary school teachers, we investigated the quality of students' reasoning and explored the relationship between sophistication of reasoning and the degree to which the courses were considered inquiry oriented. To probe students' reasoning, we developed open-ended written content questions with the distinguishing feature of applying recently learned concepts in a new context. We devised a protocol for developing written content questions that provided a common structure for probing and classifying students' sophistication level of reasoning. In designing our protocol, we considered several distinct criteria, and classified students' responses based on their performance for each criterion. First, we classified concepts into three types: Descriptive, Hypothetical, and Theoretical and categorized the abstraction levels of the responses in terms of the types of concepts and the inter-relationship between the concepts. Second, we devised a rubric based on Bloom's revised taxonomy with seven traits (both knowledge types and cognitive processes) and a defined set of criteria to evaluate each trait. Along with analyzing students' reasoning, we visited universities and observed the courses in which the students were enrolled. We used the Reformed Teaching Observation Protocol (RTOP) to rank the courses with respect to characteristics that are valued for the inquiry courses. We conducted logistic regression for a sample of 18courses with about 900 students and reported the results for performing logistic regression to estimate the relationship between traits of reasoning and RTOP score. In addition, we analyzed conceptual structure of students' responses, based on conceptual classification schemes, and clustered students' responses into six categories. We derived regression model, to estimate the relationship between the sophistication of the categories of conceptual structure and RTOP scores. However, the 9. Projeto de Redução do Desperdício de Matéria-Prima: Estudo de Caso na Indústria de Embalagens de Papel no Brasil Directory of Open Access Journals (Sweden) Gleison Hidalgo Hidalgo Martins 2014-02-01 Full Text Available Pode-se dizer que em se tratando de produção industrial os desperdícios que podem ocorrer ao longo dos processos são diversos, vão de matéria-prima à recursos financeiros. No entanto pode-se classificar o desperdício de matéria-prima como sendo o mais urgente deste setor e também o mais passivo de ser estudado, uma vez que impacta diretamente no fluxo fabril e na quantidade do produto acabado. O conteúdo desta pesquisa apresenta argumentos através de embasamento teórico e prático que apontam para a importância de trabalhos sobre as possíveis causas do problema do desperdício de matéria-prima nas linhas industriais de embalagem de papel assim como as formas de combater e reagir ao problema.DOI:10.5585/gep.v4i3.186 10. Asignación de primas en el seguro del automóvil utilizando el Análisis en ComponentesPrincipales Funcionales = Premium allocation in the car insurance by using Functional Principal Component Analysis. Directory of Open Access Journals (Sweden) 2007-01-01 Full Text Available El estudio de las primas de riesgo en el seguro del automóvil es de suma importancia, debido a la gran competitividad existente en el mercado asegurador. En este artículo se pretende proponer un sistema de bonificación-penalización de las primas de riesgo utilizando el Análisis Funcional en Componentes Principales. En concreto, se realiza un estudio empírico con los datos reales de una compañía aseguradora con cobertura nacional. Aplicando el sistema propuesto de bonificación-penalización a los perfiles de comportamiento de los asegurados, se obtienen las primas de riesgo para cada uno de los perfiles considerados y tramos de edad. = The study of the premium risk in the car insurance is really important because the insurance market is very competitive. In this article we show a bonus-malus method of risk premiums. To do this, we use the Functional Principal Component Analysis. More precisely, we explain an empirical study with the real data of an insurance company. By applying the bonus-malus method that we have given, we are able to obtain the premium risk for different profiles and age ranges. 11. Causal reasoning with mental models Science.gov (United States) Khemlani, Sangeet S.; Barbey, Aron K.; Johnson-Laird, Philip N. 2014-01-01 This paper outlines the model-based theory of causal reasoning. It postulates that the core meanings of causal assertions are deterministic and refer to temporally-ordered sets of possibilities: A causes B to occur means that given A, B occurs, whereas A enables B to occur means that given A, it is possible for B to occur. The paper shows how mental models represent such assertions, and how these models underlie deductive, inductive, and abductive reasoning yielding explanations. It reviews evidence both to corroborate the theory and to account for phenomena sometimes taken to be incompatible with it. Finally, it reviews neuroscience evidence indicating that mental models for causal inference are implemented within lateral prefrontal cortex. PMID:25389398 12. Causal reasoning with mental models. Science.gov (United States) Khemlani, Sangeet S; Barbey, Aron K; Johnson-Laird, Philip N 2014-01-01 This paper outlines the model-based theory of causal reasoning. It postulates that the core meanings of causal assertions are deterministic and refer to temporally-ordered sets of possibilities: A causes B to occur means that given A, B occurs, whereas A enables B to occur means that given A, it is possible for B to occur. The paper shows how mental models represent such assertions, and how these models underlie deductive, inductive, and abductive reasoning yielding explanations. It reviews evidence both to corroborate the theory and to account for phenomena sometimes taken to be incompatible with it. Finally, it reviews neuroscience evidence indicating that mental models for causal inference are implemented within lateral prefrontal cortex. 13. Causal reasoning with mental models Directory of Open Access Journals (Sweden) Sangeet eKhemlani 2014-10-01 Full Text Available This paper outlines the model-based theory of causal reasoning. It postulates that the core meanings of causal assertions are deterministic and refer to temporally-ordered sets of possibilities: A causes B to occur means that given A, B occurs, whereas A enables B to occur means that given A, it is possible for B to occur. The paper shows how mental models represent such assertions, and how these models underlie deductive, inductive, and abductive reasoning yielding explanations. It reviews evidence both to corroborate the theory and to account for phenomena sometimes taken to be incompatible with it. Finally, it reviews neuroscience evidence indicating that mental models for causal inference are implemented within lateral prefrontal cortex. 14. Paraconsistent Reasoning for OWL 2 Science.gov (United States) Ma, Yue; Hitzler, Pascal A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basic description logic mathcal{ALC}. In this paper, we further study how to extend the four-valued semantics to the more expressive description logic mathcal{SROIQ} which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapted to tractable description logics including mathcal{EL++}, DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for mathcal{ALC} and show that we can retain most of the desired properties. 15. Marine habitat mapping of the Milford Haven Waterway, Wales, UK: Comparison of facies mapping and EUNIS classification for monitoring sediment habitats in an industrialized estuary Science.gov (United States) Carey, Drew A.; Hayn, Melanie; Germano, Joseph D.; Little, David I.; Bullimore, Blaise 2015-06-01 A detailed map and dataset of sedimentary habitats of the Milford Haven Waterway (MHW) was compiled for the Milford Haven Waterway Environmental Surveillance Group (MHWESG) from seafloor images collected in May, 2012 using sediment-profile and plan-view imaging (SPI/PV) survey techniques. This is the most comprehensive synoptic assessment of sediment distribution and benthic habitat composition available for the MHW, with 559 stations covering over 40 km2 of subtidal habitats. In the context of the MHW, an interpretative framework was developed that classified each station within a 'facies' that included information on the location within the waterway and inferred sedimentary and biological processes. The facies approach provides critical information on landscape-scale habitats including relative location and inferred sediment transport processes and can be used to direct future monitoring activities within the MHW and to predict areas of greatest potential risk from contaminant transport. Intertidal sediment 'facies' maps have been compiled in the past for MHW; this approach was expanded to map the subtidal portions of the waterway. Because sediment facies can be projected over larger areas than individual samples (due to assumptions based on physiography, or landforms) they represent an observational model of the distribution of sediments in an estuary. This model can be tested over time and space through comparison with additional past or future sample results. This approach provides a means to evaluate stability or change in the physical and biological conditions of the estuarine system. Initial comparison with past results for intertidal facies mapping and grain size analysis from grab samples showed remarkable stability over time for the MHW. The results of the SPI/PV mapping effort were cross-walked to the European Nature Information System (EUNIS) classification to provide a comparison of locally derived habitat mapping with European-standard habitat 16. [Hypnoanalgesia and clinical nursing reasoning]. Science.gov (United States) Soudan, Corinne 2017-05-01 Hypnoanalgesia is practised in accordance with care ethics and as a complement to other medical and/or psychological therapies. It is aimed at people with acute, chronic or treatment-related pain. Its practice is founded on clinical nursing reasoning, which targets the health problem and the therapeutic objectives guiding the hypnosis session. A clinical assessment finalises the interactional process. Copyright © 2017 Elsevier Masson SAS. All rights reserved. 17. Is Hawking radiation physically reasonable? International Nuclear Information System (INIS) Ahmed, M. 1995-07-01 Hawking radiation is observed in a general spacetime which includes all the black hole spacetimes as well as various types of other spacetimes which are not interesting form the physical point of view like black hole spacetimes. Even Hawking radiation is observed in NUT spacetime which is sometimes considered as unphysical. So naturally arises the question whether Hawking radiation is physically reasonable. (author). 22 refs 18. Temporal Reasoning and Default Logics. Science.gov (United States) 1985-10-01 Aritificial Intelligence ", Computer Science Research Report, Yale University, forthcoming (1985). . 74 .-, A Axioms for Describing Persistences and Clipping...34Circumscription - A Form of Non-Monotonic Reasoning", Artificial Intelligence , vol. 13 (1980), pp. 27-39. [13] McCarthy, John, "Applications of...and P. J. Hayes, "Some philosophical problems from the standpoint of artificial intelligence ", in: B. Meltzer and D. Michie (eds.), Machine 19. Nudges to reason: not guilty OpenAIRE Levy, N 2017-01-01 I am to grateful to Geoff Keeling for his perceptive response to my paper. In this brief reply, I will argue that he does not succeed in his goal of showing that nudges to reason do not respect autonomy. At most, he establishes only that such nudges may threaten autonomy when used in certain ways and in certain circumstances. As I will show, this is not a conclusion that should give us grounds for particular concerns about nudges. 20. Reasoning with Annotations of Texts OpenAIRE Ma , Yue; Lévy , François; Ghimire , Sudeep 2011-01-01 International audience; Linguistic and semantic annotations are important features for text-based applications. However, achieving and maintaining a good quality of a set of annotations is known to be a complex task. Many ad hoc approaches have been developed to produce various types of annotations, while comparing those annotations to improve their quality is still rare. In this paper, we propose a framework in which both linguistic and domain information can cooperate to reason with annotat... 1. Metre-scale cyclicity in Middle Eocene platform carbonates in northern Egypt: Implications for facies development and sequence stratigraphy Science.gov (United States) Tawfik, Mohamed; El-Sorogy, Abdelbaset; Moussa, Mahmoud 2016-07-01 The shallow-water carbonates of the Middle Eocene in northern Egypt represent a Tethyan reef-rimmed carbonate platform with bedded inner-platform facies. Based on extensive micro- and biofacies documentation, five lithofacies associations were defined and their respective depositional environments were interpreted. Investigated sections were subdivided into three third-order sequences, named S1, S2 and S3. Sequence S1 is interpreted to correspond to the Lutetian, S2 corresponds to the Late Lutetian and Early Bartonian, and S3 represents the Late Bartonian. Each of the three sequences was further subdivided into fourth-order cycle sets and fifth-order cycles. The complete hierarchy of cycles can be correlated along 190 km across the study area, and highlighting a general "layer-cake" stratigraphic architecture. The documentation of the studied outcrops may contribute to the better regional understanding of the Middle Eocene formations in northern Egypt and to Tethyan pericratonic carbonate models in general. 2. Facies and carbon/oxygen isotopes of the Calabozo Formation (Middle Jurassic), Arroyo La Vaina, Mendoza, Argentina International Nuclear Information System (INIS) Cabaleri, N.G.; Valencio, S.A.; Cagnoni, M.C.; Ramos, A.M.; Armella, C.; Panarello, H.O; Riccardi, A.C 2001-01-01 Facial / microfacial studies and geochemical isotopic analyses on marine jurassic carbonates of the Calabozo Formation (Dessanti, 1973) were carried out to reconstruct the palaeoenvironment and postdepositional history of the unit. This study is part of a project which purpose is the sedimentological and geochemical characterization of the Jurassic carbonate sequences of Cuenca Neuquina, in the southwestern Mendoza, Argentina. A detailed description about this basin can be found in Legarreta and Uliana (1999) and Riccardi et al. (2000). During the Late Bathonian and Early Callovian, the basin showed a reduction of the sedimentation area and a marked marginal facies progradation. West of Malargue, in areas with low detritic contribution, limestones of the Calabozo Formation were deposited. At the end of the Early Callovian, the basin was isolated, prevailing hypersaline conditions which caused the accumulation of the evaporites of the Tabanos Formation (Stipanicic, 1966) (au) 3. Seismic Facies of Pleistocene–Holocene Channel-fill Deposits in Bawean Island and Adjacent Waters, Southeast Java Sea Directory of Open Access Journals (Sweden) Ali Albab 2017-08-01 Full Text Available The late Pleistocene-Holocene stratigraphic architecture of the Bawean Island and surrounding waters, southeast Java Sea has been analyzed by using sparker seismic profiles. Geological interpretation of these seismic profiles revealed the widespread distribution of paleochannels with different shape and size in the present-day Java Sea. Two channel types can be distinguished based on its morphology: U-shaped channels in the western part and V-shaped channels in the eastern part. The stratigraphic successions were grouped into two major seismic units separated by different seismic boundaries. Characters of marine and fluvial deposits were determined based on seismic boundaries and internal reflectors. Three seismic facies can be identified within late Pleistocene – Holocene incised channel fills associated with SB2. The internal structure of incised-channels consist of chaotic reflector at the bottom, covered by parallel–sub parallel and almost reflection-free indicating the homogenous sediment deposited during the succession. 4. Object reasoning for waste remediation International Nuclear Information System (INIS) Pennock, K.A.; Bohn, S.J.; Franklin, A.L. 1991-08-01 A large number of contaminated waste sites across the United States await size remediation efforts. These sites can be physically complex, composed of multiple, possibly interacting, contaminants distributed throughout one or more media. The Remedial Action Assessment System (RAAS) is being designed and developed to support decisions concerning the selection of remediation alternatives. The goal of this system is to broaden the consideration of remediation alternatives, while reducing the time and cost of making these considerations. The Remedial Action Assessment System is a hybrid system, designed and constructed using object-oriented, knowledge- based systems, and structured programming techniques. RAAS uses a combination of quantitative and qualitative reasoning to consider and suggest remediation alternatives. The reasoning process that drives this application is centered around an object-oriented organization of remediation technology information. This paper describes the information structure and organization used to support this reasoning process. In addition, the paper describes the level of detail of the technology related information used in RAAS, discusses required assumptions and procedural implications of these assumptions, and provides rationale for structuring RAAS in this manner. 3 refs., 3 figs 5. Pisa Question and Reasoning Skill Directory of Open Access Journals (Sweden) Ersoy Esen 2017-01-01 Full Text Available The objective of the study is to determine the level of the reasoning skills of the secondary school students. This research has been conducted during the academic year of 2015-2016 with the participation of 51 students in total, from a province in the Black Sea region of Turkey by using random sampling method. Case study method has been used in this study, since it explains an existing situation. In this study, content analysis from the qualitative research methods was carried out. In order to ensure the validity of the scope, agreement percentage formula was used and expert opinions were sought.The problem named Holiday from the Chapter 1 of the normal units in Problem Solving Questions from PISA (Program for International Student Assessments [35] are used as the data collection tool for the study. The problem named Holiday consists of two questions. Applied problems were evaluated according to the mathematical reasoning stages of TIMSS (2003. The findings suggest that the students use proportional reasoning while solving the problems and use the geometric shapes to facilitate the solution of the problem. When they come across problems related to each other, it is observed that they create connections between the problems based on the results of the previous problem. In conclusion, the students perform crosscheck to ensure that their solutions to the problems are accurate. 6. The salt that wasn't there: Mudflat facies equivalents to halite of the Permian Rustler Formation, southeastern New Mexico International Nuclear Information System (INIS) Powers, D.W.; Holt, R.M. 2000-01-01 Four halite beds of the Permian Restler Formation in southeastern New Mexico thin dramatically over horst lateral distances to correlative classic (mudstone) beds. The mudstones have long been considered residues after post-burial dissolution (subrosion) of halite, assumed to have been deposited continuously across the area. Hydraulic properties of the Culebra Dolomite Member have often been related to Rustler subrosion. In cores and three shafts at the Waste Isolation Pilot Plant (WIPP), however, these mudstones display flat bedding, graded bedding, cross-bedding, erosional contacts, and channels filled with intraformational conglomerates. Cutans indicate early stages of soil development during subaerial exposure. Smeared intraclasts developed locally as halite was removed syndepositionally during subaerial exposure. The authors interpret these beds as facies formed in salt-pan or hypersaline-lagoon, transitional, and mudflat environments. Halite is distributed approximately as it was deposited. Breccia in limited areas along one halite margin indicates post-burial dissolution, and these breccials are key to identifying areas of subrosion. A depositional model accounts for observed sedimentary features of Restler mudstones. Marked facies and thickness changes are consistent with influence by subsidence boundaries, as found in some modern continental evaporites. A subrosion model accounts for limited brecciated zones along (depositional)halite margins, but bedding observed in the mudstones would not survive 90% reduction in rock volume. Depositional margins for these halite beds will be useful in reconstructing detailed subsidence history of the Late Permian in the northern Delaware Basin, It also no longer is tenable to attribute large variations in Culebra transmissivity to Rustler subrosion 7. Facies architecture of basin-margin units in time and space: Lower to Middle Miocene Sivas Basin, Turkey Science.gov (United States) Çiner, A.; Kosun, E. 2003-04-01 The Miocene Sivas Basin is located within a collision zone, forming one of the largest basins in Central Turkey that developed unconformably on a foundered Paleozoic-Mesozoic basement and Eocene-Oligocene deposits. The time and space relationships of sedimentary environments and depositional evolution of Lower to Middle Miocene rocks exposed between Zara and Hafik towns is studied. A 4 km thick continuous section is subdivided into the Agilkaya and Egribucak Formations. Each formation shows an overall fining upward trend and contains three members. Although a complete section is present at the western part (near Hafik) of the basin, to the east the uppermost two members (near Zara) are absent. The lower members of both formations are composed of fluvial sheet-sandstone and red mudstone that migrate laterally on a flood basin within a semi-arid fan system. In the Agilkaya Formation that crops out near Zara, alluvial fans composed of red-pink volcanic pebbles are also present. The middle members are composed of bedded to massive gypsum and red-green mudstone of a coastal and/or continental sabkha environment. While the massive gypsum beds reach several 10’s of m in Hafik area, near Zara, they are only few m thick and alternate with green mudstones. In Hafik, bedded gypsums are intercalated with lagoonal dolomitic limestone and bituminous shale in the Agilkaya Formation and with fluvial red-pink sandstone-red mudstone in the Egribucak Formation. The upper members are made up of fossiliferous mudstone and discontinuous sandy limestone beds with gutter casts, HCS, and 3-D ripples. They indicate storm-induced sedimentation in a shallow marine setting. The disorganized accumulations of ostreid and cerithiid shells, interpreted as coquina bars, are the products of storm generated reworking processes in brackish environments. Rapid vertical and horizontal facies changes and the facies associations in both formations reflect the locally subsiding nature of this molassic 8. The AORTA Reasoning Framework - Adding Organizational Reasoning to Agents DEFF Research Database (Denmark) Jensen, Andreas Schmidt Intelligent agents are entities defined by, among other things, autonomy. In systems of many agents, the agents’ individual autonomy can lead to uncertainty since their behavior cannot always be predicted. Usually, this kind of uncertainty is accommodated by imposing an organization upon the system...... previously been successfully integrated into agent programming languages. However, the operationalization of an organization is usually tailored to a specific language. This makes it hard to apply the same approach to other languages and platforms. The AORTA reasoning framework distinguishes itself by being... 9. Sensibilidade à secagem da matéria-prima cerâmica da Formação Corumbataí na região do Polo Cerâmico de Santa Gertrudes, SP Directory of Open Access Journals (Sweden) A. A. Azzi 2015-06-01 Full Text Available As argilas provenientes da Formação Corumbataí são atualmente a principal fonte de matéria-prima para as indústrias do Polo Cerâmico de Santa Gertrudes. 73% das indústrias desse polo que utilizam o processo de secagem via seca são hoje alvo de crescente pressão dos órgãos de controle ambiental devido à emissão de partículas (poeira associado ao processo de secagem da matéria-prima. Neste trabalho, foram realizados quatro diferentes testes de secagem em três tipos de matéria-prima (D, I e M da Formação Corumbataí, com umidades naturais iniciais de 8%, 18% e 19%, respectivamente, para poder avaliar a sensibilidade à secagem. Dentre os testes analisados neste trabalho estão o processo natural de secagem ao sol, secagem ao vento, secagem ao sol combinado a uma corrente de vento, e secagem ao sol com matéria-prima previamente umedecida em água corrente. Os testes foram ainda correlacionados à análise termogravimétrica. A análise por difração de raios X, juntamente com as análises química e petrográfica mostrou que as amostras D, I e M contêm predominantemente filossilicatos 2:1 como illitas (25-30% e esmectitas (15-25%, e em menor quantidade caulinita (0-15% e clorita (0-5%. Os resultados dos experimentos de secagem associados à mineralogia mostram que entre 100 °C e 200 °C nos gráficos de termogravimetria pode indicar de modo rápido a sensibilidade à secagem que o material apresenta, uma vez que a maior perda de umidade obtida nesta faixa indica a maior quantidade de minerais do grupo das esmectitas, que por sua vez conferem ao material menor sensibilidade à secagem. Além disso, os procedimentos de secagem natural sugerem que secar separadamente a matéria-prima pode resultar em maior eficiência do processo de secagem. 10. Asymmetrical cross-current turbidite facies tract in a structurally-confined mini-basin (Priabonian-Rupelian, Ranzano Sandstone, northern Apennines, Italy) NARCIS (Netherlands) Tinterri, R.; Laporta, M.; Ogata, K. 2017-01-01 This work discusses the stratigraphy and facies analysis of the Ranzano Sandstone, in the northern Apennines (Italy), a confined low-efficiency turbidite system deposited in a series of small piggy-back basins, which show strong analogies with intraslope minibasins commonly observed in divergent 11. Stratigraphy, facies analysis and depositional environments of the Upper Unit of Abu Roash "E" member in the Abu Gharadig field, Western Desert, Egypt Science.gov (United States) Hewaidy, Abdel Galil; Elshahat, O. R.; Kamal, Samy 2018-03-01 Abu Roach "E" member is of an important hydrocarbon reservoir-producing horizon in the Abu Gharadig Field (north Western Desert, Egypt). This study is used to build facies analysis and depositional environments model for the Upper Unit of the Abu Roash "E" member in Abu Gharadig Field. This target has been achieved throughout the sedimentological, wire line logs, lithostratigraphic and biostratigraphic analyses of more than 528 feet cores. The high-resolution biostratigraphic analysis provides a calibration for the paleo-bathymetry and depositional environmental interpretations. Biozonation and lithostratigraphic markers are used to constrain stratigraphic correlation. Integration between the core description and petorographic microfacies analysis by microscope examination provide an excellent indication for the rock types and depositional environments. Five depositional facies types are detected including carbonate inner ramp, tidal flats, tidal channels, supra-tidal and tide dominated delta facies. This model helps in the understanding of the Upper Unit of Abu Roash "E" member reservoir distribution as well as lateral and vertical facies changes that contribute to the development strategy for the remaining hydrocarbon reserves for this important oil reservoir. 12. Implication of corona formation in a metatroctolite to the granulite facies overprint of HP-UHP rocks in the Moldanubian Zone (Bohemian Massif) Czech Academy of Sciences Publication Activity Database Faryad, S. W.; Kachlík, V.; Sláma, Jiří; Hoinkes, G. 2015-01-01 Roč. 33, č. 3 (2015), s. 295-310 ISSN 0263-4929 Institutional support: RVO:67985831 Keywords : coronitic metatroctolite * granulite facies * Moldanubian Zone * sapphirine * spinel * Variscan orogeny Subject RIV: DB - Geology ; Mineralogy Impact factor: 3.673, year: 2015 13. Trace fossils of the Moravice Formation from the southern Nízký Jeseník Mts. (Lower Carboniferous, Culm facies; Moravia, Czech Republic) Czech Academy of Sciences Publication Activity Database Mikuláš, Radek; Lehotský, T.; Bábek, O. 2004-01-01 Roč. 79, č. 2 (2004), s. 81-98 ISSN 1214-1119 R&D Projects: GA ČR(CZ) GA205/00/0118 Keywords : ichnofossils * Lower Carboniferous * Culm facies Subject RIV: DB - Geology ; Mineralogy http://www.geology.cz/bulletin/contents/2004/vol79no2/bullgeosci200402081.pdf 14. UTILIZAÇÃO DE RESÍDUOS DE MINÉRIO DE FERRO COMO MATÉRIA PRIMA PARA FABRICAÇÃO DE ARGAMASSA Directory of Open Access Journals (Sweden) 2016-04-01 Full Text Available A quantidade cada vez maior de resíduos gerados na fase de exploração e extração de minério de ferro constitui um problema ambiental às mineradoras, devido as grandes áreas requeridas para disposição dos mesmos, bem como a constante necessidade de gerenciamento desses locais. Neste estudo foi verificada a viabilidade técnica de utilização do resíduo gerado na exploração de um minério itabirítico como matéria prima para confecção de argamassa. Foram confeccionadas diferentes formulações de argamassas através da variação da proporção cimento/resíduo e da proporção água/cimento. Para cada amostra foram determinados o tempo de pega, viscosidade e densidade, no caso da amostra fresca, e densidade e resistência à compressão para a amostra solidificada. Concluiu-se que a argamassa confeccionada com maior quantidade de resíduo (traço 1:2,5 e menor relação água/cimento (0,95 foi aquela que apresentou menor tempo de pega e maior resistência à compressão. Este resultado foi bastante satisfatório, pois o aumento de resíduo incorporado favoreceu a resistência à compressão final do produto. 15. Procedimiento para la gestión de los impactos ambientales negativos asociados a la recuperación de materias primas en Cienfuegos, Cuba. Directory of Open Access Journals (Sweden) David Javier Castro Rodríguez 2016-04-01 Full Text Available El reciclaje constituye una actividad priorizada en Cuba. El objetivo fue implementar un procedimiento para la gestión de los impactos ambientales negativos asociados a los procesos operativos de la Empresa de Recuperación de Materias Primas de Cienfuegos. El procedimiento se construyó utilizando la propuesta del Instituto Andaluz de Tecnología para la gestión por procesos y los ocho pasos en la solución de problemas. Se combinaron herramientas de gestión bajo el principio de convergencia metodológica. Los impactos ambientales fueron evaluados mediante el software GAIA versión 1.0, utilizando los criterios propuestos por la Guía Metodológica de Evaluación de Impacto Ambiental de Conesa. Se identificaron 97 impactos ambientales negativos, entre severos y moderados integraron el 80.41 % de ellos. El factor ambiental más impactado fue el físico-químico con el 50.52 %. El subproceso no metálico resultó el más impactante, con el 50 % de los impactos severos negativos totales y el 34 % de los moderados. Se identificaron las principales causas asociadas y se diseñó un plan de intervención de 35 medidas con base en los principios de Producción Más Limpia. Los resultados contribuyen a lograr la gestión de los impactos ambientales negativos de la entidad y a la sostenibilidad del reciclaje. 16. Validación del sistema ultramicroelisa en la certificación de placenta humana como materia prima farmacéutica y cosmética Directory of Open Access Journals (Sweden) Maydelin Trujillo Alfonso Full Text Available Introducción: el Laboratorio de Control Viral de la Planta Derivados de la Placenta realiza la certificación de la placenta humana como materia prima farmacéutica y cosmética mediante el sistema ultramicroanalítico. Objetivo: validar el sistema ultramicroelisa de determinación de antígeno de superficie del virus de la hepatitis B, anticuerpos contra el virus de la hepatitis C y virus de inmunodeficiencia humana tipo 1 y 2 en muestras de suero de cordón umbilical. Métodos: se realizó la calificación de la operación y la validación del desempeño analítico de los sistemas UMELISA HBsAg Plus, UMELISA HCV y UMELISA HIV 1+2 Recombinant empleandocomo sistemas de referencia el Hepanostika HBsAg Uni-FormII, Hepanostika HCV Ultra y Vironostika HIV-Uni-Form II Ag/Ab. Resultados: la calificación de la operación para las tres técnicas analíticas resultó satisfactoria. Los parámetros de especificidad diagnóstica y analítica fueron de 100 %, así como la concordancia con las técnicas de referencia. El coeficiente de variación fue menor del 10 % durante el estudio de precisión interensayo, menor que el 20 % intraensayo y se demostró la robustez de las técnicas para pequeños cambios en la temperatura de incubación. Conclusiones: los sistemas ultramicroelisa utilizados como método de control de la calidad de la placenta humana resultaron específicos, precisos y robustos en las condiciones ensayadas, por lo que pueden emplearse de manera segura y confiable. 17. Crows spontaneously exhibit analogical reasoning. Science.gov (United States) Smirnova, Anna; Zorina, Zoya; Obozova, Tanya; Wasserman, Edward 2015-01-19 Analogical reasoning is vital to advanced cognition and behavioral adaptation. Many theorists deem analogical thinking to be uniquely human and to be foundational to categorization, creative problem solving, and scientific discovery. Comparative psychologists have long been interested in the species generality of analogical reasoning, but they initially found it difficult to obtain empirical support for such thinking in nonhuman animals (for pioneering efforts, see [2, 3]). Researchers have since mustered considerable evidence and argument that relational matching-to-sample (RMTS) effectively captures the essence of analogy, in which the relevant logical arguments are presented visually. In RMTS, choice of test pair BB would be correct if the sample pair were AA, whereas choice of test pair EF would be correct if the sample pair were CD. Critically, no items in the correct test pair physically match items in the sample pair, thus demanding that only relational sameness or differentness is available to support accurate choice responding. Initial evidence suggested that only humans and apes can successfully learn RMTS with pairs of sample and test items; however, monkeys have subsequently done so. Here, we report that crows too exhibit relational matching behavior. Even more importantly, crows spontaneously display relational responding without ever having been trained on RMTS; they had only been trained on identity matching-to-sample (IMTS). Such robust and uninstructed relational matching behavior represents the most convincing evidence yet of analogical reasoning in a nonprimate species, as apes alone have spontaneously exhibited RMTS behavior after only IMTS training. Copyright © 2015 Elsevier Ltd. All rights reserved. 18. Zircon and monazite petrochronologic record of prolonged amphibolite to granulite facies metamorphism in the Ivrea-Verbano and Strona-Ceneri Zones, NW Italy Science.gov (United States) Guergouz, Celia; Martin, Laure; Vanderhaeghe, Olivier; Thébaud, Nicolas; Fiorentini, Marco 2018-05-01 In order to improve the understanding of thermal-tectonic evolution of high-grade terranes, we conducted a systematic study of textures, REE content and U-Pb ages of zircon and monazite grains extracted from migmatitic metapelites across the amphibolite to granulite facies metamorphic gradient exposed in the Ivrea-Verbano and Strona-Ceneri Zones (Italy). This study documents the behaviour of these accessory minerals in the presence of melt. The absence of relict monazite grains in the metasediments and the gradual decrease in the size of inherited zircon grains from amphibolite to granulite facies cores indicate partial to total dissolution of accessory minerals during the prograde path and partial melting. The retrograde path is marked by (i) growth of new zircon rims (R1 and R2) around inherited cores in the mesosome, (ii) crystallisation of stubby zircon grains in the leucosome, especially at granulite facies, and (iii) crystallisation of new monazite in the mesosome. Stubby zircon grains have a distinctive fir-tree zoning and a constant Th/U ratio of 0.20. Together, these features reflect growth in the melt; conversely, the new zircon grains with R1 rims have dark prismatic habits and Th/U ratios ages obtained on both types are similar, indicating contemporaneous growth of stubby zircon and rims around unresorbed zircon grains, reflecting the heterogeneous distribution of the melt at the grain scale. In the Ivrea-Verbano Zone the interquartile range (IQR) of U-Pb ages on zircon and monazite are interpreted to represent the length of zircon and monazite crystallisation in the presence of melt. Accordingly, they provide an indication on the minimum duration for high-temperature metamorphism and partial melting of the lower crust: 20 Ma and 30 Ma in amphibolite and granulite facies, respectively. In amphibolite facies, zircon crystallisation between 310 and 294 Ma (IQR) is interpreted to reflect metamorphic peak condition and earlier retrograde history; conversely 19. Probabilistic reasoning in data analysis. Science.gov (United States) Sirovich, Lawrence 2011-09-20 This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrivals that are independent of prior history (Markovian events), with an emphasis on waiting times, Poisson processes, and Poisson probability distributions. The use of these various probability distributions is applied to biomedical problems, including several classic experimental studies. 20. Numeracy, frequency, and Bayesian reasoning Directory of Open Access Journals (Sweden) Gretchen B. Chapman 2009-02-01 Full Text Available Previous research has demonstrated that Bayesian reasoning performance is improved if uncertainty information is presented as natural frequencies rather than single-event probabilities. A questionnaire study of 342 college students replicated this effect but also found that the performance-boosting benefits of the natural frequency presentation occurred primarily for participants who scored high in numeracy. This finding suggests that even comprehension and manipulation of natural frequencies requires a certain threshold of numeracy abilities, and that the beneficial effects of natural frequency presentation may not be as general as previously believed.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.580447256565094, "perplexity": 16636.72193259586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221215284.54/warc/CC-MAIN-20180819184710-20180819204710-00623.warc.gz"}
http://mathhelpforum.com/calculus/22165-urgent-binomial-series-help-work-included-print.html	# urgent* binomial series help(work included) • November 6th 2007, 04:53 PM xfyz urgent* binomial series help(work included) Use the binomial series to expand the function as a power series. 1 / (2+x)^3 the answer in the back says it's (-1)^n(n+1)(n+2) * x^n all over 2^n+4 can someone help me where i went wrong or if im doing it totally wrong My work: [2(1+x/2)]^-3 = (1/8)(1+x/2)^-3 (1/8)sum (-3 n)(x/2)^n (1/8) [ 1+(-3)(x/2) + [(-3)(-4)]/2 (x/2)^2 +... (-3 + n - 1) ] (1/8) * sum [(-1)^n (345....n(n+1) ]/ n! (1/2^3) * [ (-1)^n(n+1)(n+2) ] / 2^n =[[ (-1)^n * (n+1)(n+2) ]x^n ]/ (2^n+3) ] thanks. • November 7th 2007, 06:46 AM Opalg Quote: Originally Posted by xfyz Use the binomial series to expand the function as a power series. 1 / (2+x)^3 the answer in the back says it's (-1)^n(n+1)(n+2) * x^n all over 2^n+4 can someone help me where i went wrong or if im doing it totally wrong My work: [2(1+x/2)]^-3 = (1/8)(1+x/2)^-3 (1/8)sum (-3 n)(x/2)^n (1/8) [ 1+(-3)(x/2) + [(-3)(-4)]/2 (x/2)^2 +... (-3 + n - 1) ] (1/8) * sum [(-1)^n (345....n(n+1) ]/ n! (1/2^3) * [ (-1)^n(n+1)(n+2) ] / 2^n =[[ (-1)^n * (n+1)(n+2) ]x^n ]/ (2^n+3) ] thanks. I think the only place where that calculation goes wrong is that you have lost the 2 that fails to cancel from the n!. It's often easiest to do this type of problem by writing down the first few terms of the binomial expansion, so you can see how the pattern goes. $[2(1+x/2)]^{-3} = {\textstyle\frac18}(1+x/2)^{-3}$ $\qquad= \frac18\left\{1 + \frac{-3}1\frac x2 + \frac{(-3)(-4)}{2!}\frac{x^2}{2^2} + \frac{(-3)(-4)(-5)}{3!}\frac{x^3}{2^3} + \frac{(-3)(-4)(-5)(-6)}{4!}\frac{x^4}{2^4} + \ldots \right\}$ $= \frac18\left\{1 - \frac31\,\frac x2 + \frac{3.4}{1.2}\,\frac{x^2}{2^2} - \frac{\rlap/3.4.5}{1.2.\rlap/3}\,\frac{x^3}{2^3} + \frac{\rlap/3.\rlap/4.5.6}{1.2.\rlap/3.\rlap/4}\,\frac{x^4}{2^4} - \ldots \right\}.$ You can see that term in x^n is going to be $(-1)^n\frac18\frac{(n+1)(n+2)}{2}\frac{x^n}{2^n} = \frac{(-1)^n(n+1)(n+2)}{2^{n+4}}x^n$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7863848805427551, "perplexity": 4389.744507958129}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802765616.69/warc/CC-MAIN-20141217075245-00118-ip-10-231-17-201.ec2.internal.warc.gz"}
http://mathoverflow.net/revisions/37381/list	5 added 46 characters in body Let me start with a question for which I know the answer. Consider a symmetric integral $n\times n$ matrix $A=(a_{ij})$ such that $a_{ii}=2$, and for $i\ne j$ one has $a_{ij}=0$ or $-1$. One can encode such a matrix by a graph $G$: it has $n$ vertices, and two vertices $i,j$ are connected by an edge iff $a_{ij}=-1$. Question 1: Which graphs correspond to positive definite $A$? Answer 1: (Classical, well-known, and easy) $G$ is a disjoint union of $A_n$, $D_n$, $E_n$. (http://en.wikipedia.org/wiki/Root_system) Now let me put a little twist to this. Let us also allow $a_{ij}=+1$ for $i\ne j$, and encode this by putting a broken edge between $i$ and $j$ (or an edge of different color, if you prefer). Real question: Which of these graphs correspond to positive definite $A$? Let me add some partial considerations which do not quite go far enough. (Some of these were in the helpful Gjergji's answer.) (1) Consider the set $R$ of shortest vectors in $\mathbb Z^n$; they have square 2. Reflections in elements $r\in R$ send $R$ to itself, and $R$ spans $\mathbb Z^n$ since it contains the standard basis vectors $e_i$. By the standard result about root lattices, $\mathbb Z^n$ is then a direct sum of the $A_n$, $D_n$, $E_n$ root lattices, and one can restrict to the case of a single direct summand. Hence, the question equivalent to the following: what are the graphs corresponding to all possible bases of $\mathbb R^n$ in which the basis vectors are roots? The case of $R=A_n$ is relatively easy. The roots are of the form $f_a-f_b$, with $a,b \in (1,\dots,n+1)$. Every collection $e_i$ corresponds to an oriented spanning tree on the set $(1,\dots,n+1)$. The 2-colored graph is computed from that tree. I don't see a clean description of the graphs obtained via this procedure, but it is something. For $D_n$, similarly, a basis is described by an auxiliary connected graph $S$ on $n$ vertices with $n$ edges whose ends are labeled $+$ or $-$. The graph $G$ is computed from $S$. And for $E_6,E_7,E_8$ there are of course only finitely many cases, but for me the emphasis is on MANY, very many. So has anybody done this? Is there a table in some paper or book which contains all the 2-colored graphs obtained this way, or -- better still -- a clean characterization of such graphs? (2) There is a notion of "weakly positive quadratic forms" used in the cluster algebra theory (see for example the first pages of LNM 1099 (Tame Algebras and Integral Quadratic Forms) by Ringel. And there is some kind of classification theory for them. Maybe I am mistaken, but this seems to be quite different: a quadratic form $q$ is "weakly positive" if $q\ge 0$ on the first quadrant $\mathbb Z_{\ge0}^n$. So there is no direct relation to my question, it seems. 4 added 145 characters in body; edited tags; added 10 characters in body; added 9 characters in body Let me add some partial considerations which do not quite go far enough. (Some of these were in the helpful Gjergji's answer, which I appreciated, which he unfortunately removed.answer.) (1) Clearly, Consider the standard basis set $R$ shortest vectors in $e_i$ are roots (\mathbb Z^n$; they have square 2)2. Reflections in elements$r\in R$send$R$to itself, and generate the lattice$R$spans$\mathbb Z^n$. since it contains the standard basis vectors$e_i$. By the standard result about root lattices,$\mathbb Z^n$is then a direct sum of the$A_n$,$D_n$,$E_n$root lattices, and one can restrict to the case of a single direct summand. Then$e_i$'s are some of Hence, the roots in$R$, and we askquestion equivalent to the following: what are the collections graphs corresponding to all possible bases of such roots spanning the vector space, and with the property that the pairwise dot products$(e_i,e_j)$\mathbb R^n$ in which the basis vectors are 0,-1,+1. roots? The case of $R=A_n$ is relatively easy. The roots are of the form $f_a-f_b$, with $a,b \in (1,\dots,n+1)$. Every collection $e_i$ corresponds to a an oriented spanning tree on the set $(1,\dots,n+1)$. The 2-colored graph is computed from that tree. I don't see a clean description of the graphs obtained via this procedure, but it is something. For $D_n$, the procedure may be similar but messier. similarly, a basis is described by an auxiliary connected graph $S$ on $n$ vertices with $n$ edges whose ends are labeled $+$ or $-$. The graph $G$ is computed from $S$. (2) There is a notion of "weakly positive quadratic forms" used in the cluster algebra theory (see for example the first pages of LMN1099 LNM 1099 (Tame Algebras and Integral Quadratic Forms) by Ringel. And there is some kind of classification theory for them. Maybe I am mistaken, but this seems to be quite different: a quadratic form $q$ is "weakly positive" if $q\ge 0$ on the first quadrant $\mathbb Z_{\ge0}^n$. So there is no direct relation to my question, it seems. 3 added 1850 characters in body Let me add some partial considerations which do not quite go far enough. (Some of these were in Gjergji's answer, which I appreciated, which he unfortunately removed.) (1) Clearly, the standard basis vectors $e_i$ are roots (they have square 2), and generate the lattice $\mathbb Z^n$. By the standard result about root lattices, $\mathbb Z^n$ is then a direct sum of the $A_n$, $D_n$, $E_n$ root lattices, and one can restrict to the case of a single direct summand. Then $e_i$'s are some of the roots in $R$, and we ask: what are the collections of such roots spanning the vector space, and with the property that the pairwise dot products $(e_i,e_j)$ are 0,-1,+1. The case of $R=A_n$ is relatively easy. The roots are of the form $f_a-f_b$, with $a,b \in (1,\dots,n+1)$. Every collection $e_i$ corresponds to a spanning tree on the set $(1,\dots,n+1)$. The 2-colored graph is computed from that tree. I don't see a clean description of the graphs obtained via this procedure, but it is something. For $D_n$, the procedure may be similar but messier. And for $E_6,E_7,E_8$ there are of course only finitely many cases, but for me the emphasis is on MANY, very many. So has anybody done this? Is there a table in some paper or book which contains all the 2-colored graphs obtained this way, or -- better still -- a clean characterization of such graphs? (2) There is a notion of "weakly positive quadratic forms" used in the cluster theory (see for example the first pages of LMN1099 (Tame Algebras and Integral Quadratic Forms) by Ringel. And there is some kind of classification theory for them. Maybe I am mistaken, but this seems to be quite different: a quadratic form $q$ is "weakly positive" if $q\ge 0$ on the first quadrant $\mathbb Z_{\ge0}^n$. So there is no direct relation to my question, it seems. 2 edited tags; edited title; deleted 198 characters in body 1	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9401609897613525, "perplexity": 246.52181838487033}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697420704/warc/CC-MAIN-20130516094340-00041-ip-10-60-113-184.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/121977/residue-of-a-pole-of-order-6	# Residue of a pole of order 6 I am in the process of computing an integral using the Cauchy residue theorem, and I am having a hard time computing the residue of a pole of high order. Concretely, how would one compute the residue of the function $$f(z)=\frac{(z^6+1)^2}{az^6(z-a)(z-\frac{1}{a})}$$ at $z=0$? Although it is not needed here, $a$ is a complex number with $\|a\|<1$. Thanks in advance for any insight. - Can you compute the Taylor series at $0$? – Mariano Suárez-Alvarez Mar 19 '12 at 6:50 You can write $$f(z) = \frac{1}{az^6} (z^{12} + 2z^6 + 1) \left(\sum_{k=0}^\infty \frac1{a^k} z^k \right) \left( \sum_{k=0}^\infty a^k z^k \right).$$ You want to extract the coefficient of $z^5$ in the product of the two series. $$g(z)=\frac{1}{(z-a)(z-\frac{1}{a})}=\frac{\frac{1}{a-\frac{1}{a}}}{z-a}+\frac{\frac{-1}{a-\frac{1}{a}}}{z-\frac{1}{a}}$$ we know: $$(a+b)^n =a^n+\frac{n}{1!}a^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^2+...+b^n$$ $$\text{As regards }: \|a\|<1$$ Taylor series of f(z) is: $$g(z)=\frac{\frac{1}{a-\frac{1}{a}}}{z-a}+\frac{\frac{1}{a-\frac{1}{a}}}{\frac{1}{a}-z}=(\frac{1}{a-\frac{1}{a}}) \left[ \frac{-\frac{1}{a}}{1-\frac{z}{a}}+\frac{a}{1-az} \right]$$ $$g(z)=(\frac{1}{a-\frac{1}{a}}) \left[ \frac{-1}{a} \sum_{n=0}^{\infty}(\frac{z}{a})^n+a \sum_{n=0}^{\infty} (az)^n \right]$$ $$f(z)=\frac{(z^6+1)^2}{az^6}g(z)=\frac{z^{12}+2z^2+1}{az^6}g(z)=\left( \frac{z^6}{a} + \frac{2}{az^4} + \frac{1}{az^6} \right)g(z)$$ $$f(z)= \left( \frac{z^6}{a} + \frac{2}{az^4} + \frac{1}{az^6} \right) \left(\frac{1}{a-\frac{1}{a}}\right) \left[ \frac{-1}{a} \sum_{n=0}^{\infty}(\frac{z}{a})^n+a \sum_{n=0}^{\infty} (az)^n \right]$$ $$\text{ so residue is coefficient of term }z^{-1}$$ $$f(z)=\frac{1}{a(a-\frac{1}{a})} \left[ \frac{-1}{a}\left( \sum_{n=0}^{\infty}\frac{z^{n+6}}{a^n} +2\sum_{n=0}^{\infty}\frac{z^{n-4}}{a^n} +\sum_{n=0}^{\infty} \frac{z^{n-6}}{a^n}\right) +a \left( \sum_{n=0}^{\infty} a^nz^{n+6}+2\sum_{n=0}^{\infty} a^nz^{n-4} +\sum_{n=0}^{\infty} a^nz^{n-6} \right) \right]$$ $$\text{residue of function at z=0 is :}$$ $$\frac{1}{a(a-\frac{1}{a})} \left[ \frac{-1}{a}\left( 0 +2\frac{1}{a^3} +\frac{1}{a^5}\right) +a \left( 0+2a^3 +a^5 \right) \right]$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9925040006637573, "perplexity": 103.90719329299023}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988511.77/warc/CC-MAIN-20150728002308-00254-ip-10-236-191-2.ec2.internal.warc.gz"}
https://www.math-only-math.com/compound-interest-when-interest-is-compounded-half-yearly.html	# Compound Interest when Interest is Compounded Half-Yearly We will learn how to use the formula for calculating the compound interest when interest is compounded half-yearly. Computation of compound interest by using growing principal becomes lengthy and complicated when the period is long. If the rate of interest is annual and the interest is compounded half-yearly (i.e., 6 months or, 2 times in a year) then the number of years (n) is doubled (i.e., made 2n) and the rate of annual interest (r) is halved (i.e., made $$\frac{r}{2}$$). In such cases we use the following formula for compound interest when the interest is calculated half-yearly. If the principal = P, rate of interest per unit time = $$\frac{r}{2}$$%, number of units of time = 2n, the amount = A and the compound interest = CI Then A = P(1 + $$\frac{\frac{r}{2}}{100}$$)$$^{2n}$$ Here, the rate percent is divided by 2 and the number of years is multiplied by 2 Therefore, CI = A - P = P{(1 + $$\frac{\frac{r}{2}}{100}$$)$$^{2n}$$ - 1} Note: A = P(1 + $$\frac{\frac{r}{2}}{100}$$)$$^{2n}$$ is the relation among the four quantities P, r, n and A. Given any three of these, the fourth can be found from this formula. CI = A - P = P{(1 + $$\frac{\frac{r}{2}}{100}$$)$$^{2n}$$ - 1} is the relation among the four quantities P, r, n and CI. Given any three of these, the fourth can be found from this formula. Word problems on compound interest when interest is compounded half-yearly: 1. Find the amount and the compound interest on $8,000 at 10 % per annum for 1$$\frac{1}{2}$$ years if the interest is compounded half-yearly. Solution: Here, the interest is compounded half-yearly. So, Principal (P) =$ 8,000 Number of years (n) = 1$$\frac{1}{2}$$ × 2 = $$\frac{3}{2}$$ × 2 = 3 Rate of interest compounded half-yearly (r) = $$\frac{10}{2}$$% = 5% Now, A = P (1 + $$\frac{r}{100}$$)$$^{n}$$ A = $8,000(1 + $$\frac{5}{100}$$)$$^{3}$$ A =$ 8,000(1 + $$\frac{1}{20}$$)$$^{3}$$ A = $8,000 × ($$\frac{21}{20}$$)$$^{3}$$ A =$ 8,000 × $$\frac{9261}{8000}$$ A = $9,261 and Compound interest = Amount - Principal =$ 9,261 - $8,000 =$ 1,261 Therefore, the amount is $9,261 and the compound interest is$ 1,261 2. Find the amount and the compound interest on $4,000 is 1$$\frac{1}{2}$$ years at 10 % per annum compounded half-yearly. Solution: Here, the interest is compounded half-yearly. So, Principal (P) =$ 4,000 Number of years (n) = 1$$\frac{1}{2}$$ × 2 = $$\frac{3}{2}$$ × 2 = 3 Rate of interest compounded half-yearly (r) = $$\frac{10}{2}$$% = 5% Now, A = P (1 + $$\frac{r}{100}$$)$$^{n}$$ A = $4,000(1 + $$\frac{5}{100}$$)$$^{3}$$ A =$ 4,000(1 + $$\frac{1}{20}$$)$$^{3}$$ A = $4,000 × ($$\frac{21}{20}$$)$$^{3}$$ A =$ 4,000 × $$\frac{9261}{8000}$$ A = $4,630.50 and Compound interest = Amount - Principal =$ 4,630.50 - $4,000 =$ 630.50 Therefore, the amount is $4,630.50 and the compound interest is$ 630.50 Compound Interest Compound Interest Compound Interest with Growing Principal Compound Interest by Using Formula Problems on Compound Interest Practice Test on Compound Interest Compound Interest - Worksheet Worksheet on Compound Interest Worksheet on Compound Interest with Growing Principal	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7760125994682312, "perplexity": 1832.576715736733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500058.1/warc/CC-MAIN-20230203154140-20230203184140-00839.warc.gz"}
https://www.physicsforums.com/threads/connection-and-tensor-issue-with-the-proof.715032/	Connection and tensor-issue with the proof 1. Oct 7, 2013 1. The problem statement, all variables and given/known data I am tying to prove the following: $\Gamma^{a}_{bc}$ T$^{bc}$ =0 2. Relevant equations 3. The attempt at a solution I approached this problem as follows: $dx_{b}/dx^{c} * e^{a} (e^{b} . e^{c})$ but it did not yield anything. Then I expanded the christoeffel symbols into g s and again I am not sure what to do next.So any hints please 2. Oct 7, 2013 WannabeNewton Your post is incomplete to say the least. What is $\tau^{bc}$ to start with? 3. Oct 7, 2013 That's a tensor. 4. Oct 7, 2013 a symmetric tensor. 5. Oct 7, 2013 George Jones Staff Emeritus In a coordinate basis? A non-holonomic basis? 6. Oct 7, 2013 WannabeNewton Again you are not being specific enough. $\Gamma^{a}_{bc}\tau^{bc} = 0$ is certainly not true in general for any symmetric tensor $\tau^{bc}$ if $\Gamma^{a}_{bc}$ are the coefficients of the Levi-Civita connection. It is only true in general if $\tau^{bc}$ is antisymmetric so you must specify what exactly the tensor $\tau^{bc}$ is. 7. Oct 7, 2013 Γabc are the christoffel symbols/connection and T^(bc) = (e^b,e^c) 8. Oct 7, 2013 George Jones Staff Emeritus Do you mean $T^{bc} = T \left( e^b , e^c \right)$? 9. Oct 7, 2013 yes. 10. Oct 7, 2013 George Jones Staff Emeritus And $\left\{ e_a \right\}$ is an orthonormal basis? 11. Oct 7, 2013 Yes, it is, 12. Oct 7, 2013 George Jones Staff Emeritus First, In don't think that you should write $\Gamma^a{}_{bc}$ instead of $\Gamma^a_{bc}$. Second, what anti-symmetry property does the Levi-Civita connection have with respect to an orthonormal basis?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8860675692558289, "perplexity": 2499.4809243758914}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815318.53/warc/CC-MAIN-20180224033332-20180224053332-00065.warc.gz"}
http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html?kudos=1	Find all School-related info fast with the new School-Specific MBA Forum It is currently 03 May 2015, 20:12 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # GMAT Debrief - 770 (Q50, V47) Author Message TAGS: Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [17] , given: 40 GMAT Debrief - 770 (Q50, V47) [#permalink] 24 Jun 2011, 16:41 17 KUDOS 12 This post was BOOKMARKED This post has been identified as one of the best and featured in the Best GMAT Stories - Period collection -bb Hi guys, Took the GMAT this afternoon and scored 770 (Q50, V47). I'm ecstatic about the score. I promised yesterday that I would post a full debrief after it was over, so here it goes. First of all, I have to thank GMATClub for simply being the perfect resource for anyone preparing for the test. I was lucky enough to stumble on the site on a recommendation from WallStreetOasis and all of the advice, stories and practice materials I found on here were invaluable in my preparation. I will definitely recommend the site to anyone I know who is preparing for the GMAT! A little background on me: I just graduated college with an engineering degree (so Quant wasn't a big issue). I took the LSAT a couple years ago so I had a decent foundation in CR and RC as well. Practice Scores GMATPrep 1 - 770 (50Q, 46V) Kaplan CD - 670 MGMAT 1 - 780 (51Q, 45V) Kaplan Real Test Day Experience - 760 MGMAT 2 - 770 (50Q, 45V) MGMAT 3 - 770 (50Q, 45V) MGMAT 4 - 770 (51Q, 44V) GMATPrep 2 - 780 MGMAT 5 - 750 (51Q, 41V) GMAT - 770 (50Q, 47V) Practice Materials Used I had copies of the Kaplan GMAT Premier 2011 and Princeton Review GMAT 2011 books before I discovered this forum, but on some good advice I bought the full set of Manhattan GMAT guides, the OG 12th edition and both of the other OG guides as well. I ended up only using the Kaplan and PR books for their introductions and test-taking strategies. I thought PR in particular did a good job laying out how the scoring of the test works and how you should budget your time (focus on early questions and make sure under no circumstances you let yourself needlessly run out of time). I read the entire Manhattan GMAT SC guide, but that was the only guide I used extensively. I worked through all of the hardest CR questions and all of the SC questions in the OG 12th edition (didn't end up touching the other two books) and did the Manhattan Online Question Banks for those two sections as well. I think that the biggest takeaway I got from amassing my huge collection of books was that there are a TON of GMAT practice materials out there and if you don't have the time to go through it all, you should only use the highest quality stuff. For me, that was the Manhattan guides for concepts I didn't know and the OG for real practice problems. I also found the GMATClub tests very useful for practicing Quant--take them timed and start from the end if you are already scoring well on that section. I'll say something quickly about Kaplan. I don't think that their CD tests are reliable in terms of their scoring (at least for Verbal), so if you use those tests I would take whatever score you get with a grain of salt. The Real Test Day Experience is an online test though, taken at the actual Pearson test center at an actual test station and it is EXCELLENT. I signed up for the cheapest Kaplan course just to get this opportunity (I saw somewhere that you can take the test for just $80 though--I'm going see if I can get a refund). You follow basically the same test procedures and the test looks the same on the screen as it does on test day. If it is at all possible for you to sign up for this, I would highly recommend it. Having a good feel for the test center made test day a lot less stressful. It doesn't have to be your last CAT, you can take it any time during your preparation. How I Studied I had originally planned to take the GMAT in early August, but after getting a 770 diagnostic, I decided to study intensively for 3 weeks instead. Even though I didn't improve from my diagnostic at all, I have never regretted the time I put into preparing. If anyone has just taken a diagnostic and has already reached their target score, I would caution against going into the exam without preparation. I basically knew nothing about SC (I would read the answer choices and pick the one that sounded good) and I was not managing my time well in Quant at all. Given a different set of circumstances I could easily see my diagnostic being much lower than it was. I first focused on the area that I was weakest in, SC. I read through the Manhattan guide and did some of the book exercises in my head. I also started keeping a list of idioms I ran into and looked over it every once in a while. One of the best pieces of advice that I have seen repeated over and over on this forum is that simply doing CATs is a waste of time while preparing for the GMAT. I think this is true at any level. Between CATs you should be engaging in TARGETED practice that addresses issues that you are deficient in. For me that included doing Quant sections in less than the allowed time and doing hundreds of SC questions in batches of 10 (reading the explanations for correct and incorrect questions). Error logs. These were something I didn't know about until reading this forum. I didn't do anything fancy. After each CAT I kept a list of questions that I had gotten incorrect and also any questions that I couldn't solve in under 3 minutes. Every 3 tests or so I would work through these problems again and take them off if I got them correct. Early on I also kept a stack of paper with one Quant problem on each sheet along with a solution and a quick summary of the error I had made/what to keep in mind. That was useful to review before the test. I think that everyone should create their own method of logging errors, but this seemed to work for me. Some other notable things I did were I took two CATs back to back one day to train endurance and I took a break for the two days leading up to the exam (did some practice problems and reviewed error logs, but no tests). The last CAT I did I saw a bit of a drop (down to a 41 from a 44-46 in Verbal), probably due to fatigue. Definitely take a break before your exam and don't cram. If you're working--take the day off before your test as well as the day of if you can and do something relaxing. I watched the NBA draft. Test Day I scheduled the test for the afternoon so I wouldn't have to wake up early (my Kaplan Test Day Experience was around the same time). I woke up early anyway though because I was too jumpy. I got there an hour early, but they let me get started right away (I guess not many people take the GMAT at 2PM on a Friday). I was given a locker and they explained the instructions. If you don't have a chance to do a Test Day Experience, at least watch the Youtube video that tells you exactly what happens. The two essays weren't a problem (definitely see this thread for good tips). I promised myself before the test that I would take every break to clear my head and splash cold water on my face. This was a good idea. You don't want to suddenly get sleepy or need to use the bathroom in the middle of Quant just because you felt like you were "on a roll." After a bit of a shaky point early in the section (I was unsure whether the square root of the square of a variable was plus/minus or always positive), I think I did fine for the rest. I've never gotten anything besides a 50 or 51 so I wasn't too worried. The biggest piece of advice I can give people on this section is focus on your timing because unlike in Verbal, you can't quickly eliminate bad choices when you need to solve an actual problem. Read this post and try to be ahead of schedule coming into the last 3 questions. The added time pressure of the section ending can throw you off your game. I didn't develop a "1-minute sense," but I did try my best to check the clock every couple questions and make sure I had 2 * (number of questions left) minutes remaining. I took another break before Verbal and began work on the section. I had generally finished Verbal 20+ minutes ahead of time in practice (compared to having to rush the end of Quant a couple times), so I consciously worked slower to avoid stupid mistakes. Midway through the section I felt like I was rocking it, but I was working a bit too slowly so I sped up. If you are early in the section you can try to wait for SC questions to make up time, but if you are in the last 15 questions or so, DO NOT WAIT to fix a timing problem. Near the end I was feeling good about my performance, but I thought to myself, "wow, imagine what your score would be if you got the last 10 questions of Verbal wrong." That helped me to regain focus. When I got my score I was relieved. Having read stories of people having subpar test experiences I can say this: for all the hype about the CAT and how it's an accurate predictor, there is still a lot of luck involved in taking the GMAT. I was fortunate on test day to not run into any problems and for that I'm grateful. I tried to worry about only what was under my control though: how I prepared, how I approached each question and the mindset I carried into the test center. 10 Pieces of General Advice 1. Get the MGMAT guides and the OG 2. Sign up for a Kaplan Real Test Day Experience 3. Study smart, don't just take CATs 4. Review the questions you do slowly, not just the ones you get wrong 5. Take a day or two off before the exam 6. Ask for an extra pen at the exam center if they don't give you one 7. Take all of the breaks even if you don't think you need them 8. Think positive thoughts going in and promise yourself a reward at the end 9. Do not slack off at the end of Verbal 10. Try to enjoy the experience, but always respect the test and don't cut corners I'm indebted to this forum for all of its help, so I'd be more than happy to answer any questions. I'll definitely be around for the next couple years as I get ready to apply for business school (class of '15 probably). Thanks and Cheers! _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Last edited by bb on 12 Jul 2011, 23:24, edited 1 time in total. Added to the Collection Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [2] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 12 Jul 2011, 07:39 2 This post received KUDOS Aj: For a general approach to DS questions look at the flowchart here http://gmatclub.com/forum/an-emerging-problem-studying-for-the-gmat-104013.html. For specific strategies I would consult the MGMAT guides. I completely agree with you that DS is more challenging than PS most of the time because your thinking for the problems can be disjointed and going back through your logic to check your work can be damn near impossible at times. There are a couple things you can do to help your accuracy: 1. Organize your work on the scratchpad so that it's easy to follow. On one side maybe write "Check 1," and include all of your work checking to see if (1) is sufficient. Then on the other side of the page write "Check 2," and do the same. This will ensure that you don't get the work confused. 2. Write out counterexamples explicitly and circle your conclusions. For example if you're trying to see if \|x\| > 1 is sufficient to say x > 0, you could write x = 2 (YES) and x = -2 (NO) and then in big letters circled write "INSUFFICIENT." There should be no doubt when you check through that thought process later because you have written the counterexample down explicitly. I haven't seen a way to sign up for a Kaplan Real Test Day experience without signing up for the course, but Kaplan has a good refund policy so what I did was: I signed up for the cheapest self-study course (about$450 USD) and Kaplan will refund 75% of your course fee if you only use one CAT/resource. So I ended up paying about $113 for the test (cheap compared to a$250 GMAT!!!). arp: http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html gablaze: Read chineseburned's AWA guide (linked above). I always took an AWA with my CATs. Once you are decently prepared for Quant and Verbal I recommend ALWAYS doing this for a couple of reasons: 1. Taking an AWA best simulates the actual fatigue you'll feel during the exam 2. You want to practice the templates/techniques/timing for the AWA as well as getting used to thinking of ideas quickly To be honest, from what I've seen your AWA score doesn't matter too much. Neglecting it in your prep though is likely to throw you off during the real test and if you're struggling or thinking too hard in the first hour of the GMAT, it will negatively influence your performance for the latter two sections. Hope this helps! _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html CEO Joined: 17 Nov 2007 Posts: 3578 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Followers: 406 Kudos [?]: 2140 [1] , given: 359 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 24 Jun 2011, 17:27 1 KUDOS Expert's post Wow! Congrats!!! _________________ HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ \| PrepGame SVP Affiliations: HEC Joined: 28 Sep 2009 Posts: 1638 Concentration: Economics, Finance GMAT 1: 730 Q48 V44 Followers: 91 Kudos [?]: 511 [1] , given: 432 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 24 Jun 2011, 17:32 1 KUDOS Expert's post Whoa, excellent score! And thank you for sharing your GMAT experience and providing us with some general advice. Debriefs such as this truly help others to reach their goals. Congrats! _________________ Intern Joined: 16 Jun 2011 Posts: 33 Followers: 0 Kudos [?]: 1 [1] , given: 6 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 24 Jun 2011, 18:03 1 KUDOS Manager Joined: 13 Nov 2009 Posts: 120 Location: India Concentration: Finance, Marketing GPA: 4 WE: General Management (Insurance) Followers: 1 Kudos [?]: 9 [1] , given: 16 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 24 Jun 2011, 18:50 1 KUDOS Congratulations! Manager Joined: 29 Jun 2010 Posts: 249 Schools: LBS, Oxford Followers: 9 Kudos [?]: 29 [1] , given: 12 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 24 Jun 2011, 19:15 1 KUDOS congratulations...great score alss curious about class of 15...why did you take GMAT now ? Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [1] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 25 Jun 2011, 04:26 1 KUDOS I just graduated college and have the summer off before I begin work, so I figured I'd just get it out of the way. Since the score is good for 5 years I figured taking it 2 years before I applied was still a safe bet. _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [1] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 02 Jul 2011, 10:09 1 KUDOS BearBelly: It sounds like you're on the right track! A couple recommendations: 1. Make sure your practice in the last week is a mix between doing/reviewing new CATs and looking at the mistakes you made on past tests. Especially for SC, finding patterns in the mistakes you make is critical to avoid making them in the future. 2. Take the last day or two off before your exam. Do not go into the test center CAT-fatigued. You can still review questions here and there, but don't do any full tests the day before. 3. Read chineseburned's AWA guide and do some practice there. Thanks again for your advice after I took my diagnostic, it was helpful to move my test date up. Best of luck next week! _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Intern Joined: 21 May 2011 Posts: 48 Schools: Kellogg Followers: 1 Kudos [?]: 2 [1] , given: 7 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 02 Jul 2011, 10:30 1 KUDOS gmatkoopa wrote: BearBelly: It sounds like you're on the right track! A couple recommendations: 1. Make sure your practice in the last week is a mix between doing/reviewing new CATs and looking at the mistakes you made on past tests. Especially for SC, finding patterns in the mistakes you make is critical to avoid making them in the future. 2. Take the last day or two off before your exam. Do not go into the test center CAT-fatigued. You can still review questions here and there, but don't do any full tests the day before. 3. Read chineseburned's AWA guide and do some practice there. Thanks again for your advice after I took my diagnostic, it was helpful to move my test date up. Best of luck next week! Thanks man! I will keep these pointers in my mind ... Moreover, since I am not a native English speaker (I am from India), I am facing timing issues in verbal and I am trying to minimize those too .. Wish me luck ! _________________ I was born intelligent but education ruined me ! Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [1] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 03 Jul 2011, 06:26 1 KUDOS Good luck BearBelly! _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Current Student Joined: 08 Jan 2009 Posts: 330 GMAT 1: 770 Q50 V46 Followers: 23 Kudos [?]: 105 [1] , given: 7 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 04 Jul 2011, 15:42 1 KUDOS Great debrief and impressive score. Well done! Intern Joined: 24 Jun 2011 Posts: 10 Followers: 4 Kudos [?]: 13 [1] , given: 3 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 06 Jul 2011, 09:14 1 KUDOS I loved these summary points: 5. Take a day or two off before the exam 7. Take all of the breaks even if you don't think you need them 8. Think positive thoughts going in and promise yourself a reward at the end Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [1] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 07 Jul 2011, 19:01 1 KUDOS allen: I have found that for CR and RC, experience from doing many, many questions is the most valuable tool you can bring into the test center. Once you have seen hundreds of examples of these question types you should be able to anticipate the answers to questions sometimes even before you read the answer choices. When I prepped for the LSAT I had exposure to countless difficult CR and RC questions, so I was lucky to have a good base there. It's different for SC. SC is an easier section to prepare for because there is a finite number of things that they can spring on you and they are all basically covered in the MGMAT SC Guide (and other books too I'm sure). You need to be comfortable recognizing the major patterns (verb tense, pronoun/modifier, concision) and you should avoid as much as possible "going with your gut." For that reason, I recommend reviewing both the questions you get right and the ones you get wrong in SC, reading the explanations carefully. You want to get to a point where you can answer a SC and specifically point to the reasons why the other 4 answer choices are incorrect. Doing SC questions by "feel" (reading all of the choices and picking the one that sounds best), works sometimes, but it won't be consistent enough to guarantee you the score you want. Make a list of idioms that you've learned while doing problems. Do SC questions in batches of 10 and immediately review the answers. Keep a good error log and redo questions you got incorrect (or did too slowly) periodically. Hope that helps! _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [1] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 12 Jul 2011, 17:00 1 KUDOS Best of luck! Let me know if there's any other advice I can give =) _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [1] , given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 13 Jul 2011, 05:58 1 KUDOS Thanks bb! That's an illustrious group to be part of =D _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Intern Joined: 30 Sep 2012 Posts: 28 GMAT 1: 710 Q50 V35 Followers: 0 Kudos [?]: 9 [1] , given: 30 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 19 Jan 2013, 06:25 1 KUDOS Thanks. Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [0], given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 25 Jun 2011, 04:27 Oh also just to clarify, when I say class of '15 I mean I am a '13 applicant to graduate in '15. _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Senior Manager Status: 750+ or Burst ! Joined: 01 May 2011 Posts: 388 Location: India Concentration: General Management, Strategy GMAT 1: 670 Q48 V35 GPA: 3.5 Followers: 22 Kudos [?]: 71 [0], given: 26 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 25 Jun 2011, 05:51 gmatkoopa wrote: Oh also just to clarify, when I say class of '15 I mean I am a '13 applicant to graduate in '15. Congrats on your score. I see consistently had Q50 in all mocks. I have a couple of questions for you. 1. Are MGMAT and Kaplan Quant questions close to the Real Thing ? If yes then how close are they ? 2. The same for Verbal ? Were the texts in RC n CR more complicated than the OGs or Kaplan/MGMAT Cats ? _________________ GMAT done - a mediocre score but I still have a lot of grit in me The last 20 days of my GMAT journey Current Student Joined: 04 Jun 2011 Posts: 127 Location: United States Concentration: General Management, Strategy GMAT 1: 770 Q50 V47 GPA: 3.8 Followers: 2 Kudos [?]: 64 [0], given: 40 Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 25 Jun 2011, 06:31 akhilesh: I would say that both Kaplan and MGMAT questions are pretty close to the GMAT. I didn't have as much experience with Kaplan, but at least for MGMAT I found that the real GMAT "felt" pretty close to an MGMAT section. If I had to choose one, I would say MGMAT was maybe a little tougher than the real GMAT (the toughest questions were more challenging, there were maybe a few more of them and I could see more "tricks"). Some things that MGMAT likes to do: 1. DS questions where you have to try a lot of cases with different numbers. The real GMAT had these too, but at least for my sitting they weren't as challenging. 2. Absolute value questions where some of the solutions don't work (you solve for both positive and negative and one of them doesn't agree with the original equation). I don't remember encountering that on the real GMAT. 3. Questions where if you assume everything is an integer you'll get them wrong. 4. Hard geometry problems. Of course all of this evidence is anecdotal, but from what I've read on the forums, MGMAT does tend to be a bit more tricky. I'm not saying the real GMAT doesn't have questions like those above, but I think it's more straightforward. I can't comment on the Kaplan Verbal stuff, but MGMAT was solid for that too. I would still use the OG though if you have a choice. _________________ My GMAT Experience: http://gmatclub.com/forum/gmat-debrief-770-q50-v47-115912.html Re: GMAT Debrief - 770 (Q50, V47) [#permalink] 25 Jun 2011, 06:31 Go to page 1 2 3 Next [ 55 posts ] Similar topics Replies Last post Similar Topics: 17 780 GMAT Q50/V47 Debriefing. Retake? 12 01 Jun 2014, 12:36 3 Debrief - 620 to 770 (Q50, V47) 1 04 Feb 2013, 20:46 4 GMAT 770 (Q-50, V-47) 14 17 Apr 2008, 00:23 2 GMAT 770 Q50 V47 7 24 Sep 2007, 20:55 1 770(q 50, V 47) 7 02 Dec 2006, 02:46 Display posts from previous: Sort by # GMAT Debrief - 770 (Q50, V47) Moderators: m3equals333, TGC Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2132166475057602, "perplexity": 7008.223021515048}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430453690104.75/warc/CC-MAIN-20150501041450-00055-ip-10-235-10-82.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/68154/numerical-software-to-solve-partial-differential-equations-in-spherical-coordina	# Numerical software to solve partial differential equations in spherical coordinates? Which numerical libraries / math software can allow me to solve partial differential equations in spherical coordinates? (my system consists of N degrees of freedom, each degree lives in $\mathbb{C}^{2}$ and the whole system is $(\mathbb{C}^{2})^{N}$). -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9740782976150513, "perplexity": 354.9011245233093}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464051113990.53/warc/CC-MAIN-20160524005153-00146-ip-10-185-217-139.ec2.internal.warc.gz"}
http://medcraveonline.com/MOJI/prototypic-three-pediatric-cases-of-recurrent-wheezing-attacks-associated-with-hypogammaglobulinemia.html	# Immunology Case Report Volume 1 Issue 3 # Prototypic Three Pediatric Cases of Recurrent Wheezing Attacks Associated with Hypogammaglobulinemia #### Oner Ozdemir,1 function clickButton(){ var name=document.getElementById('name').value; var descr=document.getElementById('descr').value; var unCopyslNo=document.getElementById('unCopyslNo').value; document.getElementById("mydiv").style.display = "none"; $.ajax({ type:"post", url:"https://medcraveonline.com/captchaCode/server_action", data: { 'name' :name, 'descr' :descr, 'unCopyslNo': unCopyslNo }, cache:false, success: function (html) { //alert('Data Send');$('#msg').html(html); } }); return false; } Verify Captcha × Regret for the inconvenience: we are taking measures to prevent fraudulent form submissions by extractors and page crawlers. Please type the correct Captcha word to see email ID. function refreshPage(){ $("#mydiv").load(location.href + " #mydiv"); }$(document).ready(function () { //Disable cut copy paste $('#msg').bind('cut copy paste', function (e) { e.preventDefault(); }); //Disable mouse right click$("#msg").on("contextmenu",function(e){ return false; }); }); .noselect { -webkit-touch-callout: none; /* iOS Safari / -webkit-user-select: none; / Safari / -khtml-user-select: none; / Konqueror HTML / -moz-user-select: none; / Firefox / -ms-user-select: none; / Internet Explorer/Edge / user-select: none; / Non-prefixed version, currently supported by Chrome and Opera */ cursor: none; } Sila Hidayet Bozdogan Polat,2 Hayrunnisa Bekis Bozkurt BekisBozkurt2 1Department of Pediatrics, Division of Allergy and Immunology, Research and Training Hospital of Sakarya University, Turkey 2Department of Pediatrics, Research and Training Hospital of Sakarya University, Turkey Correspondence: Oner Ozdemir, Division of Allergy and Immunology, Department of Pediatrics, Research and Training Hospital of Sakarya University, Faculty of Medicine, Sakarya University, Adnan Menderes Cad., Saglik Sok. No: 195, Adapazari, Sakarya, Turkey, Tel 90-264-444-54-00, Fax 90-264-275-91-92 Received: June 28, 2014 \| Published: July 16, 2014 Citation: Ozdemir O, Bozdogan-Polat SH, Bozkurt HB (2014) Prototypic Three Pediatric Cases of Recurrent Wheezing Attacks Associated with Hypogammaglobulinemia. MOJ Immunol 1(3): 00014. DOI: 10.15406/moji.2014.01.00014 # Abstract Bronchiolitis and infantile asthma are the most frequent causes of typical wheezing symptoms during infancy. However, persistent wheezing symptoms resistant to β2 adrenergic-agonist and anti-cholinergic therapies should be considered for hypogammaglobulinemia. Hypogammaglobulinemia is defined when immunoglobulin isotypes are below the limit of the pre-determined set of reference ranges per age. Here, prototypic three cases of recurrent and persistent wheezing attacks during infancy associated with transient low IgG suggesting hypogammaglobulinemia diagnoses are described to raise the awareness of immunodeficiency among pediatricians. In pediatric patients with recurrent and/or persistent wheezing symptoms during infancy and beyond, especially resistant to therapy, hypogammaglobulinemia should be excluded from possible diagnoses. And if a child with hypogammaglobulinemia and experiencing life threatening infections, immunoglobulin administration should be thought. Keywords: wheezing, hypogammaglobulinemia # Abbreviations THI, transient hypogammaglobulinemia of infancy; CVID, common variable immunodeficiency; IVIG, intravenous immunoglobulin; CBC, complete blood count; ESR, erythrocyte sedimentation rate # Introduction Bronchiolitis and infantile asthma are the most frequent causes for typical wheezing symptoms in infants. Recurrent wheezing resistant to β2 adrenergic-agonist and anti-cholinergic therapies are usually investigated for hypogammaglobulinemia. In fact, recurrent viral infections including lower respiratory tract infections have been reported as associated to transient hypogammaglobulinemia of infancy (THI).1–5 Yet, the main clinical feature in patients affected by infantile hypogammaglobulinemia remains recurrent infections. In fact, many studies THI is associated with history of recurrent wheezing consistent with diagnosis of asthma, allergic bronchitis and autoimmune disease.5-8 Nevertheless, most of the infantile cases resolve before early childhood and achieve normal immunoglobulin levels by age of two until five without serious infections or other illness. Infantile hypogammaglobulinemia is diagnosed when immunoglobulin isotypes are below the limit of the pre-determined set of reference ranges per age. Therefore, our 3 patients described below can be accepted as hypogammaglobulinemic during infancy.5 Hypogammaglobulinemia in early childhood is depicted among humoral immunodeficiencies, represented by a heterogeneous group of disorders in the immune system.9The condition can be congenital (due to a primary genetic deficiency), acquired (secondary to an underlying disease), or transient or physiological (due to an immature immune system). Physiologic hypogammaglobulinemia generally occurs between three to six months of age, a period during which maternal IgG decreases, and the infant′s own synthesis remains underdeveloped.9 THI is characterized by prolonged hypogammaglobulinemia, and this clinical picture resolves spontaneously by the second year of life; some may not resolve until subjects are four–five years old. Even some cases may develop into severe or chronic immunoglobulin deficiencies.10,11 For instance; common variable immunodeficiency (CVID) patients have decreased serum IgG concentrations and usually manifest a decreased serum IgA and/or IgM concentrations with normal or low numbers of circulating B cells. Other conditions can also result in infantile hypogammaglobulinemia, such as IgG subclass deficiencies and excessive loss of serum immunoglobulins.12,13 Recurrent infections causing wheezing attacks are the most common reasons for morbidity and hospitalization in patients with hypogammaglobulinemia. Physicians often choose antibiotic prophylaxis or follow-up without any medication in therapy of these patients. Supportive therapy including antimicrobial therapy for specific (bacterial or viral) infections is generally sufficient for these kinds of hypogammaglobulinemic patients. So far, there are different opinions on the immunoglobulin replacement therapy as well.14,15 The use of IVIG (intravenous immunoglobulin) as an alternative to antibiotic prophylaxis remains controversial also in symptomatic patients with THI. However, if a child with THI was to experience life-threatening infections, IVIG administration should be given right away.16,17 IVIG may stop the vicious circle of infection-immunodeficiency (hypogammaglobulinemia) and should be thought as a first line therapy in highly symptomatic THI children. IVIG was also found to be more effective than antibiotics in treating viral infections associated with wheezing in infants by means of its antiviral antibody contents. IVIG significantly improves the prognosis and the quality of life of immunodeficient (hypogammaglobulinemic) patients and might routinely be used as substitutive therapy until the disorder resolves, if necessary.14 Here we report prototypic three cases of recurrent and persistent wheezing attacks during infancy associated with transient low IgG suggesting hypogammaglobulinemia diagnoses should be excluded. # Case 1 A twenty four month young girl was affected by respiratory tract infection with coughing and persistent wheezing. Anamnesis reported wheezing symptom and breathing difficulty for two months. Her symptoms persisted despite of therapy with antibiotics, nebulized salbutamol and budesonid therapy. Her medical history revealed previous nine wheezing attacks. In the family history, her father suffers asthma. Laboratory findings showed normal routine biochemistry, complete blood count (CBC) and sedimentation rate (ESR). Chest X-ray showed normal findings. Echocardiography was normal. The pH-metry for reflux investigation was normal. Sweat test was normal. In the serological evaluation: low immunoglobulin G (IgG) levels (358mg/dl) for her age was detected at two different times where IgM, IgA and IgE levels were normal. After diagnosis of hypogammaglobulinemia, IVIG was given to her at 500mg/kg/dose. Later, her symptoms did improve and not recur for the last 5months. # Case 2 An eight month young girl suffers coughing and wheezing. At two months of age, she had urinary and upper respiratory tract infections. Despite antibiotic therapy, wheezing persisted for 2 months and wheezing severity increased not responding to β2-adrenergic agonist therapy. Thereafter, hospitalization for seven days resolved symptoms. However, she came back to hospital due to recurrence of her symptoms in next 10 days. In her medical history, grandmother and her cousins had asthma. Physical examination revealed breathing difficulty. Although salbutamol, ipratropium, antibiotherapy (clarithromycin) and anti-reflux therapies were given, her symptoms did not improve for two weeks. At the 15th day of admission, she was given IVIG at 500mg/kg/dose. Later, her respiratory system symptoms did not recur for the last several months. Once she was evaluated for persistent wheezing attacks during admission, biochemistry, CBC, ESR tests were normal. Chest X-ray and echocardiography showed normal findings. In her serological evaluation: low IgG level for her age (279 and 304mg/dl) was detected at two different times. IgG subgroups, IgM, IgA and IgE levels were normal. # Case 3 A twenty months young boy was brought to us due to complaints of having frequent viral lower respiratory tract infections (bronchiolitis). He was experiencing recurrent wheezing attacks almost every week in the last six months. In past medical history, he was diagnosed with trisomy 21 and hypothyroidism at the 3 months of age. He went thru an operation for atrio-venticular septal defect. Physical examination revealed dyspnea, tachypnea and wheezing. Crackles were heard on the chest auscultation. Abdominal, cardio-vascular and the rest of the examination were normal. When he was evaluated for frequent wheezing attacks in our outpatient clinic, routine biochemistry, CBC and ESR were normal. Chest X-ray showed normal findings. In his serological evaluation: low IgG level for his age (256 and 300mg/dl) was detected twice. IgG subgroups, IgA, IgM and IgE levels were within normal. He was given IVIG at 400mg/kg/dose. For the last three months, he did not have any lower respiratory tract infection. # Conclusion The awareness of immunodeficiency among pediatricians has been greatly improved. Recurrent respiratory tract infections are major infections in these patients. THI is a relatively common disorder among infantile hypogammaglobulinemia. In patients with recurrent and/or persistent wheezing symptoms during infancy and beyond, especially resistant to therapy, hypogammaglobulinemia should be excluded from possible diagnoses. None. # Conflicts of interest Author declares there are no conflicts of interest. None. # References ©2014 Ozdemir, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20888283848762512, "perplexity": 28669.11865585628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00291.warc.gz"}
https://www.sarthaks.com/1518738/long-capillary-radius-placed-vertically-inside-beaker-water-surface-tension-water-2xx10	# A long capillary tube of radius 0.2 mm is placed vertically inside a beaker of water. If the surface tension of water is 7.2xx10^(-2)N//m the angl 140 views in Physics closed A long capillary tube of radius 0.2 mm is placed vertically inside a beaker of water. If the surface tension of water is 7.2xx10^(-2)N//m the angle of contact between glass and water is zero, then determine the height of the water column in the tube. A. 3cm B. 9cm C. 7cm D. 5cm by (87.1k points) selected Here s=7.0x10^(-2) N//m,r=0.2xx10^(-3)m,r=10^(3)kg//m^(3) we know that the hieght of liquid in the tube is h=2sigmacostheta//rhoRg where R is the radius of the menisus, and theta is the angle of contact. Since theta=0 (given), radius of the meniscus is equal to the radius of the capillary tube i.e. R=r :. h=(2(7.0xx10^(-2)))/((10^(3))(0.2xx10^(-3))(10))=0.07m or h=7.0cm When the length of the capillary tube above the free surface of the liquid is less than the height of liquid that rise in the tube, radius R of the free surface is not equal to the radius of the tube. It is greater than r as the surface tennis to be flatter. According to the equation p_(1)-p_(2)=(4sigma//R), the pressure difference across te surface is given by /_p=(2sigmacostheta)/R If p_(1) and p_(2) are the pressure just above and below the mensisus, respectively then p_(1)-p_(2)=rhogh_(0) :. rhogh_(0)=(2sigma)/r...........i In part a we have seen than when h_(0)=h,theta=0, R=r, and rhogh=(2sigma)/r.......ii Therefore dividing eqn i by eqn ii we have r/R=(h_(0))/h From the figure, it is clear that costheta=r/R Therefore the angle of contact is theta=(cos^(-1)h_(0))/h=cos^(-1)(5/7)~~44^@	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9421091675758362, "perplexity": 1036.0657686572497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00798.warc.gz"}
https://wiki.iac.isu.edu/index.php?title=Teller_Light&diff=115761&oldid=115601	# run list ### 5/31/2017 Run 6429 3 MeV 0.5 microsecond pulse width two toroids no Faraday cup PMT in cell 390 nm filter, HV = -1800, Shawn's mirror at 1 7/8 inches from downstream side of downstream toroid. PMT RMS/mean < 10% Run 6430 Replaced 390 nm filter with 320 nm filter. Run 6431 320 nm and 330 nm filters stacked. Run 6432 Shawn's mirror on beam right which probes which part of the plume we are seeing moved to 18 inches. Still 320 + 330 nm filters in. Now just one planoconvex lens on accelerator side. Before we had two. Run 6433 Now, just 320 nm filter in. Run 6435. Beam right mirror moved to 5 feet. ADC[5]/ADC[7] = 1.55 We still have light from the extended plume getting to the PMT. We added some sewer pipe and black cloth to take care of this. Run 6437. 329 filter in. Better optics to see just end of plume. Mirror 130.5 inches from toroid. ADC[5]/ADC[7] = 0.2176 Run 6440. Looking at 18 inches. We changed several aspects of the optics. Board to block UV, no sewer pipe. Run 6442. 0.5 usec wide beam pulse, 80 mA peak, 320 nm filter, Removed sewer pipe, installed wall to block direct light from plume, removed mirror in the plume and sent light through 2" hole in plywood 18 inches downstream of toroid., used light at PMT to align light back to the beam line., ADC[5]/ADC[7] = 6.0 +/- 0.7 Run 6443. changed filter to 390 nm. ADC[5]/ADC[7] = 5.3 +/- 0.9 Run 6444. inserted 320 + 330 nm. ADC[5]/ADC[7] = 0.2 +/- 0.02 Run 6445. inserted 320 nm. hole in plywood is 29.5 inches from toroid, image from a light placed at the Cell PMT makes an image on the plywood. The plywood hole is upstream of the center of that image. ADC[5]/ADC[7] = 4.2 +/- 0.6Run 6446. hole in plywood is 40 inches from toroid, inserted two mirrors, ADC[5]/ADC[7] = 3.5 +/- 0.4 6447. hole in plywood is 51.75 inches from toroid, ADC[5]/ADC[7] = 3.085+/- 0.4 6448. hole in plywood is 88.5 inches from toroid, ADC[5]/ADC[7] = 2.8 +/- 0.37 6449. Aluminum tape is placed over the hole in the plywood board. hole in plywood is 88.5 inches from toroid as before, ADC[5]/ADC[7] = 1.965+/- 0.282 6450. Black cloth placed over hole in wall on accelerator hall side. Aluminum tape still placed over the hole in the plywood board. hole in plywood is 88.5 inches from toroid as before, ADC[5]/ADC[7] = 0.331+/- 0.04 Signal is from the accelerator hall 6451. Labeled mirrors A,B,C,D according to path of light from the beam line to the cell. Mirror "B" is poly blocked between mirror B and C, brick is closest to B. Black cloth off of hole to shielded cell.A DC[5]/ADC[7] = 1 +/- 0.2 6452. Mirror "B" is poly blocked between mirror B and C. Inserted poly brick between Mirror A and mirror B, closest to mirror B. ADC[5]/ADC[7] = 0.9 +/- 0.2 6453. Unblock the hole in the plywood. Mirror "B" is poly blocked between mirror B and C. Inserted poly brick between Mirror A and mirror B, closest to mirror B. ADC[5]/ADC[7] = 0.86 +/- 0.14 ### 6/2/2017 We put in lots of collimation with sewer pipes, etc. Line source in, 320 nm filter in. HV at -1900V. Signal is -7 mV. Go to -2001.4 V. Signal is -12 mV. With light off (-2001.4 V), signal is +1 mV. 320 + 330 nm filters in. HV at -2001.4V. 0 mV. Just 330 nm filter in. HV at -2000.6V. Signal is -11mV. I think this the line at 337 nm. 390 nm filter in. Voltage read back is 2000.6 V. Signal is -7.8 mV. Run 6454 390 nm filter in. z position (distance of hole in plywood to ) is 86 1/8 inches. Hole in plywood blocked by tape. HV -2100 V. Toroid has two peaks. Run 6455 As the last run ... 390 nm filter in. z position (distance of hole in plywood to ) is 86 1/8 inches. Hole in plywood blocked by tape. HV -2100 V. Toroid has one peak. Run 6456 Tape taken off hole in plywood. Run 6457 330 nm filter in. Run 6458 330 and 320 nm filters in. Run 6459 Just 320 nm filter in. Run 6460 Hole in plywood at 35 1/4 inches. Line source in. No beam. Junk run. Run 6461 no beam. line source. DAQ crashed. Starting anew. Run 6468. 4.8 mV on PMT with 320 nm filter. HV is 2100. Run 6469 320 + 330 filters. Run 6470 Junk. PMT not on. Run 6471 Just 330 nm filter. Run 6472 390 nm. [5]/[7]=1.136 Run 6473. Line source in. no RF. Run 6474. Line source. Hole moved to 21 3/4. No beam. RF on. Run 6475. Beam on, 390 nm filter.[5]/[7]=1.567 Run 6476. Same as last run, but hole in plywood blocked.[5]/[7]=0.175 Run 6477. z = 12 7/8 inches. Hole no longer blocked. Line source ON [5]/[7]= 32 Run 6478. z = 12 7/8 inches. Hole open. Beam ON [5]/[7]=1.69 Run 6479. Line source. Two mirrors on optics table removed. Looking down throat of sewer pipe. ADC pinned. Run 6480 Amplifier on PMT changed from 1000 to 500. Line source. [5] = 3259 Run 6481 Beam on. Still amp at 500. [5]/[7] = 1.16 Run 6483. Hole blocked. [5]/[7] = 0.245 Run 6483, Hole unblocked. Pot of boiling water installed. [5]/[7] = 1.045 Run 6484, Line source. z = 102 3/4 inches. [5] = 1412 Run 6485, Beam on. [5]/[7] = 0.28 Run 6486, amp put back to 1000. Beam on. [5]/[7] = 0.39. Run 6487, hole blocked on plywood. [5]/[7] = 0.359 (run not ended??) Run 6488 line source. z = 62 1/2 inches[5] = 3620 Cut on event number. Run 6489, Beam on, open hole [5]/[7] = 1.089 -- Put event number cut in data Run 6490, Beam on, blocked hole, [5]/[7] = 0.90	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4530162811279297, "perplexity": 16130.074099736796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662593428.63/warc/CC-MAIN-20220525182604-20220525212604-00490.warc.gz"}
http://icuequipment.blogspot.com/2008/03/relation-between-pao2fio2-ratio-and.html	## Monday, March 10, 2008 ### Relation between PaO2/FIO2 ratio and FIO2: a mathematical description Jerome Aboab Bruno Louis Bjorn Jonson Laurent Brochard The acute respiratory distress syndrome (ARDS) is characterized by severe hypoxemia, a cornerstone element in its definition. Numerous indices have been used to describe this hypoxemia, such as the arterial to alveolar O2 difference, theintrapulmonary shunt fraction, the oxygen index and the PaO2/FIO2 ratio. Of these different indices the PaO2/FIO2 ratio has been adopted for routine use because of its simplicity. This ratio is included in most ARDS definitions, such as the Lung Injury Score [1] and in the American–European Consensus Conference Definition [2]. Ferguson et al. recently proposed a new definition including static respiratory system compliance and PaO2/FIO2 measurement with PEEP set above 10 cmH2O, but FIO2 was still not fixed [3]. Important for this discussion, the PaO2/FIO2 ratio is influenced not only by ventilator settings and PEEP but also by FIO2. First, changes in FIO2 influence the intrapulmonary shunt fraction, which equals the true shunt plus ventilation–perfusion mismatching. At FIO2 1.0, the effects of ventilation–perfusion mismatch are eliminated and true intrapulmonary shunt is measured. Thus, the estimated shunt fraction may decrease as FIO2 increases if V/Q mismatch is a major component in inducing hypoxemia (e.g., chronic obstructive lung disease and asthma). Second, at an FIO2 of 1.0 absorption atelectasis may occur, increasing true shunt [4]. Thus, at high FIO2 levels (> 0.6) true shunt may progressively increase but be reversible by recruitment maneuvers. Third, because of the complex mathematical relationship between the oxy-hemoglobin dissociation curve, the arterio-venous O2 difference, the PaCO2 level and the hemoglobin level, the relation between PaO2/FIO2 ratio and FIO2 is neither constant nor linear, even when shunt remains constant. Gowda et al. [5] tried to determine the usefulness of indices of hypoxemia in ARDS patients. Using the 50- compartment model of ventilation–perfusion inhomogeneity plus true shunt and dead space, they varied the FIO2 between 0.21 and 1.0. Five indices of O2 exchange efficiency were calculated (PaO2/FIO2, venous admixture, P(A-a)O2, PaO2/alveolar PO2, and the respiratory index). They described a curvilinear shape of the curve for PaO2/FIO2 ratio as a function of FIO2, but PaO2/FIO2 ratio exhibited the most stability at FIO2 values = 0.5 and PaO2 values = 100 mmHg, and the authors concluded that PaO2/FIO2 ratio was probably a useful estimation of the degree of gas exchange abnormality under usual clinical conditions. Whiteley et al. also described identical relation with other mathematical models [6, 7].This nonlinear relation between PaO2/FIO2 and FIO2, however, underlines the limitations describing the intensity of hypoxemia using PaO2/FIO2, and is thus of major importance for the clinician. The objective of this note is to describe the relation between PaO2/FIO2 and FIO2 with a simple model, using the classic Berggren shunt equation and related calculation, and briefly illustrate the clinical consequences. Berggren shunt equation (Equation 1) The Berggren equation [8] is used to calculate the magnitude of intrapulmonary shunt (S), “comparing” the theoretical O2 content of an “ideal” capillary with the actual arterial O2 content and taking into account what comes into the lung capillary, i.e., the mixed venous content. CcO2 is the capillary O2 content in the ideal capillary, CaO2 is the arterial O2 content, and Cv¯O2 is the mixed venous O2 content, S = Q.s Q.t = (CcO2 - CaO2) (CcO2 - C¯vO2) This equation can be written incorporating the arteriovenous difference (AVD) as: CcO2 - CaO2 = S 1 - S× AVD. Blood O2 contents are calculated from PO2 and hemoglobin concentrations as: Equation of oxygen content (Equation 2) CO2 = (Hb × SO2 × 1.34) + (PO2 × 0.0031) The formula takes into account the two forms of oxygen carried in the blood, both that dissolved in the plasma and that bound to hemoglobin. Dissolved O2 follows Henry’s law – the amount of O2 dissolved is proportional to its partial pressure. For each mmHg of PO2 there is 0.003 ml O2/dl dissolved in each 100 ml of blood. O2 binding to hemoglobin is a function of the hemoglobin-carrying capacity that can vary with hemoglobinopathies and with fetal hemoglobin. In normal adults, however, each gram of hemoglobin can carry 1.34 ml of O2. Deriving blood O2 content allows calculation of both CcO2 and CaO2 and allows Eq. 1 to be rewritten as follows: (Hb × ScO2 × 1.34) + (PcO2 × 0.0031)- (Hb × SaO2 × 1.34) + (PaO2 × 0.0031) = S 1 - S× AVD In the ideal capillary (c), the saturation is 1.0 and the PcO2 is derived from the alveolar gas equation: PcO2 = PAO2 = (PB - 47) × FIO2 - PaCO2 R . This equation describes the alveolar partial pressure of O2 (PAO2) as a function, on the one hand, of barometric pressure (PB), from which is subtracted the water vapor pressure at full saturation of 47 mmHg, and FIO2, to get the inspired O2 fraction reaching the alveoli, and on the other hand of PaCO2 and the respiratory quotient (R) indicating the alveolar partial pressure of PCO2. Saturation, ScO2 and SaO2 are bound with O2 partial pressure (PO2) PcO2 and PaO2, by the oxy-hemoglobin dissociation curve, respectively. The oxy-hemoglobin dissociation curve describes the relationship of the percentage of hemoglobin saturation to the blood PO2. This relationship is sigmoid in shape and relates to the nonlinear relation between hemoglobin saturationand itsconformational changes with PO2. A simple, accurate equation for human blood O2 dissociation computations was proposed by Severinghaus et al. [9]: Blood O2 dissociation curve equation (Equation 4) SO2 = PO32 + 150PO2-1 × 23 400+ 1-1 This equation can be introduced in Eq. 1: Hb × (PB - 47) × FIO2 - PaCO2 R 3 +150 (PB - 47) × FIO2 - PaCO2 R -1 ×23 400+ 1-1 × 1.34+ (PB - 47) ×FIO2 - PaCO2 R × 0.0031 -Hb × PaO32 + 150PaO2-1 × 23 400 +1-1 × 1.34+ (PaO2 × 0.0031) = S 1 - S× AVD Equation 1 modified gives a relation between FIO2 and PaO2 with six fixed parameters: Hb, PaCO2, the respiratory quotient R, the barometric pressure (PB), S and AVD. The resolution of this equation was performed here with Mathcad® software, (Mathsoft Engineering & Education, Cambridge, MA, USA). Fig. 1 Relation between PaO2/FIO2 and FIO2 for a constant arterio-venous difference (AVD) and different shunt levels (S) Fig. 2 Relation between PaO2/FIO2 and FIO2 for a constant shunt (S) level and different values of arterio-venous differences (AVD) Resolution of the equation The equation results in a nonlinear relation between FIO2 and PaO2/FIO2 ratio. As previously mentioned, numerous factors, notably nonpulmonary factors, influence this curve: intrapulmonary shunt, AVD, PaCO2, respiratory quotient and hemoglobin. The relationship between PaO2/FIO2 and FIO2 is illustrated in two situations. Figure 1 shows this relationship for different shunt fractions and a fixed AVD. For instance, in patients with 20% shunt (a frequent value observed in ARDS), the PaO2/FIO2 ratio varies considerably with changes in FIO2. At both extremes of FIO2, the PaO2/FIO2 is substantially greater than at intermediate FIO2. In contrast, at extremely high shunt (~=60%) PaO2/FIO2 ratio is greater at low FIO2 and decreases at intermediate FIO2, but does not exhibit any further increase as inspired FIO2 continue to increase, for instance above 0.7. Figure 2 shows the same relation but with various AVDs at a fixed shunt fraction. The larger is AVD, the lower is the PaO2/FIO2 ratio for a given FIO2. AVD can vary substantially with cardiac output or with oxygen consumption. These computations therefore illustrate substantial variation in the PaO2/FIO2 index as FIO2 is modified under conditions of constant metabolism and ventilation–perfusion abnormality. Consequences This discussion and mathematical development is based on a mono-compartmental lung model and does not take into account dynamic phenomena, particularly when high FIO2 results in denitrogenation atelectasis. Despite this limitation, large nonlinear variation and important morphologic differences of PaO2/FIO2 ratio curves vary markedly with intrapulmonary shunt fraction and AVD variation. Thus, not taking into account the variable relation between FIO2 and the PaO2/FIO2 ratio couldintroduce serious errors in the diagnosis or monitoring of patients with hypoxemia on mechanical ventilation. Recently, the accuracy of the American–European consensus ARDS definition was found to be only moderate when compared with the autopsy findings of diffuse alveolar damage in a series of 382 patients [10]. The problem discussed here with FIO2 may to some extent participate in these discrepancies. A studyby Ferguson et al. [11] illustrated the clinical relevance of this discussion. They sampled arterial blood gases immediately after initiation of mechanical ventilation and 30 min after resetting the ventilator in 41 patients who had early ARDS based on the most standard definition [2]. The changes in ventilatorsettingschiefly consisted of increasing FIO2 to 1.0. In 17 patients (41%), the hypoxemia criterion for ARDS persisted after this change (PaO2/FIO2 < of =" 20%."> 0.6 (depending on the AVD value). Thus, the use of the PO2/FIO2 ratio as a dynamic variable should be used with caution if FIO2, as well as other ventilatory settings, varies greatly. References 1. Murray J,Matthay MA, Luce J, FlickM (1988) An expanded definition of the adult respiratory distress syndrome. Am Rev Respir Dis 138:720–723 2. Bernard GR, Artigas A, Brigham KL, Carlet J, Falke K, Hudson L, Lamy M, Legall JR, Morris A, Spragg R (1994) The American–European Consensus Conference on ARDS. Definitions, mechanisms, relevant outcomes, and clinical trial coordination. Am J Respir Crit Care Med 149:818–824 3. Ferguson ND, Davis AM, Slutsky AS, Stewart TE (2005) Development of a clinical definition for acute respiratory distress syndrome using the Delphi technique. J Crit Care 20:147–154 4. Santos C, Ferrer M, Roca J, Torres A, Hernandez C, Rodriguez-Roisin R (2000) Pulmonary gas exchange response to oxygen breathing in acute lung injury. Am J Respir Crit Care Med 161:26–31 5. Gowda MS, Klocke RA (1997) Variability of indices of hypoxemia in adult respiratory distress syndrome. Crit Care Med 25:41–45 6. Whiteley JP, Gavaghan DJ, Hahn CE (2002) Variation of venous admixture, SF6 shunt, PaO2, and the PaO2/FIO2 ratio with FIO2. Br J Anaesth 88:771–778 7. Whiteley JP, Gavaghan DJ, Hahn CE (2002) Mathematical modelling of oxygen transport to tissue. J Math Biol 44:503–522 8. Berggren S (1942) The oxygen deficit of arterial blood caused by nonventilating parts of the lung. Acta Physiol Scand 11:1–92 9. Severinghaus J (1979) Simple, accurate equations for human blood O2 dissociation computations. J Appl Physiol 46:599–602 10. Esteban A, Fernandez-Segoviano P, Frutos-Vivar F, Aramburu JA, Najera L, Ferguson ND, Alia I, Gordo F, Rios F (2004) Comparison of clinical criteria for the acute respiratory distress syndrome with autopsy findings. Ann Intern Med 141:440–445 11. Ferguson ND, Kacmarek RM, Chiche JD, Singh JM, Hallett DC, Mehta S, Stewart TE (2004) Screening of ARDS patients using standardized ventilator settings: influence on enrollment in a clinical trial. Intensive Care Med 30:1111–1116	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8561546802520752, "perplexity": 14285.899018310827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928520.68/warc/CC-MAIN-20150521113208-00244-ip-10-180-206-219.ec2.internal.warc.gz"}
http://mathematica.stackexchange.com/questions/34384/merging-two-line-graphs-into-manipulate-command	# Merging two line graphs into manipulate command Ultimately the goal is to make a manipulate command and turn a line into a circle. So I am supposed to take a line that is segmented into 12 equal lengths. M = {{1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 0}, {6, 0}, {7, 0}, {8, 0}, {9, 0}, {10, 0}, {11, 0}, {12, 0}, {13, 0}}; Graphics[{Thin, Line[M, VertexColors -> {Red, Blue, Orange, Green, Red, Blue, Orange, Green, Red, Blue, Orange, Green}]}] Then there is the circle L = {{1, 0}, {Cos[Pi/6], Sin[Pi/6]}, {Cos[(2 Pi)/6], Sin[(2 Pi)/6]}, {0, Sin[Pi/2]}, {-Cos[(2 Pi)/6], Sin[(2 Pi)/6]}, {-Cos[Pi/6], Sin[Pi/6]}, {-1, 0} , {-Cos[Pi/6], -Sin[Pi/6]}, {-Cos[(2 Pi)/6], -Sin[(2 Pi)/ 6]}, {0, -1}, {Cos[(2 Pi)/6], -Sin[(2 Pi)/6]}, {Cos[ Pi/6], -Sin[Pi/6]}, {1, 0}} ; Graphics[{Thin, Line[ { L }, VertexColors -> {Yellow, Red, Blue, Orange, Green, Red, Blue, Orange, Green, Red, Blue}]}] Now I am trying to merge the two. I noticed whenever I start of with the line command I can't get it to work with manipulate. Manipulate[Thin, Line[ Plot[{{1, 0}, {2, 0}}, {x, 0, 3}], {a, 0, 2 Pi} ] So now I am not sure how to go about the problem since I can't even begin on it. Should I just use the equation of a line? That doesn't seem probably given the question If you take a fraction f of a final vertex and a fraction 1-f of the corresponding initial vertex, and vary f between zero and one, you will find that a shape evolves from the initial shape to the final shape. Construct a Manipulate[] function with a slider that varies f that shows your straight line curling up into a circle. Which makes me think that I need to have the individual vertices's in. Please help, thank you - Not so didactic, but the morphing follows the principle from your assignment: mathematica.stackexchange.com/a/31642/131. – Yves Klett Oct 20 '13 at 7:13 m = {#, 0} & /@ Range@13; l = Table[{Cos[2 Pi n/12], Sin[2 Pi n /12]}, {n, 13}]; Manipulate[Graphics[{Thin, Line[l, VertexColors -> {Yellow, Red, Blue, Orange, Green, Red, Blue, Orange, Green, Red, Blue}], Line[m, VertexColors -> {Red, Blue, Orange, Green, Red, Blue, Orange, Green, Red, Blue, Orange, Green}], Line[f l + (1 - f) m]}], {f, 0, 1}] - @Megan Vineyard you can upvote an answer if you like it, too ;-) – Yves Klett Oct 22 '13 at 6:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18777737021446228, "perplexity": 2177.5621343398225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539665.16/warc/CC-MAIN-20140416005219-00558-ip-10-147-4-33.ec2.internal.warc.gz"}
https://cs.stackexchange.com/questions/13286/interactive-proofs-for-conp	# Interactive Proofs for coNP I am trying to understand interactive proof systems and tried the following problem as an exercise. We know that $PH \subseteq PSPACE$ and $IP=PSPACE$, so come up with (easy to understand) interactive proof systems for $PH$? An interactive proof system for $NP$ is trivial, but I failed to get an interactive proof system even for $coNP$. Do you know of an explicit interactive proof system (by explicit I mean without going through the $IP=PSPACE$ route) for $coNP$? • Could you clarify what you mean by interactive proof system? For those who aren't familiar with the term. – jmite Jul 15 '13 at 17:28 • Even the inclusion $coNP \subseteq IP$ requires nonrelativizing techniques; the only known way to show it is via algebrization, as in Yuval's answer. Showing $IP=PSPACE$ is merely a slight technical modification of this proof. – sdcvvc Jul 16 '13 at 14:09 • @sdcvvc, I think your comment worths being posted as an answer. It explains why there are not any examples as simple as those for NP. – Kaveh Jul 17 '13 at 8:05 Wikipedia outlines such an example. Consider the coNP-complete problem UNSAT: given a CNF $\varphi$ on $n$ variables, we want to convince the verifier that $\varphi$ is not satisfiable. We arithmetize $\varphi$ to a polynomial $p$ and choose some large prime $q$. Let $$p(x_1,\ldots,x_k) = \sum_{x_{k+1}=0}^1 \cdots \sum_{x_n=0}^1 p(x_1,\ldots,x_n).$$ The protocol proceeds as follows: 1. Prover sends verifier a prime $q \in (2^n,2^{n+1})$, and the latter verifies that $q$ is prime. 2. Prover sends verifier $p(z) \in \mathbb{Z}_q[z]$. Verifier verifies that $p(0) + p(1) = 0$, and sends prover a random $r_1$. 3. Prover sends verifier $p(r_1,z) \in \mathbb{Z}_q[z]$. Verifier verifies that $p(r_1,0) + p(r_1,1) = p(r_1)$, and sends prover a random $r_2$. 4. Eventually, verifier gets $p(r_1,\ldots,r_n) \in \mathbb{Z}_q$, and verifies that it has the correct value by evaluating $p$ directly. Because the degree of $p$ is small compared to $q$, if the prover is cheating then the verifier will probably catch her (see Wikipedia for the proof, or work it out yourself using the Schwartz-Zippel lemma). Graph non-isomorphism at Proofs that Yield Nothing But their Validity or All Languages in NP have Zero-Knowledge Proofs, Goldreich, Micali and Wigderson, JACM, 1991. Common input is a pair of graphs: $G_1, G_2$. At the start of each round, verifying party chooses an index $i \in \{1,2\}$ at random and sends a random permutation of graph $G_i$. Proving party responds with an index $b \in \{1,2\}$. Completeness property: for non-isomorphic graphs, prover always give correct response $b=i$. Soundness: for isomorphic graphs, prover give correct response with probability $\frac{1}{2}$. • Please give a proper reference to a peer-reviewed article and a short summary of the content. Links like the one you provide tend to break, and then your answer contains zero information. – Raphael Jan 31 '15 at 9:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8555546998977661, "perplexity": 674.8381316169259}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655933254.67/warc/CC-MAIN-20200711130351-20200711160351-00403.warc.gz"}
http://demonstrations.wolfram.com/GeodesicsInTheMorrisThorneWormholeSpacetime/	# Geodesics in the Morris-Thorne Wormhole Spacetime Requires a Wolfram Notebook System Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products. Requires a Wolfram Notebook System Edit on desktop, mobile and cloud with any Wolfram Language product. The simplest wormhole geometry is given by the line element , see [2]. The parameter defines the size of the throat of the wormhole, and represents the proper length radius. [more] Light rays and objects in free motion in four-dimensional spacetimes follow lightlike or timelike geodesics. In general, these geodesics must be computed numerically. However, in the Ellis wormhole spacetime, there is an analytic solution of the geodesic equation in terms of elliptic integral functions. Because of the spherical symmetry and staticity of the metric, it suffices to consider geodesics in the hypersurface . This two-dimensional surface can be embedded in the three-dimensional Euclidean space. The corresponding embedding function reads with . In this application, you can change the throat size , the initial position of the observer, and the initial angle of the geodesic with respect to the local reference frame of the observer. [less] Contributed by: Thomas Müller (July 2010) Open content licensed under CC BY-NC-SA ## Details A detailed discussion about analytic geodesics in the Morris–Thorne wormhole spacetime can be found in [1]. The metric described in [2] was first mentioned in [3]. Hence, it should be called Ellis wormhole instead. See also the apology in [4], Ref. 14. References [1] T. Müller, "Exact Geometric Optics in a Morris–Thorne Wormhole Spacetime," Physical Review D, 77(4) 2008. doi: 10.1103/PhysRevD.77.044043. [2] M. S. Morris and K. S. Thorne, "Wormholes in Spacetime and Their Use for Interstellar Travel: A Tool for Teaching General Relativity," American Journal of Physics, 56(5), 1988 pp. 395–412. [3] H. G. Ellis, "Ether Flow through a Drainhole: A Particle Model in General Relativity," Journal of Mathematical Physics, 14, 1973 pp. 104–118; 1974 Errata: 15, p. 520. [4] O. James, E. von Tunzelmann, P. Franklin, and K. S. Thorne, "Visualizing Interstellar's Wormhole," American Journal of Physics 83, 2015 pp. 483–499. ## Permanent Citation Thomas Müller Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8124597072601318, "perplexity": 1671.6002410695764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824180.12/warc/CC-MAIN-20181212225044-20181213010544-00102.warc.gz"}
https://malegislature.gov/Laws/GeneralLaws/PartI/TitleXVI/Chapter111/Section216	General Laws Section 216 Fragrance advertising inserts; microencapsulated fragrance; penalty Section 216. All fragrance advertising inserts contained in a newspaper, magazine, mailing, or other periodically printed material shall contain only microencapsulated oils. Glue tabs or binders shall be used to prevent premature activation of the fragrance advertising insert. Fragrance advertising insert shall mean a printed piece with encapsulated fragrance applied to it which is activated by opening a flap or removing an overlying ply of paper. Paperstocks employed in the manufacture of fragrance advertising inserts shall have a maximum porosity of twenty Sheffield units or one hundred and seventy-two Gurley Hill units. Any person who distributes fragrance advertising inserts in violation of this section shall be guilty of an infraction and shall, if convicted, be subject to a fine of one hundred dollars for each such distribution. The fine shall apply to each mass mailing or distribution and to each mass publication of a magazine or newspaper in violation of this section. The fine shall not apply, however, to each individual letter, magazine, newspaper or fragrance advertising insert so distributed.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9019795656204224, "perplexity": 9585.877313146153}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246641393.36/warc/CC-MAIN-20150417045721-00180-ip-10-235-10-82.ec2.internal.warc.gz"}
https://spark.apache.org/docs/3.1.1/api/python/reference/api/pyspark.mllib.fpm.PrefixSpan.html	# PrefixSpan¶ class pyspark.mllib.fpm.PrefixSpan[source] A parallel PrefixSpan algorithm to mine frequent sequential patterns. The PrefixSpan algorithm is described in Jian Pei et al (2001) [1] New in version 1.6.0. 1 Jian Pei et al., “PrefixSpan,: mining sequential patterns efficiently by prefix-projected pattern growth,” Proceedings 17th International Conference on Data Engineering, Heidelberg, Germany, 2001, pp. 215-224, doi: https://doi.org/10.1109/ICDE.2001.914830 Methods train(data[, minSupport, maxPatternLength, …]) Finds the complete set of frequent sequential patterns in the input sequences of itemsets. Methods Documentation classmethod train(data, minSupport=0.1, maxPatternLength=10, maxLocalProjDBSize=32000000)[source] Finds the complete set of frequent sequential patterns in the input sequences of itemsets. New in version 1.6.0. Parameters datapyspark.RDD The input data set, each element contains a sequence of itemsets. minSupportfloat, optional The minimal support level of the sequential pattern, any pattern that appears more than (minSupport * size-of-the-dataset) times will be output. (default: 0.1) maxPatternLengthint, optional The maximal length of the sequential pattern, any pattern that appears less than maxPatternLength will be output. (default: 10) maxLocalProjDBSizeint, optional The maximum number of items (including delimiters used in the internal storage format) allowed in a projected database before local processing. If a projected database exceeds this size, another iteration of distributed prefix growth is run. (default: 32000000)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2363383173942566, "perplexity": 7249.629601760895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103917192.48/warc/CC-MAIN-20220701004112-20220701034112-00633.warc.gz"}
http://planetmath.org/KantorovitchsTheorem	# Kantorovitch’s theorem Let $\mathbf{a}_{0}$ be a point in $\mathbb{R}^{n},U$ an open neighborhood of $\mathbf{a}_{0}$ in $\mathbb{R}^{n}$ and $\mathbf{f}\colon U\rightarrow\mathbb{R}^{n}$ a differentiable mapping, with its derivative $[\mathbf{D}\mathbf{f}(\mathbf{a}_{0})]$ invertible. Define $\mathbf{h}_{0}=-[\mathbf{D}\mathbf{f}(\mathbf{a}_{0})]^{-1}\mathbf{f}(\mathbf{% a}_{0})\>,\>\mathbf{a}_{1}=\mathbf{a}_{0}+\mathbf{h}_{0}\>,\>U_{0}=\{\mathbf{x% }\|\>\|\mathbf{x}-\mathbf{a}_{1}\|\leq\|\mathbf{h}_{0}\|\}.$ If $U_{0}\subset U$ and the derivative $[\mathbf{D}\mathbf{f}(\mathbf{x})]$ satisfies the http://planetmath.org/node/765Lipschitz condition $\|[\mathbf{D}\mathbf{f}(\mathbf{u}_{1})]-[\mathbf{D}\mathbf{f}(\mathbf{u}_{2})]% \|\leq M\|\mathbf{u}_{1}-\mathbf{u}_{2}\|$ for all points $\mathbf{u}_{1},\mathbf{u}_{2}\in U_{0}$, and if the inequality $\left\|\mathbf{f}(\mathbf{a_{0}})\right\|\left\|[\mathbf{D}\mathbf{f}(\mathbf{a_{% 0}})]^{-1}\right\|^{2}M\leq\frac{1}{2}$ is satisfied, the equation $\mathbf{f}(\mathbf{x})=\mathbf{0}$ has a unique solution in $U_{0}$, and Newton’s method with initial guess $\mathbf{a}_{0}$ converges to it. If we replace $\leq$ with $<$, then it can be shown that Newton’s method http://planetmath.org/node/793superconverges! If you want an even stronger version, one can replace $\|...\|$ with the norm $\|\|...\|\|$. ## Logic behind the theorem: Let’s look at the useful part of the theorem: $\left\|\mathbf{f}(\mathbf{a_{0}})\right\|\left\|[\mathbf{D}\mathbf{f}(\mathbf{a_{% 0}})]^{-1}\right\|^{2}M\leq\frac{1}{2}.$ It is a product of three distinct properties of your function such that the product is less than or equal to a certain number, or bound. If we call the product $R$, then it says that $\mathbf{a}_{0}$ must be within a ball of radius $R$. It also says that the solution $\mathbf{x}$ is within this same ball. How was this ball defined? The first term, $\|\mathbf{f}(\mathbf{a_{0}})\|$, is a measure of how far the function is from the domain; in the Cartesian plane, it would be how far the function is from the x-axis. Of course, if we’re solving for $\mathbf{f}(\mathbf{x})=\mathbf{0}$, we want this value to be small, because it means we’re closer to the axis. However a function can be annoyingly close to the axis, and yet just happily curve away from the axis. Thus we need more. The second term, $\|[\mathbf{D}\mathbf{f}(\mathbf{a_{0}})]^{-1}\|^{2}$ is a little more difficult. This is obviously a measure of how fast the function is changing with respect to the domain (x-axis in the plane). The larger the derivative, the faster it’s approaching wherever it’s going (hopefully the axis). Thus, we take the inverse of it, since we want this product to be less than a number. Why it’s squared though, is because it is the denominator where a product of two terms of like units is the numerator. Thus to conserve units with the numerator, it is multiplied by itself. Combined with the first term, this also seems to be enough, but what if the derivative changes sharply, but it changes the wrong way? The third term is the Lipschitz ratio $M$. This measures sharp changes in the first derivative, so we can be sure that if this is small, that the function won’t try to curve away from our goal on us too sharply. By the way, the number $\frac{1}{2}$ is unitless, so all the units on the left side cancel. Checking units is essential in applications, such as physics and engineering, where Newton’s method is used. Title Kantorovitch’s theorem KantorovitchsTheorem 2013-03-22 11:58:09 2013-03-22 11:58:09 stevecheng (10074) stevecheng (10074) 25 stevecheng (10074) Theorem msc 49K10 Kantorovitch inequality LipschitzCondition NewtonsMethod Superconvergence	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 29, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9636784791946411, "perplexity": 255.77947946478164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645824.5/warc/CC-MAIN-20180318145821-20180318165821-00167.warc.gz"}
https://www.physicsforums.com/threads/particle-anti-particle-question.89780/	# Particle/Anti-Particle question 1. Sep 19, 2005 ### mgiddy911 Can a particle say an electron, be entangled with its antt-particle partner, a positron? So could this happen for any particle antiparticle pair? I know that entanglement is often talked abut pertaining to photons, so could a photon and anti-photon be entangled? 2. Sep 19, 2005 ### mathman There is no distinction between photons and antiphotons, i.e. they are they same. 3. Sep 19, 2005 ### BenLillie Yes, you certainly can entangle a particle/anti-particle pair. I don't know if this has ever been done with electrons (and, as mathman said, it's not a relevant question for photons), but take a look at the description of the BaBar and Belle experiments. Their measurements depend on entangling pairs of $$B^0/ \bar B^0$$ mesons. It's a very cool example of something that was once a novel result (EPR correlations, i.e. enganglement) becoming a tool for measureing something else (in this case, CP violation). 4. Sep 19, 2005 ### kublai How do you keep the partical/antiparticle from annihilating before entanglement? How could they be entangled after annihlation, the annihilation products could be different for each partical? 5. Sep 19, 2005 ### mgiddy911 Thanks for the information, the reason for me asking in the first place was similar to the last poster's question about anihilation. If the entangled pair were to anihilate after entanglement would anything be different from a normal anihilation? 6. Sep 19, 2005 ### BenLillie Nothing prevents them from annihilating. In fact, the way you entangle them in the first place is by producing them in pairs from collisions or decays of other particles (sort of reverse annihilation), and they then fly apart. If you like, that's what keeping them from annihilating, the fact that they are produced with high velocities travelling in opposite directions.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5867069959640503, "perplexity": 1690.102689627809}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719547.73/warc/CC-MAIN-20161020183839-00296-ip-10-171-6-4.ec2.internal.warc.gz"}
https://en.universaldenker.org/illustrations/474	# Illustration Linearly Polarized Plane Wave (E-Field) Get illustration Share — copy and redistribute the material in any medium or format Adapt — remix, transform, and build upon the material for any purpose, even commercially. Sharing and adapting of the illustration is allowed with indication of the link to the illustration. The E-field of a linearly polarized electromagnetic wave propagating in the $$z$$ direction is:$$\boldsymbol{E} ~=~ \boldsymbol{E}_0 \, \cos(\omega \, t - k\,z)$$where $$\boldsymbol{E}_0 = (E_{0 \text x}, E_{0 \text y}, 0)$$ is the amplitude. $$\omega$$ is the angular frequency, $$t$$ time, $$k$$ wavenumber and $$z$$ spatial coordinate as a propagation direction. The electric field $$\boldsymbol{E}$$ oscillates in a plane (here $$x$$-$$y$$-plane) for a linearly polarized wave and the components of the E-field have no phase shift.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6786180734634399, "perplexity": 678.0176352932069}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500356.92/warc/CC-MAIN-20230206145603-20230206175603-00733.warc.gz"}
http://www.researchgate.net/publication/45918625_Less_space_for_a_new_family_of_fermions	Article # Less space for a new family of fermions (Impact Factor: 4.86). 05/2010; DOI: 10.1103/PhysRevD.82.095006 Source: arXiv ABSTRACT We investigate the experimentally allowed parameter space of an extension of the standard model (SM3) by one additional family of fermions. Therefore we extend our previous study of the CKM like mixing constraints of a fourth generation of quarks. In addition to the bounds from tree-level determinations of the 3$\times$3 CKM elements and FCNC processes ($K$-, $D$-, $B_d$-, $B_s$-mixing and the decay $b \to s \gamma$) we also investigate the electroweak $S$, $T$, $U$ parameters, the angle $\gamma$ of the unitarity triangle and the rare decay $B_s \to \mu^+ \mu^-$. Moreover we improve our treatment of the QCD corrections compared to our previous analysis. We also take leptonic contributions into account, but we neglect the mixing among leptons. As a result we find that typically small mixing with the fourth family is favored, but still some sizeable deviations from the SM3 results are not yet excluded. The minimal possible value of $V_{tb}$ is 0.93. Also very large CP-violating effects in $B_s$ mixing seem to be impossible within an extension of the SM3 that consists of an additional fermion family alone. We find a delicate interplay of electroweak and flavor observables, which strongly suggests that a separate treatment of the two sectors is not feasible. In particular we show that the inclusion of the full CKM dependence of the $S$ and $T$ parameters in principle allows the existence of a degenerate fourth generation of quarks. Comment: 38 pages, 26 figures; references added ### Full-text Available from: Alexander Lenz, Apr 26, 2015 0 Followers · 86 Views • Source ##### Article: On new physics in $\Delta \Gamma_d$ [Hide abstract] ABSTRACT: Motivated by the recent measurement of the dimuon asymmetry by the D{\O} collaboration, which could be interpreted as an enhanced decay rate difference in the neutral $B_d$-meson system, we investigate the possible size of new-physics contributions to $\Delta \Gamma_d$. In particular, we perform model-independent studies of non-standard effects associated to the dimension-six current-current operators $(\bar{d} p)(\bar p^{\hspace{0.25mm}\prime} b)$ with $p,p^\prime= u,c$ as well as $(\bar{d}b) (\bar\tau\tau)$. In both cases we find that for certain flavour or Lorentz structures of the operators sizable deviations of $\Delta \Gamma_d$ away from the Standard Model expectation cannot be excluded in a model-independent fashion. Journal of High Energy Physics 04/2014; 06(2014):040. DOI:10.1007/JHEP06(2014)040 · 5.62 Impact Factor • Source • Source ##### Article: Search for pair produced fourth-generation up-type quarks in $pp$ collisions at $sqrts=7$ TeV with a lepton in the final state [Hide abstract] ABSTRACT: The results of a search for the pair production of a fourth-generation up-type quark (t') in proton-proton collisions at sqrt(s) = 7 TeV are presented, using data corresponding to an integrated luminosity of about 5.0 inverse femtobarns collected by the Compact Muon Solenoid experiment at the LHC. The t' quark is assumed to decay exclusively to a W boson and a b quark. Events with a single isolated electron or muon, missing transverse momentum, and at least four hadronic jets, of which at least one must be identified as a b jet, are selected. No significant excess of events over standard model expectations is observed. Upper limits for the t' anti-t' production cross section at 95% confidence level are set as a function of t' mass, and t'-quark production for masses below 570 GeV is excluded. The search is equally sensitive to nonchiral heavy quarks decaying to Wb. In this case, the results can be interpreted as upper limits on the production cross section times the branching fraction to Wb.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9768912196159363, "perplexity": 970.2051809562627}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430457788926.49/warc/CC-MAIN-20150501052308-00060-ip-10-235-10-82.ec2.internal.warc.gz"}
https://kb.osu.edu/dspace/handle/1811/9506	# INTERDEPENDENCE OF GUEST RADIATIONLESS TRANSITIONS AND LOCALIZED PHONON STRUCTURE: NH AND ND ($A^{3}\Pi$) IN RARE GAS LATTICES Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/9506 Files Size Format View 1975-TH-05.jpg 105.8Kb JPEG image Title: INTERDEPENDENCE OF GUEST RADIATIONLESS TRANSITIONS AND LOCALIZED PHONON STRUCTURE: NH AND ND ($A^{3}\Pi$) IN RARE GAS LATTICES Creators: Bondybey, V. E.; Brus, L. E. Issue Date: 1975 Publisher: Ohio State University Abstract: NH and ND ($A^{3}\Pi$) radicals in rare gas lattices were studied by their time and wavelength resolved fluorescence. The temperature dependence of the localized phonon structure indicates that the ground $X^{3}\Sigma^{-}$ state undergoes near free rotation, while the excited $A^{3}\Pi$ state librates. A strong violation of the energy gap law for vibrational relaxation is observed with NH rates 10$-10^{2}$ higher than in ND. The vibrational relaxation rates are independent of temperature for $T < 25 ^{\circ} K$ in Ar and $< 37 ^{\circ} K$ in Kr; however, lifetimes of several $A^{3}\Pi$ vibrational levels show a dramatic temperature dependence attributed to intersystem crossing into $^{1}\Delta$. We propose that the localized near free rotation mode accepts the energy during vibrational relaxation, while delocalized Lattice phonons accept energy during intersystem crossing. Description: Author Institution: Bell Laboratories URI: http://hdl.handle.net/1811/9506 Other Identifiers: 1975-TH-05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7235760688781738, "perplexity": 8817.876808744651}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541525.50/warc/CC-MAIN-20161202170901-00339-ip-10-31-129-80.ec2.internal.warc.gz"}
https://en.m.wikipedia.org/wiki/Triple_modular_redundancy	# Triple modular redundancy Triple Modular Redundancy. Three identical logic circuits (logic gates) are used to compute the specified Boolean function. The set of data at the input of the first circuit are identical to the input of the second and third gates. In computing, triple modular redundancy, sometimes called triple-mode redundancy,[1] (TMR) is a fault-tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a majority-voting system to produce a single output. If any one of the three systems fails, the other two systems can correct and mask the fault. The TMR concept can be applied to many forms of redundancy, such as software redundancy in the form of N-version programming, and is commonly found in fault-tolerant computer systems. Some ECC memory uses triple modular redundancy hardware (rather than the more common Hamming code), because triple modular redundancy hardware is faster than Hamming error correction software.[2] Space satellite systems often use TMR,[3][4][5] although satellite RAM usually uses Hamming error correction.[6] Some communication systems use N-modular redundancy as a simple form of forward error correction. For example, 5-modular redundancy communication systems (such as FlexRay) use the majority of 5 samples – if any 2 of the 5 results are erroneous, the other 3 results can correct and mask the fault. Modular redundancy is a basic concept, dating to antiquity, while the first use of TMR in a computer was the Czechoslovak computer SAPO, in the 1950s. ## ChronometersEdit To use triple modular redundancy, a ship must have at least three chronometers; two chronometers provided dual modular redundancy, allowing a backup if one should cease to work, but not allowing any error correction if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the error detection obtained would be the same of having only one chronometer and checking it periodically). Three chronometers provided triple modular redundancy, allowing error correction if one of the three was wrong, so the pilot would take the average of the two with closer reading (vote for average precision). There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three."[7] Mainly this means that if two chronometers contradict, how do you know which one is correct? At one time this observation or rule was an expensive one as the cost of three sufficiently accurate chronometers was more than the cost of many types of smaller merchant vessels.[8] Some vessels carried more than three chronometers – for example, the HMS Beagle carried 22 chronometers.[9] However, such a large number was usually only carried on ships undertaking survey work as was the case with the Beagle. In the modern era, ships at sea use GNSS navigation receivers (with GPS, GLONASS & WAAS etc. support) -- mostly running with WAAS or ENGOS support so as to provide accurate time (and location). ## Majority logic gateEdit In TMR, three identical logic circuits (logic gates) are used to compute the same set of specified Boolean function. If there are no circuit failures, the outputs of the three circuits are identical. But due to circuit failures, the outputs of the three circuits may be different. A majority logic gate is used to decide which of the circuits’ outputs is the correct output. The majority gate output is 1 if two or more of the inputs of the majority gate are 1; output is 0 if two or more of the majority gate’s inputs are 0. The majority logic gate is a simple AND–OR circuit: if the inputs to the majority gate are denoted by x, y and z, then the output of the majority gate is ${\displaystyle xy\lor yz\lor xz}$ Thus, the majority gate is the carry output of a full adder, i.e., the majority gate is a voting machine.[10] ## TMR operationEdit Assuming the Boolean function computed by the three identical logic gates has value 1, then: (a) if no circuit has failed, all three circuits produce an output of value 1, and the majority gate output has value 1. (b) if one circuit fails and produces an output of 0, while the other two are working correctly and produce an output of 1, the majority gate output is 1, i.e., it still has the correct value. And similarly for the case when the Boolean function computed by the three identical circuits has value 0. Thus, the majority gate output is guaranteed to be correct as long as no more than one of the three identical logic circuits has failed.[10] TMR systems should use data scrubbing—rewrite flip-flops periodically—in order to avoid accumulation of errors.[11] ## VoterEdit The majority gate itself could fail. Is there a way to mask that failure? In other words, who guards the guardians?[12] In a few TMR systems, such as the Saturn Launch Vehicle Digital Computer and functional triple modular redundancy (FTMR) systems, the voters are also triplicated. Three voters are used – one for each copy of the next stage of TMR logic. In such systems there is no single point of failure. [13][14] However, in contrast to the relatively complicated Boolean functions computed in triplicate by the TMR system, the majority gate is a simple circuit, thus its probability of failure is significantly smaller than that of each of the three circuits computing the Boolean function.[10] In other systems there is only a single voter—If the voter fails in such a system, then the complete system will fail. However, in a good TMR system the voter is much more reliable than the other TMR components. ## Triple modular redundancy in popular cultureEdit • The three pre-cogs in Minority Report lead to a conviction even when one disagrees. • To rule out that a single win was "a fluke", some competitions use a two out of three falls match. This isn't true TMR, however, because the three falls are not independent of each other – each competitor knows who has most falls at any point in the competition, which influences their future actions. • In Arthur C. Clarke's science fiction novel Rendezvous with Rama, the Ramans make heavy use of triple redundancy.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7551251649856567, "perplexity": 1293.3143512428724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156418.7/warc/CC-MAIN-20180920062055-20180920082055-00172.warc.gz"}
http://econ302.wikidot.com/applying-consumer-theory	Applying Consumer Theory Perloff 5.1-3; WB 7, 8 and 9. Using the solution to the consumer's problem, we will derive the Demand curve from consumer choices and re-examine a few key Demand shifters in greater detail: the good's price, other goods' prices and income. Importantly, we will see that a consumer's price response can be decomposed into two “effects.” For the consumer's income response, we will look at two new curves — the Income Consumption Curve (ICC) and the Engel curve. Finally, we can look at cross-price and own-price responses simultaneously using the Price Consumption Curve (PCC). # Market Demand from Consumer Choice ### Deriving individual Demand Finding a consumer's individual Demand X* for a good as a function of its price PX is an easy application of the Consumer Choice model. • Derive a formula for the consumer's Demand of one good given a fixed price for the other good, fixed income and their preferences/utility (for any of the three preference types discussed earlier). ### Aggregating Demand The market Demand curve seen in the supply-and-demand model — also called the aggregate Demand — is the sum of individual Demand curves. See Perloff, p20 and the Problems referred to in the margin on that page. • Add two given Demand functions. • Add two given inverse Demand functions. # Price response We can decompose the price response in X* as the sum of two effects: the substitution effect and the income effect. Why would we want to do this? “By decomposing the change in demand into two effects, economists gain extra information that they can use to answer questions about whether inflation measures are accurate and whether an increase in tax rates will raise tax revenue.” —Jeffrey M. Perloff Given a Cobb-Douglas utility function, income and a price for Y, evaluate the effect of a change in the price of X: • What is the total effect on the quantity of X demanded? • What part of this effect is due to the substitution effect; and what part to the income effect? The substitution and income effects add up to the total effect. The substitution effect is always negative. The income effect is negative for inferior goods and positive for normal goods. • Know what it means for the income effect to be positive/negative. The price elasticity of demand can be decomposed in a similar way: $\varepsilon = \varepsilon^-\theta\cdot\xi$. The “elasticity of compensated demand” $\varepsilon^$ captures the substitution effect; and $\theta\cdot\xi$, the share of income spent on the good1 times the income elasticity $\xi$, captures the income effect. This famous decomposition is known as the Slutsky equation. ### Giffen goods A Giffen good violates the Law of Demand. This occurs because the income effect is negative and stronger than the substitution effect. • Know what a Giffen good is, and why it is possible in the Consumer Choice model. # Income and cross-price responses Change in… x-axis y-axis name of curve I X* I Engel for X I X* Y* ICC PX X* PX Demand curve PX X* Y* PCC for PX PX Y* PX XY cross-price response Curves representing the solution to the consumer's problem in the Consumer Choice model. Classification of goods based on income and own-price responses.2 The curves described in the table on the right are also straightforward applications of the Consumer Choice model. ### ICC The ICC shows the income responses of both goods simultaneously. The path tells us if each good is inferior or normal; see Perloff, Figure 5.3. It is impossible for both to be inferior, and Giffen goods are always inferior. We can also see if a normal good is a necessity or a luxury by comparing the path with a line through the origin. If one good is inferior, the other must be a luxury. A good can change from one of these to another as income rises. • Find a formula for the ICC given fixed prices and preferences/utility. Also, graph it.__ • Given a graph of an ICC, distinguish when each good is inferior/normal and a necessity/luxury. This might be multiple choice with statements like "X is normal then inferior, while Y is always a luxury." • Know which such statements cannot be true. For example, "X is inferior, while Y is a necessity." ### Engel curve These isolate the effect of income on a single good. The Engel curve bends backwards when the good is inferior. We can again distinguish necessities from luxuries using a line through the origin. • Find a formula for the Engel curve given fixed prices and preferences/utility. Also, graph it. • Given a graph of an Engel curve, distinguish when the good is inferior/normal and a necessity/luxury. This might be multiple choice with statements like "X is normal then inferior."	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7652327418327332, "perplexity": 2152.1349949621167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662018.69/warc/CC-MAIN-20160924173742-00113-ip-10-143-35-109.ec2.internal.warc.gz"}
https://link.springer.com/article/10.1007/s00466-017-1461-9?error=cookies_not_supported&code=d6f7a3d3-9a8b-46bf-9fcf-e5a72fd753cc	## Abstract Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation. This is a preview of subscription content, log in to check access. ## References 1. 1. Bhushan B, Gupta BK (1991) Handbook of tribology: materials, coatings, and surface treatments. McGraw-Hill, New York 2. 2. Roos JR, Celis JP, Fransaer J, Buelens C (1990) The development of composite plating for advanced materials. JOM 42:60–63. doi:10.1007/BF03220440 3. 3. Erdogan F (1995) Fracture mechanics of functionally graded materials. Compos Eng 5:753–770. doi:10.1016/0961-9526(95)00029-M 4. 4. Jha DK, Kant T, Singh RK (2013) A critical review of recent research on functionally graded plates. Compos Struct 96:833–849. doi:10.1016/j.compstruct.2012.09.001 5. 5. Birman V, Keil T, Hosder S (2013) Functionally graded materials in engineering. Structural interfaces and attachments in biology. Springer, New York, pp 19–41 6. 6. 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Bemporad A, Paggi M (2015) Optimization algorithms for the solution of the frictionless normal contact between rough surfaces. Int J Solids Struct 69–70:94–105. doi:10.1016/j.ijsolstr.2015.06.005 24. 24. Yang C, Persson BNJ (2008) Molecular dynamics study of contact mechanics: contact area and interfacial separation from small to full contact. Phys Rev Lett 100:24303. doi:10.1103/PhysRevLett.100.024303 25. 25. Campañá C, Müser MH (2007) Contact mechanics of real vs randomly rough surfaces: a Green’s function molecular dynamics study. EPL Europhys Lett 77:38005 26. 26. Kusche S (2016) The boundary element method for viscoelastic material applied to the oblique impact of spheres. Facta Univ Ser Mech Eng 14:293–300. doi:10.22190/FUME1603293K 27. 27. Kusche S (2016) Frictional force between a rotationally symmetric indenter and a viscoelastic half-space. ZAMM J Appl Math Mech 239:226–239. doi:10.1002/zamm.201500169 28. 28. 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Borodich FM, Galanov BA, Suarez-Alvarez MM (2014) The JKR-type adhesive contact problems for power-law shaped axisymmetric punches. J Mech Phys Solids 68:14–32. doi:10.1016/j.jmps.2014.03.003 41. 41. Argatov I, Li Q, Pohrt R, Popov VL (2016) Johnson-Kendall-Roberts adhesive contact for a toroidal indenter. Proc R Soc Lond A Math Phys Eng Sci. doi:10.1098/rspa.2016.0218 ## Author information Authors ### Corresponding author Correspondence to Valentin L. Popov. ## Rights and permissions Reprints and Permissions Li, Q., Popov, V.L. Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials. Comput Mech 61, 319–329 (2018). https://doi.org/10.1007/s00466-017-1461-9	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6467602849006653, "perplexity": 24157.889120926277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402118004.92/warc/CC-MAIN-20200930044533-20200930074533-00023.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2013.33.1157	# American Institute of Mathematical Sciences March 2013, 33(3): 1157-1175. doi: 10.3934/dcds.2013.33.1157 ## On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$ 1 Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona 2 Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona Received May 2011 Revised November 2011 Published October 2012 The problem of three bodies with equal masses in $\mathbb{S}^2$ is known to have Lagrangian homographic orbits. We study the linear stability and also a "practical'' (or effective) stability of these orbits on the unit sphere. Citation: Regina Martínez, Carles Simó. On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 1157-1175. doi: 10.3934/dcds.2013.33.1157 ##### References: [1] C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. Olivier, Users' guide to PARI/GP,, (freely available from \url{http://pari.math.u-bordeaux.fr/})., (). Google Scholar [2] F. Diacu and E. Pérez-Chavela, Homographic solutions of the curved 3-body problem, Journal of Differential Equations, 250 (2011), 340-366. doi: 10.1016/j.jde.2010.08.011. Google Scholar [3] A. Giorgilli, A. Delshams, E. Fontich, L. Galgani and C. Simó, Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem, Journal of Differential Equations, 77 (1989), 167-198. doi: 10.1016/0022-0396(89)90161-7. Google Scholar [4] T. Kapela and C. Simó, Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems,, Preprint, (). Google Scholar [5] R. Martínez, A. Samà and C. Simó, "Stability of Homographic Solutions of the Planar Three-Body Problem with Homogeneous Potentials," Proceedings EQUADIFF (2003), 1005–1010. World Scientific, 2005. Google Scholar [6] R. Martínez, A. Samà and C. Simó, Stability diagram for 4D linear periodic systems with applications to homographic solutions, Journal of Differential Equations, 226 (2006), 619-651. doi: 10.1016/j.jde.2006.01.014. Google Scholar [7] R. Martínez, A. Samà and C. Simó, Analysis of the stability of a family of singular-limit linear periodic systems in $R^4.$ applications, Journal of Differential Equations, 226 (2006), 652-686. doi: 10.1016/j.jde.2005.09.012. Google Scholar [8] C. Siegel and J. Moser, "Lectures on Celestial Mechanics," Springer, 1971. Google Scholar [9] C. Simó, On the analytical and numerical approximation of invariant manifolds, Modern methods in celestial mechanics, (eds, D. Benest and C. Froeschlé), 285-330, Editions Frontières, Paris, 1990. (Also available at {http://www.maia.ub.es/dsg/2004/}). Google Scholar [10] E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies," Cambridge Univ. Press, fourth edition, reprinted, 1970. Google Scholar show all references ##### References: [1] C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. Olivier, Users' guide to PARI/GP,, (freely available from \url{http://pari.math.u-bordeaux.fr/})., (). Google Scholar [2] F. Diacu and E. Pérez-Chavela, Homographic solutions of the curved 3-body problem, Journal of Differential Equations, 250 (2011), 340-366. doi: 10.1016/j.jde.2010.08.011. Google Scholar [3] A. Giorgilli, A. Delshams, E. Fontich, L. Galgani and C. Simó, Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem, Journal of Differential Equations, 77 (1989), 167-198. doi: 10.1016/0022-0396(89)90161-7. Google Scholar [4] T. Kapela and C. Simó, Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems,, Preprint, (). Google Scholar [5] R. Martínez, A. Samà and C. Simó, "Stability of Homographic Solutions of the Planar Three-Body Problem with Homogeneous Potentials," Proceedings EQUADIFF (2003), 1005–1010. World Scientific, 2005. Google Scholar [6] R. Martínez, A. Samà and C. Simó, Stability diagram for 4D linear periodic systems with applications to homographic solutions, Journal of Differential Equations, 226 (2006), 619-651. doi: 10.1016/j.jde.2006.01.014. Google Scholar [7] R. Martínez, A. Samà and C. Simó, Analysis of the stability of a family of singular-limit linear periodic systems in $R^4.$ applications, Journal of Differential Equations, 226 (2006), 652-686. doi: 10.1016/j.jde.2005.09.012. Google Scholar [8] C. Siegel and J. Moser, "Lectures on Celestial Mechanics," Springer, 1971. Google Scholar [9] C. Simó, On the analytical and numerical approximation of invariant manifolds, Modern methods in celestial mechanics, (eds, D. Benest and C. Froeschlé), 285-330, Editions Frontières, Paris, 1990. (Also available at {http://www.maia.ub.es/dsg/2004/}). Google Scholar [10] E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies," Cambridge Univ. Press, fourth edition, reprinted, 1970. Google Scholar [1] Gianni Arioli. Branches of periodic orbits for the planar restricted 3-body problem. Discrete & Continuous Dynamical Systems, 2004, 11 (4) : 745-755. doi: 10.3934/dcds.2004.11.745 [2] Alain Albouy, Holger R. Dullin. Relative equilibria of the 3-body problem in $\mathbb{R}^4$. Journal of Geometric Mechanics, 2020, 12 (3) : 323-341. doi: 10.3934/jgm.2020012 [3] Qunyao Yin, Shiqing Zhang. New periodic solutions for the circular restricted 3-body and 4-body problems. Communications on Pure & Applied Analysis, 2010, 9 (1) : 249-260. doi: 10.3934/cpaa.2010.9.249 [4] Holger R. Dullin, Jürgen Scheurle. Symmetry reduction of the 3-body problem in $\mathbb{R}^4$. Journal of Geometric Mechanics, 2020, 12 (3) : 377-394. doi: 10.3934/jgm.2020011 [5] Giovanni F. Gronchi, Chiara Tardioli. The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1323-1344. doi: 10.3934/dcdsb.2013.18.1323 [6] Alain Chenciner, Jacques Féjoz. The flow of the equal-mass spatial 3-body problem in the neighborhood of the equilateral relative equilibrium. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 421-438. doi: 10.3934/dcdsb.2008.10.421 [7] Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre. Periodic orbits for the perturbed planar circular restricted 3–body problem. 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