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http://math.stackexchange.com/questions/151469/how-to-bound-the-order-of-a-finite-group-under-the-following-hypotheses | # How to bound the order of a finite group under the following hypotheses?
In the book Character Theory Of Finite Groups by I.Martin Issacs as exercise 2.14
Let $G$ be a finite group with commutator subgroup $G'$. Let $H \subset G' \cap Z(G)$ be cyclic of order n and let m be the maximum of the orders of elements of G/H. Assume that n is a prime power and show that $|G| \geq n²m$.
I have tried, following the hints given, to show, taking $\chi$ to be an irreducible character whose kernel intersects trivially with $H$, that $\chi(1) \geq n$. But, thus far as I am concerned, I see no idea of how to show the inequality, not to mention the latter part of the proof, as suggested, to deploy the Problem 2.9(b) which states that $\chi(1) \leq |G:A|$ for any abelian subgroup A of G.
I have asked my teacher, who replied that one is to show that $|G/H| \geq nm$, of which the proof I have no idea either. Of course, if one can demonstrate the existence of one subgroup of $G/H$ order $\geq nm$, then the problem should be resolved, as the teacher suggested. But this still bewilders me at present.
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P.S. This question is found at the page 31. – awllower May 30 '12 at 7:57
It was not clear to me from what you wrote whether you had succeeded in proving that $\chi(1) \geq n$ for a character of the type you considered, or whether this is a homework problem. This is the case. Consider an element of $H$ of order $n.$ Let $\sigma$ be an irreducible complex representation affording a character $\chi,$ and assume that $H \cap {\rm ker} \sigma = 1.$ THen $h\sigma$ is a matrix of order $n,$ but must also be a scalar matrix since $\sigma$ is irreducible and $H \leq Z(G).$ Furthermore, ${\rm det} \sigma$ is a $1$-dimensional representation of $G,$ so contains $G^{\prime}$ in its kernel. Since $H \leq G^{\prime},$ we can now conclude that $h\sigma$ is a scalar matrix of order $n$ and determinant $1.$ Let $h \sigma = \omega I$ for some primitive $n$-th root of unity $\omega.$ Then ${\rm det}(h\sigma) = \omega^{\chi(1)}.$ Hence $\omega^{\chi(1)} = 1$ and $\chi(1)$ must be divisible by $n.$ In particular, $\chi(1) \geq n.$ Now let $g \in G$ be an element such that $gH$ has order $m$ in G/H. Let $L = \langle g,H \rangle.$ Then $H \leq Z(L)$ and $L/H$ is cyclic, so $L$ is Abelian, and has order $mn.$ Hence with our character $\chi$ as before, we now have $n \leq \chi(1) \leq [G:L].$ Thus $|G| \geq n|L| \geq n^{2}m.$ I don't think the assumption that $n$ is a prime power is necessary, in fact.
Thanks a lot!! Indeed the part that $\omega$ is of order n, and hence n divides $\chi(1)$ is excellent!! As the book describes, the assumption on n can be removed after further developpments, while I think it is not necessary now. – awllower May 30 '12 at 9:01
The assumption on n, however, turns out to be necessary. Indeed, as $H$ is then a $p$-group, and it is cyclic, we can conclude that there is a faithful irreducible character $\chi$ of $H$, and then by reciprocity find an irreducible character of $G$, whose restriction to $H$ becomes$\chi$, thus obtaining an irreducible character of $G$ which intersects trivially with $H$. Per chance there is still some other way to arrive at the same conclusion? Thanks again. – awllower May 31 '12 at 8:11
I do not understand what you are saying in the two comments above. The inequality in the problem as you originally asked is indeed true whether or not $n$ is a prime power. In any case, any finite cyclic group has a faithful irreducible necessarily degree $1$), whether or not its order is a prime power. If $H = \langle h \rangle$, where $h$ has order $n,$ then define $\sigma : H \to \mathbb{C}$ via $h^{j}\sigma = e^{\frac{2 \pi i j}{n}}.$ – Geoff Robinson May 31 '12 at 9:05 | {"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": 0.9838136434555054, "perplexity": 106.44571919261625}, "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-2013-48/segments/1386163047052/warc/CC-MAIN-20131204131727-00001-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Book%3A_Body_Physics_-_Motion_to_Metabolism_(Davis)/10%3A_Powering_the_Body/10.04%3A_Doing_Work | $$\require{cancel}$$
# 10.4: Doing Work
## Work
So far we have thought about decreasing force during collisions by increasing the time over which the force is applied. Instead of using the impulse, which combines average force and time over which it is applied:
(1)
We can instead combine average force with the distance over which it is applied to define a quantity known as the work.
(2)
The tells us whether the work is transferring energy into or out of a particular object:
1. A force applied to an object in the opposite direction to its motion will tend to slow it down, and thus would transfer kinetic energy out of the object. With energy leaving the object, the work done on the object should be negative. The angle between the object’s motion and the force in such a case is 180° and , so that checks out.
2. A force applied to an object in the same direction to its motion will tend to cause it to speed up, and thus would transfer kinetic energy in to the object. With energy entering the object, the work done on the object should be positive. The angle between the object’s motion and the force in such a case is 0° and so that also checks out.
3. Finally, if a force acts perpendicular to an objects motion it can only change its direction of motion, but won’t cause it to speed up or slow down, so the kinetic energy doesn’t change. That type of force should do zero work. The angle between the object’s motion and the force in such a case is 90° and so once again, the in the work equation gives the required result. For more on this particular type of situation read the chapter on weightlessness at the end of this unit.
Insuknawr, or Rod Pushing Sport is an indigenous game of Mizoram, one of the North Eastern States of India. A force applied in the same direction as an objects motion does positive work. A force applied in the opposite direction to motion does negative work. Image adapted from <a href=”commons.wikimedia.org/wiki/File:Insuknawr(Rod_Pushing_Sport).JPG”>Insuknawr (Rod Pushing Sport by H. Thangchungnunga via Wikimedia Commons
We see that work and kinetic energy both have units of Nm (or J). Work is a quantity of energy, however is not a type of energy. Rather, work is an amount of energy transferred by the application of a force over a distance. Doing work is the act of transferring energy from one form to another and/or one object to another. The sign of the work indicates if energy is coming in or going out, rather than indicating a direction in space like the signs on a vector such as force and velocity. Therefore, we have not made work (W) bold in the previous equation because it is not a vector. Also, when calculating work the accounts for the force direction so we only use the size of the force (F) in the equation, which is why we have not made force bold either.
#### Everyday Example
Let’s apply this concept to our crumple zone example. The crumple zone increases the distance over which the force on the car, from the wall, is applied. That force on the car points in the opposite direction of its motion, thus it will be a negative work that transfers energy out of the car (no work is “absorbed” here, just transferred from kinetic energy to another type). In order to stop, the KE of the car must change from its initial value to zero, therefore the amount of work that needs to be done is equal to the total amount of KE the car had to begin with. The initial KE is determined by the speed and mass of the car, but that work can be done by a larger force over a shorter distance or a smaller force over a longer distance. The crumple zone ensures the force is applied over a longer distance thus smaller force. (If the car didn’t crumple at all, but only received a small dent, then would only be a few centimeters).
The work equation gives the correct work done by a force, no matter the angle between the direction of force and the direction of motion, even if the force points off at some angle other than 0°, 90°, or 180°. In such a case, some part of the force will be doing work and some part won’t, but the tells us just how much of the force vector is contributing to work.
#### Reinforcement Exercises
How much work is done by the larger child pulling the smaller one for a distance of 30.0 m in a wagon as shown?
A child pulls another in a wagon, exerting a force at an angle relative to the direction of motion. “This work” by BC Open Textbooks
1. Adapted from Insuknawr (Rod Pushing Sport by H. Thangchungnunga [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], from Wikimedia Commons | {"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": 0.8746289014816284, "perplexity": 306.4030447446811}, "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-2022-05/segments/1642320301737.47/warc/CC-MAIN-20220120100127-20220120130127-00070.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc/chapter/4/lesson/4.3.1/problem/4-128 | ### Home > PC > Chapter 4 > Lesson 4.3.1 > Problem4-128
4-128.
Find the exact value of each of the following trig expressions.
1. sin $\frac { 5 \pi } { 3 }$
1. Plot the point on a unit circle.
2. Find the sides of this special triangle.
3. Be careful of the signs!
1. cos $\frac { 33 \pi } { 4 }$
$\frac{32\pi}{4}$ bring the point back to $(1,0)$.
1. cot $( - \frac { \pi } { 6 } )$
1. sec $\frac { 3 \pi } { 2 }$
Since the sec\theta; is $\frac{1}{\text{cos}\theta}$, this would be undefined because the $\operatorname{cos}=0$ at $\frac{3\pi}{2}$. | {"extraction_info": {"found_math": true, "script_math_tex": 9, "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": 0.9587125778198242, "perplexity": 3303.7662300546}, "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/1652662512249.16/warc/CC-MAIN-20220516204516-20220516234516-00354.warc.gz"} |
http://science.sciencemag.org/content/318/5854/1291 | Report
# Emission of Coherent THz Radiation from Superconductors
+ See all authors and affiliations
Science 23 Nov 2007:
Vol. 318, Issue 5854, pp. 1291-1293
DOI: 10.1126/science.1149802
## Abstract
Compact solid-state sources of terahertz (THz) radiation are being sought for sensing, imaging, and spectroscopy applications across the physical and biological sciences. We demonstrate that coherent continuous-wave THz radiation of sizable power can be extracted from intrinsic Josephson junctions in the layered high-temperature superconductor Bi2Sr2CaCu2O8. In analogy to a laser cavity, the excitation of an electromagnetic cavity resonance inside the sample generates a macroscopic coherent state in which a large number of junctions are synchronized to oscillate in phase. The emission power is found to increase as the square of the number of junctions reaching values of 0.5 microwatt at frequencies up to 0.85 THz, and persists up to ∼50 kelvin. These results should stimulate the development of superconducting compact sources of THz radiation.
View Full Text | {"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": 0.9233997464179993, "perplexity": 2224.712809843074}, "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-2017-26/segments/1498128320707.69/warc/CC-MAIN-20170626101322-20170626121322-00684.warc.gz"} |
http://cdsweb.cern.ch/collection/NPRC%20-%20Nuclear%20Physics%20Research%20Committee?ln=zh_CN | # NPRC - Nuclear Physics Research Committee
2013-05-30
17:01
PS irradiations during second period of 1962 - Nuclear Chemistry Group / Preiswerk, P 3121/p. - 1962. - 1 p. Full text
2013-05-29
11:54
Decisions of the 18th meeting of the Nuclear Physics Research Committee on December 6th, 1962 / Preiswerk, P 5395/p. - 1962. - 5 p. Fulltext - Fulltext
2007-05-16
04:28
Decisions of the 2nd meeting of the Nuclear Physics Research Committee on April 12th, 1961. (Draft Minutes) CERN-NPRC-2. - 1961. - 6 p. Fulltext
2007-02-07
04:57
Decisions of the 39th meeting of the Nuclear Physics Research Committee on December 2nd, 1964 CERN-NPRC-39. - 1964. - 5 p. Fulltext
2007-02-07
04:57
Decisions of the 38th meeting of the Nuclear Physics Research Committee on November 4th, 1964 CERN-NPRC-38. - 1964. - 5 p. Fulltext
2007-02-07
04:57
Decisions of the 37th meeting of the Nuclear Physics Research Committee on October 7th, 1964 CERN-NPRC-37. - 1964. - 3 p. Fulltext
2007-02-07
04:57
Decisions of the 36th meeting of the Nuclear Physics Research Committee on September 9th, 1964 CERN-NPRC-36. - 1964. - 3 p. Fulltext
2007-02-07
04:57
Decisions of the 35th meeting of the Nuclear Physics Research Committee on July 27th, 1964 CERN-NPRC-35. - 1964. - 4 p. Fulltext
2007-02-07
04:56
Decisions of the 34th meeting of the Nuclear Physics Research Committee on June 10th, 1964 CERN-NPRC-34. - 1964. - 2 p. Fulltext
2007-02-07
04:56
Decisions of the 33rd meeting of the Nuclear Physics Research Committee on May 6th, 1964 CERN-NPRC-33. - 1964. - 2 p. Fulltext | {"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": 0.8989315629005432, "perplexity": 3302.222957204711}, "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/1573496668910.63/warc/CC-MAIN-20191117091944-20191117115944-00520.warc.gz"} |
http://math.stackexchange.com/questions/86457/prove-that-sum-n-1-inftyxn-fracn33n-converges-when-x-2 | Prove that $\sum_{n=1}^{\infty}x^n\frac{(n!)^3}{(3n)!}$ converges when $|x|$ < 27 and diverges when $|x| > 27$
This is a homework question that I am stuck on... I am not sure which test to use to prove this statement. If someone could let me know at least which test to use to push me in the right direction that would be great.
-
Hint: Apply the ratio test. Why the ratio test? Any time there are factorial terms, and powers, it works very well. Recall that if $$r=\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}$$ then $\sum_{n=1}^\infty a_n$ converges absolutely if $r<1$ and diverges if $r>1$.
Hint 2: To get you started on the limit, notice that $$r=\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}=\lim_{n\rightarrow \infty} \frac{x^{n+1}(n+1)!^3}{(3n+3)!}\biggr/ \frac{x^{n}(n!)^3}{(3n)!}$$ $$= \lim_{n\rightarrow \infty}\frac{x^{n+1}(n+1)!^3(3n)!}{x^n(n!)^3(3n+3)!}=x\lim_{n\rightarrow \infty}\frac{(n+1)^3}{(3n+3)(3n+2)(3n+1)}.$$
Last step: This limit is $\frac{1}{27}$ so we see that $r=\frac{x}{27}$. From this when is $r>1$ and when is $r<1$?
@LoganSerman: No problem. As a wide rule the ratio test works well for things like $n!$ and $x^n$, whereas the root test works well for things like $x^n$ and $n^n$. – Eric Naslund Nov 28 '11 at 18:17 | {"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": 0.933673083782196, "perplexity": 101.02366436393338}, "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-2014-23/segments/1404776436274.65/warc/CC-MAIN-20140707234036-00010-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/factorization-and-simplifying.524114/ | # Factorization and Simplifying.
1. Aug 24, 2011
### AstrophysicsX
1. The problem statement, all variables and given/known data
Use Factorization to simplify the given expression.
2. Relevant equations
(x^3 + 3x^2 + 3x +1)/(x^4 + x^3 + x + 1)
3. The attempt at a solution
I cant get to the first step. I forgot how to factor exponents higher than x^2.
2. Aug 24, 2011
### LCKurtz
Think about the binomial expansion of (a+b)3. Also you can check for roots using synthetic division. And remember a root x = r corresponds to a factor of x-r.
3. Aug 24, 2011
### stonecoldgen
Theorem of the factor.
You can probably simplify the upper and the lower part, maybe even cancel out some stuff...
4. Aug 24, 2011
### AstrophysicsX
But how to do that is the problem.
5. Aug 24, 2011
### Dick
If x=(-1) then the numerator and denominator are both 0. That means (x-(-1))=(x+1) is a common factor of the numerator and denominator. Now start factoring it out.
6. Aug 25, 2011
### Staff: Mentor
As others have pointed out, x=-1 is a "solution" to the numerator (equaling zero). So this tells you that (x+1) is a factor of the numerator. So what is the other factor?
If you don't like doing division, you can solve by doing multiplication. To start with, let's look at just the numerator:
x3 + 3x2 + 3x + 1 = (x+1)(x2 + Mx + C)
Multiply the right hand side to remove the brackets, and equate the coefficients on each side to determine the values of the unknowns M and C.
Similar Discussions: Factorization and Simplifying. | {"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": 0.8905631303787231, "perplexity": 1100.4125920323768}, "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-2017-39/segments/1505818689411.82/warc/CC-MAIN-20170922235700-20170923015700-00159.warc.gz"} |
http://mathhelpforum.com/number-theory/204938-my-answers-correct.html | Math Help - Are my answers correct ?
1. Are my answers correct ?
Are the answers I have given correct ?
Attached Thumbnails
2. Re: Are my answers correct ?
No. The first one you checked is not correct.
3. Re: Are my answers correct ?
Are there any other statements left to be checked ? | {"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": 0.8493845462799072, "perplexity": 1254.8511820921888}, "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-2015-48/segments/1448398464386.98/warc/CC-MAIN-20151124205424-00339-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://compaland.com/relative-error/what-is-relative-error.html | ## Repair What Is Relative Error (Solved)
Home > Relative Error > What Is Relative Error
# What Is Relative Error
## Contents
Learn more You're viewing YouTube in English (United Kingdom). Another word for this variation - or uncertainty in measurement - is "error." This "error" is not the same as a "mistake." It does not mean that you got the wrong Did you mean ? ISBN0-8018-5413-X. ^ Helfrick, Albert D. (2005) Modern Electronic Instrumentation and Measurement Techniques. navigate here
When the accepted or true measurement is known, the relative error is found using which is considered to be a measure of accuracy. This works for any measurement system. Maribeth McAnally 7,245 views 2:01 How to work out percent error - Duration: 2:12. Let us see them in an example: Example: fence (continued) Length = 12.5 ±0.05 m So: Absolute Error = 0.05 m And: Relative Error = 0.05 m = 0.004 Check This Out
## Relative Error Formula
Stacie Sayles 3,829 views 8:34 Math Lessons : How to Calculate Relative Error - Duration: 1:52. Please enter a valid email address. This may apply to your measuring instruments as well. EDIT Edit this Article Home » Categories » Education and Communications » Subjects » Mathematics ArticleEditDiscuss Edit ArticleHow to Calculate Relative Error Two Methods:Calculating Absolute ErrorCalculating Relative ErrorCommunity Q&A Absolute error
Relative Error =|Measured−Actual|Actual{\displaystyle ={\frac {|{\mathrm {Measured} }-{\mathrm {Actual} }|}{\mathrm {Actual} }}} Multiply the whole thing by 100 to get Relative Error Percentage all at once.[9] 4 Always provide units as context. b.) The relative error in the length of the field is c.) The percentage error in the length of the field is 3. The precision is said to be the same as the smallest fractional or decimal division on the scale of the measuring instrument. Relative Error Physics For example, you measure a length to be 3.4 cm.
Video Tips Make sure that your experimental value and real value are all expressed in the same unit of measurement. Relative Error Chemistry b.) the relative error in the measured length of the field. Becomean Author! The absolute error is 1 mm.
this is about accuracy. Relative Error Matlab Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Given some value v and its approximation vapprox, the absolute error is ϵ = | v − v approx | , {\displaystyle \epsilon =|v-v_{\text{approx}}|\ ,} where the vertical bars denote
## Relative Error Chemistry
SEE ALSO: Absolute Error, Error Propagation, Percentage Error REFERENCES: Abramowitz, M. Create an account EXPLORE Community DashboardRandom ArticleAbout UsCategoriesRecent Changes HELP US Write an ArticleRequest a New ArticleAnswer a RequestMore Ideas... Relative Error Formula The absolute error of the measurement shows how large the error actually is, while the relative error of the measurement shows how large the error is in relation to the correct Relative Error Definition For example, if a measurement made with a metric ruler is 5.6 cm and the ruler has a precision of 0.1 cm, then the tolerance interval in this measurement is 5.6
Available at http://www.DoreyPublications.com Category Education Licence Standard YouTube Licence Show more Show less Loading... check over here But, if you tried to measure something that was 120 feet long and only missed by 6 inches, the relative error would be much smaller -- even though the value of The greatest possible error when measuring is considered to be one half of that measuring unit. If you are measuring a football field and the absolute error is 1 cm, the error is virtually irrelevant. Absolute Error Formula
Chemistry Expert Share Pin Tweet Submit Stumble Post Share By Anne Marie Helmenstine, Ph.D. Referenced on Wolfram|Alpha: Relative Error CITE THIS AS: Weisstein, Eric W. "Relative Error." From MathWorld--A Wolfram Web Resource. For example, if you measure the width of a book using a ruler with millimeter marks, the best you can do is measure the width of the book to the nearest http://compaland.com/relative-error/what-does-relative-error-mean.html Instruments In most indicating instruments, the accuracy is guaranteed to a certain percentage of full-scale reading. | {"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": 0.906751275062561, "perplexity": 1918.6975286967067}, "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-2018-09/segments/1518891815843.84/warc/CC-MAIN-20180224152306-20180224172306-00416.warc.gz"} |
https://tex.stackexchange.com/questions/111246/align-text-and-numeric-values-by-decimal-in-table-body-using-dcolumn | # Align text and numeric values by decimal in table body using dcolumn
How can I align numeric values in the body of my table by decimal point when some of those values are accompanied by character values? For example, say I wanted to report some standard deviations in a column aligned by decimal point such that each one is enclosed in parentheses. How can I do things like this?
Update Based on answer by David Carlisle
\begin{table}[h]
\begin{tabularx}{\textwidth}{lD{.}{.}{7.4}}
\toprule
\multicolumn{1}{c}{Test} & \multicolumn{1}{c}{Test 2} \\
\midrule
Test & \mathrm{abcde}(1.23)\\
Test2 & (4.321)\\
\bottomrule
\end{tabularx}
\end{table}
It always helps if you provide a document showing the problem, but basically dcolumn doesn't really mind about extra characters. (12.3) and 12.3 would both be aligned on the . If you use the centre on . form then there is nothing else to do; if you use the form D{.}{.}{3.2} to specify the space before and after the . you just need to specify enough space for the text parts, specified in multiples of the width of a digit. | {"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": 0.8537418842315674, "perplexity": 731.2554069421689}, "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-2018-47/segments/1542039746847.97/warc/CC-MAIN-20181120231755-20181121013755-00266.warc.gz"} |
https://deltaepsilons.wordpress.com/category/problem-solving/ | ## Nim-ChompAugust 19, 2010
Posted by lumixedia in combinatorics, math, Problem-solving.
Tags: , ,
Wow, I’m really not cut out for helping to maintain a blog, am I? So what finally prompted me to post was Dr. Khovanova’s description of the game of Nim-Chomp at her blog, which she suggested I respond to.
So Dr. Khovanova described Nim-Chomp to me at RSI more than a year ago, and I thought I solved it. Then a few months ago I found a flaw, thought it was hopeless, and gave up. Then a few minutes ago I realized that the flaw was in fact fixable. The point of this paragraph is that I’m not sure I’m to be trusted regarding this problem, but I’ll try.
I won’t repeat the problem statement here. Too lazy. Just read her post. Because I find it easier to think about this way, I’ll make a slight modification to the Chomp perspective on Nim-Chomp: on a given turn, each player may only eat squares from a single *column* (rather than a single *row*).
First let’s pretend the bottom left square is not actually poisoned. We can transform this easy-Nim-Chomp into regular Nim as follows: for a given position in easy-Nim-Chomp, suppose the number of squares remaining in each column is a1, a2, …, an from left to right. Let b1 = a1 – a2, b2 = a3 – a4, …, b[n/2] = (an-1 – an) or (an) depending on whether n is even or odd. Then this position is equivalent to regular Nim with piles of b1, b2, …, b[n/2]. Basically, we’re splitting the chocolate columns into pairs of adjacent columns and considering the differences between the members of each pair to be the piles of our regular game of Nim. Because the piles are in nonincreasing order, this is a well-defined transformation.
It works as follows: suppose the loser of the Nim-game (b1, b2, …, b[n/2]) eats some squares from the kth column where k is odd. This decreases the value of ak, thereby decreasing one of the Nim-piles as in a regular Nim-game, so the winner just makes the appropriate response. Instead, the loser might try to dodge by eating squares from the kth column where k is even, thus decreasing the value of ak but increasing one of the Nim-piles rather than decreasing it, which can’t be done in regular Nim. But the winner can simply decrease ak-1 by the same amount and leave the loser in the same position as before. There are a finite number of squares, so the loser can’t keep doing this. Eventually they must go back to decreasing piles, and lose.
This is how far I got at RSI. I didn’t realize the poisoned lower-left square was a significant issue, but it is. Thankfully, all it really does (I think) is turn the game into misère Nim rather than normal Nim. We make the transformation to Nim-piles in the same way as before, and the winner uses nearly the same strategy as in the previous paragraph, but they modify it to ensure that the loser is eventually faced with “bk”s which are all 0 or 1 with an odd number of 1s. (Maybe one day if I get around to writing a basic game theory post I’ll explain why this is possible. Or you can check Wikipedia. Or just think about it.) When the loser increases some bk, the winner eats squares in the corresponding column to decrease it back to 0 or 1; when the loser decreases a 1 to a 0, the winner decreases another 1 to a 0.
Eventually, the loser is forced to hand the winner a chocolate bar consisting of pairs of adjacent equal columns. At this point the winner takes a single square from any column for which this is possible, leaving a bunch of 0s with a single 1—i.e. another misère 2nd-player win. This continues until we run out of squares, at which point we conclude that the loser of the new game of misère Nim is indeed the player who consumes the poisoned square in the original game of Nim-Chomp.
Question I’m too lazy to think about right now: can we still do this or something like this if we poison not only the bottom left square of the chocolate bar, but some arbitrary section at the bottom left?
## Some unsolved problemsJanuary 3, 2010
Posted by Damien Jiang in Problem-solving.
Tags: , , , , ,
Happy New Year!
Since we have been too lazy to post lately (and the so-not-lazy Akhil posts mostly elsewhere now), I’m going to post some problems that I probably should be able to solve, but haven’t.
## USAMO 1973 #4August 19, 2009
Posted by lumixedia in algebra, Problem-solving.
Tags: , , , ,
A fairly straightforward algebra problem. Could appear on a modern AMC-12, though the decoy answers would have to be carefully written.
USAMO 1973 #4. Determine all the roots, real or complex, of the system of simultaneous equations
$\displaystyle x+y+z=3$
$\displaystyle x^2+y^2+z^2=3$
$\displaystyle x^3+y^3+z^3=3$
## USAMO 1973 #3August 17, 2009
Posted by lumixedia in combinatorics, Problem-solving.
Tags: , , , ,
1 comment so far
USAMO 1973 #3. Three distinct vertices are chosen at random from the vertices of a given regular polygon of ${(2n+1)}$ sides. If all such choices are equally likely, what is the probability that the center of the given polygon lies in the interior of the triangle determined by the three chosen random points? (more…)
## USAMO 1973 #2August 11, 2009
Posted by lumixedia in Problem-solving.
Tags: , , , , ,
USAMO 1973 #2. Let ${\{X_n\}}$ and ${\{Y_n\}}$ denote two sequences of integers defined as follows:
$\displaystyle X_0=1,\hspace{0.1cm}X_1=1,\hspace{0.1cm}X_{n+1}=X_n+2X_{n-1}\hspace{0.1cm}(n=1,2,3,...)$
$\displaystyle Y_0=1,\hspace{0.1cm}Y_1=7,\hspace{0.1cm}Y_{n+1}=2Y_n+3Y_{n-1}\hspace{0.1cm}(n=1,2,3,...)$
Thus, the first few terms of the sequence are:
$\displaystyle X:\hspace{0.1cm}1,1,3,5,11,21,...$
$\displaystyle Y:\hspace{0.1cm}1,7,17,55,161,487,...$
Prove that, except for “1”, there is no term which occurs in both sequences. (more…)
## USAMO 1973 #1August 7, 2009
Posted by lumixedia in Problem-solving.
Tags: , , , ,
USAMO 1973 #1. Two points, ${P}$ and ${Q}$, lie in the interior of a regular tetrahedron ${ABCD}$. Prove that angle ${PAQ<60^{\circ}}$. (more…)
## USAMO 1972 #5August 4, 2009
Posted by lumixedia in Problem-solving.
Tags: , , , ,
USAMO 1972 #5. A given convex pentagon ${ABCDE}$ has the property that the area of each of the five triangles ${ABC}$, ${BCD}$, ${CDE}$, ${DEA}$, ${EAB}$ is unity. Show that every non-congruent pentagon with the above property has the same area, and that, furthermore, there are an infinite number of such non-congruent pentagons. (more…)
## USAMO 1972 #4July 26, 2009
Posted by lumixedia in Problem-solving.
Tags: , , , ,
USAMO 1972 #4. Let ${R}$ denote a non-negative rational number. Determine a fixed set of integers ${a}$, ${b}$, ${c}$, ${d}$, ${e}$, ${f}$ such that, for every choice of ${R}$,
$\displaystyle |\frac{aR^2+bR+c}{dR^2+eR+f}-\sqrt[3]{2}|<|R-\sqrt[3]{2}|.$ (more…)
## Another IntegralJuly 25, 2009
Posted by Dennis in Problem-solving.
Tags: ,
This is a problem from the Putnam competition I saw two years ago as a freshman, and I did it during my stats class this year. It uses symmetry in a similar way to Akhil’s post.
Find ${\displaystyle\int_{0}^{1}{\frac{\ln(x+1)}{x^2+1}dx}}$.
Let ${\tan(u)=x}$, then
$\displaystyle \begin{array}{rcl} \frac{du}{dx}=\frac{1}{1+x^2}. \end{array}$
and
$\displaystyle \begin{array}{rcl} \int_{0}^{1}{\frac{\ln(x+1)}{x^2+1}dx}=\int_{0}^{\frac{\pi}{4}}{\ln(\tan(u)+1)du}. \end{array}$
Also, we have the identity
$\displaystyle \begin{array}{rcl} \sin(u)+\cos(u)&=&\sqrt{2}(\sin(\frac{\pi}{4})\cos(u)+\cos(\frac{\pi}{4})\sin(u))\\&=&\sqrt{2}(\sin(u+\frac{\pi}{4})) \end{array}$
So
$\displaystyle \begin{array}{rcl} \int_{0}^{\frac{\pi}{4}}{\ln(\tan(u)+1)du}&=&\int_{0}^{\frac{\pi}{4}}{\ln(\frac{\sin(u)+\cos(u)}{\cos(u)})du}\\ &=&\int_{0}^{\frac{\pi}{4}}{\ln(\sin(u)+\cos(u))-\ln(\cos(u))du}\\ &=&\int_{0}^{\frac{\pi}{4}}{\ln(\sqrt{2}(\sin(u+\frac{\pi}{4})))-\ln(\cos(u))du}\\ &=&\int_{0}^{\frac{\pi}{4}}{\frac{\ln(2)}{2}+\ln(\cos(\frac{\pi}{4}-u))-\ln(\cos(u))du}\\ &=&\frac{\pi}{4}\frac{\ln(2)}{2}\\ &=&\frac{\pi\ln(2)}{8} \end{array}$
## A quick integralJuly 24, 2009
Posted by Akhil Mathew in Problem-solving.
Tags: , ,
The integral ${I=\int_0^\pi \log \sin x dx}$ is normally computed (e.g. in Ahlfors’ book) to be ${-\pi \log 2}$ using complex integration over a suitable almost-rectangular contour. There is also a simple and direct way to get the value of this integral by a substitution and elementary calculus.
First, by the substitution ${x=2t}$ and the identity ${\sin(2x)=2\sin x \cos x}$,
$\displaystyle I = 2 \int_0^{\pi/2} \log \sin t dt + 2 \int_0^{\pi/2} \log \cos t dt + \pi \log 2;$
then using the symmetry of ${\sin}$ and ${\cos}$ gives:
$\displaystyle I = I + I + \pi \log 2,$
whence the result. There are slight technicalities regarding the improperness of these integrals, but they can be directly justified (or one may use the Lebesgue integral).
[Edit (7/25)- Todd Trimble posted solutions to similar integrals, which use the result of this post as a lemma, here. AM] | {"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": 43, "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": 0.8602679967880249, "perplexity": 752.8686091440228}, "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/1484560280504.74/warc/CC-MAIN-20170116095120-00130-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://slideplayer.com/slide/236934/ | Estimating the Value of a Parameter Using Confidence Intervals
Presentation on theme: "Estimating the Value of a Parameter Using Confidence Intervals"— Presentation transcript:
Estimating the Value of a Parameter Using Confidence Intervals
Chapter 9 Estimating the Value of a Parameter Using Confidence Intervals
Section 9.1 The Logic in Constructing Confidence Intervals for a Population Mean When the Population Standard Deviation Is Known
Objectives Compute a point estimate of the population mean
Construct and interpret a confidence interval for the population mean assuming that the population standard deviation is known Understand the role of margin of error in constructing the confidence interval Determine the sample size necessary for estimating the population mean within a specified margin of error
Objective 1 Compute a Point Estimate of the Population Mean
A point estimate is the value of a statistic that estimates the value of a parameter.
For example, the sample mean, , is a point estimate of the population mean μ.
Parallel Example 1: Computing a Point Estimate
Pennies minted after 1982 are made from 97.5% zinc and 2.5% copper. The following data represent the weights (in grams) of 17 randomly selected pennies minted after 1982. Treat the data as a simple random sample. Estimate the population mean weight of pennies minted after 1982.
Solution The sample mean is The point estimate of μ is grams.
Objective 2 Construct and Interpret a Confidence Interval for the Population Mean
A confidence interval for an unknown parameter consists of an interval of numbers.
The level of confidence represents the expected proportion of intervals that will contain the parameter if a large number of different samples is obtained. The level of confidence is denoted (1 – α)·100%.
For example, a 95% level of confidence
(α = 0.05) implies that if 100 different confidence intervals are constructed, each based on a different sample from the same population, we will expect 95 of the intervals to contain the parameter and 5 to not include the parameter.
Point estimate ± margin of error.
Confidence interval estimates for the population mean are of the form Point estimate ± margin of error. The margin of error of a confidence interval estimate of a parameter is a measure of how accurate the point estimate is.
The margin of error depends on three factors:
Level of confidence: As the level of confidence increases, the margin of error also increases. Sample size: As the size of the random sample increases, the margin of error decreases. Standard deviation of the population: The more spread there is in the population, the wider our interval will be for a given level of confidence.
The shape of the distribution of all possible sample means will be normal, provided the population is normal or approximately normal, if the sample size is large (n ≥ 30), with mean and standard deviation
Because is normally distributed, we know 95% of all sample means lie within 1.96 standard deviations of the population mean, , and 2.5% of the sample means lie in each tail.
95% of all sample means are in the interval
With a little algebraic manipulation, we can rewrite this inequality and obtain:
Point estimate ± margin of error.
It is common to write the 95% confidence interval as so that it is of the form Point estimate ± margin of error. .
Parallel Example 2: Using Simulation to Demonstrate the
Parallel Example 2: Using Simulation to Demonstrate the Idea of a Confidence Interval We will use Minitab to simulate obtaining 30 simple random samples of size n = 8 from a population that is normally distributed with μ = 50 and σ = 10. Construct a 95% confidence interval for each sample. How many of the samples result in intervals that contain μ = 50 ?
Sample Mean % CI C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , )
SAMPLE MEAN 95% CI C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , ) C ( , )
Note that 28 out of 30, or 93%, of the confidence intervals contain the population mean μ = 50.
In general, for a 95% confidence interval, any sample mean that lies within 1.96 standard errors of the population mean will result in a confidence interval that contains μ. Whether a confidence interval contains μ depends solely on the sample mean, .
Interpretation of a Confidence Interval
A (1 – α)·100% confidence interval indicates that, if we obtained many simple random samples of size n from the population whose mean, μ, is unknown, then approximately (1 – α)·100% of the intervals will contain μ. For example, if we constructed a 99% confidence interval with a lower bound of 52 and an upper bound of 71, we would interpret the interval as follows: “We are 99% confident that the population mean, μ, is between 52 and 71.”
Constructing a (1 – α)·100% Confidence Interval for μ, σ Known
Suppose that a simple random sample of size n is taken from a population with unknown mean, μ, and known standard deviation σ. A (1 – α)·100% confidence interval for μ is given by where is the critical Z-value. Note: The sample size must be large (n≥30) or the population must be normally distributed. Lower Upper Bound: Bound:
Parallel Example 3: Constructing a Confidence Interval
Construct a 99% confidence interval about the population mean weight (in grams) of pennies minted after Assume σ = 0.02 grams.
Weight (in grams) of Pennies
Lower bound: = = = 2.452 Upper bound: = = = 2.476 We are 99% confident that the mean weight of pennies minted after 1982 is between and grams.
A simple random sample of size n < 30 has been obtained
A simple random sample of size n < 30 has been obtained. From the normal probability plot and boxplot, judge whether a Z-interval should be constructed. Yes No data Copyright © 2010 Pearson Education, Inc.
A simple random sample of size n < 30 has been obtained
A simple random sample of size n < 30 has been obtained. From the normal probability plot and boxplot, judge whether a Z-interval should be constructed. Yes No data Copyright © 2010 Pearson Education, Inc.
Objective 3 Understand the Role of the Margin of Error in Constructing a Confidence Interval
where n is the sample size.
The margin of error, E, in a (1 – α)·100% confidence interval in which σ is known is given by where n is the sample size. Note: We require that the population from which the sample was drawn be normally distributed or the samples size n be greater than or equal to 30.
Parallel Example 5: Role of the Level of Confidence in the
Parallel Example 5: Role of the Level of Confidence in the Margin of Error Construct a 90% confidence interval for the mean weight of pennies minted after Comment on the effect that decreasing the level of confidence has on the margin of error.
Lower bound: = = = 2.456 Upper bound: = = = 2.472 We are 90% confident that the mean weight of pennies minted after 1982 is between and grams.
Notice that the margin of error decreased from 0. 012 to 0
Notice that the margin of error decreased from to when the level of confidence decreased from 99% to 90%. The interval is therefore wider for the higher level of confidence. Confidence Level Margin of Error Interval 90% 0.008 (2.456, 2.472) 99% 0.012 (2.452, 2.476)
Parallel Example 6: Role of Sample Size in the Margin of Error
Suppose that we obtained a simple random sample of pennies minted after Construct a 99% confidence interval with n = 35. Assume the larger sample size results in the same sample mean, The standard deviation is still σ = Comment on the effect increasing sample size has on the width of the interval.
Lower bound: = = = 2.455 Upper bound: = = = 2.473 We are 99% confident that the mean weight of pennies minted after 1982 is between and grams.
Notice that the margin of error decreased from 0. 012 to 0
Notice that the margin of error decreased from to when the sample size increased from 17 to 35. The interval is therefore narrower for the larger sample size. Sample Size Margin of Error Confidence Interval 17 0.012 (2.452, 2.476) 35 0.009 (2.455, 2.473)
Objective 4 Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error
Determining the Sample Size n
The sample size required to estimate the population mean, μ, with a level of confidence (1 – α)·100% with a specified margin of error, E, is given by where n is rounded up to the nearest whole number.
Parallel Example 7: Determining the Sample Size
Back to the pennies. How large a sample would be required to estimate the mean weight of a penny manufactured after 1982 within grams with 99% confidence? Assume σ = 0.02.
σ = 0.02 E=0.005 Rounding up, we find n=107.
A CEO wants to estimate the mean age of employees at a company
A CEO wants to estimate the mean age of employees at a company. How many employees should be in a sample to estimate the mean age to within 0.5 year with 95% confidence? Assume that σ = 4.8 years. 18 19 354 355
A CEO wants to estimate the mean age of employees at a company
A CEO wants to estimate the mean age of employees at a company. How many employees should be in a sample to estimate the mean age to within 0.5 year with 95% confidence? Assume that σ = 4.8 years. 18 19 354 355 Copyright © 2010 Pearson Education, Inc.
End Here
Section 9.2 Confidence Intervals about a Population Mean When the Population Standard Deviation is Unknown
Objectives Know the properties of Student’s t-distribution
2. Determine t-values 3. Construct and interpret a confidence interval for a population mean
Objective 1 Know the Properties of Student’s t-Distribution
Student’s t-Distribution
Suppose that a simple random sample of size n is taken from a population. If the population from which the sample is drawn follows a normal distribution, the distribution of follows Student’s t-distribution with n-1 degrees of freedom where is the sample mean and s is the sample standard deviation.
Compute and for each sample.
Parallel Example 1: Comparing the Standard Normal Distribution to the t-Distribution Using Simulation Obtain 1,000 simple random samples of size n = 5 from a normal population with μ = 50 and σ = 10. Determine the sample mean and sample standard deviation for each of the samples. Compute and for each sample. Draw a histogram for both z and t.
Histogram for z
Histogram for t
CONCLUSIONS: The histogram for z is symmetric and bell-shaped with the center of the distribution at 0 and virtually all the rectangles between -3 and 3. In other words, z follows a standard normal distribution. The histogram for t is also symmetric and bell-shaped with the center of the distribution at 0, but the distribution of t has longer tails (i.e., t is more dispersed), so it is unlikely that t follows a standard normal distribution. The additional spread in the distribution of t can be attributed to the fact that we use s to find t instead of σ. Because the sample standard deviation is itself a random variable (rather than a constant such as σ), we have more dispersion in the distribution of t.
Properties of the t-Distribution
The t-distribution is different for different degrees of freedom. The t-distribution is centered at 0 and is symmetric about 0. The area under the curve is 1. The area under the curve to the right of 0 equals the area under the curve to the left of 0 equals 1/2. As t increases without bound, the graph approaches, but never equals, zero. As t decreases without bound, the graph approaches, but never equals, zero.
Properties of the t-Distribution
The area in the tails of the t-distribution is a little greater than the area in the tails of the standard normal distribution, because we are using s as an estimate of σ, thereby introducing further variability into the t- statistic. As the sample size n increases, the density curve of t gets closer to the standard normal density curve. This result occurs because, as the sample size n increases, the values of s get closer to the values of σ, by the Law of Large Numbers.
Objective 2 Determine t-Values
Parallel Example 2: Finding t-values
Find the t-value such that the area under the t-distribution to the right of the t-value is 0.2 assuming 10 degrees of freedom. That is, find t0.20 with 10 degrees of freedom.
Solution The figure to the left shows the graph of the
t-distribution with 10 degrees of freedom. The unknown value of t is labeled, and the area under the curve to the right of t is shaded. The value of t0.20 with 10 degrees of freedom is
Objective 3 Construct and Interpret a Confidence Interval for a Population Mean
Constructing a (1 – α)×100% Confidence Interval for μ, σ Unknown
Suppose that a simple random sample of size n is taken from a population with unknown mean μ and unknown standard deviation σ. A (1– α)×100% confidence interval for μ is given by Lower Upper bound: bound: Note: The interval is exact when the population is normally distributed. It is approximately correct for non-normal populations, provided that n is large enough.
Construct a 95% confidence interval for the bacteria count.
Parallel Example 3: Constructing a Confidence Interval about a Population Mean The pasteurization process reduces the amount of bacteria found in dairy products, such as milk. The following data represent the counts of bacteria in pasteurized milk (in CFU/mL) for a random sample of 12 pasteurized glasses of milk. Data courtesy of Dr. Michael Lee, Professor, Joliet Junior College. Construct a 95% confidence interval for the bacteria count.
NOTE: Each observation is in tens of thousand.
So, 9.06 represents 9.06 x 104.
Solution: Checking Normality and Existence of Outliers
Normal Probability Plot for CFU/ml
Solution: Checking Normality and Existence of Outliers
Boxplot of CFU/mL
Lower bound: Upper The 95% confidence interval for the mean bacteria count in pasteurized milk is (3.52, 9.30).
Parallel Example 5: The Effect of Outliers
Suppose a student miscalculated the amount of bacteria and recorded a result of 2.3 x We would include this value in the data set as 23.0. What effect does this additional observation have on the 95% confidence interval?
Solution: Checking Normality and Existence of Outliers
Boxplot of CFU/mL
Solution Lower bound: Upper
The 95% confidence interval for the mean bacteria count in pasteurized milk, including the outlier is (3.86, 11.52).
CONCLUSIONS: With the outlier, the sample mean is larger because the sample mean is not resistant With the outlier, the sample standard deviation is larger because the sample standard deviation is not resistant Without the outlier, the width of the interval decreased from 7.66 to 5.78. s 95% CI Without Outlier 6.41 4.55 (3.52, 9.30) With 7.69 6.34 (3.86, 11.52)
Confidence Intervals for a Population Proportion
Section 9.3 Confidence Intervals for a Population Proportion
Objectives Obtain a point estimate for the population proportion
Construct and interpret a confidence interval for the population proportion Determine the sample size necessary for estimating a population proportion within a specified margin of error
Objective 1 Obtain a point estimate for the population proportion
A point estimate is an unbiased estimator of the parameter
A point estimate is an unbiased estimator of the parameter. The point estimate for the population proportion is where x is the number of individuals in the sample with the specified characteristic and n is the sample size.
Parallel Example 1: Calculating a Point Estimate for the
Parallel Example 1: Calculating a Point Estimate for the Population Proportion In July of 2008, a Quinnipiac University Poll asked 1783 registered voters nationwide whether they favored or opposed the death penalty for persons convicted of murder were in favor. Obtain a point estimate for the proportion of registered voters nationwide who are in favor of the death penalty for persons convicted of murder.
Solution Obtain a point estimate for the proportion of registered voters nationwide who are in favor of the death penalty for persons convicted of murder.
Objective 2 Construct and Interpret a Confidence Interval for the Population Proportion
Sampling Distribution of
For a simple random sample of size n, the sampling distribution of is approximately normal with mean and standard deviation , provided that np(1 – p) ≥ 10. NOTE: We also require that each trial be independent when sampling from finite populations.
Constructing a (1-α)·100% Confidence
Interval for a Population Proportion Suppose that a simple random sample of size n is taken from a population. A (1-α)·100% confidence interval for p is given by the following quantities Lower bound: Upper bound: Note: It must be the case that and n ≤ 0.05N to construct this interval.
Parallel Example 2: Constructing a Confidence Interval for a
Parallel Example 2: Constructing a Confidence Interval for a Population Proportion In July of 2008, a Quinnipiac University Poll asked 1783 registered voters nationwide whether they favored or opposed the death penalty for persons convicted of murder were in favor. Obtain a 90% confidence interval for the proportion of registered voters nationwide who are in favor of the death penalty for persons convicted of murder.
Solution and the sample size is definitely less than 5% of the population size α =0.10 so zα/2=z0.05=1.645 Lower bound: Upper bound:
Solution We are 90% confident that the proportion of registered voters who are in favor of the death penalty for those convicted of murder is between 0.61and 0.65.
Objective 3 Determine the Sample Size Necessary for Estimating a Population Proportion within a Specified Margin of Error
Sample size needed for a specified margin of error, E, and level of confidence (1 – α):
Problem: The formula uses which depends on n, the quantity we are trying to determine!
Two possible solutions:
Use an estimate of p based on a pilot study or an earlier study. Let = 0.5 which gives the largest possible value of n for a given level of confidence and a given margin of error.
The sample size required to obtain a (1 – α)·100% confidence interval for p with a margin of error E is given by (rounded up to the next integer), where is a prior estimate of p. If a prior estimate of p is unavailable, the sample size required is
Parallel Example 4: Determining Sample Size
A sociologist wanted to determine the percentage of residents of America that only speak English at home. What size sample should be obtained if she wishes her estimate to be within 3 percentage points with 90% confidence assuming she uses the 2000 estimate obtained from the Census 2000 Supplementary Survey of 82.4%?
Solution E=0.03 We round this value up to The sociologist must survey 437 randomly selected American residents.
Putting It Together: Which Procedure Do I Use?
Section 9.4 Putting It Together: Which Procedure Do I Use?
Objective Determine the appropriate confidence interval to construct
Objective 1 Determine the Appropriate Confidence Interval to Construct
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http://mathoverflow.net/questions/65340/paracompact-hausdorff-but-not-compactly-generated?sort=oldest | # Paracompact Hausdorff but not compactly generated?
I'm sorry to be asking a (possibly) elementary question, but I've run into a problem in point-set topology; I've just read that there exists paracompact Hausdoff spaces which are not compactly generated. I ask the following:
Question: If $X$ is paracompact Hausdorff, is its compactly generated replacement, $k\left(X\right),$ paracompact Hausdorff?
Recall: The inclusion $i:CGH \to Haus$ of compactly generated Hausdorff spaces into Hausdorff spaces has a right adjoint $k,$ which replaces the topology of $X$ with the following topology:
$U \subset X$ is open in $k\left(X\right)$ if and only if for all compact subsets $K \subset X,$ $U \cap K$ is open in $K$.
Another way of describing this topology is that it is the final topology with respect to all maps into $X$ with compact Hausdorff domain. (For the experts, $CGH$ is the mono-coreflective Hull of the category of compact Hausdorff spaces in the category of Hausdorff spaces)
-
It seems that it's certainly Hausdorff, as the topology of $k(X)$ is finer (if $U$ is open in $X$ then $U\cap K$ is open in $K$ for all compacta $K$, by definition of the subspace topology.) So the two separating sets that worked for $X$ still work for $k(X)$. – wildildildlife May 18 '11 at 22:33
Yes, it is indeed Hausdorff; I know that $k$ is a functor $$k:Haus \to CGH,$$ the question is whether or not it is paracompact. – David Carchedi May 18 '11 at 23:47
Every compactly generated space is a quotient of a locally compact Hausdorff space. That may help, but not in the naive way. You definitely can't conclude $k(X)$ is paracompact just because it's a quotient of a paracompact space. – David White May 22 '11 at 19:13
Thanks, I'm aware of this result, but I'm not sure how to use it. In fact, this is and if and only if, i.e. it characterizes compactly generated spaces. Moreover, for compactly generated Hausdorff spaces, they are the obvious quotient of the disjoint union of all their compact subsets, and if $X$ is not compactly generated, this quotient is $k\left(X\right).$ This means when $X$ is paracompact Hausdorff, $k\left(X\right)$ is a quotient of a space which is is both locally compact and paracompact Hausdorff. I'm not sure where to go from here. – David Carchedi May 23 '11 at 1:31
It suffices to find a paracompact Hausdorff space $X$ whose $k$-coreflexion $k(X)$ is not regular. For sequential coreflexions such a compact Hausdorff space was constructed by Franklin and Rajagopalan in 1970 (see repository.cmu.edu/cgi/…). – Taras Banakh Sep 13 '15 at 20:02 | {"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": 0.9134988188743591, "perplexity": 194.33342573700935}, "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/1461860116173.76/warc/CC-MAIN-20160428161516-00212-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://davefernig.com/2018/05/07/solving-sat-in-python/ | # solving SAT in python
SAT is hard, but there are algorithms that tend to do okay empirically. I recently learned about the Davis-Putnam-Logemann-Loveland (DPLL) procedure and rolled up a short Python implementation.
#### (I can’t get no) satisfaction
A boolean formula is called “satisfiable” if you can assign truth values to the underlying atoms in such a way that the entire formula comes out true. For example, the formula $p \land \lnot q$ is satisfiable: just set $p$ to true and $q$ to false. By contrast, the formula $p \land \lnot p$ is “unsatisfiable” because it comes out false irrespective of what value you assign to $p$.
The general problem – does a satisfying assignment exist for a given formula – is called boolean satisfiability (SAT). It turns out that solving SAT is equivalent to solving the restricted problem of 3SAT. This makes representation easier so I focused on that. The problem of 3SAT is the same, except that we only consider formulae in 3CNF (conjunctive normal form). That is, formulae that are conjunctions where every conjunct is a disjunction of three literals. For example, the formula $(p \lor \lnot q \lor r) \land (p \lor q \lor \lnot s)$ is in 3CNF; the formula $(p \lor \lnot q \land r) \lor (p \lor \lnot s)$ is not.
John Franco and John Martin have written extensively on the history of SAT, which goes as far back as Aristotle. The problem received attention from medieval, enlightenment, and early analytic philosophers. Modern computational approaches emerged in the middle of the last century. The DPLL procedure was published in 1962 (here’s the original paper). Its core ideas remain important ingredients in modern SAT solvers.
#### representation
After a brief and irritating foray down the OOP path, I decided to use raw types to represent everything. My code uses the following conventions:
A literal is a tuple consisting of a name and a sign. E.g. $\lnot p$ is represented as:
```("p", False)
```
A disjunctive clause is a set of literals. E.g. $p \lor \lnot q \lor r$ is represented as:
```{("p", True), ("q", False), ("r", True)}
```
A CNF formula is a list of disjunctive clauses. E.g. $(p \lor \lnot q) \land (p \lor r)$ is represented as:
```[{("p", True), ("q", False)}, {("p", True), ("r", True)}]
```
#### the naive approach
The simplest way to solve sat is to try everything. Given a single assignment (represented as a set of literals), we can determine if it satisfies the formula by testing whether it intersects with every conjunct. To test if the formula is satisfiable, we iterate over all assignments, testing each as we go.
```def brute_force(cnf):
literals = set()
for conj in cnf:
for disj in conj:
literals = list(literals)
n = len(literals)
for seq in itertools.product([True,False], repeat=n):
a = set(zip(literals, seq))
if all([bool(disj.intersection(a)) for disj in cnf]):
return True, a
return False, None
```
#### davis-putnam-logemann-loveland
The DPLL procedure is a recursive search algorithm. The base cases are those of an empty conjunct, which is true, and a conjunct containing an empty disjunct, which is false. (If you find the latter off-putting read this explanation). The recursion case then deals with a non-empty CNF formula that has no empty clauses. We pick an arbitrary literal and set it to true. This means that all conjuncts containing the literal drop out, and all conjuncts containing its negation have its negation removed. Then we recurse. If this doesn’t result in a satisfying assignment, we set the same literal to false and repeat the same procedure.
```def __select_literal(cnf):
for c in cnf:
for literal in c:
return literal[0]
def dpll(cnf, assignments={}):
if len(cnf) == 0:
return True, assignments
if any([len(c)==0 for c in cnf]):
return False, None
l = __select_literal(cnf)
new_cnf = [c for c in cnf if (l, True) not in c]
new_cnf = [c.difference({(l, False)}) for c in new_cnf]
sat, vals = dpll(new_cnf, {**assignments, **{l: True}})
if sat:
return sat, vals
new_cnf = [c for c in cnf if (l, False) not in c]
new_cnf = [c.difference({(l, True)}) for c in new_cnf]
sat, vals = dpll(new_cnf, {**assignments, **{l: False}})
if sat:
return sat, vals
return False, None
```
#### experiments
I used the following code to generate random 3CNF formulae:
```def random_kcnf(n_literals, n_conjuncts, k=3):
result = []
for _ in range(n_conjuncts):
conj = set()
for _ in range(k):
index = random.randint(0, n_literals)
str(index).rjust(10, '0'),
bool(random.randint(0,2)),
))
result.append(conj)
return result
```
I then compared the performance of the brute force approach and DPLL over various numbers of literals. Each scores is averaged over one hundred random formulae.
Full code can be found here. | {"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": 10, "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": 0.8374596238136292, "perplexity": 727.6992628576934}, "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/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00068.warc.gz"} |
https://proofwiki.org/wiki/Rational_Numbers_form_Ring | # Rational Numbers form Ring
## Theorem
The set of rational numbers $\Q$ forms a ring under addition and multiplication: $\struct {\Q, +, \times}$.
## Proof
Recall that $\struct {\Q, +, \times}$ is a field.
As a field is also by definition a division ring, which is an example of a ring, the result follows.
$\blacksquare$ | {"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": 0.9782872796058655, "perplexity": 312.9690787852338}, "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-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00031.warc.gz"} |
https://studyadda.com/solved-papers/jee-main-advanced/jee-main-online-paper-held-on-12-jan-2019-evening/610 | # Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 12-Jan-2019 Evening)
### done JEE Main Online Paper (Held On 12-Jan-2019 Evening)
• question_answer1) A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is [Take $g=10\text{ }m/{{s}^{2}}$] [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{1}{2}$
B) $\frac{\sqrt{3}}{2}$
C) $\frac{\sqrt{3}}{4}$
D) $\frac{2}{3}$
• question_answer2) Formation of real image using a biconvex lens is shown below If the whole set up is immersed in water without disturbing the object and the screen positions what will one observe on the screen? [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) Image disappears
B) Magnified image
C) Erect real image
D) No change
• question_answer3) An alpha-particle of mass m suffers -dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 4 m
B) 1.5 m
C) 3.5 m
D) 2 m
• question_answer4) A simple harmonic motion is represented by $y=5(sin3\pi t+\sqrt{3}cos3\pi t)cm$ The amplitude and time period of the motion are [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $5cm,\frac{3}{2}s$
B) $10cm,\frac{2}{3}s$
C) $5cm,\frac{2}{3}s$
D) $10cm,\frac{3}{2}s$
• question_answer5) A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 0.4
B) 2.0
C) 0.1
D) 1.2
• question_answer6) A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 m ${{s}^{-1}}$, at right angles to the horizontal component of the earths magnetic field of $0.3\times {{10}^{-4}}Wb/{{m}^{2}}.$ The value of the induced emf in wire is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $0.3\times {{10}^{-3}}V$
B) $2.5\times {{10}^{-3}}V$
C) $1.5\times {{10}^{-3}}V$
D) $1.1\times {{10}^{-3}}V$
• question_answer7) A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
E) None of these
• question_answer8) In the given circuit, $C=\frac{\sqrt{3}}{2}\mu F,{{R}_{2}}=20\Omega ,$and${{R}_{1}}=10\Omega .$Current in $L-{{R}_{1}}$path is ${{I}_{1}}$and in $C-{{R}_{2}}$ path it is ${{I}_{2}}.$The voltage of A.C source is given by, $V=200\sqrt{2}\sin (100t)$volts. The phase difference between ${{I}_{1}}$ and ${{I}_{2}}$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 0
B) $30{}^\circ$
C) $90{}^\circ$
D) $60{}^\circ$
E) None of these
• question_answer9) An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is $6\times {{10}^{-8}}s.$If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $4\times {{10}^{-8}}s$
B) $3\times {{10}^{-6}}s$
C) $0.5\times {{10}^{-8}}s$
D) $2\times {{10}^{-7}}s$
• question_answer10) In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 220 nm
B) 1700 nm
C) 250 nm
D) 2020 nm
• question_answer11) A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is${{l}_{1}}$and that below the piston is${{l}_{2}},$such that ${{l}_{1}}>{{l}_{2}}.$Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass m, will be given by (R is universal gas constant and g is the acceleration due to gravity) [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{RT}{ng}\left[ \frac{{{l}_{1}}-3{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]$
B) $\frac{nRT}{g}\left[ \frac{1}{{{l}_{2}}}+\frac{1}{{{l}_{1}}} \right]$
C) $\frac{RT}{g}\left[ \frac{2{{l}_{1}}+{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]$
D) $\frac{nRT}{g}\left[ \frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]$
• question_answer12) A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 4.0 mm
B) zero
C) 5.0 mm
D) 3.0 mm.
• question_answer13) A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1m. If the electric field between the plates is $100\,\,N\,\,{{C}^{-1}},$the magnitude of charge on each plate is $\left( \text{Take}\,{{\varepsilon }_{0}}=8.85\times {{10}^{-12}}\frac{{{C}^{2}}}{N{{m}^{2}}} \right)$ [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $8.85\times {{10}^{-10}}C$
B) $7.85\times {{10}^{-10}}C$
C) $9.85\times {{10}^{-10}}C$
D) $6.85\times {{10}^{-10}}C$
• question_answer14) The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure, What is the value of current at t = 4 s? [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $3\mu A$
B) zero
C) $1.5\mu A$
D) $2\mu A$
• question_answer15) In the circuit shown, find C if the effective capacitance of the whole circuit is to be $0.5\,\,\mu F.$All values in the circuit are in $\mu F.$ [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{6}{5}\mu F$
B) $4\mu F$
C) $\frac{7}{11}\mu F$
D) $\frac{7}{10}\mu F$
• question_answer16) Let $l,\,\,r,\,\,c$ and $v$ represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{l}{rcv}$in SI units will be [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $[L{{A}^{-2}}]$
B) $[L{{T}^{2}}]$
C) $[{{A}^{-1}}]$
D) $[LTA]$
• question_answer17) Two satellites, A and B, have masses m and 2 m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, $\frac{{{T}_{A}}}{{{T}_{B}}},$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 1
B) 2
C) $\sqrt{\frac{1}{2}}$
D) $\frac{1}{2}$
• question_answer18) The mean intensity of radiation on the surface of the Sun is about ${{10}^{8}}W/{{m}^{2}}$. The rms value of the corresponding magnetic field is closest to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{10}^{-2}}T$
B) $1T$
C) ${{10}^{-4}}T$
D) ${{10}^{2}}T$
• question_answer19) A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $335m\,{{s}^{-1}}$
B) $322m\,{{s}^{-1}}$
C) $328m\,{{s}^{-1}}$
D) $341m\,{{s}^{-1}}$
• question_answer20) In the figure, given that ${{V}_{BB}}$supply can vary from 0 to $5.0V,$${{V}_{CC}}=5V,{{\beta }_{dc}}=200,$${{R}_{B}}=100k\Omega ,$${{R}_{C}}=1\,k\Omega$and${{V}_{BE}}=1.0\,V.$ The minimum base current and the input voltage at which the transistor will go to saturation, will be respectively [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $20\mu A$and 3.5 V
B) $25\mu A$and 3.5V
C) $20\mu A$ and 2.8 V
D) $25\mu A$ and 2.8 V
• question_answer21) In the given circuit diagram, the currents, ${{I}_{1}}=0.3A,{{I}_{4}}=0.8A$and ${{I}_{5}}=0.4A,$are flowing as shown. The currents ${{I}_{2}},{{I}_{3}}$and ${{I}_{6}},$respectively, are [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $1.1\text{ }A,\text{ }0.4\text{ }A,\text{ }0.4\text{ }A$
B) $-0.4A,\,\,0.4A,\,\,1.1A$
C) $1.1\text{ }A,\,\,-0.4\text{ }A,\,\,0.4\text{ }A$
D) $0.4A,\,\,1.1A,\,\,0.4A$
• question_answer22) When a certain photosensitive surface is illuminated with monochromatic light of frequency u, the stopping potential for the photo current is$\frac{-{{V}_{0}}}{2}.$When the surface is illuminated by monochromatic light of frequency$\frac{\upsilon }{2},$the stopping potential is$-{{V}_{0}}.$ The threshold frequency for photoelectric emission is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{4\upsilon }{3}$
B) $2\upsilon$
C) $\frac{5\upsilon }{3}$
D) $\frac{3\upsilon }{2}$
• question_answer23) A paramagnetic material has${{10}^{28}}\,\,atoms/{{m}^{3}}$. Its magnetic susceptibility at temperature 350 K is $2.8\times {{10}^{-4}}.$ Its susceptibility at 300 K is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $3.267\times {{10}^{-4}}$
B) $3.672\times {{10}^{-4}}$
C) $2.672\times {{10}^{-4}}$
D) $3.726\times {{10}^{-4}}$
• question_answer24) A plano-convex lens (focal lengthy${{f}_{2}}$, refractive index ${{\mu }_{2}},$radius of curvature R) fits exactly into a plano-concave lens (focal length ${{f}_{1}},$refractive index ${{\mu }_{1}},$radius of curvature -R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{f}_{1}}+{{f}_{2}}$
B) $\frac{R}{{{\mu }_{2}}-{{\mu }_{1}}}$
C) ${{f}_{1}}-{{f}_{2}}$
D) $\frac{2{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}$
• question_answer25) A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of $4\times {{10}^{-4}}$A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 200 ohm
B) 6250 ohm
C) 6200 ohm
D) 250 ohm
• question_answer26) Two particles A, B are moving on two concentric circles of radii ${{R}_{1}}$and ${{R}_{2}}$with equal angular speed$\omega$. At t = 0, their positions and direction of motion are shown in the figure. The relative velocity ${{\vec{v}}_{A}}-{{\vec{v}}_{B}}$at $t=\frac{\pi }{2\omega }$is given by [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $-\omega ({{R}_{1}}+{{R}_{2}})\hat{i}$
B) $\omega ({{R}_{1}}-{{R}_{2}})\hat{i}$
C) $\omega ({{R}_{2}}-{{R}_{1}})\hat{i}$
D) $-\omega ({{R}_{1}}+{{R}_{2}})\hat{i}$
• question_answer27) The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is I(x). Which one of the graphs represents the variation of I(x) with x correctly? [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
• question_answer28) To double the covering range, or' a TV transmission tower, its height should be multiplied by [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{1}{\sqrt{2}}$
B) 2
C) 4
D) $\sqrt{2}$
• question_answer29) In a radioactive decay chain, the initial nucleus is $_{90}^{232}Th.$At the end there are $6\alpha -$particles and $4\beta -$particles which are emitted. it the end nucleus is $_{Z}^{A}X,$ A and Z are given by [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $A=202;\text{ }Z=80$
B) $A=200;\text{ }Z=81$
C) $A=208;\text{ }Z=80$
D) $A=208;\text{ }Z=82$
• question_answer30) A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be (Take$g=10m/{{s}^{2}}$) [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $6kg-{{m}^{2}}/s$
B) $8kg-{{m}^{2}}s$
C) $3kg-{{m}^{2}}s$
D) $2kg-{{m}^{2}}/s$
• question_answer31) The pair that does not require calcination is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $ZnO$and$F{{e}_{2}}{{O}_{3}}.x{{H}_{2}}O$
B) $ZnC{{O}_{3}}$and$CaO$
C) $ZnO$and$MgO$
D) $F{{e}_{2}}{{O}_{3}}$and$CaC{{O}_{3}}.MgC{{O}_{3}}$
• question_answer32) The two monomers for the synthesis of Nylon 6,6 are [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $HOOC{{(C{{H}_{2}})}_{6}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{6}}N{{H}_{2}}$
B) $HOOC{{(C{{H}_{2}})}_{6}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{4}}N{{H}_{2}}$
C) $HOOC{{(C{{H}_{2}})}_{4}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{6}}N{{H}_{2}}$
D) $HOOC{{(C{{H}_{2}})}_{4}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{4}}N{{H}_{2}}$
• question_answer33) 8 g of NaOH is dissolved in 18 g of ${{H}_{2}}O.$ Mole fraction of $NaOH$in solution and molality (in $mol\,k{{g}^{-1}}$) of the solution respectively are [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 0.167, 22.20
B) 0.167, 11.11
C) 0.2, 22.20
D) 0.2, 11.11
• question_answer34) The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are
I. They activate many enzymes. II. They participate in the oxidation of glucose to produce ATP. III. Along with sodium ions, they are responsible for the transmission of nerve signals.
[JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) III only
B) I and II only
C) I, II and III
D) I and III only
• question_answer35) The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 B.M. The suitable ligand for this complex is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $NC{{S}^{-}}$
B) $C{{N}^{-}}$
C) CO
D) ethylenediamine
• question_answer36) Among the following, the false statement is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) it is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane
B) lyophilic sol can be coagulated by adding an electrolyte
C) Tyndall effect can be used to distinguish between a colloidal solution and a true solution
D) latex is a colloidal solution of rubber particles which are positively charged.
• question_answer37) The element that shows greater ability to form $p\pi -p\pi$ multiple bonds is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) C
B) Ge
C) Sn
D) Si
• question_answer38) The aldehydes which will not form Grignard product with one equivalent Grignard reagent are
[JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) (C, D)
B) (B, D)
C) (B, C, D)
D) (B, C)
• question_answer39) The correct structure of histidine in a strongly acidic solution (pH = 2) is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
• question_answer40) The major product of the following reaction is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
• question_answer41) The major product of the following reaction is $C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\xrightarrow[(ii)\,\,NaN{{H}_{2}}in\,liq.N{{H}_{3}}]{(i)\,KOH\,alc.}$ [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $C{{H}_{3}}CH=C=C{{H}_{2}}$
B) $C{{H}_{3}}C{{H}_{2}}C\equiv CH$
C) $C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,$
D) $C{{H}_{3}}CH=CHC{{H}_{2}}N{{H}_{2}}$
• question_answer42) Chlorine on reaction with hot and concentrated sodium hydroxide gives [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $C{{l}^{-}}\,\text{and}\,ClO_{3}^{-}$
B) $C{{l}^{-}}\,\text{and}\,ClO_{2}^{-}$
C) $C{{l}^{-}}\,\text{and}\,ClO_{{}}^{-}$
D) $ClO_{3}^{-}\,\text{and}\,ClO_{2}^{-}$
• question_answer43) The combination of plots which does not represent isothermal expansion of an ideal gas is
[JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) B and D
B) A and D
C) B and C
D) A and C
• question_answer44) The major product of the following reaction is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
(i)${{C}_{(graphite)}}+{{O}_{2(g)}}\to C{{O}_{2(g)}};{{\Delta }_{r}}{{H}^{o}}=xkJ\,mo{{l}^{-1}}$ (ii)${{C}_{(graphite)}}+\frac{1}{2}{{O}_{2(g)}}\to C{{O}_{(g)}};$${{\Delta }_{r}}{{H}^{o}}=y\,\,kJ\,\,mo{{l}^{-1}}$ (iii)$C{{O}_{(g)}}+\frac{1}{2}{{O}_{2(g)}}\to C{{O}_{2}}_{(g)};{{\Delta }_{r}}{{H}^{o}}=z\,\,kJ\,\,mo{{l}^{-1}}$
Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct? [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $z=x+y$
B) $x=y-z$
C) $x=y+z$
D) $y=2zx$
• question_answer46) The major product of the following reaction is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
• question_answer47) The volume strength of $1M\,{{H}_{2}}{{O}_{2}}$is (molar mass of $\,{{H}_{2}}{{O}_{2}}=34g\,mo{{l}^{-1}}$) [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 22.4
B) 16.8
C) 5.6
D) 11.35
• question_answer48) The upper stratosphere consisting of the ozone layer protects us from the suns radiation that falls in the wavelength region of [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 400-550 nm
B) 600-750 nm
C) 200-315 nm
D) 0.8-1.5 nm
• question_answer49) For a reaction, consider the plot of In k versus 1/r given in the figure. If the rate constant of this reaction at 400 K is ${{10}^{-5}}{{s}^{-1}},$then the rate constant at 500 K [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{10}^{-4}}{{s}^{-1}}$
B) $4\times {{10}^{-4}}{{s}^{-1}}$
C) ${{10}^{-6}}{{s}^{-1}}$
D) $2\times {{10}^{-4}}{{s}^{-1}}$
• question_answer50) An open vessel $27{}^\circ C$ at is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 750 K
B) $750{}^\circ C$
C) $500{}^\circ C$
D) 500 K
• question_answer51) The element that does not show catenation is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) Sn
B) Ge
C) Si
D) Pb
• question_answer52) The increasing order of the reactivity of the following with $LiAl{{H}_{4}}$is
[A] [B] [C] [D]
[JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\left( A \right)<\left( B \right)<\left( D \right)<\left( C \right)$
B) $\left( B \right)<\left( A \right)<\left( D \right)<\left( C \right)$
C) $\left( B \right)<\left( A \right)<\left( C \right)<\left( D \right)$
D) $\left( A \right)<\left( B \right)<\left( C \right)<\left( D \right)$
• question_answer53) Molecules of benzoic acid $({{C}_{6}}{{H}_{5}}COOH)$dimerise in benzene. V g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is (Given that ${{K}_{f}}=5\,K\,kg\,mo{{l}^{-1}},$Molar mass of benzoic acid $=122g\,mo{{l}^{-1}}$) [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 2.4 g
B) 1.8 g
C) 1.0 g
D) 1.5 g
• question_answer54) The major product of the following reaction is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
• question_answer55) If the de Broglie wavelength of the electron in ${{n}^{th}}$ Bohr orbit in a hydrogenic atom is equal to $1.5\pi {{a}_{0}}$(${{a}_{0}}$is Bohr radius), then the value of n/z is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 1.0
B) 1.50
C) 0.75
D) 0.40
• question_answer56) $\Lambda {{{}^\circ }_{m}}$ for $NaCl,HCl$and NaA are 126.4, 425.9 and $100.5\,S\,c{{m}^{2}}\,mo{{l}^{-1}},$respectively. If the conductivity of 0.001 M HA is $5\times {{10}^{-5}}S\,c{{m}^{-1}},$degree of dissociation of HA is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 0.75
B) 0.25
C) 0.125
D) 0.50
• question_answer57) If ${{K}_{sp}}$of $A{{g}_{2}}C{{O}_{3}}$is $8\times {{10}^{-12}},$the molar solubility of $A{{g}_{2}}C{{O}_{3}}$in $0.1\,M\,AgN{{O}_{3}}$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $8\times {{10}^{-11}}M$
B) $8\times {{10}^{-10}}M$
C) $8\times {{10}^{-13}}M$
D) $8\times {{10}^{-12}}M$
• question_answer58) The compound that is not a common component of photochemical smog is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{H}_{3}}C-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-OON{{O}_{2}}$
B) $C{{H}_{2}}=CHCHO$
C) $C{{F}_{2}}C{{l}_{2}}$
D) ${{O}_{3}}$
• question_answer59) The correct order of atomic radii is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $Ce>Eu>Ho>N$
B) $Ho>N>Eu>Ce$
C) $Eu>Ce>Ho>N$
D) $N>Ce>Eu>Ho$
• question_answer60) The major product in the following conversion is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A)
B)
C)
D)
• question_answer61) Let s and $S'$ be the foci of an ellipse and B be any one of the extremities of its minor axis. If $\Delta S'BS$is a right angled triangle with right angle at B and area $(\Delta S'BS)=8sq.$units, then the length of altos rectum of the ellipse is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 2
B) 4
C) $4\sqrt{2}$
D) $2\sqrt{2}$
• question_answer62) The expression$\tilde{\ }(\tilde{\ }p\to q)$is logically equivalent to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $p\wedge q$
B) $\tilde{\ }p\wedge q$
C) $\tilde{\ }p\wedge \tilde{\ }q$
D) $p\wedge \tilde{\ }q$
• question_answer63) If the sum of the first 15 terms of the series ${{\left( \frac{3}{4} \right)}^{3}}+{{\left( 1\frac{1}{2} \right)}^{3}}+{{\left( 2\frac{1}{4} \right)}^{3}}+{{3}^{3}}+{{\left( 3\frac{3}{4} \right)}^{3}}+.....$is equal to 225 k, then k is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 27
B) 9
C) 108
D) 54
• question_answer64) If ${{\sin }^{4}}\alpha +4{{\cos }^{4}}\beta +2=4\sqrt{2}\sin \alpha \cos \beta ;$$\alpha ,\beta \in [0,\pi ],$then $\cos (\alpha +\beta )-\cos (\alpha -\beta )$is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $-1$
B) 0
C) $\sqrt{2}$
D) $-\sqrt{2}$
• question_answer65) In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and lose Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{400}{9}loss$
B) $\frac{400}{3}gain$
C) 0
D) $\frac{400}{3}loss$
• question_answer66) Let S be the set of all real values of $\lambda$ such that a plane passing through the points $(-{{\lambda }^{2}},1,1),$$(1,-{{\lambda }^{2}},1)$and $(1,1,-{{\lambda }^{2}})$also passes through the point ($-1,\text{ }-1,1$). Then S is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\{1,-1\}$
B) $\{3,-3\}$
C) $\{\sqrt{3}\}$
D) $\{\sqrt{3},-\sqrt{3}\}$
• question_answer67) The tangent to the curve $y={{x}^{2}}-\text{5}x+5,$parallel to the line $2y=4x+1,$also passes through the point [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\left( \frac{7}{2},\frac{1}{4} \right)$
B) $\left( \frac{1}{4},\frac{7}{2} \right)$
C) $\left( -\frac{1}{8},7 \right)$
D) $\left( \frac{1}{8},-7 \right)$
• question_answer68) The total number of irrational terms in the binomial expansion ${{({{7}^{1/5}}-{{3}^{1/10}})}^{60}}$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 55
B) 54
C) 48
D) 49
• question_answer69) If a straight line passing through the point $P\left( -3,\text{ }4 \right)$ is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $4x+3y=0$
B) $4x-3y+24=0$
C) $3x-4y+25=0$
D) $x-y+7=0$
• question_answer70) $\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,\frac{\sqrt{\pi }-\sqrt{2{{\sin }^{-1}}x}}{\sqrt{1-x}}$is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\sqrt{\pi }$
B) $\frac{1}{\sqrt{2\pi }}$
C) $\sqrt{\frac{\pi }{2}}$
D) $\sqrt{\frac{2}{\pi }}$
• question_answer71) If$^{n}{{C}_{4}},{{\,}^{n}}{{C}_{5}}$and ${{\,}^{n}}{{C}_{6}}$are in A.R, then n can be [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 12
B) 14
C) 9
D) 11
• question_answer72) Let f be a differentiable function such that $f(1)=2$ and $f'(x)=f(x)$for all $x\in R.$If $h(x)=f(f(x)),$then $h'(1)$ is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $2{{e}^{2}}$
B) 4e
C) 2e
D) $4{{e}^{2}}$
• question_answer73) The set of all values of$\lambda$for which the system of linear equations
$x-2y-2z=\lambda x$ $x+2y+z=\lambda y$ $-x-y=\lambda z$ has a non-trivial solution
[JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) is an empty set
B) contains exactly two elements
C) is a singleton
D) contains more than two elements
• question_answer74) The number of integral values of m for which the quadratic expression, $(1+2m){{x}^{2}}-2$$(1+3m)x+4(1+m),x\in R,$is always positive is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 8
B) 7
C) 3
D) 6
• question_answer75) The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 3
B) 1
C) 7
D) 5
• question_answer76) Let $\vec{a},\vec{b}$and $\vec{c}$be three unit vectors, out of which vectors $\vec{b}$and $\vec{c}$are non-parallel. If $\alpha$and $\beta$are the angles which vector a makes with $\vec{a}$vectors $\vec{b}$ and $\vec{c}$respectively and $\vec{a}\times (\vec{b}\times \vec{c})=\frac{1}{2}\vec{b},$then$|\alpha -\beta |$is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $45{}^\circ$
B) $60{}^\circ$
C) $90{}^\circ$
D) $30{}^\circ$
• question_answer77) If the function f given by $f(x)={{x}^{3}}-3(a-2){{x}^{2}}+3ax+7,$for some $a\in R$is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $\frac{f(x)-14}{{{(x-1)}^{2}}}=0(x\ne 1)$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 7
B) $-7$
C) 5
D) 6
• question_answer78) The integral $\int_{{}}^{{}}{\frac{3{{x}^{13}}+2{{x}^{11}}}{{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{4}}}}dx$is equal to (where C is a constant of integration) [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{{{x}^{4}}}{6{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C$
B) $\frac{{{x}^{4}}}{{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C$
C) $\frac{{{x}^{12}}}{6{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C$
D) $\frac{{{x}^{12}}}{{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C$
• question_answer79) The integral $\int\limits_{1}^{e}{\left\{ {{\left( \frac{x}{e} \right)}^{2x}}-{{\left( \frac{e}{x} \right)}^{x}} \right\}}{{\log }_{e}}xdx$equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{1}{2}-e-\frac{1}{{{e}^{2}}}$
B) $-\frac{1}{2}+\frac{1}{e}-\frac{1}{2{{e}^{2}}}$
C) $\frac{3}{2}-e-\frac{1}{2{{e}^{2}}}$
D) $\frac{3}{2}-\frac{1}{e}-\frac{1}{2{{e}^{2}}}$
• question_answer80) If a curve passes through the point ($1,\text{ }-2$) and has slope of the tangent at any point $(x,y)$on it as$\frac{{{x}^{2}}-2y}{x},$then the curve also passes through the point [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $(-\sqrt{2},1)$
B) $(-1,2)$
C) $(\sqrt{3},0)$
D) $(3,0)$
• question_answer81) There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 11
B) 9
C) 12
D) 7
• question_answer82) If the angle of elevation of a cloud from a point P which is 25 m above a lake be $30{}^\circ$ and the angle of depression of reflection of the cloud in the lake from P be $60{}^\circ$, then the height of the cloud (in metres) from the surface of the lake is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) 50
B) 45
C) 60
D) 42
• question_answer83) $\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{n}{{{n}^{2}}+{{1}^{2}}}+\frac{n}{{{n}^{2}}+{{2}^{2}}}+\frac{n}{{{n}^{2}}+{{3}^{2}}}+....+\frac{1}{5n} \right)$is equal to [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{\tan }^{-1}}(2)$
B) $\frac{\pi }{2}$
C) ${{\tan }^{-1}}(3)$
D) $\frac{\pi }{4}$
• question_answer84) If a circle of radius R passes through the origin and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from 0 on AB is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{({{x}^{2}}+{{y}^{2}})}^{3}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}$
B) ${{({{x}^{2}}+{{y}^{2}})}^{2}}=4R{{x}^{2}}{{y}^{2}}$
C) $({{x}^{2}}+{{y}^{2}})(x+y)={{R}^{2}}xy$
D) ${{({{x}^{2}}+{{y}^{2}})}^{2}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}$
• question_answer85) If an angle between the line, $\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$and the plane, $x-2y-kz=3$is ${{\cos }^{-1}}\left( \frac{2\sqrt{2}}{3} \right),$ then a value of k is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\sqrt{\frac{5}{3}}$
B) $-\frac{3}{5}$
C) $\sqrt{\frac{3}{5}}$
D) $-\frac{5}{3}$
• question_answer86) The equation of a tangent to the parabola, ${{x}^{2}}=8y,$which makes an angle $\theta$ with the positive direction of x-axis is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $x=y\cot \theta -2\tan \theta$
B) $y=x\tan \theta -2\cot \theta$
C) $x=y\cot \theta +2\tan \theta$
D) $y=x\tan \theta +2\cot \theta$
• question_answer87) In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\frac{1}{6}$
B) $\frac{5}{6}$
C) $\frac{1}{3}$
D) $\frac{2}{3}$
• question_answer88) Let ${{z}_{1}}$ and ${{z}_{2}}$be two complex numbers satisfying $|{{z}_{1}}|=9$ and $|{{z}_{2}}-3-4i|=4$.Then the minimum value of $|{{z}_{1}}-{{z}_{2}}|$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\sqrt{2}$
B) 2
C) 0
D) 1
• question_answer89) If $a=\left[ \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right];$then for all $\theta \in \left( \frac{3\pi }{4},\frac{5\pi }{4} \right),$det lies in the interval [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) $\left( \frac{3}{2},3 \right]$
B) $\left[ \frac{5}{2},4 \right)$
C) $\left( 1,\frac{5}{2} \right]$
D) $\left( 0,\frac{3}{2} \right]$
• question_answer90) Let Z be the set of integers. If $A=\{x\in Z:{{2}^{(x+2)({{x}^{2}}-5x+6)}}=1\}$and $B=\{x\in Z:-3<2x-1<9\}$then the number of subsets of the set $A\times B$is [JEE Main Online Paper Held On 12-Jan-2019 Evening]
A) ${{2}^{18}}$
B) ${{2}^{12}}$
C) ${{2}^{15}}$
D) ${{2}^{10}}$
#### Study Package
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https://docs.mosek.com/10.0/cmdtools/prob-def-conic.html | # 8.2 Conic Optimization¶
Conic optimization is an extension of linear optimization (see Sec. 8.1 (Linear Optimization)) allowing conic domains to be specified for affine expressions. A conic optimization problem to be solved by MOSEK can be written as
(8.8)$\begin{split}\begin{array}{lccccl} \mbox{minimize} & & & c^T x+c^f & & \\ \mbox{subject to} & l^c & \leq & A x & \leq & u^c, \\ & l^x & \leq & x & \leq & u^x, \\ & & & Fx+g & \in & \D, \end{array}\end{split}$
where
• $$m$$ is the number of constraints.
• $$n$$ is the number of decision variables.
• $$x \in \real^n$$ is a vector of decision variables.
• $$c \in \real^n$$ is the linear part of the objective function.
• $$c^f\in \real$$ is a constant term in the objective
• $$A \in \real^{m \times n}$$ is the constraint matrix.
• $$l^c \in \real^m$$ is the lower limit on the activity for the constraints.
• $$u^c \in \real^m$$ is the upper limit on the activity for the constraints.
• $$l^x \in \real^n$$ is the lower limit on the activity for the variables.
• $$u^x \in \real^n$$ is the upper limit on the activity for the variables.
is the same as in Sec. 8.1 (Linear Optimization) and moreover:
• $$F \in \real^{k \times n}$$ is the affine conic constraint matrix.,
• $$g \in \real^{k}$$ is the affine conic constraint constant term vector.,
• $$\D$$ is a Cartesian product of conic domains, namely $$\D = \D_1 \times \cdots \times \D_p$$, where $$p$$ is the number of individual affine conic constraints (ACCs), and each domain is one from Sec. 11.5 (Supported domains).
The total dimension of the domain $$\D$$ must be equal to $$k$$, the number of rows in $$F$$ and $$g$$. Lower and upper bounds can be infinite, or in other words the corresponding bound may be omitted.
MOSEK supports also the cone of positive semidefinite matrices. In order not to obscure this section with additional notation, that extension is discussed in Sec. 8.3 (Semidefinite Optimization).
## 8.2.1 Duality for Conic Optimization¶
Corresponding to the primal problem (8.8), there is a dual problem
(8.9)$\begin{split}\begin{array} {lcl} \mbox{maximize} & (l^c)^T s_l^c - (u^c)^T s_u^c + (l^x)^T s_l^x - (u^x)^T s_u^x - g^T\dot{y} + c^f &\\ \mbox{subject to} &\\ & A^T y + s_l^x - s_u^x + F^T \dot{y} = c, & \\ & -y + s_l^c - s_u^c = 0, &\\ & s_l^c,s_u^c,s_l^x ,s_u^x \geq 0, & \\ & \dot{y} \in \D^*, & \end{array}\end{split}$
where
• $$s_l^c$$ are the dual variables for lower bounds of constraints,
• $$s_u^c$$ are the dual variables for upper bounds of constraints,
• $$s_l^x$$ are the dual variables for lower bounds of variables,
• $$s_u^x$$ are the dual variables for upper bounds of variables,
• $$\dot{y}$$ are the dual variables for affine conic constraints,
• the dual domain $$\D^*=\D_1^* \times \cdots \times \D_p^*$$ is a Cartesian product of cones dual to $$\D_i$$.
One can check that the dual problem of the dual problem is identical to the original primal problem.
If a bound in the primal problem is plus or minus infinity, the corresponding dual variable is fixed at 0, and we use the convention that the product of the bound value and the corresponding dual variable is 0. This is equivalent to removing the corresponding dual variable $$(s_l^x)_j$$ from the dual problem. For example:
$l_j^x = -\infty \quad \Rightarrow \quad (s_l^x)_j=0 \mbox{ and } l_j^x\cdot (s_l^x)_j = 0.$
A solution
$(y,s_l^c,s_u^c,s_l^x,s_u^x,\dot{y})$
to the dual problem is feasible if it satisfies all the constraints in (8.9). If (8.9) has at least one feasible solution, then (8.9) is (dual) feasible, otherwise the problem is (dual) infeasible.
A solution
$(x^*,y^*,(s_l^c)^*,(s_u^c)^*,(s_l^x)^*,(s_u^x)^*,(\dot{y})^*)$
is denoted a primal-dual feasible solution, if $$(x^*)$$ is a solution to the primal problem (8.8) and $$(y^*,(s_l^c)^*,(s_u^c)^*,(s_l^x)^*,(s_u^x)^*,(\dot{y})^*)$$ is a solution to the corresponding dual problem (8.9). We also define an auxiliary vector
$(x^c)^* := Ax^*$
containing the activities of linear constraints.
For a primal-dual feasible solution we define the duality gap as the difference between the primal and the dual objective value,
(8.10)$\begin{split}\begin{array}{l} c^T x^* + c^f - \left\lbrace (l^c)^T (s_l^c)^* - (u^c)^T (s_u^c)^* + (l^x)^T (s_l^x)^* - (u^x)^T (s_u^x)^* -g^T (\dot{y})^*+ c^f \right\rbrace\\ = \sum_{i=0}^{m-1} \left[ (s_l^c)_i^* ( (x_i^c)^*-l_i^c) + (s_u^c)_i^* (u_i^c-(x_i^c)^*) \right] \\ + \sum_{j=0}^{n-1} \left[ (s_l^x)_j^* (x_j-l_j^x) +(s_u^x)_j^* (u_j^x-x_j^*) \right] \\ + ((\dot{y})^*)^T(Fx^*+g) \geq 0 \end{array}\end{split}$
where the first relation can be obtained by transposing and multiplying the dual constraints (8.2) by $$x^*$$ and $$(x^c)^*$$ respectively, and the second relation comes from the fact that each term in each sum is nonnegative. It follows that the primal objective will always be greater than or equal to the dual objective.
It is well-known that, under some non-degeneracy assumptions that exclude ill-posed cases, a conic optimization problem has an optimal solution if and only if there exist feasible primal-dual solution so that the duality gap is zero, or, equivalently, that the complementarity conditions
(8.11)$\begin{split}\begin{array}{rcll} (s_l^c)_i^* ((x_i^c)^*-l_i^c ) & = & 0, & i=0,\ldots ,m-1, \\ (s_u^c)_i^* (u_i^c-(x_i^c)^*) & = & 0, & i=0,\ldots ,m-1, \\ (s_l^x)_j^* (x_j^*-l_j^x ) & = & 0, & j=0,\ldots ,n-1, \\ (s_u^x)_j^* (u_j^x-x_j^* ) & = & 0, & j=0,\ldots ,n-1, \\ ((\dot{y})^*)^T(Fx^*+g) & = & 0, & \end{array}\end{split}$
are satisfied.
If (8.8) has an optimal solution and MOSEK solves the problem successfully, both the primal and dual solution are reported, including a status indicating the exact state of the solution.
## 8.2.2 Infeasibility for Conic Optimization¶
### 8.2.2.1 Primal Infeasible Problems¶
If the problem (8.8) is infeasible (has no feasible solution), MOSEK will report a certificate of primal infeasibility: The dual solution reported is the certificate of infeasibility, and the primal solution is undefined.
A certificate of primal infeasibility is a feasible solution to the modified dual problem
(8.12)$\begin{split}\begin{array} {lcl} \mbox{maximize} & (l^c)^T s_l^c - (u^c)^T s_u^c + (l^x)^T s_l^x - (u^x)^T s_u^x - g^T\dot{y} &\\ \mbox{subject to} &\\ & A^T y + s_l^x - s_u^x + F^T \dot{y} = 0, & \\ & -y + s_l^c - s_u^c = 0, &\\ & s_l^c,s_u^c,s_l^x ,s_u^x \geq 0, & \\ & \dot{y} \in \D^*, & \end{array}\end{split}$
such that the objective value is strictly positive, i.e. a solution
$(y^*,(s_l^c)^*,(s_u^c)^*,(s_l^x)^*,(s_u^x)^*,(\dot{y})^*)$
to (8.12) so that
$(l^c)^T (s_l^c)^* - (u^c)^T (s_u^c)^* + (l^x)^T (s_l^x)^* - (u^x)^T (s_u^x)^* - g^T\dot{y}> 0.$
Such a solution implies that (8.12) is unbounded, and that (8.8) is infeasible.
### 8.2.2.2 Dual Infeasible Problems¶
If the problem (8.9) is infeasible (has no feasible solution), MOSEK will report a certificate of dual infeasibility: The primal solution reported is the certificate of infeasibility, and the dual solution is undefined.
A certificate of dual infeasibility is a feasible solution to the modified primal problem
(8.13)$\begin{split}\begin{array} {lccccl} \mbox{minimize} & & & c^T x & & \\ \mbox{subject to} & \hat l^c & \leq & A x & \leq & \hat u^c, \\ & \hat l^x & \leq & x & \leq & \hat u^x, \\ & & & Fx & \in \D & \end{array}\end{split}$
where
(8.14)$\begin{split}\hat l_i^c = \left\lbrace \begin{array} {ll} 0 & \mbox{if } l_i^c > -\infty , \\ -\infty & \mbox{otherwise}, \end{array} \right\rbrace \quad \mbox{and}\quad \hat u_i^c := \left\lbrace \begin{array}{ll} 0 & \mbox{if } u_i^c < \infty , \\ \infty & \mbox{otherwise}, \end{array} \right\rbrace\end{split}$
and
(8.15)$\begin{split}\hat l_j^x = \left\lbrace \begin{array} {ll} 0 & \mbox{if } l_j^x > -\infty , \\ -\infty & \mbox{otherwise}, \end{array} \right\rbrace \quad \mbox{and}\quad \hat u_j^x := \left\lbrace \begin{array}{ll} 0 & \mbox{if } u_j^x < \infty , \\ \infty & \mbox{otherwise}, \end{array} \right\rbrace\end{split}$
such that
$c^T x<0.$
Such a solution implies that (8.13) is unbounded, and that (8.9) is infeasible.
In case that both the primal problem (8.8) and the dual problem (8.9) are infeasible, MOSEK will report only one of the two possible certificates — which one is not defined (MOSEK returns the first certificate found).
## 8.2.3 Minimalization vs. Maximalization¶
When the objective sense of problem (8.8) is maximization, i.e.
$\begin{split}\begin{array}{lccccl} \mbox{maximize} & & & c^T x+c^f & & \\ \mbox{subject to} & l^c & \leq & A x & \leq & u^c, \\ & l^x & \leq & x & \leq & u^x, \\ & & & Fx+g & \in & \D, \end{array}\end{split}$
the objective sense of the dual problem changes to minimization, and the domain of all dual variables changes sign in comparison to (8.2). The dual problem thus takes the form
$\begin{split}\begin{array}{lc} \mbox{minimize} & (l^c)^T s_l^c - (u^c)^T s_u^c + (l^x)^T s_l^x - (u^x)^T s_u^x - g^T\dot{y} + c^f\\ \mbox{subject to} & A^T y + s_l^x - s_u^x + F^T\dot{y} = c,\\ & -y + s_l^c - s_u^c = 0, \\ & s_l^c,s_u^c,s_l^x,s_u^x \leq 0,\\ & -\dot{y} \in \D^* \end{array}\end{split}$
This means that the duality gap, defined in (8.10) as the primal minus the dual objective value, becomes nonpositive. It follows that the dual objective will always be greater than or equal to the primal objective. The primal infeasibility certificate will be reported by MOSEK as a solution to the system
(8.16)$\begin{split}\begin{array}{lc} & A^T y + s_l^x - s_u^x + F^T\dot{y} = 0, \\ & -y + s_l^c - s_u^c = 0, \\ & s_l^c,s_u^c,s_l^x,s_u^x \leq 0, \\ & -\dot{y}\in\D^* \end{array}\end{split}$
such that the objective value is strictly negative
$(l^c)^T (s_l^c)^* - (u^c)^T (s_u^c)^* + (l^x)^T (s_l^x)^* - (u^x)^T (s_u^x)^* -g^T\dot{y}< 0.$
Similarly, the certificate of dual infeasibility is an $$x$$ satisfying the requirements of (8.13) such that $$c^Tx>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": 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": 0.9463990926742554, "perplexity": 397.3326575850051}, "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-2022-49/segments/1669446711074.68/warc/CC-MAIN-20221206060908-20221206090908-00309.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/125947-cauchy-density.html | # Math Help - cauchy density
1. ## cauchy density
Show that if X and Y are independent having the standard normal density,
then X/Y has the standard Cauchy density.
Any help with this question.
I tried and i'm getting double integral exp(-x^2)dxdy.
2. Well then there must be something wrong somewhere
Can you show your working ? | {"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": 0.9917823672294617, "perplexity": 1242.480960039734}, "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-2014-23/segments/1404776441023.78/warc/CC-MAIN-20140707234041-00026-ip-10-180-212-248.ec2.internal.warc.gz"} |
http://inquiryintoinquiry.com/page/2/ | ## ❦ Pyramus & Thisbe ❦
And the knots thereof
I have known beauty
I’ll bring it to you
Jon Awbrey • 12 Nov 2014
## Frankl, My Dear : 11
Let’s take a moment from the differential analysis of the proposition in Example 1 to form a handy compendium of the results obtained so far.
(1)
(3)
(4)
### Difference Map $\mathrm{D}(pqr)$ of the Conjunction $pqr$
(5)
To be continued …
## Continuity, Generality, Infinity, Law, Synechism : 1
Peircers,
The concept of continuity that Peirce highlights in his synechism is a logical principle that is somewhat more general than the concepts of either mathematical or physical continua.
Peirce’s concept of continuity is better understood as a concept of lawful regularity or parametric variation. As such, it is basic to the coherence and utility of science, whether classical, relativistic, quantum mechanical, or any conceivable future science that deserves the name. (As Aristotle already knew.)
Perhaps the most pervasive examples of this brand of continuity in physics are the “correspondence principles” that describe the connections between classical and contemporary paradigms.
The importance of lawful regularities and parametric variations is not diminished one bit in passing from continuous mathematics to discrete mathematics, nor from theory to application.
Here are some further points of information, the missing of which seems to lie at the root of many recent disputes on the Peirce List:
It is necessary to distinguish the mathematical concepts of continuity and infinity from the question of their physical realization. The mathematical concepts retain their practical utility for modeling empirical phenomena quite independently of the (meta-)physical question of whether these continua and cardinalities are literally realized in the physical universe. This is equally true of any other domain or level of phenomena — chemical, biological, mental, social, or whatever.
As far as the mathematical concept goes, continuity is relative to topology. That is, what counts as a continuous function or transformation between spaces is relative to the topology under which those spaces are considered and the same spaces may be considered under many different topologies. What topology makes the most sense in a given application is another one of those abductive matters.
Regards,
Jon
## Frankl, My Dear : 10
(5)
Figure 5 shows the 14 terms of the difference map $\mathrm{D}f$ as arcs, arrows, or directed edges in the venn diagram of the original proposition $f(p, q, r) = pqr.$ The arcs of $\mathrm{E}f$ are directed into the cell where $f$ is true from each of the other cells. The arcs of $\boldsymbol\varepsilon f$ are directed from the cell where $f$ is true into each of the other cells.
The expansion of $\mathrm{D}f$ computed in the previous post is shown again below with the terms arranged by number of positive differential features, from lowest to highest.
$\begin{array}{*{4}{l}} \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =} \\[10pt] & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} \\[10pt] + & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} \\[10pt] + & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} \end{array}$
$\begin{array}{*{4}{l}} + & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} \\[10pt] + & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} \\[10pt] + & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} & + & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \\[10pt] + & \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} & + & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \end{array}$
To be continued …
## Frankl, My Dear : 9
“It doesn’t matter what one does,” the Man Without Qualities said to himself, shrugging his shoulders. “In a tangle of forces like this it doesn’t make a scrap of difference.” He turned away like a man who has learned renunciation, almost indeed like a sick man who shrinks from any intensity of contact. And then, striding through his adjacent dressing-room, he passed a punching-ball that hung there; he gave it a blow far swifter and harder than is usual in moods of resignation or states of weakness.
Robert Musil • The Man Without Qualities
We continue with the differential analysis of the proposition in Example 1.
### Example 1
(1)
The difference operator $\mathrm{D}$ is defined as the difference $\mathrm{E} - \boldsymbol\varepsilon$ between the enlargement operator $\mathrm{E}$ and the tacit extension operator $\boldsymbol\varepsilon.$
The difference map $\mathrm{D}f$ is the result of applying the difference operator $\mathrm{D}$ to the function $f.$ When the sense is clear, we may refer to $\mathrm{D}f$ simply as the difference of $f.$
In boolean spaces there is no difference between the sum $(+)$ and the difference $(-)$ so the difference operator $\mathrm{D}$ is equally well expressed as the exclusive disjunction or symmetric difference $\mathrm{E} + \boldsymbol\varepsilon.$ In this case the difference map $\mathrm{D}f$ can be computed according to the formula $\mathrm{D}f = (\mathrm{E} + \boldsymbol\varepsilon)f = \mathrm{E}f + \boldsymbol\varepsilon f.$
The action of $\mathrm{D}$ on our present example, $f(p, q, r) = pqr,$ can be computed from the data on hand according to the following prescription.
The enlargement map $\mathrm{E}f,$ computed in Post 5 and graphed in Post 6, is shown again here:
$\mathrm{E}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =$
$\begin{smallmatrix} & p q r \,\cdot\, \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q \texttt{(} r \texttt{)} \,\cdot\, \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \mathrm{d}r & + & p \texttt{(} q \texttt{)} r \,\cdot\, \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} & + & p \texttt{(} q \texttt{)(} r \texttt{)} \,\cdot\, \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \, \mathrm{d}r \\[4pt] + & \texttt{(} p \texttt{)} q r \,\cdot\, \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & \texttt{(} p \texttt{)} q \texttt{(} r \texttt{)} \,\cdot\, \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)} \mathrm{d}r & + & \texttt{(} p \texttt{)(} q \texttt{)} r \,\cdot\, \mathrm{d}p \, \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} & + & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \,\cdot\, \mathrm{d}p \, \mathrm{d}q \, \mathrm{d}r \end{smallmatrix}$
The tacit extension $\boldsymbol\varepsilon f,$ computed in Post 7 and graphed in Post 8, is shown again here:
$\boldsymbol\varepsilon f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =$
$\begin{array}{*{8}{l}} & p q r ~ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \\[4pt] + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \end{array}$
The difference map $\mathrm{D}f$ is the sum of the enlargement map $\mathrm{E}f$ and the tacit extension $\boldsymbol\varepsilon f.$
Here we adopt a paradigm of computation for $\mathrm{D}f$ that aids not only in organizing the stages of the work but also in highlighting the diverse facets of logical meaning that may be read off the result.
The terms of the enlargement map $\mathrm{E}f$ are obtained from the table below by multiplying the base factor at the head of each column by the differential factor that appears beneath it in the body of the table.
The terms of the tacit extension $\boldsymbol\varepsilon f$ are obtained from the next table below by multiplying the base factor at the head of the first column by each of the differential factors that appear beneath it in the body of the table.
Finally, the terms of the difference map $\mathrm{D}f$ are obtained by overlaying the displays for $\mathrm{E}f$ and $\boldsymbol\varepsilon f$ and taking their boolean sum entry by entry.
Notice that the “loop” or “no change” term $p q r \cdot \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}$ cancels out, leaving 14 terms in the end.
To be continued …
## Frankl, My Dear : 8
(4)
Figure 4 shows the eight terms of the tacit extension $\boldsymbol\varepsilon f$ as arcs, arrows, or directed edges in the venn diagram of the original proposition $f(p, q, r) = pqr.$ Each term of the tacit extension $\boldsymbol\varepsilon f$ corresponds to an arc that starts from the cell where $f$ is true and ends in one of the eight cells of the venn diagram.
For ease of reference, here is the expansion of $\boldsymbol\varepsilon f$ from the previous post:
$\boldsymbol\varepsilon f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =$
$\begin{array}{*{8}{l}} & p q r ~ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \\[4pt] + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \end{array}$
Two examples suffice to convey the general idea of the extended venn diagram:
• The term $pqr \cdot \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}$ is shown as a looped arc starting in the cell where $pqr$ is true and returning back to it. The differential factor $\texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}$ corresponds to the fact that the arc crosses no logical feature boundaries from its source to its target.
• The term $pqr \cdot \mathrm{d}p \; \mathrm{d}q \, \mathrm{d}r$ is shown as an arc going from the cell where $pqr$ is true to the cell where $\texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}$ is true. The differential factor $\mathrm{d}p \; \mathrm{d}q \, \mathrm{d}r$ corresponds to the fact that the arc crosses all three logical feature boundaries from its source to its target.
To be continued …
## Frankl, My Dear : 7
We continue with the differential analysis of the proposition in Example 1.
### Example 1
(1)
A proposition defined on one universe of discourse has natural extensions to larger universes of discourse. As a matter of course in a given context of discussion, some of these extensions come to be taken for granted as the most natural extensions to make in passing from one universe to the next and they tend to be assumed automatically, by default, in the absence of explicit notice to the contrary. These are the tacit extensions that apply in that context.
Differential logic, at the first order of analysis, treats extensions from boolean spaces of type $\mathbb{B}^k$ to enlarged boolean spaces of type $\mathbb{B}^k \times \mathbb{D}^k.$ In this setting $\mathbb{B} \cong \mathbb{D} \cong \{ 0, 1 \}$ but we use different letters merely to distinguish base and differential features.
In our present example, the tacit extension $\boldsymbol\varepsilon f$ of $f$ is the boolean function $\boldsymbol\varepsilon f : \mathbb{B}^3 \times \mathbb{D}^3 \to \mathbb{B}$ defined by the following equation:
$\boldsymbol\varepsilon f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) ~=~ f(p, q, r).$
The boolean expansion of $\boldsymbol\varepsilon f$ takes the following form:
$\boldsymbol\varepsilon f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =$
$\begin{array}{*{8}{l}} & p q r ~ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \\[4pt] + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} & + & p q r ~ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} \end{array}$
In other words, $\boldsymbol\varepsilon f$ is simply $f$ on the base variables $p, q, r$ extended by a tautology — commonly known as a “Don’t Care” condition — on the differential variables $\mathrm{d}p, \mathrm{d}q, \mathrm{d}r.$
To be continued … | {"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": 76, "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": 0.8113083243370056, "perplexity": 608.4272728261701}, "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/1422122191023.37/warc/CC-MAIN-20150124175631-00091-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/198194-branching-process-martingale.html | # Math Help - Branching process with martingale
1. ## Branching process with martingale
Let $\{ X_k^n : n,k \geq 1 \}$ be i.i.d. positive interger-value random variables with $EX_k^n = \mu < \infty$ and $Var(X_k^n) = \sigma ^2 > 0$. Define $Y_0 =1$ and recursively define $Y_{n+1}=X^{n+1}_1+ . . . +X_{Y_n}^{n+1} \ \ \ n \geq 0$
a) Show that $M_n = \frac {Y_n}{ \mu ^n }$ is a martingale with respect to the filtration $\sigma (Y_0, Y_1, . . . , Y_n)$
b) Find $E(Y_{n+1}^2 | Y_0,...,Y_n)$ and deduce that M_n has uniformly bounded variance if and only if $\mu > 1$
c) For $\mu > 1$, find $Var(M_ \infty )$
My proof so far.
a) This one is easy, $E(M_{n+1}|Y_1,...,Y_n) = \frac {1}{ \mu ^{n+1} } E(Y_{n+1} | Y_1,...,Y_n)$
$= \frac {1}{ \mu ^{n+1} }E(X_1^{n+1}+...+X_{Y_n}^{n+1})$
$= \frac {1}{ \mu ^{n+1} }(E(X_1^{n+1})+...+E(X_{Y_n}^{n+1}))$
$= \frac {1}{ \mu ^{n+1} } \frac {Y_n}{ \mu ^n } = M_n$. So that proves that M_n is a martingale.
b) I'm having problem trying to break down this thing...
$E(Y_{n+1}^2 | Y_0,...,Y_n) = E[(X_1^{n+1}+...+X_{Y_n}^{n+1})^2|Y_0,...,Y_n]$
But how would I proceed from here? Thanks.
2. ## Re: Branching process with martingale
Hello,
You know the conditional variance : Var[Y|X]=E[Y^2|X]-E[Y|X]^2
This will give you E[Y^2|X], and the conditional variance is the sum of the variances, because the variables are independent. Sorry I don't use the latex, nor did I use the correct names for the variables, but it takes too much time to write them down | {"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": 16, "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": 0.9859036207199097, "perplexity": 372.85442930875007}, "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-2015-32/segments/1438042986357.49/warc/CC-MAIN-20150728002306-00302-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://scitation.aip.org/content/aip/journal/pop/19/5/10.1063/1.3694840 | • journal/journal.article
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The velocity campaign for ignition on NIFa)
a)Paper BI3 2, Bull. Am. Phys. Soc. 56, 25 (2011).
USD
10.1063/1.3694840
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Affiliations:
1 Lawrence Livermore National Laboratory, Livermore, California 94550, USA
2 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
3 Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
4 Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
5 General Atomics, San Diego, California 92186, USA
6 Atomic Weapons Establishment, Aldermaston, Reading RG7 APR, United Kingdom
b) Invited speaker.
Phys. Plasmas 19, 056305 (2012)
/content/aip/journal/pop/19/5/10.1063/1.3694840
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/5/10.1063/1.3694840
## Figures
FIG. 1.
Delivered laser pulses for shots to explore impact of increased laser energy on velocity at constant power using convergent ablator targets. Laser energy was increased from 1.25 MJ (shot N111011) to 1.47 MJ (shot N111009). Pulse is compared to a DT shot (N110914) and shows the reduction in peak power because 8 beams are used for backlighter beams in the convergent ablator shots.
FIG. 2.
With convergent ablator target, 12 backlit snapshots are taken of the shell as it implodes. These can be put together to get a radius versus time for the Imploding capsule.
FIG. 3.
The velocity of the center of mass of the shell and the mass remaining is extracted from the convergent ablator data.
FIG. 4.
Hydra calculations show that the fuel is moving faster than the center of mass of the capsule.
FIG. 5.
Calculations are used to relate the center of mass velocity and mass remaining to the fuel velocity.
FIG. 6.
Hydra calculations show that the 11 keV x-ray yield is a sensitive function of velocity. Data from the convergent ablator experiments agree with this trend.
FIG. 7.
South pole bangtime diagnostic shows 160 ps earlier bangtime with and 1.67 x higher x-ray yield with depleted uranium (DU) hohlraum compared to gold (Au) hohlraum.
FIG. 8.
Gated x-ray detector images ofthe hotspot for symcap experiments using a uranium hohlraum (P2/P0 =35.5% ± 3%) and a gold hohlraum (P2/P0 = 31.2% ± 6.9%) show no significant change in symmetry with uranium hohlraum. Neutron yield was 1.5 x higher for uranium than gold hohlraum.
FIG. 9.
Hohlraum aspect ratio was re-optimized after the first experimental campaign on NIF. New hohlraum (“575 hohlraum”) is shorter but with a larger radius, which was intended to put more laser energy near the waist of the capsule.
FIG. 10.
All shock-timed implosions with 544 hohlraums had negative P2 (oblate or “pancaked” implosions). 575 hohlraum allows P2 to be zero.
FIG. 11.
(a) Orientation of the m = 4 polar asymmetry relative to the location of the inner cone beams. 3-d Hydra calculations show a reversal—the image should be large where the beams are brighter. This image suggests the 30 degree beams are brighter than the 23.5 degree beams. (b) The m = 4 asymmetry can be corrected by changing the wavelength separation between the 23.5 and 30 degree beams.
FIG. 12.
Hydra calculations show that the P2 symmetry can swing as a function of time over the emission profile if the 2nd and 3rd cone fractions are not properly tuned.
FIG. 13.
Visar data using the mirrored keyhole target show that tuning the cone fraction in the 2nd and 3rd pulses improved the pole to equator symmetry of the shocks.
FIG. 14.
P2/P0 symmetry of the imploded capsule has a significantly smaller swing after tuning the cone fraction in the 2nd and 3rd pulses than before tuning.
FIG. 15.
After tuning the cone fraction in the 2nd and 3rd pulses, the dP2/dt is close to zero when P2 is zero.
## Tables
Table I.
Comparison of capsule performance metrics show improved performance with depleted uranium hohlraum compared to gold hohlraum.
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https://openstax.org/books/precalculus/pages/9-5-matrices-and-matrix-operations | Precalculus
# 9.5Matrices and Matrix Operations
Precalculus9.5 Matrices and Matrix Operations
### Learning Objectives
In this section, you will:
• Find the sum and difference of two matrices.
• Find scalar multiples of a matrix.
• Find the product of two matrices.
Figure 1 (credit: “SD Dirk,” Flickr)
Two club soccer teams, the Wildcats and the Mud Cats, are hoping to obtain new equipment for an upcoming season. Table 1 shows the needs of both teams.
Wildcats Mud Cats
Goals 6 10
Balls 30 24
Jerseys 14 20
Table 1
A goal costs $300; a ball costs$10; and a jersey costs 30. How can we find the total cost for the equipment needed for each team? In this section, we discover a method in which the data in the soccer equipment table can be displayed and used for calculating other information. Then, we will be able to calculate the cost of the equipment. ### Finding the Sum and Difference of Two Matrices To solve a problem like the one described for the soccer teams, we can use a matrix, which is a rectangular array of numbers. A row in a matrix is a set of numbers that are aligned horizontally. A column in a matrix is a set of numbers that are aligned vertically. Each number is an entry, sometimes called an element, of the matrix. Matrices (plural) are enclosed in [ ] or ( ), and are usually named with capital letters. For example, three matrices named $A,B, A,B,$ and $C C$ are shown below. $A=[ 1 2 3 4 ],B=[ 1 2 7 0 −5 6 7 8 2 ],C=[ −1 0 3 3 2 1 ] A=[ 1 2 3 4 ],B=[ 1 2 7 0 −5 6 7 8 2 ],C=[ −1 0 3 3 2 1 ]$ #### Describing Matrices A matrix is often referred to by its size or dimensions: $m×n m×n$ indicating $m m$ rows and $n n$ columns. Matrix entries are defined first by row and then by column. For example, to locate the entry in matrix $A A$ identified as $a ij , a ij ,$ we look for the entry in row $i, i,$ column $j. j.$ In matrix $A, A,$ shown below, the entry in row 2, column 3 is $a 23 . a 23 .$ $A=[ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] A=[ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ]$ A square matrix is a matrix with dimensions $n×n, n×n,$ meaning that it has the same number of rows as columns. The $3×3 3×3$ matrix above is an example of a square matrix. A row matrix is a matrix consisting of one row with dimensions $1×n. 1×n.$ $[ a 11 a 12 a 13 ] [ a 11 a 12 a 13 ]$ A column matrix is a matrix consisting of one column with dimensions $m×1. m×1.$ $[ a 11 a 21 a 31 ] [ a 11 a 21 a 31 ]$ A matrix may be used to represent a system of equations. In these cases, the numbers represent the coefficients of the variables in the system. Matrices often make solving systems of equations easier because they are not encumbered with variables. We will investigate this idea further in the next section, but first we will look at basic matrix operations. ### Matrices A matrix is a rectangular array of numbers that is usually named by a capital letter: $A,B,C, A,B,C,$ and so on. Each entry in a matrix is referred to as $a ij , a ij ,$ such that $i i$ represents the row and $j j$ represents the column. Matrices are often referred to by their dimensions: $m×n m×n$ indicating $m m$ rows and $n n$ columns. ### Example 1 #### Finding the Dimensions of the Given Matrix and Locating Entries Given matrix $A: A:$ 1. What are the dimensions of matrix $A? A?$ 2. What are the entries at $a 31 a 31$ and $a 22 ? a 22 ?$ $A=[ 2 1 0 2 4 7 3 1 −2 ] A=[ 2 1 0 2 4 7 3 1 −2 ]$ #### Adding and Subtracting Matrices We use matrices to list data or to represent systems. Because the entries are numbers, we can perform operations on matrices. We add or subtract matrices by adding or subtracting corresponding entries. In order to do this, the entries must correspond. Therefore, addition and subtraction of matrices is only possible when the matrices have the same dimensions. We can add or subtract a $3×3 3×3$ matrix and another $3×3 3×3$ matrix, but we cannot add or subtract a $2×3 2×3$ matrix and a $3×3 3×3$ matrix because some entries in one matrix will not have a corresponding entry in the other matrix. ### Adding and Subtracting Matrices Given matrices $A A$ and $B B$ of like dimensions, addition and subtraction of $A A$ and $B B$ will produce matrix $C C$ or matrix $D D$ of the same dimension. Matrix addition is commutative. $A+B=B+A A+B=B+A$ It is also associative. $( A+B )+C=A+( B+C ) ( A+B )+C=A+( B+C )$ ### Example 2 #### Finding the Sum of Matrices Find the sum of $A A$ and $B, B,$ given ### Example 3 #### Adding Matrix A and Matrix B Find the sum of $A A$ and $B. B.$ ### Example 4 #### Finding the Difference of Two Matrices Find the difference of $A A$ and $B. B.$ ### Example 5 #### Finding the Sum and Difference of Two 3 x 3 Matrices Given $A A$ and $B: B:$ 1. Find the sum. 2. Find the difference. ### Try It #1 Add matrix $A A$ and matrix $B. B.$ ### Finding Scalar Multiples of a Matrix Besides adding and subtracting whole matrices, there are many situations in which we need to multiply a matrix by a constant called a scalar. Recall that a scalar is a real number quantity that has magnitude, but not direction. For example, time, temperature, and distance are scalar quantities. The process of scalar multiplication involves multiplying each entry in a matrix by a scalar. A scalar multiple is any entry of a matrix that results from scalar multiplication. Consider a real-world scenario in which a university needs to add to its inventory of computers, computer tables, and chairs in two of the campus labs due to increased enrollment. They estimate that 15% more equipment is needed in both labs. The school’s current inventory is displayed in Table 2. Lab A Lab B Computers 15 27 Computer Tables 16 34 Chairs 16 34 Table 2 Converting the data to a matrix, we have $C 2013 =[ 15 16 16 27 34 34 ] C 2013 =[ 15 16 16 27 34 34 ]$ To calculate how much computer equipment will be needed, we multiply all entries in matrix $C C$ by 0.15. $(0.15) C 2013 =[ (0.15)15 (0.15)16 (0.15)16 (0.15)27 (0.15)34 (0.15)34 ]=[ 2.25 2.4 2.4 4.05 5.1 5.1 ] (0.15) C 2013 =[ (0.15)15 (0.15)16 (0.15)16 (0.15)27 (0.15)34 (0.15)34 ]=[ 2.25 2.4 2.4 4.05 5.1 5.1 ]$ We must round up to the next integer, so the amount of new equipment needed is $[ 3 3 3 5 6 6 ] [ 3 3 3 5 6 6 ]$ Adding the two matrices as shown below, we see the new inventory amounts. $[ 15 16 16 27 34 34 ]+[ 3 3 3 5 6 6 ]=[ 18 19 19 32 40 40 ] [ 15 16 16 27 34 34 ]+[ 3 3 3 5 6 6 ]=[ 18 19 19 32 40 40 ]$ This means $C 2014 =[ 18 19 19 32 40 40 ] C 2014 =[ 18 19 19 32 40 40 ]$ Thus, Lab A will have 18 computers, 19 computer tables, and 19 chairs; Lab B will have 32 computers, 40 computer tables, and 40 chairs. ### Scalar Multiplication Scalar multiplication involves finding the product of a constant by each entry in the matrix. Given $A=[ a 11 a 12 a 21 a 22 ] A=[ a 11 a 12 a 21 a 22 ]$ the scalar multiple $cA cA$ is Scalar multiplication is distributive. For the matrices $A,B, A,B,$ and $C C$ with scalars $a a$ and $b, b,$ $a(A+B)=aA+aB (a+b)A=aA+bA a(A+B)=aA+aB (a+b)A=aA+bA$ ### Example 6 #### Multiplying the Matrix by a Scalar Multiply matrix $A A$ by the scalar 3. $A=[ 8 1 5 4 ] A=[ 8 1 5 4 ]$ Try It #2 Given matrix $B, B,$ find $−2B −2B$ where $B=[ 4 1 3 2 ] B=[ 4 1 3 2 ]$ ### Example 7 #### Finding the Sum of Scalar Multiples Find the sum $3A+2B. 3A+2B.$ ### Finding the Product of Two Matrices In addition to multiplying a matrix by a scalar, we can multiply two matrices. Finding the product of two matrices is only possible when the inner dimensions are the same, meaning that the number of columns of the first matrix is equal to the number of rows of the second matrix. If $A A$ is an $m×r m×r$ matrix and $B B$ is an $r×n r×n$ matrix, then the product matrix $AB AB$ is an $m×n m×n$ matrix. For example, the product $AB AB$ is possible because the number of columns in $A A$ is the same as the number of rows in $B. B.$ If the inner dimensions do not match, the product is not defined. We multiply entries of $A A$ with entries of $B B$ according to a specific pattern as outlined below. The process of matrix multiplication becomes clearer when working a problem with real numbers. To obtain the entries in row $i i$ of $AB, AB,$ we multiply the entries in row $i i$ of $A A$ by column $j j$ in $B B$ and add. For example, given matrices $A A$ and $B, B,$ where the dimensions of $A A$ are $2×3 2×3$ and the dimensions of $B B$ are $3×3, 3×3,$ the product of $AB AB$ will be a $2×3 2×3$ matrix. Multiply and add as follows to obtain the first entry of the product matrix $AB. AB.$ 1. To obtain the entry in row 1, column 1 of $AB, AB,$ multiply the first row in $A A$ by the first column in $B, B,$ and add. $[ a 11 a 12 a 13 ][ b 11 b 21 b 31 ]= a 11 ⋅ b 11 + a 12 ⋅ b 21 + a 13 ⋅ b 31 [ a 11 a 12 a 13 ][ b 11 b 21 b 31 ]= a 11 ⋅ b 11 + a 12 ⋅ b 21 + a 13 ⋅ b 31$ 2. To obtain the entry in row 1, column 2 of $AB, AB,$ multiply the first row of $A A$ by the second column in $B, B,$ and add. $[ a 11 a 12 a 13 ][ b 12 b 22 b 32 ]= a 11 ⋅ b 12 + a 12 ⋅ b 22 + a 13 ⋅ b 32 [ a 11 a 12 a 13 ][ b 12 b 22 b 32 ]= a 11 ⋅ b 12 + a 12 ⋅ b 22 + a 13 ⋅ b 32$ 3. To obtain the entry in row 1, column 3 of $AB, AB,$ multiply the first row of $A A$ by the third column in $B, B,$ and add. $[ a 11 a 12 a 13 ][ b 13 b 23 b 33 ]= a 11 ⋅ b 13 + a 12 ⋅ b 23 + a 13 ⋅ b 33 [ a 11 a 12 a 13 ][ b 13 b 23 b 33 ]= a 11 ⋅ b 13 + a 12 ⋅ b 23 + a 13 ⋅ b 33$ We proceed the same way to obtain the second row of $AB. AB.$ In other words, row 2 of $A A$ times column 1 of $B; B;$ row 2 of $A A$ times column 2 of $B; B;$ row 2 of $A A$ times column 3 of $B. B.$ When complete, the product matrix will be $AB=[ a 11 ⋅ b 11 + a 12 ⋅ b 21 + a 13 ⋅ b 31 a 21 ⋅ b 11 + a 22 ⋅ b 21 + a 23 ⋅ b 31 a 11 ⋅ b 12 + a 12 ⋅ b 22 + a 13 ⋅ b 32 a 21 ⋅ b 12 + a 22 ⋅ b 22 + a 23 ⋅ b 32 a 11 ⋅ b 13 + a 12 ⋅ b 23 + a 13 ⋅ b 33 a 21 ⋅ b 13 + a 22 ⋅ b 23 + a 23 ⋅ b 33 ] AB=[ a 11 ⋅ b 11 + a 12 ⋅ b 21 + a 13 ⋅ b 31 a 21 ⋅ b 11 + a 22 ⋅ b 21 + a 23 ⋅ b 31 a 11 ⋅ b 12 + a 12 ⋅ b 22 + a 13 ⋅ b 32 a 21 ⋅ b 12 + a 22 ⋅ b 22 + a 23 ⋅ b 32 a 11 ⋅ b 13 + a 12 ⋅ b 23 + a 13 ⋅ b 33 a 21 ⋅ b 13 + a 22 ⋅ b 23 + a 23 ⋅ b 33 ]$ ### Properties of Matrix Multiplication For the matrices $A,B, A,B,$ and $C C$ the following properties hold. • Matrix multiplication is associative: $( AB )C=A( BC ). ( AB )C=A( BC ).$ • Matrix multiplication is distributive: $C(A+B)=CA+CB, (A+B)C=AC+BC. C(A+B)=CA+CB, (A+B)C=AC+BC.$ Note that matrix multiplication is not commutative. ### Example 8 #### Multiplying Two Matrices Multiply matrix $A A$ and matrix $B. B.$ ### Example 9 #### Multiplying Two Matrices Given $A A$ and $B: B:$ 1. Find $AB. AB.$ 2. Find $BA. BA.$ #### Analysis Notice that the products $AB AB$ and $BA BA$ are not equal. $AB=[ −7 10 30 11 ]≠[ −9 10 10 4 −8 −12 10 4 21 ]=BA AB=[ −7 10 30 11 ]≠[ −9 10 10 4 −8 −12 10 4 21 ]=BA$ This illustrates the fact that matrix multiplication is not commutative. ### Q&A Is it possible for AB to be defined but not BA? Yes, consider a matrix A with dimension $3×4 3×4$ and matrix B with dimension $4×2. 4×2.$ For the product AB the inner dimensions are 4 and the product is defined, but for the product BA the inner dimensions are 2 and 3 so the product is undefined. ### Example 10 #### Using Matrices in Real-World Problems Let’s return to the problem presented at the opening of this section. We have Table 3, representing the equipment needs of two soccer teams. Wildcats Mud Cats Goals 6 10 Balls 30 24 Jerseys 14 20 Table 3 We are also given the prices of the equipment, as shown in Table 4. Goal300 Ball $10 Jersey$30
Table 4
We will convert the data to matrices. Thus, the equipment need matrix is written as
$E=[ 6 30 14 10 24 20 ] E=[ 6 30 14 10 24 20 ]$
The cost matrix is written as
$C=[ 300 10 30 ] C=[ 300 10 30 ]$
We perform matrix multiplication to obtain costs for the equipment.
$CE=[ 300 10 30 ][ 6 10 30 24 14 20 ] =[ 300(6)+10(30)+30(14) 300(10)+10(24)+30(20) ] =[ 2,520 3,840 ] CE=[ 300 10 30 ][ 6 10 30 24 14 20 ] =[ 300(6)+10(30)+30(14) 300(10)+10(24)+30(20) ] =[ 2,520 3,840 ]$
The total cost for equipment for the Wildcats is $2,520, and the total cost for equipment for the Mud Cats is$3,840.
### How To
Given a matrix operation, evaluate using a calculator.
1. Save each matrix as a matrix variable $[ A ],[ B ],[ C ],... [ A ],[ B ],[ C ],...$
2. Enter the operation into the calculator, calling up each matrix variable as needed.
3. If the operation is defined, the calculator will present the solution matrix; if the operation is undefined, it will display an error message.
### Example 11
#### Using a Calculator to Perform Matrix Operations
Find $AB−C AB−C$ given
### Media
Access these online resources for additional instruction and practice with matrices and matrix operations.
### 9.5 Section Exercises
#### Verbal
1.
Can we add any two matrices together? If so, explain why; if not, explain why not and give an example of two matrices that cannot be added together.
2.
Can we multiply any column matrix by any row matrix? Explain why or why not.
3.
Can both the products $AB AB$ and $BA BA$ be defined? If so, explain how; if not, explain why.
4.
Can any two matrices of the same size be multiplied? If so, explain why, and if not, explain why not and give an example of two matrices of the same size that cannot be multiplied together.
5.
Does matrix multiplication commute? That is, does $AB=BA? AB=BA?$ If so, prove why it does. If not, explain why it does not.
#### Algebraic
For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined.
$A=[ 1 3 0 7 ],B=[ 2 14 22 6 ],C=[ 1 5 8 92 12 6 ],D=[ 10 14 7 2 5 61 ],E=[ 6 12 14 5 ],F=[ 0 9 78 17 15 4 ] A=[ 1 3 0 7 ],B=[ 2 14 22 6 ],C=[ 1 5 8 92 12 6 ],D=[ 10 14 7 2 5 61 ],E=[ 6 12 14 5 ],F=[ 0 9 78 17 15 4 ]$
6.
$A+B A+B$
7.
$C+D C+D$
8.
$A+C A+C$
9.
$B−E B−E$
10.
$C+F C+F$
11.
$D−B D−B$
For the following exercises, use the matrices below to perform scalar multiplication.
$A=[ 4 6 13 12 ],B=[ 3 9 21 12 0 64 ],C=[ 16 3 7 18 90 5 3 29 ],D=[ 18 12 13 8 14 6 7 4 21 ] A=[ 4 6 13 12 ],B=[ 3 9 21 12 0 64 ],C=[ 16 3 7 18 90 5 3 29 ],D=[ 18 12 13 8 14 6 7 4 21 ]$
12.
$5A 5A$
13.
$3B 3B$
14.
$−2B −2B$
15.
$−4C −4C$
16.
$1 2 C 1 2 C$
17.
$100D 100D$
For the following exercises, use the matrices below to perform matrix multiplication.
$A=[ −1 5 3 2 ],B=[ 3 6 4 −8 0 12 ],C=[ 4 10 −2 6 5 9 ],D=[ 2 −3 12 9 3 1 0 8 −10 ] A=[ −1 5 3 2 ],B=[ 3 6 4 −8 0 12 ],C=[ 4 10 −2 6 5 9 ],D=[ 2 −3 12 9 3 1 0 8 −10 ]$
18.
$AB AB$
19.
$BC BC$
20.
$CA CA$
21.
$BD BD$
22.
$DC DC$
23.
$CB CB$
For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed.
$A=[ 2 −5 6 7 ],B=[ −9 6 −4 2 ],C=[ 0 9 7 1 ],D=[ −8 7 −5 4 3 2 0 9 2 ],E=[ 4 5 3 7 −6 −5 1 0 9 ] A=[ 2 −5 6 7 ],B=[ −9 6 −4 2 ],C=[ 0 9 7 1 ],D=[ −8 7 −5 4 3 2 0 9 2 ],E=[ 4 5 3 7 −6 −5 1 0 9 ]$
24.
$A+B−C A+B−C$
25.
$4A+5D 4A+5D$
26.
$2C+B 2C+B$
27.
$3D+4E 3D+4E$
28.
$C−0.5D C−0.5D$
29.
$100D−10E 100D−10E$
For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. (Hint: $A 2 =A⋅A A 2 =A⋅A$ )
$A=[ −10 20 5 25 ],B=[ 40 10 −20 30 ],C=[ −1 0 0 −1 1 0 ] A=[ −10 20 5 25 ],B=[ 40 10 −20 30 ],C=[ −1 0 0 −1 1 0 ]$
30.
$AB AB$
31.
$BA BA$
32.
$CA CA$
33.
$BC BC$
34.
$A 2 A 2$
35.
$B 2 B 2$
36.
$C 2 C 2$
37.
$B 2 A 2 B 2 A 2$
38.
$A 2 B 2 A 2 B 2$
39.
$(AB) 2 (AB) 2$
40.
$(BA) 2 (BA) 2$
For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. (Hint: $A 2 =A⋅A A 2 =A⋅A$ )
$A=[ 1 0 2 3 ],B=[ −2 3 4 −1 1 −5 ],C=[ 0.5 0.1 1 0.2 −0.5 0.3 ],D=[ 1 0 −1 −6 7 5 4 2 1 ] A=[ 1 0 2 3 ],B=[ −2 3 4 −1 1 −5 ],C=[ 0.5 0.1 1 0.2 −0.5 0.3 ],D=[ 1 0 −1 −6 7 5 4 2 1 ]$
41.
$AB AB$
42.
$BA BA$
43.
$BD BD$
44.
$DC DC$
45.
$D 2 D 2$
46.
$A 2 A 2$
47.
$D 3 D 3$
48.
$(AB)C (AB)C$
49.
$A(BC) A(BC)$
#### Technology
For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution.
$A=[ −2 0 9 1 8 −3 0.5 4 5 ],B=[ 0.5 3 0 −4 1 6 8 7 2 ],C=[ 1 0 1 0 1 0 1 0 1 ] A=[ −2 0 9 1 8 −3 0.5 4 5 ],B=[ 0.5 3 0 −4 1 6 8 7 2 ],C=[ 1 0 1 0 1 0 1 0 1 ]$
50.
$AB AB$
51.
$BA BA$
52.
$CA CA$
53.
$BC BC$
54.
$ABC ABC$
#### Extensions
For the following exercises, use the matrix below to perform the indicated operation on the given matrix.
$B=[ 1 0 0 0 0 1 0 1 0 ] B=[ 1 0 0 0 0 1 0 1 0 ]$
55.
$B 2 B 2$
56.
$B 3 B 3$
57.
$B 4 B 4$
58.
$B 5 B 5$
59.
Using the above questions, find a formula for $B n . B n .$ Test the formula for $B 201 B 201$ and $B 202 , B 202 ,$ using a calculator.
Order a print copy
As an Amazon Associate we earn from qualifying purchases. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 249, "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": 0.8675549626350403, "perplexity": 292.15668820068714}, "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/1614178369420.71/warc/CC-MAIN-20210304143817-20210304173817-00340.warc.gz"} |
https://blog.advantagelumber.com/tag/wormy-maple/ | # Wood of the Month: Ambrosia Maple (Wormy Maple)
Covered with unique patterns, Ambrosia Maple is the perfect wood for anyone who seeks a one of a kind wood.
Ambrosia Maple is a highly coveted wood for many projects because of its very unique and colored patterns. A lot of people often wonder if Ambrosia Maple is a specific species of wood, or if some sort of chemicals were added to give it the interesting patterns. The truth is that Ambrosia maple isn’t a different species, its regular soft maple that has had small beetles called ambrosia beetles nesting in it which carry a certain type of fungus for food.
# Wood of the Week
## Ambrosia Maple
An Ambrosia Maple floor is truly memorable.
Perfect for rustic and traditional homes, Ambrosia Maple flooring creates captivating spaces. I don’t think it’s far fetched to say that you’ll be telling the story of your floor to every person who sees it for the first time. What makes Ambrosia Maple so special?
Each plank of Ambrosia Maple has been touched by life itself. When the Ambrosia beetle makes it home in a maple tree, it leaves a trail that creates the wormy pattern. It is this wormy maple pattern in Soft Maple lumber that creates such a lasting impression.
Many people ask whether the tiny holes left by the Ambrosia beetle compromise the wood in any way. The answer is no. Once the wood is finished, those holes are filled in and add to the wood’s overall appeal. With beautiful brown and grey stripes, the small worm holes act as accents and really do look great.
At Advantage, we hand-pick the best Ambrosia maple lumber by hand. By picking best looking wormy maple, you can have a floor that is a true conversation piece.
Contact us today to buy Ambrosia Maple flooring and wormy maple lumber: | {"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": 0.8749893307685852, "perplexity": 4572.687355963581}, "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-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00504.warc.gz"} |
https://www.physicsforums.com/threads/lorentz-invariance-and-non-galilean-invariance-of-maxwells-equations.199800/ | # Lorentz Invariance and Non-Galilean Invariance of Maxwell's Equations
1. Nov 21, 2007
### Dahaka14
I am having trouble going about proving the Lorentz invariance and non-Galilean invariance of Maxwell's equations. Can someone help me find a simple way to do it? I've looked online and in textbooks, but they hardly give any explicit examples.
2. Nov 21, 2007
### robphy
You have to specify how the fields transform.
To do it in general, it's easiest to do it tensorially.
You could do it vectorially... or possibly less elegantly component-wise.
Can you show some of your attempts so far?
3. Nov 24, 2007
### Dahaka14
I've tried transforming the coordinates of the wave equations for Maxwell's equations into Lorentz transformed equations via the x and t components, excluding the y and z components of the wave equation for simplicity. I figuredsince the equations are homogeneous, the x and t components should be either equal to each other or each equal to zero when taking the second derivatives of each component (since the x - t components equal zero). I received a very messy x components after partially differentiating it twice, and noticed that the electric field doesn't have a time component in it, so it should equal zer, but I didn't see how my differentiated x part could equal zero too. Is this a good way to go about it? With the wave equations, substitute in the transformed coordinates? Otherwise, I've started the tensor formation that you said, with the field strength and the dual tensors, I derived Maxwell's equations via the four-vectors of current and potential. I figured I could simply transform the field strength tensor and the dual tensor each by Lorentz transformation matrices, then take those transformed tensors and try to derive Maxwell's equations by the same previous method, and receive the same result. But, I was confused as to what transformation matrices to use on the tensors, since they are second-rank tensors. What matrices would I use? Which way is better, if either of them are good?
4. Nov 26, 2007
### robphy
You can show that the 1+1 wave equation is not invariant under a Galilean-boost. [Take care with the Chain Rule.]
It is invariant under a Lorentz-boost (as suggested by the d'Alembert form of the solution). [Use the d'Alembert form and light-cone coordinates.]
The calculations in terms of components are tedious. It's worth doing explicitly... then doing it tensorially.
I don't have the patience right now to $$\LaTeX$$ the steps in this exercise. It might be best if you show your explicit steps, which we can comment on. You might find some help from
http://farside.ph.utexas.edu/teaching/jk1/lectures/node6.html
http://www2.maths.ox.ac.uk/~nwoodh/sr/index.html
Last edited: Nov 26, 2007
5. Nov 27, 2007
### Mentz114
Dahaka,
Have a look here. I managed to boost (Lorentz transform) the F tensor after some help. | {"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": 0.8830832242965698, "perplexity": 646.2089356980916}, "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/1474738662527.91/warc/CC-MAIN-20160924173742-00234-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://www.allaboutcircuits.com/tools/broadside-coupled-trace-inductance-calculator/ | This calculator helps you compute the inductance of a broadside coupled trace.
H
### Overview
This calculator will help you calculate the inductance of a broadside coupled trace given its dimensions. It is common to find the broadside coupled trace in printed circuit boards where differential pair signals are routed. Traces such as these are found on adjacent planes with the return being identical to the trace both in length and in width. In the industrial setting, this routing techique is done to ensure strong coupling although the actual return for the signal is commonly on the power plane.
### Equation
$$L_{bs}=\frac{\mu_{0} \mu_{r} H}{W}$$
Note:
$$W >> H, H > T$$
Where:
$$W$$ – trace width
$$T$$ – trace thickness
$$H$$ – distance between traces
$$L$$ – trace length
### Applications
It is important for an engineer to calculate the inductance between two traces in a printed circuit board as it contributes to the overall circuit's performance. As the cost in the production of printed circuit boards increases, manufacturers are forced to used higher density routing of high speed signal traces. This can only result in increased crosstalk among the traces. If the inductance of the broadside trace can be determined beforehand, then necessary adjustments can be made. | {"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": 0.8746211528778076, "perplexity": 1802.7984426594035}, "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-2017-39/segments/1505818696681.94/warc/CC-MAIN-20170926193955-20170926213955-00542.warc.gz"} |
http://mathhelpforum.com/calculus/103043-multivariable-limit-problem.html | # Math Help - Multivariable Limit Problem
1. ## Multivariable Limit Problem
I am having some problems with the following problems:
1. $\lim_{\theta\to 0}\frac{sin\theta}{\theta}
$
Using
l'Hôpital's rule I got that the limit equals.
2. $\lim_{(x,y)\to (0,0)}\frac{sin(x + y)}{x + y}
$
I am not really sure how to proceed here. I mean, I could approach along the y axis, then am I able to use
l'Hôpital's rule?Also, if I approach along y = x afterward I believe I would get 2 for the limit, whereas along the y-axis would yield 1 provided I could use l'Hôpital's rule. In that case the limit would not exist.
3. $\lim_{(x,y)\to (0,0)}\frac{sin(xy)}{xy}
$
On this one I don't really know what to do.
2. Originally Posted by Alterah
I am having some problems with the following problems:
1. $\lim_{\theta\to 0}\frac{sin\theta}{\theta}
$
Using
l'Hôpital's rule I got that the limit equals.
2. $\lim_{(x,y)\to (0,0)}\frac{sin(x + y)}{x + y}
$
I am not really sure how to proceed here. I mean, I could approach along the y axis, then am I able to use
l'Hôpital's rule?Also, if I approach along y = x afterward I believe I would get 2 for the limit, whereas along the y-axis would yield 1 provided I could use l'Hôpital's rule. In that case the limit would not exist.
3. $\lim_{(x,y)\to (0,0)}\frac{sin(xy)}{xy}
$
On this one I don't really know what to do.
1. L'Hopital's rule allows you to take $\lim_{\theta\to0}\frac{\cos\theta}{1}$, which is clearly $1$.
2 & 3. The rule: $\lim_{anything\to0}\frac{\sin(anything)}{anything} =1$. To cover all possible directions at once (except $x=0$, which you can check manually), simply let $y=f(x)$. Since $f(x)$ must pass through the origin, $f(0)=0$, so both $x+f(x)$ and $x\cdot f(x)$ approach $0$ as $x\to 0$ Therefore both questions fall under this rule and have limits of $1$.
3. Originally Posted by Alterah
I am having some problems with the following problems:
1. $\lim_{\theta\to 0}\frac{sin\theta}{\theta}$ $
$
Using l'Hôpital's rule I got that the limit equals.
2. $\lim_{(x,y)\to (0,0)}\frac{sin(x + y)}{x + y}$ $
$
I am not really sure how to proceed here. I mean, I could approach along the y axis, then am I able to use
l'Hôpital's rule?Also, if I approach along y = x afterward I believe I would get 2 for the limit, whereas along the y-axis would yield 1 provided I could use l'Hôpital's rule. In that case the limit would not exist.
3. $\lim_{(x,y)\to (0,0)}\frac{sin(xy)}{xy}$ $
$
On this one I don't really know what to do.
I wouldn't use L'Hospital's Rule to solve 1.
This is because, to find the derivative of $\sin{x}$, you need to know the limit $\lim_{x \to 0}\frac{\sin{x}}{x}$, so you have a circular argument.
You can use the sandwich theorem instead - there is plenty of information you can find on google regarding this limit.
4. Originally Posted by redsoxfan325
1. L'Hopital's rule allows you to take $\lim_{\theta\to0}\frac{\cos\theta}{1}$, which is clearly $1$.
2 & 3. The rule: $\lim_{anything\to0}\frac{\sin(anything)}{anything} =1$. To cover all possible directions at once (except $x=0$, which you can check manually), simply let $y=f(x)$. Since $f(x)$ must pass through the origin, $f(0)=0$, so both $x+f(x)$ and $x\cdot f(x)$ approach $0$ as $x\to 0$ Therefore both questions fall under this rule and have limits of $1$.
Thanks...I forgot to put that I got the limit equals 1 for question 1. I am trying to follow what you have for part two and three. I see how it can work for part 2. But it seems for part three if we use y = f(x) I feel like we get something along the lines of sin(x*f(x))/(x*f(x)) and we still wind up with zero in the denominator. As far as not using L'Hopital's rule for part 1, I Don't really see why not. It's an indeterminate form of 0/0. So I can apply it to it.
5. Originally Posted by Alterah
Thanks...I forgot to put that I got the limit equals 1 for question 1. I am trying to follow what you have for part two and three. I see how it can work for part 2. But it seems for part three if we use y = f(x) I feel like we get something along the lines of sin(x*f(x))/(x*f(x)) and we still wind up with zero in the denominator.
We do get $\frac{\sin(x\cdot f(x))}{x\cdot f(x)}$. But that's good, because $x\cdot f(x)\to 0$ as $x\to 0$, which means we can apply that rule I stated.
Originally Posted by Alterah
As far as not using L'Hopital's rule for part 1, I Don't really see why not. It's an indeterminate form of 0/0. So I can apply it to it.
What Prove It is saying is that in order to take the derivative of $\sin x$ at $0$ using the definition of the derivative, you need to take that limit.
$\lim_{h\to 0}\frac{\sin(h)-\sin(0)}{h-0} = \lim_{h\to0}\frac{\sin h}{h}$
6. Originally Posted by redsoxfan325
We do get $\frac{\sin(x\cdot f(x))}{x\cdot f(x)}$. But that's good, because $x\cdot f(x)\to 0$ as $x\to 0$, which means we can apply that rule I stated.
Ok. Thanks for the help, how did the rule come about? I suppose I am wanting to verify for myself that this rule holds. At this point the rule seems like "hand waving." Thanks again.
7. Originally Posted by Alterah
Ok. Thanks for the help, how did the rule come about? I suppose I am wanting to verify for myself that this rule holds. At this point the rule seems like "hand waving." Thanks again.
L'Hopital's Rule shows that it works, though you probably wouldn't want to use it in a proof, for the reasons discussed above.
$\lim_{anything\to0}\frac{\sin(anything)}{anything} =\lim_{anything\to0}\frac{\cos(anything)\cdot\frac {d}{dx}[anything]}{\frac{d}{dx}[anything]}$ $=\lim_{anything\to0}\frac{\cos(anything)}{1}$, which is clearly $1$.
More officially, you'd probably use something like $u(x)$ instead of "anything", i.e.
$\lim_{u(x)\to0}\frac{\sin(u(x))}{u(x)}=1$
but I used "anything" to try to make it easier to understand.
8. Originally Posted by redsoxfan325
L'Hopital's Rule shows that it works, though you probably wouldn't want to use it in a proof, for the reasons discussed above.
$\lim_{anything\to0}\frac{\sin(anything)}{anything} =\lim_{anything\to0}\frac{\cos(anything)\cdot\frac {d}{dx}[anything]}{\frac{d}{dx}[anything]}$ $=\lim_{anything\to0}\frac{\cos(anything)}{1}$, which is clearly $1$.
More officially, you'd probably use something like $u(x)$ instead of "anything", i.e.
$\lim_{u(x)\to0}\frac{\sin(u(x))}{u(x)}=1$
but I used "anything" to try to make it easier to understand.
I see...I suppose it's a bit of a challenge to see with multivariable functions because we actually describe partial derivatives. It makes absolute sense with f(x). Alternatively using the rule I'd think you can get the following:
$\lim_{u(x)\to0}\frac{\cos(u(x))}{u(x)}=0$
correct?
9. Originally Posted by Alterah
I see...I suppose it's a bit of a challenge to see with multivariable functions because we actually describe partial derivatives. It makes absolute sense with f(x). Alternatively using the rule I'd think you can get the following:
$\lim_{u(x)\to0}\frac{\cos(u(x))}{u(x)}=0$
correct?
NO!
l'Hopital's can only be used when your limit has the indeterminant form of either $\frac{0}{0}$ or $\frac{\infty}{\infty}$. I doubt $\lim_{u(x)\to 0}\frac{\cos(u(x))}{u(x)}$ will have either of these two forms, regardless of what u(x) is ....
10. Originally Posted by mr fantastic
NO!
l'Hopital's can only be used when your limit has the indeterminant form of either $\frac{0}{0}$ or $\frac{\infty}{\infty}$. I doubt $\lim_{u(x)\to 0}\frac{\cos(u(x))}{u(x)}$ will have either of these two forms, regardless of what u(x) is ....
True...I completely forgot about that when I said that about cosine.
11. Originally Posted by Alterah
I am having some problems with the following problems:
1. $\lim_{\theta\to 0}\frac{sin\theta}{\theta}
$
Using
l'Hôpital's rule I got that the limit equals.
2. $\lim_{(x,y)\to (0,0)}\frac{sin(x + y)}{x + y}
$
I am not really sure how to proceed here. I mean, I could approach along the y axis, then am I able to use
l'Hôpital's rule?Also, if I approach along y = x afterward I believe I would get 2 for the limit, whereas along the y-axis would yield 1 provided I could use l'Hôpital's rule. In that case the limit would not exist.
3. $\lim_{(x,y)\to (0,0)}\frac{sin(xy)}{xy}
$
On this one I don't really know what to do.
First I will talk about 2 and 3, which follows from 1.
Clearly, for 2, if $(x,y)\to(0,0)$, then $x+y\to0$, and similarly for 3.
Let $C$ be the unit ball (hence its area is $\pi$).
Draw an equilateral triangle in $C$ such that its corners touch $C$, denote by $A_{3}$ the area of the triangle.
Then $A_{3}=3\frac{1}{2}\sin\bigg(\frac{2\pi}{3}\bigg)$.
Now draw a square in $C$, again let it corners touch $C$, denote by $A_{4}$ the area of the square.
Then $A_{4}=4\frac{1}{2}\sin\bigg(\frac{2\pi}{4}\bigg)$.
Similarly, draw a polygon (with $n$ edges of the same lenght), and by $A_{n}$ denote the area of the polygon.
As the number of the corners (edges) increase, the area of the polygon tends to the area of the unit ball (exactly $\pi$), i.e.,
$\pi=\lim_{n\to\infty}A_{n}=\lim_{n\to\infty}\frac{ n}{2}\sin\bigg(\dfrac{2\pi}{n}\bigg)$
or equivalently
$\lim_{n\to\infty}\frac{n}{2\pi}\sin\bigg(\dfrac{2\ pi}{n}\bigg)=1\qquad(*)$.
Now let $u:=2\pi/n$, and as $n\to\infty$, we have $u\to0$, therefore (*) takes the following form
$\lim_{u\to0}\frac{\sin(u)}{u}=1$.
I hope this helps. :]
12. Alternatively, look at the unit circle.
It should be pretty clear from the diagram that the area of the sector is squeezed between the area of the two triangles made by $\sin{\theta}$ and $\tan{\theta}$.
So we have
$\frac{1}{2}\sin{\theta}\cos{\theta} \leq \frac{1}{2}\theta \leq \frac{1}{2}\tan{\theta}$
$\sin{\theta}\cos{\theta} \leq \theta \leq \frac{\sin{\theta}}{\cos{\theta}}$
$\frac{\cos{\theta}}{\sin{\theta}} \leq \frac{1}{\theta} \leq \frac{1}{\sin{\theta}\cos{\theta}}$
$\cos{\theta} \leq \frac{\sin{\theta}}{\theta} \leq \frac{1}{\cos{\theta}}$.
Now apply the sandwich theorem by letting $\theta \to 0$.
13. Yes, both of those helped immensely. Thanks for all your help! | {"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": 96, "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": 0.9632284641265869, "perplexity": 246.55354099235376}, "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-2016-07/segments/1454701158811.82/warc/CC-MAIN-20160205193918-00038-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/159452/how-can-i-recreate-a-weibull-distribution-given-mean-and-standard-deviation-and | # How can I recreate a Weibull distribution given mean and standard deviation and the shape and scale parameters are unknown?
Figure 2 is a Weibull distribution of three different wind farms in Canada. These 3 probability distributions were combined in a study to obtain a common wind speed model. I will be using this common wind speed model to obtain the wind speed probability distribution of a particular wind farm.
Table II shows the 5 of 100 steps in the model for a sample site used in the study. I know how to compute the wind speed, given that I have the mean and standard deviation of the wind farm. The problem is how will I compute for the specific probability for every speed if I do not know how to recreate the common wind speed model.
Is it possible to use Excel for this?
All images are from here
• Note that Table II is misleading: it must be providing probability densities, not "probabilities" as claimed. Because the study is behind a paywall, you cannot expect readers to know the details. In particular, how many parameters do these Weibull distributions have? Are you sure the study does not report the parameter values? (It would be strange if they did not.)
– whuber
Jul 1 '15 at 13:20
• Hi @whuber. I have added images of the paragraphs pertaining to the said table. The mean and sd of each of the three sites are given and used to create their corresponding weibull using the formulas above. Then they were combined into one weibull? How exactly? I understand that the probability is an average of the three. Another queston: If I already solved the value of shape and scale parameters for the regina site, can I use it for the particular site that I will be evaluating? In short, are they constant?
– Lara
Jul 1 '15 at 18:09
See also: Weibull distribution parameters $k$ and $c$ for wind speed data - a very similar question, as it turns out. I'm pasting the relevant process below (assuming a 2-parameter Weibull).
You can use the 'method-of-moments' to estimate the parameters.
If $\lambda$ is the scale parameter and $k$ is the shape parameter, then:
$$\mathrm{E}(X) = \lambda \Gamma\left(1+\frac{1}{k}\right)\$$
$$\textrm{var}(X) = \lambda^2\left[\Gamma\left(1+\frac{2}{k}\right) - \left(\Gamma\left(1+\frac{1}{k}\right)\right)^2\right]\,$$
This system can estimate values for $k$ and $\lambda$.
$$k = (\frac{\sigma}{\bar x})^{-1.086} \\ \lambda = \frac{\bar x}{\Gamma(1 + 1/k)}$$
With $\bar x$ as the observed mean and $\sigma$ as the observed standard deviation.
This is of course implementable in Excel:
Call B1 the observed mean, and B2 the observed variance. Call B4 to be the estimated $\lambda$ and B5 to be the estimated $k$, I entered dummy values of 1 to begin with.
Then, define B7 as E(X) and B8 as Var(X). Use the formulas above, I've reproduced mine below:
=(B4*EXP(GAMMALN(1+(1/B5)))) =B4^2*(EXP(GAMMALN(1+(2/B5)))-EXP((GAMMALN(1+(1/B5))^2)))
Define B10 as the squared sum of errors in your estimation: =SQRT((B7-B1)^2+(B8-B2)^2).
Then, with Solver, minimize B10 while changing B4 and B5. This should yield a very good estimate of the true parameters. My spreadsheet gives $\lambda=0.708$ and $k=0.244$.
• This might be useful, but the equations cannot be solved as you state. This is an approximation. Jul 2 '15 at 2:02
• @Chris What is the value of the gamma?
– Lara
Jul 2 '15 at 2:35
• @soakley you mean I cannot use those equations given by Chris in my evaluation? Please elaborate. Thanks.
– Lara
Jul 2 '15 at 2:36
• You can use them (many approximations are good, it's just not always easy to know when). But if you are going to implement in Excel, you might as well use the solver and find the parameters that match the moments more accurately. There is no direct gamma function in Excel. You have to exponentiate the gammaln function. So, for example, to find the gamma function at 5, you would use "=exp(gammaln(5))" Jul 2 '15 at 13:15
• @Lara there are several other approaches like maximum likelihood, besides method of moments described by chris. This is pretty standard in any standard wind engineering books, I vaguely remember this when I took an aerodynamic class. Comprehensive list of approaches and equation can be found in the article with an example. Jul 2 '15 at 19:38 | {"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": 0.9242551922798157, "perplexity": 556.1883634640785}, "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/1631780057225.38/warc/CC-MAIN-20210921131252-20210921161252-00282.warc.gz"} |
https://tex.stackexchange.com/questions/354620/align-multiline-equation-in-bold-font | # Align multiline equation in bold font
I want to align an equation:
\begin{align*}
a &= b\\
c &= d
\end{align*}
Which works. But having it in \mathbf{}:
\begin{align*}
\mathbf{a &= b}\\
c &= d
\end{align*}
gives me an error.
Of course, I could end the \mathbf at &= and apply it afterwards, but is there an easier way? (I have long and complicated equations)
you can use \boldmath, but be careful -- this will make all math within its scope bold:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
text $a + b$.
\boldmath
text $a + b$.
\begin{align*}
a &= b\\
c &= d
\end{align*}
\unboldmath
text $a + b$.
\end{document}
you can also limit the scope by placing the intended material within braces.
• ,@barbarabeeton -- I think the OP asks for a single line within the align environment to be in bold math, and not to repeat \mathbf, did I understand the question correctly? Feb 19, 2017 at 14:40
• @AboAmmar -- i may have misunderstood the question. if the op confirms that, i will delete this answer, since \boldmath can be used only outside a math environment. Feb 19, 2017 at 14:45
The error in your example is because the alignment markers & only work inside the same group. So, the easiest solution may be to locally bold the symbols you want using the bm package (better than \mathbf{...}).
\documentclass{article}
\usepackage{amsmath,bm}
\begin{document}
\begin{align*}
\bm a &=\bm b\\
c &= d
\end{align*}
\end{document} | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9996771812438965, "perplexity": 2071.4287506811934}, "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/1659882571210.98/warc/CC-MAIN-20220810191850-20220810221850-00741.warc.gz"} |
http://mathschallenge.net/full/quadratic_differences | #### Problem
The positive integers, $x$, $y$, and $z$ are consecutive terms in an arithmetic progression. Given that $n$ is also a positive integer, for how many values of $n$ below one-thousand does the equation $x^2 - y^2 - z^2 = n$ have no solutions?
#### Solution
Let $x = a + d$, $y = a$, and $z = a - d$.
$\therefore (a + d)^2 - a^2 - (a - d)^2 = n$
$a^2 + 2ad + d^2 - a^2 - a^2 + 2ad - d^2 = n$
$\therefore 4ad - a^2 = a(4d - a) = n$.
Let $u = a$ and $v = 4d - a \implies u + v = 4d \equiv 0 \mod 4$. In other words, for a solution to exist the factors of $n$ must add to a multiple of four.
We shall deal with $n$ being of the form $2^m r$, where $r$ is odd, and for increasing values of $m$.
• $m = 0$ ($n$ is odd):
If $n = r$ then the factors $u$ and $v$ must both be odd. But if they are both congruent with 1 or both congruent with -1 modulo 4 then $u + v \equiv 2 \mod 4$, and there will be no solution; if they are different then $u + v \equiv 0 mod 4$, and there will always be a solution.
Hence if they are the same then $n = uv \equiv 1 \mod 4$, or $n$ being of the form 4$k$ + 1, will have no solutions.
• $m = 1 \implies n = 2r = a(4d - a)$:
If $a = 2r$, $4d - a = 1 \implies 4d = 2r + 1$. But as the RHS is odd, this is impossible.
If $a = r$, $4d - a = 2 \implies 4d = r + 2$. Impossible, as RHS is odd.
In other words if $n = 2(2k + 1) = 4k + 2$ then there will be no solutions.
• $m = 2 \implies n = 4r$:
If $a = 2r$, $4d - a = 2 \implies 4d = 2r + 2 = 2(r + 1)$.
And as $r + 1$ is even, we will always have at least one solution if $n = 4r$.
• $m = 3 \implies n = 8r$:
If $a = 8r$, $4d - a = 1 \implies 4d = 8r + 1$. Impossible.
If $a = 4r$, $4d - a = 2 \implies 4d = 4r + 2$. Impossible.
If $a = 2r$, $4d - a = 4 \implies 4d = 2r + 4$. Impossible.
If $a = r$, $4d - a = 8 \implies 4d = r + 8$. Impossible.
Hence if $n = 8(2k + 1) = 16k + 8$ then there will be no solutions.
• $m \ge 4$:
If $a = 4r$, $4d - a = 2^{m-2} \implies 4d = 4(r+2^{m-4})$.
Hence for $m \ge 4$ there will always be at least one solution.
Thus there will be no solutions for numbers of the form $4k + 1$, $4k + 2$, and $16k + 8$. As the first and second cases are odd and even respectively, they are mutually exclusive, and although the the second and third are both even, the third is divisible by 4, whereas the second is not divisible by 4. Hence all three forms are mutually exclusive.
As $4 \times 249 + 1 = 997$, $4 \times 249 + 2 = 998$, and $16 \times 61 + 8 = 984$, there are exactly $249 + 249 + 61 = 559$ values of $n$ below one-thousand that have no solution.
For which values of $n$ will there be exactly one solution?
Problem ID: 295 (26 Nov 2006) Difficulty: 4 Star
Only Show Problem | {"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": 0.9341041445732117, "perplexity": 165.7649538138609}, "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-2014-42/segments/1414637904722.39/warc/CC-MAIN-20141030025824-00208-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/42745-equation-gives-unexpected-result.html | # Thread: Equation Gives Unexpected Result
1. ## Equation Gives Unexpected Result
Ok im not exactly sure where to post this as i am really bad with math lol
ok to all you geniuses
This Equation Works fine:
0+79*0/(0+1)+293*0/(1+0-(0/62)*62)+479
as it equals 479
This also works fine:
0+79*0/(61+1)+293*(61/1+0-(0/62)*62)+479
as it equals 3352
Unfortunately this gives unexpected results:
479+79*479/(1+1)+293*1/(1+479-(479/62)*62)+479 = 20171.5
20171.5 Should Be: 19884
----
To people who want to know the above equations are actually from a PHP Script. I am trying to convert a JASS script to PHP and im hoping this is the last thing to solve :P.
Thanks for all your help
2. Originally Posted by uniflare
Ok im not exactly sure where to post this as i am really bad with math lol
ok to all you geniuses
This Equation Works fine:
0+79*0/(0+1)+293*0/(1+0-(0/62)*62)+479
as it equals 479
This also works fine:
0+79*0/(61+1)+293*(61/1+0-(0/62)*62)+479
as it equals 3352
Unfortunately this gives unexpected results:
479+79*479/(1+1)+293*1/(1+479-(479/62)*62)+479 = 20171.5
20171.5 Should Be: 19884
----
To people who want to know the above equations are actually from a PHP Script. I am trying to convert a JASS script to PHP and im hoping this is the last thing to solve :P.
Thanks for all your help
Check your use of brackets and the rules of precedence for PHP. Under the usualy rules your last expression must have a .5 at the end, so your should be cannot be right if the expression is correct.
479 - integer
79*479/(1+1) - is a half integer
293*1/(1+479-(479/62)*62) - integer
479 - is an integer
I would guess 293*1/(1+479-(479/62)*62) is not what is intended
RonL
3. ## Thanks
Thank you very much for the suggestion.
The Equation seems to be put off by the scripting language im using.
its called JASS. JASS seems to interpret 479 / 62 * 62 = 343 ??? lol
Strange language.
I have posted on a JASS forum to see if there is a reason....
Thanks again
4. Originally Posted by CaptainBlack
293*1/(1+479-(479/62)*62) is a half integer
How is this a half integer?
293*1/(1 + 479 - (479/62)*62)
= 293*1/(1 + 479 - 479)
= 293*1/(1 + 0)
= 293*1/1
= 293
-Dan
5. Originally Posted by topsquark
How is this a half integer?
293*1/(1 + 479 - (479/62)*62)
= 293*1/(1 + 479 - 479)
= 293*1/(1 + 0)
= 293*1/1
= 293
-Dan
Opps... sorry its the one before that:
79*479/(1+1)
That is the half integer!
RonL
6. Thank you for your help i have the answer.
If your interested its here:
JASS Math does not make sense ??? - The Helper Forums | {"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": 0.8644803762435913, "perplexity": 2732.701176320118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2016-50/segments/1480698543315.68/warc/CC-MAIN-20161202170903-00029-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/39626-laplace-transform.html | # Math Help - Laplace Transform
1. ## Laplace Transform
Hello…
I’m seeking a detailed derivation of the Laplace transform of the Gamma distribution:
$F(x) = \mathcal{L}\{f(t)\}=
\int_0^\infty g(t)\ e^{-st} dt=
(1 + s/\beta)^{-\alpha}
$
Where the PDF of the gamma distribution is:
$
g(t;\alpha, \beta) = \frac{\beta}{\Gamma(\alpha)}\ (\beta t)^{\alpha-1}\ e^{-\beta t}
$
Can someone please either give me a link with all the steps or show me how to get to the transform?
2. Originally Posted by paolopiace
Hello…
I’m seeking a detailed derivation of the Laplace transform of the Gamma distribution:
$F(x) = \mathcal{L}\{f(t)\}=
\int_0^\infty g(t)\ e^{-st} dt=
(1 + s/\beta)^{-\alpha}
$
Where the PDF of the gamma distribution is:
$
g(t;\alpha, \beta) = \frac{\beta}{\Gamma(\alpha)}\ (\beta t)^{\alpha-1}\ e^{-\beta t}
$
Can someone please either give me a link with all the steps or show me how to get to the transform?
assuming that $\alpha, \beta,$ and $s$ are positive numbers we have:
$\mathcal{L}\{g(t)\}=\int_0^{\infty} g(t)e^{-st} \ dt=\int_0^{\infty} \frac{\beta}{\Gamma(\alpha)} (\beta t)^{\alpha - 1} e^{-\beta t}e^{-st} \ dt=\frac{\beta^{\alpha}}{\Gamma(\alpha)} \int_0^{\infty}t^{\alpha - 1}e^{-(\beta + s)t} \ dt.$
now let $(\beta + s)t = u.$ then $t=\frac{u}{\beta + s}$ and $dt=\frac{du}{\beta + s}.$ hence:
$\mathcal{L}\{g(t)\}=\frac{\beta^{\alpha}}{\Gamma(\ alpha)} \int_0^{\infty}\left(\frac{u}{\beta + s} \right)^{\alpha - 1}e^{-u} \frac{du}{\beta + s}=\frac{\beta^{\alpha}}{(\beta + s)^{\alpha} \Gamma(\alpha)} \int_0^{\infty}u^{\alpha - 1}e^{-u} \ du.$ but by definition
$\int_0^{\infty}u^{\alpha - 1} e^{-u}du=\Gamma(\alpha).$ thus $\mathcal{L}\{g(t)\}=\frac{\beta^{\alpha}}{(\beta + s)^{\alpha}}=\left(1 + \frac{s}{\beta} \right)^{-\alpha}. \ \ \ \square$ | {"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": 13, "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": 0.9977495670318604, "perplexity": 234.91479631173007}, "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-2015-32/segments/1438042981576.7/warc/CC-MAIN-20150728002301-00244-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/23775-real-analysis-continuous-functions.html | # Math Help - Real Analysis continuous functions
1. ## Real Analysis continuous functions
Given that $h$ is a continuous func. on the compact set $K$ such that $h(x) \neq 0$ on $K$, and also given that $(g_n)$ is a sequence of functions such that they converge uniformly to $g$ on $K$, prove $\left(\frac{g_n}{h}\right)$ converges uniformly to $\frac{g}{h}$ on $K$.
Not sure. Apparently its a very hard proof.
2. From the topic title, is it safe to assume that these are function defined on the real numbers to the real numbers?
3. Originally Posted by Plato
From the topic title, is it safe to assume that these are function defined on the real numbers to the real numbers?
Mmhmm.
4. Originally Posted by Ideasman
Mmhmm.
I will take that as an "yes you can".
Because h is never zero and K compact we may assume that |h| has a minimum positive value in K. That is: $\left( {\exists x_0 \in K} \right)\left( {\forall y \in K} \right)\left[ {\left| {h(y)} \right| \ge \left| {h(x_0 )} \right| > 0} \right]$. Moreover, $\left( {\exists x_0 \in K} \right)\left( {\forall y \in K} \right)\left[ {\left| {\frac{1}{{h(y)}}} \right| \le \left| {\frac{1}{{h(x_0 )}}} \right|} \right]$.
Now you can get: $\left| {\frac{{g_n (y)}}{{h(y)}} - \frac{{g(y)}}{{h(y)}}} \right| \le \frac{{\left| {g_n (y) - g(y)} \right|}}{{\left| {h(x_0 )} \right|}}$.
So if $\varepsilon > 0$ by the uniform convergence of the $g_n$ choose N such that $n \ge N\quad \Rightarrow \quad \left| {g_n (y) - g(y)} \right| < \varepsilon \left| {h(x_0 )} \right|$. | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "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": 0.9654847979545593, "perplexity": 254.56754195206332}, "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/1438044271733.81/warc/CC-MAIN-20150728004431-00118-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://umj.imath.kiev.ua/authors/name/?lang=en&author_id=3527 | 2019
Том 71
№ 4
# Joseph J.
Articles: 1
Brief Communications (English)
### Some Remarks on Spectral Synthesis Sets
Ukr. Mat. Zh. - 2015. - 67, № 10. - pp. 1434-1438
Relations between the difference spectra of unions and intersections are studied and their implications on some problems in spectral synthesis are observed. | {"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": 0.8332117795944214, "perplexity": 4027.838246829418}, "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/1555578526923.39/warc/CC-MAIN-20190419001419-20190419023419-00419.warc.gz"} |
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# A school administrator will assign each student in a group
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SVP
Joined: 28 May 2005
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07 Oct 2005, 14:46
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A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
(2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
OPEN DISCUSSION OF THIS QUESTION IS HERE: a-school-administrator-will-assign-each-student-in-a-group-127509.html
[Reveal] Spoiler: OA
Director
Joined: 21 Aug 2005
Posts: 789
### Show Tags
07 Oct 2005, 21:19
i think the answer is D
Question basically asks whether n/m is an integer.
from A, we can say 3(n/m) is an integer. So, n/m must be an integer.
This will fail if n=1 and m=3 and other lower numbers, but the range of values for n and m exclude this possibility.
Similarly with B.
Director
Joined: 21 Aug 2005
Posts: 789
### Show Tags
08 Oct 2005, 10:22
I don't think it is D.
A) n=17 & m=7 --> 3n/m is not an integer
B) n=15 & m=4 ---> 13n/m is not an integer
Both cases wont work
Is it E?
Last edited by gsr on 08 Oct 2005, 15:47, edited 3 times in total.
Intern
Joined: 14 Jun 2005
Posts: 37
### Show Tags
08 Oct 2005, 12:53
I think ans should be B.
13n/m is an integer. And the question stem says 3<m<13<n
Suppose n = 14 [any no. greater than13] then for 13n/m to be an integer m has to be a factor of n. And so i think the statement alone is sufficient.
Lemme know if i am wrong.
SVP
Joined: 28 May 2005
Posts: 1705
Location: Dhaka
### Show Tags
09 Oct 2005, 11:42
OA is A.
can anybody has any explnation.
_________________
hey ya......
Director
Joined: 17 Oct 2005
Posts: 928
### Show Tags
04 Feb 2006, 16:37
A school administrator will assign each student in a group of n students to one of m classrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
1) it is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it
2) it is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
Director
Joined: 04 Jan 2006
Posts: 922
### Show Tags
04 Feb 2006, 17:49
B?
If 13n is assigned to m classes... then the number n is surely divisible by m since m cannot be 13 or 1.. So we are sure that m can be divided into n..
Is that right?
OA?
Senior Manager
Joined: 05 Jan 2006
Posts: 381
### Show Tags
05 Feb 2006, 01:32
I could not solve! but convinced with willget800 explaination!
btw where did you get this question!
VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA
### Show Tags
05 Feb 2006, 02:19
1
KUDOS
willget800 wrote:
B?
If 13n is assigned to m classes... then the number n is surely divisible by m since m cannot be 13 or 1.. So we are sure that m can be divided into n..
Is that right?
OA?
Good explanation.
_________________
"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds
Senior Manager
Joined: 11 Jan 2006
Posts: 269
Location: Chennai,India
### Show Tags
05 Feb 2006, 11:53
yeah! agree with willget800 , seems simple yet a good question!
_________________
vazlkaiye porkalam vazltuthan parkanum.... porkalam maralam porkalthan maruma
Director
Joined: 17 Oct 2005
Posts: 928
### Show Tags
05 Feb 2006, 14:00
i am stuck here
using the same reasoning can't I be sufficent also?
3n/m , 3 is prime so n has to be divisible by m?
VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA
### Show Tags
05 Feb 2006, 14:36
joemama142000 wrote:
i am stuck here
using the same reasoning can't I be sufficent also?
3n/m , 3 is prime so n has to be divisible by m?
For n = 14 and m = 6
3n/m is divisible but n/m is not!
For n=15, and m = 5 both 3n/m and n/m are divisible.
Hence 1 is INSUFF.
HTH
_________________
"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds
Manager
Joined: 17 Jan 2006
Posts: 92
### Show Tags
02 May 2006, 03:00
A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1) It is possible to assign each of 3n students to one of m classrooms so that eachclassroom has the same number of students assigned to it.
(2) It is possible to assign each of 13n students to one of m classrooms so that eachclassroom has the same number of students assigned to it.
Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA
### Show Tags
02 May 2006, 03:43
Hallo,
Think that A is insufficient
From A) 3n=K*m now n-15 then m can be 5 or 9 which makes A insuff
From B) 13n=K*m then m can not be a prime bigger than 13 , n=15 m can be 3 or 5, n=20 m can be 2,4,10
So think that B Is sufficient
Intern
Joined: 24 Apr 2006
Posts: 14
### Show Tags
26 Jun 2006, 16:48
CAREFUL !
OA is not A but B !!!!
See http://www.gmatclub.com/phpbb/viewtopic ... inistrator for explanation !!!
Director
Joined: 06 May 2006
Posts: 791
### Show Tags
26 Jun 2006, 17:12
#1. 3n/m is an integer.
Since m > 3, m could be a multiple of 3. However, n may or may not be a multiple of m.
e.g. n = 16, m = 12. or n = 15, m = 5
#2. 13n/m is an integer.
Since 13 > m, m cannot be a multiple of 13. Hence m has to be a factor of n. Sufficient.
B.
_________________
Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?
Senior Manager
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### Show Tags
26 Jun 2006, 18:15
Good question.
shd be (B)
Intern
Joined: 27 Jun 2006
Posts: 1
### Show Tags
27 Jun 2006, 09:49
Ive just decided to start studying for the gmat, so im a rookie here, but....
The question asks: is it possible to do so. and i think that (D) is correct b/c they both are sufficient to recognizing that it is possible.
CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
### Show Tags
27 Jun 2006, 14:35
mthizzle wrote:
Ive just decided to start studying for the gmat, so im a rookie here, but....
The question asks: is it possible to do so. and i think that (D) is correct b/c they both are sufficient to recognizing that it is possible.
This should be B.
In A if 3n = 42 and m = 6 then stem fails but if 3n = 48 and m = 4 then it works. So its INSUFF.
In B it works always.
_________________
SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008
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Joined: 30 Mar 2006
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### Show Tags
28 Jun 2006, 03:25
B.
1) Say there are 14 students hence 42 students can be divided into m classrooms
M can be 6, 7 etc but with 6 classrooms, each classroom won't have equal number of students
2) Say there are 14 students hence 182 students can be divided into m class rooms
here we only get 7 classrooms....
Pick any other value for students and u will see you only get classrooms that are factors of students
28 Jun 2006, 03:25
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https://www.physicsforums.com/threads/closed-form-determinant-of-a-hermitian-banded-toeplitz-matrix.661861/ | # Closed-form determinant of a hermitian banded toeplitz matrix!
1. Jan 1, 2013
### phd_student
Hello everyone,
I found that you're actively discussing math problems here and thought to share my problem with you.
[Givens:]
I have a specially structured complex-valued $n \times n$ matrix, that has only three non-zero constant diagonals (the main diagonal, the $j^{th}$ subdiagonal and the $j^{th}$ superdiagonal), $1 \leq j \leq n-1$. Moreover, it is a hermitian matrix, where the element composing the superdiagonal is actually the conjugate of that of the subdiagonal. For example, if $n=7, j=3$, the matrix is given by:
\begin{eqnarray}
A &=& \left[\begin{array}{ccccccc}
a &0 &0 &b^* &0 &0 &0 \\
0 &a &0 &0 &b^* &0 &0 \\
0 &0 &a &0 &0 &b^* &0 \\
b &0 &0 &a &0 &0 &b^* \\
0 &b &0 &0 &a &0 &0 \\
0 &0 &b &0 &0 &a &0 \\
0 &0 &0 &b &0 &0 &a
\end{array} \right]
\end{eqnarray}.
[Question:] I want to get the determinant, or the eigenvalues in closed form.
[Some hints:]
- It is clear that the determinant will be only a function of $a$, $b$, the shift $j$ and the order of the matrix, $n$.
- The matrix has the following properties:
1- It is a sparse Toeplitz matrix, that has only three non-zero diagonals.
2- It is a hermitian matrix.
3- It can be regarded as a special banded matrix, with zero diagonals inside the band.
4- We can also consider it as a diagonally dominant matrix. However, neglecting $b$ may not give a good approximation.
- A Tridiagonal Toeplitz matrix (for the special case when $j=1$) already has a known closed form expression for its eigen values, and consequently the determinant which is their direct product. It would be helpful also if we can express this shift in the diagonals as a certain simple operator, and use the known results of the tridiagonal case.
Any ideas?
Last edited: Jan 1, 2013
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http://www.boundaryvalueproblems.com/content/2012/1/83 | Research
# Bifurcation of positive periodic solutions of first-order impulsive differential equations
Ruyun Ma*, Bianxia Yang and Zhenyan Wang
Author Affiliations
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P.R. China
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Boundary Value Problems 2012, 2012:83 doi:10.1186/1687-2770-2012-83
The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2012/1/83
Received: 18 May 2012 Accepted: 20 July 2012 Published: 1 August 2012
© 2012 Ma et al.; licensee Springer
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
### Abstract
We give a global description of the branches of positive solutions of first-order impulsive boundary value problem:
which is not necessarily linearizable. Where is a parameter, are given impulsive points. Our approach is based on the Krein-Rutman theorem, topological degree, and global bifurcation techniques.
MSC: 34B10, 34B15, 34K15, 34K10, 34C25, 92D25.
##### Keywords:
Krein-Rutman theorem; topological degree; bifurcation from interval; impulsive boundary value problem; existence and multiplicity
### 1 Introduction
Some evolution processes are distinguished by the circumstance that at certain instants their evolution is subjected to a rapid change, that is, a jump in their states. Mathematically, this leads to an impulsive dynamical system. Differential equations involving impulsive effects occur in many applications: physics, population dynamics, ecology, biological systems, biotechnology, industrial robotic, pharmacokinetics, optimal control, etc. Therefore, the study of this class of impulsive differential equations has gained prominence and it is a rapidly growing field. See [1-9] and the references therein.
Let us consider the equation
(1.1)
subjected to the impulsive boundary condition
(1.2)
where is a real parameter, , are given impulsive points. We make the following assumptions:
(H1) is a 1-periodic function and ;
(H2) , , for , there exist positive constants such that
(H3) is 1-periodic function with respect to the first variable, and , exist, . Moreover, there exist functions with in any subinterval of such that
where with as uniformly for (), and
where with as uniformly for ();
(H4) , ;
(H5) there exists function and in any subinterval of such that
Some special cases of (1.1), (1.2) have been investigated. For example, Nieto [3] considered the (1.1), (1.2) with , . By using Schaeffer’s theorem, some sufficient conditions for existence of solutions of the IBVP (1.1), (1.2) with , were obtained.
Li, Nieto, and Shen [4] studied the existence of at least one positive periodic solutions of (1.1), (1.2) with , (m is a constant). By using Schaeffer’s fixed-point theorem, they got the solvability under f satisfied at most linear growth and is bounded or f is bounded and satisfied at most linear growth.
Liu [7] studied the existence and multiplicity of (1.1), (1.2) with , by using the fixed- point theorem in cones, and he proved the following:
Theorem A ([7], Theorem 3.1.1])
Let (H1) hold. Assume that, , , and
(1.3)
and
(1.4)
Then the problem (1.1), (1.2) withhas at least one positive solution wherewill be defined in (2.2) and
(1.5)
Theorem B ([7], Theorem 3.1.2])
Let (H1) hold. Assume that, , and
(1.6)
and
(1.7)
Then the problem (1.1), (1.2) withhas at least one positive solution whereW, wdefined as (1.5) and
(1.8)
It is worth remarking that the [3,4,7] only get the existence of solutions, and there is not any information of global structure of positive periodic solutions.
By using global bifurcation techniques, we obtain a complete description of the global structure of positive solutions for (1.1), (1.2) under weaker conditions. More precisely, our main result is the following theorem.
Theorem 1.1Let (H1), (H2), and (H3) hold. Suppose, , , . Then
(i) is a bifurcation interval of positive solutions from infinity for (1.1), (1.2), and there exists no bifurcation interval of positive solutions from infinity which is disjoint with. More precisely, there exists a componentof positive solutions of (1.1), (1.2) which meets, where, will be defined in Section 2;
(ii) is a bifurcation interval of positive solutions from the trivial solutions for (1.1), (1.2), and there exists no bifurcation interval of positive solutions from the trivial solutions which is disjoint with. More precisely, there exists a componentof positive solutions of (1.1), (1.2) which meets, where, will be defined in Section 4;
(iii) If (H4) and (H5) also hold, then there is a numbersuch that problem (1.1), (1.2) admits no positive solution with. In this case, .
Remark 1.1 There is no paper except [9] studying impulsive differential equations using bifurcation ideas. However, in [9], they only dealt with the case that , i.e., do exist. Where
From (H3), it is easy to see that the , may be not exist, the method used in [9] is not helpful any more in this case.
Remark 1.2 From (iii) of Theorem 1.1, we know that , are involved in . Moreover, is a unique bifurcation interval of positive solutions from infinity for (1.1), (1.2), and is a unique bifurcation interval of positive solutions from the trivial solutions for (1.1), (1.2). Therefore, must be intersected with .
Remark 1.3 Obviously, (H3) is more general than (1.5), (1.8). Moreover, if we let , , under conditions (1.3), (1.4), we get , , respectively. Hence, cross the hyperplane . Therefore, Theorem 3.1.1 of [7] is the corollary of Theorems 1.1 even in the special case.
Remark 1.4 Similar, if we let , , only under condition (1.6), we can obtain . From Proposition 3.1, we will know that is unbounded in λ direction, so, cross the hyperplane . Therefore, Theorem 3.1.2 of [7] is the corollary of Theorems 1.1 even in the special case and weaker condition.
Remark 1.5 There are many papers which get the positive solutions using bifurcation from the interval. For example, see [10,11]. However, in those papers, the linear operator corresponding problem is self-adjoint. It is easy to see that the linear operator corresponding (1.1), (1.2) is not self-adjoint. So, the method used in [9,10] is not helpful in this case.
Remark 1.6 Condition (H3) means that f is not necessarily linearizable near 0 and infinity. So, we will apply the following global bifurcation theorems for mappings which are not necessarily smooth to get a global description of the branches of positive solutions of (1.1), (1.2), and then, we obtain the existence and multiplicity of positive solutions of (1.1), (1.2).
Theorem C (K. Schmitt, R. C. Thompson [12])
LetVbe a real reflexive Banach space. Letbe completely continuous such that, . Let () be such thatis an isolated solution of the equation
(1.9)
forand, where, are not bifurcation points of (1.9). Furthermore, assume that
whereis an isolating neighborhood of the trivial solution. Let
Then there exists a connected componentofcontainingin, and either
(i) is unbounded in, or
(ii) .
Theorem D (K. Schmitt [13])
LetVbe a real reflexive Banach space. Letbe completely continuous, and let () be such that the solution of (1.9) are, a priori, bounded inVforand, i.e., there exists ansuch that
for alluwith. Furthermore, assume that
forlarge. Then there exists a closed connected setof solutions of (1.9) that is unbounded in, and either
(i) is unbounded inλdirection, or
(ii) there exist an intervalsuch that, andbifurcates from infinity in.
The rest of the paper is organized as follows: In Section 2, we state some notations and preliminary results. Sections 3 and 4 are devoted to study the bifurcation from infinity and from the trivial solution for a nonlinear problem which are not necessarily linearizable, respectively. Finally, in Section 5, we consider the intertwining of the branches bifurcating from infinity and from the trivial solution.
### 2 Preliminaries
Let
Then is a Banach space with the norm .
By a positive solution of the problem (1.1), (1.2), we mean a pair , where and u is a solution of (1.1), (1.2) with . Let be the closure of the set of positive solutions of (1.1), (1.2), where .
Lemma 2.1 ([14], Theorem 6.26])
The spectrumof compact linear operatorThas following properties:
(i) is a countable set with no accumulation point which is different from zero;
(ii) each nonzerois an eigenvalue ofTwith finite multiplicity, andis an eigenvalue ofwith the same multiplicity, wheredenote the conjugate ofλ, denote the conjugate operator ofT.
Let , with inner product and norm .
Let and in any subinterval of . Further define the linear operator ,
(2.1)
where as defined in (H2), is the Green’s function of
and
(2.2)
where , it is easy to see that (H1) implies that .
By virtue of Krein-Rutman theorems (see [15]), we have the following lemma.
Lemma 2.2Suppose that (H1) holds, then for the operatordefined by (2.1), has a unique characteristic value, which is positive, real, simple, and the corresponding eigenfunctionis of one sign, i.e., we have.
Proof It is a direct consequence of the Krein-Rutman theorem [15], Theorem 19.3]. □
Remark 2.1 Since is real number, so from Lemma 2.1, is also the characteristic value of , let denote the nonnegative eigenfunction of corresponding to , where denote the conjugate operator of . Therefore, we have
We extend the function f to function , defined on by
Then on .
For , the problem
(2.3)
is equivalent to the operator equation .
Remark 2.2 For , if u is a nontrivial solution of (2.3), from the positivity of and , we have that on , so u is a nontrivial solution of (1.1), (1.2). Therefore, the closure of the set of nontrivial solutions of (2.3) in is exactly Σ.
The problem (2.3) is now equivalent to the operator equation
(2.4)
In the following, we shall apply the Leray-Schauder degree theory, mainly to the mapping ,
For , let , let denote the degree of on with respect to 0.
### 3 Bifurcation from infinity
In this section, we are devoted to study the bifurcation from infinity.
Lemma 3.1Letbe a compact interval with. Then there exists a numbersuch that
Proof Suppose on the contrary that there exists with (), such that . We may assume . By Remark 2.2, in . Set . Then
From (H2), (H3), we know that is bounded in , so is a relatively compact set in since is bounded and continuous and . Suppose in . Then and in .
Now, from condition (H2), we know that there exist , such that
From (H3), we have that
So,
and
accordingly, we have
(3.1)
and
(3.2)
Let and denote the nonnegative eigenfunctions of , corresponding to , and , respectively. Then we have from the (3.1) that
Letting , we have
we obtain that
and consequently
Similarly, we deduce from (3.2) that
Thus, . This contradicts . □
Corollary 3.1Forand. Then.
Proof Lemma 3.1, applied to the interval , guarantees the existence of such that for ,
Hence, for any ,
which implies the assertion. □
On the other hand, we have
Lemma 3.2Suppose. Then there existswith the property thatwith, ,
whereis the nonnegative eigenfunction ofcorresponding to.
Proof Let us assume that for some sequence in with and numbers , such that . Then
and we conclude from Remark 2.2 that in . So we have
Choose such that
(3.3)
By (H3), there exists , such that
From , then exists , such that
and consequently
(3.4)
Let , applying (3.4), it follows that
Thus,
this contradicts (3.3). □
Corollary 3.2Forand, .
Proof By Lemma 3.2, there exists such that
Then
for all . The assertion follows. □
We are now ready to prove
Proposition 3.1is a bifurcation interval of positive solutions from infinity for the problem (2.4). There exists an unbounded componentof positive solutions of (2.4) which meets, and is unbounded inλdirection. Moreover, there exists no bifurcation interval of positive solutions from infinity which is disjointed with.
Proof For fixed with , let us take that , and . It is easy to check that for , all of the conditions of Theorem D are satisfied. So, there exists a closed connected set of solutions of (2.4) that is unbounded in , and either
(i) is unbounded in λ direction, or else
(ii) such that and bifurcates from infinity in .
By Lemma 3.1, the case (ii) cannot occur. Thus, bifurcates from infinity in and is unbounded in λ direction. Furthermore, we have from Lemma 3.1 that for any closed interval , the set is bounded in . So, must be bifurcated from infinity in and is unbounded in λ direction. □
Assertion (i) of Theorem 1.1 follows directly.
### 4 Bifurcation from the trivial solutions
In this section, we shall study the bifurcation from the trivial solution for a nonlinear problem which is not necessarily linearizable near 0 and infinity.
As in Section 2, let and in any subinterval of . Further define the linear operator ,
(4.1)
where is defined in (H2), is defined in (2.2).
Similar as Lemma 2.2, we have the following lemma.
Lemma 4.1Suppose that (H1) holds, then the operatorhas a unique characteristic value, which is positive, real, simple, and the corresponding eigenfunctionis of one sign, i.e., we have.
Remark 4.1 Since is real number, so from Lemma 2.1, is also the characteristic value of , where denote the conjugate operator of , let denote the nonnegative eigenfunction of corresponding to . Therefore, we have
Lemma 4.2Letbe a compact interval with. Then there exists a numbersuch that
Proof Suppose on the contrary that there exists with (), such that . We may assume . By Remark 2.2, in . Set . Then
From (H2), (H3), we know that is bounded in , so we infer that is a relatively compact set in , hence (for a subsequence) with in , .
Now, from condition (H2), we know that there exist , such that
From (H3), we have that
So,
and
accordingly, we have
(4.2)
and
(4.3)
Let and denote the nonnegative eigenfunctions of , corresponding to , and , respectively. Then we have from the (4.2) that
Letting , we have
we obtain that
and consequently
Similarly, we deduce from (4.3) that
Thus, . This contradicts . □
Corollary 4.1Forand. Then.
On the other hand, we have
Lemma 4.3Suppose. Then there existswith the property thatwith, ,
whereis the nonnegative eigenfunction of thecorresponding to.
Proof We assume again on the contrary that there exists and a sequence with and in , such that for all .
Then
and we conclude from Remark 2.2 that in . So, we have
Choose such that
(4.4)
By (H3), there exists , such that
From , then exists , such that
and consequently
(4.5)
Let , applying (4.5), it follows that
Thus,
this contradicts with (4.4). □
Corollary 4.2Forand. Then.
Proof By Lemma 4.3, there exists such that
Then
for all . Then the assertion follows. □
Now, using Theorem C and the similar method to prove Proposition 3.1 with obvious changes, we may prove the following proposition.
Proposition 4.1is a bifurcation interval of positive solutions from the trivial solution for the problem (2.4). There exists an unbounded componentof positive solutions of (2.4) which meets. Moreover, there exists no bifurcation interval of positive solutions from the trivial solution which is disjointed with.
This is exactly the assertion (ii) of Theorem 1.1.
### 5 Global behavior of the component of positive solutions
In this section, we consider the intertwining of the branches bifurcating from infinity and from the trivial solution.
Let , for . From (H2), we have , .
Define the linear operator ,
(5.1)
where is defined in (H5), is defined in (2.2).
Similar as Lemma 2.2, we have the following lemma.
Lemma 5.1The operatorhas a unique characteristic value, which is positive, real, simple, and the corresponding eigenfunctionis of one sign, i.e., we have.
Remark 5.1 Since is real number, so from Lemma 2.1, is also the characteristic value of , where denote the conjugate operator of , let denote the nonnegative eigenfunction of corresponding to . Therefore, we have
Lemma 5.2Let (H1)-(H5) hold. Then there exists a numbersuch that there is no positive solutionofwith.
Proof Let be a positive solution of . Then
From (H5) and the definition of , we have
(5.2)
From (5.2), we have
Thus,
□
The assertion that in Theorem 1.1(iii) now easily follows. For, in the case, and are contained in . Moreover, there exists no bifurcation interval of positive solution from infinity which is disjointed with , there exists no bifurcation interval of positive solution from the trivial solution which is disjointed with . In Theorem 1.1(iii), the unbounded component has to meet .
### Competing interests
The authors declare that they have no competing interests.
### Authors’ contributions
RM completed the main study and carried out the results of this article. BY drafted the manuscript. ZW checked the proofs and verified the calculation. All the authors read and approved the final manuscript.
### Acknowledgements
The authors are very grateful to the anonymous referees for their valuable suggestions. This work was supported by the NSFC (No. 11061030), NSFC (No. 11126296), and the Fundamental Research Funds for the Gansu Universities.
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15. Deimling, K: Nonlinear Functional Analysis, Springer, Berlin (1985) | {"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": 0.9870148301124573, "perplexity": 1122.3652046180516}, "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-2015-06/segments/1422122127848.98/warc/CC-MAIN-20150124175527-00128-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://arxiv.org/abs/1106.4775 | hep-ex
(what is this?)
(what is this?)
# Title: Search for New Physics with a Mono-Jet and Missing Transverse Energy in pp Collisions at sqrt(s) = 7 TeV
Abstract: A study of events with missing transverse energy and an energetic jet is performed using pp collision data at a centre-of-mass energy of 7 TeV. The data were collected by the CMS detector at the LHC, and correspond to an integrated luminosity of 36 inverse picobarns. An excess of these events over standard model contributions is a signature of new physics such as large extra dimensions and unparticles. The number of observed events is in good agreement with the prediction of the standard model, and significant extension of the current limits on parameters of new physics benchmark models is achieved.
Subjects: High Energy Physics - Experiment (hep-ex) Journal reference: Phys. Rev. Lett. 107, 201804 (2011) DOI: 10.1103/PhysRevLett.107.201804 Report number: CMS-EXO-11-003, CERN-PH-EP-2011-070 Cite as: arXiv:1106.4775 [hep-ex] (or arXiv:1106.4775v1 [hep-ex] for this version)
## Submission history
From: Cms Collaboration [view email]
[v1] Thu, 23 Jun 2011 17:10:12 GMT (282kb,D) | {"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": 0.9276831746101379, "perplexity": 1808.001964577343}, "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/1480698542217.43/warc/CC-MAIN-20161202170902-00183-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/9220/what-does-the-generating-function-x-1-e-x-count | # What does the generating function $x/(1 - e^{-x})$ count?
Let $x$ be a formal (or small, since the function is analytic) variable, and consider the power series $$A(x) = \frac{x}{1 - e^{-x}} = \sum_{m=0}^\infty \left( -\sum_{n=1}^\infty \frac{(-x)^n}{(n+1)!} \right)^m = 1 + \frac12 x + \frac1{12}x^2 + 0x^3 - \frac1{720}x^4 + \dots$$ where I might have made an arithmetic error in expanding it out.
1. Are all the coefficients egyptian, in the sense that they are given by $A^{(n)}(0)/n! = 1/N$ for $N$ an integer? The answer is no, unless I made an error, e.g. the third coefficient. But maybe every non-zero coefficient is egyptian?
2. If all the coefficients were positive eqyptian, then the sequence of denominators might count something — one hopes that the $n$th element of any sequence of nonnegative integers counts the number of ways of putting some type of structure on an $n$-element set.
Of course, generating functions really come in two types: ordinary and exponential. The difference is whether you think of the coefficients as $\sum a_n x^n$ or as $\sum A^{(n)} x^n/n!$. If it makes more sense as an exponential generating function, that's cool too.
So my question really is: is there a way of computing the $n$th coefficient of $A(x)$, or equivalently of computing $A^{(n)}(0)/n!$, without expanding products of power series the long way?
### Where you might have seen this series
Let $\xi,\psi$ be non-commuting variables over a field of characteristic $0$, and let $B(\xi,\psi) = \log(\exp \xi \exp \psi)$ be the Baker-Campbell-Hausdorff series. Fixing $\xi$ and thinking of this as a power series in $\psi$, it is given by $$B(\xi,\psi) = \xi + A(\text{ad }\xi)(\psi) + O(\psi^2)$$ where $A$ is the series above, and $\text{ad }\xi$ is the linear operator given by the commutator: $(\text{ad }\xi)(\psi) = [\xi,\psi] = \xi\psi - \psi\xi$.
More generally, $B$ can be written entirely in terms of the commutator, and so makes sense as a $\mathfrak g$-valued power series on $\mathfrak g$ for any Lie algebra $\mathfrak g$. It converges in a neighborhood of $0$ when $\mathfrak g$ is finite-dimensional over $\mathbb R$, in which case $\mathfrak g$ is a (generally noncommutative) "partial group".
(More generally, you can consider the "formal group" of $\mathfrak g$. Namely, take the commutative ring $\mathcal P(\mathfrak g)$ of formal power series on $\mathfrak g$; then $B$ defines a non-cocommutative comultiplication, making $\mathcal P = \mathcal P(\mathfrak g)$ into a Hopf algebra. Or rather, $B(\mathcal P)$ does not land in the algebraic tensor product $\mathcal P \otimes \mathcal P$. Instead, $\mathcal P$ is cofiltered, in the sense that it is a limit $\dots \to \mathcal P_2 \to \mathcal P_1 \to \mathcal P_0 = 0$, where (over characteristic 0, anyway) $\mathcal P_n = \text{Poly}(\mathfrak g)/(\mathfrak g \text{Poly}(\mathfrak g))^n$, where $\text{Poly}(\mathfrak g)$ is the ring of polynomial functions on $\mathfrak g$, and $\mathfrak g \text{Poly}(\mathfrak g)$ is the ideal of functions vanishing at $0$. Then $B$ lands in the cofiltered tensor product, which is just what it sounds like. (In arbitrary characteristic, $\mathcal P$ is the cofiltered dual of the filtered Hopf algebra $\mathcal S \mathfrak g$, the symmetric algebra of $\mathfrak g$, filtered by degree.))
### Why I care
When $\mathfrak g$ is finite-dimensional over $\mathbb R$, and $U$ is the open neighborhood of $0$ in which $B$ converges, then $\mathfrak g$ acts as left-invariant derivations on $U$, where by left-invariant I mean under the multiplication $B$. Hence there is a canonical identification of the universal enveloping algebra $\mathcal U\mathfrak g$ with the algebra of left-invariant differential operators on $U$. Since $\mathfrak g$ is in particular a vector space, the "symbol" map gives a canonical identification between the algebra of differential operators on $U$ and the algebra of functions on the cotangent bundle $T^\*U$ that are polynomial (of uniformly bounded degree) in the cotangent directions. Left-invariance then means that the operators are uniquely determined by their restrictions to the fiber $T^\*_0\mathfrak g = \mathfrak g^\*$, and the space of polynomials on $\mathfrak g^\*$ is canonically the symmetric algebra $\mathcal S \mathfrak g$. This gives a canonical PBW map $\mathcal U \mathfrak g \to \mathcal S \mathfrak g$, a fact I learned from J. Baez and J. Dolan.
(In the formal group language, the noncocommutative cofiltered Hopf algebra $\mathcal P(\mathfrak g)$ is precisely the cofiltered dual to the filtered algebra $\mathcal U\mathfrak g$, whereas with its cocommutative Hopf structure $\mathcal P(\mathfrak g)$ is dual to $\mathcal S \mathfrak g$. But as algebras these are the same, and unpacking the dualizations gives the PBW map $\mathcal U\mathfrak g \cong \mathcal S \mathfrak g$, and explains why it is actually an isomorphism of coalgebras.)
Anyway, in one direction, the isomorphism $\mathcal U\mathfrak g \cong \mathcal S \mathfrak g$ is easy. Namely, the map $\mathcal S \mathfrak g \to \mathcal U \mathfrak g$ is given on monomials by the "symmetrization map" $\xi_1\cdots \xi_n \mapsto \frac1{n!} \sum_{\sigma \in S_n} \prod_{k=1}^n \xi_{\sigma(k)}$, where $S_n$ is the symmetric group on $n$ letters, and the product is ordered. (In this direction, the isomorphism of coalgebras is obvious. In fact, the corresponding symmetrization map into the full tensor algebra is a coalgebra homomorphism.)
In the reverse direction, I can explain the map $\mathcal U \mathfrak g \to \mathcal S \mathfrak g$ as follows. On a monomial $\xi_1\cdots \xi_n$, it acts as follows. Draw $n$ dots on a line, and label them $\xi_1,\dots,\xi_n$. Draw arrows between the dots so that each arrow goes to the right (from a lower index to a higher index), and each dot has either 0 or 1 arrow out of it. At each dot, totally order the incoming arrows. Then for each such diagram, evaluate it as follows. What you want to do is collapse each arrow $\psi\to \phi$ into a dot labeled by $[\psi,\phi]$ at the spot that was $\phi$, but never collapse $\psi\to \phi$ unless $\psi$ has no incoming arrows, and if $\phi$ has multiple incoming arrows, collapse them following your chosen total ordering. So at the end of the day, you'll have some dots with no arrows left, each labeled by an element of $\mathfrak g$; multiply these elements together in $\mathcal S\mathfrak g$. Also, multiply each such element by a numerical coefficient as follows: for each dot in your original diagram, let $m$ be the number of incoming arrows, and multiply the final product by the $m$th coefficient of the power series $A(x)$. Sum over all diagrams.
Anyway, the previous paragraph is all well and cool, but it would be better if the numerical coefficient could be read more directly off the diagram somehow, without having to really think about the function $A(x)$.
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I am sort of astonished that you gave so much background without mentioning the name of this sequence: en.wikipedia.org/wiki/Bernoulli_number – Qiaochu Yuan Dec 18 '09 at 1:57
@Qiaochu: See, I'm neither a combinatorialist nor a number theorist, and although I guess I've seen the Bernoulli numbers before, I never really encoded them in memory. Anyway, I've accepted Pete's answer below, but I'm secretly hoping that someone will connect it with the diagrams I described. – Theo Johnson-Freyd Dec 18 '09 at 2:55
@Theo: I didn't actually remember these were the Bernoulli numbers until I did the expansion (by computer, of course) and saw the mysterious numerator 691. – Michael Lugo Dec 18 '09 at 3:27
Given your background you might be interested to know that this power series is used to define the Todd class: en.wikipedia.org/wiki/Todd_class – Steve Huntsman Dec 18 '09 at 6:22
Another place to see this series, though shifted by two: the Planck black-body distribution. en.wikipedia.org/wiki/Planck's_law – Allen Knutson Feb 26 '10 at 4:51
Two people have pointed it out already, but somehow I can't resist: your formal power series is precisely the defining power series of the Bernoulli numbers:
http://en.wikipedia.org/wiki/Bernoulli_number#Generating_function
Accordingly, they are far from Egyptian: as came up recently in response to the question
When does the zeta function take on integer values?
the odd-numbered terms (except the first) are all zero, whereas the even-numbered terms alternate in sign and grow rapidly in absolute value, so only finitely many are reciprocals of integers.
I find it curious that you are looking at this sequence from such a sophisticated perspective and didn't know its classical roots. I feel like there should be a lesson here, but I don't know exactly what it is. Here's a possibility: every young mathematician should learn some elementary number theory regardless of their primary interests. Comments?
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You win. I know a lot about Lie algebras, and I've never studied any number theory. I think I've seen the Bernoulli numbers once or twice, but never really encoded them. – Theo Johnson-Freyd Dec 18 '09 at 2:50
Bernoulli numbers are fairly ubiquitous. They come up, for example, in very basic real analysis; namely in Euler-Maclaurin summation formula. So I am not sure if these numbers should be thought of as pertaining to number theory. – Idoneal Jan 3 '10 at 4:19
Well, certainly not only to number theory, anyway. – Pete L. Clark Jan 3 '10 at 4:29
I'd certainly agree with your last suggestion (and in particular wish I knew more about number theory than I do). Next, take a roomful of mathematicians, get all their suggestions for fields that should be added to "elementary number theory" here. What would you guess is the probability that any one of the mathematicians in the room has any real knowledge of all the fields that have been named? – Mark Meckes Jun 3 '10 at 17:02
I would add that it's nearly impossible to learn the BCH formula (with the proof, of course) and $\mathit{not}$ to see Bernoulli numbers mentioned. There is another lesson here, possibly that one needs to read textbooks systematically rather than just pick up bits and pieces. – Victor Protsak Jul 15 '10 at 18:11
Here's another way to get at the answer. You think you have a sequence of rationals that may be familiar:
1, 1/2,1/12,0,-1/720,...
The denominators seem more interesting than the numerator, so maybe the "right" sequence is:
1,2,12,1,720,...
You go to Sloane's Encyclopedia and enter the sequence, to no avail. You could now try superseeker, which looks at many transformations of the sequence, but for this few terms that will return too many hits. Let's try the one transformation you mentioned, and look at the exponential generating function, whose coefficients have denominators:
1, 2, 6, 1, 30, ...
Sloane's immediately identifies that sequence as the denominators of Bernoulli numbers, giving not only the generating function you started with but many other interesting factoids and references.
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I think Sloane's should always be consulted when faced with an unknown sequence of integers or of numbers from which integers may be reasonably extracted. – Omar Antolín-Camarena Mar 9 '10 at 12:40
My favourite introduction to the Bernoulli numbers is section 3 of Pierre Cartier's paper Mathemagics. I quote:
I claim that they are defined by the equation $(B + 1)^n = B^n$ for $n \geq 2$, together with the initial condition $B^0 = 1$. The meaning is the following: expand $(B + 1)^n$ by the binomial theorem, then replace the power $B^k$ by $B_k$.
There's a whole lot of great stuff in this paper, besides Bernoulli numbers.
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Ah, yes, I have seen that definition. What I've never done is calculated out more than the first two or so terms, and 1, 1/2, 1/12 is meaningless, and when today I got 1, 1/2, 1/12, 0, -1/720, I still didn't have anything with which to recognize it. – Theo Johnson-Freyd Dec 18 '09 at 5:48
You might already know this, but that 1/12 is part of the "reason" for the appearances of 12 and 24 in mathematics, as described by John Baez here: math.ucr.edu/home/baez/week126.html – Qiaochu Yuan Dec 18 '09 at 8:43
I am adding the following remark because it may be of some interest to the number theorists who recognized the Bernoulli numbers to know that the relationship with Lie theory explained in the question has number-theoretic substance: namely, in his article on the thrice-punctured sphere, Deligne uses the Lie algebra point of view on Bernoulli numbers described in the question (together with other ingredients, of course, and applied to a specific Lie algebra) to derive Euler's formula for the values of $\zeta(2n)$.
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The Bernoulli numbers are closely related to alternating permutations. That is to say, permutations like $1524376$ where the numbers alternately go up and down. Specifically, if $A_n$ is the number of such permutations of an $n$ element set, then $$B_{2n} = (-1)^{n-1} \frac{2n}{4^{2n}-2^{2n}} A_{2n-1}.$$ It's possible you could somehow relate your sums over diagrams to alternating permutations.
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To have a geometric interpretation of this generating function in Lie theory you do not need to work over reals, in fact any commutative ground ring containing rationals suffices. For a version of such interpretation utilizing functors representing a version of "formal schemes" see chapters 7-10 (and introduction) to our paper
N. Durov, S. Meljanac, A. Samsarov, Z. Škoda, A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra, Journal of Algebra 309, Issue 1, pp.318-359 (2007), math.RT/0604096
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This isn't an answer, but I saw that you said a couple of times that you were doing the expansion by hand. I'll just point out that you can get a free sage notebook account, and then do
f(x) = x/(1 - e^(-x))
f.series(x,10)
in a new worksheet to get the expansion to the $x^{10}$ term. Wolfram Alpha probably has something similar. Of course, one sometimes learns something by doing things manually, but it is often useful to have an easy way to check your answer.
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If you expand this out a bit further, you get
$1 + {1 \over 2} x + {1 \over 12} x^2 - {1 \over 720} x^4 + {1 \over 30240} x^6 - {1 \over 1209600} x^8 + {1 \over 47900160} x^{10} - {691 \over 1307674368000} x^{12} + \cdots$
Notice that the nonzero coefficients are alternating in sign.
In fact it turns out that the sequence you call $A^{(n)}$ are exactly the Bernoulli numbers.
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Nice. I was surprised when the first 0 showed up, since I've been expanding by hand. – Theo Johnson-Freyd Dec 18 '09 at 2:52
You will find what you describe in the first reference. This describes how the Bernouilli numbers arise when studying the universal enveloping algebra. I have seen unpublished notes on this from a talk by Kostant in the '70s. This is a strong form of the PBW theorem and is closer to Poincare's result. This is discussed in the second reference. This is an early version of universal quantisation.
MR2301242 (2008d:17015) Durov, Nikolai ; Meljanac, Stjepan ; Samsarov, Andjelo ; Škoda, Zoran . A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra. J. Algebra 309 (2007), no. 1, 318--359.
MR1793103 (2001f:01039) Ton-That, Tuong ; Tran, Thai-Duong . Poincaré's proof of the so-called Birkhoff-Witt theorem. Rev. Histoire Math. 5 (1999), no. 2, 249--284 (2000).
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You can generate the Bernoullis through the combinatorics of permutahedra and graphical interpretations of surjections presented in OEIS-A133314 (cf. A049019, A019538, A008292) weighted by the reciprocal integers. (See also MOQ-61252.)
This is equivalent to determining the reciprocal of the exponential generating function
$$\frac{e^t-1}{t}=1+\frac{1}{2}t+ \frac{1}{3}\frac{t^2}{2!}+ \frac{1}{4}\frac{t^3}{3!}+\cdots\;\;.$$
Naturally, it's an involution, so you can go in the reverse direction from the Bernoullis to the reciprocal integers by the same weighted surjections.
But, with the o.g.f., using the normalized Bernoulli numbers, compositional inversion, rather than reciprocation enters the picture and, therefore, weighted noncrossing partitions and Dyck lattice paths (and myriad other related combinatoric structures). See the last paragraphs of my answer to the MOQ referenced above.
These number arrays can be related to volumes of structures, as well as the Bernoullis (see Noam Elkies).
For relations to binary trees, see A000182.
Also see these papers relating the Bernoullis to quantum algebras:
Hodges and Sukumar, Sukumar and Hodges, Hetyei.
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Here you can find all sorts of information, different representations and connections concerning the Bernoulli numbers:
http://www.wolframalpha.com/input/?i=Bernoulli+numbers
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https://arxiv.org/abs/hep-ph/0307136 | hep-ph
# Title:Target Mass Effects in Polarized Virtual Photon Structure Functions
Abstract: We study target mass effects in the polarized virtual photon structure functions $g_1^\gamma (x,Q^2,P^2)$, $g_2^\gamma (x,Q^2,P^2)$ in the kinematic region $\Lambda^2\ll P^2 \ll Q^2$, where $-Q^2 (-P^2)$ is the mass squared of the probe (target) photon. We obtain the expressions for $g_1^\gamma (x,Q^2,P^2)$ and $g_2^\gamma (x,Q^2,P^2)$ in closed form by inverting the Nachtmann moments for the twist-2 and twist-3 operators. Numerical analysis shows that target mass effects appear at large $x$ and become sizable near $x_{\rm max}(=1/(1+\frac{P^2}{Q^2}))$, the maximal value of $x$, as the ratio $P^2/Q^2$ increases. Target mass effects for the sum rules of $g_1^\gamma$ and $g_2^\gamma$ are also discussed.
Comments: 24 pages, LaTeX, 9 eps figures Subjects: High Energy Physics - Phenomenology (hep-ph) Journal reference: Phys.Rev. D68 (2003) 054025 DOI: 10.1103/PhysRevD.68.054025 Report number: YNU-HEPTh-03-102, KUNS-1845 Cite as: arXiv:hep-ph/0307136 (or for this version)
## Submission history
From: Tsuneo Uematsu [view email]
[v1] Thu, 10 Jul 2003 07:43:17 UTC (69 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": 0.9028012752532959, "perplexity": 2531.667957036048}, "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-2019-47/segments/1573496665573.50/warc/CC-MAIN-20191112124615-20191112152615-00543.warc.gz"} |
https://arxiv.org/abs/1809.03475 | quant-ph
Title:Operational foundations of complementarity and uncertainty relations
Abstract: The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand side of uncertainty relation is generally not operational as it depends on the quantum formalism. Also, while joint non-measurability of observables is an operational notion, the complementarity in Bohr sense (i.e. excess of information needed to describe the system) has not yet been expressed in purely operational terms.
In this paper we propose a solution to these problems, by introducing an operational definition for complementarity, and further postulating uncertainty as a necessary price for complementarity in physical theories. In other words, we propose to put the (operational) complementarity as the right-hand side of uncertainty relation.
Concretely, we first identify two different notions of uncertainty and complementarity for which the above principle holds in quantum mechanics. We also introduce postulates for the general measures of uncertainty and complementarity. In order to define quantifiers of complementarity we first turn to the simpler notion of independence that is defined solely in terms of statistics two observables.
We also use our framework to define new complementarity indicators based on (i) performance of random access codes, (ii) geometrical properties of the body of observed statistics, and (iii) variation of information. We then show that they can be used to state uncertainty relations. Moreover, we show that non-signaling and uncertainty relation expressed by complementarity of type (ii) leads to the Tsirelson bound for CHSH inequality. Lastly, we show that a variant of Information Causality called Information Content Principle, can be interpreted as uncertainty relation in the above sense.
Comments: 24 pages, 13 Figures, Comments and suggestions are welcome, v3: additional results about RACs added, more emphasis put on the interplay between convexity of physical theories and complementarity Subjects: Quantum Physics (quant-ph) Cite as: arXiv:1809.03475 [quant-ph] (or arXiv:1809.03475v3 [quant-ph] for this version)
Submission history
From: Michał Oszmaniec [view email]
[v1] Mon, 10 Sep 2018 17:47:44 UTC (439 KB)
[v2] Tue, 11 Sep 2018 14:28:51 UTC (439 KB)
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https://wpblog.wyzant.com/resources/lessons/math/algebra/simplifying-exponents-variables/ | # Exponents of Variables Lesson
The last lesson explained how to simplify exponents of numbers by multiplying as shown below. You know that 3 squared is the same as 1 * 3 * 3.
Exponents of variables work the same way – the exponent indicates how many times 1 is multiplied by the base of the exponent. Take a look at the example below.
The first problem we will work on is below. It doesn’t contain a variable, but it will help us to learn how to simplify a similar problem with a varable in place of the first 3.
Normally, you would simplify this problem by simplifying the inside of the parentheses first:
Then, simplify the exponent outside the parentheses.
This method gives a correct answer, but there is an easier way.
## Exponents of Variables
We will be solving the same problem again:
This time, instead simplifying inside of the parentheses first, we will “distribute” the exponent of the parentheses to the inside of the parentheses.
Now the only thing left to do is simplify the exponent that is left.
As you can see this method also gives an answer of 729.
## Exponents of Variables
The first example with variables is
We will try simplifying it the first way, by simplifying the inside of the parentheses followed by simplifying the exponent on the outside.
Now that the inside is simplified, the exponent on the parentheses indicates that the expression is equivalent to a 1 multiplied by the parentheses, three times. As you can see x is being multiplied 6 times, hence the answer x to the sixth power.
## Exponents of Variables
Again, the problem we are working is
As with the second number example earlier in this lesson, simply multiply the two exponents:
Then remove the parentheses, and as you can see the answer is the same.
## Exponents of Variables
The problem below has two key differences.
• First, it has a term with two variables, and as you can see the exponent from outside the parentheses must multiply EACH of them.
• Second, there is a negative sign inside the parentheses. Since the exponent on the parentheses is 3, the negative sign is written in front of the term three times. Then the multiple signs are simplified.
Both the problem above and below this have a negative sign inside a set of parentheses which is raised to some power. If you did a lot of these you’d notice that when the parentheses are raised to an odd power such as 3, the answer will be negative. If
the parentheses are raised to an even power like the one below, the answer will be positive.
The last problem, shown below has a negative sign outisde the parentheses. Again, because of the Order of Operations which is presented in a later lesson, the exponent must be simplified before you do anything with the negative sign. Look at the work
below:
Note that even though the exponent on the parentheses was a 4 which is an even number, the final answer is negative. This is because the negative sign was outside of the parentheses, not inside as in the previous example.
## Exponents of Variables Resources
Practice Problems / WorksheetPractice all of the methods you learned in this lesson. Next Lesson: Exponents of Polynomials (Parentheses) Learn how to simplify an exponent of a polynomial, or two or more terms inside a parenthesis.
## Tutoring
Looking for someone to help you with algebra? At Wyzant, connect with algebra tutors and math tutors nearby. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of clicks.
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http://mathlake.com/Statistics-Class-11 | # Statistics Class 11
## Statistics Class 11 Notes
In statistics class 11, the importance of statistics in studying the measures of dispersion and the methods of calculating the grouped and ungrouped data has been explained. In applied mathematics, statistics is a branch that deals with the collection, organization and interpretation of data. It is similar to the study of the probability of events occurring based on the collection of data or the known quantities of data. Some of the concepts with examples and the scope of the statistics are explained in the Class 11 maths chapter 15 Statistics.
## Statistics Class 11 Chapter 15 Concepts
The concepts covered in this chapter 15 of Class 11 Statistics are:
• Introduction
• Measures of Dispersion
• Range
• Mean Deviation
• Variance and Standard Deviation
• Analysis of Frequency Distributions
Let’s have a look at the brief explanation of all these concepts with examples given below:
A measure of central tendency gives us a rough idea of wherever data points are centred. However, to better understand the data, we should know how the data are scattered or how much they are bunched around a measure of central tendency. However, the measures of central tendency are not adequate to give exhaustive information about a given data. Variability is another essential factor that is expected to be studied in statistics. Similar to the measures of central tendency, we need to have a unique number that describes the variability, and this single number is called a measure of dispersion. In this chapter, you will learn some of the important measures of dispersion and the methods for calculating these measured for both ungrouped and grouped data.
## Measures of Dispersion
The dispersion or scatter in the data is measured based on the observations and the types of the measure of central tendency. The different types of measures of dispersion are:
• Range
• Quartile deviation
• Mean deviation
• Standard deviation.
In Class 11 statistics, you get an explicit knowledge of all the measures of dispersion except quartile deviation, which will be studied in your higher classes.
## Range
The range is the difference between the maximum value and the minimum value
Range = Maximum Value – Minimum Value
## Mean Deviation
Mean deviation is the basic measure of deviations from value, and the value is generally a mean value or a median value. In order to find out the mean deviation, first take the mean of deviation for the observations from value is d = x – a Here x is the observation, and a is the fixed value.
The basic formula to find out the mean deviation is
Mean Deviation = Sum of absolute values of deviations from ‘a’ / Number of observations
### Mean Deviation for Ungrouped Data
Calculation of mean deviation for ungrouped data involves the following steps :
Let us assume the observations x1, x2, x3, …..xn
Step 1: Calculate the central tendency measures to find the mean deviation and let it be ‘a’.
Step 2: Find the deviation of xi from a, i.e., x1 – a, x2– a, x3 – a,. . . , xn– a
Step 3: Find the absolute values of the deviations, i.e., | x1 – a |, | x2– a |, |x3 – a|,. . . ,|xn– a| and drop the minus sign (–), if it is there,
Step 4: calculate the mean of the absolute values of the deviations. This mean obtained is the mean deviation about a, i.e.,
$M.D (a)= \frac{\sum_{i=1}^{n}\left |x_{i}-a \right |}{n}$
$M.D (\bar{x})= \frac{\sum_{i=1}^{n}\left |x_{i}-\bar{x} \right |}{n}$, where $\bar{x}$ = Mean
$M.D (M)= \frac{\sum_{i=1}^{n}\left |x_{i}-M \right |}{n}$, Where M = Median
### Mean Deviation for Grouped Data
The data can be grouped into two ways namely,
• Discrete frequency distribution
• Continuous frequency distribution
The methods of finding the mean deviation for both the types are given below
## Discrete Frequency Distribution
Here, the given data consist of n distinct values x1, x2, x3,….xn has frequencies f1, f2, f3,….fn respectively. This data is represented in the tabular form as and is called discrete frequency distribution, and the data are given below
x x1 x2 x3 …… xn f f1 f2 f3 …… fn
First find the mean $\bar{x}$, using the given formula :
$\bar{x}=\frac{\sum_{i=1}^{n}x_{i}f_{i}}{\sum_{i=1}^{n}f_{i}}=\frac{1}{N}\sum_{i=1}^{n}x_{i}f_{i}$
Where the numerator denotes the sum of products of observations xi with the respective frequencies fi and the denominator denotes the sum of frequencies.
Now take the absolute values, $\left | x_{i}-\bar{x} \right |$ , for all i = 1, 2, 3, ..n
Therefore, the required mean deviation about the mean is given by
$M.D(\bar{x})=\frac{\sum_{i=1}^{n}f_{i}\left | x_{i}-\bar{x} \right |}{\sum_{i=1}^{n}f_{i}}=\frac{1}{N}\sum_{i=1}^{n}f_{i}\left | x_{i}-\bar{x} \right |$
To find the mean deviation about the median for the given discrete frequency distribution. First arrange the observation in ascending order to get cumulative frequency which is equal to or greater than N/2, where N is the sum of the frequencies.
Therefore, the mean deviation for median is given by,
$M.D(M)= \frac{1}{N}\sum_{i=1}^{n}f_{i}\left | x_{i}-M \right |$
Also, check:
## Continuous Frequency Distribution
To find the mean deviation for the continuous frequency distribution, assume that the frequency in each class is centred at its midpoint. After finding the midpoint, proceed further to find the mean deviation similar to the discrete frequency distribution.
### Standard Deviation
The positive square root of the variance is called standard deviation (S.D) and it is denoted by the symbol, | {"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": 0.9377121329307556, "perplexity": 692.023278448589}, "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-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00043.warc.gz"} |
https://repository.uantwerpen.be/link/irua/106346 | Publication
Title
Molecular-dynamics simulation of galanin in aqueous and nonaqueous solution
Author
Abstract
In order to increase our knowledge about the 29-residue-long neuropeptide galanin, computer simulations were carried out. As is the case with many other small peptides, galanin has nearly no secondary structure in water, unlike the situation when solvated in 2,2,2-trifluoroethanol. The galanin peptide was therefore subjected to periodic boundary molecular dynamics simulations with explicit treatment of solvent. One simulation in water (220 ps) and one simulation in 2,2,2-trifluoroethanol (120 ps) were carried out. In both cases the initial conformation was the structure, in 2,2,2-trifluoroethanol, as determined with NMR techniques (Wennerberg, A. B. A.; et al. Biochem. Biophys. Res. Commun. 1990, 166, 1102-1109). A very different behavior was observed in these different environments: the peptide remained stable in 2,2,2-trifluoroethanol while in the aqueous solution progressive unfolding of the C-terminal domain took place. The stability of the peptide in 2,2,2-trifluoroethanol validates the original structure determination. In addition, as a control experiment, the simulation points to the unique role of the water molecules in promoting the unfolding of the galanin molecule. In both simulations the probability of finding i-i + 3 hydrogen bonds was increased at the helix termini. The conformational changes occurring in the H2O simulation were studied in more detail, and 3(10)-type helices, or the presence of i-i + 3 hydrogen bonds, were detected during the unfolding. Water molecules thus replace the backbone hydrogen bonds during the unfolding, but this does not require the insertion of a "single" water molecule, as the analysis showed that different water molecules can pair up with the original atoms involved in the backbone hydrogen bond. Other observations point to the importance of side chain-side chain and side chain-main chain interactions during the unfolding process, giving each transition its specific characteristics. In conclusion these results show that molecular dynamics simulations allow, at least qualitatively, the study of solvent effects on peptide structure and folding.
Language
English
Source (journal)
Journal of the American Chemical Society. - Washington, D.C., 1879, currens
Publication
Washington, D.C. : American Chemical Society , 1992
ISSN
0002-7863
Volume/pages
114 :11 (1992) , p. 4028-4035
ISI
A1992HV67500002
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department Publication type Subject | {"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": 0.897425651550293, "perplexity": 3108.7393929438826}, "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/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00796.warc.gz"} |
https://brilliant.org/problems/ages/ | # Ages
Algebra Level 2
The ages of two persons are in the ratio 8/11. 8 years later the ratio becomes to 4/5.
What is the difference between their ages.
× | {"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": 0.9960619807243347, "perplexity": 1974.295402739688}, "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-2017-43/segments/1508187822513.17/warc/CC-MAIN-20171017215800-20171017235800-00130.warc.gz"} |
https://de.maplesoft.com/support/help/maplesim/view.aspx?path=DifferentialGeometry%2FLieAlgebras%2FSimpleLieAlgebraData | obtain the structure equations for a classical matrix Lie algebra - Maple Programming Help
LieAlgebras[SimpleLieAlgebraData] - obtain the structure equations for a classical matrix Lie algebra
Calling Sequences
SimpleLieAlgebraData(algtype, algname, option)
Parameters
algtype - a string, describing the type and dimension of a classical matrix algebra
algname - an unassigned name or a string, the name of the classical matrix algebra to be constructed
options - (optional) keyword arguments labelformat, labels which specify the labelling of the basis for the Lie algebra. Different standard basis for some of the Lie algebras can be specified with the keyword version.
Description
This command returns the structure equations (see LieAlgebraData) for any one of the following Lie algebras:
Type Lie algebra A (two versions), B (two versions) C , D (two versions), F or , or G or or(two versions) Other ,
• The Lie algebras are all simple Lie algebras. The are classical matrix algebras which are often used in Lie theory and differential geometry.
• The precise definitions and examples of each of these Lie algebras are found in SimpleLieAlgebraDataDetails .
• The command StandardRepresentation generates the standard matrix representations of these algebras.
• Cartan matrices, Dynkin diagram, Satake diagrams, positive roots can easily be found for each of the simple Lie algebra. See also SimpleLieAlgebraProperties .
• Subalgebras of any of these Lie algebras can be calculate using the command MatrixSubalgebras.
• Two versions of the Lie algebras and are available, corresponding the choices
for the quadratic form preserved by these algebras. The keyword argument version.specifies the choice. The default is version =1. This choice is preferred for roots space computations.
• The keyword arguments labelformat, labels allow for the labeling of the basis of the abstract Lie algebra which characterizes the basis elements in terms of their standard matrix elements. See LieAlgebraData, DGsetup.
Examples
> with(DifferentialGeometry): with(LieAlgebras):
Example 1.
Initialize the Lie algebra the Lie algebra of trace-free 3×3 matrices.
> LD1 := SimpleLieAlgebraData("sl(3)", alg1, labelformat = "gl", labels = ['E', 'theta']);
${\mathrm{LD1}}{:=}\left[\left[{\mathrm{e1}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e3}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{2}{}{\mathrm{e4}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e5}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e6}}\right]{=}{\mathrm{e6}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e7}}\right]{=}{-}{2}{}{\mathrm{e7}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e8}}\right]{=}{-}{\mathrm{e8}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{-}{\mathrm{e3}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e4}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e5}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e6}}\right]{=}{2}{}{\mathrm{e6}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e7}}\right]{=}{-}{\mathrm{e7}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e8}}\right]{=}{-}{2}{}{\mathrm{e8}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e1}}{-}{\mathrm{e2}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e6}}\right]{=}{\mathrm{e4}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e7}}\right]{=}{-}{\mathrm{e8}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e6}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e7}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e8}}\right]{=}{\mathrm{e3}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e8}}\right]{=}{-}{\mathrm{e7}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e7}}\right]{=}{\mathrm{e5}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e8}}\right]{=}{\mathrm{e2}}\right]{,}\left[{\mathrm{E11}}{,}{\mathrm{E22}}{,}{\mathrm{E12}}{,}{\mathrm{E13}}{,}{\mathrm{E21}}{,}{\mathrm{E23}}{,}{\mathrm{E31}}{,}{\mathrm{E32}}\right]{,}\left[{\mathrm{θ11}}{,}{\mathrm{θ22}}{,}{\mathrm{θ12}}{,}{\mathrm{θ13}}{,}{\mathrm{θ21}}{,}{\mathrm{θ23}}{,}{\mathrm{θ31}}{,}{\mathrm{θ32}}\right]$ (2.1)
When this output is passed to DGsetup, the 8-dimensional Lie algebra with the foregoing structure equations is initialized and the unassigned names are assigned as vectors and 1-forms for this Lie algebra.
> DGsetup(LD1);
${\mathrm{Lie algebra: alg1}}$ (2.2)
Here is the Lie bracket multiplication table for $\mathrm{sl}\left(3\right)$.
alg1 > MultiplicationTable("LieTable");
$\left[\begin{array}{cccccccccc}{}& {|}& {\mathrm{E11}}& {\mathrm{E22}}& {\mathrm{E12}}& {\mathrm{E13}}& {\mathrm{E21}}& {\mathrm{E23}}& {\mathrm{E31}}& {\mathrm{E32}}\\ {}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}\\ {\mathrm{E11}}& {|}& {0}& {0}& {\mathrm{E12}}& {2}{}{\mathrm{E13}}& {-}{\mathrm{E21}}& {\mathrm{E23}}& {-}{2}{}{\mathrm{E31}}& {-}{\mathrm{E32}}\\ {\mathrm{E22}}& {|}& {0}& {0}& {-}{\mathrm{E12}}& {\mathrm{E13}}& {\mathrm{E21}}& {2}{}{\mathrm{E23}}& {-}{\mathrm{E31}}& {-}{2}{}{\mathrm{E32}}\\ {\mathrm{E12}}& {|}& {-}{\mathrm{E12}}& {\mathrm{E12}}& {0}& {0}& {\mathrm{E11}}{-}{\mathrm{E22}}& {\mathrm{E13}}& {-}{\mathrm{E32}}& {0}\\ {\mathrm{E13}}& {|}& {-}{2}{}{\mathrm{E13}}& {-}{\mathrm{E13}}& {0}& {0}& {-}{\mathrm{E23}}& {0}& {\mathrm{E11}}& {\mathrm{E12}}\\ {\mathrm{E21}}& {|}& {\mathrm{E21}}& {-}{\mathrm{E21}}& {-}{\mathrm{E11}}{+}{\mathrm{E22}}& {\mathrm{E23}}& {0}& {0}& {0}& {-}{\mathrm{E31}}\\ {\mathrm{E23}}& {|}& {-}{\mathrm{E23}}& {-}{2}{}{\mathrm{E23}}& {-}{\mathrm{E13}}& {0}& {0}& {0}& {\mathrm{E21}}& {\mathrm{E22}}\\ {\mathrm{E31}}& {|}& {2}{}{\mathrm{E31}}& {\mathrm{E31}}& {\mathrm{E32}}& {-}{\mathrm{E11}}& {0}& {-}{\mathrm{E21}}& {0}& {0}\\ {\mathrm{E32}}& {|}& {\mathrm{E32}}& {2}{}{\mathrm{E32}}& {0}& {-}{\mathrm{E12}}& {\mathrm{E31}}& {-}{\mathrm{E22}}& {0}& {0}\end{array}\right]$ (2.3)
This coincides with the commutator formulas for the standard matrix representation of $\mathrm{sl}\left(3\right)$.
alg1 > StandardRepresentation(alg1);
$\left[\left[\begin{array}{rrr}{1}& {0}& {0}\\ {0}& {0}& {0}\\ {0}& {0}& {-}{1}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {1}& {0}\\ {0}& {0}& {-}{1}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {1}& {0}\\ {0}& {0}& {0}\\ {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {1}\\ {0}& {0}& {0}\\ {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {1}& {0}& {0}\\ {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {0}& {1}\\ {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {0}& {0}\\ {1}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {0}& {0}\\ {0}& {1}& {0}\end{array}\right]\right]$ (2.4)
The 3rd basis element $\mathrm{E12}$ matches the 3rd matrix in the standard representation and is precisely the elementary matrix with a 1 in the 1st column, 2nd row.
Example 2
We initialize the Lie algebra in two different basis. Our first version is:
alg1 > LD2a := SimpleLieAlgebraData("so(3, 1)", so31a, labelformat = "gl", labels = ['X', 'zeta']);
${\mathrm{LD2a}}{:=}\left[\left[{\mathrm{e1}}{,}{\mathrm{e2}}\right]{=}{\mathrm{e2}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e3}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{-}{\mathrm{e4}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e5}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{-}{\mathrm{e1}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e6}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e6}}\right]{=}{-}{\mathrm{e3}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e4}}\right]{=}{-}{\mathrm{e6}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e6}}\right]{=}{\mathrm{e2}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e6}}\right]{=}{-}{\mathrm{e5}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e6}}\right]{=}{\mathrm{e4}}\right]{,}\left[{\mathrm{X11}}{,}{\mathrm{X13}}{,}{\mathrm{X14}}{,}{\mathrm{X23}}{,}{\mathrm{X24}}{,}{\mathrm{X34}}\right]{,}\left[{\mathrm{ζ11}}{,}{\mathrm{ζ13}}{,}{\mathrm{ζ14}}{,}{\mathrm{ζ23}}{,}{\mathrm{ζ24}}{,}{\mathrm{ζ34}}\right]$ (2.5)
alg1 > DGsetup(LD2a);
${\mathrm{Lie algebra: so31a}}$ (2.6)
so31a > MultiplicationTable("LieTable");
$\left[\begin{array}{cccccccc}{}& {|}& {\mathrm{X11}}& {\mathrm{X13}}& {\mathrm{X14}}& {\mathrm{X23}}& {\mathrm{X24}}& {\mathrm{X34}}\\ {}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}\\ {\mathrm{X11}}& {|}& {0}& {\mathrm{X13}}& {\mathrm{X14}}& {-}{\mathrm{X23}}& {-}{\mathrm{X24}}& {0}\\ {\mathrm{X13}}& {|}& {-}{\mathrm{X13}}& {0}& {0}& {-}{\mathrm{X11}}& {\mathrm{X34}}& {-}{\mathrm{X14}}\\ {\mathrm{X14}}& {|}& {-}{\mathrm{X14}}& {0}& {0}& {-}{\mathrm{X34}}& {-}{\mathrm{X11}}& {\mathrm{X13}}\\ {\mathrm{X23}}& {|}& {\mathrm{X23}}& {\mathrm{X11}}& {\mathrm{X34}}& {0}& {0}& {-}{\mathrm{X24}}\\ {\mathrm{X24}}& {|}& {\mathrm{X24}}& {-}{\mathrm{X34}}& {\mathrm{X11}}& {0}& {0}& {\mathrm{X23}}\\ {\mathrm{X34}}& {|}& {0}& {\mathrm{X14}}& {-}{\mathrm{X13}}& {\mathrm{X24}}& {-}{\mathrm{X23}}& {0}\end{array}\right]$ (2.7)
Our second version is :
so31a > LD2b := SimpleLieAlgebraData("so(3, 1)", so31b, labelformat = "gl", labels = ['Y', 'xi'], version = 2);
${\mathrm{LD2b}}{:=}\left[\left[{\mathrm{e1}}{,}{\mathrm{e2}}\right]{=}{\mathrm{e3}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e3}}\right]{=}{-}{\mathrm{e2}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e5}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e4}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e6}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e6}}\right]{=}{-}{\mathrm{e4}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e6}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e6}}\right]{=}{-}{\mathrm{e5}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e1}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e6}}\right]{=}{-}{\mathrm{e2}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e6}}\right]{=}{-}{\mathrm{e3}}\right]{,}\left[{\mathrm{Y12}}{,}{\mathrm{Y13}}{,}{\mathrm{Y23}}{,}{\mathrm{Y14}}{,}{\mathrm{Y24}}{,}{\mathrm{Y34}}\right]{,}\left[{\mathrm{ξ12}}{,}{\mathrm{ξ13}}{,}{\mathrm{ξ23}}{,}{\mathrm{ξ14}}{,}{\mathrm{ξ24}}{,}{\mathrm{ξ34}}\right]$ (2.8)
alg1 > DGsetup(LD2b);
${\mathrm{Lie algebra: so31b}}$ (2.9)
so31a > MultiplicationTable("LieTable");
$\left[\begin{array}{cccccccc}{}& {|}& {\mathrm{Y12}}& {\mathrm{Y13}}& {\mathrm{Y23}}& {\mathrm{Y14}}& {\mathrm{Y24}}& {\mathrm{Y34}}\\ {}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}& {\mathrm{----}}\\ {\mathrm{Y12}}& {|}& {0}& {\mathrm{Y23}}& {-}{\mathrm{Y13}}& {\mathrm{Y24}}& {-}{\mathrm{Y14}}& {0}\\ {\mathrm{Y13}}& {|}& {-}{\mathrm{Y23}}& {0}& {\mathrm{Y12}}& {\mathrm{Y34}}& {0}& {-}{\mathrm{Y14}}\\ {\mathrm{Y23}}& {|}& {\mathrm{Y13}}& {-}{\mathrm{Y12}}& {0}& {0}& {\mathrm{Y34}}& {-}{\mathrm{Y24}}\\ {\mathrm{Y14}}& {|}& {-}{\mathrm{Y24}}& {-}{\mathrm{Y34}}& {0}& {0}& {-}{\mathrm{Y12}}& {-}{\mathrm{Y13}}\\ {\mathrm{Y24}}& {|}& {\mathrm{Y14}}& {0}& {-}{\mathrm{Y34}}& {\mathrm{Y12}}& {0}& {-}{\mathrm{Y23}}\\ {\mathrm{Y34}}& {|}& {0}& {\mathrm{Y14}}& {\mathrm{Y24}}& {\mathrm{Y13}}& {\mathrm{Y23}}& {0}\end{array}\right]$ (2.10)
From the standard matrix representations for these 2 Lie algebras we can construct a Lie algebra isomorphism . First let us define the quadratic forms used in each version.
so31b > with(LinearAlgebra):
so31b > Qa := Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]);
${\mathrm{Qa}}{:=}\left[\begin{array}{rrrr}{0}& {1}& {0}& {0}\\ {1}& {0}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {0}& {0}& {0}& {1}\end{array}\right]$ (2.11)
so31b > Qb := Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]]);
${\mathrm{Qb}}{:=}\left[\begin{array}{rrrr}{1}& {0}& {0}& {0}\\ {0}& {1}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {0}& {0}& {0}& {-}{1}\end{array}\right]$ (2.12)
Here is the change of basis matrix relating $\mathrm{Qa}$ to $\mathrm{Qb}$.
so31b > P := Matrix([[0,0,1/sqrt(2), 1/sqrt(2)],[0,0,1/sqrt(2), -1/sqrt(2)], [0, 1, 0, 0], [1, 0, 0, 0]]);
${P}{:=}\left[\begin{array}{cccc}{0}& {0}& \frac{{1}}{{2}}{}\sqrt{{2}}& \frac{{1}}{{2}}{}\sqrt{{2}}\\ {0}& {0}& \frac{{1}}{{2}}{}\sqrt{{2}}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}\\ {0}& {1}& {0}& {0}\\ {1}& {0}& {0}& {0}\end{array}\right]$ (2.13)
so31b > Transpose(P).Qa.P;
$\left[\begin{array}{rrrr}{1}& {0}& {0}& {0}\\ {0}& {1}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {0}& {0}& {0}& {-}{1}\end{array}\right]$ (2.14)
Here is the standard representation for using $\mathrm{Qa}$.
so31b > A := StandardRepresentation(so31a);
${A}{:=}\left[\left[\begin{array}{rrrr}{1}& {0}& {0}& {0}\\ {0}& {-}{1}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {1}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {-}{1}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {1}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {-}{1}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {-}{1}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {1}\\ {0}& {0}& {0}& {0}\\ {-}{1}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {-}{1}\\ {0}& {0}& {1}& {0}\end{array}\right]\right]$ (2.15)
Here is the standard representation for using $\mathrm{Qb}.$
so31b > B := StandardRepresentation(so31b);
${B}{:=}\left[\left[\begin{array}{rrrr}{0}& {-}{1}& {0}& {0}\\ {1}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {-}{1}& {0}\\ {0}& {0}& {0}& {0}\\ {1}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {-}{1}& {0}\\ {0}& {1}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {1}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {1}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {1}\\ {0}& {0}& {0}& {0}\\ {0}& {1}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {1}\\ {0}& {0}& {1}& {0}\end{array}\right]\right]$ (2.16)
Here are the matrices $A$ under the change of basis defined by $P.$ Since the resulting matrices now preserve $\mathrm{Qb}$, they must be linear combinations of the matrices B.
so31b > A1 := [seq(P^(-1).a.P, a = A)];
${\mathrm{A1}}{:=}\left[\left[\begin{array}{rrrr}{0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {1}\\ {0}& {0}& {1}& {0}\end{array}\right]{,}\left[\begin{array}{cccc}{0}& {0}& {0}& {0}\\ {0}& {0}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}& \frac{{1}}{{2}}{}\sqrt{{2}}\\ {0}& \frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}\\ {0}& \frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{cccc}{0}& {0}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}& \frac{{1}}{{2}}{}\sqrt{{2}}\\ {0}& {0}& {0}& {0}\\ \frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}& {0}\\ \frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{cccc}{0}& {0}& {0}& {0}\\ {0}& {0}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}\\ {0}& \frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}\\ {0}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{cccc}{0}& {0}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}\\ {0}& {0}& {0}& {0}\\ \frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}& {0}\\ {-}\frac{{1}}{{2}}{}\sqrt{{2}}& {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrrr}{0}& {1}& {0}& {0}\\ {-}{1}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {0}& {0}\end{array}\right]\right]$ (2.17)
so31b > C := GetComponents(A1, B);
${C}{:=}\left[\left[{0}{,}{0}{,}{0}{,}{0}{,}{0}{,}{1}\right]{,}\left[{0}{,}{0}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}\right]{,}\left[{0}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}{,}{0}\right]{,}\left[{0}{,}{0}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}{,}{-}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}\right]{,}\left[{0}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}{,}{-}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{0}{,}{0}\right]{,}\left[{-}{1}{,}{0}{,}{0}{,}{0}{,}{0}{,}{0}\right]\right]$ (2.18)
These components specify the matrix of the isomorphism we want.
so31b > Phi := Transformation(so31a, so31b, Transpose(Matrix(C)));
${\mathrm{Φ}}{:=}\left[\left[{\mathrm{X11}}{,}{\mathrm{Y34}}\right]{,}\left[{\mathrm{X13}}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y23}}{+}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y24}}\right]{,}\left[{\mathrm{X14}}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y13}}{+}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y14}}\right]{,}\left[{\mathrm{X23}}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y23}}{-}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y24}}\right]{,}\left[{\mathrm{X24}}{,}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y13}}{-}\frac{{1}}{{2}}{}\sqrt{{2}}{}{\mathrm{Y14}}\right]{,}\left[{\mathrm{X34}}{,}{-}{\mathrm{Y12}}\right]\right]$ (2.19)
so31b > Query(Phi, "Homomorphism");
${\mathrm{true}}$ (2.20)
Example 3.
Two versions of the split real form of the exception Lie algebraare available. The first version gives a Chevalley basis.
> LD3a := SimpleLieAlgebraData("g(2, Split)", g2a, version = 1);
${\mathrm{LD3a}}{:=}\left[\left[{\mathrm{e1}}{,}{\mathrm{e3}}\right]{=}{2}{}{\mathrm{e3}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{-}{3}{}{\mathrm{e4}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e5}}\right]{=}{-}{\mathrm{e5}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e6}}\right]{=}{\mathrm{e6}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e7}}\right]{=}{3}{}{\mathrm{e7}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e9}}\right]{=}{-}{2}{}{\mathrm{e9}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e10}}\right]{=}{3}{}{\mathrm{e10}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e11}}\right]{=}{\mathrm{e11}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e12}}\right]{=}{-}{\mathrm{e12}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e13}}\right]{=}{-}{3}{}{\mathrm{e13}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{-}{\mathrm{e3}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{2}{}{\mathrm{e4}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e5}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e7}}\right]{=}{-}{\mathrm{e7}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e8}}\right]{=}{\mathrm{e8}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e9}}\right]{=}{\mathrm{e9}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e10}}\right]{=}{-}{2}{}{\mathrm{e10}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e11}}\right]{=}{-}{\mathrm{e11}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e13}}\right]{=}{\mathrm{e13}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e14}}\right]{=}{-}{\mathrm{e14}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e5}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{2}{}{\mathrm{e6}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e6}}\right]{=}{-}{3}{}{\mathrm{e7}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e9}}\right]{=}{-}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e11}}\right]{=}{-}{3}{}{\mathrm{e10}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e12}}\right]{=}{-}{2}{}{\mathrm{e11}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e13}}\right]{=}{\mathrm{e12}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e7}}\right]{=}{-}{\mathrm{e8}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e10}}\right]{=}{-}{\mathrm{e2}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e11}}\right]{=}{\mathrm{e9}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e14}}\right]{=}{\mathrm{e13}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e6}}\right]{=}{-}{3}{}{\mathrm{e8}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e9}}\right]{=}{3}{}{\mathrm{e4}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e10}}\right]{=}{-}{\mathrm{e3}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e11}}\right]{=}{-}{\mathrm{e1}}{-}{3}{}{\mathrm{e2}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e12}}\right]{=}{2}{}{\mathrm{e9}}{,}\left[{\mathrm{e5}}{,}{\mathrm{e14}}\right]{=}{\mathrm{e12}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e9}}\right]{=}{2}{}{\mathrm{e5}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e11}}\right]{=}{-}{2}{}{\mathrm{e3}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e12}}\right]{=}{-}{2}{}{\mathrm{e1}}{-}{3}{}{\mathrm{e2}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e13}}\right]{=}{-}{\mathrm{e9}}{,}\left[{\mathrm{e6}}{,}{\mathrm{e14}}\right]{=}{-}{\mathrm{e11}}{,}\left[{\mathrm{e7}}{,}{\mathrm{e9}}\right]{=}{-}{\mathrm{e6}}{,}\left[{\mathrm{e7}}{,}{\mathrm{e12}}\right]{=}{\mathrm{e3}}{,}\left[{\mathrm{e7}}{,}{\mathrm{e13}}\right]{=}{-}{\mathrm{e1}}{-}{\mathrm{e2}}{,}\left[{\mathrm{e7}}{,}{\mathrm{e14}}\right]{=}{-}{\mathrm{e10}}{,}\left[{\mathrm{e8}}{,}{\mathrm{e10}}\right]{=}{-}{\mathrm{e7}}{,}\left[{\mathrm{e8}}{,}{\mathrm{e11}}\right]{=}{-}{\mathrm{e6}}{,}\left[{\mathrm{e8}}{,}{\mathrm{e12}}\right]{=}{\mathrm{e5}}{,}\left[{\mathrm{e8}}{,}{\mathrm{e13}}\right]{=}{\mathrm{e4}}{,}\left[{\mathrm{e8}}{,}{\mathrm{e14}}\right]{=}{-}{\mathrm{e1}}{-}{2}{}{\mathrm{e2}}{,}\left[{\mathrm{e9}}{,}{\mathrm{e10}}\right]{=}{\mathrm{e11}}{,}\left[{\mathrm{e9}}{,}{\mathrm{e11}}\right]{=}{2}{}{\mathrm{e12}}{,}\left[{\mathrm{e9}}{,}{\mathrm{e12}}\right]{=}{-}{3}{}{\mathrm{e13}}{,}\left[{\mathrm{e10}}{,}{\mathrm{e13}}\right]{=}{-}{\mathrm{e14}}{,}\left[{\mathrm{e11}}{,}{\mathrm{e12}}\right]{=}{-}{3}{}{\mathrm{e14}}\right]$ (2.21)
> DGsetup(LD3a, ['h1', 'h2', 'x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'y1', 'y2', 'y3', 'y4', 'y5', 'y6'], ['omega']);
${\mathrm{Lie algebra: g2a}}$ (2.22)
We note that this basis is adapted to a root space decomposition.
g2a > RootSpaceDecomposition([h1, h2]);
${\mathrm{table}}\left(\left[\left[{0}{,}{-}{1}\right]{=}{\mathrm{y6}}{,}\left[{3}{,}{-}{2}\right]{=}{\mathrm{y2}}{,}\left[{-}{1}{,}{1}\right]{=}{\mathrm{x3}}{,}\left[{-}{1}{,}{0}\right]{=}{\mathrm{y4}}{,}\left[{0}{,}{1}\right]{=}{\mathrm{x6}}{,}\left[{1}{,}{0}\right]{=}{\mathrm{x4}}{,}\left[{3}{,}{-}{1}\right]{=}{\mathrm{x5}}{,}\left[{1}{,}{-}{1}\right]{=}{\mathrm{y3}}{,}\left[{-}{3}{,}{2}\right]{=}{\mathrm{x2}}{,}\left[{-}{2}{,}{1}\right]{=}{\mathrm{y1}}{,}\left[{-}{3}{,}{1}\right]{=}{\mathrm{y5}}{,}\left[{2}{,}{-}{1}\right]{=}{\mathrm{x1}}\right]\right)$ (2.23)
The second version is adapted to the Cartan decomposition.
g2a > LD3b := SimpleLieAlgebraData("g(2, Split)", g2b, version = 2);
${\mathrm{LD3b}}{:=}\left[\left[{\mathrm{e1}}{,}{\mathrm{e2}}\right]{=}{\mathrm{e3}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e3}}\right]{=}{-}{\mathrm{e2}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e7}}\right]{=}{-}\frac{{1}}{{4}}{}{\mathrm{e14}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e8}}\right]{=}{-}\frac{{3}}{{4}}{}{\mathrm{e11}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e9}}\right]{=}\frac{{3}}{{2}}{}{\mathrm{e10}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e10}}\right]{=}{-}\frac{{3}}{{2}}{}{\mathrm{e9}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e11}}\right]{=}{3}{}{\mathrm{e8}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e12}}\right]{=}{-}\frac{{1}}{{2}}{}{\mathrm{e13}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e13}}\right]{=}\frac{{1}}{{2}}{}{\mathrm{e12}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e14}}\right]{=}{\mathrm{e7}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e7}}\right]{=}{-}\frac{{3}}{{4}}{}{\mathrm{e10}}{+}\frac{{1}}{{2}}{}{\mathrm{e13}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e8}}\right]{=}\frac{{1}}{{4}}{}{\mathrm{e13}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e9}}\right]{=}\frac{{1}}{{2}}{}{\mathrm{e14}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e10}}\right]{=}{\mathrm{e7}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e11}}\right]{=}{-}\frac{{1}}{{2}}{}\right]$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 39, "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": 0.8867445588111877, "perplexity": 2585.913510104628}, "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-2021-17/segments/1618038863420.65/warc/CC-MAIN-20210419015157-20210419045157-00203.warc.gz"} |
https://www.math10.com/en/algebra/fractions.html | # Fractions
## Free Fraction Calculator (by Radu Turcan)
Operator: + - * /
=
Solution:
#### Definition of a fraction
A number written as $\frac{a}{b}$ or a/b, where $a$ is an integer and $b$ is a non-zero integer, is called a fraction.
The number $a$ is numerator, and $b$ is the denominator. A fraction represents either a part of a whole or any number of equal parts.
The denominator shows how many equal parts make up a whole, and the numerator shows how many of these parts we have in mind.
#### Examples of fractions
Example 1: Becky, Merry and John want to share a chocolate bar evenly.
What part of the bar will each of them take?
What part of the bar will Becky and Merry have together?
The children need to divide the bar into three pieces. So everyone will take $\frac{1}{3}$ of the chocolate bar.
Two girls together will have two pieces, hence, mathematically speaking, they will have $\frac{2}{3}$ of the bar.
Example 2: What part of the soldiers are yellow?
Example 3: What part of the apples is missing?
#### Fraction Rules
Addition:(same denominators)
$\frac{A}{B} +\frac{C}{B} = \frac{A + C}{B}$
Subtraction:(same denominators)
$\frac{A}{B} -\frac{C}{B} = \frac{A - C}{B}$
Addition:(different denominators)
$\frac{A}{B} +\frac{C}{D} = \frac{A\cdot D}{B\cdot D} +\frac{B\cdot C}{B\cdot D} = \frac{A\cdot D + B\cdot C}{B\cdot D}$
Subtraction:(different denominators)
$\frac{A}{B} -\frac{C}{D} = \frac{A\cdot D}{B\cdot D} -\frac{B\cdot C}{B\cdot D} = \frac{A\cdot D - B\cdot C}{B\cdot D}$
Multiplication:
$\frac{A}{B}\times\frac{C}{D} = \frac{A\cdot C}{B\cdot D}$
Division:
$\frac{A}{B}\div\frac{C}{D} = \frac{A}{B}\times\frac{D}{C}= \frac{A\cdot D}{B\cdot C}$
#### Properties of fractions
Property I: All hatched parts of the circles represent one half $\frac{1}{2}, \frac{2}{4}$ and $\frac{3}{6}$, hence $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$
We get $\frac{2}{4}$ when we multiply the numerator and the denominator of the fraction $\frac{1}{2}$ by $2$.
We obtain $\frac{3}{6}$ by multiplying the numerator and the denominator of $\frac{1}{2}$ by $3$.
Let $a$ be an integer and $b$ and $c$ be non-zero integers.
Then:
$\frac{a}{b}=\frac{a\cdot c}{b\cdot c}$ and $\frac{a}{b}=\frac{a:c}{b:c}$
Property II: If two fractions have equal denominators, the fraction with the greater numerator is greater.
If $a$, $b$ and $c$ are integers and $c \ne 0$ then:
$\frac{a}{c}>\frac{b}{c}$, if $a>b$
Example: $\frac{4}{5} > \frac{3}{5} > \frac{2}{5}$
Property III: If two fractions have equal numerators, the fraction with the smaller denominator is greater.
If $a$, $b$ and $c$ are integers, and $b$ and $c$ are non-zero then:
$\frac{a}{b}>\frac{a}{c}$, if $b< c$
Example: $\frac{3}{4} > \frac{3}{5} > \frac{3}{20}$
#### Fraction Test
1. A tennis player won $6$ out of first $12$ sets. Then he won all of the remaining $6$ sets. What part of the sets did the player win?
$\frac{1}{3}$ $\frac{2}{3}$ $\frac{1}{2}$
2. A boy had $\$36$. After a couple of hours of shopping he had$\$8$ left. What part of his money did he spend?
$\frac{2}{9}$ $\frac{2}{7}$ $\frac{7}{9}$
3. There were $12$ girls in a class of $30$ students. Then $6$ boys joined the class. What part of the class are the girls?
$\frac{1}{2}$ $\frac{3}{5}$ $\frac{1}{3}$
4. If the fraction $\frac{n}{40}$ is between $\frac{1}{5}$ and $\frac{1}{4}$ then n is
$8$ $9$ $10$
5. $\frac{6}{24}$ is equal to:
$\frac{1}{4}$ $\frac{3}{4}$ $\frac{6}{12}$
6. Which of the fractions is twice greater than $\frac{3}{8}$?
$\frac{6}{16}$ $\frac{3}{16}$ $\frac{3}{4}$
7.* Which of the following fractions is the largest: $\frac{12}{13}, \frac{13}{14}, \frac{14}{15}$ or $\frac{15}{16}$?
$\frac{15}{16}$ $\frac{12}{13}$ $\frac{14}{15}$
8. Which of the following sequences has fractions arranged in a descending order?
1: $\frac{7}{11}, \frac{5}{8}, \frac{3}{5}, \frac{2}{3}$;
2: $\frac{4}{3}, \frac{7}{11}, \frac{5}{8}, \frac{3}{5}$;
3: $\frac{21}{11}, \frac{2}{3}, \frac{3}{5}, \frac{5}{8}$
$2$ $3$ $1$
9.* Which of the following sequences has fractions arranged in an ascending order?
1: $\frac{13}{19}, \frac{13}{23}, \frac{17}{23}$;
2: $\frac{13}{23}, \frac{17}{23}, \frac{13}{19}$;
3: $\frac{13}{23}, \frac{13}{19}, \frac{17}{23}$;
$1$ $2$ $3$
10. Calculate $\frac{20+4\cdot3}{120}$:
$\frac{2}{5}$ $\frac{3}{5}$ $\frac{4}{15}$
11. Calculate $\frac{1+2+3+4+5}{1\cdot2\cdot3\cdot4\cdot5}$:
$5$ $1$ $\frac{1}{8}$
#### More about fractions in the math forum
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Copyright © 2005 - 2021 | {"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": 0.9228200316429138, "perplexity": 1406.9860829072054}, "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-2021-31/segments/1627046152000.25/warc/CC-MAIN-20210726031942-20210726061942-00679.warc.gz"} |
https://worldwidescience.org/topicpages/b/binary+collision+model.html | #### Sample records for binary collision model
1. Kinetic models with randomly perturbed binary collisions
CERN Document Server
Bassetti, Federico; Toscani, Giuseppe
2010-01-01
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases.
2. Molecular dynamics and binary collision modeling of the primary damage state of collision cascades
DEFF Research Database (Denmark)
Heinisch, H.L.; Singh, B.N.
1992-01-01
Quantitative information on defect production in cascades in copper obtained from recent molecular dynamics simulations is compared to defect production information determined earlier with a model based on the binary collision approximation (BCA). The total numbers of residual defects, the fracti...
3. Binary collisions in popovici’s photogravitational model
Directory of Open Access Journals (Sweden)
Mioc V.
2002-01-01
Full Text Available The dynamics of bodies under the combined action of the gravitational attraction and the radiative repelling force has large and deep implications in astronomy. In the 1920s, the Romanian astronomer Constantin Popovici proposed a modified photogravitational law (considered by other scientists too. This paper deals with the collisions of the two-body problem associated with Popovici’s model. Resorting to McGehee-type transformations of the second kind, we obtain regular equations of motion and define the collision manifold. The flow on this boundary manifold is wholly described. This allows to point out some important qualitative features of the collisional motion: existence of the black-hole effect, gradientlikeness of the flow on the collision manifold, regularizability of collisions under certain conditions. Some questions, coming from the comparison of Levi-Civita’s regularizing transformations and McGehee’s ones, are formulated.
4. Macroscopic Model for Head-On Binary Droplet Collisions in a Gaseous Medium
Science.gov (United States)
Li, Jie
2016-11-01
In this Letter, coalescence-bouncing transitions of head-on binary droplet collisions are predicted by a novel macroscopic model based entirely on fundamental laws of physics. By making use of the lubrication theory of Zhang and Law [Phys. Fluids 23, 042102 (2011)], we have modified the Navier-Stokes equations to accurately account for the rarefied nature of the interdroplet gas film. Through the disjoint pressure model, we have incorporated the intermolecular van der Waals forces. Our model does not use any adjustable (empirical) parameters. It therefore encompasses an extreme range of length scales (more than 5 orders of magnitude): from those of the external flow in excess of the droplet size (a few hundred μ m ) to the effective range of the van der Waals force around 10 nm. A state of the art moving adaptive mesh method, capable of resolving all the relevant length scales, has been employed. Our numerical simulations are able to capture the coalescence-bouncing and bouncing-coalescence transitions that are observed as the collision intensity increases. The predicted transition Weber numbers for tetradecane and water droplet collisions at different pressures show good agreement with published experimental values. Our study also sheds new light on the roles of gas density, droplet size, and mean free path in the rupture of the gas film.
5. Binary droplet collision at high Weber number.
Science.gov (United States)
Pan, Kuo-Long; Chou, Ping-Chung; Tseng, Yu-Jen
2009-09-01
By using the techniques developed for generating high-speed droplets, we have systematically investigated binary droplet collision when the Weber number (We) was increased from the range usually tested in previous studies on the order of 10 to a much larger value of about 5100 for water (a droplet at 23 m/s with a diameter of 0.7 mm). Various liquids were also used to explore the effects of viscosity and surface tension. Specifically, beyond the well-known regimes at moderate We's, which exhibited coalescence, separation, and separation followed by satellite droplets, we found different behaviors showing a fingering lamella, separation after fingering, breakup of outer fingers, and prompt splattering into multiple secondary droplets as We was increased. The critical Weber numbers that mark the boundaries between these impact regimes are identified. The specific impact behaviors, such as fingering and prompt splattering or splashing, share essential similarity with those also observed in droplet-surface impacts, whereas substantial variations in the transition boundaries may result from the disparity of the boundary conditions at impacts. To compare the outcomes of both types of collisions, a simple model based on energy conservation was carried out to predict the maximum diameter of an expanding liquid disk for a binary droplet collision. The results oppose the dominance of viscous drag, as proposed by previous studies, as the main deceleration force to effect a Rayleigh-Taylor instability and ensuing periphery fingers, which may further lead to the formations of satellite droplets.
6. Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Science.gov (United States)
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
7. Binary collision model for neon Auger spectra from neon ion bombardment of the aluminum surface
Science.gov (United States)
Pepper, S. V.
1986-01-01
A model is developed to account for the angle-resolved Auger spectra from neon ion bombardment of the aluminum surface recently obtained by Pepper and Aron. The neon is assumed to be excited in a single asymmetric neon-aluminum-collision and scattered back into the vacuum where it emits an Auger electron. The velocity of the Auger electron acquires a Doppler shift by virtue of the emission from a moving source. The dependence of the Auger peak shape and energy on the incident ion energy, angle of incidence and on the angle of Auger electron emission with respect to the surface is presented. Satisfactory agreement with the angle resolved experimental observations is obtained. The dependence of the angle-integrated Auger yield on the incident ion energy and angle of incidence is also obtained and shown to be in satisfactory agreement with available experimental evidence.
8. Planet Scattering Around Binaries: Ejections, Not Collisions
CERN Document Server
Smullen, Rachel A; Shannon, Andrew
2016-01-01
Transiting circumbinary planets discovered by Kepler provide unique insight into binary and planet formation. Several features of this new found population, for example the apparent pile-up of planets near the innermost stable orbit, may distinguish between formation theories. In this work, we determine how planet-planet scattering shapes planetary systems around binaries as compared to single stars. In particular, we look for signatures that arise due to differences in dynamical evolution in binary systems. We carry out a parameter study of N-body scattering simulations for four distinct planet populations around both binary and single stars. While binarity has little influence on the final system multiplicity or orbital distribution, the presence of a binary dramatically effects the means by which planets are lost from the system. Most circumbinary planets are lost due to ejections rather than planet-planet or planet-star collisions. The most massive planet in the system tends to control the evolution. Asid...
9. Planet scattering around binaries: ejections, not collisions
Science.gov (United States)
Smullen, Rachel A.; Kratter, Kaitlin M.; Shannon, Andrew
2016-09-01
Transiting circumbinary planets discovered by Kepler provide unique insight into binary star and planet formation. Several features of this new found population, for example the apparent pile-up of planets near the innermost stable orbit, may distinguish between formation theories. In this work, we determine how planet-planet scattering shapes planetary systems around binaries as compared to single stars. In particular, we look for signatures that arise due to differences in dynamical evolution in binary systems. We carry out a parameter study of N-body scattering simulations for four distinct planet populations around both binary and single stars. While binarity has little influence on the final system multiplicity or orbital distribution, the presence of a binary dramatically affects the means by which planets are lost from the system. Most circumbinary planets are lost due to ejections rather than planet-planet or planet-star collisions. The most massive planet in the system tends to control the evolution. Systems similar to the only observed multiplanet circumbinary system, Kepler-47, can arise from much more tightly packed, unstable systems. Only extreme initial conditions introduce differences in the final planet populations. Thus, we suggest that any intrinsic differences in the populations are imprinted by formation.
10. Experiments and Direct Numerical Simulations of binary collisions of miscible liquid droplets with different viscosities
CERN Document Server
Focke, C; Kuschel, M; Sommerfeld, M
2012-01-01
Binary droplet collisions are of importance in a variety of practical applications comprising dispersed two-phase flows. The background of our research is the prediction of properties of particulate products formed in spray processes. To gain a more thorough understanding of the elementary sub-processes inside a spray, experiments and direct numerical simulations of binary droplet collisions are used. The aim of these investigations is to develop semi-analytical descriptions for the outcome of droplet collisions. Such collision models can then be employed as closure terms for scale-reduced simulations. In the present work we focus on the collision of droplets of different liquids. These kinds of collisions take place in every spray drying process when droplets with different solids contents collide in recirculation zones. A new experimental method has been developed allowing for high spatial and time resolved recordings via Laser-induced fluorescence. The results obtained with the proposed method will be comp...
11. On non-binary nature of the collisions of heavy hyperthermal particles with solid surfaces
Energy Technology Data Exchange (ETDEWEB)
Ferleger, V.Kh. E-mail: [email protected]; Wojciechowski, I.A
2000-04-01
The limits of applicability of the binary collision approximation for a description of scattering of atomic particles by a solid surface are discussed. The experimental data of energy losses of atoms of hyperthermal energies (HT) scattered by a solid surface were found to bring in evidence for the non-binary nature of collisions in the hyperthermal energy region (1-30 eV). The dependence of the energy losses on the initial energy of the particles and their angles of incidence was shown to be well described by the following model: the particle is being single-scattered by certain complex of surface atoms forming an effective mass. A contribution of the non-binary collisions to the processes of atomic and cluster sputtering is also discussed.
12. Explosions Triggered by Violent Binary-Star Collisions: Application to Eta Carinae and other Eruptive Transients
CERN Document Server
Smith, Nathan
2010-01-01
This paper discusses a model where a violent periastron collision of stars in an eccentric binary system induces an eruption or explosion seen as a brief transient source, attributed to LBVs, SN impostors, or other transients. The key ingredient is that an evolved primary increases its photospheric radius on relatively short timescales, to a point where the radius is comparable to or larger than the periastron separation in an eccentric binary. In such a configuration, a violent and sudden collision would ensue, possibly leading to substantial mass ejection instead of a binary merger. Repeated periastral grazings in an eccentric system could quickly escalate to a catastrophic encounter, wherein the companion star actually plunges deep inside the photosphere of a bloated primary during periastron, as a result of the primary star increasing its own radius. This is motivated by the case of $\\eta$~Carinae, where such a collision must have occured if conventional estimates of the present-day orbit are correct, and...
13. A binary collision route for purely hydrodynamic orientational ordering of microswimmers
CERN Document Server
Oyama, Norihiro; Yamamoto, Ryoichi
2016-01-01
We have investigated the causes for the onset of collective motion in systems of model microswimmers, by performing a comprehensive analysis of the binary collision dynamics using direct numerical simulations (DNS). From this data, we have constructed a simple Vicsek-like model which accurately reproduces the collective behavior obtained from the DNS, which include the full hydrodynamic interactions among the swimmers. Thus, we show that global alignment can arise solely from binary collisions. Although the agreement between both models (DNS and binary-Vicsek) is not perfect, the parameter range in which notable differences appear is also that for which strong density fluctuations are present in the system (where pseudo-sound mode can be observed[1]).
14. A mesoscopic model for binary fluids
CERN Document Server
Echeverria, C; Alvarez-Llamoza, O; Orozco-Guillén, E E; Morales, M; Cosenza, M G
2016-01-01
We propose a model to study symmetric binary fluids, based in the mesoscopic molecular simulation technique known as multiparticle collision, where space and state variables are continuous while time is discrete. We include a repulsion rule to simulate segregation processes that does not require the calculation of the interaction forces between particles, thus allowing the description of binary fluids at a mesoscopic scale. The model is conceptually simple, computationally efficient, maintains Galilean invariance, and conserves the mass and the energy in the system at micro and macro scales; while momentum is conserved globally. For a wide range of temperatures and densities, the model yields results in good agreement with the known properties of binary fluids, such as density profile, width of the interface, phase separation and phase growth. We also apply the model to study binary fluids in crowded environments with consistent results.
15. Vocal Fold Collision Modeling
DEFF Research Database (Denmark)
Granados, Alba; Brunskog, Jonas; Misztal, M. K.
2015-01-01
When vocal folds vibrate at normal speaking frequencies, collisions occurs. The numerics and formulations behind a position-based continuum model of contact is an active field of research in the contact mechanics community. In this paper, a frictionless three-dimensional finite element model...... of the vocal fold collision is proposed, which incorporates different procedures used in contact mechanics and mathematical optimization theories. The penalty approach and the Lagrange multiplier method are investigated. The contact force solution obtained by the penalty formulation is highly dependent...
16. Parameter estimates in binary black hole collisions using neural networks
Science.gov (United States)
Carrillo, M.; Gracia-Linares, M.; González, J. A.; Guzmán, F. S.
2016-10-01
We present an algorithm based on artificial neural networks (ANNs), that estimates the mass ratio in a binary black hole collision out of given gravitational wave (GW) strains. In this analysis, the ANN is trained with a sample of GW signals generated with numerical simulations. The effectiveness of the algorithm is evaluated with GWs generated also with simulations for given mass ratios unknown to the ANN. We measure the accuracy of the algorithm in the interpolation and extrapolation regimes. We present the results for noise free signals and signals contaminated with Gaussian noise, in order to foresee the dependence of the method accuracy in terms of the signal to noise ratio.
17. Parameter estimates in binary black hole collisions using neural networks
CERN Document Server
Carrillo, M; González, J A; Guzmán, F S
2016-01-01
We present an algorithm based on artificial neural networks (ANNs), that estimates the mass ratio in a binary black hole collision out of given Gravitational Wave (GW) strains. In this analysis, the ANN is trained with a sample of GW signals generated with numerical simulations. The effectiveness of the algorithm is evaluated with GWs generated also with simulations for given mass ratios unknown to the ANN. We measure the accuracy of the algorithm in the interpolation and extrapolation regimes. We present the results for noise free signals and signals contaminated with Gaussian noise, in order to foresee the dependence of the method accuracy in terms of the signal to noise ratio.
18. Binary collision rates of relativistic thermal plasmas. I Theoretical framework
Science.gov (United States)
Dermer, C. D.
1985-01-01
Binary collision rates for arbitrary scattering cross sections are derived in the case of a beam of particles interacting with a Maxwell-Boltzmann (MB) plasma, or in the case of two MB plasmas interacting at generally different temperatures. The expressions are valid for all beam energies and plasma temperatures, from the nonrelativistic to the extreme relativistic limits. The calculated quantities include the reaction rate, the energy exchange rate, and the average rate of change of the squared transverse momentum component of a monoenergetic particle beam as a result of scatterings with particles of a MB plasma. Results are specialized to elastic scattering processes, two-temperature reaction rates, or the cold plasma limit, reproducing previous work.
19. Binary Collision Density in a Non-Ideal Gas as a Function of Particle Density, Collision Diameter, and Temperature
Science.gov (United States)
Mohazzabi, Pirooz
2017-09-01
Using molecular dynamics simulations, binary collision density in a dense non-ideal gas with Lennard-Jones interactions is investigated. It is shown that the functional form of the dependence of collision density on particle density and collision diameter remains the same as that for an ideal gas. The temperature dependence of the collision density, however, has a very different form at low temperatures, where it decreases as temperature increases. But at higher temperatures the functional form becomes the same as that for an ideal gas.
20. Towards an understanding of staggering effects in dissipative binary collisions
Energy Technology Data Exchange (ETDEWEB)
D' Agostino, M., E-mail: [email protected] [Dipartimento di Fisica dell' Universita, Bologna (Italy); INFN, Bologna (Italy); Bruno, M. [Dipartimento di Fisica dell' Universita, Bologna (Italy); INFN, Bologna (Italy); Gulminelli, F. [CNRS, UMR6534, LPC, F-14050 Caen cedex and ENSICAEN, UMR6534, LPC, F-14050 Caen cedex (France); Morelli, L. [Dipartimento di Fisica dell' Universita, Bologna (Italy); INFN, Bologna (Italy); Baiocco, G. [Dipartimento di Fisica dell' Universita, Bologna (Italy); INFN, Bologna (Italy); CNRS, UMR6534, LPC, F-14050 Caen cedex and ENSICAEN, UMR6534, LPC, F-14050 Caen cedex (France); Bardelli, L. [INFN, Firenze (Italy); INFN, Catania (Italy); Barlini, S. [INFN, Firenze (Italy); Cannata, F. [INFN, Bologna (Italy); Casini, G. [INFN, Firenze (Italy); Geraci, E. [Dipartimento di Fisica dell' Universita, Catania (Italy); INFN, Catania (Italy); Gramegna, F.; Kravchuk, V.L. [INFN, Laboratori Nazionali di Legnaro (Italy); Marchi, T. [INFN, Laboratori Nazionali di Legnaro (Italy); Dipartimento di Fisica dell' Universita, Padova,Italy (Italy); Moroni, A. [INFN, Milano (Italy); Ordine, A. [INFN, Napoli (Italy); Raduta, Ad.R. [NIPNE, Bucharest-Magurele, POB-MG6 (Romania)
2012-02-01
The reactions {sup 32}S+{sup 58,64}Ni are studied at 14.5 A MeV. Evidence is found for important odd-even effects in isotopic observables of selected peripheral collisions corresponding to the decay of a projectile-like source. The influence of secondary decays on the staggering is studied with a correlation function technique. It is shown that this method is a powerful tool to get experimental information on the evaporation chain, in order to constrain model calculations. Specifically, we show that odd-even effects are due to interplay between pairing effects in the nuclear masses and in the level densities.
1. Towards an understanding of staggering effects in dissipative binary collisions
Science.gov (United States)
D'Agostino, M.; Bruno, M.; Gulminelli, F.; Morelli, L.; Baiocco, G.; Bardelli, L.; Barlini, S.; Cannata, F.; Casini, G.; Geraci, E.; Gramegna, F.; Kravchuk, V. L.; Marchi, T.; Moroni, A.; Ordine, A.; Raduta, Ad. R.
2012-02-01
The reactions S32+58Ni are studied at 14.5 A MeV. Evidence is found for important odd-even effects in isotopic observables of selected peripheral collisions corresponding to the decay of a projectile-like source. The influence of secondary decays on the staggering is studied with a correlation function technique. It is shown that this method is a powerful tool to get experimental information on the evaporation chain, in order to constrain model calculations. Specifically, we show that odd-even effects are due to interplay between pairing effects in the nuclear masses and in the level densities.
2. Binary and triple collisions causing instability in the free-fall three-body problem
Science.gov (United States)
Umehara, Hiroaki; Tanikawa, Kiyotaka
2000-04-01
Dominant factors for escape after the first triple-encounter are searched for in the three-body problem with zero initial velocities and equal masses. By a global numerical survey on the whole initial-value space, it is found that not only a triple-collision orbit but also a particular family of binary-collision orbits exist in the set of escape orbits. This observation is justified from various viewpoints. Binary-collision orbits experiencing close triple-encounter turn out to be close to isosceles orbits after the encounter and hence lead to escape. Except for a few cases, binary-collision orbits of near-isosceles slingshot also escape.
3. DROPLET COLLISION AND COALESCENCE MODEL
Institute of Scientific and Technical Information of China (English)
LI Qiang; CAI Ti-min; HE Guo-qiang; HU Chun-bo
2006-01-01
A new droplet collision and coalescence model was presented, a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results, further advancement was made to the droplet collision outcome.The advantages of the two implementations of smoothed particle hydrodynamics (SPH)method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence, numerical simulations were carried out for model validation. Results show that the model presented is mesh-independent and less time consuming, it can not only maintains the system momentum conservation perfectly, but not susceptible to initial droplet size distribution as well.
4. Numerical Simulation on Head-On Binary Collision of Gel Propellant Droplets
Directory of Open Access Journals (Sweden)
Zejun Liu
2013-01-01
Full Text Available Binary collision of droplets is a fundamental form of droplet interaction in the spraying flow field. In order to reveal the central collision mechanism of two gel droplets with equal diameters, an axi-symmetric form of the Navier-Stokes equations are firstly solved and the method of VOF (volume of fluid is utilized to track the evolution of the gas-liquid free interface. Then, the numerical computation model is validated with Qian’s experimental results on Newtonian liquids. Phenomena of rebound, coalescence and reflexive separation of droplets after collision are investigated, and structures of the complicated flow fields during the collision process are also analyzed in detail. Results show that the maximum shear rate will appear at the point where the flow is redirected and accelerated. Rebound of droplets is determined by the Weber number and viscosity of the fluid together. It can be concluded that the gel droplets are easier to rebound in comparison with the base fluid droplets. The results also show that the alternant appearance along with the deformation of droplets in the radial and axial direction is the main characteristic of the droplet coalescence process, and the deformation amplitude attenuates gradually. Moreover, the reflexive separation process of droplets can be divided into three distinctive stages including the radial expansion, the recovery of the spherical shape, and the axial extension and reflexive separation. The variation trend of the kinetic energy is opposite to that of the surface energy. The maximum deformation of droplets appears in the radial expansion stage; in the case of a low Weber number, the minimum central thickness of a droplet appears later than its maximum deformation, however, this result is on the contrary in the case of a high Weber number.
5. Binary cluster collision dynamics and minimum energy conformations
Energy Technology Data Exchange (ETDEWEB)
2013-10-15
The collision dynamics of one Ag or Cu atom impinging on a Au{sub 12} cluster is investigated by means of DFT molecular dynamics. Our results show that the experimentally confirmed 2D to 3D transition of Au{sub 12}→Au{sub 13} is mostly preserved by the resulting planar Au{sub 12}Ag and Au{sub 12}Cu minimum energy clusters, which is quite remarkable in view of the excess energy, well larger than the 2D–3D potential barrier height. The process is accompanied by a large s−d hybridization and charge transfer from Au to Ag or Cu. The dynamics of the collision process mainly yields fusion of projectile and target, however scattering and cluster fragmentation also occur for large energies and large impact parameters. While Ag projectiles favor fragmentation, Cu favors scattering due to its smaller mass. The projectile size does not play a major role in favoring the fragmentation or scattering channels. By comparing our collision results with those obtained by an unbiased minimum energy search of 4483 Au{sub 12}Ag and 4483 Au{sub 12}Cu configurations obtained phenomenologically, we find that there is an extra bonus: without increase of computer time collisions yield the planar lower energy structures that are not feasible to obtain using semi-classical potentials. In fact, we conclude that phenomenological potentials do not even provide adequate seeds for the search of global energy minima for planar structures. Since the fabrication of nanoclusters is mainly achieved by synthesis or laser ablation, the set of local minima configurations we provide here, and their distribution as a function of energy, are more relevant than the global minimum to analyze experimental results obtained at finite temperatures, and is consistent with the dynamical coexistence of 2D and 3D liquid Au clusters conformations obtained previously.
6. Polar pattern formation in driven filament systems requires non-binary particle collisions
Science.gov (United States)
Suzuki, Ryo; Weber, Christoph A.; Frey, Erwin; Bausch, Andreas R.
2015-10-01
From the self-organization of the cytoskeleton to the synchronous motion of bird flocks, living matter has the extraordinary ability to behave in a concerted manner. The Boltzmann equation for self-propelled particles is frequently used in silico to link a system’s meso- or macroscopic behaviour to the microscopic dynamics of its constituents. But so far such studies have relied on an assumption of simplified binary collisions owing to a lack of experimental data suggesting otherwise. We report here experimentally determined binary-collision statistics by studying a recently introduced molecular system, the high-density actomyosin motility assay. We demonstrate that the alignment induced by binary collisions is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, indicating that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. Our findings demonstrate that the unique properties of biological active-matter systems require a description that goes well beyond that developed in the framework of kinetic theories.
7. Polar Pattern Formation in Driven Filament Systems Require Non-Binary Particle Collisions.
Science.gov (United States)
Suzuki, Ryo; Weber, Christoph A; Frey, Erwin; Bausch, Andreas R
2015-10-01
Living matter has the extraordinary ability to behave in a concerted manner, which is exemplified throughout nature ranging from the self-organisation of the cytoskeleton to flocks of animals [1-4]. The microscopic dynamics of constituents have been linked to the system's meso- or macroscopic behaviour in silico via the Boltzmann equation for propelled particles [5-10]. Thereby, simplified binary collision rules between the constituents had to be assumed due to the lack of experimental data. We report here experimentally determined binary collision statistics by studying the recently introduced molecular system, the high density actomyosin motility assay [11-13]. We demonstrate that the alignment effect of the binary collision statistics is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, which indicates that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. The presented findings demonstrate that the unique properties of biological active matter systems require a description that goes well beyond a gas-like picture developed in the framework of kinetic theories.
8. Lorentz invariant relative velocity and relativistic binary collisions
Science.gov (United States)
Cannoni, Mirco
2017-01-01
This paper reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross-section without recurring to nonphysical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.
9. Lorentz invariant relative velocity and relativistic binary collisions
CERN Document Server
Cannoni, Mirco
2016-01-01
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross section without recurring to non--physical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.
10. Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity
Science.gov (United States)
Willis, K.; Orme, M.
An experimental investigation of viscous binary droplet collisions in a vacuum environment is conducted. The fundamental ramifications of conducting such experiments in a vacuum environment are twofold. The first, which is the motivating factor of this work, assures that the collision products are unimpeded by aerodynamic effects which tend to disrupt the collision process at a much earlier stage in the processes than if they were absent, and second, the phenomenon of encapsulation of the host medium between the colliding droplets is not present in this study; a fact that limits the scope of direct application of this study to a number of (but not all) applications. Droplets are generated from capillary stream breakup with the imposition of an amplitude-modulated disturbance which results in the generation of highly uniform pre-collision drops at separations far extending those which are possible from a standard (monochromatic) sinusoidal disturbance. Hence, the collision products are able to deform unimpeded by interactions with neighboring collision products. Measurements over a broad range of Weber number, We, indicate that the value of the critical Weber number, Wec, is more than 100 times greater for the 30-cSt fluid than the corresponding value for similarly sized water drops in a standard ambient environment. Measurements of the oblate and prolate half-cycle oscillation periods resulting from the binary collision reveal a distinct behavior that is observed and documented here for the first time. Additionally, measurements of the radial extent of the deformed mass at the instant of maximum deformation have been conducted and allow quantification of the energy dissipation. These measurements show that the energy dissipation increases with increasing fluid viscosity, which contradicts the results published by others.
11. Cascade statistics in the binary collision approximation and in full molecular dynamics
Energy Technology Data Exchange (ETDEWEB)
Hou, M. [Universite Libre de Bruxelles (Belgium). Physique des Solides Irradies; Pan, Z.Y. [Fudan Univ., Shanghai (China). Dept. of Physics
1995-08-01
The Binary Collision Approximation (BCA) and Molecular Dynamics (MD) are used to simulate low energy atomic collision cascades in solids. Results are compared and discussed on the example of copper and gold self irradiation. For MD, long range N-body potentials are built, similar to those deduced from the second moment semi-empirical tight binding model. The pair interaction contribution is splined to a Moliere screened Coulomb potential at small separation distances. The BCA calculations are performed with the MARLOWE program, using the same Moliere potential as for MD, and modelling the N-body contribution by a binding of the atoms to their equilibrium lattice sites. The scattering integrals are estimated by means of a 4 points Gauss-Mehler quadrature. In MD, the NVT equations of motion are integrated with a constant time step of 2 fs. For the NVE cascade simulations, the Newton equations of motion are solved with a dynamically adjusted time step, kept lower than 2 fs. The influence of the time step on the simulated trajectories is discussed. The mean number of moving atoms with total energy above threshold values ranging from 1 to 100 eV is estimated as a function of time over 300 fs both with MARLOWE and by MD. This estimate is repeated for external primary energies ranging from 250 eV to 1 keV. In the case of copper, the BCA results are found to be in remarkable agreement with MD over about 200 fs cascade development, provided the size of the crystallite used in MD is sufficiently large in order to account for the early mechanical response of the close environment. This agreement between the two methods is found to be the best when the binding energy of the target atoms as modelled in the BCA is adjusted to a value close to the cohesive energy. In the case of gold, the agreement between BCA and MD is reasonable and the results suggest the need of an accurate modelling of linear collision sequences in the BCA. (orig.).
12. Markov Modelling of Fingerprinting Systems for Collision Analysis
Directory of Open Access Journals (Sweden)
Guénolé C. M. Silvestre
2008-03-01
Full Text Available Multimedia fingerprinting, also known as robust or perceptual hashing, aims at representing multimedia signals through compact and perceptually significant descriptors (hash values. In this paper, we examine the probability of collision of a certain general class of robust hashing systems that, in its binary alphabet version, encompasses a number of existing robust audio hashing algorithms. Our analysis relies on modelling the fingerprint (hash symbols by means of Markov chains, which is generally realistic due to the hash synchronization properties usually required in multimedia identification. We provide theoretical expressions of performance, and show that the use of M-ary alphabets is advantageous with respect to binary alphabets. We show how these general expressions explain the performance of Philips fingerprinting, whose probability of collision had only been previously estimated through heuristics.
13. Energy loss of ions in a magnetized plasma: conformity between linear response and binary collision treatments.
Science.gov (United States)
Nersisyan, H B; Zwicknagel, G; Toepffer, C
2003-02-01
The energy loss of a heavy ion moving in a magnetized electron plasma is considered within the linear response (LR) and binary collision (BC) treatments with the purpose to look for a connection between these two models. These two complementary approaches yield close results if no magnetic field is present, but there develop discrepancies with growing magnetic field at ion velocities that are lower than, or comparable with, the thermal velocity of the electrons. We show that this is a peculiarity of the Coulomb interaction which requires cutoff procedures to account for its singularity at the origin and its infinite range. The cutoff procedures in the LR and BC treatments are different as the order of integrations in velocity and in ordinary (Fourier) spaces is reversed in both treatments. While BC involves a velocity average of Coulomb logarithms, there appear in LR Coulomb logarithms of velocity averaged cutoffs. The discrepancies between LR and BC vanish, except for small contributions of collective modes, for smoothened potentials that require no cutoffs. This is shown explicitly with the help of an improved BC in which the velocity transfer is treated up to second order in the interaction in Fourier space.
14. A model for collisions in granular gases
OpenAIRE
Brilliantov, Nikolai V.; Spahn, Frank; Hertzsch, Jan-Martin; Poeschel, Thorsten
2002-01-01
We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and...
15. Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs' collision factor theory
Institute of Scientific and Technical Information of China (English)
Lu Yi-Gang; Dong Yan-Wu
2006-01-01
Based on Schaaff's collision factor theory (CFT) in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules,several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components.Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel's and Sehgal's laws for liquid binary mixtures.
16. Modelling droplet collision outcomes for different substances and viscosities
Science.gov (United States)
Sommerfeld, Martin; Kuschel, Matthias
2016-12-01
The main objective of the present study is the derivation of models describing the outcome of binary droplet collisions for a wide range of dynamic viscosities in the well-known collision maps (i.e. normalised lateral droplet displacement at collision, called impact parameter, versus collision Weber number). Previous studies by Kuschel and Sommerfeld (Exp Fluids 54:1440, 2013) for different solution droplets having a range of solids contents and hence dynamic viscosities (here between 1 and 60 mPa s) revealed that the locations of the triple point (i.e. coincidence of bouncing, stretching separation and coalescence) and the critical Weber number (i.e. condition for the transition from coalescence to separation for head-on collisions) show a clear dependence on dynamic viscosity. In order to extend these findings also to pure liquids and to provide a broader data basis for modelling the viscosity effect, additional binary collision experiments were conducted for different alcohols (viscosity range 1.2-15.9 mPa s) and the FVA1 reference oil at different temperatures (viscosity range 3.0-28.2 mPa s). The droplet size for the series of alcohols was around 365 and 385 µm for the FVA1 reference oil, in each case with fixed diameter ratio at Δ= 1. The relative velocity between the droplets was varied in the range 0.5-3.5 m/s, yielding maximum Weber numbers of around 180. Individual binary droplet collisions with defined conditions were generated by two droplet chains each produced by vibrating orifice droplet generators. For recording droplet motion and the binary collision process with good spatial and temporal resolution high-speed shadow imaging was employed. The results for varied relative velocity and impact angle were assembled in impact parameter-Weber number maps. With increasing dynamic viscosity a characteristic displacement of the regimes for the different collision scenarios was also observed for pure liquids similar to that observed for solutions. This
17. Asteroseismic modelling of the Binary HD 176465
CERN Document Server
Nsamba, B; Campante, T L; Reese, D R; White, T R; Hernández, A García; Jiang, C
2016-01-01
The detection and analysis of oscillations in binary star systems is critical in understanding stellar structure and evolution. This is partly because such systems have the same initial chemical composition and age. Solar-like oscillations have been detected by Kepler in both components of the asteroseismic binary HD 176465. We present an independent modelling of each star in this binary system. Stellar models generated using MESA (Modules for Experiments in Stellar Astrophysics) were fitted to both the observed individual frequencies and complementary spectroscopic parameters. The individual theoretical oscillation frequencies for the corresponding stellar models were obtained using GYRE as the pulsation code. A Bayesian approach was applied to find the probability distribution functions of the stellar parameters using AIMS (Asteroseismic Inference on a Massive Scale) as the optimisation code. The ages of HD 176465 A and HD 176465 B were found to be 2.81 $\\pm$ 0.48 Gyr and 2.52 $\\pm$ 0.80 Gyr, respectively. ...
18. A Model for Contact Binary Systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
A model for contact binary systems is presented, which incorporates the following special features: a) The energy exchange between the components is based on the understanding that the energy exchange is due to the release of potential, kinetic and thermal energies of the exchanged mass. b) A special form of mass and angular momentum loss occurring in contact binaries is losses via the outer Lagrangian point. c) The effects of spin, orbital rotation and tidal action on the stellar structure as well as the effect of meridian circulation on the mixing of the chemical elements are considered. d) The model is valid not only for low-mass contact binaries but also for high-mass contact binaries. For illustration, we used the model to trace the evolution of a massive binary system consisting of one 12M⊙ and one 5M⊙ star. The result shows that the start and end of the contact stage fall within the semi-detached phase during which the primary continually transfers mass to the secondary. The time span of the contact stage is short and the mass transfer rate is very large. Therefore, the contact stage can be regarded as a special part of the semi-detached phase with a large mass transfer rate. Both mass loss through the outer Lagrangian point and oscillation between contact and semi-contact states can occur during the contact phase, and the effective temperatures of the primary and the secondary are almost equal.
19. Recommended direct simulation Monte Carlo collision model parameters for modeling ionized air transport processes
Energy Technology Data Exchange (ETDEWEB)
Swaminathan-Gopalan, Krishnan; Stephani, Kelly A., E-mail: [email protected] [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)
2016-02-15
A systematic approach for calibrating the direct simulation Monte Carlo (DSMC) collision model parameters to achieve consistency in the transport processes is presented. The DSMC collision cross section model parameters are calibrated for high temperature atmospheric conditions by matching the collision integrals from DSMC against ab initio based collision integrals that are currently employed in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and Data Parallel Line Relaxation (DPLR) high temperature computational fluid dynamics solvers. The DSMC parameter values are computed for the widely used Variable Hard Sphere (VHS) and the Variable Soft Sphere (VSS) models using the collision-specific pairing approach. The recommended best-fit VHS/VSS parameter values are provided over a temperature range of 1000-20 000 K for a thirteen-species ionized air mixture. Use of the VSS model is necessary to achieve consistency in transport processes of ionized gases. The agreement of the VSS model transport properties with the transport properties as determined by the ab initio collision integral fits was found to be within 6% in the entire temperature range, regardless of the composition of the mixture. The recommended model parameter values can be readily applied to any gas mixture involving binary collisional interactions between the chemical species presented for the specified temperature range.
20. Recommended direct simulation Monte Carlo collision model parameters for modeling ionized air transport processes
Science.gov (United States)
Swaminathan-Gopalan, Krishnan; Stephani, Kelly A.
2016-02-01
A systematic approach for calibrating the direct simulation Monte Carlo (DSMC) collision model parameters to achieve consistency in the transport processes is presented. The DSMC collision cross section model parameters are calibrated for high temperature atmospheric conditions by matching the collision integrals from DSMC against ab initio based collision integrals that are currently employed in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and Data Parallel Line Relaxation (DPLR) high temperature computational fluid dynamics solvers. The DSMC parameter values are computed for the widely used Variable Hard Sphere (VHS) and the Variable Soft Sphere (VSS) models using the collision-specific pairing approach. The recommended best-fit VHS/VSS parameter values are provided over a temperature range of 1000-20 000 K for a thirteen-species ionized air mixture. Use of the VSS model is necessary to achieve consistency in transport processes of ionized gases. The agreement of the VSS model transport properties with the transport properties as determined by the ab initio collision integral fits was found to be within 6% in the entire temperature range, regardless of the composition of the mixture. The recommended model parameter values can be readily applied to any gas mixture involving binary collisional interactions between the chemical species presented for the specified temperature range.
1. Modeling gravitational radiation from coalescing binary black holes
CERN Document Server
Baker, J; Loustó, C O; Takahashi, R
2002-01-01
With the goal of bringing theory, particularly numerical relativity, to bear on an astrophysical problem of critical interest to gravitational wave observers we introduce a model for coalescence radiation from binary black hole systems. We build our model using the "Lazarus approach", a technique that bridges far and close limit approaches with full numerical relativity to solve Einstein equations applied in the truly nonlinear dynamical regime. We specifically study the post-orbital radiation from a system of equal-mass non-spinning black holes, deriving waveforms which indicate strongly circularly polarized radiation of roughly 3% of the system's total energy and 12% of its total angular momentum in just a few cycles. Supporting this result we first establish the reliability of the late-time part of our model, including the numerical relativity and close-limit components, with a thorough study of waveforms from a sequence of black hole configurations varying from previously treated head-on collisions to rep...
2. Heat Source Characterization In A TREAT Fuel Particle Using Coupled Neutronics Binary Collision Monte-Carlo Calculations
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Schwen, Daniel; Ghassemi, Pedram; Baker, Benjamin; Zabriskie, Adam; Ortensi, Javier; Wang, Yaqi; Gleicher, Frederick; DeHart, Mark; Martineau, Richard
2017-04-01
This work presents a multi-physics, multi-scale approach to modeling the Transient Test Reactor (TREAT) currently prepared for restart at the Idaho National Laboratory. TREAT fuel is made up of microscopic fuel grains (r ˜ 20µm) dispersed in a graphite matrix. The novelty of this work is in coupling a binary collision Monte-Carlo (BCMC) model to the Finite Element based code Moose for solving a microsopic heat-conduction problem whose driving source is provided by the BCMC model tracking fission fragment energy deposition. This microscopic model is driven by a transient, engineering scale neutronics model coupled to an adiabatic heating model. The macroscopic model provides local power densities and neutron energy spectra to the microscpic model. Currently, no feedback from the microscopic to the macroscopic model is considered. TREAT transient 15 is used to exemplify the capabilities of the multi-physics, multi-scale model, and it is found that the average fuel grain temperature differs from the average graphite temperature by 80 K despite the low-power transient. The large temperature difference has strong implications on the Doppler feedback a potential LEU TREAT core would see, and it underpins the need for multi-physics, multi-scale modeling of a TREAT LEU core.
3. Binary hidden Markov models and varieties
CERN Document Server
Critch, Andrew J
2012-01-01
The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly non-linear statistical models, and just as linear models are amenable to linear algebraic techniques, non-linear models are amenable to commutative algebra and algebraic geometry. This paper examines closely those HMMs in which all the random variables, called nodes, are binary. Its main contributions are (1) minimal defining equations for the 4-node model, comprising 21 quadrics and 29 cubics, which were computed using Gr\\"obner bases in the cumulant coordinates of Sturmfels and Zwiernik, and (2) a birational parametrization for every binary HMM, with an explicit inverse for recovering the hidden parameters in terms of observables. The new model parameters in (2) are hence rationally identifiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zar...
4. Eclipsing binary stars modeling and analysis
CERN Document Server
Kallrath, Josef
1999-01-01
This book focuses on the formulation of mathematical models for the light curves of eclipsing binary stars, and on the algorithms for generating such models Since information gained from binary systems provides much of what we know of the masses, luminosities, and radii of stars, such models are acquiring increasing importance in studies of stellar structure and evolution As in other areas of science, the computer revolution has given many astronomers tools that previously only specialists could use; anyone with access to a set of data can now expect to be able to model it This book will provide astronomers, both amateur and professional, with a guide for - specifying an astrophysical model for a set of observations - selecting an algorithm to determine the parameters of the model - estimating the errors of the parameters It is written for readers with knowledge of basic calculus and linear algebra; appendices cover mathematical details on such matters as optimization, coordinate systems, and specific models ...
5. Modelling colliding wind binaries with RAMSES, extension to special relativity
CERN Document Server
Lamberts, Astrid; Dubus, Guillaume; Lesur, Geoffroy
2012-01-01
We present high resolution simulations with RAMSES of supersonic colliding stellar winds. The collision results in a double shock structure which is subject to different instabilities. The Kelvin-Helmholtz instability (KHI) introduces some mixing and variability. For isothermal winds, the Non-linear Thin Shell Instability violently affects the interaction region. Properly modelling these instabilities requires a high enough resolution and an adapted numerical method, especially when one of the winds strongly dominates the other one. At large scale, orbital motion is expected to turn the shocked zone into a spiral but we find that in some configurations the KHI may disrupt the spiral. A colliding wind structure is also expected in gamma-ray binaries composed of a massive star and a young pulsar which emits a highly relativistic wind. Numerical simulations are necessary to understand the geometry of such systems and should take into account the relativistic nature of the pulsar wind. We implemented a second ord...
6. Model-independent inference on compact-binary observations
OpenAIRE
Mandel, Ilya; Farr, Will M.; Colonna, Andrea; Stevenson, Simon; Tiňo, Peter; Veitch, John
2016-01-01
The recent advanced LIGO detections of gravitational waves from merging binary black holes enhance the prospect of exploring binary evolution via gravitational-wave observations of a population of compact-object binaries. In the face of uncertainty about binary formation models, model-independent inference provides an appealing alternative to comparisons between observed and modelled populations. We describe a procedure for clustering in the multi-dimensional parameter space of observations t...
7. Model-independent inference on compact-binary observations
Science.gov (United States)
Mandel, Ilya; Farr, Will M.; Colonna, Andrea; Stevenson, Simon; Tiňo, Peter; Veitch, John
2017-03-01
The recent advanced LIGO detections of gravitational waves from merging binary black holes enhance the prospect of exploring binary evolution via gravitational-wave observations of a population of compact-object binaries. In the face of uncertainty about binary formation models, model-independent inference provides an appealing alternative to comparisons between observed and modelled populations. We describe a procedure for clustering in the multidimensional parameter space of observations that are subject to significant measurement errors. We apply this procedure to a mock data set of population-synthesis predictions for the masses of merging compact binaries convolved with realistic measurement uncertainties, and demonstrate that we can accurately distinguish subpopulations of binary neutron stars, binary black holes, and mixed neutron star-black hole binaries with tens of observations.
8. Model-independent inference on compact-binary observations
CERN Document Server
Mandel, Ilya; Colonna, Andrea; Stevenson, Simon; Tiňo, Peter; Veitch, John
2016-01-01
The recent advanced LIGO detections of gravitational waves from merging binary black holes enhance the prospect of exploring binary evolution via gravitational-wave observations of a population of compact-object binaries. In the face of uncertainty about binary formation models, model-independent inference provides an appealing alternative to comparisons between observed and modelled populations. We describe a procedure for clustering in the multi-dimensional parameter space of observations that are subject to significant measurement errors. We apply this procedure to a mock data set of population-synthesis predictions for the masses of merging compact binaries convolved with realistic measurement uncertainties, and demonstrate that we can accurately distinguish subpopulations of binary neutron stars, binary black holes, and mixed black hole -- neutron star binaries.
9. Binary progenitor models of type IIb supernovae
CERN Document Server
Claeys, J S W; Pols, O R; Eldridge, J J; Baes, M
2011-01-01
Massive stars that lose their hydrogen-rich envelope down to a few tenths of a solar mass explode as extended type IIb supernovae, an intriguing subtype that links the hydrogen-rich type II supernovae with the hydrogen-poor type Ib and Ic. The progenitors may be very massive single stars that lose their envelope due to their stellar wind, but mass stripping due to interaction with a companion star in a binary system is currently considered to be the dominant formation channel. We computed an extensive grid of binary models with the Eggleton binary evolution code. The predicted rate from our standard models, which assume conservative mass transfer, is about 6 times smaller than the current rate indicated by observations. It is larger but still comparable to the rate expected from single stars. To recover the observed rate we must generously allow for uncertainties and low accretion efficiencies in combination with limited angular momentum loss from the system. Motivated by the claims of detection and non-detec...
10. Non-Hertzian behavior in binary collisions of plastic balls derived from impact acoustics.
Science.gov (United States)
Riner, Joshua; Petculescu, Andi
2010-07-01
This paper presents slight deviations from Hertz's impact law, inferred from acoustic signatures of polypropylene ball collisions. An impact acoustics model is used to fit the acoustic data. The model is built upon a generalized relationship between impact force (F) and deformation (xi) of the form F=kappaxi(alpha). Agreement with experiment is reached when alpha and kappa differ from Hertz's values by -6.25% and +1%, respectively. The difference is ascribable to non-idealities such as slight material inhomogeneities, impact-point asymmetry, plasticity etc. Also, the collision energy released as sound, which is usually dismissed as negligible, is derived from data fitting. The acoustic-to-incident energy ratio, dependent on impact duration, is constrained to be on the order of 100 ppm.
11. Fan Affinity Laws from a Collision Model
Science.gov (United States)
Bhattacharjee, Shayak
2012-01-01
The performance of a fan is usually estimated using hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this paper we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour…
12. Fan Affinity Laws from a Collision Model
Science.gov (United States)
Bhattacharjee, Shayak
2012-01-01
The performance of a fan is usually estimated using hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this paper we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour…
13. A numerical 4D Collision Risk Model
Science.gov (United States)
Schmitt, Pal; Culloch, Ross; Lieber, Lilian; Kregting, Louise
2017-04-01
With the growing number of marine renewable energy (MRE) devices being installed across the world, some concern has been raised about the possibility of harming mobile, marine fauna by collision. Although physical contact between a MRE device and an organism has not been reported to date, these novel sub-sea structures pose a challenge for accurately estimating collision risks as part of environmental impact assessments. Even if the animal motion is simplified to linear translation, ignoring likely evasive behaviour, the mathematical problem of establishing an impact probability is not trivial. We present a numerical algorithm to obtain such probability distributions using transient, four-dimensional simulations of a novel marine renewable device concept, Deep Green, Minesto's power plant and hereafter referred to as the 'kite' that flies in a figure-of-eight configuration. Simulations were carried out altering several configurations including kite depth, kite speed and kite trajectory while keeping the speed of the moving object constant. Since the kite assembly is defined as two parts in the model, a tether (attached to the seabed) and the kite, collision risk of each part is reported independently. By comparing the number of collisions with the number of collision-free simulations, a probability of impact for each simulated position in the cross- section of the area is considered. Results suggest that close to the bottom, where the tether amplitude is small, the path is always blocked and the impact probability is 100% as expected. However, higher up in the water column, the collision probability is twice as high in the mid line, where the tether passes twice per period than at the extremes of its trajectory. The collision probability distribution is much more complex in the upper end of the water column, where the kite and tether can simultaneously collide with the object. Results demonstrate the viability of such models, which can also incorporate empirical
14. ACOUSTIC EFFECTS ON BINARY AEROELASTICITY MODEL
Directory of Open Access Journals (Sweden)
Kok Hwa Yu
2011-10-01
Full Text Available Acoustics is the science concerned with the study of sound. The effects of sound on structures attract overwhelm interests and numerous studies were carried out in this particular area. Many of the preliminary investigations show that acoustic pressure produces significant influences on structures such as thin plate, membrane and also high-impedance medium like water (and other similar fluids. Thus, it is useful to investigate the structure response with the presence of acoustics on aircraft, especially on aircraft wings, tails and control surfaces which are vulnerable to flutter phenomena. The present paper describes the modeling of structural-acoustic interactions to simulate the external acoustic effect on binary flutter model. Here, the binary flutter model which illustrated as a rectangular wing is constructed using strip theory with simplified unsteady aerodynamics involving flap and pitch degree of freedom terms. The external acoustic excitation, on the other hand, is modeled using four-node quadrilateral isoparametric element via finite element approach. Both equations then carefully coupled and solved using eigenvalue solution. The mentioned approach is implemented in MATLAB and the outcome of the simulated result are later described, analyzed and illustrated in this paper.
15. Modeling and analysis of advanced binary cycles
Energy Technology Data Exchange (ETDEWEB)
Gawlik, K.
1997-12-31
A computer model (Cycle Analysis Simulation Tool, CAST) and a methodology have been developed to perform value analysis for small, low- to moderate-temperature binary geothermal power plants. The value analysis method allows for incremental changes in the levelized electricity cost (LEC) to be determined between a baseline plant and a modified plant. Thermodynamic cycle analyses and component sizing are carried out in the model followed by economic analysis which provides LEC results. The emphasis of the present work is on evaluating the effect of mixed working fluids instead of pure fluids on the LEC of a geothermal binary plant that uses a simple Organic Rankine Cycle. Four resources were studied spanning the range of 265{degrees}F to 375{degrees}F. A variety of isobutane and propane based mixtures, in addition to pure fluids, were used as working fluids. This study shows that the use of propane mixtures at a 265{degrees}F resource can reduce the LEC by 24% when compared to a base case value that utilizes commercial isobutane as its working fluid. The cost savings drop to 6% for a 375{degrees}F resource, where an isobutane mixture is favored. Supercritical cycles were found to have the lowest cost at all resources.
16. Fan affinity laws from a collision model
CERN Document Server
Bhattacharjee, Shayak
2012-01-01
The performance of a fan is usually estimated from hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this work we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour of air is incorporated. Our calculations prove the affinity laws and provide numerical estimates of the air delivery, thrust and drag on a rotating fan.
17. Spectral modelling of massive binary systems
CERN Document Server
Palate, Matthieu; Koenigsberger, Gloria; Moreno, Edmundo
2013-01-01
Aims: We simulate the spectra of massive binaries at different phases of the orbital cycle, accounting for the gravitational influence of the companion star on the shape and physical properties of the stellar surface. Methods: We used the Roche potential modified to account for radiation pressure to compute the stellar surface of close circular systems and we used the TIDES code for surface computation of eccentric systems. In both cases, we accounted for gravity darkening and mutual heating generated by irradiation to compute the surface temperature. We then interpolated NLTE plane-parallel atmosphere model spectra in a grid to obtain the local spectrum at each surface point. We finally summed all contributions, accounting for the Doppler shift, limb-darkening, and visibility to obtain the total synthetic spectrum. We computed different orbital phases and sets of physical and orbital parameters. Results: Our models predict line strength variations through the orbital cycle, but fail to completely reproduce t...
18. Quasi-binary incident electron–centre of mass collision in (, 3) process on He and He-like ions
R Choubisa; K K Sud
2005-07-01
We present in this communication the results of our first Born calculation in the three-Coulomb (3C) wave approach for the (, 3) process on He and He-like ions at an incident electron energy 5599 eV in the coplanar constant 12 as well as out-of-plane constant 12 modes. These two geometrical modes are such that the quasi-binary collision between the incident electron and centre of mass of the ejected electrons is in the scattering plane. The theoretical formalism has been developed using plane waves, Le Sech wave function and approximated BBK-type wave function respectively for the incident and scattered, bound and ejected electrons to calculate five-fold differential cross-section (FDCS) of the (, 3) process. We emphasize on the similarities and dissimilarities (asymmetries) in the angular profile of the FDCS in two modes as well as the effects of post-collision interaction (between the ejected electrons) and nuclear charge on the angular profile of the FDCS. We observe that with the increment of nuclear charge the two quasi-binary collisions approach towards identical behaviour at larger mutual angles and thus bringing less asymmetry in FDCS for higher target.
19. A Lattice Boltzmann Model of Binary Fluid Mixture
CERN Document Server
Orlandini, E; Yeomans, J M; Orlandini, Enzo; Swift, Michael R.
1995-01-01
We introduce a lattice Boltzmann for simulating an immiscible binary fluid mixture. Our collision rules are derived from a macroscopic thermodynamic description of the fluid in a way motivated by the Cahn-Hilliard approach to non-equilibrium dynamics. This ensures that a thermodynamically consistent state is reached in equilibrium. The non-equilibrium dynamics is investigated numerically and found to agree with simple analytic predictions in both the one-phase and the two-phase region of the phase diagram.
20. Modeling Flows Around Merging Black Hole Binaries
Science.gov (United States)
Centrella, Joan
2008-01-01
Coalescing massive black hole binaries are produced by the merger of galaxies. The final stages of the black hole coalescence produce strong gravitational radiation that can be detected by the space-borne LISA. In cases in which the black hole merger takes place in the presence of gas and magnetic fields, various types of electromagnetic signals may also be produced. Modeling such electromagnetic counterparts of the final merger requires evolving the behavior of both gas and fields in the strong-field regions around the black holes. We have taken a first step towards this problem by mapping the flow of pressureless matter in the dynamic, 3-D general relativistic spacetime around the merging black holes. We report on the results of these initial simulations and discuss their likely importance for future hydrodynamical simulations.
1. Binary and Ternary Fission Within the Statistical Model
Science.gov (United States)
Adamian, Gurgen G.; Andreev, Alexander V.; Antonenko, Nikolai V.; Scheid, Werner
The binary and ternary nuclear fission are treated within the statistical model. At the scission point we calculate the potentials as functions of the deformations of the fragments in the dinuclear model. The potentials give the mass and charge distributions of the fission fragments. The ternary fission is assumed to occur during the binary fission.
2. Alternative treatment for the energy-transfer and transport cross section in dressed electron-ion binary collisions
Science.gov (United States)
Grande, P. L.
2016-10-01
A formula for determining the electronic stopping power and the transport cross section in electron-ion binary collisions is derived from the induced density for spherically symmetric potentials using the partial-wave expansion. In contrast to the previous one found in many textbooks, the present formula converges to the Bethe and Bloch stopping-power formulas at high ion velocities and agrees rather well with experimental stopping-power data, as shown here for Al, C, and H2O targets. It can be employed in plasma physics and particularly in any application that requires electronic stopping-power values of quasifree electrons with high accuracy.
3. On Sparse, Spectral and Other Parameterizations of Binary Probabilistic Models
OpenAIRE
Buchman, David; Schmidt, Mark; Mohamed, Shakir; Poole,David; de Freitas, Nando
2012-01-01
International audience; This paper studies issues relating to the parameterization of probability distributions over binary data sets. Several such parameterizations of models for binary data are known, including the Ising, generalized Ising, canonical and full parameterizations. We also discuss a parameterization that we call the "spectral parameterization", which has received significantly less coverage in existing literature. We provide this parameterization with a spectral interpretation ...
4. Accretion Disks Around Binary Black Holes: A Quasistationary Model
CERN Document Server
Liu, Yuk Tung
2010-01-01
Tidal torques acting on a gaseous accretion disk around a binary black hole can create a gap in the disk near the orbital radius. At late times, when the binary inspiral timescale due to gravitational wave emission becomes shorter than the viscous timescale in the disk, the binary decouples from the disk and eventually merges. Prior to decoupling the balance between tidal and viscous torques drives the disk to a quasistationary equilibrium state, perturbed slightly by small amplitude, spiral density waves emanating from the edges of the gap. We consider a black hole binary with a companion of smaller mass and construct a simple Newtonian model for a geometrically thin, Keplerian disk in the orbital plane of the binary. We solve the disk evolution equations in steady state to determine the quasistationary, (orbit-averaged) surface density profile prior to decoupling. We use our solution, which is analytic up to simple quadratures, to compute the electromagnetic flux and approximate radiation spectrum during th...
5. Spectral modelling of the Alpha Virginis (Spica) binary system
CERN Document Server
Palate, M; Rauw, G; Harrington, D; Moreno, E
2013-01-01
Context: The technique of matching synthetic spectra computed with theoretical stellar atmosphere models to the observations is widely used in deriving fundamental parameters of massive stars. When applied to binaries, however, these models generally neglect the interaction effects present in these systems Aims: The aim of this paper is to explore the uncertainties in binary stellar parameters that are derived from single-star models Methods: Synthetic spectra that include the tidal perturbations and irradiation effects are computed for the binary system alpha Virginis (Spica) using our recently-developed CoMBiSpeC model. The synthetic spectra are compared to S/N~2000 observations and optimum values of Teff and log(g) are derived. Results: The binary interactions have only a small effect on the strength of the photospheric absorption lines in Spica (<2% for the primary and <4% for the secondary). These differences are comparable to the uncertainties inherent to the process of matching synthetic spectra ...
6. Newton's cradle undone: Experiments and collision models for the normal collision of three solid spheres
Science.gov (United States)
Donahue, C. M.; Hrenya, C. M.; Zelinskaya, A. P.; Nakagawa, K. J.
2008-11-01
Using an apparatus inspired by Newton's cradle, the simultaneous, normal collision between three solid spheres is examined. Namely, an initially touching, motionless pair of "target" particles (doublet) is impacted on one end by a third "striker" particle. Measurements of postcollisional velocities and collision durations are obtained via high-speed photography and an electrical circuit, respectively. Contrary to intuition, the expected Newton's cradle outcome of a motionless, touching particle pair at the bottom of the pendulum arc is not observed in either case. Instead, the striker particle reverses its direction and separates from the middle particle after collision. This reversal is not observed, however, if the target particles are separated by a small distance (not in contact) initially, although a separation still occurs between the striker and middle particle after the collision, with both particles traveling in the same direction. For the case of initially touching target particles, contact duration measurements indicate that the striker separates from the three particles before the two target particles separate. However, when the targets are slightly separated, a three-particle collision is never observed, and the collision is, in fact, a series of two-body collisions. A subsequent implementation of a variety of hard-sphere and soft-sphere collision models indicates that a three-body (soft-sphere) treatment is essential for predicting the velocity reversal, consistent with the experimental findings. Finally, a direct comparison between model predictions and measurements of postcollisional velocities and contact durations provides a gauge of the relative merits of existing collision models for three-body interactions.
7. Collisions of Small Nuclei in the Thermal Model
CERN Document Server
Cleymans, J; Oeschler, H.; Redlich, K.; Sharma, N.
2016-01-01
An analysis is presented of the expectations of the thermal model for particle production in collisions of small nuclei. The maxima observed in particle ratios of strange particles to pions as a function of beam energy in heavy ion collisions, are reduced when considering smaller nuclei. Of particular interest is the $\\Lambda/\\pi^+$ ratio shows the strongest maximum which survives even in collisions of small nuclei.
8. Rotation Periods of Binary Asteroids with Large Separations - Confronting the Escaping Ejecta Binaries Model with Observations
CERN Document Server
Polishook, D; Prialnik, D
2010-01-01
Durda et al. (2004), using numerical models, suggested that binary asteroids with large separation, called Escaping Ejecta Binaries (EEBs), can be created by fragments ejected from a disruptive impact event. It is thought that six binary asteroids recently discovered might be EEBs because of the high separation between their components (~100 > a/Rp > ~20). However, the rotation periods of four out of the six objects measured by our group and others and presented here show that these suspected EEBs have fast rotation rates of 2.5 to 4 hours. Because of the small size of the components of these binary asteroids, linked with this fast spinning, we conclude that the rotational-fission mechanism, which is a result of the thermal YORP effect, is the most likely formation scenario. Moreover, scaling the YORP effect for these objects shows that its timescale is shorter than the estimated ages of the three relevant Hirayama families hosting these binary asteroids. Therefore, only the largest (D~19 km) suspected astero...
9. Physics Of Eclipsing Binaries. II. The Increased Model Precision
CERN Document Server
Prsa, Andrej; Horvat, Martin; Pablo, Herbert; Kochoska, Angela; Bloemen, Steven; Nemravova, Jana; Giammarco, Joseph; Hambleton, Kelly M; Degroote, Pieter
2016-01-01
The precision of photometric and spectroscopic observations has been systematically improved in the last decade, mostly thanks to space-borne photometric missions and ground-based spectrographs dedicated to finding exoplanets. The field of eclipsing binary stars strongly benefited from this development. Eclipsing binaries serve as critical tools for determining fundamental stellar properties (masses, radii, temperatures and luminosities), yet the models are not capable of reproducing observed data well, either because of the missing physics or because of insufficient precision. This led to a predicament where radiative and dynamical effects, insofar buried in noise, started showing up routinely in the data, but were not accounted for in the models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an open source modeling code for computing theoretical light and radial velocity curves that addresses both problems by incorporating missing physics and by increasing the computational fidelity. ...
10. Effective-one-body modeling of precessing black hole binaries
Science.gov (United States)
Taracchini, Andrea; Babak, Stanislav; Buonanno, Alessandra
2016-03-01
Merging black hole binaries with generic spins that undergo precessional motion emit complicated gravitational-wave signals. We discuss how such waveforms can be accurately modeled within an effective-one-body approach by (i) exploiting the simplicity of the signals in a frame that corotates with the orbital plane of the binary and (ii) relying on an accurate model of nonprecessing black hole binaries. The model is validated by extensive comparisons to 70 numerical relativity simulations of precessing black hole binaries and can generate inspiral-merger-ringdown waveforms for mass ratios up to 100 and any spin configuration. This work is an essential tool for studying and characterizing candidate gravitational-wave events in science runs of advanced LIGO.
11. Modelling binary rotating stars by new population synthesis code BONNFIRES
CERN Document Server
Lau, Herbert H B; Schneider, Fabian R N
2013-01-01
BONNFIRES, a new generation of population synthesis code, can calculate nuclear reaction, various mixing processes and binary interaction in a timely fashion. We use this new population synthesis code to study the interplay between binary mass transfer and rotation. We aim to compare theoretical models with observations, in particular the surface nitrogen abundance and rotational velocity. Preliminary results show binary interactions may explain the formation of nitrogen-rich slow rotators and nitrogen-poor fast rotators, but more work needs to be done to estimate whether the observed frequencies of those stars can be matched.
12. Energy and angular momentum radiated for non head-on binary black hole collisions
CERN Document Server
Moreschi, O M; Lehner, L; Moreschi, Osvaldo; Perez, Alejandro; Lehner, Luis
2002-01-01
We investigate the possible total radiated energy produced by a binary black hole system containing non-vanishing total angular momentum. For the scenearios considered we find that the total radiated energy does not exceed 1%. Additionally we explore the gravitational radiation field and the variation of angular momentum in the process.
13. Modelling seabird collision risk with off-shore wind farms
Energy Technology Data Exchange (ETDEWEB)
Mateos, Maria; Arroyo, Gonzalo Munoz; Rosario, Jose Juan Alonso del
2011-07-01
Full text: Recent concern about the adverse effects of collision mortality of avian migrants at wind farms has highlighted the need to understand bird-wind turbine interactions. Here, a stochastic collision model, based on data of seabird behaviour collected on- site, is presented, as a flexible and easy to take tool to assess the collisions probabilities of off-shore wind farms in a pre-construction phase. The collision prediction model considering the wind farm area as a risk window has been constructed as a stochastic model for avian migrants, based on Monte Carlo simulation. The model calculates the probable number of birds collided per time unit. Migration volume, wind farm dimensions, vertical and horizontal distribution of the migratory passage, flight direction and avoidance rates, between other variables, are taken into account in different steps of the model as the input variables. In order to assess the weighted importance of these factors on collision probability predictions, collision probabilities obtained from the set of scenarios resulting from the different combinations of the input variables were modelled by using Generalised Additive Models. The application of this model to a hypothetical project for erecting a wind farm at the Strait of Gibraltar showed that collision probability, and consequently mortality rates, strongly depend on the values of the avoidance rates taken into account, and the distribution of birds into the different altitude layers. These parameters should be considered as priorities to be addressed in post-construction studies. (Author)
14. Binary outcome variables and logistic regression models
Institute of Scientific and Technical Information of China (English)
Xinhua LIU
2011-01-01
Biomedical researchers often study binary variables that indicate whether or not a specific event,such as remission of depression symptoms,occurs during the study period.The indicator variable Y takes two values,usually coded as one if the event (remission) is present and zero if the event is not present(non-remission).Let p be the probability that the event occurs ( Y =1),then 1-p will be the probability that the event does not occur ( Y =0).
15. Modeling the Collision with Friction of Rigid Bodies
Science.gov (United States)
Zabuga, A. G.
2016-09-01
Different models of a perfectly inelastic collision of rigid bodies in plane motion are compared. Formulas for the impact impulses are derived for the Kane-Levinson-Whittaker model based on the kinematic restitution factor, the Routh model based on the kinetic restitution factor, and the Stronge model based on the energy restitution factor. It is shown that these formulas coincide if the collision of rough rigid bodies in plane motion is perfectly inelastic
16. Hans A. Bethe Prize: Cosmic Collisions Online - Compact Binary Mergers, Gravitational Waves and Gamma-Ray Bursts
Science.gov (United States)
Shapiro, Stuart
2017-01-01
Hans A. Bethe elucidated our understanding of the fundamental forces of Nature by exploring and explaining countless phenomena occurring in nuclear laboratories and in stars. With the dawn of gravitational wave astronomy we now can probe compact binary mergers - Nature's cosmic collision experiments - to deepen our understanding, especially where strong-field gravitation is involved. In addition to gravitational waves, some mergers are likely to generate observable electromagnetic and/or neutrino radiation, heralding a new era of multimessenger astronomy. Robust numerical algorithms now allow us to simulate these events in full general relativity on supercomputers. We will describe some recent magnetohydrodynamic simulations that show how binary black hole-neutron star and neutron star-neutron star mergers can launch jets, lending support to the idea that such mergers could be the engines that power short gamma-ray bursts. We will also show how the magnetorotational collapse of very massive stars to spinning black holes immersed in magnetized accretion disks can launch jets as well, reinforcing the belief that such collapsars'' are the progenitors of long gamma-ray bursts. Computer-generated movies highlighting some of these simulations will be shown. We gratefully acknowledge support from NSF Grants 1300903 and 1602536 and NASA Grant NNX13AH44G.
17. Binary fish passage models for uniform and nonuniform flows
Energy Technology Data Exchange (ETDEWEB)
Neary, Vincent S [ORNL
2011-01-01
Binary fish passage models are considered by many fisheries managers to be the best 21 available practice for culvert inventory assessments and for fishway and barrier design. 22 Misunderstandings between different binary passage modeling approaches often arise, 23 however, due to differences in terminology, application and presentation. In this paper 24 one-dimensional binary fish passage models are reviewed and refined to clarify their 25 origins and applications. For uniform flow, a simple exhaustion-threshold (ET) model 26 equation is derived that predicts the flow speed threshold in a fishway or velocity barrier 27 that causes exhaustion at a given maximum distance of ascent. Flow speeds at or above 28 the threshold predict failure to pass (exclusion). Flow speeds below the threshold predict 29 passage. The binary ET model is therefore intuitive and easily applied to predict passage 30 or exclusion. It is also shown to be consistent with the distance-maximizing model. The 31 ET model s limitation to uniform flow is addressed by deriving a passage model that 32 accounts for nonuniform flow conditions more commonly found in the field, including 33 backwater profiles and drawdown curves. Comparison of these models with 34 experimental observations of volitional passage for Gambusia affinis in uniform and 35 nonuniform flows indicates reasonable prediction of binary outcomes (passage or 36 exclusion) if the flow speed is not near the threshold flow velocity. More research is 37 needed on fish behavior, passage strategies under nonuniform flow regimes and 38 stochastic methods that account for individual differences in swimming performance at or 39 near the threshold flow speed. Future experiments should track and measure ground 40 speeds of ascending fish to test nonuniform flow passage strategies and to improve model 41 predictions. Stochastic models, such as Monte-Carlo techniques, that account for 42 different passage performance among individuals and allow
18. VQ-based model for binary error process
Science.gov (United States)
Csóka, Tibor; Polec, Jaroslav; Csóka, Filip; Kotuliaková, Kvetoslava
2017-05-01
A variety of complex techniques, such as forward error correction (FEC), automatic repeat request (ARQ), hybrid ARQ or cross-layer optimization, require in their design and optimization phase a realistic model of binary error process present in a specific digital channel. Past and more recent modeling approaches focus on capturing one or more stochastic characteristics with precision sufficient for the desired model application, thereby applying concepts and methods severely limiting the model applicability (eg in the form of modeled process prerequisite expectations). The proposed novel concept utilizing a Vector Quantization (VQ)-based approach to binary process modeling offers a viable alternative capable of superior modeling of most commonly observed small- and large-scale stochastic characteristics of a binary error process on the digital channel. Precision of the proposed model was verified using multiple statistical distances against the data captured in a wireless sensor network logical channel trace. Furthermore, the Pearson's goodness of fit test of all model variants' output was performed to conclusively demonstrate usability of the model for realistic captured binary error process. Finally, the presented results prove the proposed model applicability and its ability to far surpass the capabilities of the reference Elliot's model.
19. Hydrodynamical Models of Gas Cloud - Galaxy Collisions
Science.gov (United States)
Franklin, M.; Dinge, D.; Jones, T.; Benjamin, B.
1999-05-01
Clouds of neutral hydrogen falling toward the Galactic plane with a speed of about 100 km/s or more are among those considered to be "high velocity clouds" (HVCs). As HVCs are often observed approaching the midplane, the collision of such clouds with the gaseous disk of the Galaxy has been proposed as a precursor event to the phenomena known as "supershells" and as a catalyst to star formation. While many previous analytic calculations have assumed that ram pressure of the resisting medium was negligible, and a ballistic approximation was valid, observations showing a correlation between speed and increased height above the plane, the opposite of what is expected for free fall, suggest otherwise. Benjamin & Danly suggested in 1997 that clouds falling at terminal velocity provide a simple explanation for the observed velocity distribution. In this work, numerical models are used to test the above hypotheses with clouds falling through a more modern model of the interstellar medium than that used in the seminal work by Tenorio-Tagle et al. (TT) in 1987. With the addition of more dense material to the model background, clouds were still able to form supershell-like remnants, though star formation does not appear to be triggered. Further, though agreement was not perfect, the terminal velocity model was found to be a better approximation for these clouds' fall than the ballistic case. Cooling was a physical process included in TT's work which was not included here, but was found to be non-negligible. Simulations which include a cooling algorithm must be done to confirm these results. This work was supported in part by NSF grant AST96-19438.
20. Hydrodynamics of passing-over motion during binary droplet collision in shear flow
Science.gov (United States)
Wang, Cheng-Yao; Zhang, Cheng-Bin; Huang, Xiang-Yong; Liu, Xiang-Dong; Chen, Yong-Ping
2016-10-01
A combined experimental and numerical study is undertaken to investigate the hydrodynamic characteristics of single-phase droplet collision in a shear flow. The passing-over motion of interactive droplets is observed, and the underlying hydrodynamic mechanisms are elucidated by the analysis of the motion trajectory, transient droplet deformation and detailed hydrodynamic information (e.g., pressure and flow fields). The results indicate that the hydrodynamic interaction process under shear could be divided into three stages: approaching, colliding, and separating. With the increasing confinement, the interaction time for the passing-over process is shorter and the droplet processes one higher curvature tip and more stretched profile. Furthermore, the lateral separation Δy/R 1 exhibits larger decrease in the approaching stage and the thickness of the lubrication film is decreased during the interaction. As the initial lateral separation increases, the maximum trajectory shift by the collision interaction is getting smaller. During the collision between two droplets with different sizes, the amplitude of the deformation oscillation of the larger droplet is decreased by reducing the size ratio of the smaller droplet to the bigger one. Project supported by the NSAF (Grants No. U1530260), the National Natural Science Foundation of China (Grant No. 51306158), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130621), and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).
1. A 3D dynamical model of the colliding winds in binary systems
CERN Document Server
Parkin, E R
2008-01-01
We present a 3D dynamical model of the orbital induced curvature of the wind-wind collision region in binary star systems. Momentum balance equations are used to determine the position and shape of the contact discontinuity between the stars, while further downstream the gas is assumed to behave ballistically. An archimedean spiral structure is formed by the motion of the stars, with clear resemblance to high resolution images of the so-called pinwheel nebulae''. A key advantage of this approach over grid or smoothed particle hydrodynamic models is its significantly reduced computational cost, while it also allows the study of the structure obtained in an eccentric orbit. The model is relevant to symbiotic systems and Gamma-ray binaries, as well as systems with O-type and Wolf-Rayet stars. As an example application, we simulate the X-ray emission from hypothetical O+O and WR+O star binaries, and describe a method of ray tracing through the 3D spiral structure to account for absorption by the circumstellar m...
2. Rotation periods of binary asteroids with large separations - Confronting the Escaping Ejecta Binaries model with observations
Science.gov (United States)
Polishook, D.; Brosch, N.; Prialnik, D.
2011-03-01
Durda et al. (Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M. [2004]. Icarus 170, 243-257), using numerical models, suggested that binary asteroids with large separation, called Escaping Ejecta Binaries (EEBs), can be created by fragments ejected from a disruptive impact event. It is thought that six binary asteroids recently discovered might be EEBs because of the high separation between their components (∼100 > a/Rp > ∼20). However, the rotation periods of four out of the six objects measured by our group and others and presented here show that these suspected EEBs have fast rotation rates of 2.5-4 h. Because of the small size of the components of these binary asteroids, linked with this fast spinning, we conclude that the rotational-fission mechanism, which is a result of the thermal YORP effect, is the most likely formation scenario. Moreover, scaling the YORP effect for these objects shows that its timescale is shorter than the estimated ages of the three relevant Hirayama families hosting these binary asteroids. Therefore, only the largest (D ∼ 19 km) suspected asteroid, (317) Roxane, could be, in fact, the only known EEB. In addition, our results confirm the triple nature of (3749) Balam by measuring mutual events on its lightcurve that match the orbital period of a nearby satellite in addition to its distant companion. Measurements of (1509) Esclangona at different apparitions show a unique shape of the lightcurve that might be explained by color variations.
3. Coulomb Collision for Plasma Simulations: Modelling and Numerical Methods
Science.gov (United States)
Geiser, Juergen
2016-09-01
We are motivated to model weakly ionized Plasma applications. The modeling problem is based on an incorporated explicit velocity-dependent small-angle Coulomb collision terms into a Fokker-Planck equation. Such a collision is done with so called test and field particles, which are scattered stochastically based on a Langevin equation. Based on such different model approaches, means the transport part is done with kinetic equations, while the collision part is done via the Langevin equations, we present a splitting of these models. Such a splitting allow us to combine different modeling parts. For the transport part, we can apply particle models and solve them with particle methods, e.g., PIC, while for the collision part, we can apply the explicit Coulomb collision model, e.g., with fast stochastic differential equation solvers. Additional, we also apply multiscale approaches for the different parts of the transport part, e.g., different time-scales of an explicit electric field, and model-order reduction approaches. We present first numerical results for particle simulations with the deterministic-stochastic splitting schemes. Such ideas can be applied to sputtering problems or plasma applications with dominant Coulomb collisions.
4. Modelling of a collision between two smartphones
Science.gov (United States)
de Jesus, V. L. B.; Sasaki, D. G. G.
2016-09-01
In the predominant approach in physics textbooks, the collision between particles is treated as a black box, where no physical quantity can be measured. This approach becomes even more evident in experimental classes where collisions are the simplest and most common way of applying the theorem of conservation of linear momentum in the asymptotic behavior. In this paper we develop and analyse an experiment on collisions using only two smartphones. The experimental setup is amazingly simple; the two devices are aligned on a horizontal table of lacquered wood, in order to slide more easily. At the edge of one of them a piece of common sponge is glued using double-sided tape. By using a free smartphone application, the values generated by the accelerometer of the two devices in full motion are measured and tabulated. Through numerical iteration, the speed graphs of the smartphones before, during, and after the collision are obtained. The main conclusions were: (i) the demonstration of the feasibility of using smartphones as an alternative to air tracks and electronic sensors employed in a teaching lab, (ii) the possibility of investigating the collision itself, its characteristics and effects; this is the great advantage of the use of smartphones over traditional experiments, (iii) the compatibility of the results with the impulse-momentum theorem, within the margin of uncertainty.
5. Currency Arbitrage Detection Using a Binary Integer Programming Model
Science.gov (United States)
Soon, Wanmei; Ye, Heng-Qing
2011-01-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…
6. Model of Centauro and strangelet production in heavy ion collisions
CERN Document Server
Angelis, Aris L S; Kharlov, Yu V; Korotkikh, V L; Mavromanolakis, G; Panagiotou, A D; Sadovsky, S A; Kharlov, Yu.V.
2004-01-01
We discuss the phenomenological model of Centauro event production in relativistic nucleus-nucleus collisions. This model makes quantitative predictions for kinematic observables, baryon number and mass of the Centauro fireball and its decay products. Centauros decay mainly to nucleons, strange hyperons and possibly strangelets. Simulations of Centauro events for the CASTOR detector in Pb-Pb collisions at LHC energies are performed. The signatures of these events are discussed in detail.
7. Structure and selection in an autocatalytic binary polymer model
DEFF Research Database (Denmark)
Tanaka, Shinpei; Fellermann, Harold; Rasmussen, Steen
2014-01-01
An autocatalytic binary polymer system is studied as an abstract model for a chemical reaction network capable to evolve. Due to autocatalysis, long polymers appear spontaneously and their concentration is shown to be maintained at the same level as that of monomers. When the reaction starts from....... Stability, fluctuations, and dynamic selection mechanisms are investigated for the involved self-organizing processes. Copyright (C) EPLA, 2014......An autocatalytic binary polymer system is studied as an abstract model for a chemical reaction network capable to evolve. Due to autocatalysis, long polymers appear spontaneously and their concentration is shown to be maintained at the same level as that of monomers. When the reaction starts from...
8. A complete waveform model for compact binaries on eccentric orbits
Science.gov (United States)
Huerta, Eliu; Agarwal, Bhanu; George, Daniel; Kumar, Prayush
2016-03-01
The detection of compact binaries with significant eccentricity in the sensitivity band of gravitational wave detectors will provide critical insights on the dynamics and formation channels of these events. In order to search for these systems and place constraints on their rates, we present an inspiral-merger-ringdown time domain waveform model that describes the GW emission from compact binaries on orbits with low to moderate values of eccentricity. We use this model to explore the detectability of these events in the context of advanced LIGO.
9. Accuracy of Binary Black Hole Waveform Models for Advanced LIGO
Science.gov (United States)
Kumar, Prayush; Fong, Heather; Barkett, Kevin; Bhagwat, Swetha; Afshari, Nousha; Chu, Tony; Brown, Duncan; Lovelace, Geoffrey; Pfeiffer, Harald; Scheel, Mark; Szilagyi, Bela; Simulating Extreme Spacetimes (SXS) Team
2016-03-01
Coalescing binaries of compact objects, such as black holes and neutron stars, are the primary targets for gravitational-wave (GW) detection with Advanced LIGO. Accurate modeling of the emitted GWs is required to extract information about the binary source. The most accurate solution to the general relativistic two-body problem is available in numerical relativity (NR), which is however limited in application due to computational cost. Current searches use semi-analytic models that are based in post-Newtonian (PN) theory and calibrated to NR. In this talk, I will present comparisons between contemporary models and high-accuracy numerical simulations performed using the Spectral Einstein Code (SpEC), focusing at the questions: (i) How well do models capture binary's late-inspiral where they lack a-priori accurate information from PN or NR, and (ii) How accurately do they model binaries with parameters outside their range of calibration. These results guide the choice of templates for future GW searches, and motivate future modeling efforts.
10. Avian collision risk models for wind energy impact assessments
Energy Technology Data Exchange (ETDEWEB)
Masden, E.A., E-mail: [email protected] [Environmental Research Institute, North Highland College-UHI, University of the Highlands and Islands, Ormlie Road, Thurso, Caithness KW14 7EE (United Kingdom); Cook, A.S.C.P. [British Trust for Ornithology, The Nunnery, Thetford IP24 2PU (United Kingdom)
2016-01-15
With the increasing global development of wind energy, collision risk models (CRMs) are routinely used to assess the potential impacts of wind turbines on birds. We reviewed and compared the avian collision risk models currently available in the scientific literature, exploring aspects such as the calculation of a collision probability, inclusion of stationary components e.g. the tower, angle of approach and uncertainty. 10 models were cited in the literature and of these, all included a probability of collision of a single bird colliding with a wind turbine during passage through the rotor swept area, and the majority included a measure of the number of birds at risk. 7 out of the 10 models calculated the probability of birds colliding, whilst the remainder used a constant. We identified four approaches to calculate the probability of collision and these were used by others. 6 of the 10 models were deterministic and included the most frequently used models in the UK, with only 4 including variation or uncertainty in some way, the most recent using Bayesian methods. Despite their appeal, CRMs have their limitations and can be ‘data hungry’ as well as assuming much about bird movement and behaviour. As data become available, these assumptions should be tested to ensure that CRMs are functioning to adequately answer the questions posed by the wind energy sector. - Highlights: • We highlighted ten models available to assess avian collision risk. • Only 4 of the models included variability or uncertainty. • Collision risk models have limitations and can be ‘data hungry’. • It is vital that the most appropriate model is used for a given task.
11. Collision-free speed model for pedestrian dynamics
CERN Document Server
Tordeux, Antoine; Seyfried, Armin
2015-01-01
We propose in this paper a minimal speed-based pedestrian model for which particle dynamics are intrinsically collision-free. The speed model is an optimal velocity function depending on the agent length (i.e.\\ particle diameter), maximum speed and time gap parameters. The direction model is a weighted sum of exponential repulsion from the neighbors, calibrated by the repulsion rate and distance. The model's main features like the reproduction of empirical phenomena are analysed by simulation. We point out that phenomena of self-organisation observable in force-based models and field studies can be reproduced by the collision-free model with low computational effort.
12. Two models with rescattering for high energy heavy ion collisions
Science.gov (United States)
Bøggild, H.; Hansen, Ole; Humanic, T. J.
2006-12-01
The effects of hadronic rescattering in high energy relativistic Au+Au collisions are studied using two very different models to describe the early stages of the collision. One model is based on a hadronic thermal picture and the other on a superposition of parton-parton collisions. Operationally, the output hadrons from each of these models are used as input to a hadronic rescattering calculation. The results of the rescattering calculations from each model are then compared with rapidity and transverse momentum distributions from the BNL Relativistic Heavy Ion Collider BRAHMS experiment. In spite of the different points of view of the two models of the initial stage, after rescattering, the observed differences between the models are mostly “washed out” and both models give observables that agree roughly with each other and with experimental data.
13. Phemenological Modeling of Eclipsing Binary Stars
CERN Document Server
Andronov, Ivan L; Chinarova, Lidia L
2016-01-01
We review the method NAV (New Algol Variable) first introduced in 2012Ap.....55..536A, which uses the locally-dependent shapes of eclipses in an addition to the trigonometric polynomial of the second order (which typically describes the "out-of-eclipse" part of the light curve with effects of reflection, ellipticity and O'Connell). Eclipsing binary stars are believed to show distinct eclipses only if belonging to the EA type. With a decreasing eclipse width, the statistically optimal value of the trigonometric polynomial s (2003ASPC..292..391A) drastically increases from ~2 for elliptic (EL) variables without eclipses, ~6-8 for EW and up to ~30-50 for some EA with narrow eclipses. In this case of large number of parameters, the smoothing curve becomes very noisy and apparent waves (the Gibbs phenomenon) may be seen. The NAV set of the parameters may be used for classification in the GCVS, VSX and similar catalogs. The maximal number of parameters is m=12, which corresponds to s=5, if correcting both the perio...
14. Guidance on the Choice of Threshold for Binary Forecast Modeling
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper proposes useful guidance on the choice of threshold for binary forecasts. In weather forecast systems, the probabilistic forecast cannot be used directly when estimated too smoothly. In this case, the binary forecast, whether a meteorological event will occur or not, is preferable to the probabilistic forecast.A threshold is needed to generate a binary forecast, and the guidance in this paper encompasses the use of skill scores for the choice of threshold according to the forecast pattern. The forecast pattern consists of distribution modes of estimated probabilities, occurrence rates of observations, and variation modes.This study is performed via Monte-Carlo simulation, with 48 forecast patterns considered. Estimated probabilities are generated by random variate sampling from five distributions separately. Varying the threshold from 0 to 1, binary forecasts are generated by threshold. For the assessment of binary forecast models, a 2×2 contingency table is used and four skill scores (Heidke skill score, hit rate, true skill statistic,and threat score) are compared for each forecast pattern. As a result, guidance on the choice of skill score to find the optimal threshold is proposed.
CERN Document Server
2014-01-01
We introduce the Weibull distribution as a simple parametrization of charged particle multiplicities in hadron-hadron collisions at all available energies, ranging from ISR energies to the most recent LHC energies. In statistics, the Weibull distribution has wide applicability in natural processes involving fragmentation processes. This gives a natural connection to the available state-of-the-art models for multi-particle production in hadron hadron collisions involving QCD parton fragmentation and hadronization.
16. Three-dimensional modeling of radiative disks in binaries
CERN Document Server
Picogna, Giovanni
2013-01-01
Circumstellar disks in binaries are perturbed by the companion gravity causing significant alterations of the disk morphology. Spiral waves due to the companion tidal force also develop in the vertical direction and affect the disk temperature profile. These effects may significantly influence the process of planet formation. We perform 3D numerical simulations of disks in binaries with different initial dynamical configurations and physical parameters. Our goal is to investigate their evolution and their propensity to grow planets. We use an improved version of the SPH code VINE modified to better account for momentum and energy conservation. The energy equation includes a flux--limited radiative transfer algorithm and the disk cooling is obtained via "boundary particles". We model a system made of star/disk + star/disk where the secondary star (and relative disk) is less massive than the primary. The numerical simulations performed for different values of binary separation and disk density show that the dis...
17. Trimmed Likelihood-based Estimation in Binary Regression Models
NARCIS (Netherlands)
Cizek, P.
2005-01-01
The binary-choice regression models such as probit and logit are typically estimated by the maximum likelihood method.To improve its robustness, various M-estimation based procedures were proposed, which however require bias corrections to achieve consistency and their resistance to outliers is rela
18. Physics Of Eclipsing Binaries. II. Toward the Increased Model Fidelity
Science.gov (United States)
Prša, A.; Conroy, K. E.; Horvat, M.; Pablo, H.; Kochoska, A.; Bloemen, S.; Giammarco, J.; Hambleton, K. M.; Degroote, P.
2016-12-01
The precision of photometric and spectroscopic observations has been systematically improved in the last decade, mostly thanks to space-borne photometric missions and ground-based spectrographs dedicated to finding exoplanets. The field of eclipsing binary stars strongly benefited from this development. Eclipsing binaries serve as critical tools for determining fundamental stellar properties (masses, radii, temperatures, and luminosities), yet the models are not capable of reproducing observed data well, either because of the missing physics or because of insufficient precision. This led to a predicament where radiative and dynamical effects, insofar buried in noise, started showing up routinely in the data, but were not accounted for in the models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an open source modeling code for computing theoretical light and radial velocity curves that addresses both problems by incorporating missing physics and by increasing the computational fidelity. In particular, we discuss triangulation as a superior surface discretization algorithm, meshing of rotating single stars, light travel time effects, advanced phase computation, volume conservation in eccentric orbits, and improved computation of local intensity across the stellar surfaces that includes the photon-weighted mode, the enhanced limb darkening treatment, the better reflection treatment, and Doppler boosting. Here we present the concepts on which PHOEBE is built and proofs of concept that demonstrate the increased model fidelity.
19. Vaporization wave model for ion-ion central collisions
Energy Technology Data Exchange (ETDEWEB)
Baldo, M.; Giansiracusa, G.; Piccitto, G. (Catania Univ. (Italy). Ist. di Fisica; Istituto Nazionale di Fisica Nucleare, Catania (Italy))
1983-09-24
We propose a simple model for central or nearly central ion-ion collisions at intermediate energies. It is based on the ''vaporization wave model'' developed by Bennett for macroscopic objects. The model offers a simple explanation of the observed deuteron/proton abundancy ratio as a function of the beam energy.
20. Vaporization wave model for ion-ion central collisions
Energy Technology Data Exchange (ETDEWEB)
Baldo, M.; Giansiracusa, G.; Piccitto, G. (Catania Univ. (Italy). Ist. di Fisica)
1983-09-24
A simple model for central or nearly central ion-ion collisions at intermediate energies is proposed. It is based on the ''vaporization wave model'' developed by Bennet for macroscopic objects. The model offers a simple explanation of the observed deuteron/proton abundancy ratio as a function of the beam energy.
1. Latent Classification Models for Binary Data
DEFF Research Database (Denmark)
Langseth, Helge; Nielsen, Thomas Dyhre
2009-01-01
One of the simplest, and yet most consistently well-performing set of classifiers is the naive Bayes models (a special class of Bayesian network models). However, these models rely on the (naive) assumption that all the attributes used to describe an instance are conditionally independent given...
2. Discovering binary codes for documents by learning deep generative models.
Science.gov (United States)
Hinton, Geoffrey; Salakhutdinov, Ruslan
2011-01-01
We describe a deep generative model in which the lowest layer represents the word-count vector of a document and the top layer represents a learned binary code for that document. The top two layers of the generative model form an undirected associative memory and the remaining layers form a belief net with directed, top-down connections. We present efficient learning and inference procedures for this type of generative model and show that it allows more accurate and much faster retrieval than latent semantic analysis. By using our method as a filter for a much slower method called TF-IDF we achieve higher accuracy than TF-IDF alone and save several orders of magnitude in retrieval time. By using short binary codes as addresses, we can perform retrieval on very large document sets in a time that is independent of the size of the document set using only one word of memory to describe each document.
3. A complete waveform model for compact binaries on eccentric orbits
CERN Document Server
Huerta, E A; Agarwal, Bhanu; George, Daniel; Schive, Hsi-Yu; Pfeiffer, Harald P; Chu, Tony; Boyle, Michael; Hemberger, Daniel A; Kidder, Lawrence E; Scheel, Mark A; Szilagyi, Bela
2016-01-01
We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. This framework reduces to the post-Newtonian approximant $\\texttt{TaylorT4}$ at third post-Newtonian order in the zero eccentricity limit. To improve phase accuracy, we also incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a c...
4. Kuiper Binary Object Formation
CERN Document Server
Nazzario, R C; Covington, C; Kagan, D; Hyde, T W
2005-01-01
It has been observed that binary Kuiper Belt Objects (KBOs) exist contrary to theoretical expectations. Their creation presents problems to most current models. However, the inclusion of a third body (for example, one of the outer planets) may provide the conditions necessary for the formation of these objects. The presence of a third massive body not only helps to clear the primordial Kuiper Belt but can also result in long lived binary Kuiper belt objects. The gravitational interaction between the KBOs and the third body causes one of four effects; scattering into the Oort cloud, collisions with the growing protoplanets, formation of binary pairs, or creation of a single Kuiper belt object. Additionally, the initial location of the progenitors of the Kuiper belt objects also has a significant effect on binary formation.
5. Preon Model and a Possible New Physics in ep Collisions
Science.gov (United States)
Senju, H.
1993-03-01
The properties of predicted new particles in a preon-subpreon model are discussed. The model contains several new particles which could be detected in the near future. It is shown that ep colliders are especially adequate to study properties of a few of them. Production cross sections and signatures in ep collisions are discussed.
6. Preon model and a possible new physics in ep collisions
Energy Technology Data Exchange (ETDEWEB)
Senju, Hirofumi (Nagoya Municipal Women' s Coll. (Japan))
1993-03-01
The properties of predicted new particles in a preon-subpreon model are discussed. The model contains several new particles which could be detected in the near future. It is shown that ep colliders are especially adequate to study properties of a few of them. Production cross sections and signatures in ep collisions are discussed. (author).
7. Comprehensive Gravity and Dynamics Model Determination of Binary Asteroid Systems
Science.gov (United States)
Fahnestock, Eugene G.
2009-09-01
I present the development of additional tools within the framework of JPL's in-house Mirage / Orbit Determination Program (ODP) software to allow the determination of a comprehensive gravity and dynamics model for any binary asteroid system potentially visited by a spacecraft rendezvous mission. This involves a concurrent global solution for the gravity fields of both components, sufficient parametric description of their fully-coupled translational and rotational dynamics, the spacecraft state, and all other relevant force model parameters. This estimation process primarily uses spacecraft radio tracking data (range and Doppler measurements), supplemented by in-situ imaging observations data types. A solution for the gravity field (gravity analysis) and a simultaneous solution for the spacecraft motion and other system properties has been performed before using the ODP for solitary irregular small solar system bodies (e.g. Eros, visited by the NEAR mission), but never for any closely gravitationally bound pair of irregular small solar system bodies. I am expanding NASA's tool set to allow the latter, in preparation for potential future spacecraft rendezvous missions. This is nontrivial, because of the need to incorporate propagation of the binary system's fully-coupled rigid-body dynamical model either along with the spacecraft state within Mirage/ODP or "offline", followed by interpolating an appropriate "binary dynamics ephemeris” representation. Further, this model optionally incorporates formulations for body gravity fields not previously used in this context, and it can be computationally very expensive. However, successfully performing this model determination at a binary asteroid yields valuable science results concerning internal mass distributions and structures of the components and insight into the system's formation and evolution. In this poster I present my current progress in the development of this capability and results for the quality of science
8. Examining of the Collision Breakup Model between Geostationary Orbit Objects
Science.gov (United States)
This paper will examine the applicability of the hypervelocity collision model included in the NASA standard breakup model 2000 revision to low-velocity collisions possible in space, especially in the geosynchronous regime. The analytic method used in the standard breakup model will be applied to experimental data accumulated through low-velocity impact experiments performed at Kyushu Institute of Technology at a velocity about 300m/s and 800m/s. The projectiles and target specimens used were aluminum solid balls and aluminum honeycomb sandwich panels with face sheets of carbon fiber reinforced plastic, respectively. Then, we have found that a kind of lower boundary exists on fragment area-to-mass distribution at a smaller characteristic length range. This paper will describe the theoretical derivation of lower boundary and propose another modification on fragment area-to-mass distribution and it will conclude that the hypervelocity collision model in the standard breakup model can be applied to low-velocity collisions possible with some modifications.
9. Marginal and Random Intercepts Models for Longitudinal Binary Data with Examples from Criminology
Science.gov (United States)
Long, Jeffrey D.; Loeber, Rolf; Farrington, David P.
2009-01-01
Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides…
10. Marginal and Random Intercepts Models for Longitudinal Binary Data with Examples from Criminology
Science.gov (United States)
Long, Jeffrey D.; Loeber, Rolf; Farrington, David P.
2009-01-01
Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides…
Science.gov (United States)
Dash, Sadhana; Nandi, Basanta K.; Sett, Priyanka
2016-06-01
We introduce the use of the Weibull distribution as a simple parametrization of charged particle multiplicities in hadron-hadron collisions at all available energies, ranging from ISR energies to the most recent LHC energies. In statistics, the Weibull distribution has wide applicability in natural processes that involve fragmentation processes. This provides a natural connection to the available state-of-the-art models for multiparticle production in hadron-hadron collisions, which involve QCD parton fragmentation and hadronization. The Weibull distribution describes the multiplicity data at the most recent LHC energies better than the single negative binomial distribution.
12. Modeling binary correlated responses using SAS, SPSS and R
CERN Document Server
Wilson, Jeffrey R
2015-01-01
Statistical tools to analyze correlated binary data are spread out in the existing literature. This book makes these tools accessible to practitioners in a single volume. Chapters cover recently developed statistical tools and statistical packages that are tailored to analyzing correlated binary data. The authors showcase both traditional and new methods for application to health-related research. Data and computer programs will be publicly available in order for readers to replicate model development, but learning a new statistical language is not necessary with this book. The inclusion of code for R, SAS, and SPSS allows for easy implementation by readers. For readers interested in learning more about the languages, though, there are short tutorials in the appendix. Accompanying data sets are available for download through the book s website. Data analysis presented in each chapter will provide step-by-step instructions so these new methods can be readily applied to projects. Researchers and graduate stu...
13. Binary galaxy models with mond and Mannheim-Kazanas gravity
CERN Document Server
Soares, D S L
1995-01-01
Binary galaxies are modeled as point-masses obeying non-Newtonian gravity laws, namely, those prescribed by MOND and Mannheim-Kazanas theory of gravity. Random samples of such systems are generated by means of Monte Carlo simulations of binary orbits. Model pairs have equal mass galaxies, for which three cases are considered, with respect to individual galaxy masses, namely, galaxies with (a) 1 x 10^10 M_o, (b) 1 x 10^11 M_o and (c) 1 x 10^12 M_o. General features of synthetic samples are derived from a comparison with observed data of galaxy pairs. The main conclusions, provided that wide pairs be removed from the simulated samples by selection effects, are as follows. Case (a): MOND pairs on circular orbits may represent solutions to the binary dynamics. The galaxy mass-to-light ratio (M/L) implied is ~ 5 solar units, while medium and high eccentricity orbits require unrealistic small M/L, even smaller than 1 solar unit. For pairs obeying Mannheim-Kazanas gravity, even circular orbits give only marginal fit...
14. Models for Sixty Double-Lined Binaries containing Giants
CERN Document Server
Eggleton, Peter P
2016-01-01
The observed masses, radii and temperatures of 60 medium- to long-period binaries, most of which contain a cool, evolved star and a hotter less-evolved one, are compared with theoretical models which include (a) core convective overshooting, (b)mass loss, possibly driven by dynamo action as in RS CVn binaries, and (c) tidal friction, including its effect on orbital period through magnetic braking. A reasonable fit is found in about 42 cases, but in 11 other cases the primaries appear to have lost either more mass or less mass than the models predict, and in 4 others the orbit is predicted to be either more or less circular than observed. Of the remaining 3 systems, two ($\\gamma$ Per and HR 8242) have a markedly over-evolved' secondary, our explanation being that the primary component is the merged remnant of a former short-period sub-binary in a former triple system. The last system (V695 Cyg) defies any agreement at present. Mention is also made of three other systems (V643 Ori, OW Gem and V453 Cep), which ...
15. Behaviour of ion velocity distributions for a simple collision model
Science.gov (United States)
St-Maurice, J.-P.; Schunk, R. W.
1974-01-01
Calculation of the ion velocity distributions for a weakly ionized plasma subjected to crossed electric and magnetic fields. An exact solution to Boltzmann's equation has been obtained by replacing the Boltzmann collision integral with a simple relaxation model. At altitudes above about 150 km, where the ion collision frequency is much less than the ion cyclotron frequency, the ion distribution takes the shape of a torus in velocity space for electric fields greater than 40 mV/m. This shape persists for one to two hours after application of the electric field. At altitudes where the ion collision and cyclotron frequencies are approximately equal (about 120 km), the ion velocity distribution is shaped like a bean for large electric field strengths. This bean-shaped distribution persists throughout the lifetime of ionospheric electric fields. These highly non-Maxwellian ion velocity distributions may have an appreciable affect on the interpretation of ion temperature measurements.
16. Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models
Science.gov (United States)
Almog, Assaf; Garlaschelli, Diego
2014-09-01
The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of multiple time series of activity of the constituent units, such as stocks or neurons, respectively. While the main focus of time series analysis is on the magnitude of temporal increments, a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. In this paper we provide further evidence of this by showing strong nonlinear relations between binary and non-binary properties of financial time series. These relations are a novel quantification of the fact that extreme price increments occur more often when most stocks move in the same direction. We then introduce an information-theoretic approach to the analysis of the binary signature of single and multiple time series. Through the definition of maximum-entropy ensembles of binary matrices and their mapping to spin models in statistical physics, we quantify the information encoded into the simplest binary properties of real time series and identify the most informative property given a set of measurements. Our formalism is able to accurately replicate, and mathematically characterize, the observed binary/non-binary relations. We also obtain a phase diagram allowing us to identify, based only on the instantaneous aggregate return of a set of multiple time series, a regime where the so-called ‘market mode’ has an optimal interpretation in terms of collective (endogenous) effects, a regime where it is parsimoniously explained by pure noise, and a regime where it can be regarded as a combination of endogenous and exogenous factors. Our approach allows us to connect spin models, simple stochastic processes, and ensembles of time series inferred from partial information.
17. Gaussian Process Model for Collision Dynamics of Complex Molecules.
Science.gov (United States)
Cui, Jie; Krems, Roman V
2015-08-14
We show that a Gaussian process model can be combined with a small number (of order 100) of scattering calculations to provide a multidimensional dependence of scattering observables on the experimentally controllable parameters (such as the collision energy or temperature) as well as the potential energy surface (PES) parameters. For the case of Ar-C_{6}H_{6} collisions, we show that 200 classical trajectory calculations are sufficient to provide a ten-dimensional hypersurface, giving the dependence of the collision lifetimes on the collision energy, internal temperature, and eight PES parameters. This can be used for solving the inverse scattering problem, for the efficient calculation of thermally averaged observables, for reducing the error of the molecular dynamics calculations by averaging over the PES variations, and for the analysis of the sensitivity of the observables to individual parameters determining the PES. Trained by a combination of classical and quantum calculations, the model provides an accurate description of the quantum scattering cross sections, even near scattering resonances.
18. Wounded nucleon model with realistic nucleon-nucleon collision profile and observables in relativistic heavy-ion collisions
CERN Document Server
Rybczyński, Maciej
2011-01-01
We investigate the influence of the nucleon-nucleon collision profile (probability of interaction as a function of the nucleon-nucleon impact parameter) in the wounded nucleon model and its extensions on several observables measured in relativistic heavy-ion collisions. We find that the participant eccentricity coefficient, $\\epsilon^\\ast$, as well as the higher harmonic coefficients, $\\epsilon_n^\\ast$, are reduced by 10-20% for mid-peripheral collisions when the realistic (Gaussian) profile is used, as compared to the case with the commonly-used hard-sphere profile. Similarly, the multiplicity fluctuations, treated as the function of the number of wounded nucleons in one of the colliding nuclei, are reduced by 10-20%. This demonstrates that the Glauber Monte Carlo codes should necessarily use the realistic nucleon-nucleon collision profile in precision studies of these observables. The Gaussian collision profile is built-in in {\\tt GLISSANDO}.
19. Optimum Binary Search Trees on the Hierarchical Memory Model
CERN Document Server
2008-01-01
The Hierarchical Memory Model (HMM) of computation is similar to the standard Random Access Machine (RAM) model except that the HMM has a non-uniform memory organized in a hierarchy of levels numbered 1 through h. The cost of accessing a memory location increases with the level number, and accesses to memory locations belonging to the same level cost the same. Formally, the cost of a single access to the memory location at address a is given by m(a), where m: N -> N is the memory cost function, and the h distinct values of m model the different levels of the memory hierarchy. We study the problem of constructing and storing a binary search tree (BST) of minimum cost, over a set of keys, with probabilities for successful and unsuccessful searches, on the HMM with an arbitrary number of memory levels, and for the special case h=2. While the problem of constructing optimum binary search trees has been well studied for the standard RAM model, the additional parameter m for the HMM increases the combinatorial comp...
20. Thin shell morphology in the circumstellar medium of massive binaries
NARCIS (Netherlands)
van Marle, A. -J; Keppens, R.; Meliani, Z.
2011-01-01
Context. In massive binaries, the powerful stellar winds of the two stars collide, leading to the formation of shock-dominated environments that can be modeled only in 3D. Aims. We investigate the morphology of the collision-front shell between the stellar winds of binary components in two long-peri
1. Structural classification and a binary structure model for superconductors
Institute of Scientific and Technical Information of China (English)
Dong Cheng
2006-01-01
Based on structural and bonding features, a new classification scheme of superconductors is proposed to classify conductors can be partitioned into two parts, a superconducting active component and a supplementary component.Partially metallic covalent bonding is found to be a common feature in all superconducting active components, and the electron states of the atoms in the active components usually make a dominant contribution to the energy band near the Fermi surface. Possible directions to explore new superconductors are discussed based on the structural classification and the binary structure model.
2. Critical mingling and universal correlations in model binary active liquids
Science.gov (United States)
Bain, Nicolas; Bartolo, Denis
2017-06-01
Ensembles of driven or motile bodies moving along opposite directions are generically reported to self-organize into strongly anisotropic lanes. Here, building on a minimal model of self-propelled bodies targeting opposite directions, we first evidence a critical phase transition between a mingled state and a phase-separated lane state specific to active particles. We then demonstrate that the mingled state displays algebraic structural correlations also found in driven binary mixtures. Finally, constructing a hydrodynamic theory, we single out the physical mechanisms responsible for these universal long-range correlations typical of ensembles of oppositely moving bodies.
3. Modeling adsorption of binary and ternary mixtures on microporous media
DEFF Research Database (Denmark)
Monsalvo, Matias Alfonso; Shapiro, Alexander
2007-01-01
The goal of this work is to analyze the adsorption of binary and ternary mixtures on the basis of the multicomponent potential theory of adsorption (MPTA). In the MPTA, the adsorbate is considered as a segregated mixture in the external potential field emitted by the solid adsorbent. This makes...... it possible using the same equation of state to describe the thermodynamic properties of the segregated and the bulk phases. For comparison, we also used the ideal adsorbed solution theory (IAST) to describe adsorption equilibria. The main advantage of these two models is their capabilities to predict...
4. ALICE measurements in p–Pb collisions: Charged particle multiplicity, centrality determination and implications for binary scaling
Energy Technology Data Exchange (ETDEWEB)
Toia, Alberica, E-mail: [email protected] [Istituto Nazionale di Fisica Nucleare, Padova (Italy); Goethe University Frankfurt (Germany)
2014-06-15
Measurements of particle production in proton–nucleus collisions provide a reference to disentangle final state effects, i.e. signatures of the formation of a deconfined hot medium, from initial state effects, already present in cold nuclear matter. Since many initial state effects are expected to vary as function of the number of collisions suffered by the incoming proton, it is crucial to estimate the centrality of the collision. In p-Pb collisions categorization of events into different centrality classes using a particle multiplicity distribution is complicated by the low particle multiplicities and the large multiplicity fluctuations. We present ALICE measurements of particle production in p-Pb collisions at √(s{sub NN})=5.02 TeV, including the pseudo-rapidity and transverse momentum dependence, and we discuss the event classification in centrality classes and its implications for the measurements of nuclear modification factors.
5. ALICE Measurements in p-Pb Collisions: Charged Particle Multiplicity, Centrality Determination and implications for Binary Scaling
CERN Document Server
Toia, Alberica
2014-01-01
Measurements of particle production in proton-nucleus collisions provide a reference to disentangle final state effects, i.e. signatures of the formation of a deconfined hot medium, from initial state effects, already present in cold nuclear matter. Since many initial state effects are expected to vary as a function of the number of collisions suffered by the incoming proton, it is crucial to estimate the centrality of the collision. In p-Pb collisions categorization of events into different centrality classes using a particle multiplicity distribution is complicated by the low particle multiplicities and the large multiplicity fluctuations. We present ALICE measurements of particle production in p-Pb collisions at sqrt(sNN) = 5.02$TeV, including the pseudo-rapidity and transverse momentum dependence, we discuss the event classification in centrality classes and its implications for the measurements of nuclear modification factors. 6. Models of Vortices and Spirals in White Dwarf's Accretion Binaries Science.gov (United States) Boneva, Daniela 2010-11-01 The main aim in the current survey is to suggest models of the development of structures, such as vortices and spirals, in accretion white dwarf's binaries. On the base of hydrodynamical analytical considerations it is applied numerical methods and simulations. It is suggested in the theoretical model the perturbation's parameters of the accretion flow, caused by the influences of the tidal wave over the flux of accretion matter around the secondary star. To examine such disturbed flow, the numerical code has involved in the calculations. The results reveal us an appearing of structure with spiral shape due to the tidal interaction in the close binaries. Our further simulations give the solution, which expresses the formation of vortical configurations in the accretion disc's zone. The evolution of vortices in areas of the flow's interaction is explored using single vortex and composite vortex models. Gas in the disc matter is considered to be compressible and non-ideal. The longevity of all these structures is different and each depends of time period of the rotation, density and velocity of the accretion matter. 7. Modified binary encounter Bethe model for electron-impact ionization CERN Document Server Guerra, M; Indelicato, P; Santos, J P 2013-01-01 Theoretical expressions for ionization cross sections by electron impact based on the binary encounter Bethe (BEB) model, valid from ionization threshold up to relativistic energies, are proposed. The new modified BEB (MBEB) and its relativistic counterpart (MRBEB) expressions are simpler than the BEB (nonrelativistic and relativistic) expressions because they require only one atomic parameter, namely the binding energy of the electrons to be ionized, and use only one scaling term for the ionization of all sub-shells. The new models are used to calculate the K-, L- and M-shell ionization cross sections by electron impact for several atoms with Z from 6 to 83. Comparisons with all, to the best of our knowledge, available experimental data show that this model is as good or better than other models, with less complexity. 8. A new collision avoidance model for pedestrian dynamics Science.gov (United States) Wang, Qian-Ling; Chen, Yao; Dong, Hai-Rong; Zhou, Min; Ning, Bin 2015-03-01 The pedestrians can only avoid collisions passively under the action of forces during simulations using the social force model, which may lead to unnatural behaviors. This paper proposes an optimization-based model for the avoidance of collisions, where the social repulsive force is removed in favor of a search for the quickest path to destination in the pedestrian’s vision field. In this way, the behaviors of pedestrians are governed by changing their desired walking direction and desired speed. By combining the critical factors of pedestrian movement, such as positions of the exit and obstacles and velocities of the neighbors, the choice of desired velocity has been rendered to a discrete optimization problem. Therefore, it is the self-driven force that leads pedestrians to a free path rather than the repulsive force, which means the pedestrians can actively avoid collisions. The new model is verified by comparing with the fundamental diagram and actual data. The simulation results of individual avoidance trajectories and crowd avoidance behaviors demonstrate the reasonability of the proposed model. Project supported by the National Natural Science Foundation of China (Grant Nos. 61233001 and 61322307) and the Fundamental Research Funds for Central Universities of China (Grant No. 2013JBZ007). 9. 3D Hydrodynamic & Radiative Transfer Models of X-ray Emission from Colliding Wind Binaries CERN Document Server Russell, Christopher M P; Owocki, Stanley P; Corcoran, Michael F; Hamaguchi, Kenji; Sugawara, Yasuharu 2014-01-01 Colliding wind binaries (CWBs) are unique laboratories for X-ray astrophysics. The massive stars in these systems possess powerful stellar winds with speeds up to$\\sim$3000 km s$^{-1}$, and their collision leads to hot plasma (up to$\\sim10^8$K) that emit thermal X-rays (up to$\\sim$10 keV). Many X-ray telescopes have observed CWBs, including Suzaku, and our work aims to model these X-ray observations. We use 3D smoothed particle hydrodynamics (SPH) to model the wind-wind interaction, and then perform 3D radiative transfer to compute the emergent X-ray flux, which is folded through X-ray telescopes' response functions to compare directly with observations. In these proceedings, we present our models of Suzaku observations of the multi-year-period, highly eccentric systems$\\eta$Carinae and WR 140. The models reproduce the observations well away from periastron passage, but only$\\eta$Carinae's X-ray spectrum is reproduced at periastron; the WR 140 model produces too much flux during this more complicated p... 10. Non-equilibrium of charged particles in swarms and plasmas—from binary collisions to plasma effects Science.gov (United States) Petrović, Z. Lj; Simonović, I.; Marjanović, S.; Bošnjaković, D.; Marić, D.; Malović, G.; Dujko, S. 2017-01-01 In this article we show three quite different examples of low-temperature plasmas, where one can follow the connection of the elementary binary processes (occurring at the nanoscopic scale) to the macroscopic discharge behavior and to its application. The first example is on the nature of the higher-order transport coefficient (second-order diffusion or skewness); how it may be used to improve the modelling of plasmas and also on how it may be used to discern details of the relevant cross sections. A prerequisite for such modeling and use of transport data is that the hydrodynamic approximation is applicable. In the second example, we show the actual development of avalanches in a resistive plate chamber particle detector by conducting kinetic modelling (although it may also be achieved by using swarm data). The current and deposited charge waveforms may be predicted accurately showing temporal resolution, which allows us to optimize detectors by adjusting the gas mixture composition and external fields. Here kinetic modeling is necessary to establish high accuracy and the details of the physics that supports fluid models that allows us to follow the transition to streamers. Finally, we show an example of positron traps filled with gas that, for all practical purposes, are a weakly ionized gas akin to swarms, and may be modelled in that fashion. However, low pressures dictate the need to apply full kinetic modelling and use the energy distribution function to explain the kinetics of the system. In this way, it is possible to confirm a well established phenomenology, but in a manner that allows precise quantitative comparisons and description, and thus open doors to a possible optimization. 11. A family of models for Schelling binary choices Science.gov (United States) Cavalli, Fausto; Naimzada, Ahmad; Pireddu, Marina 2016-02-01 We introduce and study a family of discrete-time dynamical systems to model binary choices based on the framework proposed by Schelling in 1973. The model we propose uses a gradient-like adjustment mechanism by means of a family of smooth maps and allows understanding and analytically studying the phenomena qualitatively described by Schelling. In particular, we investigate existence of steady states and their relation to the equilibria of the static model studied by Schelling, and we analyze local stability, linking several examples and considerations provided by Schelling with bifurcation theory. We provide examples to confirm the theoretical results and to numerically investigate the possible destabilizations, as well as the emergence of coexisting attractors. We show the existence of chaos for a particular example. 12. Modeling non-radial oscillations on components of close binaries Science.gov (United States) Latković, Olivera; Cséki, Attila 2014-02-01 We developed an advanced binary system model that includes stellar oscillations on one or both stars, with the goal of mode identification by fitting of the photometric light curves. The oscillations are modeled as perturbations of the local surface temperature and the local gravitational potential. In the case of tidally distorted stars, it is assumed that the pulsation axis coincides with the direction connecting the centers of the components rather than with the rotation axis. The mode identification method, originally devised by B. Bíró, is similar to eclipse mapping in that it utilizes the amplitude, phase and frequency modulation of oscillations during the eclipse; but the identification is achieved by grid-fitting of the observed light curve rather than by image reconstruction. The proposed model and the mode identification method have so far been tested on synthetic data with encouraging results. 13. Sensor Fusion Based Model for Collision Free Mobile Robot Navigation Directory of Open Access Journals (Sweden) Marwah Almasri 2015-12-01 Full Text Available Autonomous mobile robots have become a very popular and interesting topic in the last decade. Each of them are equipped with various types of sensors such as GPS, camera, infrared and ultrasonic sensors. These sensors are used to observe the surrounding environment. However, these sensors sometimes fail and have inaccurate readings. Therefore, the integration of sensor fusion will help to solve this dilemma and enhance the overall performance. This paper presents a collision free mobile robot navigation based on the fuzzy logic fusion model. Eight distance sensors and a range finder camera are used for the collision avoidance approach where three ground sensors are used for the line or path following approach. The fuzzy system is composed of nine inputs which are the eight distance sensors and the camera, two outputs which are the left and right velocities of the mobile robot’s wheels, and 24 fuzzy rules for the robot’s movement. Webots Pro simulator is used for modeling the environment and the robot. The proposed methodology, which includes the collision avoidance based on fuzzy logic fusion model and line following robot, has been implemented and tested through simulation and real time experiments. Various scenarios have been presented with static and dynamic obstacles using one robot and two robots while avoiding obstacles in different shapes and sizes. 14. Sensor Fusion Based Model for Collision Free Mobile Robot Navigation. Science.gov (United States) Almasri, Marwah; Elleithy, Khaled; Alajlan, Abrar 2015-12-26 Autonomous mobile robots have become a very popular and interesting topic in the last decade. Each of them are equipped with various types of sensors such as GPS, camera, infrared and ultrasonic sensors. These sensors are used to observe the surrounding environment. However, these sensors sometimes fail and have inaccurate readings. Therefore, the integration of sensor fusion will help to solve this dilemma and enhance the overall performance. This paper presents a collision free mobile robot navigation based on the fuzzy logic fusion model. Eight distance sensors and a range finder camera are used for the collision avoidance approach where three ground sensors are used for the line or path following approach. The fuzzy system is composed of nine inputs which are the eight distance sensors and the camera, two outputs which are the left and right velocities of the mobile robot's wheels, and 24 fuzzy rules for the robot's movement. Webots Pro simulator is used for modeling the environment and the robot. The proposed methodology, which includes the collision avoidance based on fuzzy logic fusion model and line following robot, has been implemented and tested through simulation and real time experiments. Various scenarios have been presented with static and dynamic obstacles using one robot and two robots while avoiding obstacles in different shapes and sizes. 15. Modelling the brightness increase signature due to asteroid collisions CERN Document Server McLoughlin, Ev; McLoughlin, Alan 2015-01-01 We have developed a model to predict the post-collision brightness increase of sub-catastrophic collisions between asteroids and to evaluate the likelihood of a survey detecting these events. It is based on the cratering scaling laws of Holsapple and Housen (2007) and models the ejecta expansion following an impact as occurring in discrete shells each with their own velocity. We estimate the magnitude change between a series of target/impactor pairs, assuming it is given by the increase in reflecting surface area within a photometric aperture due to the resulting ejecta. As expected the photometric signal increases with impactor size, but we find also that the photometric signature decreases rapidly as the target asteroid diameter increases, due to gravitational fallback. We have used the model results to make an estimate of the impactor diameter for the (596) Scheila collision of D=49-65m depending on the impactor taxonomy, which is broadly consistent with previous estimates. We varied both the strength regi... 16. Extended hard-sphere model and collisions of cohesive particles. Science.gov (United States) Kosinski, Pawel; Hoffmann, Alex C 2011-09-01 In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are "dry," e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model. 17. Quark model and high energy collisions CERN Document Server Anisovich, V V; Nyíri, J; Shabelski, Yu M 2004-01-01 This is an updated version of the book published in 1985. QCD-motivated, it gives a detailed description of hadron structure and soft interactions in the additive quark model, where hadrons are regarded as composite systems of dressed quarks. In the past decade it has become clear that nonperturbative QCD, responsible for soft hadronic processes, may differ rather drastically from perturbative QCD. The understanding of nonperturbative QCD requires a detailed investigation of the experiments and the theoretical approaches. Bearing this in mind, the book has been rewritten paying special attenti 18. Numerical models of trench migration in continental collision zones Directory of Open Access Journals (Sweden) V. Magni 2012-03-01 Full Text Available Continental collision is an intrinsic feature of plate tectonics. The closure of an oceanic basin leads to the onset of subduction of buoyant continental material, which slows down and eventually stops the subduction process. We perform a parametric study of the geometrical and rheological influence on subduction dynamics during the subduction of continental lithosphere. In 2-D numerical models of a free subduction system with temperature and stress-dependent rheology, the trench and the overriding plate move self-consistently as a function of the dynamics of the system (i.e. no external forces are imposed. This setup enables to study how continental subduction influences the trench migration. We found that in all models the trench starts to advance once the continent enters the subduction zone and continues to migrate until few million years after the ultimate slab detachment. Our results support the idea that the trench advancing is favoured and, in part provided by, the intrinsic force balance of continental collision. We suggest that the trench advance is first induced by the locking of the subduction zone and the subsequent steepening of the slab, and next by the sinking of the deepest oceanic part of the slab, during stretching and break-off of the slab. The amount of trench advancing ranges from 40 to 220 km and depends on the dip angle of the slab before the onset of collision. 19. Modeling the Asymmetric Wind of Massive LBV Binary MWC 314 CERN Document Server Lobel, A; Dozinel, K Torres; Gorlova, N; Martayan, C; Raskin, G; Van Winckel, H; Prins, S; Pessemier, W; Waelkens, C; Frémat, Y; Hensberge, H; Dummortier, L; Jorissen, A; Van Eck, S; Lehmann, H 2011-01-01 Spectroscopic monitoring with Mercator-HERMES over the past two years reveals that MWC 314 is a massive binary system composed of an early B-type primary LBV star and a less-luminous supergiant companion. We determine an orbital period Porb of 60.85 d from optical S II and Ne I absorption lines observed in this single-lined spectroscopic binary. We find an orbital eccentricity of e=0.26, and a large amplitude of the radial velocity curve of 80.6 km/s. The ASAS V light-curve during our spectroscopic monitoring reveals two brightness minima (\\Delta V~0.1 mag.) over the orbital period due to partial eclipses at an orbital inclination angle of ~70 degrees. We find a clear correlation between the orbital phases and the detailed shapes of optical and near-IR P Cygni-type line profiles of He I, Si II, and double- or triple-peaked stationary cores of prominent Fe II emission lines. A preliminary 3-D radiative transfer model computed with Wind3D shows that the periodic P Cygni line profile variability results from an ... 20. A model for the non-thermal emission of the very massive colliding-wind binary HD 93129A CERN Document Server del Palacio, Santiago; Romero, Gustavo E; Benaglia, Paula 2016-01-01 The binary stellar system HD 93129A is one of the most massive known binaries in our Galaxy. This system presents non-thermal emission in the radio band, which can be used to infer its physical conditions and predict its emission in the high-energy band. We intend to constrain some of the unknown parameters of HD 93129A through modelling the non-thermal emitter, and also to analyse the detectability of this source in hard X-rays and$\\gamma$-rays. We develop a broadband radiative model for the wind-collision region taking into account the evolution of the accelerated particles streaming along the shocked region, the emission by different radiative processes, and the attenuation of the emission propagating through the local matter and radiation fields. From the analysis of the radio emission, we find that the binary HD~93129A is more likely to have a low inclination and a high eccentricity. The minimum energy of the non-thermal electrons seems to be between$\\sim 20 - 100$MeV, depending on the intensity of the... 1. Numerical models of slab migration in continental collision zones Directory of Open Access Journals (Sweden) V. Magni 2012-09-01 Full Text Available Continental collision is an intrinsic feature of plate tectonics. The closure of an oceanic basin leads to the onset of subduction of buoyant continental material, which slows down and eventually stops the subduction process. In natural cases, evidence of advancing margins has been recognized in continental collision zones such as India-Eurasia and Arabia-Eurasia. We perform a parametric study of the geometrical and rheological influence on subduction dynamics during the subduction of continental lithosphere. In our 2-D numerical models of a free subduction system with temperature and stress-dependent rheology, the trench and the overriding plate move self-consistently as a function of the dynamics of the system (i.e. no external forces are imposed. This setup enables to study how continental subduction influences the trench migration. We found that in all models the slab starts to advance once the continent enters the subduction zone and continues to migrate until few million years after the ultimate slab detachment. Our results support the idea that the advancing mode is favoured and, in part, provided by the intrinsic force balance of continental collision. We suggest that the advance is first induced by the locking of the subduction zone and the subsequent steepening of the slab, and next by the sinking of the deepest oceanic part of the slab, during stretching and break-off of the slab. These processes are responsible for the migration of the subduction zone by triggering small-scale convection cells in the mantle that, in turn, drag the plates. The amount of advance ranges from 40 to 220 km and depends on the dip angle of the slab before the onset of collision. 2. A model for the non-thermal emission of the very massive colliding-wind binary HD 93129A Science.gov (United States) del Palacio, S.; Romero, G. E.; Bosch-Ramon, V.; Benaglia, P. 2016-08-01 Recently, the wind collision region of the system HD 93129A was resolved for the first time using very large baseline interferometry. This system is one of the most massive known binaries in our Galaxy. In this work we develop a broadband radiative model for the wind collision region. The model takes into account the evolution of accelerated particles streaming along the shocked region, their emission through different radiative processes, and the attenuation of the radiation while it propagates across all local fields. We reproduce the available radio data, and analyze the consequent detectability of the source in hard X/gamma-rays. We predict how the emission from the system will evolve in the forthcoming years when the stars come closer, and we also provide synthetic radio maps that allow to interpret the future observations with very large baseline interferometry in 2.3 GHz and 8.6 GHz. According to our results, the non-thermal emission from this system will enhance in the near future. With instruments such as NuSTAR, Fermi, and CTA, it will be possible to determine whether the relativistic particle content is hadron or lepton dominated, and other parameters such as the strength of the magnetic field in the wind collision region and, indirectly, the magnetic field in the surface of the very massive stars. 3. Atomic collision processes for modelling cool star spectra Science.gov (United States) Barklem, Paul 2015-05-01 The abundances of chemical elements in cool stars are very important in many problems in modern astrophysics. They provide unique insight into the chemical and dynamical evolution of the Galaxy, stellar processes such as mixing and gravitational settling, the Sun and its place in the Galaxy, and planet formation, to name a just few examples. Modern telescopes and spectrographs measure stellar spectral lines with precision of order 1 per cent, and planned surveys will provide such spectra for millions of stars. However, systematic errors in the interpretation of observed spectral lines leads to abundances with uncertainties greater than 20 per cent. Greater precision in the interpreted abundances should reasonably be expected to lead to significant discoveries, and improvements in atomic data used in stellar atmosphere models play a key role in achieving such advances in precision. In particular, departures from the classical assumption of local thermodynamic equilibrium (LTE) represent a significant uncertainty in the modelling of stellar spectra and thus derived chemical abundances. Non-LTE modelling requires large amounts of radiative and collisional data for the atomic species of interest. I will focus on inelastic collision processes due to electron and hydrogen atom impacts, the important perturbers in cool stars, and the progress that has been made. I will discuss the impact on non-LTE modelling, and what the modelling tells us about the types of collision processes that are important and the accuracy required. More specifically, processes of fundamentally quantum mechanical nature such as spin-changing collisions and charge transfer have been found to be very important in the non-LTE modelling of spectral lines of lithium, oxygen, sodium and magnesium. 4. Transverse-energy distributions at midrapidity in$p$$+$$p$,$d$$+Au, and Au+Au collisions at \\sqrt{s_{_{NN}}}=62.4--200~GeV and implications for particle-production models OpenAIRE Adler, S. S.; Afanasiev, S.; Aidala, C.; Ajitanand, N. N.; Akiba, Y.; Al-Jamel, A.; Alexander, J.; Aoki, K.; Aphecetche, L.; Armendariz, R. (R.); Aronson, S H; Averbeck, R.; T.C. Awes; Azmoun, B.; Babintsev, V. 2013-01-01 Measurements of the midrapidity transverse energy distribution, d\\Et/d\\eta, are presented for p$$+$$p, d$$+$Au, and Au$+$Au collisions at$\\sqrt{s_{_{NN}}}=200$GeV and additionally for Au$+$Au collisions at$\\sqrt{s_{_{NN}}}=62.4$and 130 GeV. The$d\\Et/d\\eta$distributions are first compared with the number of nucleon participants$N_{\\rm part}$, number of binary collisions$N_{\\rm coll}$, and number of constituent-quark participants$N_{qp}$calculated from a Glauber model based on th... 5. A radiative model of quark masses with binary tetrahedral symmetry Science.gov (United States) Natale, Alexander 2017-01-01 A radiative model of quark and lepton masses utilizing the binary tetrahedral (T‧) flavor symmetry, or horizontal symmetry, is proposed which produces the first two generation of quark masses through their interactions with vector-like quarks that carry charges under an additional U (1). By softly-breaking the T‧ to a residual Z4 through the vector-like quark masses, a CKM mixing angle close to the Cabibbo angle is produced. In order to generate the cobimaximal neutrino oscillation pattern (θ13 ≠ 0 ,θ23 = π / 4 ,δCP = ± π / 2) and protect the horizontal symmetry from arbitrary corrections in the lepton sector, there are automatically two stabilizing symmetries in the dark sector. Several benchmark cases where the correct relic density is achieved in a multi-component DM scenario, as well as the potential collider signatures of the vector-like quarks are discussed. 6. Thermodynamic modeling of the Ba - Mg binary system Energy Technology Data Exchange (ETDEWEB) Ren, Xin; Li, Changrong; Du, Zhenmin; Guo, Cuiping; Chen, Sicheng [Univ. of Science and Technology, Beijing (China). School of Materials Science and Engineering 2013-04-15 On the basis of the thermochemical and phase equilibrium experimental data, the phase diagram of the Ba - Mg binary system has been assessed by means of the calculation of phase diagrams technique. The liquid phase is of unlimited solubility and modeled as a solution phase using the Redlich-Kister equation. The intermetallic compounds, Mg{sub 17}Ba{sub 2}, Mg{sub 23}Ba{sub 6} and Mg{sub 2}Ba, with no solubility ranges are treated as strict stoichiometric compounds with the formula Mg{sub m} Ba{sub n}. Two terminal phases, BccBa and HcpMg, are kept as solution phases, since the solubilities of the two phases are of considerable importance. After optimization, a set of self-consistent thermodynamic parameters has been obtained. The calculated values agree well with the available experimental data. 7. Development of topography in 3-D continental-collision models Science.gov (United States) Pusok, A. E.; Kaus, Boris J. P. 2015-05-01 Understanding the formation and evolution of high mountain belts, such as the Himalayas and the adjacent Tibetan Plateau, has been the focus of many tectonic and numerical models. Here we employ 3-D numerical simulations to investigate the role that subduction, collision, and indentation play on lithosphere dynamics at convergent margins, and to analyze the conditions under which large topographic plateaus can form in an integrated lithospheric and upper mantle-scale model. Distinct dynamics are obtained for the oceanic subduction side (trench retreat, slab rollback) and the continental-collision side (trench advance, slab detachment, topographic uplift, lateral extrusion). We show that slab pull alone is insufficient to generate high topography in the upper plate, and that external forcing and the presence of strong blocks such as the Tarim Basin are necessary to create and shape anomalously high topographic fronts and plateaus. Moreover, scaling is used to predict four different modes of surface expression in continental-collision models: (I) low-amplitude homogeneous shortening, (II) high-amplitude homogeneous shortening, (III) Alpine-type topography with topographic front and low plateau, and (IV) Tibet-Himalaya-type topography with topographic front and high plateau. Results of semianalytical models suggest that the Argand number governs the formation of high topographic fronts, while the amplitude of plateaus is controlled by the initial buoyancy ratio of the upper plate. Applying these results to natural examples, we show that the Alps belong to regime (III), the Himalaya-Tibet to regime (IV), whereas the Andes-Altiplano fall at the boundary between regimes (III) and (IV). 8. Model-free linkage analysis of a binary trait. Science.gov (United States) Xu, Wei; Bull, Shelley B; Mirea, Lucia; Greenwood, Celia M T 2012-01-01 Genetic linkage analysis aims to detect chromosomal regions containing genes that influence risk of specific inherited diseases. The presence of linkage is indicated when a disease or trait cosegregates through the families with genetic markers at a particular region of the genome. Two main types of genetic linkage analysis are in common use, namely model-based linkage analysis and model-free linkage analysis. In this chapter, we focus solely on the latter type and specifically on binary traits or phenotypes, such as the presence or absence of a specific disease. Model-free linkage analysis is based on allele-sharing, where patterns of genetic similarity among affected relatives are compared to chance expectations. Because the model-free methods do not require the specification of the inheritance parameters of a genetic model, they are preferred by many researchers at early stages in the study of a complex disease. We introduce the history of model-free linkage analysis in Subheading 1. Table 1 describes a standard model-free linkage analysis workflow. We describe three popular model-free linkage analysis methods, the nonparametric linkage (NPL) statistic, the affected sib-pair (ASP) likelihood ratio test, and a likelihood approach for pedigrees. The theory behind each linkage test is described in this section, together with a simple example of the relevant calculations. Table 4 provides a summary of popular genetic analysis software packages that implement model-free linkage models. In Subheading 2, we work through the methods on a rich example providing sample software code and output. Subheading 3 contains notes with additional details on various topics that may need further consideration during analysis. 9. Modeling and Observations of Massive Binaries with the B[e] Phenomenon Science.gov (United States) Lobel, A.; Martayan, C.; Mehner, A.; Groh, J. H. 2017-02-01 We report a long-term high-resolution spectroscopic monitoring program of LBVs and candidate LBVs with Mercator-HERMES. Based on 7 years of data, we recently showed that supergiant MWC 314 is a (Galactic) semi-detached eccentric binary with stationary permitted and forbidden emission lines in the optical and near-IR region. MWC 314 is a luminous and massive probable LBV star showing a strongly orbitally-modulated wind variability. We observe discrete absorption components in P Cyg He I lines signaling large-scale wind structures. In 2014 XMM observed X-rays indicating strong wind-wind collision in the close binary system (a ≃1 AU). A VLT-NACO imaging survey recently revealed that MWC 314 is a triple hierarchical system. We present a 3-D non-LTE radiative transfer model of the extended asymmetric wind structure around the primary B0 supergiant for modeling the orbital variability of P Cyg absorption (v∞˜1200 km s-1) in He I lines. An analysis of the HERMES monitoring spectra of the Galactic LBV star MWC 930 however does not show clear indications of a spectroscopic binary. The detailed long-term spectroscopic variability of this massive B[e] star is very similar to the spectroscopic variability of the prototypical blue hypergiant S Dor in the LMC. We observe prominent P Cyg line shapes in MWC 930 that temporarily transform into split absorption line cores during variability phases of its S Dor cycle over the past decade with a brightening in V of ˜ 1.2 mag. The line splitting phenomenon is very similar to the split metal line cores observed in pulsating Yellow Hypergiants ρ Cas (F-K Ia+) and HR 8752 (A-K Ia+) with [Ca II] and [N II] emission lines. We propose the line core splitting in MWC 930 is due to optically thick central line emission produced in the inner ionized wind region becoming mechanically shock-excited with the increase of R* and decrease of Teff of the LBV. 10. Formation of anions and cations via a binary-encounter process in OH$^+$+ Ar collisions: the role of dissociative excitation and statistical aspects CERN Document Server Lattouf, E; Chesnel, J -Y; Kovács, S T S; Bene, E; Herczku, P; Huber, B A; Méry, A; Poully, J -C; Rangama, J; Sulik, B 2015-01-01 Molecular fragmentation leading to the formation of negatively and positively charged hydrogen ions in 7-keV OH$^+$+ Ar collisions is investigated experimentally. The most striking finding is that negative and positive hydrogen ions are emitted with very similar angular dependences. Also, the kinetic energy distribution of the H$^+$fragment shows strong similarities with that of the ejected H$^-$ion. The kinematics of the emitted H core is found to be essentially driven by its scattering on the atomic target. However, in addition to this binary-encounter process, dissociative electronic excitation of the molecular projectile has to be invoked to explain the observed fragmentation patterns. Though the electron capture process is complex, it is shown that the relative population of the different final charge states of the outgoing fragments can be described by simple statistical laws. 11. Progenitor models of Wolf-Rayet+O binary systems NARCIS (Netherlands) Petrovic, J.; Langer, N. 2007-01-01 Since close WR+O binaries are the result of a strong interaction of both stars in massive close binary systems, they can be used to constrain the highly uncertain mass and angular momentum budget during the major mass- transfer phase. We explore the progenitor evolution of the three best suited WR+O 12. Double pendulum model for tennis stroke including a collision process CERN Document Server Youn, Sun-Hyun 2015-01-01 By means of adding a collision process between the ball and racket in double pendulum model, we analyzed the tennis stroke. It is possible that the speed of the rebound ball does not simply depend on the angular velocity of the racket, and higher angular velocity sometimes gives lower ball speed. We numerically showed that the proper time lagged racket rotation increases the speed of the rebound ball by 20%. We also showed that the elbow should move in order to add the angular velocity of the racket. 13. Model for hypernucleus production in heavy ion collisions CERN Document Server Pop, V Topor 2010-01-01 We estimate the production cross sections of hypernuclei in projectile like fragment (PLF) in heavy ion collisions. The discussed scenario for the formation cross section of hypernucleus is: (a) Lambda particles are produced in the participant region but have a considerable rapidity spread and (b) Lambda with rapidity close to that of the PLF and total momentum (in the rest system of PLF) up to Fermi motion can then be trapped and produce hypernuclei. The process (a) is considered here within Heavy Ion Jet Interacting Generator HIJING-BBbar model and the process (b) in the canonical thermodynamic model (CTM). We estimate the production cross-sections for light hypernuclei for C + C at 3.7 GeV total nucleon-nucleon center of mass energy and for Ne+Ne and Ar+Ar collisions at 5.0 GeV. By taking into account explicitly the impact parameter dependence of the colliding systems, it is found that the cross section is different from that predicted by the coalescence model and large discrepancy is obtained for 6_He and... 14. Eikonal model analysis of elastic hadron collisions at high energies CERN Document Server Prochazka, Jiri 2016-01-01 Elastic collisions of protons at different energies represent main background in studying the structure of fundamental particles at the present. On the basis of standardly used model proposed by West and Yennie the protons have been then interpreted as transparent objects; elastic events have been interpreted as more central than inelastic ones. It will be shown that using eikonal model the protons may be interpreted in agreement with usual ontological conception; elastic processes being more peripheral than inelastic ones. The corresponding results (differing fundamentally from those of WY model) will be presented by analyzing the most ample elastic data set measured at ISR energy of 53 GeV. Detailed analysis of measured differential cross section will be performed and different alternatives of peripheral behavior on the basis of eikonal model will be presented. The impact of recently established electromagnetic form factors on determination of quantities specifying hadron interaction determined from the fit... 15. A Simple Model of Wings in Heavy-Ion Collisions CERN Document Server Parikh, Aditya 2015-01-01 We create a simple model of heavy ion collisions independent of any generators as a way of investigating a possible source of the wings seen in data. As a first test, we reproduce a standard correlations plot to verify the integrity of the model. We then proceed to test whether an η dependent v2 could be a source of the wings and take projections along multiple Δφ intervals and compare with data. Other variations of the model are tested by having dN/dφ and v2 depend on η as well as including pions and protons into the model to make it more realistic. Comparisons with data seem to indicate that an η dependent v2 is not the main source of the wings. 16. An extended topological model for binary phosphate glasses Energy Technology Data Exchange (ETDEWEB) Hermansen, Christian [Section of Chemistry, Aalborg University, 9220 Aalborg (Denmark); Rodrigues, Bruno P.; Wondraczek, Lothar [Otto Schott Institute of Materials Research, University of Jena, 07743 Jena (Germany); Yue, Yuanzheng, E-mail: [email protected] [Section of Chemistry, Aalborg University, 9220 Aalborg (Denmark); State Key Laboratory of Silicate Materials for Architecture, Wuhan University of Technology, Wuhan 430070 (China) 2014-12-28 We present a topological model for binary phosphate glasses that builds on the previously introduced concepts of the modifying ion sub-network and the strength of modifier constraints. The validity of the model is confirmed by the correct prediction of T{sub g}(x) for covalent polyphosphoric acids where the model reduces to classical constraint counting. The constraints on the modifying cations are linear constraints to first neighbor non-bridging oxygens, and all angular constraints are broken as expected for ionic bonding. For small modifying cations, such as Li{sup +}, the linear constraints are almost fully intact, but for larger ions, a significant fraction is broken. By accounting for the fraction of intact modifying ion related constraints, q{sub γ}, the T{sub g}(x) of alkali phosphate glasses is predicted. By examining alkali, alkaline earth, and rare earth metaphosphate glasses, we find that the effective number of intact constraints per modifying cation is linearly related to the charge-to-distance ratio of the modifying cation to oxygen. 17. Generalized Fiducial Inference for Binary Logistic Item Response Models. Science.gov (United States) Liu, Yang; Hannig, Jan 2016-06-01 Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a Bayesian posterior distribution. However, no prior distribution needs to be specified, which renders GFI more suitable when no a priori information about model parameters is available. In the current paper, we apply GFI to a family of binary logistic item response theory models, which includes the two-parameter logistic (2PL), bifactor and exploratory item factor models as special cases. Asymptotic properties of the resulting fiducial distribution are discussed. Random draws from the fiducial distribution can be obtained by the proposed Markov chain Monte Carlo sampling algorithm. We investigate the finite-sample performance of our fiducial percentile CI and two commonly used Wald-type CIs associated with maximum likelihood (ML) estimation via Monte Carlo simulation. The use of GFI in high-dimensional exploratory item factor analysis was illustrated by the analysis of a set of the Eysenck Personality Questionnaire data. 18. 改进的返回式二进制防碰撞算法%Improved return binary anti-collision algorithm Institute of Scientific and Technical Information of China (English) 张航; 唐明浩; 程晖 2011-01-01 As the key technology of Internet of Things applications, Radio Frequency Identification(RFID) is a hot research area in recent years.In the large-scale RFID applications, there will be inevitable collision of tags identification.As a reference to the number of bytes and the number of search instructions sent in a time slot,an improved return binary anti-collision algorithm is proposed to reduce data throughput and search instructions in per time slot.%作为物联网应用中的关键技术,射频识别(RFID)技术是近年来的热门研究领域.在大规模的RFID应用中,不可避免地会有标签识别的碰撞问题.以每个时隙传输数据的字节数以及搜索命令的发送次数作为参考指标,对已有算法进行分析比较,在已有算法的基础上提出一种改进的返回式二进制防碰撞算法,减少每个时隙数据的传输量和命令搜索次数,使得新的改进算法性能有较大的提升. 19. Unobserved Heterogeneity in the Binary Logit Model with Cross-Sectional Data and Short Panels DEFF Research Database (Denmark) Holm, Anders; Jæger, Mads Meier; Pedersen, Morten This paper proposes a new approach to dealing with unobserved heterogeneity in applied research using the binary logit model with cross-sectional data and short panels. Unobserved heterogeneity is particularly important in non-linear regression models such as the binary logit model because, unlike...... in linear regression models, estimates of the effects of observed independent variables are biased even when omitted independent variables are uncorrelated with the observed independent variables. We propose an extension of the binary logit model based on a finite mixture approach in which we conceptualize... 20. Constraining the minute amount of audible energy radiated from binary collisions of light plastic spheres in conditions of incomplete angular coverage of the measured pressure. Science.gov (United States) Petculescu, Andi; Riner, Joshua 2010-10-01 Usually, the energy released as air-coupled sound following a collision is dismissed as negligible. The goal of this Letter is to quantify the value of this small but measurable quantity, since it can be useful to impact studies. Measurements of sound radiation from binary collisions of polypropylene balls were performed in order to constrain the fraction of incident energy radiated as sound in air. In the experiments, one ball is released from rest, directly above a stationary target ball. The transient acoustic waveforms are detected by a microphone rotated about the impact point at a radius of 10 cm. The sound pressure was measured as a function of the polar angle θ (the azimuthal symmetry of the problem was verified by rotating the microphone in the horizontal plane). The angular pattern has two main lobes that are asymmetric with respect to the impact plane. This asymmetry is ascribable to interference and/or scattering effects. Gaps in the acoustic measurements at the "poles" (i.e., around 0° and 180°) pose a challenge similar to that of extrapolating the cosmic microwave background in the galactic "cut." The data was continued in the gaps by polynomial interpolation rather than least-squares fitting, a choice dictated by the accuracy of the reconstructed pattern. The acoustic energy radiated during the impact, estimated by multiplying the collision time by the sound intensity integrated over a spherical surface centered at the impact point, is calculated as four orders of magnitude smaller than the incident energy (0.23 μJ versus 1.6 mJ). 1. A Covariant OBE Model for$\\eta$Production in NN Collisions CERN Document Server Gedalin, E; Razdolskaya, L A 1998-01-01 A relativistic covariant one boson exchange model, previously applied to describe elastic nucleon-nucleon scattering, is extended to study$\\eta$production in NN collisions. The transition amplitude for the elementary BN->$\\eta$N process with B being the meson exchanged (B=$\\pi$,$|sigma$,$\\eta$, corresponding to s and u-channels with a nucleon or a nucleon isobar N*(1535MeV) in the intermediate states. Taking the relative phases of the various exchange amplitudes to be +1, the model reproduces the cross sections for the$NN\\to X\\eta$reactions in a consistent manner. In the limit where all overall contributions from the exchange of pseudoscalart and scalar mesons with that of vector mesons cancel out. Consequently, much of the ambiguities in the model predictions due to unknown relative phases of different vector pseudoscalar exchanges are strongly reduced. 2. Phenomenological Modelling of a Group of Eclipsing Binary Stars Science.gov (United States) Andronov, Ivan L.; Tkachenko, Mariia G.; Chinarova, Lidia L. 2016-03-01 Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the field of previously known variable star RS Car) and compare results to that obtained using the TP fits. For this system, the statistically optimal number of parameters is 44, but the fit is still worse than that of the NAV fit. Application to the system GSC 3692-00624 argues that the NAV fit is better than the TP one even for the case of EW-type stars with much wider eclipses. Model parameters are listed. 3. Sparse Representation Based Binary Hypothesis Model for Hyperspectral Image Classification Directory of Open Access Journals (Sweden) Yidong Tang 2016-01-01 Full Text Available The sparse representation based classifier (SRC and its kernel version (KSRC have been employed for hyperspectral image (HSI classification. However, the state-of-the-art SRC often aims at extended surface objects with linear mixture in smooth scene and assumes that the number of classes is given. Considering the small target with complex background, a sparse representation based binary hypothesis (SRBBH model is established in this paper. In this model, a query pixel is represented in two ways, which are, respectively, by background dictionary and by union dictionary. The background dictionary is composed of samples selected from the local dual concentric window centered at the query pixel. Thus, for each pixel the classification issue becomes an adaptive multiclass classification problem, where only the number of desired classes is required. Furthermore, the kernel method is employed to improve the interclass separability. In kernel space, the coding vector is obtained by using kernel-based orthogonal matching pursuit (KOMP algorithm. Then the query pixel can be labeled by the characteristics of the coding vectors. Instead of directly using the reconstruction residuals, the different impacts the background dictionary and union dictionary have on reconstruction are used for validation and classification. It enhances the discrimination and hence improves the performance. 4. A synthetic model of the gravitational wave background from evolving binary compact objects CERN Document Server Dvorkin, Irina; Vangioni, Elisabeth; Silk, Joseph 2016-01-01 Modeling the stochastic gravitational wave background from various astrophysical sources is a key objective in view of upcoming observations with ground- and space-based gravitational wave observatories such as Advanced LIGO, VIRGO, eLISA and PTA. We develop a synthetic model framework that follows the evolution of single and binary compact objects in an astrophysical context. We describe the formation and merger rates of binaries, the evolution of their orbital parameters with time and the spectrum of emitted gravitational waves at different stages of binary evolution. Our approach is modular and allows us to test and constrain different ingredients of the model, including stellar evolution, black hole formation scenarios and the properties of binary systems. We use this framework in the context of a particularly well-motivated astrophysical setup to calculate the gravitational wave background from several types of sources, including inspiraling stellar-mass binary black holes that have not merged during a H... 5. Modeling and analysis of periodic orbits around a contact binary asteroid NARCIS (Netherlands) Feng, J.; Noomen, R.; Visser, P.N.A.M.; Yuan, J. 2015-01-01 The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is repre 6. Modeling and analysis of periodic orbits around a contact binary asteroid NARCIS (Netherlands) Feng, J.; Noomen, R.; Visser, P.N.A.M.; Yuan, J. 2015-01-01 The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is 7. Thermal Model Description of Collisions of Small Nuclei CERN Document Server Cleymans, J.; Oeschler, H.; Redlich, K.; Sharma, N. 2016-01-01 The dependence of particle production on the size of the colliding nuclei is analyzed in terms of the thermal model using the canonical ensemble. The concept of strangeness correlation in clusters of sub-volume$V_c$is used to account for the suppression of strangeness. A systematic analysis is presented of the predictions of the thermal model for particle production in collisions of small nuclei. The pattern of the maxima in particle ratios of strange particles to pions as a function of beam energy is quite special, as they do not occur at the same beam energy and are sensitive to system size. In particular, the$\\Lambda/\\pi^+$ratio shows a clear maximum even for the smallest systems while the maximum in the K$^+/\\pi^+$ratio disappears in small systems. 8. Heavy Ions Collision evolution modeling with ECHO-QGP CERN Document Server Rolando, Valentina; Beraudo, Andrea; Del Zanna, Luca; Becattini, Francesco; Chandra, Vinod; De Pace, Arturo; Nardi, Marzia 2014-01-01 We present a numerical code modeling the evolution of the medium formed in relativistic heavy ion collisions, ECHO-QGP. The code solves relativistic hydrodynamics in$(3+1)-$D, with dissipative terms included within the framework of Israel-Stewart theory; it can work both in Minkowskian and in Bjorken coordinates. Initial conditions are provided through an implementation of the Glauber model (both Optical and Monte Carlo), while freezeout and particle generation are based on the Cooper-Frye prescription. The code is validated against several test problems and shows remarkable stability and accuracy with the combination of a conservative (shock-capturing) approach and the high-order methods employed. In particular it beautifully agrees with the semi-analytic solution known as Gubser flow, both in the ideal and in the viscous Israel-Stewart case, up to very large times and without any ad hoc tuning of the algorithm. 9. Phemenological Modelling of a Group of Eclipsing Binary Stars CERN Document Server Andronov, Ivan L; Chinarova, Lidia L 2015-01-01 Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the... 10. Modeling Mergers of Known Galactic Systems of Binary Neutron Stars CERN Document Server Feo, Alessandra; Maione, Francesco; Löffler, Frank 2016-01-01 We present a study of the merger of six different known galactic systems of binary neutron stars (BNS) of unequal mass with a mass ratio between$0.75$and$0.99$. Specifically, these systems are J1756-2251, J0737-3039A, J1906+0746, B1534+12, J0453+1559 and B1913+16. We follow the dynamics of the merger from the late stage of the inspiral process up to$\\sim$20 ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH), using a semi-realistic equation of state (EOS), namely the seven-segment piece-wise polytropic SLy with a thermal component. For the most extreme of these systems ($q=0.75$, J0453+1559), we also investigate the effects of different EOSs: APR4, H4, and MS1. Our numerical simulations are performed using only publicly available open source code such as, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. We show results on the gravitational wave signals, spectrogram and fr... 11. A compact binary merger model for GRB 050509b CERN Document Server Lee, W H; Granot, J; Lee, William H.; Ramirez-Ruiz, Enrico; Granot, Jonathan 2005-01-01 The first X-ray afterglow for a short (30 ms), hard gamma-ray burst was detected by Swift on 9 May 2005 (GRB 050509b). No optical or radio counterpart was identified in follow--up observations. The tentative association of the GRB with a nearby giant elliptical galaxy at redshift z=0.2248 would imply the progenitor had traveled several tens of kpc from its point of origin, in agreement with expectations linking these events to the final merger of compact binaries driven by gravitational wave emission. We model the dynamical merger of such a system and the time--dependent evolution of the accretion tori thus created. The resulting energetics, variability, and expected durations are consistent with GRB 050509b originating from the tidal disruption of a neutron star by a stellar mass black hole, or of the merger of two neutron stars followed by prompt gravitational collapse of the massive remnant. We discuss how the available gamma-ray and X-ray data provides a probe for the nature of the relativistic ejecta and... 12. A discrete-time model for binary detection with rectangular hysteresis operators Science.gov (United States) Korman, Can E. 2006-02-01 The operation of a nonlinear binary detector with hysteresis is investigated. Prior models developed for continuous time inputs are extended for the computationally more efficient discrete-time inputs. The input to the rectangular hysteresis detector is modeled to be a binary signal in the presence of additive independent identically distributed noise. The rectangular hysteresis loop models one of a number of rate independent repeaters in an optical communication link. The link is terminated by a binary discriminator that is tuned to a particular bit duration. The study shows that key calculations to compute the bit error probability can be performed by employing the formalism of discrete Markov chains. 13. Estimate Lock Bit Binary Anti-collision Algorithm is Applied to RFID%预估计锁位RFID二进制防碰撞算法 Institute of Scientific and Technical Information of China (English) 王民; 王磊 2014-01-01 As RFID (radio frequency identification technology) from concept to enter the stage of commercial application,The tags collision problems of the RFID affect the completeness and correctness of data transmission. To solve the problem in a better way, DBS algorithm in electronic tag to the reader sends identification number when there are repeated to send information, makes the system channel utilization rate is low, at the same time identify efficiency reduced, an improved algorithm is proposed on the basis of binary anti-collision algorithm. First detect the location of collision bits, with only the collision position informa⁃tion method to reduce the total number of transmission according to the quantity. The fallback strategy is used to reduce the read⁃er sends the request command. After experimental verification, the algorithm is effective to reduce the search times and delay, im⁃prove the efficiency of the system identification.%随着RFID(射频识别技术)逐渐从概念步入到商业应用阶段，标签碰撞问题影响着数据传输的完整性和正确性，为了解决标签冲突，现有的DBS算法在电子标签向阅读器发送识别码时都存在重复信息的发送，使得系统信道利用率低，同时识别效率降低。为了提高RFID系统防冲撞算法的有效性，该文研究了一种改进的二进制冲撞比特搜索算法。首先检测冲撞比特的位置信息，通过只传输具体冲撞位信息的方法减少传输的总数据量。采用回退策略以降低阅读器发送请求命令的次数。经过实验验证，该算法有效的减少了搜索次数和时延，提高了系统识别效率。 14. A collision model for safety evaluation of autonomous intelligent cruise control. Science.gov (United States) Touran, A; Brackstone, M A; McDonald, M 1999-09-01 This paper describes a general framework for safety evaluation of autonomous intelligent cruise control in rear-end collisions. Using data and specifications from prototype devices, two collision models are developed. One model considers a train of four cars, one of which is equipped with autonomous intelligent cruise control. This model considers the car in front and two cars following the equipped car. In the second model, none of the cars is equipped with the device. Each model can predict the possibility of rear-end collision between cars under various conditions by calculating the remaining distance between cars after the front car brakes. Comparing the two collision models allows one to evaluate the effectiveness of autonomous intelligent cruise control in preventing collisions. The models are then subjected to Monte Carlo simulation to calculate the probability of collision. Based on crash probabilities, an expected value is calculated for the number of cars involved in any collision. It is found that given the model assumptions, while equipping a car with autonomous intelligent cruise control can significantly reduce the probability of the collision with the car ahead, it may adversely affect the situation for the following cars. 15. Multisource thermal model to the transverse momentum spectra in pp collisions at RHIC and LHC energies CERN Document Server Li, BC; Liu, F; Wen, XJ 2016-01-01 In an improved multisource thermal model, we systematically investigate the transverse momentum spectra in pp collisions at high energies ranging from 62.4 GeV to 7 TeV. The results are compared with the experimental data in RHIC and LHC. Based on the collision energy dependence of the source-excitation factors, we estimate the transverse momentum spectra in pp collisions at higher energies, potential future pp colliders operating at 33 and 100 TeV. 16. Modelling early stages of relativistic heavy-ion collisions Directory of Open Access Journals (Sweden) Ruggieri M. 2016-01-01 Full Text Available In this study we model early time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism. The dynamics of the many particles system produced by the decay is described by relativistic kinetic theory, taking into account the backreaction on the color field by solving self-consistently the kinetic and the field equations. Our main results concern isotropization and thermalization for a 1+1D expanding geometry. In case of small η/s (η/s ≲ 0.3 we find τisotropization ≈ 0.8 fm/c and τthermalization ≈ 1 fm/c in agreement with the common lore of hydrodynamics. 17. Large-scale model-based assessment of deer-vehicle collision risk. Science.gov (United States) Hothorn, Torsten; Brandl, Roland; Müller, Jörg 2012-01-01 Ungulates, in particular the Central European roe deer Capreolus capreolus and the North American white-tailed deer Odocoileus virginianus, are economically and ecologically important. The two species are risk factors for deer-vehicle collisions and as browsers of palatable trees have implications for forest regeneration. However, no large-scale management systems for ungulates have been implemented, mainly because of the high efforts and costs associated with attempts to estimate population sizes of free-living ungulates living in a complex landscape. Attempts to directly estimate population sizes of deer are problematic owing to poor data quality and lack of spatial representation on larger scales. We used data on >74,000 deer-vehicle collisions observed in 2006 and 2009 in Bavaria, Germany, to model the local risk of deer-vehicle collisions and to investigate the relationship between deer-vehicle collisions and both environmental conditions and browsing intensities. An innovative modelling approach for the number of deer-vehicle collisions, which allows nonlinear environment-deer relationships and assessment of spatial heterogeneity, was the basis for estimating the local risk of collisions for specific road types on the scale of Bavarian municipalities. Based on this risk model, we propose a new "deer-vehicle collision index" for deer management. We show that the risk of deer-vehicle collisions is positively correlated to browsing intensity and to harvest numbers. Overall, our results demonstrate that the number of deer-vehicle collisions can be predicted with high precision on the scale of municipalities. In the densely populated and intensively used landscapes of Central Europe and North America, a model-based risk assessment for deer-vehicle collisions provides a cost-efficient instrument for deer management on the landscape scale. The measures derived from our model provide valuable information for planning road protection and defining hunting quota. Open 18. Simple model of complete precessing black-hole-binary gravitational waveforms. Science.gov (United States) Hannam, Mark; Schmidt, Patricia; Bohé, Alejandro; Haegel, Leïla; Husa, Sascha; Ohme, Frank; Pratten, Geraint; Pürrer, Michael 2014-10-10 The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger, and ringdown, is one of the most pressing theoretical problems in the buildup to the era of GW astronomy. We present the first such model in the frequency domain, PhenomP, which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binary's mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying nonprecessing-binary model. The nonprecessing-binary waveforms are then twisted up with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, χ(p). All other parameters (total mass, sky location, orientation and polarization, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the model's fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations--although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modeling in the advanced-detector era. 19. Nucleate Pool Boiling of Pure Liquids and Binary Mixtures：part II—Analytical Model for Boiling Heat Transfer of Binary Mixtures on Smooth Tubes and Comparison of Analytical Models for both Pure Liqu Institute of Scientific and Technical Information of China (English) GuoqingWang; YingkeTan 1996-01-01 A combined physical model of bubbel growth is propsed along with a corresponding bubble growth model for binary mixtures on smooth tubes.Using the general model of Wang et al.[1].and the bubble growth model for binary mixtures,an analytical model for nucleate pool boiling heat transfer of binary mixtures on smooth tubes is developed.In addition,nucleate pool boiling heat transfer of pure liquids and binary mixtrues on a horizontal smooth tube was studied experimentally.The pure liquids and binary mixtures included water methanol,ehanol,and their binary mixtures.The analytical models for both pure liquids and binary mixtures are in good agreement with the experimental data. 20. Hunting for brown dwarf binaries and testing atmospheric models with X-Shooter CERN Document Server Manjavacas, E; Alcalá, J M; Zapatero-Osorio, M R; Béjar, V J S; Homeier, D; Bonnefoy, M; Smart, R L; Henning, T; Allard, F 2015-01-01 The determination of the brown dwarf binary fraction may contribute to the understanding of the substellar formation mechanisms. Unresolved brown dwarf binaries may be revealed through their peculiar spectra or the discrepancy between optical and near-infrared spectral type classification. We obtained medium-resolution spectra of 22 brown dwarfs with these characteristics using the X-Shooter spectrograph at the VLT. We aimed to identify brown dwarf binary candidates, and to test if the BT-Settl 2014 atmospheric models reproduce their observed spectra. To find binaries spanning the L-T boundary, we used spectral indices and compared the spectra of the selected candidates to single spectra and synthetic binary spectra. We used synthetic binary spectra with components of same spectral type to determine as well the sensitivity of the method to this class of binaries. We identified three candidates to be combination of L plus T brown dwarfs. We are not able to identify binaries with components of similar spectral ... 1. Modeling Vehicle Collision Angle in Traffic Crashes Based on Three-Dimensional Laser Scanning Data Directory of Open Access Journals (Sweden) Nengchao Lyu 2017-02-01 Full Text Available In road traffic accidents, the analysis of a vehicle’s collision angle plays a key role in identifying a traffic accident’s form and cause. However, because accurate estimation of vehicle collision angle involves many factors, it is difficult to accurately determine it in cases in which less physical evidence is available and there is a lack of monitoring. This paper establishes the mathematical relation model between collision angle, deformation, and normal vector in the collision region according to the equations of particle deformation and force in Hooke’s law of classical mechanics. At the same time, the surface reconstruction method suitable for a normal vector solution is studied. Finally, the estimation model of vehicle collision angle is presented. In order to verify the correctness of the model, verification of multi-angle collision experiments and sensitivity analysis of laser scanning precision for the angle have been carried out using three-dimensional (3D data obtained by a 3D laser scanner in the collision deformation zone. Under the conditions with which the model has been defined, validation results show that the collision angle is a result of the weighted synthesis of the normal vector of the collision point and the weight value is the deformation of the collision point corresponding to normal vectors. These conclusions prove the applicability of the model. The collision angle model proposed in this paper can be used as the theoretical basis for traffic accident identification and cause analysis. It can also be used as a theoretical reference for the study of the impact deformation of elastic materials. 2. Forecast Modelling via Variations in Binary Image-Encoded Information Exploited by Deep Learning Neural Networks. Science.gov (United States) Liu, Da; Xu, Ming; Niu, Dongxiao; Wang, Shoukai; Liang, Sai 2016-01-01 Traditional forecasting models fit a function approximation from dependent invariables to independent variables. However, they usually get into trouble when date are presented in various formats, such as text, voice and image. This study proposes a novel image-encoded forecasting method that input and output binary digital two-dimensional (2D) images are transformed from decimal data. Omitting any data analysis or cleansing steps for simplicity, all raw variables were selected and converted to binary digital images as the input of a deep learning model, convolutional neural network (CNN). Using shared weights, pooling and multiple-layer back-propagation techniques, the CNN was adopted to locate the nexus among variations in local binary digital images. Due to the computing capability that was originally developed for binary digital bitmap manipulation, this model has significant potential for forecasting with vast volume of data. The model was validated by a power loads predicting dataset from the Global Energy Forecasting Competition 2012. 3. Model of two-stream non-radial accretion for binary X-ray pulsars Energy Technology Data Exchange (ETDEWEB) Lipunov, V.M. (Sternberg Astronomical Inst., Moscow (USSR)) 1982-03-01 The general case of non-radial accretion is assumed to occur in real binary systems containing X-ray pulsars. The structure and the stability of the magnetosphere, the interaction between the magnetosphere and accreted matter, as well as evolution of neutron star in close binary system are examined within the framework of the two-stream model of nonradial accretion onto a magnetized neutron star. Observable parameters of X-ray pulsars are explained in terms of the model considered. 4. Modeling AGN outbursts from supermassive black hole binaries Directory of Open Access Journals (Sweden) Tanaka T. 2012-12-01 Full Text Available When galaxies merge to assemble more massive galaxies, their nuclear supermassive black holes (SMBHs should form bound binaries. As these interact with their stellar and gaseous environments, they will become increasingly compact, culminating in inspiral and coalescence through the emission of gravitational radiation. Because galaxy mergers and interactions are also thought to fuel star formation and nuclear black hole activity, it is plausible that such binaries would lie in gas-rich environments and power active galactic nuclei (AGN. The primary difference is that these binaries have gravitational potentials that vary – through their orbital motion as well as their orbital evolution – on humanly tractable timescales, and are thus excellent candidates to give rise to coherent AGN variability in the form of outbursts and recurrent transients. Although such electromagnetic signatures would be ideally observed concomitantly with the binary’s gravitational-wave signatures, they are also likely to be discovered serendipitously in wide-field, high-cadence surveys; some may even be confused for stellar tidal disruption events. I discuss several types of possible “smoking gun” AGN signatures caused by the peculiar geometry predicted for accretion disks around SMBH binaries. 5. Modeling of Ship Collision Risk Index Based on Complex Plane and Its Realization Directory of Open Access Journals (Sweden) Xiaoqin Xu 2016-07-01 Full Text Available Ship collision risk index is the basic and important concept in the domain of ship collision avoidance. In this paper, the advantages and deficiencies of the various calculation methods of ship collision risk index are pointed out. Then the ship collision risk model based on complex plane, which can well make up for the deficiencies of the widely-used evaluation model proposed by Kearon.J and Liu ruru is proposed. On this basis, the calculation method of collision risk index under the encountering situation of multi-ships is constructed, then the three-dimensional image and spatial curve of the risk index are figured out. Finally, single chip microcomputer is used to realize the model. And attaching this single chip microcomputer to ARPA is helpful to the decision-making of the marine navigators. 6. Statistical model predictions for p+p and Pb+Pb collisions at LHC NARCIS (Netherlands) Kraus, I.; Cleymans, J.; Oeschler, H.; Redlich, K.; Wheaton, S. 2009-01-01 Particle production in p+p and central collisions at LHC is discussed in the context of the statistical thermal model. For heavy-ion collisions, predictions of various particle ratios are presented. The sensitivity of several ratios on the temperature and the baryon chemical potential is studied in 7. Midrapidity inclusive densities in high energy pp collisions in additive quark model Science.gov (United States) Shabelski, Yu. M.; Shuvaev, A. G. 2016-08-01 High energy (CERN SPS and LHC) inelastic pp (pbar{p}) scattering is treated in the framework of the additive quark model together with Pomeron exchange theory. We extract the midrapidity inclusive density of the charged secondaries produced in a single quark-quark collision and investigate its energy dependence. Predictions for the π p collisions are presented. 8. A semi-holographic model for heavy-ion collisions CERN Document Server Iancu, Edmond 2014-01-01 We develop a semi-holographic model for the out-of-equilibrium dynamics during the partonic stages of an ultrarelativistic heavy-ion collision. The model combines a weakly-coupled hard sector, involving gluon modes with energy and momenta of the order of the saturation momentum and relatively large occupation numbers, with a strongly-coupled soft sector, which physically represents the soft gluons radiated by the hard partons. The hard sector is described by perturbative QCD, more precisely, by its semi-classical approximation (the classical Yang-Mills equations) which becomes appropriate when the occupation numbers are large. The soft sector is described by a marginally deformed conformal field theory, which in turn admits a holographic description in terms of classical Einstein's equations in$AdS_5$with a minimally coupled massless dilaton'. The model involve two free parameters which characterize the gauge-invariant couplings between the hard and soft sectors. Via these couplings, the hard modes provide... 9. Evaluation of interatomic potentials for noble gas atoms from rainbow scattering under axial channeling at Ag(1 1 1) surface by computer simulations based on binary collision approximation Energy Technology Data Exchange (ETDEWEB) Takeuchi, Wataru, E-mail: [email protected] 2016-01-01 The rainbow angles corresponding to pronounced peaks in the angular distributions of scattered projectiles with small angle, attributed to rainbow scattering (RS), under axial surface channeling conditions are strongly dependent on the interatomic potentials between projectiles and target atoms. The dependence of rainbow angles on normal energy of projectile energy to the target surface that has been experimentally obtained by Schüller and Winter (SW) (2007) for RS of He, Ne and Ar atoms from a Ag(1 1 1) surface with projectile energies of 3–60 keV was evaluated by the three-dimensional computer simulations using the ACOCT code based on the binary collision approximation with interatomic pair potentials. Consequently, the ACOCT results employing the Moliere pair potential with screening length correction close to adjustable one of O’Connor and Biersack (OB) formula are almost in agreement with the experimental ones, being self-consistent with the SW’s ones analyzed by computer simulations of classical trajectory calculations as RS from corrugated equipotential planes based on continuum potentials including the Moliere pair potential with screening length correction of the OB formula. 10. Heavy ion collisions with A = 10/sup 57/: Aspects of nuclear stability and the nuclear equation of state in coalescing neutron-star binary systems Energy Technology Data Exchange (ETDEWEB) Mathews, G.J.; Wilson, J.R.; Evans, C.R.; Detweiler, S.L. 1987-12-01 The dynamics of the final stages of the coalescence of two neturon stars (such as the binary pulsar PSR 1913+16) is an unsolved problem in astrophysics. Such systems are probably efficient generators of gravitational radiation, and may be significant contributors to heavy-element nucleosynthesis. The input physics for the study of such systems is similar to that required for the strudy of heavy-ion collision hydrodynamics; e.g., a finite temperature nuclear equation of state, properties of nuclei away from stability, etc. We discuss the development of a relativistic hydrodynamics code in three spatial dimensions for the purpose of studying such neutron-star systems. The properties of the mass-radius relation (determined by the nuclear equation of state) may lead to a proposed mechanism by which hot, highly neutronized matter is ejected from the coalescing stars. This material is photodisintegrated into a free (mostly) neutron gas which may subsequently experience rapid-neutron capture (r-process) nucleosynthesis. 15 refs., 4 figs. 11. Replacement collision sequence studies in iron CERN Document Server Hou, M; Becquart, C S 2002-01-01 The properties of replacement collision sequences (RCS) in iron and their contribution to radiation damage are studied as they are generated in atomic collision cascades with the binary collision approximation Marlowe. Length distributions of RCS in collision cascades generated by primaries with a couple of ten keV kinetic energies are predicted short. Whatever the interatomic potential employed, at least 90% of the generated RCS have a length of no more than three successive collisions, whatever the directions. This property was found for all the known phases of iron at standard pressure (bcc and fcc). The RCS length distributions are not significantly influenced by the temperature nor by the accurate form of the model describing the energy loss in RCS. Close to 50% of the stable Frenkel pairs (FP) created result from RCS that are shorter than the vacancy-interstitial recombination distance estimated on the basis of molecular dynamics calculations. The other half results from longer RCS (about five successiv... 12. Efficient modelling of particle collisions using a non-linear viscoelastic contact force CERN Document Server Ray, Shouryya; Fröhlich, Jochen 2015-01-01 In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an efficient approximate solution of sufficient accuracy for this problem which can be used in soft-sphere collision models for Discrete Element Methods and for particle transport in viscous fluids. First, by the choice of appropriate units, the number of governing parameters of the collision process is reduced to one, thus providing a dimensionless parameter that characterizes all such collisions up to dynamic similitude. It is a simple combination of known material parameters as well as initial conditions. A rigorous calculation of the collision time and restitution coefficient from the governing equations, in the form of a series expansion in this parameter is provided. Such a first principles calculation is particularly interesting from a theoretical perspective. Since the gov... 13. Testing eccentricity pumping mechanisms to model eccentric long period sdB binaries with MESA CERN Document Server Vos, Joris; Marchant, Pablo; Van Winckel, Hans 2015-01-01 Hot subdwarf-B stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts those objects to be circularised before the onset of Roche-lobe overflow (RLOF). We aim to find binary-evolution mechanisms that can explain these eccentric long-period orbits, and reproduce the currently observed period-eccentricity diagram. Three different processes are considered; tidally-enhanced wind mass-loss, phase-dependent RLOF on eccentric orbits and the interaction between a circumbinary disk and the binary. The binary module of the stellar-evolution code MESA (Modules for Experiments in Stellar Astrophysics) is extended to include the eccentricity-pumping processes. The effects of different input parameters on the final period and eccentricity of a binary-evolution model are tested with MESA. The end products of models with only tidally-enhanced wind mass-loss can indeed be eccentric, but these models need to lose too much mass, and invariably end up with a helium ... 14. Synthetic model of the gravitational wave background from evolving binary compact objects Science.gov (United States) Dvorkin, Irina; Uzan, Jean-Philippe; Vangioni, Elisabeth; Silk, Joseph 2016-11-01 Modeling the stochastic gravitational wave background from various astrophysical sources is a key objective in view of upcoming observations with ground- and space-based gravitational wave observatories such as Advanced LIGO, VIRGO, eLISA, and the pulsar timing array. We develop a synthetic model framework that follows the evolution of single and binary compact objects in an astrophysical context. We describe the formation and merger rates of binaries, the evolution of their orbital parameters with time, and the spectrum of emitted gravitational waves at different stages of binary evolution. Our approach is modular and allows us to test and constrain different ingredients of the model, including stellar evolution, black hole formation scenarios, and the properties of binary systems. We use this framework in the context of a particularly well-motivated astrophysical setup to calculate the gravitational wave background from several types of sources, including inspiraling stellar-mass binary black holes that have not merged during a Hubble time. We find that this signal, albeit weak, has a characteristic shape that can help constrain the properties of binary black holes in a way complementary to observations of the background from merger events. We discuss possible applications of our framework in the context of other gravitational wave sources, such as supermassive black holes. 15. Modeling Multi-Wavelength Stellar Astrometry. I. SIM Lite Observations of Interacting Binaries CERN Document Server Coughlin, Jeffrey L; Harrison, Thomas E; Hoard, D W; Ciardi, David R; Benedict, G Fritz; Howell, Steve B; McArthur, Barbara E; Wachter, Stefanie 2010-01-01 Interacting binaries consist of a secondary star which fills or is very close to filling its Roche lobe, resulting in accretion onto the primary star, which is often, but not always, a compact object. In many cases, the primary star, secondary star, and the accretion disk can all be significant sources of luminosity. SIM Lite will only measure the photocenter of an astrometric target, and thus determining the true astrometric orbits of such systems will be difficult. We have modified the Eclipsing Light Curve code (Orosz & Hauschildt 2000) to allow us to model the flux-weighted reflex motions of interacting binaries, in a code we call REFLUX. This code gives us sufficient flexibility to investigate nearly every configuration of interacting binary. We find that SIM Lite will be able to determine astrometric orbits for all sufficiently bright interacting binaries where the primary or secondary star dominates the luminosity. For systems where there are multiple components that comprise the spectrum in the op... 16. Memory-Based Simple Heuristics as Attribute Substitution: Competitive Tests of Binary Choice Inference Models. Science.gov (United States) Honda, Hidehito; Matsuka, Toshihiko; Ueda, Kazuhiro 2016-07-20 Some researchers on binary choice inference have argued that people make inferences based on simple heuristics, such as recognition, fluency, or familiarity. Others have argued that people make inferences based on available knowledge. To examine the boundary between heuristic and knowledge usage, we examine binary choice inference processes in terms of attribute substitution in heuristic use (Kahneman & Frederick, 2005). In this framework, it is predicted that people will rely on heuristic or knowledge-based inference depending on the subjective difficulty of the inference task. We conducted competitive tests of binary choice inference models representing simple heuristics (fluency and familiarity heuristics) and knowledge-based inference models. We found that a simple heuristic model (especially a familiarity heuristic model) explained inference patterns for subjectively difficult inference tasks, and that a knowledge-based inference model explained subjectively easy inference tasks. These results were consistent with the predictions of the attribute substitution framework. Issues on usage of simple heuristics and psychological processes are discussed. 17. ELLC - a fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets CERN Document Server Maxted, P F L 2016-01-01 Very high quality light curves are now available for thousands of detached eclipsing binary stars and transiting exoplanet systems as a result of surveys for transiting exoplanets and other large-scale photometric surveys. I have developed a binary star model (ELLC) that can be used to analyse the light curves of detached eclipsing binary stars and transiting exoplanet systems that is fast and accurate, and that can include the effects of star spots, Doppler boosting and light-travel time within binaries with eccentric orbits. The model represents the stars as triaxial ellipsoids. The apparent flux from the binary is calculated using Gauss-Legendre integration over the ellipses that are the projection of these ellipsoids on the sky. The model can also be used to calculate the flux-weighted radial velocity of the stars during an eclipse (Rossiter-McLaughlin effect). The main features of the model have tested by comparison to observed data and other light curve models. The model is found to be accurate enough t... 18. PREDICTION OF THE MIXING ENTHALPIES OF BINARY LIQUID ALLOYS BY MOLECULAR INTERACTION VOLUME MODEL Institute of Scientific and Technical Information of China (English) H.W.Yang; D.P.Tao; Z.H.Zhou 2008-01-01 The mixing enthalpies of 23 binary liquid alloys are calculated by molecular interaction volume model (MIVM), which is a two-parameter model with the partial molar infinite dilute mixing enthalpies. The predicted values are in agreement with the experimental data and then indicate that the model is reliable and convenient. 19. Charged-particle pseudorapidity distributions in Au+Au collisions at RHIC Institute of Scientific and Technical Information of China (English) WANG Zeng-Wei; JIANG Zhi-Jin 2009-01-01 Using the Glauber model, we present the formulas for calculating the numbers of participants,spectators and binary nucleon-nucleon collisions. Based on this work, we get the pseudorapidity distributions of charged particles as the function of the impact parameter in nucleus-nucleus collisions. The theoretical results agree well with the experimental observations made by the BRAHMS Collaboration in Au+Au collisions at √SNN=200 GeV in different centrality bins over the whole pseudorapidity range. 20. A Cross-domain Survey of Metrics for Modelling and Evaluating Collisions Directory of Open Access Journals (Sweden) Jeremy A. Marvel 2014-09-01 Full Text Available This paper provides a brief survey of the metrics for measuring probability, degree, and severity of collisions as applied to autonomous and intelligent systems. Though not exhaustive, this survey evaluates the state-of-the-art of collision metrics, and assesses which are likely to aid in the establishment and support of autonomous system collision modelling. The survey includes metrics for 1 robot arms; 2 mobile robot platforms; 3 nonholonomic physical systems such as ground vehicles, aircraft, and naval vessels, and; 4 virtual and mathematical models. 1. Anomalous transport model study of chiral magnetic effects in heavy ion collisions CERN Document Server Sun, Yifeng; Li, Feng 2016-01-01 Using an anomalous transport model for massless quarks, we study the effect of magnetic field on the elliptic flows of quarks and antiquarks in relativistic heavy ion collisions. With initial conditions from a blast wave model and assuming that the strong magnetic field produced in non-central heavy ion collisions can last for a sufficiently long time, we obtain an appreciable electric quadrupole moment in the transverse plane of a heavy ion collision, which subsequently leads to a splitting between the elliptic flows of quarks and antiquarks as expected from the chiral magnetic wave formed in the produced QGP and observed in experiments at the Relativistic Heavy Ion Collider (RHIC). 2. A Cross-Domain Survey of Metrics for Modelling and Evaluating Collisions Directory of Open Access Journals (Sweden) Jeremy A. Marvel 2014-09-01 Full Text Available This paper provides a brief survey of the metrics for measuring probability, degree, and severity of collisions as applied to autonomous and intelligent systems. Though not exhaustive, this survey evaluates the state-of-the-art of collision metrics, and assesses which are likely to aid in the establishment and support of autonomous system collision modelling. The survey includes metrics for 1 robot arms; 2 mobile robot platforms; 3 nonholonomic physical systems such as ground vehicles, aircraft, and naval vessels, and; 4 virtual and mathematical models. 3. Relativistic model of neutron stars in X-ray binary Science.gov (United States) Kalam, Mehedi; Hossein, Sk Monowar; Islam, Rabiul; Molla, Sajahan 2017-02-01 In this paper, we study the inner structure of some neutron stars from theoretical as well as observational points of view. We calculate the probable radii, compactness (u) and surface redshift (Zs) of five neutron stars (X-ray binaries) namely 4U 1538-52, LMC X-4, 4U 1820-30, 4U 1608-52, EXO 1745-248. Here, we propose a stiff equation of state (EoS) of matter distribution which relates pressure with matter density. Finally, we check the stability of such kind of theoretical structure. 4. INVESTIGATION OF DIFFERENT MODELS OF COMBINED PARALLEL FLASH BINARY CYCLES OpenAIRE A. Jafar Yazdi* 2017-01-01 The aim of this paper is a comparative study of the different geothermal power plant concepts, based on the energy and exergy analysis. The cycles studied in this paper are the combination of single and double flash power plants with two different ORC cycles as basic Organic Rankine Cycle (ORC), ORC with IHE, regenerative ORC and regenerative ORC with an IHE. The main gain due to using combined flash-binary power plants with various types of ORCs is to achieve optimum and efficient energy uti... 5. Wide low-mass binary model for the origin of axially symmetric non-thermal radio sources Energy Technology Data Exchange (ETDEWEB) Kool, M. de; Heuvel, E.P.J. van den 1985-10-17 An accreting binary model has been proposed by recent workers to account for the origin of the axially symmetric non-thermal radio sources. The authors show that the only type of binary system that can produce the observed structural properties, is a relatively wide neutron star binary, in which the companion of the neutron star is a low-mass giant. Binaries of this type are expected to resemble closely the eight brightest galactic bulge X-ray sources as well as the progenitors of the two wide radio pulsar binaries. 6. Centrality Dependence of Hadron Multiplicities in Nuclear Collisions in the Dual Parton Model CERN Document Server Capella, A 2001-01-01 We show that, even in purely soft processes, the hadronic multiplicity in nucleus-nucleus interactions contains a term that scales with the number of binary collisions. In the absence of shadowing corrections, this term dominates at mid rapidities and high energies. Shadowing corrections are calculated as a function of impact parameter and the centrality dependence of mid-rapidity multiplicities is determined. The multiplicity per participant increases with centrality with a rate that increases between SPS and RHIC energies, in agreement with experiment. 7. From many body wee partons dynamics to perfect fluid: a standard model for heavy ion collisions Energy Technology Data Exchange (ETDEWEB) Venugopalan, R. 2010-07-22 We discuss a standard model of heavy ion collisions that has emerged both from experimental results of the RHIC program and associated theoretical developments. We comment briefly on the impact of early results of the LHC program on this picture. We consider how this standard model of heavy ion collisions could be solidified or falsified in future experiments at RHIC, the LHC and a future Electro-Ion Collider. 8. X-ray-binary spectra in the lamp post model CERN Document Server Vincent, F H; Zdziarski, A A; Madej, J 2016-01-01 [Abridged] Context. The high-energy radiation from black-hole binaries may be due to the reprocessing of a lamp located on the black hole axis, emitting X-rays. The observed spectrum is made of 3 components: the direct spectrum; the thermal bump; and the reflected spectrum made of the Compton hump and the iron-line complex. Aims. We aim at computing accurately the complete reprocessed spectrum (thermal bump + reflected) of black-hole binaries over the entire X-ray band. We also determine the strength of the direct component. Our choice of parameters is adapted to a source showing an important thermal component. Methods. We compute in full GR the illumination of a thin disk by a lamp along the rotation axis. We use the ATM21 radiative transfer code to compute the spectrum emitted along the disk. We ray trace this local spectrum to determine the reprocessed spectrum as observed at infinity. We discuss the dependence of the local and ray-traced spectra on the emission angle and spin. Results. We show the importa... 9. ellc: A fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets Science.gov (United States) Maxted, P. F. L. 2016-06-01 Context. Very high quality light curves are now available for thousands of detached eclipsing binary stars and transiting exoplanet systems as a result of surveys for transiting exoplanets and other large-scale photometric surveys. Aims: I have developed a binary star model (ellc) that can be used to analyse the light curves of detached eclipsing binary stars and transiting exoplanet systems that is fast and accurate, and that can include the effects of star spots, Doppler boosting and light-travel time within binaries with eccentric orbits. Methods: The model represents the stars as triaxial ellipsoids. The apparent flux from the binary is calculated using Gauss-Legendre integration over the ellipses that are the projection of these ellipsoids on the sky. The model can also be used to calculate the flux-weighted radial velocity of the stars during an eclipse (Rossiter-McLaghlin effect). The main features of the model have been tested by comparison to observed data and other light curve models. Results: The model is found to be accurate enough to analyse the very high quality photometry that is now available from space-spaced instruments, flexible enough to model a wide range of eclipsing binary stars and extrasolar planetary systems, and fast enough to enable the use of modern Monte Carlo methods for data analysis and model testing. The software package is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/591/A111 10. Light curve modeling of eclipsing binaries towards the constellation of Carina CERN Document Server Dey, Aniruddha; Kumar, Subhash; Bhardwaj, Hrishabh; Bhattacharya, Barnmoy; Richa,; Sharma, Angad; Chauhan, Akshyata; Tiwari, Neha; Kaur, Sharanjit; Kumar, Suman; Abhishek, 2015-01-01 We present a detailed V-band photometric light curve modeling of 30 eclipsing binaries using the data from Pietrukowicz et al. (2009) collected with the European Southern Observatory Very Large Telescope (ESO VLT) of diameter 8-m. The light curve of these 30 eclipsing binaries were selected out of 148 of them available in the database on the basis of complete phase coverage, regular and smooth phased light curve shapes. Eclipsing binaries play pivotal role in the direct measurement of astronomical distances more accurately simply from their geometry of light curves. The accurate value of Hubble constant (H0) which measures the rate of expansion of the Universe heavily relies on extragalactic distance scale measurements. Classification of the selected binary stars in the sample were done, preliminarily on the basis of Fourier parameters in the a2-a4 plane and final classification was obtained from the Roche lobe geometry. Out of these 30 eclipsing binaries, only one was found to be detached binary system while... 11. Confronting Numerical Relativity With Nature: A model-independent characterization of binary black-hole systems in LIGO Science.gov (United States) Jani, Karan; Clark, James; Shoemaker, Deirdre; LIGO Scientific Collaboration; Virgo Collaboration 2016-03-01 Stellar and Intermediate mass binary black hole systems (10-1000 solar masses) are likely to be among the strongest sources of gravitational wave detection in Advanced LIGO. In this talk we discuss the prospects for the detection and characterization of these extreme astrophysical system using robust, morphology-independent analysis techniques. In particular, we demonstrate how numerical relativity simulations of black hole collisions may be combined with waveform reconstructions to constrain properties of a binary black-hole system using only exact solutions from general relativity and any potential gravitational wave signal in the data. 12. Beyond the thermal model in relativistic heavy-ion collisions CERN Document Server Wolschin, Georg 2016-01-01 Deviations from thermal distribution functions of produced particles in relativistic heavy-ion collisions are discussed as indicators for nonequilibrium processes. The focus is on rapidity distributions of produced charged hadrons as functions of collision energy and centrality which are used to infer the fraction of produced particles from a central fireball as compared to the one from the fragmentation sources that are out of equilibrium with the rest of the system. Overall thermal equilibrium would only be reached for large times t -> infinity. 13. Control for Population Structure and Relatedness for Binary Traits in Genetic Association Studies via Logistic Mixed Models Science.gov (United States) Chen, Han; Wang, Chaolong; Conomos, Matthew P.; Stilp, Adrienne M.; Li, Zilin; Sofer, Tamar; Szpiro, Adam A.; Chen, Wei; Brehm, John M.; Celedón, Juan C.; Redline, Susan; Papanicolaou, George J.; Thornton, Timothy A.; Laurie, Cathy C.; Rice, Kenneth; Lin, Xihong 2016-01-01 Linear mixed models (LMMs) are widely used in genome-wide association studies (GWASs) to account for population structure and relatedness, for both continuous and binary traits. Motivated by the failure of LMMs to control type I errors in a GWAS of asthma, a binary trait, we show that LMMs are generally inappropriate for analyzing binary traits when population stratification leads to violation of the LMM’s constant-residual variance assumption. To overcome this problem, we develop a computationally efficient logistic mixed model approach for genome-wide analysis of binary traits, the generalized linear mixed model association test (GMMAT). This approach fits a logistic mixed model once per GWAS and performs score tests under the null hypothesis of no association between a binary trait and individual genetic variants. We show in simulation studies and real data analysis that GMMAT effectively controls for population structure and relatedness when analyzing binary traits in a wide variety of study designs. PMID:27018471 14. Three-dimensional computer simulation at vehicle collision using dynamic model. Application to various collision types; Rikigaku model ni yoru jidosha shototsuji no sanjigen kyodo simulation. Shushu no shototsu keitai eno tekiyo Energy Technology Data Exchange (ETDEWEB) Abe, M.; Morisawa, M. [Musashi Institute of Technology, Tokyo (Japan); Sato, T. [Keio University, Tokyo (Japan); Kobayashi, K. [Molex-Japan Co. Ltd., Tokyo (Japan) 1997-10-01 The past study of safety at vehicle collision pays attention to phenomena within the short time from starting collision, and the behavior of rollover is studied separating from that at collision. Most simulations of traffic accident are two-dimensional simulations. Therefore, it is indispensable for vehicle design to the analyze three-dimensional and continuous behavior from crash till stopping. Accordingly, in this study, the three-dimensional behavior of two vehicles at collision was simulated by computer using dynamic models. Then, by comparison of the calculated results with real vehicles collision test data, it was confirmed that dynamic model of this study was reliable. 10 refs., 6 figs., 3 tabs. 15. Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models CERN Document Server Almog, Assaf 2014-01-01 The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of time series of activity of their fundamental elements (such as stocks or neurons respectively). While the main focus of time series analysis is on the magnitude of temporal increments, a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. In this paper we provide further evidence of this by showing strong nonlinear relationships between binary and non-binary properties of financial time series. We then introduce an information-theoretic approach to the analysis of the binary signature of single and multiple time series. Through the definition of maximum-entropy ensembles of binary matrices, we quantify the information encoded into the simplest binary properties of real time series and identify the most informative property given a set of measurements. Our formalism is able to replicate the observed binary/non-binary relations very well, and to mathematically... 16. Updates to the dust-agglomerate collision model and implications for planetesimal formation Science.gov (United States) Blum, Jürgen; Brisset, Julie; Bukhari, Mohtashim; Kothe, Stefan; Landeck, Alexander; Schräpler, Rainer; Weidling, René 2016-10-01 Since the publication of our first dust-agglomerate collision model in 2010, several new laboratory experiments have been performed, which have led to a refinement of the model. Substantial improvement of the model has been achieved in the low-velocity regime (where we investigated the abrasion in bouncing collisions), in the high-velocity regime (where we have studied the fragmentation behavior of colliding dust aggregates), in the erosion regime (in which we extended the experiments to impacts of small projectile agglomerates into large target agglomerates), and in the very-low velocity collision regime (where we studied further sticking collisions). We also have applied the new dust-agglomerate collision model to the solar nebula conditions and can constrain the potential growth of planetesimals by mass transfer to a very small parameter space, which makes this growth path very unlikely. Experimental examples, an outline of the new collision model, and applications to dust agglomerate growth in the solar nebula will be presented. 17. Analysis of statistical thermodynamic model for binary protein adsorption equilibria on cation exchange adsorbent Institute of Scientific and Technical Information of China (English) ZHOU Xiaopeng; SU Xueli; SUN Yan 2007-01-01 A study of nonlinear competitive adsorption equilibria of proteins is of fundamental importance in understanding the behavior of preparative chromatographic separation.This work describes the nonlinear binary protein adsorption equilibria on ion exchangers by the statistical thermodynamic (ST) model.The single-component and binary protein adsorption isotherms of bovine hemoglobin (Hb) and bovine serum albumin(BSA)on SP Sepharose FF were determined by batch adsorption experiments in 0.05 mol/L sodium acetate buffer at three pH values(4.5,5.0 and 5.5)and three NaCl concentrations(0.05,0.10 and 0.15 mol/L)at pH 5.0.The ST model was found to depict the effects of pH and ionic strength on the single-component equilibria well,with model parameters depending on the pH and ionic strength.Moreover,the ST model gave acceptable fitting to the binary adsorption data with the fltted singlecomponent model parameters,leading to the estimation of the binary ST model parameter.The effects of pH and ionic strength on the model parameters are reasonably interpreted by the electrostatic and thermodynamic theories.Results demonstrate the availability of the ST model for describing nonlinear competitive protein adsorption equilibria in the presence of two proteins. 18. Large-scale model-based assessment of deer-vehicle collision risk. Directory of Open Access Journals (Sweden) Torsten Hothorn Full Text Available Ungulates, in particular the Central European roe deer Capreolus capreolus and the North American white-tailed deer Odocoileus virginianus, are economically and ecologically important. The two species are risk factors for deer-vehicle collisions and as browsers of palatable trees have implications for forest regeneration. However, no large-scale management systems for ungulates have been implemented, mainly because of the high efforts and costs associated with attempts to estimate population sizes of free-living ungulates living in a complex landscape. Attempts to directly estimate population sizes of deer are problematic owing to poor data quality and lack of spatial representation on larger scales. We used data on >74,000 deer-vehicle collisions observed in 2006 and 2009 in Bavaria, Germany, to model the local risk of deer-vehicle collisions and to investigate the relationship between deer-vehicle collisions and both environmental conditions and browsing intensities. An innovative modelling approach for the number of deer-vehicle collisions, which allows nonlinear environment-deer relationships and assessment of spatial heterogeneity, was the basis for estimating the local risk of collisions for specific road types on the scale of Bavarian municipalities. Based on this risk model, we propose a new "deer-vehicle collision index" for deer management. We show that the risk of deer-vehicle collisions is positively correlated to browsing intensity and to harvest numbers. Overall, our results demonstrate that the number of deer-vehicle collisions can be predicted with high precision on the scale of municipalities. In the densely populated and intensively used landscapes of Central Europe and North America, a model-based risk assessment for deer-vehicle collisions provides a cost-efficient instrument for deer management on the landscape scale. The measures derived from our model provide valuable information for planning road protection and defining 19. Logic functions and equations binary models for computer science CERN Document Server Posthoff, Christian 2004-01-01 Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications. Based on our long-time teaching experience, a comprehensive presentation of these concepts is given, especially emphasising a thorough understanding as well as numerical and computer-based solution methods. Any applications and examples from all the respective areas are given that can be dealt with in a unified way. They offer a broad understanding of the recent developments in Computer Science and are directly applicable in professional life. Logic Functions and Equations is highly recommended for a one- or two-semester course in many Computer Science or computer Science-oriented programmes. It allows students an easy high-level access to these methods and enables sophist... 20. Testing Models of Circum-Binary-AGN Accretion for PSO J334.2028+01.4075 Science.gov (United States) Foord, Adi; Gultekin, Kayhan; Reynolds, Mark 2017-08-01 We present analysis of new Chandra data of PSO J334.2028+01.4075 (PSO J334 hereafter), a strong binary AGN candidate discovered by Liu et al. (2015) based on periodic variation of the optical flux. Recent radio coverage presented in Mooley et al. (2017) further supports that PSO J334 is a binary black hole system, as the quasar was found to be lobe-dominated with a twisted radio structure, possibly due to a precessing jet. With no prior X-ray coverage for PSO J334, our new 50 ksec Chandra observation allows for the unique opportunity to differentiate between a single or binary-AGN system, and if a binary, can characterize the mode of accretion. The two most basic sets of predictions via simulations of circum-binary accretion model are a “cavity”, where the inner region of the accretion disk is mostly empty and emission is truncated blueward of the wavelength associated with the temperature of the innermost ring, or “minidisks”, where there is substantial accretion onto one or both of the members of the binary, each with their own shock-heated thin-disk accretion system. We find the X-ray emission to be well-fit with a heavily absorbed power-law, incompatible with the cavity scenario. Further, we construct an SED of PSO J334 by combining radio through X-ray observations and compare it to standard QSO SEDs. We discuss the implications of the comparison between the SED of PSO J334 and that of a single AGN, and assess the likelihood of the binary model for PSO J334. 1. Model-Based Optimization of Airborne Collision Avoidance Logic Science.gov (United States) 2010-01-26 According to Kuchar and Drumm [4], the mid-air collision of a Russian Tu-154 and a DHL B-757 over Uberlingen in 2002 may have been averted if TCAS...had properly reversed the RA it had issued to the DHL aircraft. The current version of TCAS incorporates reversal logic. According to TCAS monitoring 2. Integrating economic and psychological insights in binary choice models with social interactions CERN Document Server Ostasiewicz, K; Magnuszewski, P; Radosz, A; Sendzimir, J; Tyc, M H; Goliczewski, Piotr; Magnuszewski, Piotr; Ostasiewicz, Katarzyna; Radosz, Andrzej; Sendzimir, Jan; Tyc, Michal H. 2006-01-01 We investigate a class of binary choice models with social interactions. We propose a unifying perspective that integrates economic models using a utility function and psychological models using an impact function. A general approach for analyzing the equilibrium structure of these models within mean-field approximation is developed. It is shown that within a mean-field approach both the utility function and the impact function models are equivalent to threshold models. The interplay between heterogeneity and randomness in model formulation is discussed. A general framework is applied in a number of examples leading to some well-known models but also showing the possibility of more complex dynamics related to multiple equilibria. Our synthesis can provide a basis for many practical applications extending the scope of binary choice models. 3. One-dimensional collision carts computer model and its design ideas for productive experiential learning CERN Document Server Wee, Loo Kang 2012-01-01 We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In the field of designing computer simulations, we discuss briefly three pedagogical considerations such as 1) consistent simulation world view with pen paper representation, 2) data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and 3) game for simple concept testing that can further support learning. We also suggest using physical world setup to be augmented complimentarily with simulation while highlighting three advantages of real collision carts equipment like tacit 3D experience, random errors in measurement and conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive,... 4. Gluon production in the Color Glass Condensate model of collisions of ultrarelativistic finite nuclei CERN Document Server Krasnitz, A; Venugopalan, R; Krasnitz, Alex; Nara, Yasushi; Venugopalan, Raju 2003-01-01 We extend previous work on high energy nuclear collisions in the Color Glass Condensate model to study collisions of finite ultrarelativistic nuclei. The changes implemented include a) imposition of color neutrality at the nucleon level and b) realistic nuclear matter distributions of finite nuclei. The saturation scale characterizing the fields of color charge is explicitly position dependent,$\\Lambda_s=\\Lambda_s(x_T)$. We compute gluon distributions both before and after the collisions. The gluon distribution in the nuclear wavefunction before the collision is significantly suppressed below the saturation scale when compared to the simple McLerran-Venugopalan model prediction, while the behavior at large momentum$p_T\\gg \\Lambda_s$remains unchanged. We study the centrality dependence of produced gluons and compare it to the centrality dependence of charged hadrons exhibited by the RHIC data. We demonstrate the geometrical scaling property of the initial gluon transverse momentum distributions for differen... 5. Characteristics of particle production in high energy nuclear collisions a model-based analysis CERN Document Server Guptaroy, P; Bhattacharya, S; Bhattacharya, D P 2002-01-01 The present work pertains to the production of some very important negatively charged secondaries in lead-lead and gold-gold collisions at AGS, SPS and RHIC energies. We would like to examine here the role of the particular version of sequential chain model (SCM), which was applied widely in the past in analysing data on various high-energy hadronic collisions, in explaining now the latest findings on the features of particle production in the relativistic nucleus-nucleus collisions. The agreement between the model of our choice and the measured data is found to be modestly satisfactory in cases of the most prominent and abundantly produced varieties of the secondaries in the above-stated two nuclear collisions. (25 refs). 6. One-dimensional collision carts computer model and its design ideas for productive experiential learning Science.gov (United States) Wee, Loo Kang 2012-05-01 We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In designing the simulations, we discuss briefly three pedagogical considerations namely (1) a consistent simulation world view with a pen and paper representation, (2) a data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and (3) a game for simple concept testing that can further support learning. We also suggest using a physical world setup augmented by simulation by highlighting three advantages of real collision carts equipment such as a tacit 3D experience, random errors in measurement and the conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive, and we hope teachers will find the simulation useful in their own classes. 7. On the multiplicity distribution in statistical model: (II) most central collisions CERN Document Server Xu, Hao-jie 2016-01-01 This work is a continuation of our effort [arXiv:1602.06378] to investigate the statistical expectations for cumulants of (net-conserved) charge distributions in relativistic heavy ion collisions, by using a simple but quantitatively more realistic geometric model, i.e. optical Glauber model. We suggest a new approach for centrality definition in studying of multiplicity fluctuations, which aim at eliminating the uncertainties between experimental measurements and theoretical calculations, as well as redoubling the statistics. We find that the statistical expectations of multiplicity distribution mimic the negative binomial distribution at non-central collisions, but tend to approach the Poisson one at most central collisions due to the "boundary effect" from distribution of volume. We conclude that the collisional geometry (distribution of volume and its fluctuations) play a crucial role in studying of event-by-event multiplicity fluctuations in relativistic heavy ion collisions. 8. Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects CERN Document Server Hannam, Mark 2013-01-01 The inspiral and merger of two orbiting black holes is among the most promising sources for the first (hopefully imminent) direct detection of gravitational waves (GWs), and measurements of these signals could provide a wealth of information about astrophysics, fundamental physics and cosmology. Detection and measurement require a theoretical description of the GW signals from all possible black-hole-binary configurations, which can include complicated precession effects due to the black-hole spins. Modelling the GW signal from generic precessing binaries is therefore one of the most urgent theoretical challenges facing GW astronomy. This article briefly reviews the phenomenology of generic-binary dynamics and waveforms, and recent advances in modelling them. 9. Clusterwise HICLAS: a generic modeling strategy to trace similarities and differences in multiblock binary data. Science.gov (United States) Wilderjans, T F; Ceulemans, E; Kuppens, P 2012-06-01 In many areas of the behavioral sciences, different groups of objects are measured on the same set of binary variables, resulting in coupled binary object × variable data blocks. Take, as an example, success/failure scores for different samples of testees, with each sample belonging to a different country, regarding a set of test items. When dealing with such data, a key challenge consists of uncovering the differences and similarities between the structural mechanisms that underlie the different blocks. To tackle this challenge for the case of a single data block, one may rely on HICLAS, in which the variables are reduced to a limited set of binary bundles that represent the underlying structural mechanisms, and the objects are given scores for these bundles. In the case of multiple binary data blocks, one may perform HICLAS on each data block separately. However, such an analysis strategy obscures the similarities and, in the case of many data blocks, also the differences between the blocks. To resolve this problem, we proposed the new Clusterwise HICLAS generic modeling strategy. In this strategy, the different data blocks are assumed to form a set of mutually exclusive clusters. For each cluster, different bundles are derived. As such, blocks belonging to the same cluster have the same bundles, whereas blocks of different clusters are modeled with different bundles. Furthermore, we evaluated the performance of Clusterwise HICLAS by means of an extensive simulation study and by applying the strategy to coupled binary data regarding emotion differentiation and regulation. 10. Thermal Radio Emission from Radiative Shocks in Colliding Wind Binaries Science.gov (United States) Montes, G.; González, R. F.; Cantó, J.; Pérez-Torres, M. A.; Alberdi, A. 2011-10-01 We present a semi-analytic model for computing the thermal radio continuum emission from radiative shocks within colliding wind binaries. Assuming a thin shell approximation, we calculate the contribution of the wind collision region (WCR) to the total thermal emission for close binaries. We investigate the effect of the binary separation on the total spectrum. In addition, we point out the relevance of taking into account this contribution for the correct interpretation of the observations, and the accuracy of parameters derived from them. 11. D-meson observables in heavy-ion collisions at LHC with EPOSHQ model Science.gov (United States) Ozvenchuk, Vitalii; Aichelin, Joerg; Gossiaux, Pol-Bernard; Guiot, Benjamin; Nahrgang, Marlene; Werner, Klaus 2016-11-01 We study the propagation of charm quarks in the quark-gluon plasma (QGP) created in ultrarelativistic heavy-ion collisions at LHC within EPOSHQ model. The interactions of heavy quarks with the light partons in ultrarelativistic heavy-ion collisions through the collisional and radiative processes lead to a large suppression of final D-meson spectra at high transverse momentum and a finite D-meson elliptic flow. Our results are in a good agreement with the available experimental data. 12. Mean transverse momenta correlations in hadron-hadron collisions in MC toy model with repulsing strings Energy Technology Data Exchange (ETDEWEB) Altsybeev, Igor [St. Petersburg State University (Russian Federation) 2016-01-22 In the present work, Monte-Carlo toy model with repulsing quark-gluon strings in hadron-hadron collisions is described. String repulsion creates transverse boosts for the string decay products, giving modifications of observables. As an example, long-range correlations between mean transverse momenta of particles in two observation windows are studied in MC toy simulation of the heavy-ion collisions. 13. Towards a construction of inclusive collision cross-sections in the massless Nelson model OpenAIRE 2011-01-01 The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the i... 14. Collision detection and modeling of rigid and deformable objects in laparoscopic simulator Science.gov (United States) Dy, Mary-Clare; Tagawa, Kazuyoshi; Tanaka, Hiromi T.; Komori, Masaru 2015-03-01 Laparoscopic simulators are viable alternatives for surgical training and rehearsal. Haptic devices can also be incorporated with virtual reality simulators to provide additional cues to the users. However, to provide realistic feedback, the haptic device must be updated by 1kHz. On the other hand, realistic visual cues, that is, the collision detection and deformation between interacting objects must be rendered at least 30 fps. Our current laparoscopic simulator detects the collision between a point on the tool tip, and on the organ surfaces, in which haptic devices are attached on actual tool tips for realistic tool manipulation. The triangular-mesh organ model is rendered using a mass spring deformation model, or finite element method-based models. In this paper, we investigated multi-point-based collision detection on the rigid tool rods. Based on the preliminary results, we propose a method to improve the collision detection scheme, and speed up the organ deformation reaction. We discuss our proposal for an efficient method to compute simultaneous multiple collision between rigid (laparoscopic tools) and deformable (organs) objects, and perform the subsequent collision response, with haptic feedback, in real-time. 15. Removing Specification Errors from the Usual Formulation of Binary Choice Models Directory of Open Access Journals (Sweden) P.A.V.B. Swamy 2016-06-01 Full Text Available We develop a procedure for removing four major specification errors from the usual formulation of binary choice models. The model that results from this procedure is different from the conventional probit and logit models. This difference arises as a direct consequence of our relaxation of the usual assumption that omitted regressors constituting the error term of a latent linear regression model do not introduce omitted regressor biases into the coefficients of the included regressors. 16. Bayesian inference for joint modelling of longitudinal continuous, binary and ordinal events. Science.gov (United States) Li, Qiuju; Pan, Jianxin; Belcher, John 2016-12-01 In medical studies, repeated measurements of continuous, binary and ordinal outcomes are routinely collected from the same patient. Instead of modelling each outcome separately, in this study we propose to jointly model the trivariate longitudinal responses, so as to take account of the inherent association between the different outcomes and thus improve statistical inferences. This work is motivated by a large cohort study in the North West of England, involving trivariate responses from each patient: Body Mass Index, Depression (Yes/No) ascertained with cut-off score not less than 8 at the Hospital Anxiety and Depression Scale, and Pain Interference generated from the Medical Outcomes Study 36-item short-form health survey with values returned on an ordinal scale 1-5. There are some well-established methods for combined continuous and binary, or even continuous and ordinal responses, but little work was done on the joint analysis of continuous, binary and ordinal responses. We propose conditional joint random-effects models, which take into account the inherent association between the continuous, binary and ordinal outcomes. Bayesian analysis methods are used to make statistical inferences. Simulation studies show that, by jointly modelling the trivariate outcomes, standard deviations of the estimates of parameters in the models are smaller and much more stable, leading to more efficient parameter estimates and reliable statistical inferences. In the real data analysis, the proposed joint analysis yields a much smaller deviance information criterion value than the separate analysis, and shows other good statistical properties too. 17. Numerical modelling of the binary alloys solidification with solutal undercooling Directory of Open Access Journals (Sweden) T. Skrzypczak 2008-03-01 Full Text Available In thc papcr descrip~ion of mathcmn~icaI and numerical modcl of binay alloy sot idification is prcscntcd. Mctal alloy consisting of maincomponent and solulc is introduced. Moving, sharp solidification rmnt is assumcd. Conaitulional undcrcooling phcnomcnon is tnkcn intoconsidcralion. As a solidifica~ionf ront advances, solutc is rcdistributcd at thc intcrfacc. Commonly, solutc is rejccted into Itlc liquid. whcrcit accumuIatcs into solittc boundary laycr. Depending on thc tcmpcrature gradient, such tiquid may be undcrcoolcd hclow its mclting point,cvcn though it is hot~crth an liquid at thc Front. This phcnomcnon is orten callcd constitutional or soIr~talu ndcrcool ing, to cmphasizc that itariscs from variations in solutal distribution or I iquid. An important conscqucncc of this accurnulntion of saIutc is that it can cause thc frontto brcak down into cclls or dendri~csT. his occurs bccausc thcrc is a liquid ahcad of thc front with lowcr solutc contcnt, and hcncc a highcrme1 ting tcmpcraturcs than liquid at thc front. In rhc papcr locarion and shapc of wndcrcoolcd rcgion dcpcnding on solidification pararnctcrsis discussed. Nurncrical mcthod basing on Fini tc Elelncnt Mctbod (FEM allowi~lgp rcdiction of breakdown of inoving planar front duringsolidification or binary alloy is proposed. 18. Photometric Modelling of Close Binary Star CN And Indian Academy of Sciences (India) D. M. Z. Jassur; A. Khodadadi 2006-03-01 The results of two color photometry of active close binary CN And are presented and analyzed. The light curves of the system are obviously asymmetric, with the primary maximum brighter than the secondary maximum, which is known as the O’Conell effect. The most plausible explanation of the asymmetry is expected to be due to spot activity of the primary component. For the determination of physical and geometrical parameters, the most new version of W–D code was used, but the presence of asymmetry prevented the convergence of the method when the whole light curves were used. The solutions were obtained by applying mode 3 of W–D code to the first half of the light curves, assuming synchronous rotation and zero eccentricity. Absolute parameters of the system were obtained from combining the photometric solution with spectroscopic data obtained from radial velocity curve analysis. The results indicate the poor thermal contact of the components and transit primary minimum. Finally the O–C diagram was analyzed. It was found that the orbital period of the system is changing with a rate of / = -2.2(6) × 10-10 which corresponds to mass transfer from more massive component to less massive with the rate of / ∼ 4.82 × 10-88sun/year. 19. Wind mass transfer in S-type symbiotic binaries I. Focusing by the wind compression model CERN Document Server Skopal, Augustin 2014-01-01 Context: Luminosities of hot components in symbiotic binaries require accretion rates that are higher than those that can be achieved via a standard Bondi-Hoyle accretion. This implies that the wind mass transfer in symbiotic binaries has to be more efficient. Aims: We suggest that the accretion rate onto the white dwarfs (WDs) in S-type symbiotic binaries can be enhanced sufficiently by focusing the wind from their slowly rotating normal giants towards the binary orbital plane. Methods: We applied the wind compression model to the stellar wind of slowly rotating red giants in S-type symbiotic binaries. Results: Our analysis reveals that for typical terminal velocities of the giant wind, 20 to 50 km/s, and measured rotational velocities between 6 and 10 km/s, the densities of the compressed wind at a typical distance of the accretor from its donor correspond to the mass-loss rate, which can be a factor of$\\sim$10 higher than for the spherically symmetric wind. This allows the WD to accrete at rates of$10^{-...
20. Collision Energy Evolution of Elliptic and Triangular Flow in a Hybrid Model
CERN Document Server
Auvinen, Jussi
2013-01-01
While the existence of a strongly interacting state of matter, known as 'quark-gluon plasma' (QGP), has been established in heavy ion collision experiments in the past decade, the task remains to map out the transition from the hadronic matter to the QGP. This is done by measuring the dependence of key observables (such as particle suppression and elliptic flow) on the collision energy of the heavy ions. This procedure, known as 'beam energy scan', has been most recently performed at the Relativistic Heavy Ion Collider (RHIC). Utilizing a Boltzmann+hydrodynamics hybrid model, we study the collision energy dependence of initial state eccentricities and the final state elliptic and triangular flow. This approach is well suited to investigate the relative importance of hydrodynamics and hadron transport at different collision energies.
1. Measurement and modelling of hydrogen bonding in 1-alkanol plus n-alkane binary mixtures
DEFF Research Database (Denmark)
von Solms, Nicolas; Jensen, Lars; Kofod, Jonas L.;
2007-01-01
Two equations of state (simplified PC-SAFT and CPA) are used to predict the monomer fraction of 1-alkanols in binary mixtures with n-alkanes. It is found that the choice of parameters and association schemes significantly affects the ability of a model to predict hydrogen bonding in mixtures, even...... studies, which is clarified in the present work. New hydrogen bonding data based on infrared spectroscopy are reported for seven binary mixtures of alcohols and alkanes. (C) 2007 Elsevier B.V. All rights reserved....
2. Sensor Fusion Based Model for Collision Free Mobile Robot Navigation
OpenAIRE
Marwah Almasri; Khaled Elleithy; Abrar Alajlan
2015-01-01
Autonomous mobile robots have become a very popular and interesting topic in the last decade. Each of them are equipped with various types of sensors such as GPS, camera, infrared and ultrasonic sensors. These sensors are used to observe the surrounding environment. However, these sensors sometimes fail and have inaccurate readings. Therefore, the integration of sensor fusion will help to solve this dilemma and enhance the overall performance. This paper presents a collision free mobile robot...
3. Benchmarking binary classification models on data sets with different degrees of imbalance
Institute of Scientific and Technical Information of China (English)
Ligang ZHOU; Kin Keung LAI
2009-01-01
In practice, there are many binary classification problems, such as credit risk assessment, medical testing for determining if a patient has a certain disease or not, etc.However, different problems have different characteristics that may lead to different difficulties of the problem. One important characteristic is the degree of imbalance of two classes in data sets. For data sets with different degrees of imbalance, fire the commonly used binary classification methods still feasible? In this study, various binary classifi-cation models, including traditional statistical methods andnewly emerged methods from artificial intelligence, such as linear regression, discriminant analysis, decision tree, neural network, support vector machines, etc., are reviewed, and their performance in terms of the measure of classification accuracy and area under Receiver Operating Characteristic (ROC) curve are tested and compared on fourteen data sets with different imbalance degrees. The results help to select the appropriate methods for problems with different degrees of imbalance.
4. A dynamic analysis of Schelling’s binary corruption model : A competitive equilibrium approach
NARCIS (Netherlands)
Caulkins, J.P.; Feichtinger, G.; Grass, D.; Hartl, R.F.; Kort, P.M.; Novak, A.J.; Seidl, A.; Wirl, F.
2014-01-01
Schelling (in Micromotives and Macrobehavior, Norton, New York, 1978) suggested a simple binary choice model to explain the variation of corruption levels across societies. His basic idea was that the expected profitability of engaging in corruption depends on its prevalence. The key result of the s
5. Exploiting mid-range DNA patterns for sequence classification: binary abstraction Markov models
Science.gov (United States)
Shepard, Samuel S.; McSweeny, Andrew; Serpen, Gursel; Fedorov, Alexei
2012-01-01
Messenger RNA sequences possess specific nucleotide patterns distinguishing them from non-coding genomic sequences. In this study, we explore the utilization of modified Markov models to analyze sequences up to 44 bp, far beyond the 8-bp limit of conventional Markov models, for exon/intron discrimination. In order to analyze nucleotide sequences of this length, their information content is first reduced by conversion into shorter binary patterns via the application of numerous abstraction schemes. After the conversion of genomic sequences to binary strings, homogenous Markov models trained on the binary sequences are used to discriminate between exons and introns. We term this approach the Binary Abstraction Markov Model (BAMM). High-quality abstraction schemes for exon/intron discrimination are selected using optimization algorithms on supercomputers. The best MM classifiers are then combined using support vector machines into a single classifier. With this approach, over 95% classification accuracy is achieved without taking reading frame into account. With further development, the BAMM approach can be applied to sequences lacking the genetic code such as ncRNAs and 5′-untranslated regions. PMID:22344692
6. A rear-end collision risk assessment model based on drivers' collision avoidance process under influences of cell phone use and gender-A driving simulator based study.
Science.gov (United States)
Li, Xiaomeng; Yan, Xuedong; Wu, Jiawei; Radwan, Essam; Zhang, Yuting
2016-12-01
Driver's collision avoidance performance has a direct link to the collision risk and crash severity. Previous studies demonstrated that the distracted driving, such as using a cell phone while driving, disrupted the driver's performance on road. This study aimed to investigate the manner and extent to which cell phone use and driver's gender affected driving performance and collision risk in a rear-end collision avoidance process. Forty-two licensed drivers completed the driving simulation experiment in three phone use conditions: no phone use, hands-free, and hand-held, in which the drivers drove in a car-following situation with potential rear-end collision risks caused by the leading vehicle's sudden deceleration. Based on the experiment data, a rear-end collision risk assessment model was developed to assess the influence of cell phone use and driver's gender. The cell phone use and driver's gender were found to be significant factors that affected the braking performances in the rear-end collision avoidance process, including the brake reaction time, the deceleration adjusting time and the maximum deceleration rate. The minimum headway distance between the leading vehicle and the simulator during the rear-end collision avoidance process was the final output variable, which could be used to measure the rear-end collision risk and judge whether a collision occurred. The results showed that although cell phone use drivers took some compensatory behaviors in the collision avoidance process to reduce the mental workload, the collision risk in cell phone use conditions was still higher than that without the phone use. More importantly, the results proved that the hands-free condition did not eliminate the safety problem associated with distracted driving because it impaired the driving performance in the same way as much as the use of hand-held phones. In addition, the gender effect indicated that although female drivers had longer reaction time than male drivers in
7. Fast and accurate prediction of numerical relativity waveforms from binary black hole mergers using surrogate models
CERN Document Server
Blackman, Jonathan; Galley, Chad R; Szilagyi, Bela; Scheel, Mark A; Tiglio, Manuel; Hemberger, Daniel A
2015-01-01
Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. In this paper, we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios from $1$ to $10$ and durations corresponding to about $15$ orbits before merger. Our surrogate, which is built using reduced order modeling techniques, is distinct from traditional modeling efforts. We find that the full multi-mode surrogate model agrees with waveforms generated by NR to within the numerical error of the NR code. In particular, we show that our modeling strategy produces surrogates which can correctly predict NR waveforms that were {\\em not} used for the surrogate's training. For all practical purposes, then, the surrogate waveform model is equivalent to the high-accuracy, large-scale simulation waveform but can be evaluated in a millisecond to a second dependin...
8. Model of the humanoid body for self collision detection based on elliptical capsules
CSIR Research Space (South Africa)
Dube, C
2011-12-01
Full Text Available . The humanoid body is modeled using elliptical capsules, while the moving segments, i.e. arms and legs, of the humanoid are modeled using circular capsules. This collision detection model provides a good fit to the humanoid body shape while being simple...
9. Pseudorapidity distribution of multiplicity in Au+Au collisions at √sNN = 200 GeV
Science.gov (United States)
Dong, Ya-Fei; Jiang, Zhi-Jin; Wang, Zeng-Wei
2008-04-01
Using the Glauber model, we discuss the number of binary nucleon-nucleon collisions in heavy-ion collisions. Based on the latter, after considering the effect of energy loss of the nucleons in multiple collisions, we derive the pseudorapidity distribution of the multiplicity as a function of the impact parameter in nucleus-nucleus collisions. Using this, we analyze the experimental measurements carried out by the BRAHMS Collaboration in Au + Au collisions at √sNN = 200 GeV. The results are in good agreement with the experimental observations. Supported by Key Foundation of Shanghai (06JC14075)
10. Pseudorapidity distribution of multiplicity in Au+Au collisions at √SNN=200 GeV
Institute of Scientific and Technical Information of China (English)
DONG Ya-Fei; JIANG Zhi-Jin; WANG ZengWei
2008-01-01
Using the Glauber model,we discuss the number of binary nucleon-nucleon collisions in heavy-ion collisions.Based on the latter,after considering the effect of energy loss of the nucleons in multiple collisions,we derive the pseudorapidity distribution of the multiplicity as a function of the impact parameter in nucleus-nucleus collisions.Using this,we analyze the experimental measurements carried out by the BRAHMS Collaboration in Au+Au collisions at √SNN=200 GeV.The results are in good agreement with the experimental observations.
11. Azimuthal Anisotropy in U +U and Au +Au Collisions at RHIC
Science.gov (United States)
Adamczyk, L.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z.; Alekseev, I.; Alford, J.; Aparin, A.; Arkhipkin, D.; Aschenauer, E. C.; Averichev, G. S.; Banerjee, A.; Bellwied, R.; Bhasin, A.; Bhati, A. K.; Bhattarai, P.; Bielcik, J.; Bielcikova, J.; Bland, L. C.; Bordyuzhin, I. G.; Bouchet, J.; Brandin, A. V.; Bunzarov, I.; Burton, T. P.; Butterworth, J.; Caines, H.; Calderón de la Barca Sánchez, M.; Campbell, J. M.; Cebra, D.; Cervantes, M. C.; Chakaberia, I.; Chaloupka, P.; Chang, Z.; Chattopadhyay, S.; Chen, J. H.; Chen, X.; Cheng, J.; Cherney, M.; Christie, W.; Contin, G.; Crawford, H. J.; Das, S.; De Silva, L. C.; Debbe, R. R.; Dedovich, T. G.; Deng, J.; Derevschikov, A. A.; di Ruzza, B.; Didenko, L.; Dilks, C.; Dong, X.; Drachenberg, J. L.; Draper, J. E.; Du, C. M.; Dunkelberger, L. E.; Dunlop, J. C.; Efimov, L. G.; Engelage, J.; Eppley, G.; Esha, R.; Evdokimov, O.; Eyser, O.; Fatemi, R.; Fazio, S.; Federic, P.; Fedorisin, J.; Feng, Z.; Filip, P.; Fisyak, Y.; Flores, C. E.; Fulek, L.; Gagliardi, C. A.; Garand, D.; Geurts, F.; Gibson, A.; Girard, M.; Greiner, L.; Grosnick, D.; Gunarathne, D. S.; Guo, Y.; Gupta, S.; Gupta, A.; Guryn, W.; Hamad, A.; Hamed, A.; Haque, R.; Harris, J. W.; He, L.; Heppelmann, S.; Heppelmann, S.; Hirsch, A.; Hoffmann, G. W.; Hofman, D. J.; Horvat, S.; Huang, H. Z.; Huang, B.; Huang, X.; Huck, P.; Humanic, T. J.; Igo, G.; Jacobs, W. W.; Jang, H.; Jiang, K.; Judd, E. G.; Kabana, S.; Kalinkin, D.; Kang, K.; Kauder, K.; Ke, H. W.; Keane, D.; Kechechyan, A.; Khan, Z. H.; Kikola, D. P.; Kisel, I.; Kisiel, A.; Koetke, D. D.; Kollegger, T.; Kosarzewski, L. K.; Kotchenda, L.; Kraishan, A. F.; Kravtsov, P.; Krueger, K.; Kulakov, I.; Kumar, L.; Kycia, R. A.; Lamont, M. A. C.; Landgraf, J. M.; Landry, K. D.; Lauret, J.; Lebedev, A.; Lednicky, R.; Lee, J. H.; Li, W.; Li, Y.; Li, C.; Li, Z. M.; Li, X.; Li, X.; Lisa, M. A.; Liu, F.; Ljubicic, T.; Llope, W. J.; Lomnitz, M.; Longacre, R. S.; Luo, X.; Ma, L.; Ma, R.; Ma, Y. G.; Ma, G. L.; Magdy, N.; Majka, R.; Manion, A.; Margetis, S.; Markert, C.; Masui, H.; Matis, H. S.; McDonald, D.; Meehan, K.; Minaev, N. G.; Mioduszewski, S.; Mohanty, B.; Mondal, M. M.; Morozov, D. A.; Mustafa, M. K.; Nandi, B. K.; Nasim, Md.; Nayak, T. K.; Nigmatkulov, G.; Nogach, L. V.; Noh, S. Y.; Novak, J.; Nurushev, S. B.; Odyniec, G.; Ogawa, A.; Oh, K.; Okorokov, V.; Olvitt, D. L.; Page, B. S.; Pak, R.; Pan, Y. X.; Pandit, Y.; Panebratsev, Y.; Pawlik, B.; Pei, H.; Perkins, C.; Peterson, A.; Pile, P.; Planinic, M.; Pluta, J.; Poljak, N.; Poniatowska, K.; Porter, J.; Posik, M.; Poskanzer, A. M.; Pruthi, N. K.; Putschke, J.; Qiu, H.; Quintero, A.; Ramachandran, S.; Raniwala, S.; Raniwala, R.; Ray, R. L.; Ritter, H. G.; Roberts, J. B.; Rogachevskiy, O. V.; Romero, J. L.; Roy, A.; Ruan, L.; Rusnak, J.; Rusnakova, O.; Sahoo, N. R.; Sahu, P. K.; Sakrejda, I.; Salur, S.; Sandweiss, J.; Sarkar, A.; Schambach, J.; Scharenberg, R. P.; Schmah, A. M.; Schmidke, W. B.; Schmitz, N.; Seger, J.; Seyboth, P.; Shah, N.; Shahaliev, E.; Shanmuganathan, P. V.; Shao, M.; Sharma, B.; Sharma, M. K.; Shen, W. Q.; Shi, S. S.; Shou, Q. Y.; Sichtermann, E. P.; Sikora, R.; Simko, M.; Skoby, M. J.; Smirnov, D.; Smirnov, N.; Song, L.; Sorensen, P.; Spinka, H. M.; Srivastava, B.; Stanislaus, T. D. S.; Stepanov, M.; Stock, R.; Strikhanov, M.; Stringfellow, B.; Sumbera, M.; Summa, B. J.; Sun, X.; Sun, X. M.; Sun, Z.; Sun, Y.; Surrow, B.; Svirida, D. N.; Szelezniak, M. A.; Tang, Z.; Tang, A. H.; Tarnowsky, T.; Tawfik, A. N.; Thomas, J. H.; Timmins, A. R.; Tlusty, D.; Tokarev, M.; Trentalange, S.; Tribble, R. E.; Tribedy, P.; Tripathy, S. K.; Trzeciak, B. A.; Tsai, O. D.; Ullrich, T.; Underwood, D. G.; Upsal, I.; Van Buren, G.; van Nieuwenhuizen, G.; Vandenbroucke, M.; Varma, R.; Vasiliev, A. N.; Vertesi, R.; Videbaek, F.; Viyogi, Y. P.; Vokal, S.; Voloshin, S. A.; Vossen, A.; Wang, F.; Wang, Y.; Wang, H.; Wang, J. S.; Wang, Y.; Wang, G.; Webb, G.; Webb, J. C.; Wen, L.; Westfall, G. D.; Wieman, H.; Wissink, S. W.; Witt, R.; Wu, Y. F.; Xiao, Z.; Xie, W.; Xin, K.; Xu, Y. F.; Xu, N.; Xu, Z.; Xu, Q. H.; Xu, H.; Yang, Y.; Yang, Y.; Yang, C.; Yang, S.; Yang, Q.; Ye, Z.; Yepes, P.; Yi, L.; Yip, K.; Yoo, I.-K.; Yu, N.; Zbroszczyk, H.; Zha, W.; Zhang, X. P.; Zhang, J. B.; Zhang, J.; Zhang, Z.; Zhang, S.; Zhang, Y.; Zhang, J. L.; Zhao, F.; Zhao, J.; Zhong, C.; Zhou, L.; Zhu, X.; Zoulkarneeva, Y.; Zyzak, M.; STAR Collaboration
2015-11-01
Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, v2{2 } and v2{4 }, for charged hadrons from U +U collisions at √{sNN }=193 GeV and Au +Au collisions at √{sNN}=200 GeV . Nearly fully overlapping collisions are selected based on the energy deposited by spectators in zero degree calorimeters (ZDCs). Within this sample, the observed dependence of v2{2 } on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U +U collisions. We also show that v2 vs multiplicity can be better described by models, such as gluon saturation or quark participant models, that eliminate the dependence of the multiplicity on the number of binary nucleon-nucleon collisions.
12. NUCLEAR AND HEAVY ION PHYSICS: Charged-particle pseudorapidity distributions in Au+Au collisions at RHIC
Science.gov (United States)
Wang, Zeng-Wei; Jiang, Zhi-Jin
2009-04-01
Using the Glauber model, we present the formulas for calculating the numbers of participants, spectators and binary nucleon-nucleon collisions. Based on this work, we get the pseudorapidity distributions of charged particles as the function of the impact parameter in nucleus-nucleus collisions. The theoretical results agree well with the experimental observations made by the BRAHMS Collaboration in Au + Au collisions at GeV in different centrality bins over the whole pseudorapidity range.
13. 3D models of radiatively driven colliding winds in massive O+O star binaries - III. Thermal X-ray emission
CERN Document Server
Pittard, J M
2009-01-01
The X-ray emission from the wind-wind collision in short-period massive O+O-star binaries is investigated. The emission is calculated from three-dimensional hydrodynamical models which incorporate gravity, the driving of the winds, orbital motion of the stars, and radiative cooling of the shocked plasma. Changes in the amount of stellar occultation and circumstellar attenuation introduce phase-dependent X-ray variability in systems with circular orbits, while strong variations in the intrinsic emission also occur in systems with eccentric orbits. The X-ray emission in eccentric systems can display strong hysteresis, with the emission softer after periastron than at corresponding orbital phases prior to periastron, reflecting the physical state of the shocked plasma at these times. Furthermore, the rise of the luminosity to maximum does not necessarily follow a 1/D law. Our models further demonstrate that the effective circumstellar column can be highly energy dependent. We simulate Chandra and Suzaku observat...
14. A model for energy transfer in collisions of atoms with highly excited molecules.
Science.gov (United States)
Houston, Paul L; Conte, Riccardo; Bowman, Joel M
2015-05-21
A model for energy transfer in the collision between an atom and a highly excited target molecule has been developed on the basis of classical mechanics and turning point analysis. The predictions of the model have been tested against the results of trajectory calculations for collisions of five different target molecules with argon or helium under a variety of temperatures, collision energies, and initial rotational levels. The model predicts selected moments of the joint probability distribution, P(Jf,ΔE) with an R(2) ≈ 0.90. The calculation is efficient, in most cases taking less than one CPU-hour. The model provides several insights into the energy transfer process. The joint probability distribution is strongly dependent on rotational energy transfer and conservation laws and less dependent on vibrational energy transfer. There are two mechanisms for rotational excitation, one due to motion normal to the intermolecular potential and one due to motion tangential to it and perpendicular to the line of centers. Energy transfer is found to depend strongly on the intermolecular potential and only weakly on the intramolecular potential. Highly efficient collisions are a natural consequence of the energy transfer and arise due to collisions at "sweet spots" in the space of impact parameter and molecular orientation.
15. Using Gaussian Processes to Model Noise in Eclipsing Binary Light Curves
Science.gov (United States)
Prsa, Andrej; Hambleton, Kelly M.
2017-01-01
The most precise data we have at hand arguably comes from NASA's Kepler mission, for which there is no good flux calibration available since it was designed to measure relative flux changes down to ~20ppm level. Instrumental artifacts thus abound in the data, and they vary with the module, location on the CCD, target brightness, electronic cross-talk, etc. In addition, Kepler's near-uninterrupted mode of observation reveals astrophysical signals and transient phenomena (i.e. spots, flares, protuberances, pulsations, magnetic field features, etc) that are not accounted for in the models. These "nuisance" signals, along with instrumental artifacts, are considered noise when modeling light curves; this noise is highly correlated and it cannot be considered poissonian or gaussian. Detrending non-white noise from light curve data has been an ongoing challenge in modeling eclipsing binary star and exoplanet transit light curves. Here we present an approach using Gaussian Processes (GP) to model noise as part of the overall likelihood function. The likelihood function consists of the eclipsing binary light curve generator PHOEBE, correlated noise model using GP, and a poissonian (shot) noise attributed to the actual stochastic component of the entire noise model. We consider GP parameters and poissonian noise amplitude as free parameters that are being sampled within the likelihood function, so the end result is the posterior probability not only for eclipsing binary model parameters, but for the noise parameters as well. We show that the posteriors of principal parameters are significantly more robust when noise is modeled rigorously compared to modeling detrended data with an eclipsing binary model alone. This work has been funded by NSF grant #1517460.
16. Modeling the Formation and Evolution of Wind-Capture Disks In Binary Systems
Science.gov (United States)
Huarte-Espinosa, M.; Carroll-Nellenback, J.; Nordhaus, J.; Frank, A.; Blackman, E.
2014-04-01
In this talk I will present results of recent models of the formation, evolution and physical properties of accretion disks formed via wind capture in binary systems. Using the AMR code AstroBEAR, we have carried out high resolution 3D simulations that follow a stellar mass secondary in the co-rotating frame as it orbits a wind producing AGB primary. A resolution criteria, based on considerations of Bondi-Hoyle flows, must be met in order to properly resolve the formation of accretion disks around the secondary. We then compare simulations of binaries with three different orbital radii (10, 15, 20 AU). Disks are formed in all three cases, however the size of the disk and, most importantly, its accretion rate decreases with orbital radii. In addition, the shape of the orbital motions of material within the disk becomes increasingly elliptical with increasing binary separation. The flow is mildly unsteady with "fluttering" around the bow shock observed. The disks are generally well aligned with the orbital plane after a few binary orbits. We do not observe the presence of any large scale, violent instabilities (such as the flip-flop mode). For the first time it is observed that the wind component that is accreted towards the secondary has a vortex tube-like structure. In the context of AGB binary systems that might be precursors to Pre-Planetary and Planetary Nebula, we find that the wind accretion rates at the chosen orbital separations are generally too small to produce the most powerful outflows observed in these systems if the companions are main sequence stars but marginally capable if the companions are white dwarfs. It is likely that many of the more powerful PPN and PN involve closer binaries than the ones considered here.
17. Understanding discs in binary YSOs - detailed modelling of VV CrA
Science.gov (United States)
Scicluna, P.; Wolf, S.; Ratzka, T.; Costigan, G.; Launhardt, R.; Leinert, C.; Ober, F.; Manara, C. F.; Testi, L.
2016-05-01
Given that a majority of stars form in multiple systems, in order to fully understand the star- and planet-formation processes we must seek to understand them in multiple stellar systems. With this in mind, we present an analysis of the enigmatic binary T-Tauri system VV Corona Australis, in which both components host discs, but only one is visible at optical wavelengths. We seek to understand the peculiarities of this system by searching for a model for the binary which explains all the available continuum observations of the system. We present new mid-infrared interferometry and near-infrared (NIR) spectroscopy along with archival millimetre-wave observations, which resolve the binary at 1.3 mm for the first time. We compute a grid of pre-main-sequence radiative transfer models and calculate their posterior probabilities given the observed spectral energy distributions and mid-infrared interferometric visibilities of the binary components, beginning with the assumption that the only differences between the two components are their inclination and position angles. Our best-fitting solution corresponds to a relatively low-luminosity T-tauri binary, with each component's disc having a large scaleheight and viewed at moderate inclination (˜50°), with the infrared companion inclined by ˜5° more than the primary. Comparing the results of our model to evolutionary models suggests stellar masses ˜1.7 M⊙ and an age for the system of 3.5 Myr, towards the upper end of previous estimates. Combining these results with accretion indicators from NIR spectroscopy, we determine an accretion rate of 4.0 × 10-8 M⊙ yr-1 for the primary. We suggest that future observations of VV Corona Australis and similar systems should prioritize high angular resolution sub-mm and NIR imaging of the discs and high-resolution optical/NIR spectroscopy of the central stars.
18. Modeling and optimization of a binary geothermal power plant
OpenAIRE
2012-01-01
A model is developed for an existing organic Rankine cycle (ORC) utilizing a low temperature geothermal source. The model is implemented in Aspen Plus® and used to simulate the performance of the existing ORC equipped with an air-cooled condensation system. The model includes all the actual characteristics of the components. The model is validated by approximately 5000 measured data in a wide range of ambient temperatures. The net power output of the system is maximized. The results suggest d...
19. Towards models of gravitational waveforms from generic binaries II: Modelling precession effects with a single effective precession parameter
CERN Document Server
Schmidt, Patricia; Hannam, Mark
2014-01-01
Gravitational waves (GWs) emitted by generic black-hole binaries show a rich structure that directly reflects the complex dynamics introduced by the precession of the orbital plane, which poses a real challenge to the development of generic waveform models. Recent progress in modelling these signals relies on an approximate decoupling between the non-precessing secular inspiral and a precession-induced rotation. However, the latter depends in general on all physical parameters of the binary which makes modelling efforts as well as understanding parameter-estimation prospects prohibitively complex. Here we show that the dominant precession effects can be captured by a reduced set of spin parameters. Specifically, we introduce a single \\emph{effective precession spin} parameter, $\\chi_p$, which is defined from the spin components that lie in the orbital plane at some (arbitrary) instant during the inspiral. We test the efficacy of this parameter by considering binary inspiral configurations specified by the phy...
20. A combined model for pseudorapidity distributions in Cu-Cu collisions at BNL-RHIC energies
CERN Document Server
Jiang, Zhjin; Huang, Yan
2016-01-01
The charged particles produced in nucleus-nucleus collisions come from leading particles and those frozen out from the hot and dense matter created in collisions. The leading particles are conventionally supposed having Gaussian rapidity distributions normalized to the number of participants. The hot and dense matter is assumed to expand according to the unified hydrodynamics, a hydro model which unifies the features of Landau and Hwa-Bjorken model, and freeze out into charged particles from a space-like hypersurface with a proper time of Tau_FO . The rapidity distribution of this part of charged particles can be derived out analytically. The combined contribution from both leading particles and unified hydrodynamics is then compared against the experimental data performed by BNL-RHIC-PHOBOS Collaboration in different centrality Cu-Cu collisions at sqrt(s_NN)=200 and 62.4 GeV, respectively. The model predictions are in well consistent with experimental measurements.
1. A numerical strategy for finite element modeling of frictionless asymmetric vocal fold collision
DEFF Research Database (Denmark)
Granados, Alba; Misztal, Marek Krzysztof; Brunskog, Jonas;
2016-01-01
Analysis of voice pathologies may require vocal fold models that include relevant features such as vocal fold asymmetric collision. The present study numerically addresses the problem of frictionless asymmetric collision in a self-sustained three-dimensional continuum model of the vocal folds....... Theoretical background and numerical analysis of the finite-element position-based contact model are presented, along with validation. A novel contact detection mechanism capable to detect collision in asymmetric oscillations is developed. The effect of inexact contact constraint enforcement on vocal fold...... dynamics is examined by different variational methods for inequality constrained minimization problems, namely the Lagrange multiplier method and the penalty method. In contrast to the penalty solution, which is related to classical spring-like contact forces, numerical examples show that the parameter...
2. Understanding discs in binary YSOs: detailed modelling of VV CrA
CERN Document Server
Scicluna, P; Ratzka, T; Costigan, G; Launhardt, R; Leinert, C; Ober, F; Manara, C F; Testi, L
2016-01-01
Given that a majority of stars form in multiple systems, in order to fully understand the star- and planet-formation processes we must seek to understand them in multiple stellar systems. With this in mind, we present an analysis of the enigmatic binary T-Tauri system VV Corona Australis, in which both components host discs, but only one is visible at optical wavelengths. We seek to understand the peculiarities of this system by searching for a model for the binary which explains all the available continuum observations of the system. We present new mid-infrared interferometry and near-infrared spectroscopy along with archival millimetre-wave observations, which resolve the binary at 1.3mm for the first time. We compute a grid of pre-main-sequence radiative transfer models and calculate their posterior probabilities given the observed spectral energy distributions and mid-infrared interferometric visibilities of the binary components, beginning with the assumption that the only differences between the two com...
3. COLLISION AVOIDANCE DECISION- MAKING MODEL OF MULTI-AGENTS IN VIRTUAL DRIVING ENVIRONMENT WITH ANALYTIC HIERARCHY PROCESS
Institute of Scientific and Technical Information of China (English)
LU Hong; YI Guodong; TAN Jianrong; LIU Zhenyu
2008-01-01
Collision avoidance decision-making models of multiple agents in virtual driving environ- ment are studied. Based on the behavioral characteristics and hierarchical structure of the collision avoidance decision-making in real life driving, delphi approach and mathematical statistics method are introduced to construct pair-wise comparison judgment matrix of collision avoidance decision choices to each collision situation. Analytic hierarchy process (AHP) is adopted to establish the agents' collision avoidance decision-making model. To simulate drivers' characteristics, driver factors are added to categorize driving modes into impatient mode, normal mode, and the cautious mode. The results show that this model can simulate human's thinking process, and the agents in the virtual environment can deal with collision situations and make decisions to avoid collisions without intervention. The model can also reflect diversity and uncertainty of real life driving behaviors, and solves the multi-objective, multi-choice ranking priority problem in multi-vehicle collision scenarios. This collision avoidance model of multi-agents model is feasible and effective, and can provide richer and closer-to-life virtual scene for driving simulator, reflecting real-life traffic environment more truly, this model can also promote the practicality of driving simulator.
4. Efficient and robust estimation for longitudinal mixed models for binary data
DEFF Research Database (Denmark)
Holst, René
2009-01-01
This paper proposes a longitudinal mixed model for binary data. The model extends the classical Poisson trick, in which a binomial regression is fitted by switching to a Poisson framework. A recent estimating equations method for generalized linear longitudinal mixed models, called GEEP, is used...... as a vehicle for fitting the conditional Poisson regressions, given a latent process of serial correlated Tweedie variables. The regression parameters are estimated using a quasi-score method, whereas the dispersion and correlation parameters are estimated by use of bias-corrected Pearson-type estimating...... equations, using second moments only. Random effects are predicted by BLUPs. The method provides a computationally efficient and robust approach to the estimation of longitudinal clustered binary data and accommodates linear and non-linear models. A simulation study is used for validation and finally...
5. On models of the genetic code generated by binary dichotomic algorithms.
Science.gov (United States)
Gumbel, Markus; Fimmel, Elena; Danielli, Alberto; Strüngmann, Lutz
2015-02-01
In this paper we introduce the concept of a BDA-generated model of the genetic code which is based on binary dichotomic algorithms (BDAs). A BDA-generated model is based on binary dichotomic algorithms (BDAs). Such a BDA partitions the set of 64 codons into two disjoint classes of size 32 each and provides a generalization of known partitions like the Rumer dichotomy. We investigate what partitions can be generated when a set of different BDAs is applied sequentially to the set of codons. The search revealed that these models are able to generate code tables with very different numbers of classes ranging from 2 to 64. We have analyzed whether there are models that map the codons to their amino acids. A perfect matching is not possible. However, we present models that describe the standard genetic code with only few errors. There are also models that map all 64 codons uniquely to 64 classes showing that BDAs can be used to identify codons precisely. This could serve as a basis for further mathematical analysis using coding theory, for example. The hypothesis that BDAs might reflect a molecular mechanism taking place in the decoding center of the ribosome is discussed. The scan demonstrated that binary dichotomic partitions are able to model different aspects of the genetic code very well. The search was performed with our tool Beady-A. This software is freely available at http://mi.informatik.hs-mannheim.de/beady-a. It requires a JVM version 6 or higher.
6. Insight into collision zone dynamics from topography: numerical modelling results and observations
Directory of Open Access Journals (Sweden)
A. D. Bottrill
2012-11-01
Full Text Available Dynamic models of subduction and continental collision are used to predict dynamic topography changes on the overriding plate. The modelling results show a distinct evolution of topography on the overriding plate, during subduction, continental collision and slab break-off. A prominent topographic feature is a temporary (few Myrs basin on the overriding plate after initial collision. This "collisional mantle dynamic basin" (CMDB is caused by slab steepening drawing, material away from the base of the overriding plate. Also, during this initial collision phase, surface uplift is predicted on the overriding plate between the suture zone and the CMDB, due to the subduction of buoyant continental material and its isostatic compensation. After slab detachment, redistribution of stresses and underplating of the overriding plate cause the uplift to spread further into the overriding plate. This topographic evolution fits the stratigraphy found on the overriding plate of the Arabia-Eurasia collision zone in Iran and south east Turkey. The sedimentary record from the overriding plate contains Upper Oligocene-Lower Miocene marine carbonates deposited between terrestrial clastic sedimentary rocks, in units such as the Qom Formation and its lateral equivalents. This stratigraphy shows that during the Late Oligocene–Early Miocene the surface of the overriding plate sank below sea level before rising back above sea level, without major compressional deformation recorded in the same area. Our modelled topography changes fit well with this observed uplift and subsidence.
7. Insight into collision zone dynamics from topography: numerical modelling results and observations
Science.gov (United States)
Bottrill, A. D.; van Hunen, J.; Allen, M. B.
2012-11-01
Dynamic models of subduction and continental collision are used to predict dynamic topography changes on the overriding plate. The modelling results show a distinct evolution of topography on the overriding plate, during subduction, continental collision and slab break-off. A prominent topographic feature is a temporary (few Myrs) basin on the overriding plate after initial collision. This "collisional mantle dynamic basin" (CMDB) is caused by slab steepening drawing, material away from the base of the overriding plate. Also, during this initial collision phase, surface uplift is predicted on the overriding plate between the suture zone and the CMDB, due to the subduction of buoyant continental material and its isostatic compensation. After slab detachment, redistribution of stresses and underplating of the overriding plate cause the uplift to spread further into the overriding plate. This topographic evolution fits the stratigraphy found on the overriding plate of the Arabia-Eurasia collision zone in Iran and south east Turkey. The sedimentary record from the overriding plate contains Upper Oligocene-Lower Miocene marine carbonates deposited between terrestrial clastic sedimentary rocks, in units such as the Qom Formation and its lateral equivalents. This stratigraphy shows that during the Late Oligocene-Early Miocene the surface of the overriding plate sank below sea level before rising back above sea level, without major compressional deformation recorded in the same area. Our modelled topography changes fit well with this observed uplift and subsidence.
8. Insight into collision zone dynamics from topography: numerical modelling results and observations
Directory of Open Access Journals (Sweden)
A. D. Bottrill
2012-07-01
Full Text Available Dynamic models of subduction and continental collision are used to predict dynamic topography changes on the overriding plate. The modelling results show a distinct evolution of topography on the overriding plate, during subduction, continental collision and slab break-off. A prominent topographic feature is a temporary (few Myrs deepening in the area of the back arc-basin after initial collision. This collisional mantle dynamic basin (CMDB is caused by slab steepening drawing material away from the base of the overriding plate. Also during this initial collision phase, surface uplift is predicted on the overriding plate between the suture zone and the CMDB, due to the subduction of buoyant continental material and its isostatic compensation. After slab detachment, redistribution of stresses and underplating of the overriding plate causes the uplift to spread further into the overriding plate. This topographic evolution fits the stratigraphy found on the overriding plate of the Arabia-Eurasia collision zone in Iran and south east Turkey. The sedimentary record from the overriding plate contains Upper Oligocene-Lower Miocene marine carbonates deposited between terrestrial clastic sedimentary rocks, in units such as the Qom Formation and its lateral equivalents. This stratigraphy shows that during the Late Oligocene-Early Miocene the surface of the overriding plate sank below sea level before rising back above sea level, without major compressional deformation recorded in the same area. This uplift and subsidence pattern correlates well with our modelled topography changes.
9. Assessment of high-fidelity collision models in the direct simulation Monte Carlo method
Science.gov (United States)
Weaver, Andrew B.
Advances in computer technology over the decades has allowed for more complex physics to be modeled in the DSMC method. Beginning with the first paper on DSMC in 1963, 30,000 collision events per hour were simulated using a simple hard sphere model. Today, more than 10 billion collision events can be simulated per hour for the same problem. Many new and more physically realistic collision models such as the Lennard-Jones potential and the forced harmonic oscillator model have been introduced into DSMC. However, the fact that computer resources are more readily available and higher-fidelity models have been developed does not necessitate their usage. It is important to understand how such high-fidelity models affect the output quantities of interest in engineering applications. The effect of elastic and inelastic collision models on compressible Couette flow, ground-state atomic oxygen transport properties, and normal shock waves have therefore been investigated. Recommendations for variable soft sphere and Lennard-Jones model parameters are made based on a critical review of recent ab-initio calculations and experimental measurements of transport properties.
10. A Clustering-Based Model-Building EA for Optimization Problems with Binary and Real-Valued Variables
NARCIS (Netherlands)
Sadowski, Krzysztof L.; Bosman, Peter A. N.; Thierens, Dirk
2015-01-01
We propose a novel clustering-based model-building evolutionary algorithm to tackle optimization problems that have both binary and real-valued variables. The search space is clustered every generation using a distance metric that considers binary and real-valued variables jointly in order to captur
11. Prediction of vapor-liquid equilibriafor hydrocarbon binary systems by regular solution model
OpenAIRE
下山, 裕介; 米澤, 節子; 小渕, 茂寿; 福地, 賢治; 荒井, 康彦; Shimoyama, Yusuke; Yonezawa, Setsuko; Kobuchi, Shigetoshi; Fukuchi, Kenii; Arai, Yasuhiko
2007-01-01
Vapor-liquid equilibria (VLE) of hydrocarbon binary systems : hexane + benzene (25 °C)， toluene + octane (60°C) and cyclohexane + toluene (50°C) were predicted by using a regular solution model. In the present model, the mixing entropy term (Flory-Huggins equation) is included and an interaction parameter between unlike molecules is introduced. Solubility parameters and molar volumes at each temperature required in calculation are estimated by previously proposed methods. VLE of hexane + benz...
12. Modeling diffusion coefficients in binary mixtures of polar and non-polar compounds
DEFF Research Database (Denmark)
Medvedev, Oleg; Shapiro, Alexander
2005-01-01
The theory of transport coefficients in liquids, developed previously, is tested on a description of the diffusion coefficients in binary polar/non-polar mixtures, by applying advanced thermodynamic models. Comparison to a large set of experimental data shows good performance of the model. Only...... components and to only one parameter for mixtures consisting of non-polar components. A possibility of complete prediction of the parameters is discussed....
13. Polynomial algorithm for exact calculation of partition function for binary spin model on planar graphs
CERN Document Server
Karandashev, Yakov M
2016-01-01
In this paper we propose and realize (the code is publicly available at https://github.com/Thrawn1985/2D-Partition-Function) an algorithm for exact calculation of partition function for planar graph models with binary spins. The complexity of the algorithm is O(N^2). Test experiments shows good agreement with Onsager's analytical solution for two-dimensional Ising model of infinite size.
14. Multiplicity and pseudorapidity distributions of charged particles in asymmetric and deformed nuclear collisions in the wounded quark model
Science.gov (United States)
Chaturvedi, O. S. K.; Srivastava, P. K.; Kumar, Ashwini; Singh, B. K.
2016-12-01
The charged particle multiplicity (n_{ch}) and pseudorapidity density (dn_{ch}/dη) are key observables to characterize the properties of matter created in heavy-ion collisions. The dependence of these observables on collision energy and the collision geometry are a key tool to understand the underlying particle production mechanism. Recently much interest has been focused on asymmetric and deformed nuclei collisions since these collisions can provide a deeper understanding about the nature of quantum chromodynamics (QCD). From the phenomenological perspective, a unified model which describes the experimental data coming from various kinds of collision experiments is much needed to provide physical insights on the production mechanism. In this paper, we have calculated the charged hadron multiplicities for nucleon-nucleus, such as proton-lead ( p-Pb) and asymmetric nuclei collisions like deutron-gold ( d-Au), and copper-gold (Cu-Au) within a new version of the wounded quark model (WQM) and we have shown their variation with respect to centrality. Further we have used a suitable density function within our WQM to calculate pseudorapidity density of charged hadrons at midrapidity in the collisions of deformed uranium nuclei. We found that our model with suitable density functions describes the experimental data for symmetric, asymmetric and deformed nuclei collisions simultaneously over a wide range of the collision energy.
15. Functionally unidimensional item response models for multivariate binary data
DEFF Research Database (Denmark)
Ip, Edward; Molenberghs, Geert; Chen, Shyh-Huei;
2013-01-01
16. Non-linear mixed models in the analysis of mediated longitudinal data with binary outcomes.
Science.gov (United States)
Blood, Emily A; Cheng, Debbie M
2012-01-24
Structural equation models (SEMs) provide a general framework for analyzing mediated longitudinal data. However when interest is in the total effect (i.e. direct plus indirect) of a predictor on the binary outcome, alternative statistical techniques such as non-linear mixed models (NLMM) may be preferable, particularly if specific causal pathways are not hypothesized or specialized SEM software is not readily available. The purpose of this paper is to evaluate the performance of the NLMM in a setting where the SEM is presumed optimal. We performed a simulation study to assess the performance of NLMMs relative to SEMs with respect to bias, coverage probability, and power in the analysis of mediated binary longitudinal outcomes. Both logistic and probit models were evaluated. Models were also applied to data from a longitudinal study assessing the impact of alcohol consumption on HIV disease progression. For the logistic model, the NLMM adequately estimated the total effect of a repeated predictor on the repeated binary outcome and were similar to the SEM across a variety of scenarios evaluating sample size, effect size, and distributions of direct vs. indirect effects. For the probit model, the NLMM adequately estimated the total effect of the repeated predictor, however, the probit SEM overestimated effects. Both logistic and probit NLMMs performed well relative to corresponding SEMs with respect to bias, coverage probability and power. In addition, in the probit setting, the NLMM may produce better estimates of the total effect than the probit SEM, which appeared to overestimate effects.
17. Modeling of Inelastic Collisions in a Multifluid Plasma: Ionization and Recombination
CERN Document Server
Le, H P
2016-01-01
A model for ionization and recombination collisions in a multifluid plasma is formulated using the framework introduced in previous work [{Phys. Plasmas} \\textbf{22}, 093512 (2015)]. The exchange source terms for density, momentum and energy are detailed for the case of electron induced ionization and three body recombination collisions with isotropic scattering. The principle of detailed balance is enforced at the microscopic level. We describe how to incorporate the standard collisional-radiative model into the multifluid equations using the current formulation. Numerical solutions of the collisional-radiative rate equations for atomic hydrogen are presented to highlight the impact of the multifluid effect on the kinetics.
18. Evolution of Binaries in Dense Stellar Systems
CERN Document Server
Ivanova, Natalia
2011-01-01
In contrast to the field, the binaries in dense stellar systems are frequently not primordial, and could be either dynamically formed or significantly altered from their primordial states. Destruction and formation of binaries occur in parallel all the time. The destruction, which constantly removes soft binaries from a binary pool, works as an energy sink and could be a reason for cluster entering the binary-burning phase. The true binary fraction is greater than observed, as a result, the observable binary fraction evolves differently from the predictions. Combined measurements of binary fractions in globular clusters suggest that most of the clusters are still core-contracting. The formation, on other hand, affects most the more evolutionary advanced stars, which significantly enhances the population of X-ray sources in globular clusters. The formation of binaries with a compact objects proceeds mainly through physical collisions, binary-binary and single-binary encounters; however, it is the dynamical for...
19. Particle Production in Ultrarelativistic Heavy-Ion Collisions: A Statistical-Thermal Model Review
Directory of Open Access Journals (Sweden)
S. K. Tiwari
2013-01-01
Full Text Available The current status of various thermal and statistical descriptions of particle production in the ultrarelativistic heavy-ion collisions experiments is presented in detail. We discuss the formulation of various types of thermal models of a hot and dense hadron gas (HG and the methods incorporated in the implementing of the interactions between hadrons. It includes our new excluded-volume model which is thermodynamically consistent. The results of the above models together with the experimental results for various ratios of the produced hadrons are compared. We derive some new universal conditions emerging at the chemical freeze-out of HG fireball showing independence with respect to the energy as well as the structure of the nuclei used in the collision. Further, we calculate various transport properties of HG such as the ratio of shear viscosity-to-entropy using our thermal model and compare with the results of other models. We also show the rapidity as well as transverse mass spectra of various hadrons in the thermal HG model in order to outline the presence of flow in the fluid formed in the collision. The purpose of this review article is to organize and summarize the experimental data obtained in various experiments with heavy-ion collisions and then to examine and analyze them using thermal models so that a firm conclusion regarding the formation of quark-gluon plasma (QGP can be obtained.
20. Binary choices in small and large groups: A unified model
Science.gov (United States)
Bischi, Gian-Italo; Merlone, Ugo
2010-02-01
Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers individuals interacting in one large group, with payoff functions that describe how collective choices influence individual preferences. We incorporate these two approaches into a unified general discrete-time dynamic model for studying individual interactions in variously sized groups. We first illustrate how the two original models can be obtained as particular cases of the more general model we propose, then we show how several other situations can be analyzed. The model we propose goes beyond a theoretical exercise as it allows modeling situations which are relevant in economic and social systems. We consider also other aspects such as the propensity to switch choices and the behavioral momentum, and show how they may affect the dynamics of the whole population.
1. Model reductions for inference: generality of pairwise, binary, and planar factor graphs.
Science.gov (United States)
Eaton, Frederik; Ghahramani, Zoubin
2013-05-01
We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.
2. Verification of a binary fluid solidification model in the finite-volume flow solver
CERN Document Server
Waclawczyk, Tomasz
2015-01-01
The aim of this paper is to verify the new numerical implementation of a binary fluid, heat conduction dominated solidification model. First, we extend a semi-analytical solution to the heat diffusion equation, next, the range of its applicability is investigated. It was found that the linearization introduced to the heat diffusion equation negatively affects the ability to predict solidus and liquidus lines positions whenever the magnitude of latent heat of fusion exceeds a certain value. Next, a binary fluid solidification model is coupled with a flow solver, and is used in a numerical study of Al-4.1%Cu alloy solidification in a two-dimensional rectangular cavity. An accurate coupling between the solidification model and the flow solver is crucial for the correct forecast of solidification front positions and macrosegregation patterns.
3. Thermo-mechanical modeling of turbulent heat transfer in gas-solid flows including particle collisions
Energy Technology Data Exchange (ETDEWEB)
Mansoori, Zohreh; Saffar-Avval, Majid; Basirat-Tabrizi, Hassan; Ahmadi, Goodarz; Lain, Santiago
2002-12-01
A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas-solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k{sub {theta}}-{tau}{sub {theta}} equations, in addition to the hydrodynamic k-{tau} transport, and accounts for the particle-particle and particle-wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.
4. Modeling of Emission Signatures of Massive Black Hole Binaries: I Methods
CERN Document Server
Bogdanovic, Tamara; Sigurdsson, Steinn; Eracleous, Michael
2007-01-01
We model the electromagnetic signatures of massive black hole binaries (MBHBs) with an associated gas component. The method comprises numerical simulations of relativistic binaries and gas coupled with calculations of the physical properties of the emitting gas. We calculate the UV/X-ray and the Halpha light curves and the Halpha emission profiles. The simulations are carried out with a modified version of the parallel tree SPH code Gadget. The heating, cooling, and radiative processes are calculated for two different physical scenarios, where the gas is approximated as a black-body or a solar metallicity gas. The calculation for the solar metallicity scenario is carried out with the photoionization code Cloudy. We focus on sub-parsec binaries which have not yet entered the gravitational radiation phase. The results from the first set of calculations, carried out for a coplanar binary and gas disk, suggest that there are pronounced outbursts in the X-ray light curve during pericentric passages. If such outbur...
5. High-Performance Computer Modeling of the Cosmos-Iridium Collision
Science.gov (United States)
Olivier, S.
This paper describes the application of a new, integrated modeling and simulation framework, encompassing the space situational awareness (SSA) enterprise, to the recent Cosmos-Iridium collision. This framework is based on a flexible, scalable architecture to enable efficient simulation of the current SSA enterprise, and to accommodate future advancements in SSA systems. In particular, the code is designed to take advantage of massively parallel computer systems available, for example, at Lawrence Livermore National Laboratory. We will describe the application of this framework to the recent collision of the Cosmos and Iridium satellites, including (1) detailed hydrodynamic modeling of the satellite collision and resulting debris generation, (2) orbital propagation of the simulated debris and analysis of the increased risk to other satellites (3) calculation of the radar and optical signatures of the simulated debris and modeling of debris detection with space surveillance radar and optical systems (4) determination of simulated debris orbits from modeled space surveillance observations and analysis of the resulting orbital accuracy, (5) comparison of these modeling and simulation results with Space Surveillance Network observations. We will also discuss the use of this integrated modeling and simulation framework to analyze the risks and consequences of future satellite collisions and to assess strategies for mitigating or avoiding future incidents, including the addition of new sensor systems, used in conjunction with the Space Surveillance Network, for improving space situational awareness.
6. High-Performance Computer Modeling of the Cosmos-Iridium Collision
Energy Technology Data Exchange (ETDEWEB)
Olivier, S; Cook, K; Fasenfest, B; Jefferson, D; Jiang, M; Leek, J; Levatin, J; Nikolaev, S; Pertica, A; Phillion, D; Springer, K; De Vries, W
2009-08-28
This paper describes the application of a new, integrated modeling and simulation framework, encompassing the space situational awareness (SSA) enterprise, to the recent Cosmos-Iridium collision. This framework is based on a flexible, scalable architecture to enable efficient simulation of the current SSA enterprise, and to accommodate future advancements in SSA systems. In particular, the code is designed to take advantage of massively parallel, high-performance computer systems available, for example, at Lawrence Livermore National Laboratory. We will describe the application of this framework to the recent collision of the Cosmos and Iridium satellites, including (1) detailed hydrodynamic modeling of the satellite collision and resulting debris generation, (2) orbital propagation of the simulated debris and analysis of the increased risk to other satellites (3) calculation of the radar and optical signatures of the simulated debris and modeling of debris detection with space surveillance radar and optical systems (4) determination of simulated debris orbits from modeled space surveillance observations and analysis of the resulting orbital accuracy, (5) comparison of these modeling and simulation results with Space Surveillance Network observations. We will also discuss the use of this integrated modeling and simulation framework to analyze the risks and consequences of future satellite collisions and to assess strategies for mitigating or avoiding future incidents, including the addition of new sensor systems, used in conjunction with the Space Surveillance Network, for improving space situational awareness.
7. Binary tree models of high-Reynolds-number turbulence
Science.gov (United States)
Aurell, Erik; Dormy, Emmanuel; Frick, Peter
1997-08-01
We consider hierarchical models for turbulence, that are simple generalizations of the standard Gledzer-Ohkitani-Yamada shell models (E. B. Gledzer, Dokl, Akad. Nauk SSSR 209, 5 (1973) [Sov. Phys. Dokl. 18, 216 (1973)]; M. Yamada and K. Ohkitani, J. Phys. Soc. Jpn. 56, 4210 (1987)). The density of degrees of freedom is constant in wave-number space. Looking only at this behavior and at the quadratic invariants in the inviscid unforced limit, the models can be thought of as systems living naturally in one spatial dimension, but being qualitatively similar to hydrodynamics in two (2D) and three dimensions. We investigated cascade phenomena and intermittency in the different cases. We observed and studied a forward cascade of enstrophy in the 2D case.
8. Functionally Unidimensional Item Response Models for Multivariate Binary Data.
Science.gov (United States)
Ip, Edward H; Molenberghs, Geert; Chen, Shyh-Huei; Goegebeur, Yuri; De Boeck, Paul
2013-07-01
The problem of fitting unidimensional item response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that have a strong dimension but also contain minor nuisance dimensions. Fitting a unidimensional model to such multidimensional data is believed to result in ability estimates that represent a combination of the major and minor dimensions. We conjecture that the underlying dimension for the fitted unidimensional model, which we call the functional dimension, represents a nonlinear projection. In this article we investigate 2 issues: (a) can a proposed nonlinear projection track the functional dimension well, and (b) what are the biases in the ability estimate and the associated standard error when estimating the functional dimension? To investigate the second issue, the nonlinear projection is used as an evaluative tool. An example regarding a construct of desire for physical competency is used to illustrate the functional unidimensional approach.
9. A Simple Quantum Model of Ultracold Polar Molecule Collisions
CERN Document Server
Idziaszek, Zbigniew; Bohn, John L; Julienne, Paul S
2010-01-01
We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a $C_6$ coefficient) for each asymptotic value of partial wave quantum numbers $|L,M \\rangle$. From this, the electric field dependence of the collision rates follows automatically. We present examples for reactive species such as KRb, and non-reactive species, such as RbCs.
10. An extended topological model for binary phosphate glasses
DEFF Research Database (Denmark)
Hermansen, Christian; Rodrigues, B.P.; Wondraczek, L.
2014-01-01
the model reduces to classical constraint counting. The constraints on the modifying cations are linear constraints to first neighbor NBOs, and all angular constraints are broken as expected for ionic bonding. For small modifying cations, such as Li+, the linear constraints are almost fully intact...
11. From p+p to Pb+Pb Collisions: Wounded Nucleon versus Statistical Models
CERN Document Server
Gazdzicki, Marek
2013-01-01
System size dependence of hadron production properties is discussed within the Wounded Nucleon Model and the Statistical Model in the grand canonical, canonical and micro-canonical formulations. Similarities and differences between predictions of the models related to the treatment of conservation laws are exposed. A need for models which would combine a hydrodynamical-like expansion with conservation laws obeyed in individual collisions is stressed.
12. Littlest Higgs model with T-parity and single top production in ep collisions
Institute of Scientific and Technical Information of China (English)
WEN Jia; YUE Chong-Xing; LIU Jin-Yan; LIU Wei
2009-01-01
Based on calculating the contributions of the littlest Higgs model with T-parity (called LHT model) to the anomalous top coupling tqγ (q=u or c), we consider single top production via the t-channel partonic process eq → et in ep collisions. Our numerical results show that the production cross section in the LHT model can be significantly enhanced relative to that in the standard model (SM).
13. Radar Shape Modeling of Binary Near-Earth Asteroid 2000 CO101
Science.gov (United States)
Jimenez, Nicholas; Howell, E. S.; Nolan, M. C.; Taylor, P. A.; Benner, L. A. M.; Brozovic, M.; Giorgini, J. D.; Vervack, R. J.; Fernandez, Y. R.; Mueller, M.; Margot, J.; Shepard, M. K.
2010-10-01
We observed the near-Earth binary system 2000 CO101 in 2009 September using the Goldstone and Arecibo radar systems and inverted these images to create shape models of the primary. Asteroid 2000 CO101 was discovered to be a binary system from Arecibo images taken on 2009 September 26 (Taylor et al. 2009). Analyzing the images, we were able to determine approximate values for the radius of the primary (310 m) and the radius of the secondary (22 m). The maximum observed range separation was approximately 610 m. The images show it to appear spherical. Shape modeling of the primary of this system will constrain the asteroid's size, spin rate, and pole orientation. Because other NEA binary systems have exhibited shapes similar to that of 1999 KW4 (Ostro et al. 2006, Scheeres et al. 2006), we initially adopted this shape for 2000 CO101 and have allowed only the linear scales along the three principal axes to adjust to the radar data. This enables us to constrain the volume. With some constraints on the orbit of the satellite we will place limits on the density of the primary. The near-infrared spectrum of 2000 CO101 was measured on 2009 September 21 and 2010 March 13. The 0.8-2.5 micron spectrum was measured on both dates, and shows a featureless, red-sloped spectrum. On September 21 we also measured the thermal emission between 2-4 microns to determine the albedo and thermal properties. Both standard thermal models and thermophysical models have been applied to these data. The albedo we derive from the thermal modeling must also be consistent with the radar size. Characterization of this unusual NEA binary system will be presented.
14. A probabilistic model for hydrokinetic turbine collision risks: exploring impacts on fish.
Directory of Open Access Journals (Sweden)
Linus Hammar
Full Text Available A variety of hydrokinetic turbines are currently under development for power generation in rivers, tidal straits and ocean currents. Because some of these turbines are large, with rapidly moving rotor blades, the risk of collision with aquatic animals has been brought to attention. The behavior and fate of animals that approach such large hydrokinetic turbines have not yet been monitored at any detail. In this paper, we conduct a synthesis of the current knowledge and understanding of hydrokinetic turbine collision risks. The outcome is a generic fault tree based probabilistic model suitable for estimating population-level ecological risks. New video-based data on fish behavior in strong currents are provided and models describing fish avoidance behaviors are presented. The findings indicate low risk for small-sized fish. However, at large turbines (≥5 m, bigger fish seem to have high probability of collision, mostly because rotor detection and avoidance is difficult in low visibility. Risks can therefore be substantial for vulnerable populations of large-sized fish, which thrive in strong currents. The suggested collision risk model can be applied to different turbine designs and at a variety of locations as basis for case-specific risk assessments. The structure of the model facilitates successive model validation, refinement and application to other organism groups such as marine mammals.
15. A probabilistic model for hydrokinetic turbine collision risks: exploring impacts on fish.
Science.gov (United States)
Hammar, Linus; Eggertsen, Linda; Andersson, Sandra; Ehnberg, Jimmy; Arvidsson, Rickard; Gullström, Martin; Molander, Sverker
2015-01-01
A variety of hydrokinetic turbines are currently under development for power generation in rivers, tidal straits and ocean currents. Because some of these turbines are large, with rapidly moving rotor blades, the risk of collision with aquatic animals has been brought to attention. The behavior and fate of animals that approach such large hydrokinetic turbines have not yet been monitored at any detail. In this paper, we conduct a synthesis of the current knowledge and understanding of hydrokinetic turbine collision risks. The outcome is a generic fault tree based probabilistic model suitable for estimating population-level ecological risks. New video-based data on fish behavior in strong currents are provided and models describing fish avoidance behaviors are presented. The findings indicate low risk for small-sized fish. However, at large turbines (≥5 m), bigger fish seem to have high probability of collision, mostly because rotor detection and avoidance is difficult in low visibility. Risks can therefore be substantial for vulnerable populations of large-sized fish, which thrive in strong currents. The suggested collision risk model can be applied to different turbine designs and at a variety of locations as basis for case-specific risk assessments. The structure of the model facilitates successive model validation, refinement and application to other organism groups such as marine mammals.
16. STELLAR LOCI II. A MODEL-FREE ESTIMATE OF THE BINARY FRACTION FOR FIELD FGK STARS
Energy Technology Data Exchange (ETDEWEB)
Yuan, Haibo; Liu, Xiaowei [Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871 (China); Xiang, Maosheng; Huang, Yang; Chen, Bingqiu [Department of Astronomy, Peking University, Beijing 100871 (China); Wu, Yue [Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China); Hou, Yonghui; Zhang, Yong, E-mail: [email protected], E-mail: [email protected] [Nanjing Institute of Astronomical Optics and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Nanjing 210042 (China)
2015-02-01
We propose a stellar locus outlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass ratio distributions of binaries and is able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the Sloan Digital Sky Survey (SDSS) Stripe 82, constructed by combining the recalibrated SDSS photometric data with the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of 41% ± 2%. The fractions decrease toward late spectral types and are 44% ± 5%, 43% ± 3%, 35% ± 5%, and 28% ± 6% for stars with g – i colors in the range 0.3-0.6 mag, 0.6-0.9 mag, 0.9-1.2 mag, and 1.2-1.6 mag, respectively. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars with [Fe/H] between –0.5 and 0.0 dex, –1.0 and –0.5 dex, –1.5 and –1.0 dex, and –2.0 and –1.5 dex, the inferred binary fractions are 37% ± 3%, 39% ± 3%, 50% ± 9%, and 53% ± 20%, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.
17. The NINJA-2 project: Detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations
CERN Document Server
2014-01-01
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave astrophysics communities. The purpose of NINJA is to study the ability to detect gravitational waves emitted from merging binary black holes and recover their parameters with next-generation gravitational-wave observatories. We report here on the results of the second NINJA project, NINJA-2, which employs 60 complete binary black hole hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. In a "blind injection challenge" similar to that conducted in recent LIGO and Virgo science runs, we added 7 hybrid waveforms to two months of data recolored to predictions of Advanced LIGO and Advanced Virgo sensitivity curves during their first observing runs. The resulting data was analyzed by gravitational-wave detection algorithms and 6 of the waveforms were recovered w...
18. Modelling variability in black hole binaries: linking simulations to observations
CERN Document Server
2011-01-01
Black hole accretion flows show rapid X-ray variability. The Power Spectral Density (PSD) of this is typically fit by a phenomenological model of multiple Lorentzians for both the broad band noise and Quasi-Periodic Oscillations (QPOs). Our previous paper (Ingram & Done 2011) developed the first physical model for the PSD and fit this to observational data. This was based on the same truncated disc/hot inner flow geometry which can explain the correlated properties of the energy spectra. This assumes that the broad band noise is from propagating fluctuations in mass accretion rate within the hot flow, while the QPO is produced by global Lense-Thirring precession of the same hot flow. Here we develop this model, making some significant improvements. Firstly we specify that the viscous frequency (equivalently, surface density) in the hot flow has the same form as that measured from numerical simulations of precessing, tilted accretion flows. Secondly, we refine the statistical techniques which we use to fit...
19. A Correlated Binary Model for Ignorable Missing Data: Application to Rheumatoid Arthritis Clinical Data.
Science.gov (United States)
Erebholo, Francis; Apprey, Victor; Bezandry, Paul; Kwagyan, John
2016-04-01
Incomplete data are common phenomenon in research that adopts the longitudinal design approach. If incomplete observations are present in the longitudinal data structure, ignoring it could lead to bias in statistical inference and interpretation. We adopt the disposition model and extend it to the analysis of longitudinal binary outcomes in the presence of monotone incomplete data. The response variable is modeled using a conditional logistic regression model. The nonresponse mechanism is assumed ignorable and developed as a combination of Markov's transition and logistic regression model. MLE method is used for parameter estimation. Application of our approach to rheumatoid arthritis clinical trials is presented.
20. Three-dimensional simulations of phase separation in model binary alloy systems with elasticity
Energy Technology Data Exchange (ETDEWEB)
Orlikowski, D.; Roland, C. [North Carolina State Univ., Raleigh, NC (United States); Sagui, C. [McGill Univ., Montreal, Quebec (Canada). Dept. of Physics; Somoza, A.S. [Univ. de Murcia (Spain). Dept. de Fisica
1998-12-31
The authors report on large-scale three-dimensional simulations of phase separation in model binary alloy systems in the presence of elastic fields. The elastic field has several important effects on the morphology of the system: the ordered domains are subject to shape transformations, and spatial ordering. In contrast to two-dimensional system, no significant slowing down in the growth is observed. There is also no evidence of any reverse coarsening of the domains.
1. Double pendulum model for a tennis stroke including a collision process
Science.gov (United States)
Youn, Sun-Hyun
2015-10-01
By means of adding a collision process between the ball and racket in the double pendulum model, we analyzed the tennis stroke. The ball and the racket system may be accelerated during the collision time; thus, the speed of the rebound ball does not simply depend on the angular velocity of the racket. A higher angular velocity sometimes gives a lower rebound ball speed. We numerically showed that the proper time-lagged racket rotation increased the speed of the rebound ball by 20%. We also showed that the elbow should move in the proper direction in order to add the angular velocity of the racket.
2. D-meson observables in heavy-ion collisions at LHC with EPOSHQ model
Directory of Open Access Journals (Sweden)
Ozvenchuk Vitalii
2016-01-01
Full Text Available We study the propagation of charm quarks in the quark-gluon plasma (QGP created in ultrarelativistic heavy-ion collisions at LHC within EPOSHQ model. The interactions of heavy quarks with the light partons in ultrarelativistic heavy-ion collisions through the collisional and radiative processes lead to a large suppression of final D-meson spectra at high transverse momentum and a finite D-meson elliptic flow. Our results are in a good agreement with the available experimental data.
3. Dynamical Analysis of Sputtering at Threshold Energy Range: Modelling of Ar+Ni(100) Collision System
Institute of Scientific and Technical Information of China (English)
HUNDUR Yakup; G(U)VEN(C) Ziya B; HIPPLER Rainer
2008-01-01
The sputtering process of Ar+Ni(100) collision systems is investigated by means of constant energy molecular dynamics simulations.The Ni(100) slab is mimicked by an embedded-atom potential,and the interaction between the projectile and the surface is modelled by using the reparametrized ZBL potential.Ni atom emission from the lattice is analysed over the range of 20-50 eV collision energy.Sputtering yield,angular and energy distributions of the scattered Ar and of the sputtered Ni atoms are calculated,and compared to the available theoretical and experimental data.
4. Towards a construction of inclusive collision cross-sections in massless Nelson's model
CERN Document Server
Dybalski, Wojciech
2011-01-01
The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in massless Nelson's model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.
5. Modeling of molecular nitrogen collisions and dissociation processes for direct simulation Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Parsons, Neal, E-mail: [email protected]; Levin, Deborah A., E-mail: [email protected] [Department of Aerospace Engineering, The Pennsylvania State University, 233 Hammond Building, University Park, Pennsylvania 16802 (United States); Duin, Adri C. T. van, E-mail: [email protected] [Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 136 Research East, University Park, Pennsylvania 16802 (United States); Zhu, Tong, E-mail: [email protected] [Department of Aerospace Engineering, The Pennsylvania State University, 136 Research East, University Park, Pennsylvania 16802 (United States)
2014-12-21
The Direct Simulation Monte Carlo (DSMC) method typically used for simulating hypersonic Earth re-entry flows requires accurate total collision cross sections and reaction probabilities. However, total cross sections are often determined from extrapolations of relatively low-temperature viscosity data, so their reliability is unknown for the high temperatures observed in hypersonic flows. Existing DSMC reaction models accurately reproduce experimental equilibrium reaction rates, but the applicability of these rates to the strong thermal nonequilibrium observed in hypersonic shocks is unknown. For hypersonic flows, these modeling issues are particularly relevant for nitrogen, the dominant species of air. To rectify this deficiency, the Molecular Dynamics/Quasi-Classical Trajectories (MD/QCT) method is used to accurately compute collision and reaction cross sections for the N{sub 2}({sup 1}Σ{sub g}{sup +})-N{sub 2}({sup 1}Σ{sub g}{sup +}) collision pair for conditions expected in hypersonic shocks using a new potential energy surface developed using a ReaxFF fit to recent advanced ab initio calculations. The MD/QCT-computed reaction probabilities were found to exhibit better physical behavior and predict less dissociation than the baseline total collision energy reaction model for strong nonequilibrium conditions expected in a shock. The MD/QCT reaction model compared well with computed equilibrium reaction rates and shock-tube data. In addition, the MD/QCT-computed total cross sections were found to agree well with established variable hard sphere total cross sections.
6. A circumbinary disc model for the variability of the eclipsing binary CoRoT 223992193
CERN Document Server
Terquem, Caroline; Bouvier, Jérôme
2015-01-01
We calculate the flux received from a binary system obscured by a circumbinary disc. The disc is modelled using two dimensional hydrodynamical simulations, and the vertical structure is derived by assuming it is isothermal. The gravitational torque from the binary creates a cavity in the disc's inner parts. If the line of sight along which the system is observed has a high inclination $I$, it intersects the disc and some absorption is produced. As the system is not axisymmetric, the resulting light curve displays variability. We calculate the absorption and produce light curves for different values of the dust disc aspect ratio $H/r$ and mass of dust in the cavity $M_{\\rm dust}$. This model is applied to the high inclination ($I=85^{\\circ}$) eclipsing binary CoRoT 223992193, which shows 5-10% residual photometric variability after the eclipses and a spot model are subtracted. We find that such variations for $I \\sim 85^{\\circ}$ can be obtained for $H/r=10^{-3}$ and $M_{\\rm dust} \\ge 10^{-12}$ M$_{\\odot}$. For...
7. Binary Classifier Calibration using an Ensemble of Near Isotonic Regression Models
Science.gov (United States)
Naeini, Mahdi Pakdaman; Cooper, Gregory F.
2017-01-01
Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called ensemble of near isotonic regression (ENIR). The method can be considered as an extension of BBQ [20], a recently proposed calibration method, as well as the commonly used calibration method based on isotonic regression (IsoRegC) [27]. ENIR is designed to address the key limitation of IsoRegC which is the monotonicity assumption of the predictions. Similar to BBQ, the method post-processes the output of a binary classifier to obtain calibrated probabilities. Thus it can be used with many existing classification models to generate accurate probabilistic predictions. We demonstrate the performance of ENIR on synthetic and real datasets for commonly applied binary classification models. Experimental results show that the method outperforms several common binary classifier calibration methods. In particular on the real data, ENIR commonly performs statistically significantly better than the other methods, and never worse. It is able to improve the calibration power of classifiers, while retaining their discrimination power. The method is also computationally tractable for large scale datasets, as it is O(N log N) time, where N is the number of samples.
8. Effective-one-body waveforms for binary neutron stars using surrogate models
CERN Document Server
Lackey, Benjamin D; Galley, Chad R; Meidam, Jeroen; Broeck, Chris Van Den
2016-01-01
Gravitational-wave observations of binary neutron star systems can provide information about the masses, spins, and structure of neutron stars. However, this requires accurate and computationally efficient waveform models that take <1s to evaluate for use in Bayesian parameter estimation codes that perform 10^7 - 10^8 waveform evaluations. We present a surrogate model of a nonspinning effective-one-body waveform model with l = 2, 3, and 4 tidal multipole moments that reproduces waveforms of binary neutron star numerical simulations up to merger. The surrogate is built from compact sets of effective-one-body waveform amplitude and phase data that each form a reduced basis. We find that 12 amplitude and 7 phase basis elements are sufficient to reconstruct any binary neutron star waveform with a starting frequency of 10Hz. The surrogate has maximum errors of 3.8% in amplitude (0.04% excluding the last 100M before merger) and 0.043 radians in phase. The version implemented in the LIGO Algorithm Library takes ~...
9. Modelling of binary alloy solidification in the MEPHISTO experiment
Science.gov (United States)
Leonardi, Eddie; de Vahl Davis, Graham; Timchenko, Victoria; Chen, Peter; Abbaschian, Reza
2004-05-01
A modified enthalpy method was used to numerically model experiments on solidification of a bismuth-tin alloy which were performed during the 1997 flight of the MEPHISTO-4 experiment on the US Space Shuttle Columbia. This modified enthalpy method was incorporated into an in-house code SOLCON and a commercial CFD code CFX; Soret effect was taken into account by including an additional thermo-diffusion term into the solute transport equation and the effects of thermal and solutal convection in the microgravity environment and of concentration-dependent melting temperature on the phase change processes were also included. In this paper an overview of the results obtained as part of MEPHISTO project is presented. The numerical solutions are compared with actual microprobe results obtained from the MEPHISTO experiment. To cite this article: E. Leonardi et al., C. R. Mecanique 332 (2004).
10. MATHEMATICAL MODEL FOR ACCESS MODE OF CONTENTION-COLLISION CANCELLATION IN A STAR LAN
Institute of Scientific and Technical Information of China (English)
Lu Zhaoyi; Sun Lijun
2004-01-01
I type system model of CCCAM(Contention-Collision Cancellation Access Mode)is studied through mathematical modelling and simulation. There are two innovations: (1) in the account; (2) the time at which customers depart after having been served successfully are chosen to be the embedded point, thereby "free period" is introduced reasonably. So the mathematical modelling and analysis result in this paper are significant for application of wire star LAN and wireless star LAN.
11. MHD Wind Models in X-Ray Binaries and AGN
Science.gov (United States)
Behar, Ehud; Fukumura, Keigo; Kazanas, Demosthenes; Shrader, Chris R.; Tombesi, Francesco; Contopoulos, Ioannis
2017-08-01
Self-similar magnetohydrodynamic (MHD) wind models that can explain both the kinematics and the ionization structure of outflows from accretion sources will be presented.The X-ray absorption-line properties of these outflows are diverse, their velocity ranging from 0.001c to 0.1c, and their ionization ranging from neutral to fully ionized.We will show how the velocity structure and density profile of the wind can be tightly constrained, by finding the scaling of the magnetic flux with the distance from the center that best matches observations, and with no other priors.It will be demonstrated that the same basic MHD wind structure that successfully accounts for the X-ray absorber properties of outflows from supermassive black holes, also reproduces the high-resolution X-ray spectrum of the accreting stellar-mass black hole GRO J1655-40 for a series of ions between ~1A and ~12A.These results support both the magnetic nature of these winds, as well as the universal nature of magnetic outflows across all black hole sizes.
12. The Be/X-ray Binary LSI+61303 in terms of Ejector-Propeller Model
CERN Document Server
Zamanov, R K; Marziani, P
2001-01-01
We tested the ejector-propeller model of the Be/X-ray binary LSI+61303 (V 615 Cas, GT 0236+620) by using the parameters predicted by the model in the calculations of the X-ray and radio variability. The results are: (1) in terms of the Ejector-Propeller model, the X-ray maximum is due to the periastron passage; (2) the radio outburst can be really a result of the transition from the propeller to ejector regimes; (3) the radio outburst will delay with respect to the X-ray maximum every orbital period. The proposed scenario seems to be in good agreement with the observations.
13. Modelling the energy dependencies of high-frequency QPO in black hole X-ray binaries
OpenAIRE
Zycki, P. T.; A. Niedzwiecki(University of Lodz, Poland); Sobolewska, M. A.
2007-01-01
We model energy dependencies of the quasi periodic oscillations (QPO) in the model of disc epicyclic motions, with X-ray modulation caused by varying relativistic effects. The model was proposed to explain the high frequency QPO observed in X-ray binaries. We consider two specific scenarios for the geometry of accretion flow and spectral formation. Firstly, a standard cold accretion disc with an active X-ray emitting corona is assumed to oscillate. Secondly, only a hot X-ray emitting accretio...
14. Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model
Science.gov (United States)
Vallejo, Jonathon; Hejduk, Matt; Stamey, James
2015-01-01
We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.
15. Spectral modeling of circular massive binary systems: Towards an understanding of the Struve--Sahade effect?
CERN Document Server
Palate, Matthieu
2011-01-01
Context: Some secondary effects are known to introduce variations in spectra of massive binaries. These phenomena (such as the Struve--Sahade effect, difficulties to determine properly the spectral type,...) have been reported and documented in the literature. Aims: We simulate the spectra of circular massive binaries at different phases of the orbital cycle and accounting for the gravitational influence of the companion star on the shape and physical properties of the stellar surface. Methods: We use the Roche potential to compute the stellar surface, von Zeipel theorem and reflection effects to compute the surface temperature. We then interpolate in a grid of NLTE plan-parallel atmosphere model spectra to obtain the local spectrum at each surface point. We finally sum all the contributions (accounting for the Doppler shift, limb-darkening, ...) to obtain the total spectrum. The computation is done for different orbital phases and for different sets of physical and orbital parameters. Results: Our first mode...
16. A new non-randomized model for analysing sensitive questions with binary outcomes.
Science.gov (United States)
Tian, Guo-Liang; Yu, Jun-Wu; Tang, Man-Lai; Geng, Zhi
2007-10-15
We propose a new non-randomized model for assessing the association of two sensitive questions with binary outcomes. Under the new model, respondents only need to answer a non-sensitive question instead of the original two sensitive questions. As a result, it can protect a respondent's privacy, avoid the usage of any randomizing device, and be applied to both the face-to-face interview and mail questionnaire. We derive the constrained maximum likelihood estimates of the cell probabilities and the odds ratio for two binary variables associated with the sensitive questions via the EM algorithm. The corresponding standard error estimates are then obtained by bootstrap approach. A likelihood ratio test and a chi-squared test are developed for testing association between the two binary variables. We discuss the loss of information due to the introduction of the non-sensitive question, and the design of the co-operative parameters. Simulations are performed to evaluate the empirical type I error rates and powers for the two tests. In addition, a simulation is conducted to study the relationship between the probability of obtaining valid estimates and the sample size for any given cell probability vector. A real data set from an AIDS study is used to illustrate the proposed methodologies.
17. Models of galaxy collisions in Stephan's quintet and other interacting systems
Science.gov (United States)
Hwang, Jeong-Sun
2010-12-01
This dissertation describes numerical studies of three interacting galaxy systems. First, hydrodynamical models of the collisions in the famous compact galaxy group, Stephan's Quintet, were constructed to investigate the dynamical interaction history and evolution of the intergalactic gas. It has been found that with a sequence of two-at-a-time collisions, most of the major morphological and kinematical features of the group were well reproduced in the models. The models suggest the two long tails extending from NGC 7319 toward NGC 7320c may be formed simultaneously from a strong collisional encounter between the two galaxies, resulting in a thinner and denser inner tail than the outer one. The tails then also run parallel to each other as observed. The model results support the idea that the group-wide shock detected in multi-wavelength observations between NGC 7319 and 7318b and the starburst region north of NGC 7318b are triggered by the current high-speed collision between NGC 7318b and the intergalactic gas. It is expected that other compact groups containing rich extended features like Stephan's Quintet can be modeled in similar ways, and that sequences of two-at-a-time collisions will be the general rule. The second set of hydrodynamical simulations were performed to model the peculiar galaxy pair, Arp 285. This system possesses a series of star-forming complexes in an unusual tail-like feature extending out perpendicular to the disk of the northern galaxy. Several conceptual ideas for the origin of the tail-like feature were examined. The models suggest that the bridge material falling into the gravitational potential of the northern disk overshoots the disk; as more bridge material streams into the region, compression drives star formation. This work on star-formation in the pile-up region can be extended to the studies of the formation of tidal dwarf galaxies or globular clusters. Thirdly, the development of spiral waves was studied with numerical models
18. SU-E-T-754: Three-Dimensional Patient Modeling Using Photogrammetry for Collision Avoidance
Energy Technology Data Exchange (ETDEWEB)
Popple, R; Cardan, R [Univ Alabama Birmingham, Birmingham, AL (United States)
2015-06-15
Purpose: To evaluate photogrammetry for creating a three-dimensional patient model. Methods: A mannequin was configured on the couch of a CT scanner to simulate a patient setup using an indexed positioning device. A CT fiducial was placed on the indexed CT table-overlay at the reference index position. Two dimensional photogrammetry targets were placed on the table in known positions. A digital SLR camera was used to obtain 27 images from different positions around the CT table. The images were imported into a commercial photogrammetry package and a 3D model constructed. Each photogrammetry target was identified on 2 to 5 images. The CT DICOM metadata and the position of the CT fiducial were used to calculate the coordinates of the photogrammetry targets in the CT image frame of reference. The coordinates were transferred to the photogrammetry software to orient the 3D model. The mannequin setup was transferred to the treatment couch of a linear accelerator and positioned at isocenter using in-room lasers. The treatment couch coordinates were noted and compared with prediction. The collision free regions were measured over the full range of gantry and table motion and were compared with predictions obtained using a general purpose polygon interference algorithm. Results: The reconstructed 3D model consisted of 180000 triangles. The difference between the predicted and measured couch positions were 5 mm, 1 mm, and 1 mm for longitudinal, lateral, and vertical, respectively. The collision prediction tested 64620 gantry table combinations in 11.1 seconds. The accuracy was 96.5%, with false positive and negative results occurring at the boundaries of the collision space. Conclusion: Photogrammetry can be used as a tool for collision avoidance during treatment planning. The results indicate that a buffer zone is necessary to avoid false negatives at the boundary of the collision-free zone. Testing with human patients is underway. Research partially supported by a grant
19. Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach.
Science.gov (United States)
Chen, Yong; Hong, Chuan; Ning, Yang; Su, Xiao
2016-01-15
When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration.
20. A New Algorithm for Self-Consistent 3-D Modeling of Collisions in Dusty Debris Disks
CERN Document Server
Stark, Christopher C
2009-01-01
We present a new "collisional grooming" algorithm that enables us to model images of debris disks where the collision time is less than the Poynting Robertson time for the dominant grain size. Our algorithm uses the output of a collisionless disk simulation to iteratively solve the mass flux equation for the density distribution of a collisional disk containing planets in 3 dimensions. The algorithm can be run on a single processor in ~1 hour. Our preliminary models of disks with resonant ring structures caused by terrestrial mass planets show that the collision rate for background particles in a ring structure is enhanced by a factor of a few compared to the rest of the disk, and that dust grains in or near resonance have even higher collision rates. We show how collisions can alter the morphology of a resonant ring structure by reducing the sharpness of a resonant ring's inner edge and by smearing out azimuthal structure. We implement a simple prescription for particle fragmentation and show how Poynting-Ro...
1. A Distributed and Deterministic TDMA Algorithm for Write-All-With-Collision Model
CERN Document Server
Arumugam, Mahesh
2008-01-01
Several self-stabilizing time division multiple access (TDMA) algorithms are proposed for sensor networks. In addition to providing a collision-free communication service, such algorithms enable the transformation of programs written in abstract models considered in distributed computing literature into a model consistent with sensor networks, i.e., write all with collision (WAC) model. Existing TDMA slot assignment algorithms have one or more of the following properties: (i) compute slots using a randomized algorithm, (ii) assume that the topology is known upfront, and/or (iii) assign slots sequentially. If these algorithms are used to transform abstract programs into programs in WAC model then the transformed programs are probabilistically correct, do not allow the addition of new nodes, and/or converge in a sequential fashion. In this paper, we propose a self-stabilizing deterministic TDMA algorithm where a sensor is aware of only its neighbors. We show that the slots are assigned to the sensors in a concu...
2. A viscous blast-wave model for high energy heavy-ion collisions
Science.gov (United States)
Jaiswal, Amaresh; Koch, Volker
2016-07-01
Employing a viscosity-based survival scale for initial geometrical perturbations formed in relativistic heavy-ion collisions, we model the radial flow velocity at freeze-out. Subsequently, we use the Cooper-Frye freeze-out prescription, with viscous corrections to the distribution function, to extract the transverse momentum dependence of particle yields and flow harmonics. We fit the model parameters for central collisions, by fitting the spectra of identified particles at the Large Hadron Collider (LHC), and estimate them for other centralities using simple hydrodynamic relations. We use the results of Monte Carlo Glauber model for initial eccentricities. We demonstrate that this improved viscous blast-wave model leads to good agreement with transverse momentum distribution of elliptic and triangular flow for all centralities and estimate the shear viscosity to entropy density ratio η/s ≃ 0.24 at the LHC.
3. Activity Calculation by Application of Sub-Regular Solution Model in Binary Oxide Systems
Institute of Scientific and Technical Information of China (English)
HOU Yan-qing; XIE Gang; TAO Dong-ping; LI Rong-xing; YU Xiao-hua
2012-01-01
To confirm sub-regular solution model valid for predicting the activity of component in binary oxide systems, seven systems in the whole concentration and twelve systems presenting saturation concentration have been studied. The total average relative errors of component 1 and 2 are 3.2 % and 4.1% respectively by application of the sub-regular solution model into the systems within the whole concentration. However, the total average relative errors are 16 % and 1088 % in the systems presenting saturation concentration. The results show that sub-regular solu- tion model is not good for predicting the systems presenting saturation concentration, especially for the systems con- taining acidic or neutral oxide. The reason may be that the influence of the two types of oxide on the configuration is greater in binary oxide systems. These oxides can be present in the form of complex anion partly, Si-O, Al-O, Ti-O and so on, for example （SiO4）4-. That is contrary to sub-regular solution model which is supposed that the oxide systems consist of cation and O2-. But compared with regular solution model and quasi-regular solution model, sub- regular solution model is closer to the characteristics of actual solution and the calculated results are superior.
4. Blind Separation of Acoustic Signals Combining SIMO-Model-Based Independent Component Analysis and Binary Masking
Directory of Open Access Journals (Sweden)
Hiekata Takashi
2006-01-01
Full Text Available A new two-stage blind source separation (BSS method for convolutive mixtures of speech is proposed, in which a single-input multiple-output (SIMO-model-based independent component analysis (ICA and a new SIMO-model-based binary masking are combined. SIMO-model-based ICA enables us to separate the mixed signals, not into monaural source signals but into SIMO-model-based signals from independent sources in their original form at the microphones. Thus, the separated signals of SIMO-model-based ICA can maintain the spatial qualities of each sound source. Owing to this attractive property, our novel SIMO-model-based binary masking can be applied to efficiently remove the residual interference components after SIMO-model-based ICA. The experimental results reveal that the separation performance can be considerably improved by the proposed method compared with that achieved by conventional BSS methods. In addition, the real-time implementation of the proposed BSS is illustrated.
5. Non-linear mixed models in the analysis of mediated longitudinal data with binary outcomes
Directory of Open Access Journals (Sweden)
Blood Emily A
2012-01-01
Full Text Available Abstract Background Structural equation models (SEMs provide a general framework for analyzing mediated longitudinal data. However when interest is in the total effect (i.e. direct plus indirect of a predictor on the binary outcome, alternative statistical techniques such as non-linear mixed models (NLMM may be preferable, particularly if specific causal pathways are not hypothesized or specialized SEM software is not readily available. The purpose of this paper is to evaluate the performance of the NLMM in a setting where the SEM is presumed optimal. Methods We performed a simulation study to assess the performance of NLMMs relative to SEMs with respect to bias, coverage probability, and power in the analysis of mediated binary longitudinal outcomes. Both logistic and probit models were evaluated. Models were also applied to data from a longitudinal study assessing the impact of alcohol consumption on HIV disease progression. Results For the logistic model, the NLMM adequately estimated the total effect of a repeated predictor on the repeated binary outcome and were similar to the SEM across a variety of scenarios evaluating sample size, effect size, and distributions of direct vs. indirect effects. For the probit model, the NLMM adequately estimated the total effect of the repeated predictor, however, the probit SEM overestimated effects. Conclusions Both logistic and probit NLMMs performed well relative to corresponding SEMs with respect to bias, coverage probability and power. In addition, in the probit setting, the NLMM may produce better estimates of the total effect than the probit SEM, which appeared to overestimate effects.
6. New approach in modeling Cr(VI) sorption onto biomass from metal binary mixtures solutions
Energy Technology Data Exchange (ETDEWEB)
Liu, Chang [College of Environmental Science and Engineering, Anhui Normal University, South Jiuhua Road, 189, 241002 Wuhu (China); Chemical Engineering Department, Escola Politècnica Superior, Universitat de Girona, Ma Aurèlia Capmany, 61, 17071 Girona (Spain); Fiol, Núria [Chemical Engineering Department, Escola Politècnica Superior, Universitat de Girona, Ma Aurèlia Capmany, 61, 17071 Girona (Spain); Villaescusa, Isabel, E-mail: [email protected] [Chemical Engineering Department, Escola Politècnica Superior, Universitat de Girona, Ma Aurèlia Capmany, 61, 17071 Girona (Spain); Poch, Jordi [Applied Mathematics Department, Escola Politècnica Superior, Universitat de Girona, Ma Aurèlia Capmany, 61, 17071 Girona (Spain)
2016-01-15
In the last decades Cr(VI) sorption equilibrium and kinetic studies have been carried out using several types of biomasses. However there are few researchers that consider all the simultaneous processes that take place during Cr(VI) sorption (i.e., sorption/reduction of Cr(VI) and simultaneous formation and binding of reduced Cr(III)) when formulating a model that describes the overall sorption process. On the other hand Cr(VI) scarcely exists alone in wastewaters, it is usually found in mixtures with divalent metals. Therefore, the simultaneous removal of Cr(VI) and divalent metals in binary mixtures and the interactive mechanism governing Cr(VI) elimination have gained more and more attention. In the present work, kinetics of Cr(VI) sorption onto exhausted coffee from Cr(VI)–Cu(II) binary mixtures has been studied in a stirred batch reactor. A model including Cr(VI) sorption and reduction, Cr(III) sorption and the effect of the presence of Cu(II) in these processes has been developed and validated. This study constitutes an important advance in modeling Cr(VI) sorption kinetics especially when chromium sorption is in part based on the sorbent capacity of reducing hexavalent chromium and a metal cation is present in the binary mixture. - Highlights: • A kinetic model including Cr(VI) reduction, Cr(VI) and Cr(III) sorption/desorption • Synergistic effect of Cu(II) on Cr(VI) elimination included in the modelModel validation by checking it against independent sets of data.
7. PACIAE 2.0: An Updated Parton and Hadron Cascade Model (Program) for Relativistic Nuclear Collisions
Institute of Scientific and Technical Information of China (English)
SA; Ben-hao; ZHOU; Dai-mei; YAN; Yu-liang; LI; Xiao-mei; FENG; Sheng-qing; DONG; Bao-guo; CAI; Xu
2012-01-01
<正>We have updated the parton and hadron cascade model PACIAE for the relativistic nuclear collisions, from based on JETSET 6.4 and PYTHIA 5.7, and referred to as PACIAE 2.0. The main physics concerning the stages of the parton initiation, parton rescattering, hadronization, and hadron rescattering were discussed. The structures of the programs were briefly explained. In addition, some calculated examples were compared with the experimental data. It turns out that this model (program) works well.
8. Compactified pulsar wind nebula model of gamma-ray loud binary LSI +61 303
CERN Document Server
Neronov, A
2007-01-01
We show that radio-to-TeV properties of the binary system LSI +61 303 can be explained by interaction of the compact object (a young pulsar) with the inhomogeneities of the wind from companion Be star. We develop a model scenario of "compactified" pulsar wind nebula formed in result of such interaction. To test the model assumptions about geometry of the system we re-analyze the available X-ray observations to study in more details the variations of the hydrogen column density on long (orbital) and short (several kilosecond) time scales.
9. Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion.
Science.gov (United States)
Ramirez, J C; Beckermann, C; Karma, A; Diepers, H-J
2004-05-01
A phase-field model is developed for simulating quantitatively microstructural pattern formation in solidification of dilute binary alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i). the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii). kinetic effects are negligible. A recently derived antitrapping current [Phys. Rev. Lett. 87, 115701 (2001)
10. Modelling the observed properties of carbon-enhanced metal-poor stars using binary population synthesis
CERN Document Server
Abate, C; Stancliffe, R J; Izzard, R G; Karakas, A I; Beers, T C; Lee, Y S
2015-01-01
The stellar population in the Galactic halo is characterised by a large fraction of CEMP stars. Most CEMP stars are enriched in $s$-elements (CEMP-$s$ stars), and some of these are also enriched in $r$-elements (CEMP-$s/r$ stars). One formation scenario proposed for CEMP stars invokes wind mass transfer in the past from a TP-AGB primary star to a less massive companion star which is presently observed. We generate low-metallicity populations of binary stars to reproduce the observed CEMP-star fraction. In addition, we aim to constrain our wind mass-transfer model and investigate under which conditions our synthetic populations reproduce observed abundance distributions. We compare the CEMP fractions and the abundance distributions determined from our synthetic populations with observations. Several physical parameters of the binary stellar population of the halo are uncertain, e.g. the initial mass function, the mass-ratio and orbital-period distributions, and the binary fraction. We vary the assumptions in o...
11. Reconstruction of binary geological images using analytical edge and object models
Science.gov (United States)
2016-04-01
Reconstruction of fields using partial measurements is of vital importance in different applications in geosciences. Solving such an ill-posed problem requires a well-chosen model. In recent years, training images (TI) are widely employed as strong prior models for solving these problems. However, in the absence of enough evidence it is difficult to find an adequate TI which is capable of describing the field behavior properly. In this paper a very simple and general model is introduced which is applicable to a fairly wide range of binary images without any modifications. The model is motivated by the fact that nearly all binary images are composed of simple linear edges in micro-scale. The analytic essence of this model allows us to formulate the template matching problem as a convex optimization problem having efficient and fast solutions. The model has the potential to incorporate the qualitative and quantitative information provided by geologists. The image reconstruction problem is also formulated as an optimization problem and solved using an iterative greedy approach. The proposed method is capable of recovering the image unknown values with accuracies about 90% given samples representing as few as 2% of the original image.
12. Application of JAERI quantum molecular dynamics model for collisions of heavy nuclei
Directory of Open Access Journals (Sweden)
Ogawa Tatsuhiko
2016-01-01
Full Text Available The quantum molecular dynamics (QMD model incorporated into the general-purpose radiation transport code PHITS was revised for accurate prediction of fragment yields in peripheral collisions. For more accurate simulation of peripheral collisions, stability of the nuclei at their ground state was improved and the algorithm to reject invalid events was modified. In-medium correction on nucleon-nucleon cross sections was also considered. To clarify the effect of this improvement on fragmentation of heavy nuclei, the new QMD model coupled with a statistical decay model was used to calculate fragment production cross sections of Ag and Au targets and compared with the data of earlier measurement. It is shown that the revised version can predict cross section more accurately.
13. Modeling chiral criticality and its consequences for heavy-ion collisions
CERN Document Server
Almási, Gábor András; Redlich, Krzysztof
2016-01-01
We explore the critical fluctuations near the chiral critical endpoint (CEP) in a chiral effective model and discuss possible signals of the CEP, recently explored experimentally in nuclear collision. Particular attention is paid to the dependence of such signals on the location of the phase boundary and the EP relative to the chemical freeze-out conditions in nuclear collisions. We argue that in effective models, standard freeze-out fits to heavy-ion data should not be used directly. Instead, the relevant quantities should be examined on lines in the phase diagram that are defined self-consistently, within the framework of the model. We discuss possible choices for such an approach.
14. Model for fast, nonadiabatic collisions between alkali atoms and diatomic molecules
Science.gov (United States)
Hickman, A. P.
1980-11-01
Equations for collisions involving two potential surfaces are presented in the impact parameter approximation. In this approximation, a rectilinear classical trajectory is assumed for the translational motion, leading to a time-dependent Schroedinger's equation for the remaining degrees of freedom. Model potentials are considered for collisions of alkali atoms with diatomic molecules that lead to a particularly simple form of the final equations. Using the Magnus approximation, these equations are solved for parameters chosen to model the process Cs+O2→Cs++O2-, and total cross sections for ion-pair formation are obtained as a function of energy. The results exhibit oscillations that correspond qualitatively to those seen in recent measurements. In addition, the model predicts that the oscillations will become less pronounced as the initial vibrational level of O2 is increased.
15. Theoretical Model of Non-Conservative Mass Transfer with Uniform Mass Accretion Rate in Contact Binary Stars
Science.gov (United States)
Gharami, Prabir; Ghosh, Koushik; Rahaman, Farook
2016-01-01
In contact binaries mass transfer is usually non-conservative which ends into loss of mass as well as angular momentum in the system. In the present work we have presented a new mathematical model of the non-conservative mass transfer with a uniform mass accretion rate in a contact binary system with lower angular momentum. The model has been developed under the consideration of reverse mass transfer which may occur simultaneously with the original mass transfer as a result of the large scale circulations encircling the entire donor and a significant portion of the gainer. These circulations in contact binaries with lower angular momentum are caused by the overflow of the critical equipotential surface by both the components of the binary system making the governing system more intricate and uncertain.
16. Charged-particle rapidity density in Au+Au collisions in a quark combination model
Science.gov (United States)
Shao, Feng-Lan; Yao, Tao; Xie, Qu-Bing
2007-03-01
Rapidity/pseudorapidity densities for charged particles and their centrality, rapidity, and energy dependence in Au+Au collisions at the Relativistic Heavy Ion Collider are studied in a quark combination model. Using a Gaussian-type rapidity distribution for constituent quarks as a result of Landau hydrodynamic evolution, the data at sNN=130,200 GeV at various centralities in full pseudorapidity range are well described, and the charged-particle multiplicities are reproduced as functions of the number of participants. The energy dependence of the shape of the dNch/dη distribution is also described at various collision energies sNN=200,130,62.4 GeV in central collisions with same value of parameters except 19.6 GeV. The calculated rapidity distributions and yields for the charged pions and kaons in central Au+Au collisions at sNN=200 GeV are compared with experimental data of the BRAHMS Collaboration.
17. Modelling spatiotemporal olfactory data in two steps: from binary to Hodgkin-Huxley neurones.
Science.gov (United States)
Quenet, Brigitte; Dubois, Rémi; Sirapian, Sevan; Dreyfus, Gérard; Horn, David
2002-01-01
Network models of synchronously updated McCulloch-Pitts neurones exhibit complex spatiotemporal patterns that are similar to activities of biological neurones in phase with a periodic local field potential, such as those observed experimentally by Wehr and Laurent (1996, Nature 384, 162-166) in the locust olfactory pathway. Modelling biological neural nets with networks of simple formal units makes the dynamics of the model analytically tractable. It is thus possible to determine the constraints that must be satisfied by its connection matrix in order to make its neurones exhibit a given sequence of activity (see, for instance, Quenet et al., 2001, Neurocomputing 38-40, 831-836). In the present paper, we address the following question: how can one construct a formal network of Hodgkin-Huxley (HH) type neurones that reproduces experimentally observed neuronal codes? A two-step strategy is suggested in the present paper: first, a simple network of binary units is designed, whose activity reproduces the binary experimental codes; second, this model is used as a guide to design a network of more realistic formal HH neurones. We show that such a strategy is indeed fruitful: it allowed us to design a model that reproduces the Wehr-Laurent olfactory codes, and to investigate the robustness of these codes to synaptic noise.
18. Frequency domain reduced order models for gravitational waves from aligned-spin black-hole binaries
CERN Document Server
Pürrer, Michael
2014-01-01
Black-hole binary coalescences are one of the most promising sources for the first detection of gravitational waves. Fast and accurate theoretical models of the gravitational radiation emitted from these coalescences are highly important for the detection and extraction of physical parameters. Spinning effective-one-body (EOB) models for binaries with aligned spins have been shown to be highly faithful, but are slow to generate and thus have not yet been used for parameter estimation studies. I provide a frequency-domain singular value decomposition (SVD)-based surrogate reduced order model that is thousands to hundred thousands times faster for typical system masses and has a faithfulness mismatch of better than $\\sim 0.1\\%$ with the original SEOBNRv1 model for advanced LIGO detectors. This model enables parameter estimation studies up to signal-to-noise ratios (SNRs) of 20 and even up to SNR 50 for masses below $50 M_\\odot$. This article discusses various choices for approximations and interpolation over th...
19. MODELING VAPOR LIQUID EQUILIBRIUM OF IONIC LIQUIDS plus GAS BINARY SYSTEMS AT HIGH PRESSURE WITH CUBIC EQUATIONS OF STATE
OpenAIRE
Freitas, ACD; Cunico, LP; M. Aznar; Guirardello,R.
2013-01-01
Ionic liquids (IL) have been described as novel environmentally benign solvents because of their remarkable characteristics. Numerous applications of these solvents continue to grow at an exponential rate. In this work, high pressure vapor liquid equilibria for 17 different IL + gas binary systems were modeled at different temperatures with Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state, combined with the van der Waals mixing rule with two binary interaction parameters (v...
20. An effective model for entropy deposition in high-energy pp, pA, and AA collisions
CERN Document Server
Moreland, J Scott; Bass, Steffen A
2014-01-01
We introduce TRENTO, a new initial condition model for high-energy nuclear collisions based on eikonal entropy deposition via a "reduced thickness" function. The model simultaneously predicts the shapes of experimental proton-proton, proton-nucleus, and nucleus-nucleus multiplicity distributions, and generates nucleus-nucleus eccentricity harmonics consistent with experimental flow constraints. In addition, the model provides a possible resolution to the "knee" puzzle in ultra-central uranium-uranium collisions.
1. The development and verification of a highly accurate collision prediction model for automated noncoplanar plan delivery
Energy Technology Data Exchange (ETDEWEB)
Yu, Victoria Y.; Tran, Angelia; Nguyen, Dan; Cao, Minsong; Ruan, Dan; Low, Daniel A.; Sheng, Ke, E-mail: [email protected] [Department of Radiation Oncology, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California 90024 (United States)
2015-11-15
Purpose: Significant dosimetric benefits had been previously demonstrated in highly noncoplanar treatment plans. In this study, the authors developed and verified an individualized collision model for the purpose of delivering highly noncoplanar radiotherapy and tested the feasibility of total delivery automation with Varian TrueBeam developer mode. Methods: A hand-held 3D scanner was used to capture the surfaces of an anthropomorphic phantom and a human subject, which were positioned with a computer-aided design model of a TrueBeam machine to create a detailed virtual geometrical collision model. The collision model included gantry, collimator, and couch motion degrees of freedom. The accuracy of the 3D scanner was validated by scanning a rigid cubical phantom with known dimensions. The collision model was then validated by generating 300 linear accelerator orientations corresponding to 300 gantry-to-couch and gantry-to-phantom distances, and comparing the corresponding distance measurements to their corresponding models. The linear accelerator orientations reflected uniformly sampled noncoplanar beam angles to the head, lung, and prostate. The distance discrepancies between measurements on the physical and virtual systems were used to estimate treatment-site-specific safety buffer distances with 0.1%, 0.01%, and 0.001% probability of collision between the gantry and couch or phantom. Plans containing 20 noncoplanar beams to the brain, lung, and prostate optimized via an in-house noncoplanar radiotherapy platform were converted into XML script for automated delivery and the entire delivery was recorded and timed to demonstrate the feasibility of automated delivery. Results: The 3D scanner measured the dimension of the 14 cm cubic phantom within 0.5 mm. The maximal absolute discrepancy between machine and model measurements for gantry-to-couch and gantry-to-phantom was 0.95 and 2.97 cm, respectively. The reduced accuracy of gantry-to-phantom measurements was
2. Modeling the dynamics of tidally-interacting binary neutron stars up to merger
CERN Document Server
Bernuzzi, Sebastiano; Dietrich, Tim; Damour, Thibault
2014-01-01
We propose an effective-one-body (EOB) model that describes the general relativistic dynamics of neutron star binaries from the early inspiral up to merger. Our EOB model incorporates an enhanced attractive tidal potential motivated by recent analytical advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. No fitting parameters are introduced for the description of tidal interaction in the late, strong-field dynamics. We compare the model dynamics (described by the gauge invariant relation between binding energy and orbital angular momentum), and the gravitational wave phasing, with new high-resolution multi-orbit numerical relativity simulations of equal-mass configurations with different equations of state. We find agreement essentially within the uncertainty of the numerical data for all the configurations. Our model is the first semi-analytical model which captures the tidal amplification effects close to merger. It thereby provides the most accurate a...
3. The role of metallicity in high mass X-ray binaries in galaxy formation models
CERN Document Server
Artale, M C; Tissera, P B
2014-01-01
Context: Recent theoretical works claim that high-mass X-ray binaries (HMXBs) could have been important sources of energy feedback into the interstellar and intergalactic media, playing a major role in the reionization epoch. A metallicity dependence of the production rate or luminosity of the sources is a key ingredient generally assumed but not yet probed. Aims: Our goal is to explore the relation between the X-ray luminosity (Lx) and star formation rate of galaxies as a possible tracer of a metallicity dependence of the production rates and/or X-ray luminosities of HMXBs. Methods: We developed a model to estimate the Lx of star forming galaxies based on stellar evolution models which include metallicity dependences. We applied our X-ray binary models to galaxies selected from hydrodynamical cosmological simulations which include chemical evolution of the stellar populations in a self-consistent way. Results: Our models successfully reproduce the dispersion in the observed relations as an outcome of the com...
4. User manual for GEOCOST: a computer model for geothermal cost analysis. Volume 2. Binary cycle version
Energy Technology Data Exchange (ETDEWEB)
Huber, H.D.; Walter, R.A.; Bloomster, C.H.
1976-03-01
A computer model called GEOCOST has been developed to simulate the production of electricity from geothermal resources and calculate the potential costs of geothermal power. GEOCOST combines resource characteristics, power recovery technology, tax rates, and financial factors into one systematic model and provides the flexibility to individually or collectively evaluate their impacts on the cost of geothermal power. Both the geothermal reservoir and power plant are simulated to model the complete energy production system. In the version of GEOCOST in this report, geothermal fluid is supplied from wells distributed throughout a hydrothermal reservoir through insulated pipelines to a binary power plant. The power plant is simulated using a binary fluid cycle in which the geothermal fluid is passed through a series of heat exchangers. The thermodynamic state points in basic subcritical and supercritical Rankine cycles are calculated for a variety of working fluids. Working fluids which are now in the model include isobutane, n-butane, R-11, R-12, R-22, R-113, R-114, and ammonia. Thermodynamic properties of the working fluids at the state points are calculated using empirical equations of state. The Starling equation of state is used for hydrocarbons and the Martin-Hou equation of state is used for fluorocarbons and ammonia. Physical properties of working fluids at the state points are calculated.
5. Dynamical model of binary asteroid systems through patched three-body problems
Science.gov (United States)
Ferrari, Fabio; Lavagna, Michèle; Howell, Kathleen C.
2016-08-01
The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.
6. Symmetrization of excess Gibbs free energy: A simple model for binary liquid mixtures
Energy Technology Data Exchange (ETDEWEB)
Castellanos-Suarez, Aly J., E-mail: [email protected] [Centro de Estudios Interdisciplinarios de la Fisica (CEIF), Instituto Venezolano de Investigaciones Cientificas (IVIC), Apartado 21827, Caracas 1020A (Venezuela, Bolivarian Republic of); Garcia-Sucre, Maximo, E-mail: [email protected] [Centro de Estudios Interdisciplinarios de la Fisica (CEIF), Instituto Venezolano de Investigaciones Cientificas (IVIC), Apartado 21827, Caracas 1020A (Venezuela, Bolivarian Republic of)
2011-03-15
A symmetric expression for the excess Gibbs free energy of liquid binary mixtures is obtained using an appropriate definition for the effective contact fraction. We have identified a mechanism of local segregation as the main cause of the contact fraction variation with the concentration. Starting from this mechanism we develop a simple model for describing binary liquid mixtures. In this model two parameters appear: one adjustable, and the other parameter depending on the first one. Following this procedure we reproduce the experimental data of (liquid + vapor) equilibrium with a degree of accuracy comparable to well-known more elaborated models. The way in which we take into account the effective contacts between molecules allows identifying the compound which may be considered to induce one of the following processes: segregation, anti-segregation and dispersion of the components in the liquid mixture. Finally, the simplicity of the model allows one to obtain only one resulting interaction energy parameter, which makes easier the physical interpretation of the results.
7. Satellite Collision Modeling with Physics-Based Hydrocodes: Debris Generation Predictions of the Iridium-Cosmos Collision Event and Other Impact Events
Energy Technology Data Exchange (ETDEWEB)
Springer, H K; Miller, W O; Levatin, J L; Pertica, A J; Olivier, S S
2010-09-06
Satellite collision debris poses risks to existing space assets and future space missions. Predictive models of debris generated from these hypervelocity collisions are critical for developing accurate space situational awareness tools and effective mitigation strategies. Hypervelocity collisions involve complex phenomenon that spans several time- and length-scales. We have developed a satellite collision debris modeling approach consisting of a Lagrangian hydrocode enriched with smooth particle hydrodynamics (SPH), advanced material failure models, detailed satellite mesh models, and massively parallel computers. These computational studies enable us to investigate the influence of satellite center-of-mass (CM) overlap and orientation, relative velocity, and material composition on the size, velocity, and material type distributions of collision debris. We have applied our debris modeling capability to the recent Iridium 33-Cosmos 2251 collision event. While the relative velocity was well understood in this event, the degree of satellite CM overlap and orientation was ill-defined. In our simulations, we varied the collision CM overlap and orientation of the satellites from nearly maximum overlap to partial overlap on the outermost extents of the satellites (i.e, solar panels and gravity boom). As expected, we found that with increased satellite overlap, the overall debris cloud mass and momentum (transfer) increases, the average debris size decreases, and the debris velocity increases. The largest predicted debris can also provide insight into which satellite components were further removed from the impact location. A significant fraction of the momentum transfer is imparted to the smallest debris (< 1-5mm, dependent on mesh resolution), especially in large CM overlap simulations. While the inclusion of the smallest debris is critical to enforcing mass and momentum conservation in hydrocode simulations, there seems to be relatively little interest in their
8. Ion-biomolecule collisions studied within the independent atom model including geometric screening corrections
Science.gov (United States)
Lüdde, H. J.; Achenbach, A.; Kalkbrenner, T.; Jankowiak, H. C.; Kirchner, T.
2016-05-01
A recently introduced model to account for geometric screening corrections in an independent-atom-model description of ion-molecule collisions is applied to proton collisions from amino acids and DNA and RNA nucleobases. The correction coefficients are obtained from using a pixel counting method (PCM) for the exact calculation of the effective cross sectional area that emerges when the molecular cross section is pictured as a structure of (overlapping) atomic cross sections. This structure varies with the relative orientation of the molecule with respect to the projectile beam direction and, accordingly, orientation-independent total cross sections are obtained from averaging the pixel count over many orientations. We present net capture and net ionization cross sections over wide ranges of impact energy and analyze the strength of the screening effect by comparing the PCM results with Bragg additivity rule cross sections and with experimental data where available. Work supported by NSERC, Canada.
9. An Oriented-Eddy Collision Model for Turbulence Prediction
Science.gov (United States)
2007-06-15
kinetic energy, K, and dissipation rate, E). There is also a hypothesized algebraic constitutive equation relating these two scalar quantities and the...elliptic relaxation ( Durbin ) have even expanded the predictive scope of these models. Nevertheless, it is well understood at this time, even by CFD users...Publisher, 1993 P.A. Durbin , Near-wall turbulence closure modeling without ’damping functions’, Theoret. Comput. Fluid Dynamics 3, 1-13, 1991. W. C
10. An inequality for correlations in unidimensional monotone latent variable models for binary variables.
Science.gov (United States)
Ellis, Jules L
2014-04-01
It is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations: The negative logarithm of the correlations satisfies the triangle inequality. This inequality is not implied by the condition that the correlations are nonnegative, the criterion that coefficient H exceeds 0.30, or manifest monotonicity. The inequality implies both a lower bound and an upper bound for each correlation between two items, based on the correlations of those two items with every possible third item. It is discussed how this can be used in Mokken's (A theory and procedure of scale-analysis, Mouton, The Hague, 1971) scale analysis.
11. Correlation of liquid-liquid equilibria of non-ideal binary systems by NRTL model
Directory of Open Access Journals (Sweden)
Grozdanić Nikola D.
2013-01-01
Full Text Available Non Random Two Liquid model (NRTL with three different forms of temperature dependant parameters was used to correlate the liquid - liquid equilibrium data for systems of alcohols with alkanes, and alcohols with two ionic liquids: 1-butyl-2,3-dimethylimidazolium tetrafluoroborate ([bmmim][BF4] and 1-butyl-3-ethylimidazolium tetrafluoroborate ([beim][BF4]. Different temperature dependences of NRTL parameters were tested on thirteen literature experimental liquid - liquid equilibrium data for binary systems. [Projekat Ministarstva nauke Republike Srbije, br. 172063
12. Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition
KAUST Repository
van der Zee, Kristoffer G.
2010-10-27
A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward-in-time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one- and two-dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc.
13. Phase field modeling of multiple dendrite growth of AI-Si binary alloy under isothermal solidification
Institute of Scientific and Technical Information of China (English)
Sun Qiang; Zhang Yutuo; Cui Haixia; Wang Chengzhi
2008-01-01
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in Ai-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.
14. Testing Lorentz violation with binary pulsars: constraints on standard model extension
Institute of Scientific and Technical Information of China (English)
Yi Xie
2013-01-01
Under the standard model extension (SME) framework,Lorentz invariance is tested in five binary pulsars:PSR J0737-3039,PSR B 1534+ 12,PSR J 1756-2251,PSR B1913+16 and PSR B2127+11C.By analyzing the advance of periastron,we obtain the constraints on a dimensionless combination of SME parameters that is sensitive to timing observations.The results imply no evidence for the break of Lorentz invariance at the 10-10 level,one order of magnitude larger than the previous estimation.
15. Non-convex model of the binary asteroid (809) Lundia and its density estimation
Science.gov (United States)
Kryszczynska, A.; Bartczak, P.; Polinska, M.; Colas, F.
2014-07-01
Introduction: (809) Lundia was classified as a V-type asteroid in the Flora family (Florczak et.al. 2002). The binary nature of (809) Lundia was discovered in September 2005 based on photometric observations. The first modeling of the Lundia synchronous binary system was based on 22 lightcurves obtained at Borowiec and Pic du Midi Observatories during two oppositions in 2005/2006 and 2006/2007. Two methods of modeling --- modified Roche ellipsoids and kinematic --- gave similar parameters for the system (Kryszczynska et al. 2009). The poles of the orbit in ecliptic coordinates were: longitude 118° and latitude 28° in the modified Roche model and 120°, 18°, respectively, in the kinematic model. The orbital period obtained from the lightcurve analysis as well as from modeling was 15.418 h. The obtained bulk density of both components was 1.64 or 1.71 g/ccm. Observations: We observed (809) Lundia in the 2008, 2009/2010, 2011, and 2012 oppositions at the Borowiec, Pic du Midi, Prompt, and Rozhen Observatories. As predicted, the visible eclipses/occultation events were observed only in 2011. Currently, our dataset consists of 45 individual lightcurves and they were all used in the new modeling. Method: We used new method of modeling based on a genetic algorithm that is able to create a non-convex asteroid shape model, rotational period, and spin-axis orientation of a single or binary asteroid, using only photometric observations. The details of the method are presented in the poster by Bartczak et al., at this conference. Results: The new non-convex model of (809) Lundia is presented in the figure. The parameters of the system in the ecliptic coordinates are: longitude 122°, latitude 22°, and sidereal period 15.41574 h. They are very similar to the values obtained before. However, assuming an equivalent diameter of a single body of 9.1 km from the Spitzer observations (Marchis et al. 2012) and the volume of the two modeled bodies, the separation of the components
16. Modeling the Collision Phenomena of Ø11X19 Size Rolls
Directory of Open Access Journals (Sweden)
Tiberiu Manescu jr.
2011-09-01
Full Text Available This paper presents a numerical comparison using dynamic modeling techniques, of physical phenomena occurring at collisions between two rollers in a lot of distinct situations: impact on the edge at angles of 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80° and impact on generator. These situations occur frequently in the manufacturing process of small cylindrical rollers.
17. Gluon Saturation Model with Geometric Scaling for Net-Baryon Distributions in Relativistic Heavy Ion Collisions
Institute of Scientific and Technical Information of China (English)
李双; 冯笙琴
2012-01-01
The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. The net-baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions are investigated by taking advantage of the gluon saturation model with geometric scaling. Predications are made for the net-baryon rapidity distributions, mean rapidity loss and gluon saturation features in central Pb ＋ Pb collisions at LHC.
18. Modeling and simulation for a new virtual-clock-based collision resolution algorithm
Institute of Scientific and Technical Information of China (English)
Yin rupo; Cai yunze; He xing; Zhang weidong; Xu xiaoming
2006-01-01
Virtual time Ethernet is a multiple access protocol proposed to provide FCFS transmission service over the predominant Ethernet bus. It incorporates a novel message-rescheduling algorithm based on the virtual clock mechanism. By manipulating virtual clocks back up over a common virtual time axis and performing timely collision resolution, the algorithm guarantees the system's queuing strictness. The protocol is particularly modeled as a finite state machine and implemented using OPNET tools. Simulation studies prove its correctness and effectiveness.
19. A Habitat-based Wind-Wildlife Collision Model with Application to the Upper Great Plains Region
Energy Technology Data Exchange (ETDEWEB)
Forcey, Greg, M.
2012-08-28
Most previous studies on collision impacts at wind facilities have taken place at the site-specific level and have only examined small-scale influences on mortality. In this study, we examine landscape-level influences using a hierarchical spatial model combined with existing datasets and life history knowledge for: Horned Lark, Red-eyed Vireo, Mallard, American Avocet, Golden Eagle, Whooping Crane, red bat, silver-haired bat, and hoary bat. These species were modeled in the central United States within Bird Conservation Regions 11, 17, 18, and 19. For the bird species, we modeled bird abundance from existing datasets as a function of habitat variables known to be preferred by each species to develop a relative abundance prediction for each species. For bats, there are no existing abundance datasets so we identified preferred habitat in the landscape for each species and assumed that greater amounts of preferred habitat would equate to greater abundance of bats. The abundance predictions for bird and bats were modeled with additional exposure factors known to influence collisions such as visibility, wind, temperature, precipitation, topography, and behavior to form a final mapped output of predicted collision risk within the study region. We reviewed published mortality studies from wind farms in our study region and collected data on reported mortality of our focal species to compare to our modeled predictions. We performed a sensitivity analysis evaluating model performance of 6 different scenarios where habitat and exposure factors were weighted differently. We compared the model performance in each scenario by evaluating observed data vs. our model predictions using spearmans rank correlations. Horned Lark collision risk was predicted to be highest in the northwestern and west-central portions of the study region with lower risk predicted elsewhere. Red-eyed Vireo collision risk was predicted to be the highest in the eastern portions of the study region and in
20. A Habitat-based Wind-Wildlife Collision Model with Application to the Upper Great Plains Region
Energy Technology Data Exchange (ETDEWEB)
Forcey, Greg, M.
2012-08-28
Most previous studies on collision impacts at wind facilities have taken place at the site-specific level and have only examined small-scale influences on mortality. In this study, we examine landscape-level influences using a hierarchical spatial model combined with existing datasets and life history knowledge for: Horned Lark, Red-eyed Vireo, Mallard, American Avocet, Golden Eagle, Whooping Crane, red bat, silver-haired bat, and hoary bat. These species were modeled in the central United States within Bird Conservation Regions 11, 17, 18, and 19. For the bird species, we modeled bird abundance from existing datasets as a function of habitat variables known to be preferred by each species to develop a relative abundance prediction for each species. For bats, there are no existing abundance datasets so we identified preferred habitat in the landscape for each species and assumed that greater amounts of preferred habitat would equate to greater abundance of bats. The abundance predictions for bird and bats were modeled with additional exposure factors known to influence collisions such as visibility, wind, temperature, precipitation, topography, and behavior to form a final mapped output of predicted collision risk within the study region. We reviewed published mortality studies from wind farms in our study region and collected data on reported mortality of our focal species to compare to our modeled predictions. We performed a sensitivity analysis evaluating model performance of 6 different scenarios where habitat and exposure factors were weighted differently. We compared the model performance in each scenario by evaluating observed data vs. our model predictions using spearmans rank correlations. Horned Lark collision risk was predicted to be highest in the northwestern and west-central portions of the study region with lower risk predicted elsewhere. Red-eyed Vireo collision risk was predicted to be the highest in the eastern portions of the study region and in
1. Modelling of the Internal Mechanics in Ship Collisions
DEFF Research Database (Denmark)
Paik, Jeom Kee; Pedersen, Preben Terndrup
1996-01-01
on the stiffness and the strength is considered as well. In order to include the coupling effects between local and global failure of the structure, the usual non-linear finite-element technique is applied. In order to deal with the gap and contact conditions between the striking and the struck ships, gap....../contact elements are employed. Dynamic effects are considered by inclusion of the influence of strain-Rate sensitivity in the material model. On the basis of the theory a computer program has been written. The procedure is verified by a comparison of experimental results obtained from test models of double...
2. Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation
Science.gov (United States)
Ren, Feng; Song, Baowei; Sukop, Michael C.; Hu, Haibao
2016-08-01
The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp-interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen-Cahn equation (ACE) [Geier et al., Phys. Rev. E 91, 063309 (2015), 10.1103/PhysRevE.91.063309] under the framework of the lattice Boltzmann method (LBM), with incorporation of the incompressible hydrodynamic equations [Liang et al., Phys. Rev. E 89, 053320 (2014), 10.1103/PhysRevE.89.053320]. Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman-Enskog analysis. We also simulate four phase-tracking benchmark cases, including one three-dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh-Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g., high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling.
3. Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states
CERN Document Server
Thiele, Uwe; Frastia, Lubor
2007-01-01
A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibrium thermodynamics for a general non-isothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.
4. A magnetic model for low/hard state of black hole binaries
CERN Document Server
Ye, Yong-Chun; Huang, Chang-Yin; Cao, Xiao-Feng
2015-01-01
A magnetic model for low/hard state (LHS) of black hole X-ray binaries (BHXBs),H1743-322 and GX 339-4, is proposed based on the transportation of magnetic field from a companion into an accretion disk around a black hole (BH). This model consists of a truncated thin disk with an inner advection-dominated accretion flow (ADAF). The spectral profiles of the sources are fitted in agreement with the data observed at four different dates corresponding to the rising phase of the LHS. In addition, the association of the LHS with quasi-steady jet is modelled based on transportation of magnetic field, where the Blandford-Znajek (BZ) and Blandford-Payne (BP) processes are invoked to drive the jets from BH and inner ADAF. It turns out that the steep radio/X-ray correlations observed in H1743-322 and GX 339-4 can be interpreted based on our model.
5. Phase-field simulation of dendritic growth for binary alloys with complicate solution models
Institute of Scientific and Technical Information of China (English)
LI Xin-zhong; GUO Jing-jie; SU Yan-qing; WU Shi-ping; FU Heng-zhi
2005-01-01
A phase-field method for simulation of dendritic growth in binary alloys with complicate solution models was studied. The free energy densities of solid and liquid used to construct the free energy of a solidification system in the phase-field model were derived from the Calphad thermodynamic modeling of phase diagram. The dendritic growth of Ti-Al alloy with a quasi-sub regular solution model was simulated in both an isothermal and a nonisothermal regime. In the isothermal one, different initial solute compositions and melt temperatures were chosen.And in the non-isothermal one, release of latent heat during solidification was considered. Realistic growth patterns of dendrite are derived. Both the initial compositions and melt temperatures affect isothermal dendritic morphology and solute distributions much, especially the latter. Release of latent heat will cause a less developed structure of dendrite and a lower interfacial composition.
6. On the use of the dual process Langmuir model for predicting unary and binary isosteric heats of adsorption.
Science.gov (United States)
Bhadra, Shubhra J; Ebner, Armin D; Ritter, James A
2012-05-01
7. A Data-Based Approach for Modeling and Analysis of Vehicle Collision by LPV-ARMAX Models
Directory of Open Access Journals (Sweden)
Qiugang Lu
2013-01-01
Full Text Available Vehicle crash test is considered to be the most direct and common approach to assess the vehicle crashworthiness. However, it suffers from the drawbacks of high experiment cost and huge time consumption. Therefore, the establishment of a mathematical model of vehicle crash which can simplify the analysis process is significantly attractive. In this paper, we present the application of LPV-ARMAX model to simulate the car-to-pole collision with different initial impact velocities. The parameters of the LPV-ARMAX are assumed to have dependence on the initial impact velocities. Instead of establishing a set of LTI models for vehicle crashes with various impact velocities, the LPV-ARMAX model is comparatively simple and applicable to predict the responses of new collision situations different from the ones used for identification. Finally, the comparison between the predicted response and the real test data is conducted, which shows the high fidelity of the LPV-ARMAX model.
8. Influence of Earth crust composition on continental collision style in Precambrian conditions: Results of supercomputer modelling
Science.gov (United States)
2016-04-01
A number of issues concerning Precambrian geodynamics still remain unsolved because of uncertainity of many physical (thermal regime, lithosphere thickness, crust thickness, etc.) and chemical (mantle composition, crust composition) parameters, which differed considerably comparing to the present day values. In this work, we show results of numerical supercomputations based on petrological and thermomechanical 2D model, which simulates the process of collision between two continental plates, each 80-160 km thick, with various convergence rates ranging from 5 to 15 cm/year. In the model, the upper mantle temperature is 150-200 ⁰C higher than the modern value, while the continental crust radiogenic heat production is higher than the present value by the factor of 1.5. These settings correspond to Archean conditions. The present study investigates the dependence of collision style on various continental crust parameters, especially on crust composition. The 3 following archetypal settings of continental crust composition are examined: 1) completely felsic continental crust; 2) basic lower crust and felsic upper crust; 3) basic upper crust and felsic lower crust (hereinafter referred to as inverted crust). Modeling results show that collision with completely felsic crust is unlikely. In the case of basic lower crust, a continental subduction and subsequent continental rocks exhumation can take place. Therefore, formation of ultra-high pressure metamorphic rocks is possible. Continental subduction also occurs in the case of inverted continental crust. However, in the latter case, the exhumation of felsic rocks is blocked by upper basic layer and their subsequent interaction depends on their volume ratio. Thus, if the total inverted crust thickness is about 15 km and the thicknesses of the two layers are equal, felsic rocks cannot be exhumed. If the total thickness is 30 to 40 km and that of the felsic layer is 20 to 25 km, it breaks through the basic layer leading to
9. Galilean invariance in the exponential model of atomic collisions
Energy Technology Data Exchange (ETDEWEB)
del Pozo, A.; Riera, A.; Yaez, M.
1986-11-01
Using the X/sup n//sup +/(1s/sup 2/)+He/sup 2+/ colliding systems as specific examples, we study the origin dependence of results in the application of the two-state exponential model, and we show the relevance of polarization effects in that study. Our analysis shows that polarization effects of the He/sup +/(1s) orbital due to interaction with X/sup (//sup n//sup +1)+/ ion in the exit channel yield a very small contribution to the energy difference and render the dynamical coupling so strongly origin dependent that it invalidates the basic premises of the model. Further study, incorporating translation factors in the formalism, is needed.
10. Border Collision Bifurcations in a Generalized Model of Population Dynamics
Directory of Open Access Journals (Sweden)
2016-01-01
Full Text Available We analyze the dynamics of a generalized discrete time population model of a two-stage species with recruitment and capture. This generalization, which is inspired by other approaches and real data that one can find in literature, consists in considering no restriction for the value of the two key parameters appearing in the model, that is, the natural death rate and the mortality rate due to fishing activity. In the more general case the feasibility of the system has been preserved by posing opportune formulas for the piecewise map defining the model. The resulting two-dimensional nonlinear map is not smooth, though continuous, as its definition changes as any border is crossed in the phase plane. Hence, techniques from the mathematical theory of piecewise smooth dynamical systems must be applied to show that, due to the existence of borders, abrupt changes in the dynamic behavior of population sizes and multistability emerge. The main novelty of the present contribution with respect to the previous ones is that, while using real data, richer dynamics are produced, such as fluctuations and multistability. Such new evidences are of great interest in biology since new strategies to preserve the survival of the species can be suggested.
11. Sensitivity Analysis for Iceberg Geometry Shape in Ship-Iceberg Collision in View of Different Material Models
OpenAIRE
Yan Gao; Zhiqiang Hu; Jin Wang
2014-01-01
The increasing marine activities in Arctic area have brought growing interest in ship-iceberg collision study. The purpose of this paper is to study the iceberg geometry shape effect on the collision process. In order to estimate the sensitivity parameter, five different geometry iceberg models and two iceberg material models are adopted in the analysis. The FEM numerical simulation is used to predict the scenario and the related responses. The simulation results including energy dissipation ...
12. Radar observations and physical modeling of binary near-Earth asteroid (1862) Apollo
Science.gov (United States)
Ford, Thomas F.; Benner, Lance A.; Brozovic, Marina; Leford, Bruce; Nolan, Michael C.; Giorgini, Jon D.; Ostro, Steve J.; Margot, Jean-Luc
2014-11-01
Binary asteroid 1862 Apollo has an extensive observational history allowing many of its characteristics to be investigated. Apollo was one of the first objects to show evidence for the YORP effect (Kaasalainen et al. 2007, Nature 446, 420) and its mass has been estimated by detection of the Yarkovsky effect (Nugent et al. 2012, AJ 144, 60; Farnocchia et al. 2013, Icarus 224, 1). We observed Apollo at Arecibo and Goldstone from Oct. 29-Nov. 13, 2005, obtaining a series of echo power spectra and delay-Doppler images that achieved resolutions as high as 7.5 m/pixel. The Arecibo images show that Apollo is a binary system with a rounded primary that has two large protrusions about 120 deg apart in longitude. We used the Arecibo data and published lightcurves to estimate the primary's 3D shape. Our best fit has major axes of ~1.8x1.5x1.3 km and a volume of ~1.6 km^3. The protrusions have lengths of ~300 and 200 m, are on the primary's equator, and give Apollo a distinctly different appearance from the primaries with equatorial ridges seen with other binary near-Earth asteroids. We estimated the pole by starting with the Kaasalainen et al. spin vector of ecliptic (longitude, latitude)=(50 deg, -71 deg) +- 7 deg and letting it float. Our best fit has a pole within 11 deg of (longitude, latitude)=(71, -72). Convex models produced from inversion of lightcurves by Kaasalainen et al. and thermal infrared data by Rozitis et al. (2013, A&A 555, A20) are more oblate than our model, do not show protrusions, and have somewhat different pole directions. The Arecibo images reveal weak but persistent echoes from a satellite on Nov. 1 and 2 but cover only a fraction of its orbit. The images are insufficient to estimate the satellite's shape and yield a rough estimate for its long axis of 190 m. Preliminary fits give an orbital period of ~27.0-27.5 h and a semimajor axis of ~3.5-4.0 km, implying a mass of 2.8-3.9E12 kg and a bulk density of 1.7-2.4 g/cm^3. The density is consistent with
13. Binding of Solvent Molecules to a Protein Surface in Binary Mixtures Follows a Competitive Langmuir Model.
Science.gov (United States)
Kulschewski, Tobias; Pleiss, Jürgen
2016-09-06
The binding of solvent molecules to a protein surface was modeled by molecular dynamics simulations of of Candida antarctica (C. antarctica) lipase B in binary mixtures of water, methanol, and toluene. Two models were analyzed: a competitive Langmuir model which assumes identical solvent binding sites with a different affinity toward water (KWat), methanol (KMet), and toluene (KTol) and a competitive Langmuir model with an additional interaction between free water and already bound water (KWatWat). The numbers of protein-bound molecules of both components of a binary mixture were determined for different compositions as a function of their thermodynamic activities in the bulk phase, and the binding constants were simultaneously fitted to the six binding curves (two components of three different mixtures). For both Langmuir models, the values of KWat, KMet, and KTol were highly correlated. The highest binding affinity was found for methanol, which was almost 4-fold higher than the binding affinities of water and toluene (KMet ≫ KWat ≈ KTol). Binding of water was dominated by the water-water interaction (KWatWat). Even for the three protein surface patches of highest water affinity, the binding affinity of methanol was 2-fold higher than water and 8-fold higher than toluene (KMet > KWat > KTol). The Langmuir model provides insights into the protein destabilizing mechanism of methanol which has a high binding affinity toward the protein surface. Thus, destabilizing solvents compete with intraprotein interactions and disrupt the tertiary structure. In contrast, benign solvents such as water or toluene have a low affinity toward the protein surface. Water is a special solvent: only few water molecules bind directly to the protein; most water molecules bind to already bound water molecules thus forming water patches. A quantitative mechanistic model of protein-solvent interactions that includes competition and miscibility of the components contributes a robust basis
14. Experimental determination and thermodynamic modeling of the Ni-Re binary system
Energy Technology Data Exchange (ETDEWEB)
Yaqoob, Khurram [Chimie Metallurgique des Terres Rares (CMTR), Institut de Chimie et des Materiaux Paris-Est (ICMPE), 2-8 rue Henri Dunant, 94320 Thiais Cedex (France); Joubert, Jean-Marc, E-mail: [email protected] [Chimie Metallurgique des Terres Rares (CMTR), Institut de Chimie et des Materiaux Paris-Est (ICMPE), 2-8 rue Henri Dunant, 94320 Thiais Cedex (France)
2012-12-15
The phase diagram of the Ni-Re binary system has been partially reinvestigated by chemical, structural and thermal characterization of the arc melted alloys. The experimental results obtained during the present investigation were combined with the literature data and a new phase diagram of the Ni-Re binary system is proposed. In comparison with the Ni-Re phase diagram proposed by Nash et al. in 1985 [1], significant differences in the homogeneity domains, freezing ranges and peritectic reaction temperature were evidenced. On the other hand, thermodynamic modeling of the studied system by using the new experimental information has also been carried out with the help of the CALPHAD method. The calculated Ni-Re phase diagram showed a good agreement with the selected experimental information. - Graphical abstract: Ni-Re phase diagram according to the present study. Highlights: Black-Right-Pointing-Pointer Re-investigation of the Ni-Re phase diagram. Black-Right-Pointing-Pointer Extended phase field of the hcp phase. Black-Right-Pointing-Pointer Different freezing ranges and peritectic reaction temperature. Black-Right-Pointing-Pointer Thermodynamic modeling of the studied system by using the CALPHAD method.
15. Analytic modeling of tidal effects in the relativistic inspiral of binary neutron stars.
Science.gov (United States)
Baiotti, Luca; Damour, Thibault; Giacomazzo, Bruno; Nagar, Alessandro; Rezzolla, Luciano
2010-12-31
To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB) model. The typical numerical phasing errors over the ≃22 GW cycles are Δϕ≃±0.24 rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.
16. FUV Emission from AGB Stars: Modeling Accretion Activity Associated with a Binary Companion
Science.gov (United States)
Stevens, Alyx Catherine; Sahai, Raghvendra
2012-01-01
It is widely believed that the late stages of evolution for Asymptotic Giant Branch (AGB) stars are influenced by the presence of binary companions. Unfortunately, there is a lack of direct observational evidence of binarity. However, more recently, strong indirect evidence comes from the discovery of UV emission in a subsample of these objects (fuvAGB stars). AGB stars are comparatively cool objects (< or =3000 K), thus their fluxes falls off drastically for wavelengths 3000 Angstroms and shorter. Therefore, ultraviolet observations offer an important, new technique for detecting the binary companions and/or associated accretion activity. We develop new models of UV emission from fuvAGB stars constrained by GALEX photometry and spectroscopy of these objects. We compare the GALEX UV grism spectra of the AGB M7 star EY Hya to predictions using the spectral synthesis code Cloudy, specifically investigating the ultraviolet wavelength range (1344-2831 Angstroms). We investigate models composed of contributions from a photoionized "hot spot" due to accretion activity around the companion, and "chromospheric" emission from collisionally ionized plasma, to fit the UV observations.
17. 3D MODELING OF TRANSPORT BINARY ELECTROLYTE IN THE GALVANOSTATIC MODE IN THE CONDITION OF ELECTRONEUTRALITY
Directory of Open Access Journals (Sweden)
Kovalenko A. V.
2015-06-01
Full Text Available In the article we have derived mathematical models of non-stationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc. for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus and EMS with RMD (rotating membrane disk. We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of Nernst-Planck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form
18. Gamma-ray binaries beyond one-zone models: an application to LS 5039
CERN Document Server
del Palacio, Santiago; Romero, Gustavo E
2014-01-01
Context. Several binary systems hosting massive stars present gamma-ray emission. In most of these systems, despite detailed observational information is available, the nature and the structure of the emitter are still poorly known. Aims. We investigate the validity of the so-called one-zone approximation for the high-energy emitter in binary systems hosting a massive star. In particular, the case of LS 5039 is considered. Methods. Assuming a point-like emitter at rest, the presence of a nearby massive star, and taking as a reference the observed MeV and GeV fluxes, a non-thermal leptonic model is systematically applied for di?erent locations, magnetic fields, and non-radiative losses. This allows the identification of both the emitter configurations most compatible with observations and inconsistencies between model predictions and the available data. Results. In the case of LS 5039, the best parameter combination is fast non-radiative cooling and a low magnetic field. However, discrepancies appear when comp...
19. Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests
CERN Document Server
Barnes, M; Dorland, W; Ernst, D R; Hammett, G W; Ricci, P; Rogers, B N; Schekochihin, A A; Tatsuno, T
2008-01-01
A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-Theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2 is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.
20. A simplified model of collision-driven dynamo action in small bodies
CERN Document Server
Wei, Xing
2013-01-01
We investigate numerically the self-sustained dynamo action in a spinning sphere whose sense of rotation reverses periodically. This system serves as a simple model of a dynamo in small bodies powered by frequent collisions. It is found that dynamo action is possible in some intervals of collision rates. At high Ekman numbers the laminar spin-up flow is helical in the boundary layers and the Ekman circulation together with the azimuthal shear powers the dynamo action. At low Ekman number a non-axisymmetric instability helps the dynamo action. The intermittency of magnetic field occurs at low Ekman number. A lower bound of magnetic energy is numerically obtained, and the space-averaged field in the fluid core and the surface field of a small body are roughly estimated.
1. Anomalous transport model study of chiral magnetic effects in heavy ion collisions
Science.gov (United States)
Sun, Yifeng; Ko, Che Ming; Li, Feng
2016-10-01
Using an anomalous transport model for massless quarks and antiquarks, we study the effect of a magnetic field on the elliptic flows of quarks and antiquarks in relativistic heavy ion collisions. With initial conditions from a blast wave model and assuming that the strong magnetic field produced in noncentral heavy ion collisions can last for a sufficiently long time, we obtain an appreciable electric quadrupole moment in the transverse plane of a heavy ion collision. The electric quadrupole moment subsequently leads to a splitting between the elliptic flows of quarks and antiquarks. The slope of the charge asymmetry dependence of the elliptic flow difference between positively and negatively charged particles is positive, which is expected from the chiral magnetic wave formed in the produced QGP and observed in experiments at the BNL Relativistic Heavy Ion Collider, only if the Lorentz force acting on the charged particles is neglected and the quark-antiquark scattering is assumed to be dominated by the chirality changing channel.
2. A selection model for longitudinal binary responses subject to non-ignorable attrition.
Science.gov (United States)
Alfò, Marco; Maruotti, Antonello
2009-08-30
Longitudinal studies collect information on a sample of individuals which is followed over time to analyze the effects of individual and time-dependent characteristics on the observed response. These studies often suffer from attrition: individuals drop out of the study before its completion time and thus present incomplete data records. When the missing mechanism, once conditioned on other (observed) variables, does not depend on current (eventually unobserved) values of the response variable, the dropout mechanism is known to be ignorable. We propose a selection model extending semiparametric variance component models for longitudinal binary responses to allow for dependence between the missing data mechanism and the primary response process. The model is applied to a data set from a methadone maintenance treatment programme held in Sidney, 1986.
3. A binary logistic regression model for discriminating real protein-protein interface
Institute of Scientific and Technical Information of China (English)
2003-01-01
The selection and study of descriptive variables of protein-protein complex interface is a major question that many biologists come across when the research of protein-protein recognition is concerned. Several variables have been proposed to understand the structural or energetic features of complex interfaces. Here a systematic study of some of these "traditional" variables, as well as a few new ones, is introduced. With the values of these variables extracted from 42 PDB samples with real or false complex interfaces, a binary logistic regression analysis is performed, which results in an effective empirical model for the evaluation of binding probabilities of protein-protein interfaces. The model is validated with 12 samples, and satisfactory results are obtained for both the training and validation sets. Meanwhile, three potential dimeric interfaces of staphylokinase have been investigated and one with the best suitability to our model is proposed.
4. Shape model of the binary near-Earth asteroid (285263) 1998 QE_2
Science.gov (United States)
Springmann, A.; Taylor, P.; Nolan, M.; Howell, E.; Benner, L.; Brozović, M.; Giorgini, J.; Busch, M.; Margot, J.; Lee, C.; Gao, J.
2014-07-01
5. A Bio-inspired Collision Avoidance Model Based on Spatial Information Derived from Motion Detectors Leads to Common Routes.
Science.gov (United States)
Bertrand, Olivier J N; Lindemann, Jens P; Egelhaaf, Martin
2015-11-01
Avoiding collisions is one of the most basic needs of any mobile agent, both biological and technical, when searching around or aiming toward a goal. We propose a model of collision avoidance inspired by behavioral experiments on insects and by properties of optic flow on a spherical eye experienced during translation, and test the interaction of this model with goal-driven behavior. Insects, such as flies and bees, actively separate the rotational and translational optic flow components via behavior, i.e. by employing a saccadic strategy of flight and gaze control. Optic flow experienced during translation, i.e. during intersaccadic phases, contains information on the depth-structure of the environment, but this information is entangled with that on self-motion. Here, we propose a simple model to extract the depth structure from translational optic flow by using local properties of a spherical eye. On this basis, a motion direction of the agent is computed that ensures collision avoidance. Flying insects are thought to measure optic flow by correlation-type elementary motion detectors. Their responses depend, in addition to velocity, on the texture and contrast of objects and, thus, do not measure the velocity of objects veridically. Therefore, we initially used geometrically determined optic flow as input to a collision avoidance algorithm to show that depth information inferred from optic flow is sufficient to account for collision avoidance under closed-loop conditions. Then, the collision avoidance algorithm was tested with bio-inspired correlation-type elementary motion detectors in its input. Even then, the algorithm led successfully to collision avoidance and, in addition, replicated the characteristics of collision avoidance behavior of insects. Finally, the collision avoidance algorithm was combined with a goal direction and tested in cluttered environments. The simulated agent then showed goal-directed behavior reminiscent of components of the navigation
6. Multiplicity and Pseudorapidity distributions of charged particles in asymmetric and deformed nuclear collisions in a Wounded Quark Model
CERN Document Server
Chaturvedi, O S K; Kumar, Ashwini; Singh, B K
2016-01-01
The charged particle multiplicity ($n_{ch}$) and pseudorapidity density $(dn_{ch}/d\\eta)$ are key observables to characterize the properties of matter created in heavy ion collisions. The dependence of these observables on collision energy and the collision geometry are a key tool to understand the underlying particle production mechanism. Recently a lot of focus on asymmetric nuclei as well as deformed nuclei collisions has been made as these collisions can provide a deeper understanding of the nature of quantum chromodynamics (QCD). On phenomenological perspective a unified model which describes the experimental data coming from various kind of collision experiments, is much needed to provide the physical insights about the production mechanism. In this paper, firstly we have calculated the charged hadron multiplicities for nucleon-nucleus (such as proton-lead (p-Pb) and asymmetric nuclei collisions like deutron-gold (d-Au), and copper-gold (Cu-Au) within our recently proposed wounded quark model (WQM) and ...
7. Modeling the Effect of Kick Velocity during the Accretion Induced Collapse of White Dwarfs on Binary Pulsars
Science.gov (United States)
Taani, Ali
2016-07-01
The kick velocity which arises during the binary interaction plays an important role in disruption or surviving the binary systems. This paper attempts to draw an evolutionary connection of the long-period (Porb ≥ 2 d) millisecond pulsars (MSPs) with orbits of low eccentricity (e ≤ 0.2). We propose that a kick velocity caused by dynamical effects of asymmetric collapse imparted to the companion star through an accretion induced collapse (AIC) of white dwarfs-that become unstable once they approach the Chandrasekhar limit-can account for the differences in their orbital period distributions. Furthermore, in some cases, an appropriate kick can disrupt the binary system and result in the birth of isolated MSPs. Otherwise, the binary survives and an eccentric binary MSP is formed. In this case only the binding energy equivalent (0.2M⊙) of mass is lost and the system remains intact in a symmetric collapse. Consequently, the AIC decreases the mass of the neutron star and increases the orbital period leading to orbit circularization. We present the results of our model and discuss the possible implications for the binary MSPs in galactic disk and globular clusters.
8. Modelling the effect of absorption from the interstellar medium on transient black hole X-ray binaries
Science.gov (United States)
Eckersall, A. J.; Vaughan, S.; Wynn, G. A.
2017-10-01
All observations of Galactic X-ray binaries are affected by absorption from gas and dust in the interstellar medium (ISM) which imprints narrow (line) and broad (photoelectric edges) features on the continuum emission spectrum of the binary. Any spectral model used to fit data from a Galactic X-ray binary must therefore take account of these features; when the absorption is strong (as for most Galactic sources) it becomes important to accurately model the ISM absorption in order to obtain unbiased estimates of the parameters of the (emission) spectrum of the binary system. In this paper, we present analysis of some of the best spectroscopic data from the XMM-Newton RGS instrument using the most up-to-date photoabsorption model of the gaseous ISM ISMabs. We calculate column densities for H, O, Ne and Fe for seven transient black hole X-ray binary systems. We find that the hydrogen column densities in particular can vary greatly from those presented elsewhere in the literature. We assess the impact of using inaccurate column densities and older X-ray absorption models on spectral analysis using simulated data. We find that poor treatment of absorption can lead to large biases in inferred disc properties and that an independent analysis of absorption parameters can be used to alleviate such issues.
9. Multilevel models for evaluating the risk of pedestrian-motor vehicle collisions at intersections and mid-blocks
Science.gov (United States)
Quistberg, D. Alex; Howard, Eric J.; Ebel, Beth E.; Moudon, Anne V.; Saelens, Brian E.; Hurvitz, Philip M.; Curtin, James E.; Rivara, Frederick P.
2015-01-01
10. Constraints on Planetesimal Collision Models in Debris Disks
CERN Document Server
MacGregor, Meredith A; Chandler, Claire; Ricci, Luca; Maddison, Sarah T; Cranmer, Steven R; Andrews, Sean M; Hughes, A Meredith; Steele, Amy
2016-01-01
Observations of debris disks offer a window into the physical and dynamical properties of planetesimals in extrasolar systems through the size distribution of dust grains. In particular, the millimeter spectral index of thermal dust emission encodes information on the grain size distribution. We have made new VLA observations of a sample of seven nearby debris disks at 9 mm, with 3" resolution and $\\sim5$ $\\mu$Jy/beam rms. We combine these with archival ATCA observations of eight additional debris disks observed at 7 mm, together with up-to-date observations of all disks at (sub)millimeter wavelengths from the literature to place tight constraints on the millimeter spectral indices and thus grain size distributions. The analysis gives a weighted mean for the slope of the power law grain size distribution, $n(a)\\propto a^{-q}$, of $\\langle q \\rangle = 3.36\\pm0.02$, with a possible trend of decreasing $q$ for later spectral type stars. We compare our results to a range of theoretical models of collisional casca...
11. D-meson observables in Pb-Pb and p-Pb collisions at LHC with EPOSHQ model
Science.gov (United States)
Ozvenchuk, V.; Aichelin, J.; Gossiaux, P. B.; Guiot, B.; Nahrgang, M.; Werner, K.
2017-01-01
We study the propagation of charm quarks in the quark-gluon plasma (QGP) created in ultrarelativistic heavy-ion and proton-nucleus collisions at LHC within EPOSHQ model. The interactions of heavy quarks with the light partons in ultrarelativistic heavy-ion collisions through the collisional and radiative processes lead to a large suppression of nal D-meson spectra at high transverse momentum and a nite D-meson elliptic ow, v 2, whereas in proton-nucleus collisions the D-meson nuclear modi cation factor, RpA , at high transverse momentum is compatible with unity. Our results are in good agreement with the available experimental data.
12. Predictions from a Simple Hadron Rescattering Model for pp Collisions at the LHC
Science.gov (United States)
Truesdale, David C.
13. Semiparametric Bayesian joint modeling of a binary and continuous outcome with applications in toxicological risk assessment.
Science.gov (United States)
Hwang, Beom Seuk; Pennell, Michael L
2014-03-30
Many dose-response studies collect data on correlated outcomes. For example, in developmental toxicity studies, uterine weight and presence of malformed pups are measured on the same dam. Joint modeling can result in more efficient inferences than independent models for each outcome. Most methods for joint modeling assume standard parametric response distributions. However, in toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by standard models. To address this issue, we propose a semiparametric Bayesian joint model for a binary and continuous response. In our model, a kernel stick-breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows flexible changes in distribution shape with dose shared across outcomes. The model also includes outcome-specific fixed effects to allow different location effects. In simulation studies, we found that the proposed model provides accurate estimates of toxicological risk when the data do not satisfy assumptions of standard parametric models. We apply our method to data from a developmental toxicity study of ethylene glycol diethyl ether.
14. Multi-fluid modeling of density segregation in a dense binary fluidized bed
Institute of Scientific and Technical Information of China (English)
Zhongxi Chao; Yuefa Wang; Jana P.Jakobsen; Maria Fernandino; Hugo A.Jakobsen
2012-01-01
This paper presents simulation results of the density segregation in a dense binary gas fluidized bed using a multi-fluid model from Chao et al.(2011).The segregation behavior of two types of particles with approximately same particle diameters and different particle densities was studied and validated using the experimental data from Formisani et al.(2008),Some detailed information regarding the gas,particle velocity profiles,the distributions of the particle volume fractions and the flotsam-to-total particle volume fraction ratios is presented.The simulation results show that the simulated axial average flotsam-to-total particle volume fraction ratio distribution agrees reasonably with the experimental data of Formisani et al.(2008).The binary particle velocities are closely coupled though the segregation exists.The segregation behavior and the particle velocity profiles are superficial gas velocity dependent.The number and distribution of particle velocity vortices change dramatically with superficial gas velocity:at a comparatively low superficial gas velocity,the particles mainly segregate axially,and at a comparatively high superficial gas velocity,the particles segregate both axially and radially.
15. Modelling of Sigma Scorpii, a high-mass binary with a Beta Cep variable primary component
CERN Document Server
Tkachenko, A; Pavlovski, K; Degroote, P; Papics, P I; Moravveji, E; Lehmann, H; Kolbas, V; Clemer, K
2014-01-01
High-mass binary stars are known to show an unexplained discrepancy between the dynamical masses of the individual components and those predicted by models. In this work, we study Sigma Scorpii, a double-lined spectroscopic binary system consisting of two B-type stars residing in an eccentric orbit. The more massive primary component is a Beta Cep-type pulsating variable star. Our analysis is based on a time-series of some 1000 high-resolution spectra collected with the CORALIE spectrograph in 2006, 2007, and 2008. We use two different approaches to determine the orbital parameters of the star; the spectral disentangling technique is used to separate the spectral contributions of the individual components in the composite spectra. The non-LTE based spectrum analysis of the disentangled spectra reveals two stars of similar spectral type and atmospheric chemical composition. Combined with the orbital inclination angle estimate found in the literature, our orbital elements allow a mass estimate of 14.7 +/- 4.5 a...
16. Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars
CERN Document Server
Baiotti, Luca; Giacomazzo, Bruno; Nagar, Alessandro; Rezzolla, Luciano
2010-01-01
To detect the gravitational-wave signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We have performed the longest (to date) general-relativistic simulations of binary neutron stars with different compactnesses and used them to constrain a tidal extension of the effective-one-body model so that it reproduces the numerical waveforms accurately and essentially up to the merger. The typical errors in the phase over the $\\simeq 22$ gravitational-wave cycles are $\\Delta \\phi\\simeq \\pm 0.24$ rad, thus with relative phase errors $\\Delta \\phi/\\phi \\simeq 0.2%$. We also show that with a single choice of parameters, the effective-one-body approach is able to reproduce all of the numerically-computed phase evolutions, in contrast with what found when adopting a tidally corrected post-Newtonian Taylor-T4 expansion.
17. Modelling the asymmetric wind of the luminous blue variable binary MWC 314
CERN Document Server
Lobel, A; Martayan, C; Frémat, Y; Dozinel, K Torres; Raskin, G; Van Winckel, H; Prins, S; Pessemier, W; Waelkens, C; Hensberge, H; Dummortier, L; Jorissen, A; Van Eck, S; Lehmann, H
2013-01-01
We present a spectroscopic analysis of MWC 314, a luminous blue variable (LBV) candidate with an extended bipolar nebula. The detailed spectroscopic variability is investigated to determine if MWC 314 is a massive binary system with a supersonically accelerating wind or a low-mass B[e] star. We compare the spectrum and spectral energy distribution to other LBVs (such as P Cyg) and find very similar physical wind properties, indicating strong kinship. We combined long-term high-resolution optical spectroscopic monitoring and V-band photometric observations to determine the orbital elements and stellar parameters and to investigate the spectral variability with the orbital phases. We developed an advanced model of the large-scale wind-velocity and wind-density structure with 3-D radiative transfer calculations that fit the orbitally modulated P Cyg profile of He I lam5876, showing outflow velocities above 1000 km/s. We find that MWC 314 is a massive semi-detached binary system of ~1.22 AU, observed at an inclin...
18. Extension of the hard-sphere particle-wall collision model to account for particle deposition.
Science.gov (United States)
Kosinski, Pawel; Hoffmann, Alex C
2009-06-01
Numerical simulations of flows of fluids with granular materials using the Eulerian-Lagrangian approach involve the problem of modeling of collisions: both between the particles and particles with walls. One of the most popular techniques is the hard-sphere model. This model, however, has a major drawback in that it does not take into account cohesive or adhesive forces. In this paper we develop an extension to a well-known hard-sphere model for modeling particle-wall interactions, making it possible to account for adhesion. The model is able to account for virtually any physical interaction, such as van der Waals forces or liquid bridging. In this paper we focus on the derivation of the new model and we show some computational results.
19. A new non-convex model of the binary asteroid 90 Antiope obtained with the SAGE modelling technique
Science.gov (United States)
Bartczak, P.; Michałowski, T.; Santana-Ros, T.; Dudziński, G.
2014-09-01
We present a new non-convex model of the 90 Antiope binary asteroid, derived with a modified version of the Shaping Asteroids with Genetic Evolution (SAGE) method using disc-integrated photometry only. A new variant of the SAGE algorithm capable of deriving models of binary systems is described. The model of 90 Antiope confirms the system's pole solution (λ = 199°, β = 38°, σ = ±5°) and the orbital period (16.505 046 ± 0.000 005 h). A comparison between the stellar occultation chords obtained during the 2011 occultation and the projected shape solution has been used to scale the model. The resulting scaled model allowed us to obtain the equivalent radii (R1 = 40.4 ± 0.9 km and R2 = 40.2 ± 0.9 km) and the distance between the two system components (176 ± 4 km), leading to a total system mass of (9.14 ± 0.62) · 1017 kg. The non-convex shape description of the components permitted a refined calculation of the components' volumes, leading to a density estimation of 1.67 ± 0.23 g cm-3. The intermediate-scale features of the model may also offer new clues on the components' origin and evolution.
20. Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification
Science.gov (United States)
Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam
2017-05-01
The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.
1. STATE SPACE GENERATION FRAMEWORK BASED ON BINARY DECISION DIAGRAM FOR DISTRIBUTED EXPLICIT MODEL CHECKING
Directory of Open Access Journals (Sweden)
Nacer Tabib
2016-01-01
Full Text Available This paper proposes a new framework based on Binary Decision Diagrams (BDD for the graph distribution problem in the context of explicit model checking. The BDD are yet used to represent the state space for a symbolic verification model checking. Thus, we took advantage of high compression ratio of BDD to encode not only the state space, but also the place where each state will be put. So, a fitness function that allows a good balance load of states over the nodes of an homogeneous network is used. Furthermore, a detailed explanation of how to calculate the inter-site edges between different nodes based on the adapted data structure is presented.
2. Erosion study of Fe–W binary mixed layer prepared as model system for RAFM steel
Energy Technology Data Exchange (ETDEWEB)
Sugiyama, K., E-mail: [email protected] [Max-Planck-Institut für Plasmaphysik, Garching (Germany); Roth, J. [Max-Planck-Institut für Plasmaphysik, Garching (Germany); Alimov, V.Kh. [Max-Planck-Institut für Plasmaphysik, Garching (Germany); Hydrogen Isotope Research Center, University of Toyama, Toyama (Japan); Schmid, K.; Balden, M.; Elgeti, S.; Koch, F.; Höschen, T. [Max-Planck-Institut für Plasmaphysik, Garching (Germany); Baldwin, M.J.; Doerner, R.P. [Center for Energy Research, University of California at San Diego, La Jolla, CA (United States); Maier, H.; Jacob, W. [Max-Planck-Institut für Plasmaphysik, Garching (Germany)
2015-08-15
Fe–W binary mixed layers were prepared as a model system for reduced-activation ferritic–martensitic (RAFM) steel for studying their dynamic erosion behavior resulting from energetic deuterium (D) irradiation. This investigation aims toward an assessment of RAFM steels as plasma-facing material. The surface composition of the model layers is modified by D irradiation. W is enriched at the surface with D irradiation fluence due to the preferential sputtering of Fe. It depends on the D impinging energy as well as the initial W fraction of the Fe–W layer. No significant development of surface topography was observed within the examined conditions. The erosion yield of a Fe–W layer is comparable to that of pure Fe in the low-fluence range and decreases with increasing D fluence. These results indicate that the dynamic change of erosion yield is significantly correlated with the surface W enrichment.
3. Modelling of an eclipsing RS CVn-binary: V405 And
CERN Document Server
Vida, K; Kővári, Zs; 10.1017/S1743921311027347
2012-01-01
V405 And is an ultrafast-rotating (P_rot ~ 0.46 days) eclipsing binary. The system consists of a primary star with radiative core and convective envelope, and a fully convective secondary. Theories have shown, that stellar structure can depend on magnetic activity, i.e., magnetically active M-dwarfs should have larger radii. Earlier light curve modelling of V405 And indeed showed this behaviour: we found that the radius of the primary is significantly larger than the theoretically predicted value for inactive main sequence stars (the discrepancy is the largest of all known objects), while the secondary fits well to the mass-radius relation. By modelling our recently obtained light curves, which show significant changes of the spotted surface of the primary, we can find further proof for this phenomenon.
4. Relativistic Accretion Disk Models of High State Black Hole X-ray Binary Spectra
CERN Document Server
Davis, S W; Hubeny, I; Turner, N J; Davis, Shane W.; Blaes, Omer M.; Hubeny, Ivan; Turner, Neal J.
2004-01-01
We present calculations of non-LTE, relativistic accretion disk models applicable to the high/soft state of black hole X-ray binaries. We include the effects of thermal Comptonization and bound-free and free-free opacities of all abundant ion species. We present spectra calculated for a variety of accretion rates, black hole spin parameters, disk inclinations, and stress prescriptions. We also consider nonzero inner torques on the disk, and explore different vertical dissipation profiles, including some which are motivated by recent radiation MHD simulations of magnetorotational turbulence. Bound-free metal opacity generally produces significantly less spectral hardening than previous models which only considered Compton scattering and free-free opacity. It also tends to keep the effective photosphere near the surface, resulting in spectra which are remarkably independent of the stress prescription and vertical dissipation profile, provided little dissipation occurs above the effective photosphere. We provide...
5. Diagnostic Power of Broad Emission Line Profiles in Searches for Binary Supermassive Black Holes: Comparison of Models with Observations
Science.gov (United States)
Nguyen, Khai; Bogdanovic, Tamara; Eracleous, Michael; Runnoe, Jessie C.; Sigurdsson, Steinn
2017-01-01
Motivated by observational searches for sub-parsec supermassive black hole binaries (SBHBs) we develop a semi-analytic model to describe the spectral emission line signatures of these systems. We are particularly interested in modeling the profiles of the broad emission lines, which have been used as a tool to search for SBHBs. The goal of this work is to test one of the leading models of binary accretion flows in the literature: SBHB in a circumbinary disk. In this context, we model SBHB accretion flows as a set of three accretion disks: two mini-disks that are gravitationally bound to the individual black holes and a circumbinary disk that forms a common envelope about a gravitationally bound binary. Our first generation model shows that emission line profiles tend to have different statistical properties depending on the semi-major axis, mass ratio, eccentricity of the binary, and the alignment of the triple-disk system, and can in principle be used to constrain the statistical distribution of these parameters. We present the results of a second generation model, which improves upon the treatment of radiative transfer by taking into account the effect of line-driven winds on the properties of the model emission line profiles. This improvement allows a preliminary comparison of the model profiles with the observed SBHB candidates and AGN population in general.
6. Modeling near-barrier collisions of heavy ions based on a Langevin-type approach
Science.gov (United States)
Karpov, A. V.; Saiko, V. V.
2017-08-01
Background: Multinucleon transfer in low-energy nucleus-nucleus collisions is proposed as a method of production of yet-unknown neutron-rich nuclei hardly reachable by other methods. Purpose: Modeling of dynamics of nuclear reactions induced by heavy ions in their full complexity of competing reaction channels remains to be a challenging task. The work is aimed at development of such a model and its application to the analysis of multinucleon transfer in deep inelastic collisions of heavy ions leading, in particular, to formation of neutron-rich isotopes in the vicinity of the N =126 shell closure. Method: Multidimensional dynamical model of nucleus-nucleus collisions based on the Langevin equations has been proposed. It is combined with a statistical model for simulation of de-excitation of primary reaction fragments. The model provides a continuous description of the system evolution starting from the well-separated target and projectile in the entrance channel of the reaction up to the formation of final reaction products. Results: A rather complete set of experimental data available for reactions 136Xe+198Pt,208Pb,209Bi was analyzed within the developed model. The model parameters have been determined. The calculated energy, mass, charge, and angular distributions of reaction products, their various correlations as well as cross sections for production of specific isotopes agree well with the data. On this basis, optimal experimental conditions for synthesizing the neutron-rich nuclei in the vicinity of the N =126 shell were formulated and the corresponding cross sections were predicted. Conclusions: The production yields of neutron-rich nuclei with N =126 weakly depend on the incident energy. At the same time, the corresponding angular distributions are strongly energy dependent. They are peaked at grazing angles for larger energies and extend up to the forward angles at low near-barrier collision energies. The corresponding cross sections exceed 100 nb for
7. A Search for Collision Orbits in the Free-Fall Three-Body Problem. I. Numerical Procedure
Science.gov (United States)
Tanikawa, Kiyotaka; Umehara, Hiroaki; Abe, Hiroshi
1995-12-01
A numerical procedure is devised to find binary collision orbits in the free-fall three-body problem. Applying this procedure, families of binary collision orbits are found and a sequence of triple collision orbits are positioned. A property of sets of binary collision orbits which is convenient to search triple collision orbits is found. Important numerical results are formulated and summarized in the final section.
8. A model for the non-thermal emission of the very massive colliding-wind binary HD 93129A
OpenAIRE
del Palacio, Santiago; Bosch-Ramon, Valentí; Romero, Gustavo E.; Benaglia, Paula
2016-01-01
The binary stellar system HD 93129A is one of the most massive known binaries in our Galaxy. This system presents non-thermal emission in the radio band, which can be used to infer its physical conditions and predict its emission in the high-energy band. We intend to constrain some of the unknown parameters of HD 93129A through modelling the non-thermal emitter, and also to analyse the detectability of this source in hard X-rays and $\\gamma$-rays. We develop a broadband radiative model for th...
9. A new non-convex model of the binary asteroid 90 Antiope obtained with the SAGE modelling technique
CERN Document Server
Bartczak, P; Santana-Ros, T; Dudziński, G
2014-01-01
We present a new non-convex model of the 90 Antiope binary asteroid, derived with a modified version of the SAGE (Shaping Asteroids with Genetic Evolution) method using disk-integrated photometry only. A new variant of the SAGE algorithm capable of deriving models of binary systems is described. The model of 90 Antiope confirms the system's pole solution ($\\lambda=199^{\\circ}$, $\\beta=38^{\\circ}$, $\\sigma=\\pm5^{\\circ}$) and the orbital period ($16.505046 \\pm 0.000005$ h). A comparison between the stellar occultation chords obtained during the 2011 occultation and the projected shape solution has been used to scale the model. The resulting scaled model allowed us to obtain the equivalent radii ($R_{1}=40.4\\pm0.9$ km and $R_{2}=40.2\\pm0.9$ km) and the distance between the two system components ($176\\pm4$ km), leading to a total system mass of ($9.14\\pm0.62$)$\\cdot10^{17}$ kg. The non-convex shape description of the components permitted a refined calculation of the components' volumes, leading to a density estim...
10. Probabilistic model for vessel-bridge collisions in the Three Gorges Reservoir
Institute of Scientific and Technical Information of China (English)
Bo GENG; Hong WANG; Junjie WANG
2009-01-01
Based on a field observation on vessel transit path of three bridges over the Yangtze River in the Three Gorges Reservoir, and an analysis of the geometric probabilistic model of transiting vessels in collision probability calculation, the aberrancy angle and vessel velocity probabilistic model related with impact force, a probabilistic model is established and also verified by goodness-of-fit test. The vessel transit path distribution can be expressed by the normal distribution model. For the Three Gorges Reservoir, the mean and standard deviation adopt 0.2w and 0.1w, respectively (w is the channel width).The aberrancy angle distribution of vessels accepts maximum I distribution model, and its distribution parameters can be taken as 0.314 and 4.354. The velocity distribution of up-bound and down-bound vessels can also be expressed by the normal distribution model.
11. EREM: Parameter Estimation and Ancestral Reconstruction by Expectation-Maximization Algorithm for a Probabilistic Model of Genomic Binary Characters Evolution
Directory of Open Access Journals (Sweden)
Liran Carmel
2010-01-01
Full Text Available Evolutionary binary characters are features of species or genes, indicating the absence (value zero or presence (value one of some property. Examples include eukaryotic gene architecture (the presence or absence of an intron in a particular locus, gene content, and morphological characters. In many studies, the acquisition of such binary characters is assumed to represent a rare evolutionary event, and consequently, their evolution is analyzed using various flavors of parsimony. However, when gain and loss of the character are not rare enough, a probabilistic analysis becomes essential. Here, we present a comprehensive probabilistic model to describe the evolution of binary characters on a bifurcating phylogenetic tree. A fast software tool, EREM, is provided, using maximum likelihood to estimate the parameters of the model and to reconstruct ancestral states (presence and absence in internal nodes and events (gain and loss events along branches.
12. Carrying the physics of black-hole binary evolution into gravitational-wave models for pulsar-timing arrays
Science.gov (United States)
Taylor, Stephen; Sampson, Laura; Simon, Joseph
2016-03-01
There has recently been significant interest in how the galactic environments of supermassive black-hole binaries influences the stochastic gravitational-wave background signal from a population of these systems, and in how the resulting detection prospects for pulsar-timing arrays are effected. Tackling these problems requires us to have robust and computationally-efficient models for the strain spectrum as a function of different environment influences or the binary orbital eccentricity. In this talk we describe a new method of constructing these models from a small number of synthesized black-hole binary populations which have varying input physics. We use these populations to train an interpolant via Gaussian-process regression, allowing us to carry real physics into our subsequent pulsar-timing array inferences, and to also correctly propagate forward uncertainties from our interpolation.
13. Modeling of Sunspot Numbers by a Modified Binary Mixture of Laplace Distribution Functions
Science.gov (United States)
Sabarinath, A.; Anilkumar, A. K.
2008-07-01
This paper presents a new approach for describing the shape of 11-year sunspot cycles by considering the monthly averaged values. This paper also brings out a prediction model based on the analysis of 22 sunspot cycles from the year 1749 onward. It is found that the shape of the sunspot cycles with monthly averaged values can be described by a functional form of modified binary mixture of Laplace density functions, modified suitably by introducing two additional parameters in the standard functional form. The six parameters, namely two locations, two scales, and two area parameters, characterize this model. The nature of the estimated parameters for the sunspot cycles from 1749 onward has been analyzed and finally we arrived at a sufficient set of the parameters for the proposed model. It is seen that this model picks up the sunspot peaks more closely than any other model without losing the match at other places at the same time. The goodness of fit for the proposed model is also computed with the Hathaway Wilson Reichmann overline{χ} measure, which shows, on average, that the fitted model passes within 0.47 standard deviations of the actual averaged monthly sunspot numbers.
14. Modelling of volumetric properties of binary and ternary mixtures by CEOS, CEOS/GE and empirical models
Directory of Open Access Journals (Sweden)
BOJAN D. DJORDJEVIC
2007-12-01
Full Text Available Although many cubic equations of state coupled with van der Waals-one fluid mixing rules including temperature dependent interaction parameters are sufficient for representing phase equilibria and excess properties (excess molar enthalpy HE, excess molar volume VE, etc., difficulties appear in the correlation and prediction of thermodynamic properties of complex mixtures at various temperature and pressure ranges. Great progress has been made by a new approach based on CEOS/GE models. This paper reviews the last six-year of progress achieved in modelling of the volumetric properties for complex binary and ternary systems of non-electrolytes by the CEOS and CEOS/GE approaches. In addition, the vdW1 and TCBT models were used to estimate the excess molar volume VE of ternary systems methanol + chloroform + benzene and 1-propanol + chloroform + benzene, as well as the corresponding binaries methanol + chloroform, chloroform + benzene, 1-propanol + chloroform and 1-propanol + benzene at 288.15–313.15 K and atmospheric pressure. Also, prediction of VE for both ternaries by empirical models (Radojković, Kohler, Jackob–Fitzner, Colinet, Tsao–Smith, Toop, Scatchard, Rastogi was performed.
15. Complexity modeling for context-based adaptive binary arithmetic coding (CABAC) in H.264/AVC decoder
Science.gov (United States)
Lee, Szu-Wei; Kuo, C.-C. Jay
2007-09-01
One way to save the power consumption in the H.264 decoder is for the H.264 encoder to generate decoderfriendly bit streams. By following this idea, a decoding complexity model of context-based adaptive binary arithmetic coding (CABAC) for H.264/AVC is investigated in this research. Since different coding modes will have an impact on the number of quantized transformed coeffcients (QTCs) and motion vectors (MVs) and, consequently, the complexity of entropy decoding, the encoder with a complexity model can estimate the complexity of entropy decoding and choose the best coding mode to yield the best tradeoff between the rate, distortion and decoding complexity performance. The complexity model consists of two parts: one for source data (i.e. QTCs) and the other for header data (i.e. the macro-block (MB) type and MVs). Thus, the proposed CABAC decoding complexity model of a MB is a function of QTCs and associated MVs, which is verified experimentally. The proposed CABAC decoding complexity model can provide good estimation results for variant bit streams. Practical applications of this complexity model will also be discussed.
16. Modelling of binary logistic regression for obesity among secondary students in a rural area of Kedah
Science.gov (United States)
2014-07-01
Logistic regression analysis examines the influence of various factors on a dichotomous outcome by estimating the probability of the event's occurrence. Logistic regression, also called a logit model, is a statistical procedure used to model dichotomous outcomes. In the logit model the log odds of the dichotomous outcome is modeled as a linear combination of the predictor variables. The log odds ratio in logistic regression provides a description of the probabilistic relationship of the variables and the outcome. In conducting logistic regression, selection procedures are used in selecting important predictor variables, diagnostics are used to check that assumptions are valid which include independence of errors, linearity in the logit for continuous variables, absence of multicollinearity, and lack of strongly influential outliers and a test statistic is calculated to determine the aptness of the model. This study used the binary logistic regression model to investigate overweight and obesity among rural secondary school students on the basis of their demographics profile, medical history, diet and lifestyle. The results indicate that overweight and obesity of students are influenced by obesity in family and the interaction between a student's ethnicity and routine meals intake. The odds of a student being overweight and obese are higher for a student having a family history of obesity and for a non-Malay student who frequently takes routine meals as compared to a Malay student.
17. A multiscale transport model for binary Lennard Jones mixtures in slit nanopores
Science.gov (United States)
2016-11-01
We present a quasi-continuum multiscale hydrodynamic transport model for one dimensional isothermal, non-reacting binary mixture confined in slit shaped nanochannels. We focus on species transport equation that includes the viscous dissipation and interspecies diffusion term of the Maxwell-Stefan form. Partial viscosity variation is modeled by van der Waals one fluid approximation and the Local Average Density Method. We use friction boundary conditions where the wall-species friction parameter is computed using a novel species specific Generalized Langevin Equation model. The transport model accuracy is tested by predicting the velocity profiles of Lennard-Jones (LJ) methane-hydrogen and LJ methane-argon mixtures in graphene slit channels of different width. The resultant slip length from the continuum model is found to be invariant of channel width for a fixed mixture molar concentration. The mixtures considered are observed to behave as single species pseudo fluid, with the friction parameter displaying a linear dependence on the molar composition. The proposed model yields atomistic level accuracy with continuum scale efficiency.
18. A general binomial regression model to estimate standardized risk differences from binary response data.
Science.gov (United States)
Kovalchik, Stephanie A; Varadhan, Ravi; Fetterman, Barbara; Poitras, Nancy E; Wacholder, Sholom; Katki, Hormuzd A
2013-02-28
Estimates of absolute risks and risk differences are necessary for evaluating the clinical and population impact of biomedical research findings. We have developed a linear-expit regression model (LEXPIT) to incorporate linear and nonlinear risk effects to estimate absolute risk from studies of a binary outcome. The LEXPIT is a generalization of both the binomial linear and logistic regression models. The coefficients of the LEXPIT linear terms estimate adjusted risk differences, whereas the exponentiated nonlinear terms estimate residual odds ratios. The LEXPIT could be particularly useful for epidemiological studies of risk association, where adjustment for multiple confounding variables is common. We present a constrained maximum likelihood estimation algorithm that ensures the feasibility of risk estimates of the LEXPIT model and describe procedures for defining the feasible region of the parameter space, judging convergence, and evaluating boundary cases. Simulations demonstrate that the methodology is computationally robust and yields feasible, consistent estimators. We applied the LEXPIT model to estimate the absolute 5-year risk of cervical precancer or cancer associated with different Pap and human papillomavirus test results in 167,171 women undergoing screening at Kaiser Permanente Northern California. The LEXPIT model found an increased risk due to abnormal Pap test in human papillomavirus-negative that was not detected with logistic regression. Our R package blm provides free and easy-to-use software for fitting the LEXPIT model.
19. Reduced order model for binary neutron star waveforms with tidal interactions
Science.gov (United States)
Lackey, Benjamin; Bernuzzi, Sebastiano; Galley, Chad
2016-03-01
Observations of inspiralling binary neutron star (BNS) systems with Advanced LIGO can be used to determine the unknown neutron-star equation of state by measuring the phase shift in the gravitational waveform due to tidal interactions. Unfortunately, this requires computationally efficient waveform models for use in parameter estimation codes that typically require 106-107 sequential waveform evaluations, as well as accurate waveform models with phase errors less than 1 radian over the entire inspiral to avoid systematic errors in the measured tidal deformability. The effective one body waveform model with l = 2 , 3, and 4 tidal multipole moments is currently the most accurate model for BNS systems, but takes several minutes to evaluate. We develop a reduced order model of this waveform by constructing separate orthonormal bases for the amplitude and phase evolution. We find that only 10-20 bases are needed to reconstruct any BNS waveform with a starting frequency of 10 Hz. The coefficients of these bases are found with Chebyshev interpolation over the waveform parameter space. This reduced order model has maximum errors of 0.2 radians, and results in a speedup factor of more than 103, allowing parameter estimation codes to run in days to weeks rather than decades.
20. Inelastic e+Mg collision data and its impact on modelling stellar and supernova spectra
Science.gov (United States)
Barklem, P. S.; Osorio, Y.; Fursa, D. V.; Bray, I.; Zatsarinny, O.; Bartschat, K.; Jerkstrand, A.
2017-09-01
Results of calculations for inelastic e+Mg effective collision strengths for the lowest 25 physical states of Mg i (up to 3s6p1P), and thus 300 transitions, from the convergent close-coupling (CCC) and the B-spline R-matrix (BSR) methods are presented. At temperatures of interest, 5000 K, the results of the two calculations differ on average by only 4%, with a scatter of 27%. As the methods are independent, this suggests that the calculations provide datasets for e+Mg collisions accurate to this level. Comparison with the commonly used dataset compiled by Mauas et al. (1988, ApJ, 330, 1008), covering 25 transitions among 12 states, suggests the Mauas et al. data are on average 57% too low, and with a very large scatter of a factor of 6.5. In particular the collision strength for the transition corresponding to the Mg i intercombination line at 457 nm is significantly underestimated by Mauas et al., which has consequences for models that employ this dataset. In giant stars the new data leads to a stronger line compared to previous non-LTE calculations, and thus a reduction in the non-LTE abundance correction by 0.1 dex ( 25%). A non-LTE calculation in a supernova ejecta model shows this line becomes significantly stronger, by a factor of around two, alleviating the discrepancy where the 457 nm line in typical models with Mg/O ratios close to solar tended to be too weak compared to observations. Full Tables 2 and 3 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/606/A11
1. Binary logistic regression modelling: Measuring the probability of relapse cases among drug addict
Science.gov (United States)
Ismail, Mohd Tahir; Alias, Siti Nor Shadila
2014-07-01
For many years Malaysia faced the drug addiction issues. The most serious case is relapse phenomenon among treated drug addict (drug addict who have under gone the rehabilitation programme at Narcotic Addiction Rehabilitation Centre, PUSPEN). Thus, the main objective of this study is to find the most significant factor that contributes to relapse to happen. The binary logistic regression analysis was employed to model the relationship between independent variables (predictors) and dependent variable. The dependent variable is the status of the drug addict either relapse, (Yes coded as 1) or not, (No coded as 0). Meanwhile the predictors involved are age, age at first taking drug, family history, education level, family crisis, community support and self motivation. The total of the sample is 200 which the data are provided by AADK (National Antidrug Agency). The finding of the study revealed that age and self motivation are statistically significant towards the relapse cases..
2. Contour-based models for 3D binary reconstruction in X-ray tomography
Science.gov (United States)
2001-05-01
We study the reconstruction of a 3D compact homogeneous object lying inside a homogeneous background for computer aided design (CAD) or nondestructive testing (NDT) applications. Such a binary scene describes either a solid object or an homogeneous material in which a fault is sought. The goal in both cases is to reconstruct the shape of the scene from sparse radiographic data. This problem is under-determined and one needs to use all prior information about the scene to find a satisfactory solution. A natural approach is to model the exterior contour of the fault by a deformable geometric template, which we reconstruct directly from the radiographic data. In this communication, we give a synthetic view of these contour-based methods and compare their relative performances and limitations to recover complex faults. .
3. Model investigation of non-thermal phase transition in high energy collisions
Institute of Scientific and Technical Information of China (English)
2000-01-01
The non-thermal phase transition in high energy collisions is studied in detail in the framework of random cascade model. The relation between the characteristic parameter λq of phase transition and the rank q of moment is obtained using Monte Carlo simulation, and the existence of two phases in self-similar cascading multiparticle systems is shown. The relation between the critical point qc of phase transition on the fluctuation parameter α is obtained and compared with the experimental results from NA22. The same study is carried out also by analytical calculation under central limit approximation. The range of validity of the central limit approximation is discussed.
4. Parity-odd effects in heavy-ion collisions in the HSD model
CERN Document Server
Teryaev, O
2014-01-01
Helicity separation effect in non-central heavy ion collisions is investigated using the Hadron-String Dynamics (HSD) model. Computer simulations are done to calculate velocity and hydrodynamic helicity on a mesh in a small volume around the center of the reaction. The time dependence of hydrodynamic helicity is observed for various impact parameters and different calculation methods. Comparison with a similar earlier work is carried out. A new quantity is used to ananlyze particles in the final state. It is used to probe for p-odd effects in the final state.
5. A new non-convex model of the binary asteroid (809) Lundia obtained with the SAGE modelling technique
Science.gov (United States)
Bartczak, P.; Kryszczyńska, A.; Dudziński, G.; Polińska, M.; Colas, F.; Vachier, F.; Marciniak, A.; Pollock, J.; Apostolovska, G.; Santana-Ros, T.; Hirsch, R.; Dimitrow, W.; Murawiecka, M.; Wietrzycka, P.; Nadolny, J.
2017-10-01
We present a new non-convex model of the binary asteroid (809) Lundia. A SAGE (Shaping Asteroids with Genetic Evolution) method using disc-integrated photometry only was used for deriving physical parameters of this binary system. The model of (809) Lundia improves former system's pole solution and gives the ecliptic coordinates of the orbit pole - λ = 122°, β = 22°, σ = ±5° - and the orbital period of 15.415 74 ± 0.000 01 h. For scaling our results, we used an effective diameter (Deff) of 9.6 ± 1.1 km obtained from Spitzer observations. The non-convex shape description of the components permitted a refined calculation of the components' volumes, leading to a density estimation of 2.5 ± 0.2 g cm-3 and a macroporosity of 13-23 per cent. The intermediate-scale features of the model may also offer new clues on the components' origin and evolution.
6. A poromechanical model for coal seams saturated with binary mixtures of CH4 and CO2
Science.gov (United States)
Nikoosokhan, Saeid; Vandamme, Matthieu; Dangla, Patrick
2014-11-01
Underground coal bed reservoirs naturally contain methane which can be produced. In parallel of the production of this methane, carbon dioxide can be injected, either to enhance the production of methane, or to have this carbon dioxide stored over geological periods of time. As a prerequisite to any simulation of an Enhanced Coal Bed Methane recovery process (ECBM), we need state equations to model the behavior of the seam when cleats are saturated with a miscible mixture of CH4 and CO2. This paper presents a poromechanical model of coal seams exposed to such binary mixtures filling both the cleats in the seam and the porosity of the coal matrix. This model is an extension of a previous work which dealt with pure fluid. Special care is dedicated to keep the model consistent thermodynamically. The model is fully calibrated with a mix of experimental data and numerical data from molecular simulations. Predicting variations of porosity or permeability requires only calibration based on swelling data. With the calibrated state equations, we predict numerically how porosity, permeability, and adsorbed amounts of fluid vary in a representative volume element of coal seam in isochoric or oedometric conditions, as a function of the pressure and of the composition of the fluid in the cleats.
7. Binary mask optimization for forward lithography based on the boundary layer model in coherent systems.
Science.gov (United States)
Ma, Xu; Arce, Gonzalo R
2009-07-01
8. Statistical Model of the Early Stage of nucleus-nucleus collisions with exact strangeness conservation
CERN Document Server
Poberezhnyuk, R V; Gorenstein, M I
2015-01-01
The Statistical Model of the Early Stage, SMES, describes a transition between confined and deconfined phases of strongly interacting matter created in nucleus-nucleus collisions. The model was formulated in the late 1990s for central Pb+Pb collisions at the CERN SPS energies. It predicted several signals of the transition (onset of deconfinement) which were later observed by the NA49 experiment. The grand canonical ensemble was used to calculate entropy and strangeness production. This approximation is valid for reactions with mean multiplicities of particles carrying conserved charges being significantly larger than one. Recent results of NA61/SHINE on hadron production in inelastic p+p interactions suggest that the deconfinement may also take place in these reactions. However, in this case mean multiplicity of particles with non-zero strange charge is smaller than one. Thus for the modeling of p+p interactions the exact strangeness conservation has to be implemented in the SMES. This extension of the SMES ...
9. An evaluation of collision models in the Method of Moments for rarefied gas problems
Science.gov (United States)
Emerson, David; Gu, Xiao-Jun
2014-11-01
The Method of Moments offers an attractive approach for solving gaseous transport problems that are beyond the limit of validity of the Navier-Stokes-Fourier equations. Recent work has demonstrated the capability of the regularized 13 and 26 moment equations for solving problems when the Knudsen number, Kn (where Kn is the ratio of the mean free path of a gas to a typical length scale of interest), is in the range 0.1 and 1.0-the so-called transition regime. In comparison to numerical solutions of the Boltzmann equation, the Method of Moments has captured both qualitatively, and quantitatively, results of classical test problems in kinetic theory, e.g. velocity slip in Kramers' problem, temperature jump in Knudsen layers, the Knudsen minimum etc. However, most of these results have been obtained for Maxwell molecules, where molecules repel each other according to an inverse fifth-power rule. Recent work has incorporated more traditional collision models such as BGK, S-model, and ES-BGK, the latter being important for thermal problems where the Prandtl number can vary. We are currently investigating the impact of these collision models on fundamental low-speed problems of particular interest to micro-scale flows that will be discussed and evaluated in the presentation. Engineering and Physical Sciences Research Council under Grant EP/I011927/1 and CCP12.
10. Rovibrationally Inelastic Atom-Molecule Collision Cross Sections from a Hard Sphere Model
Science.gov (United States)
Lashner, Jacob; Stewart, Brian
2016-05-01
Hard-shell models have long been used to elucidate the principal features of molecular energy transfer and exchange reaction in the A + BC system. Nevertheless, no three-dimensional hard-shell calculation of inelastic collision cross sections has been reported. This work aims to fill that void. A particular motivation comes from our experimental results, which show the importance of equatorial impacts in the vibrational excitation process. Working with the simple hard-sphere model, we incorporated secondary impacts, defined as those in which A strikes C after striking B. Such collisions are important in systems such as Li2 - X, in which vibrational energy transfer occurs principally through side impacts. We discuss the complexity this adds to the model and present fully three-dimensional cross sections for rovibrational excitation of an initially stationary molecule in the homonuclear A + B2 system, examining the cross section as a function of the masses and radii of the atoms. We show how the features in the cross section evolve as these parameters are varied and calculate the contribution of secondary (near-equatorial) impacts to the dynamics. We compare with recent measurements in our laboratory and with the results of quasiclassical trajectories.
11. Performance of models for estimating absolute risk difference in multicenter trials with binary outcome
Directory of Open Access Journals (Sweden)
Claudia Pedroza
2016-08-01
Full Text Available Abstract Background Reporting of absolute risk difference (RD is recommended for clinical and epidemiological prospective studies. In analyses of multicenter studies, adjustment for center is necessary when randomization is stratified by center or when there is large variation in patients outcomes across centers. While regression methods are used to estimate RD adjusted for baseline predictors and clustering, no formal evaluation of their performance has been previously conducted. Methods We performed a simulation study to evaluate 6 regression methods fitted under a generalized estimating equation framework: binomial identity, Poisson identity, Normal identity, log binomial, log Poisson, and logistic regression model. We compared the model estimates to unadjusted estimates. We varied the true response function (identity or log, number of subjects per center, true risk difference, control outcome rate, effect of baseline predictor, and intracenter correlation. We compared the models in terms of convergence, absolute bias and coverage of 95 % confidence intervals for RD. Results The 6 models performed very similar to each other for the majority of scenarios. However, the log binomial model did not converge for a large portion of the scenarios including a baseline predictor. In scenarios with outcome rate close to the parameter boundary, the binomial and Poisson identity models had the best performance, but differences from other models were negligible. The unadjusted method introduced little bias to the RD estimates, but its coverage was larger than the nominal value in some scenarios with an identity response. Under the log response, coverage from the unadjusted method was well below the nominal value (<80 % for some scenarios. Conclusions We recommend the use of a binomial or Poisson GEE model with identity link to estimate RD for correlated binary outcome data. If these models fail to run, then either a logistic regression, log Poisson
12. A viscous blast-wave model for relativistic heavy-ion collisions
CERN Document Server
Jaiswal, Amaresh
2015-01-01
Using a viscosity-based survival scale for geometrical perturbations formed in the early stages of relativistic heavy-ion collisions, we model the radial flow velocity during freeze-out. Subsequently, we employ the Cooper-Frye freeze-out prescription, with first-order viscous corrections to the distribution function, to obtain the transverse momentum distribution of particle yields and flow harmonics. For initial eccentricities, we use the results of Monte Carlo Glauber model. We fix the blast-wave model parameters by fitting the transverse momentum spectra of identified particles at the Large Hadron Collider (LHC) and demonstrate that this leads to a fairly good agreement with transverse momentum distribution of elliptic and triangular flow for various centralities. Within this viscous blast-wave model, we estimate the shear viscosity to entropy density ratio $\\eta/s\\simeq 0.24$ at the LHC.
13. APPLICATION OF A LATTICE GAS MODEL FOR SUBPIXEL PROCESSING OF LOW-RESOLUTION IMAGES OF BINARY STRUCTURES
Directory of Open Access Journals (Sweden)
Zbisław Tabor
2011-05-01
Full Text Available In the study an algorithm based on a lattice gas model is proposed as a tool for enhancing quality of lowresolution images of binary structures. Analyzed low-resolution gray-level images are replaced with binary images, in which pixel size is decreased. The intensity in the pixels of these new images is determined by corresponding gray-level intensities in the original low-resolution images. Then the white phase pixels in the binary images are assumed to be particles interacting with one another, interacting with properly defined external field and allowed to diffuse. The evolution is driven towards a state with maximal energy by Metropolis algorithm. This state is used to estimate the imaged object. The performance of the proposed algorithm and local and global thresholding methods are compared.
14. A model for emission from jets in X-ray binaries: consequences of a single acceleration episode
NARCIS (Netherlands)
A. Pe'er; P. Casella
2009-01-01
There is strong evidence for powerful jets in the low/hard state of black hole X-ray binaries (BHXRBs). Here, we present a model in which electrons are accelerated once at the base of the jet, and are cooled by synchrotron emission and possible adiabatic energy losses. The accelerated electrons assu
15. Investigating the X-ray emission from the massive WR+O binary WR 22 using 3D hydrodynamical models
CERN Document Server
Parkin, E R
2011-01-01
We examine the dependence of the wind-wind collision and subsequent X-ray emission from the massive WR+O star binary WR~22 on the acceleration of the stellar winds, radiative cooling, and orbital motion. Simulations were performed with instantaneously accelerated and radiatively driven stellar winds. Radiative transfer calculations were performed on the simulation output to generate synthetic X-ray data, which are used to conduct a detailed comparison against observations. When instantaneously accelerated stellar winds are adopted in the simulation, a stable wind-wind collision region (WCR) is established at all orbital phases. In contrast, when the stellar winds are radiatively driven, and thus the acceleration regions of the winds are accounted for, the WCR is far more unstable. As the stars approach periastron, the ram pressure of the WR's wind overwhelms the O star's and, following a significant disruption of the shocks by non-linear thin-shell instabilities (NTSIs), the WCR collapses onto the O star. X-r...
16. Asteroid fission, binaries and the small main belt population
Science.gov (United States)
Rossi, A.; Jacobson, S.; Marzari, F.; Scheeres, D.
2011-10-01
Using a Monte Carlo method we model the spin evolution of small Main Belt asteroids under the joint effects of YORP and collisions. Our simulations allow us to estimate the fraction of asteroids undergoing rotational fission in different size ranges. When an asteroid reaches its disruption spin limit we determine the outcome of its subsequent evolution based on accumulated statistics on their evolution based on numerical integrations (i.e., binary or ternary formation, binary disruption, etc..). Our aim is to predict the percentage of binary asteroids and their properties in the Belt, the number of objects like P/2010 A2 per year and the effects of YORP-induced fission on the overall asteroid size distribution at the small size end.
17. Numerical modeling of two-phase binary fluid mixing using mixed finite elements
KAUST Repository
Sun, Shuyu
2012-07-27
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy\\'s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.
18. Bayesian informative dropout model for longitudinal binary data with random effects using conditional and joint modeling approaches.
Science.gov (United States)
Chan, Jennifer S K
2016-05-01
Dropouts are common in longitudinal study. If the dropout probability depends on the missing observations at or after dropout, this type of dropout is called informative (or nonignorable) dropout (ID). Failure to accommodate such dropout mechanism into the model will bias the parameter estimates. We propose a conditional autoregressive model for longitudinal binary data with an ID model such that the probabilities of positive outcomes as well as the drop-out indicator in each occasion are logit linear in some covariates and outcomes. This model adopting a marginal model for outcomes and a conditional model for dropouts is called a selection model. To allow for the heterogeneity and clustering effects, the outcome model is extended to incorporate mixture and random effects. Lastly, the model is further extended to a novel model that models the outcome and dropout jointly such that their dependency is formulated through an odds ratio function. Parameters are estimated by a Bayesian approach implemented using the user-friendly Bayesian software WinBUGS. A methadone clinic dataset is analyzed to illustrate the proposed models. Result shows that the treatment time effect is still significant but weaker after allowing for an ID process in the data. Finally the effect of drop-out on parameter estimates is evaluated through simulation studies.
19. Binary mask optimization for forward lithography based on boundary layer model in coherent systems
Science.gov (United States)
Ma, Xu; Arce, Gonzalo R.
2010-04-01
20. HARDWARE MODELING OF BINARY CODED DECIMAL ADDER IN FIELD PROGRAMMABLE GATE ARRAY
Directory of Open Access Journals (Sweden)
2013-01-01
Full Text Available There are insignificant relevant research works available which are involved with the Field Programmable Gate Array (FPGA based hardware implementation of Binary Coded Decimal (BCD adder. This is because, the FPGA based hardware realization is quiet new and still developing field of research. The article illustrates the design and hardware modeling of a BCD adder. Among the types of adders, Carry Look Ahead (CLA and Ripple Carry (RC adder have been studied, designed and compared in terms of area consumption and time requirement. The simulation results show that the CLA adder performs faster with optimized area consumption. Verilog Hardware Description Language (HDL is used for designing the model with the help of Altera Quartus II Electronic Design Automation (EDA tool. EDA synthesis tools make it easy to develop an HDL model and which can be synthesized into target-specific architectures. Whereas, the HDL based modeling provides shorter development phases with continuous testing and verification of the system performance and behavior. After successful functional and timing simulations of the CLA based BCD adder, the design has been downloaded to physical FPGA device. For FPGA implementation, the Altera DE2 board has been used which contains Altera Cyclone II 2C35 FPGA device.
1. A note on prognostic accuracy evaluation of regression models applied to longitudinal autocorrelated binary data
Directory of Open Access Journals (Sweden)
Giulia Barbati
2014-11-01
Full Text Available Background: Focus of this work was on evaluating the prognostic accuracy of two approaches for modelling binary longitudinal outcomes, a Generalized Estimating Equation (GEE and a likelihood based method, Marginalized Transition Model (MTM, in which a transition model is combined with a marginal generalized linear model describing the average response as a function of measured predictors.Methods: A retrospective study on cardiovascular patients and a prospective study on sciatic pain were used to evaluate discrimination by computing the Area Under the Receiver-Operating-Characteristics curve, (AUC, the Integrated Discrimination Improvement (IDI and the Net Reclassification Improvement (NRI at different time occasions. Calibration was also evaluated. A simulation study was run in order to compare model’s performance in a context of a perfect knowledge of the data generating mechanism. Results: Similar regression coefficients estimates and comparable calibration were obtained; an higher discrimination level for MTM was observed. No significant differences in calibration and MSE (Mean Square Error emerged in the simulation study, that instead confirmed the MTM higher discrimination level. Conclusions: The choice of the regression approach should depend on the scientific question being addressed, i.e. if the overall population-average and calibration or the subject-specific patterns and discrimination are the objectives of interest, and some recently proposed discrimination indices are useful in evaluating predictive accuracy also in a context of longitudinal studies.
2. A New Model of Roche Lobe Overflow for Short-period Gaseous Planets and Binary Stars
Science.gov (United States)
Jackson, Brian; Arras, Phil; Penev, Kaloyan; Peacock, Sarah; Marchant, Pablo
2017-02-01
Some close-in gaseous exoplanets are nearly in Roche lobe contact, and previous studies show that tidal decay can drive hot Jupiters into contact during the main sequence of their host stars. Improving on a previous model, we present a revised model for mass transfer in a semidetached binary system that incorporates an extended atmosphere around the donor and allows for an arbitrary mass ratio. We apply this new formalism to hypothetical, confirmed, and candidate planetary systems to estimate mass-loss rates and compare with models of evaporative mass loss. Overflow may be significant for hot Neptunes out to periods of ∼2 days, while for hot Jupiters, it may only be important inward of 0.5 days. We find that CoRoT-24 b may be losing mass at a rate of more than an Earth mass in a gigayear. The hot Jupiter WASP-12 b may lose an Earth mass in a megayear, while the putative planet PTFO8-8695 orbiting a T Tauri star might shed its atmosphere in a few megayears. We point out that the orbital expansion that can accompany mass transfer may be less effective than previously considered because the gas accreted by the host star removes some of the angular momentum from the orbit, but simple scaling arguments suggest that the Roche lobe overflow might remain stable. Consequently, the recently discovered small planets in ultrashort periods (model presented here has been incorporated into Modules for Experiments in Stellar Astrophysics (MESA).
3. Self Regulated Shocks in Massive Star Binary Systems
CERN Document Server
Parkin, E R
2013-01-01
In an early-type, massive star binary system, X-ray bright shocks result from the powerful collision of stellar winds driven by radiation pressure on spectral line transitions. We examine the influence of the X-rays from the wind-wind collision shocks on the radiative driving of the stellar winds using steady state models that include a parameterized line force with X-ray ionization dependence. Our primary result is that X-ray radiation from the shocks inhibits wind acceleration and can lead to a lower pre-shock velocity, and a correspondingly lower shocked plasma temperature, yet the intrinsic X-ray luminosity of the shocks, LX remains largely unaltered, with the exception of a modest increase at small binary separations. Due to the feedback loop between the ionizing X-rays from the shocks and the wind-driving, we term this scenario as self regulated shocks. This effect is found to greatly increase the range of binary separations at which a wind-photosphere collision is likely to occur in systems where the m...
4. The Binary Fission Model for the Formation of the Pluto system
Science.gov (United States)
Prentice, Andrew
2016-10-01
The ratio F of the mass of Pluto (P) to Charon (C), viz. F ≈ 8:1, is the largest ratio of any planet-satellite pair in the solar system. Another measure of the PC binary is its normalized angular momentum density J (see McKinnon 1989). Analysis of astrometric data (Brozovic et al 2015) acquired before the New Horizons (NH) arrival at Pluto and new measurements made by NH (Stern et al 2015) show that J = 0.39. Yet these F & J values are ones expected if the PC binary had formed by the rotational fission of a single liquid mass (Darwin 1902; Lyttleton 1953). At first glance, therefore, the fission model seems to be a viable model for the formation of the Pluto system. In fact, Prentice (1993 Aust J Astron 5 111) had used this model to successfully predict the existence of several moons orbiting beyond Charon, before their discovery in 2005-2012. The main problem with the fission model is that the observed mean density of Charon, namely 1.70 g/cm3, greatly exceeds that of water ice. Charon thus could not have once been a globe of pure water. Here I review the fission model within the framework of the modern Laplacian theory of solar system origin (Prentice 1978 Moon Planets 19 341; 2006 PASA 23 1) and the NH results. I assume that Pluto and Charon were initially a single object (proto-Pluto [p-P]) which had condensed within the same gas ring shed by the proto-solar cloud at orbital distance ~43 AU, where the Kuiper belt was born. The temperature of this gas ring is 26 K and the mean orbit pressure is 1.3 × 10-9 bar. After the gas ring is shed, chemical condensation takes place. The bulk chemical composition of the condensate is anhydrous rock (mass fraction 0.5255), graphite (0.0163), water ice (0.1858), CO2 ice (0.2211) and methane ice (0.0513). Next I assume that melting of the ices in p-P takes place through the decay of short-lived radioactive nuclides, thus causing internal segregation of the rock & graphite. Settling of heavy grains to the centre lowers the
5. Collision energy dependence of elliptic flow splitting between particles and their antiparticles from an extended multiphase transport model
CERN Document Server
Xu, Jun
2016-01-01
Based on an extended multiphase transport model, which includes mean-field potentials in both the partonic and hadronic phases, uses the mix-event coalescence, and respects charge conservation during the hadronic evolution, we have studied the collision energy dependence of the elliptic flow splitting between particles and their antiparticles. This extended transport model reproduces reasonably well the experimental data at lower collision energies but only describes qualitatively the elliptic flow splitting at higher beam energies. The present study thus indicates the existence of other mechanisms for the elliptic flow splitting besides the mean-field potentials and the need of further improvements of the multiphase transport model.
6. A Bhatnagar-Gross-Krook kinetic model with velocity-dependent collision frequency and corrected relaxation of moments
Science.gov (United States)
Alekseenko, Alexander; Euler, Craig
2016-05-01
We propose a Bhatnagar-Gross-Krook (BGK) kinetic model in which the collision frequency is a linear combination of polynomials in the velocity variable. The coefficients of the linear combination are determined so as to enforce proper relaxation rates for a selected group of moments. The relaxation rates are obtained by a direct numerical evaluation of the full Boltzmann collision operator. The model is conservative by construction. Simulations of the problem of spatially homogeneous relaxation of hard spheres gas show improvement in accuracy of controlled moments as compared to solutions obtained by the classical BGK, ellipsoidal-statistical BGK and the Shakhov models in cases of strong deviations from continuum.
7. Modelling of Be Disks in Binary Systems Using the Hydrodynamic Code PLUTO
Science.gov (United States)
Cyr, I. H.; Panoglou, D.; Jones, C. E.; Carciofi, A. C.
2016-11-01
The study of the gas structure and dynamics of Be star disks is critical to our understanding of the Be star phenomenon. The central star is the major force driving the evolution of these disks, however other external forces may also affect the formation of the disk, for example, the gravitational torque produced in a close binary system. We are interested in understanding the gravitational effects of a low-mass binary companion on the formation and growth of a disk in a close binary system. To study these effects, we used the grid-based hydrodynamic code PLUTO. Because this code has not been used to study such systems before, we compared our simulations against codes used in previous work on binary systems. We were able to simulate the formation of a disk in both an isolated and binary system. Our current results suggest that PLUTO is in fact a well suited tool to study the dynamics of Be disks.
8. Pion Transverse Momentum Spectrum, Elliptic Flow, and Interferometry in the Granular Source Model for RHIC and LHC Heavy Ion Collisions
Directory of Open Access Journals (Sweden)
Jing Yang
2015-01-01
Full Text Available We systematically investigate the pion transverse momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss (HBT interferometry in the granular source model for the heavy ion collisions of Au-Au at sNN=200 GeV and Pb-Pb at sNN=2.76 TeV with different centralities. The granular source model can well reproduce the experimental results of the heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC and the Large Hadron Collider (LHC. We examine the parameters involved in the granular source model. The experimental data of the momentum spectrum, elliptic flow, and HBT radii for the two collision energies and different centralities impose very strict constraints on the model parameters. They exhibit certain regularities for collision centrality and energy. The space-time structure and expansion velocities of the granular sources for the heavy ion collisions at the RHIC and LHC energies with different centralities are investigated.
9. Modeling X-Ray Binary Evolution in Normal Galaxies: Insights from SINGS
Science.gov (United States)
Tzanavaris, P.; Fragos, T.; Tremmel, M.; Jenkins, L.; Zezas, A.; Lehmer, B. D.; Hornschemeier, A.; Kalogera, V.; Ptak, A; Basu-Zych, A.
2013-01-01
We present the largest-scale comparison to date between observed extragalactic X-ray binary (XRB) populations and theoretical models of their production. We construct observational X-ray luminosity functions (oXLFs) using Chandra observations of 12 late-type galaxies from the Spitzer Infrared Nearby Galaxy Survey (SINGS). For each galaxy, we obtain theoretical XLFs (tXLFs) by combining XRB synthetic models, constructed with the population synthesis code StarTrack, with observational star formation histories (SFHs). We identify highest-likelihood models both for individual galaxies and globally, averaged over the full galaxy sample. Individual tXLFs successfully reproduce about half of oXLFs, but for some galaxies we are unable to find underlying source populations, indicating that galaxy SFHs and metallicities are not well matched and/or XRB modeling requires calibration on larger observational samples. Given these limitations, we find that best models are consistent with a product of common envelope ejection efficiency and central donor concentration approx.. = 0.1, and a 50% uniform - 50% "twins" initial mass-ratio distribution. We present and discuss constituent subpopulations of tXLFs according to donor, accretor and stellar population characteristics. The galaxy-wide X-ray luminosity due to low-mass and high-mass XRBs, estimated via our best global model tXLF, follows the general trend expected from the L(sub X) - star formation rate and L(sub X) - stellar mass relations of Lehmer et al. Our best models are also in agreement with modeling of the evolution both of XRBs over cosmic time and of the galaxy X-ray luminosity with redshift.
10. The SED in the hot continuum of the symbiotic binary AR Pavonis. I. Tests with the current models
CERN Document Server
Skopal, A
2003-01-01
We present the spectral energy distribution (SED) in the continuum of the eclipsing symbiotic binary AR Pav between 0.12 and 3.4 microns. This revealed a high luminosity of the hot object in the binary, L(hot) = 2200(d/4.9 kpc)**2 L(Sun). We introduce a method of disentangling the total continuum spectrum into its individual components of radiation for current models of symbiotic binaries. Applying a standard ionization model we show that the configuration of AR Pav differs significantly from that typical for symbiotic binaries during their quiescent phases. The best fit of the observed SED is provided by radiation of a simple blackbody accretion disk with L(AD)=1700(d/4.9 kpc)**2 L(Sun), which is embedded in an extended hot corona with Te=40000+/-5000K and L(neb)=500 (d/4.9 kpc)**2 L(Sun). This basic configuration of the hot object explains also the observed wavelength-dependent depth and width of the eclipse profile. The standard thin disk model requires a high accretion rate dot M(acc) > 2x1E-4M(Sun)/yr on...
11. Strangeness production in heavy ion collisions at SPS and RHIC within two-source statistical model
CERN Document Server
Lu, Z D; Fuchs, C; Zabrodin, E E; Lu, Zhong-Dao; Faessler, Amand
2002-01-01
The experimental data on hadron yields and ratios in central Pb+Pb and Au+Au collisions at SPS and RHIC energies, respectively, are analysed within a two-source statistical model of an ideal hadron gas. These two sources represent the expanding system of colliding heavy ions, where the hot central fireball is embedded in a larger but cooler fireball. The volume of the central source increases with rising bombarding energy. Results of the two-source model fit to RHIC experimental data at midrapidity coincide with the results of the one-source thermal model fit, indicating the formation of an extended fireball, which is three times larger than the corresponding core at SPS.
12. Anomalous dynamical scaling in anharmonic chains and plasma models with multi-particle collisions
CERN Document Server
Di Cintio, Pierfrancesco; Bufferand, Hugo; Ciraolo, Guido; Lepri, Stefano; Straka, Mika J
2015-01-01
We study the anomalous dynamical scaling of equilibrium correlations in one dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through the Multi-Particle Collision dynamics. For both models -that admit three conservation laws- by means of detailed numerical simulations we verify the predictions of Nonlinear Fluctuating Hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite of this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.
13. Logic models to predict continuous outputs based on binary inputs with an application to personalized cancer therapy
Science.gov (United States)
Knijnenburg, Theo A.; Klau, Gunnar W.; Iorio, Francesco; Garnett, Mathew J.; McDermott, Ultan; Shmulevich, Ilya; Wessels, Lodewyk F. A.
2016-01-01
Mining large datasets using machine learning approaches often leads to models that are hard to interpret and not amenable to the generation of hypotheses that can be experimentally tested. We present ‘Logic Optimization for Binary Input to Continuous Output’ (LOBICO), a computational approach that infers small and easily interpretable logic models of binary input features that explain a continuous output variable. Applying LOBICO to a large cancer cell line panel, we find that logic combinations of multiple mutations are more predictive of drug response than single gene predictors. Importantly, we show that the use of the continuous information leads to robust and more accurate logic models. LOBICO implements the ability to uncover logic models around predefined operating points in terms of sensitivity and specificity. As such, it represents an important step towards practical application of interpretable logic models. PMID:27876821
14. Logic models to predict continuous outputs based on binary inputs with an application to personalized cancer therapy
Science.gov (United States)
Knijnenburg, Theo A.; Klau, Gunnar W.; Iorio, Francesco; Garnett, Mathew J.; McDermott, Ultan; Shmulevich, Ilya; Wessels, Lodewyk F. A.
2016-11-01
Mining large datasets using machine learning approaches often leads to models that are hard to interpret and not amenable to the generation of hypotheses that can be experimentally tested. We present ‘Logic Optimization for Binary Input to Continuous Output’ (LOBICO), a computational approach that infers small and easily interpretable logic models of binary input features that explain a continuous output variable. Applying LOBICO to a large cancer cell line panel, we find that logic combinations of multiple mutations are more predictive of drug response than single gene predictors. Importantly, we show that the use of the continuous information leads to robust and more accurate logic models. LOBICO implements the ability to uncover logic models around predefined operating points in terms of sensitivity and specificity. As such, it represents an important step towards practical application of interpretable logic models.
15. Soot modeling of counterflow diffusion flames of ethylene-based binary mixture fuels
KAUST Repository
Wang, Yu
2015-03-01
A soot model was developed based on the recently proposed PAH growth mechanism for C1-C4 gaseous fuels (KAUST PAH Mechanism 2, KM2) that included molecular growth up to coronene (A7) to simulate soot formation in counterflow diffusion flames of ethylene and its binary mixtures with methane, ethane and propane based on the method of moments. The soot model has 36 soot nucleation reactions from 8 PAH molecules including pyrene and larger PAHs. Soot surface growth reactions were based on a modified hydrogen-abstraction-acetylene-addition (HACA) mechanism in which CH3, C3H3 and C2H radicals were included in the hydrogen abstraction reactions in addition to H atoms. PAH condensation on soot particles was also considered. The experimentally measured profiles of soot volume fraction, number density, and particle size were well captured by the model for the baseline case of ethylene along with the cases involving mixtures of fuels. The simulation results, which were in qualitative agreement with the experimental data in the effects of binary fuel mixing on the sooting structures of the measured flames, showed in particular that 5% addition of propane (ethane) led to an increase in the soot volume fraction of the ethylene flame by 32% (6%), despite the fact that propane and ethane are less sooting fuels than is ethylene, which is in reasonable agreement with experiments of 37% (14%). The model revealed that with 5% addition of methane, there was an increase of 6% in the soot volume fraction. The average soot particle sizes were only minimally influenced while the soot number densities were increased by the fuel mixing. Further analysis of the numerical data indicated that the chemical cross-linking effect between ethylene and the dopant fuels resulted in an increase in PAH formation, which led to higher soot nucleation rates and therefore higher soot number densities. On the other hand, the rates of soot surface growth per unit surface area through the HACA mechanism were
16. MODELING DISPERSION FROM CHEMICALS RELEASED AFTER A TRAIN COLLISION IN GRANITEVILLE, SOUTH CAROLINA
Energy Technology Data Exchange (ETDEWEB)
Buckley, R; Chuck Hunter, C; Robert Addis, R; Matt Parker, M
2006-08-07
The Savannah River National Laboratory's (SRNL) Weather INformation and Display (WIND) System was used to provide meteorological and atmospheric modeling/consequence assessment support to state and local agencies following the collision of two Norfolk Southern freight trains on the morning of January 6, 2005. This collision resulted in the release of several toxic chemicals to the environment, including chlorine. The dense and highly toxic cloud of chlorine gas that formed in the vicinity of the accident was responsible for nine fatalities, and caused injuries to more than five hundred others. Transport model results depicting the forecast path of the ongoing release were made available to emergency managers in the county's Unified Command Center shortly after SRNL received a request for assistance. Support continued over the ensuing two days of the active response. The SRNL also provided weather briefings and transport/consequence assessment model results to responders from South Carolina Department of Health and Environmental Control (SCDHEC), the Savannah River Site's (SRS) Emergency Operations Center (EOC), Department of Energy Headquarters, and hazmat teams dispatched from the SRS. Although model-generated forecast winds used in consequence assessments conducted during the incident were provided at 2-km horizontal grid spacing during the accident response, a high-resolution Regional Atmospheric Modeling System (RAMS, version 4.3.0) simulation was later performed to examine potential influences of local topography on plume migration. The detailed RAMS simulation was used to determine meteorology using multiple grids with an innermost grid spacing of 125 meters. Results from the two simulations are shown to generally agree with meteorological observations at the time; consequently, local topography did not significantly affect wind in the area. Use of a dense gas dispersion model to simulate localized plume behavior using the higher resolution
17. Modeling dispersion from toxic gas released after a train collision in Graniteville, SC.
Science.gov (United States)
Buckley, Robert L; Hunter, Charles H; Addis, Robert P; Parker, Matthew J
2007-03-01
The Savannah River National Laboratory (SRNL) Weather Information and Display System was used to provide meteorological and atmospheric modeling/consequence assessment support to state and local agencies after the collision of two Norfolk Southern freight trains on the morning of January 6, 2005. This collision resulted in the release of several toxic chemicals to the environment, including chlorine. The dense and highly toxic cloud of chlorine gas that formed in the vicinity of the accident was responsible for 9 fatalities and caused injuries to more than 500 others. Transport model results depicting the forecast path of the ongoing release were made available to emergency managers in the county's Unified Command Center shortly after SRNL received a request for assistance. Support continued over the ensuing 2 days of the active response. The SRNL also provided weather briefings and transport/consequence assessment model results to responders from the South Carolina Department of Health and Environmental Control, the Savannah River Site (SRS) Emergency Operations Center, Department of Energy headquarters, and hazard material teams dispatched from the SRS. Operational model-generated forecast winds used in consequence assessments conducted during the incident were provided at 2-km horizontal grid spacing during the accident response. High-resolution Regional Atmospheric Modeling System (RAMS, version 4.3.0) simulation was later performed to examine potential influences of local topography on plume migration in greater detail. The detailed RAMS simulation was used to determine meteorology using multiple grids with an innermost grid spacing of 125 m. Results from the two simulations are shown to generally agree with meteorological observations at the time; consequently, local topography did not significantly affect wind in the area. Use of a dense gas dispersion model to simulate localized plume behavior using the higher-resolution winds indicated agreement with
18. A New Dynamical Model for the Black Hole Binary LMC X-1
CERN Document Server
Orosz, Jerome A; McClintock, Jeffrey E; Torres, Manuel A P; Bochkov, Ivan; Gou, Lijun; Narayan, Ramesh; Blaschak, Michael; Levine, Alan M; Remillard, Ronald A; Bailyn, Charles D; Dwyer, Morgan M; Buxton, Michelle
2008-01-01
We present a dynamical model of the high mass X-ray binary LMC X-1 based on high-resolution optical spectroscopy and extensive optical and near-infrared photometry. From our new optical data we find an orbital period of P=3.90917 +/- 0.00005 days. We present a refined analysis of the All Sky Monitor data from RXTE and find a period of P=3.9093 +/- 0.0008 days, which is consistent with the optical period. A simple model of Thomson scattering in the stellar wind accounts for the modulation seen in the X-ray light curves. The V-K color of the star (1.17 +/- 0.05) implies A_V=2.28 +/- 0.06, which is much larger than previously assumed. For the secondary star we measure a radius of R_2=17.0 +/- 0.8 solar radii and a projected rotational velocity of V_{rot}*sin(i)= 129.9 +/- 2.22 km/sec. Using these measured properties to constrain the dynamical model, we find an orbital eccentricity of e=0.0256 +/- 0.0066, an inclination of i=37.00 +/- 1.87 deg, a secondary star mass of M_2=30.62 +/- 3.22 solar masses, and a black...
19. Features of non-congruent phase transition in modified Coulomb model of the binary ionic mixture
Science.gov (United States)
Stroev, N. E.; Iosilevskiy, I. L.
2016-11-01
Non-congruent gas-liquid phase transition (NCPT) have been studied previously in modified Coulomb model of a binary ionic mixture C(+6) + O(+8) on a uniformly compressible ideal electronic background /BIM(∼)/. The features of NCPT in improved version of the BIM(∼) model for the same mixture on background of non-ideal electronic Fermi-gas and comparison it with the previous calculations are the subject of present study. Analytical fits for Coulomb corrections to equation of state of electronic and ionic subsystems were used in present calculations within the Gibbs-Guggenheim conditions of non-congruent phase equilibrium. Parameters of critical point-line were calculated on the entire range of proportions of mixed ions 0 BIM(∼) model. Just similar distillation was obtained in the variant of NCPT in dense nuslear matter. The absence of azeotropic compositions was revealed in studied variants of BIM(∼) in contrast to an explicit existence of the azeotropic compositions for the NCPT in chemically reacting plasmas and in astrophysical applications.
20. Features of non-congruent phase transition in modified Coulomb model of the binary ionic mixture
CERN Document Server
Stroev, N E
2016-01-01
Non-congruent gas-liquid phase transition (NCPT) have been studied in modified Coulomb model of a binary ionic mixture C(+6) + O(+8) on a \\textit{uniformly compressible} ideal electronic background /BIM($\\sim$)/. The features of NCPT in improved version of the BIM($\\sim$) model for the same mixture on background of \\textit{non-ideal} electronic Fermi-gas and comparison it with the previous calculations are the subject of present study. Analytical fits for Coulomb corrections to EoS of electronic and ionic subsystems were used in present calculations within the Gibbs--Guggenheim conditions of non-congruent phase equilibrium.Parameters of critical point-line (CPL) were calculated on the entire range of proportions of mixed ions $0model. Just similar distillation was obtained in variant of NCPT in dense nuslear matter. The absence of azeotropic compositions was revealed in studied variants of BIM($\\sim$) in contrast to explicit e... 1. Modeling Equal and Unequal Mass Binary Neutron Star Mergers Using Public Codes CERN Document Server De Pietri, Roberto; Maione, Francesco; Löffler, Frank 2015-01-01 We present three-dimensional simulations of the dynamics of binary neutron star (BNS) mergers from the late stage of the inspiral process up to$\\sim 20$ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH). We investigate five equal-mass models of total gravitational mass$2.207$,$2.373$,$2.537$,$2.697$and$2.854 M_\\odot$, respectively, and four unequal mass models with$M_{\\mathrm{ADM}}\\simeq 2.53\\ M_\\odot$and$q\\simeq 0.94$,$0.88$,$0.82$, and$0.77$(where$q = M^{(1)}/M^{(2)}$is the mass ratio). We use a semi-realistic equation of state (EOS) namely, the seven-segment piece-wise polytropic SLyPP with a thermal component given by$\\Gamma_{th} = 1.8$. We have also compared the resulting dynamics (for one model) using both, the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector, and also different reconstruction methods for the matter sector, namely PPM, WENO and MP5. Our results show agreement and high resolution, but sup... 2. Modelling the high-energy emission from gamma-ray binaries using numerical relativistic hydrodynamics CERN Document Server Dubus, Guillaume; Fromang, Sébastien 2015-01-01 Detailed modeling of the high-energy emission from gamma-ray binaries has been propounded as a path to pulsar wind physics. Fulfilling this ambition requires a coherent model of the flow and its emission in the region where the pulsar wind interacts with the stellar wind of its companion. We developed a code that follows the evolution and emission of electrons in the shocked pulsar wind based on inputs from a relativistic hydrodynamical simulation. The code is used to model the well-documented spectral energy distribution and orbital modulations from LS 5039. The pulsar wind is fully confined by a bow shock and a back shock. The particles are distributed into a narrow Maxwellian, emitting mostly GeV photons, and a power law radiating very efficiently over a broad energy range from X-rays to TeV gamma rays. Most of the emission arises from the apex of the bow shock. Doppler boosting shapes the X-ray and VHE lightcurves, constraining the system inclination to$i\\approx 35^{\\rm o}$. There is a tension between th... 3. Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity Science.gov (United States) Babak, Stanislav; Taracchini, Andrea; Buonanno, Alessandra 2017-01-01 In Abbott et al. [Phys. Rev. X 6, 041014 (2016), 10.1103/PhysRevX.6.041014], the properties of the first gravitational wave detected by LIGO, GW150914, were measured by employing an effective-one-body (EOB) model of precessing binary black holes whose underlying dynamics and waveforms were calibrated to numerical-relativity (NR) simulations. Here, we perform the first extensive comparison of such an EOBNR model to 70 precessing NR waveforms that span mass ratios from 1 to 5, dimensionless spin magnitudes up to 0.5, generic spin orientations, and length of about 20 orbits. We work in the observer's inertial frame and include all ℓ=2 modes in the gravitational-wave polarizations. We introduce new prescriptions for the EOB ringdown signal concerning its spectrum and time of onset. For total masses between 10 M⊙ and 200 M⊙ , we find that precessing EOBNR waveforms have unfaithfulness within about 3% to NR waveforms when considering the Advanced-LIGO design noise curve. This result is obtained without recalibration of the inspiral-plunge signal of the underlying nonprecessing EOBNR model. The unfaithfulness is computed with maximization over time and phase of arrival, sky location, and polarization of the EOBNR waveform, and it is averaged over sky location and polarization of the NR signal. We also present comparisons between NR and EOBNR waveforms in a frame that tracks the orbital precession. 4. Modelling the energy dependencies of high-frequency QPO in black hole X-ray binaries CERN Document Server Zycki, P T; Sobolewska, M A 2007-01-01 We model energy dependencies of the quasi periodic oscillations (QPO) in the model of disc epicyclic motions, with X-ray modulation caused by varying relativistic effects. The model was proposed to explain the high frequency QPO observed in X-ray binaries. We consider two specific scenarios for the geometry of accretion flow and spectral formation. Firstly, a standard cold accretion disc with an active X-ray emitting corona is assumed to oscillate. Secondly, only a hot X-ray emitting accretion flow oscillates, while the cold disc is absent at the QPO radius. We find that the QPO spectra are generally similar to the spectrum of radiation emitted at the QPO radius, and they are broadened by the relativistic effects. In particular, the QPO spectrum contains the disc component in the oscillating disc with a corona scenario. We also review the available data on energy dependencies of high frequency QPO, and we point out that they appear to lack the disc component in their energy spectra. This would suggest the hot... 5. Calculating the Probability of Returning a Loan with Binary Probability Models Directory of Open Access Journals (Sweden) Julian Vasilev 2014-12-01 Full Text Available The purpose of this article is to give a new approach in calculating the probability of returning a loan. A lot of factors affect the value of the probability. In this article by using statistical and econometric models some influencing factors are proved. The main approach is concerned with applying probit and logit models in loan management institutions. A new aspect of the credit risk analysis is given. Calculating the probability of returning a loan is a difficult task. We assume that specific data fields concerning the contract (month of signing, year of signing, given sum and data fields concerning the borrower of the loan (month of birth, year of birth (age, gender, region, where he/she lives may be independent variables in a binary logistics model with a dependent variable “the probability of returning a loan”. It is proved that the month of signing a contract, the year of signing a contract, the gender and the age of the loan owner do not affect the probability of returning a loan. It is proved that the probability of returning a loan depends on the sum of contract, the remoteness of the loan owner and the month of birth. The probability of returning a loan increases with the increase of the given sum, decreases with the proximity of the customer, increases for people born in the beginning of the year and decreases for people born at the end of the year. 6. Radiative-transfer models for supernovae IIb/Ib/Ic from binary-star progenitors CERN Document Server Dessart, Luc; Woosley, Stan; Livne, Eli; Waldman, Roni; Yoon, Sung-Chul; Langer, Norbert 2015-01-01 We present 1-D non-Local-Thermodynamic-Equilibrium time-dependent radiative-transfer simulations for supernovae (SNe) of type IIb, Ib, and Ic that result from the terminal explosion of the mass donor in a close-binary system. Here, we select three ejecta with a total kinetic energy of ~1.2e51erg, but characterised by different ejecta masses (2-5Msun), composition, and chemical mixing. The type IIb/Ib models correspond to the progenitors that have retained their He-rich shell at the time of explosion. The type Ic model arises from a progenitor that has lost its helium shell, but retains 0.32Msun of helium in a CO-rich core of 5.11Msun. We discuss their photometric and spectroscopic properties during the first 2-3 months after explosion, and connect these to their progenitor and ejecta properties including chemical stratification. For these three models, Arnett's rule overestimates the 56Ni mass by ~50% while the procedure of Katz et al., based on an energy argument, yields a more reliable estimate. The presenc... 7. Intent-Estimation- and Motion-Model-Based Collision Avoidance Method for Autonomous Vehicles in Urban Environments Directory of Open Access Journals (Sweden) Rulin Huang 2017-04-01 Full Text Available Existing collision avoidance methods for autonomous vehicles, which ignore the driving intent of detected vehicles, thus, cannot satisfy the requirements for autonomous driving in urban environments because of their high false detection rates of collisions with vehicles on winding roads and the missed detection rate of collisions with maneuvering vehicles. This study introduces an intent-estimation- and motion-model-based (IEMMB method to address these disadvantages. First, a state vector is constructed by combining the road structure and the moving state of detected vehicles. A Gaussian mixture model is used to learn the maneuvering patterns of vehicles from collected data, and the patterns are used to estimate the driving intent of the detected vehicles. Then, a desirable long-term trajectory is obtained by weighting time and comfort. The long-term trajectory and the short-term trajectory, which are predicted using a constant yaw rate motion model, are fused to achieve an accurate trajectory. Finally, considering the moving state of the autonomous vehicle, collisions can be detected and avoided. Experiments have shown that the intent estimation method performed well, achieving an accuracy of 91.7% on straight roads and an accuracy of 90.5% on winding roads, which is much higher than that achieved by the method that ignores the road structure. The average collision detection distance is increased by more than 8 m. In addition, the maximum yaw rate and acceleration during an evasive maneuver are decreased, indicating an improvement in the driving comfort. 8. Seismotectonics of New Guinea: a Model for Arc Reversal Following Arc-Continent Collision Science.gov (United States) Cooper, Patricia; Taylor, Brian 1987-02-01 The structure and evolution of the northern New Guinea collision zone is deduced from International Seismological Center (ISC) seismicity (1964-1985), new and previously published focal mechanisms and a reexamination of pertinent geological data. A tectonic model for the New Guinea margin is derived which illustrates the sequential stages in the collision and suturing of the Bewani-Toricelli-Adelbert-Finisterre-Huon-New Britain arc to central New Guinea followed by subduction polarity reversal in the west. East of 149°E, the Solomon plate is being subducted both to the north and south; bringing the New Britain and Trobriand forearcs toward collision. West of 149°E the forearcs have collided, and together they override a fold in the doubly subducted Solomon plate lithosphere, which has an axis that is parallel to the strike of the Ramu-Markham suture and that plunges westward at an angle of 5° beneath the coast ranges of northern New Guinea. Active volcanism off the north coast of New Guinea is related to subduction of the Solomon plate beneath the Bismarck plate. Active volcanism of the Papuan peninsula and Quaternary volcanism of the New Guinea highlands are related to slow subduction of the Solomon plate beneath the Indo-Australian plate along the Trobriand Trough and the trough's former extension to the west, respectively. From 144°-148°E, seismicity and focal mechanisms reveal that convergence between the sutured Bismarck and Indo-Australian plates is accommodated by thrusting within the Finisterre and Adelbert ranges and compression of the New Guinea orogenic belt, together with basement-involved foreland folding and thrusting to the south. The Finisterre block overthrusts the New Guinea orogenic belt, whereas the Adelbert block is sutured to New Guinea and overthrusts the oceanic lithosphere of the Bismarck Sea. Along the New Guinea Trench, west of 144°E, seismicity defines a southward dipping Wadati-Benioif zone, and focal mechanisms indicate oblique 9. Higgs boson contributions to neutrino production in e-e+ collisions in a left-right symmetric model CERN Document Server Gluza, J; Gluza, J; Zralek, M 1995-01-01 In gauge models with bigger number of Higgs particles their couplings to fermions are more complicated then in the standard model (SM). The influence of the Higgs bosons exchange on the neutrino production cross section in e^-e^+ collision (e^-e^+ \\rightarrow \ 10. Winds in collision. III - Modeling the interaction nebulae of eruptive symbiotics Science.gov (United States) Girard, T.; Willson, L. A. 1987-09-01 Observations of HM Sge and V1016 Cyg have been interpreted (Wallerstein et al., 1984; Wilson et al., 1984) in terms of two colliding stellar winds in an interacting binary. Here, a simplified model for the structure of the nebula which forms at the interface of the colliding winds is developed, based on momentum conservation. From this model, the geometry, mass distribution, and velocity distribution of the nebula can be found as a function of the parameters of the colliding stellar winds which sustain it. Under the assumption of negligible orbital motion, the nebular shell reaches a steady-state configuration. Its shape is roughly conical, with the cone apex angle determined by a single parameter. The time development of a cross-section of the nebula which forms in a system with nonnegligible orbital motion is also calculated, under the assumption that the nebular shell is thin relative to its overall dimensions. 11. Model investigation on the mechanism of QGP formation in relativistic heavy ion collisions Institute of Scientific and Technical Information of China (English) 邓胜华; 李家荣 1995-01-01 On the basis of the nontopological soliton bag model, it is proposed that the quark decon-finement may be indicated by the unstability and disappearance of solition solutions at finite-temperature and finite-density. The thermal effects on the vacuum structure of strongly interacting matter are investigated, and the soliton field equation of the model is solved directly in the whole range of temperature via a numerical method. The phase structure of the system and the features of deconfining phase transition are analysed in detail. In addition, the collective excitations in the vacuum caused by thermal effects are investigated by making use of an order parameter which is given to describe the vacuum condensation at finite temperature. A physical mechanism and an intuitive picture are presented for the formation of QGP from both deconfined hardon matter and the vacuum excitation in relativistic heavy ion collisions. 12. Production of excitons in grazing collisions of protons with LiF surfaces: An onion model Energy Technology Data Exchange (ETDEWEB) Miraglia, J. E.; Gravielle, M. S. [Instituto de Astronomia y Fisica del Espacio, Consejo Nacional de Investigaciones Cientificas y Tecnicas and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Casilla de Correo 67, Sucursal 28, (C1428EGA) Buenos Aires (Argentina) 2011-12-15 In this work we evaluate the production of excitons of a lithium fluoride crystal induced by proton impact in the intermediate and high energy regime (from 100 keV to 1 MeV). A simple model is proposed to account for the influence of the Coulomb grid of the target by dressing crystal ions to transform them in what we call onions. The excited states of these onions can be interpreted as excitons. Within this model, total cross section and stopping power are calculated by using the first Born and the continuum distorted-wave (CDW) eikonal initial-state (EIS) approximations. We found that between 7 and 30 excitons per incident proton are produced in grazing collisions with LiF surfaces, becoming a relevant mechanism of inelastic transitions. 13. Predicting the "graduate on time (GOT)" of PhD students using binary logistics regression model Science.gov (United States) Shariff, S. Sarifah Radiah; Rodzi, Nur Atiqah Mohd; Rahman, Kahartini Abdul; Zahari, Siti Meriam; Deni, Sayang Mohd 2016-10-01 Malaysian government has recently set a new goal to produce 60,000 Malaysian PhD holders by the year 2023. As a Malaysia's largest institution of higher learning in terms of size and population which offers more than 500 academic programmes in a conducive and vibrant environment, UiTM has taken several initiatives to fill up the gap. Strategies to increase the numbers of graduates with PhD are a process that is challenging. In many occasions, many have already identified that the struggle to get into the target set is even more daunting, and that implementation is far too ideal. This has further being progressing slowly as the attrition rate increases. This study aims to apply the proposed models that incorporates several factors in predicting the number PhD students that will complete their PhD studies on time. Binary Logistic Regression model is proposed and used on the set of data to determine the number. The results show that only 6.8% of the 2014 PhD students are predicted to graduate on time and the results are compared wih the actual number for validation purpose. 14. Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity CERN Document Server Babak, Stanislav; Buonanno, Alessandra 2016-01-01 In Ref. [1], the properties of the first gravitational wave detected by LIGO, GW150914, were measured by employing an effective-one-body (EOB) model of precessing binary black holes whose underlying dynamics and waveforms were calibrated to numerical-relativity (NR) simulations. Here, we perform the first extensive comparison of such EOBNR model to 70 precessing NR waveforms that span mass ratios from 1 to 5, dimensionless spin magnitudes up to 0.5, generic spin orientations, and length of about 20 orbits. We work in the observer's inertial frame and include all$\\ell=2$modes in the gravitational-wave polarizations. We introduce new prescriptions for the EOB ringdown signal concerning its spectrum and time of onset. For total masses between 10Msun and 200Msun, we find that precessing EOBNR waveforms have unfaithfulness within about 3% to NR waveforms when considering the Advanced-LIGO design noise curve. This result is obtained without recalibration of the inspiral-plunge of the underlying nonprecessing EOBN... 15. Sensitivity Analysis for Iceberg Geometry Shape in Ship-Iceberg Collision in View of Different Material Models Directory of Open Access Journals (Sweden) Yan Gao 2014-01-01 Full Text Available The increasing marine activities in Arctic area have brought growing interest in ship-iceberg collision study. The purpose of this paper is to study the iceberg geometry shape effect on the collision process. In order to estimate the sensitivity parameter, five different geometry iceberg models and two iceberg material models are adopted in the analysis. The FEM numerical simulation is used to predict the scenario and the related responses. The simulation results including energy dissipation and impact force are investigated and compared. It is shown that the collision process and energy dissipation are more sensitive to iceberg local shape than other factors when the elastic-plastic iceberg material model is applied. The blunt iceberg models act rigidly while the sharp ones crush easily during the simulation process. With respect to the crushable foam iceberg material model, the iceberg geometry has relatively small influence on the collision process. The spherical iceberg model shows the most rigidity for both iceberg material models and should be paid the most attention for ice-resist design for ships. 16. Conceptual model for collision detection and avoidance for runway incursion prevention Science.gov (United States) Latimer, Bridgette A. The Federal Aviation Administration (FAA), National Transportation and Safety Board (NTSB), National Aeronautics and Space Administration (NASA), numerous corporate entities, and research facilities have each come together to determine ways to make air travel safer and more efficient. These efforts have resulted in the development of a concept known as the Next Generation (Next Gen) of Aircraft or Next Gen. The Next Gen concept promises to be a clear departure from the way in which aircraft operations are performed today. The Next Gen initiatives require that modifications are made to the existing National Airspace System (NAS) concept of operations, system level requirements, software (SW) and hardware (HW) requirements, SW and HW designs and implementations. A second example of the changes in the NAS is the shift away from air traffic controllers having the responsibility for separation assurance. In the proposed new scheme of free flight, each aircraft would be responsible for assuring that it is safely separated from surrounding aircraft. Free flight would allow the separation minima for enroute aircraft to be reduced from 2000 nautical miles (nm) to 1000 nm. Simply put "Free Flight is a concept of air traffic management that permits pilots and controllers to share information and work together to manage air traffic from pre-flight through arrival without compromising safety [107]." The primary goal of this research project was to create a conceptual model that embodies the essential ingredients needed for a collision detection and avoidance system. This system was required to operate in two modes: air traffic controller's perspective and pilot's perspective. The secondary goal was to demonstrate that the technologies, procedures, and decision logic embedded in the conceptual model were able to effectively detect and avoid collision risks from both perspectives. Embodied in the conceptual model are five distinct software modules: Data Acquisition, State 17. Multifrequency Behaviour of the Gamma-Ray Binary System PSR B1259-63: Modelling the FERMI Flare Directory of Open Access Journals (Sweden) Brian van Soelen 2014-12-01 Full Text Available This paper presents a brief overview of the multifrequency properties of the gamma-ray binary system PSR B1259-63 from radio to very high energy gamma-rays. A summary is also presented of the various models put forward to explain the Fermi "flare" detected in 2011. Initial results are presented of a new turbulence driven model to explain the GeV observations. 18. A model-based circular binary segmentation algorithm for the analysis of array CGH data Directory of Open Access Journals (Sweden) Tu Shih-Hsin 2011-10-01 Full Text Available Abstract Background Circular Binary Segmentation (CBS is a permutation-based algorithm for array Comparative Genomic Hybridization (aCGH data analysis. CBS accurately segments data by detecting change-points using a maximal-t test; but extensive computational burden is involved for evaluating the significance of change-points using permutations. A recent implementation utilizing a hybrid method and early stopping rules (hybrid CBS to improve the performance in speed was subsequently proposed. However, a time analysis revealed that a major portion of computation time of the hybrid CBS was still spent on permutation. In addition, what the hybrid method provides is an approximation of the significance upper bound or lower bound, not an approximation of the significance of change-points itself. Results We developed a novel model-based algorithm, extreme-value based CBS (eCBS, which limits permutations and provides robust results without loss of accuracy. Thousands of aCGH data under null hypothesis were simulated in advance based on a variety of non-normal assumptions, and the corresponding maximal-t distribution was modeled by the Generalized Extreme Value (GEV distribution. The modeling results, which associate characteristics of aCGH data to the GEV parameters, constitute lookup tables (eXtreme model. Using the eXtreme model, the significance of change-points could be evaluated in a constant time complexity through a table lookup process. Conclusions A novel algorithm, eCBS, was developed in this study. The current implementation of eCBS consistently outperforms the hybrid CBS 4× to 20× in computation time without loss of accuracy. Source codes, supplementary materials, supplementary figures, and supplementary tables can be found at http://ntumaps.cgm.ntu.edu.tw/eCBSsupplementary. 19. Transverse-energy distributions at midrapidity in$p$$+$$p$,$d$$+Au, and Au+Au collisions at \\sqrt{s_{_{NN}}}=62.4--200~GeV and implications for particle-production models CERN Document Server Adler, S S; Aidala, C; Ajitanand, N N; Akiba, Y; Al-Jamel, A; Alexander, J; Aoki, K; Aphecetche, L; Armendariz, R; Aronson, S H; Averbeck, R; Awes, T C; Azmoun, B; Babintsev, V; Baldisseri, A; Barish, K N; Barnes, P D; Bassalleck, B; Bathe, S; Batsouli, S; Baublis, V; Bauer, F; Bazilevsky, A; Belikov, S; Bennett, R; Berdnikov, Y; Bjorndal, M T; Boissevain, J G; Borel, H; Boyle, K; Brooks, M L; Brown, D S; Bruner, N; Bucher, D; Buesching, H; Bumazhnov, V; Bunce, G; Burward-Hoy, J M; Butsyk, S; Camard, X; Campbell, S; Chai, J -S; Chand, P; Chang, W C; Chernichenko, S; Chi, C Y; Chiba, J; Chiu, M; Choi, I J; Choudhury, R K; Chujo, T; Cianciolo, V; Cleven, C R; Cobigo, Y; Cole, B A; Comets, M P; Constantin, P; Csanád, M; Csörgő, T; Cussonneau, J P; Dahms, T; Das, K; David, G; Deák, F; Delagrange, H; Denisov, A; d'Enterria, D; Deshpande, A; Desmond, E J; Devismes, A; Dietzsch, O; Dion, A; Drachenberg, J L; Drapier, O; Drees, A; Dubey, A K; Durum, A; Dutta, D; Dzhordzhadze, V; Efremenko, Y V; Egdemir, J; Enokizono, A; En'yo, H; Espagnon, B; Esumi, S; Fields, D E; Finck, C; Fleuret, F; Fokin, S L; Forestier, B; Fox, B D; Fraenkel, Z; Frantz, J E; Franz, A; Frawley, A D; Fukao, Y; Fung, S -Y; Gadrat, S; Gastineau, F; Germain, M; Glenn, A; Gonin, M; Gosset, J; Goto, Y; de Cassagnac, R Granier; Grau, N; Greene, S V; Perdekamp, M Grosse; Gunji, T; Gustafsson, H -Å; Hachiya, T; Henni, A Hadj; Haggerty, J S; Hagiwara, M N; Hamagaki, H; Hansen, A G; Harada, H; Hartouni, E P; Haruna, K; Harvey, M; Haslum, E; Hasuko, K; Hayano, R; He, X; Heffner, M; Hemmick, T K; Heuser, J M; Hidas, P; Hiejima, H; Hill, J C; Hobbs, R; Holmes, M; Holzmann, W; Homma, K; Hong, B; Hoover, A; Horaguchi, T; Hur, M G; Ichihara, T; Iinuma, H; Ikonnikov, V V; Imai, K; Inaba, M; Inuzuka, M; Isenhower, D; Isenhower, L; Ishihara, M; Isobe, T; Issah, M; Isupov, A; Jacak, B V; Jia, J; Jin, J; Jinnouchi, O; Johnson, B M; Johnson, S C; Joo, K S; Jouan, D; Kajihara, F; Kametani, S; Kamihara, N; Kaneta, M; Kang, J H; Katou, K; Kawabata, T; Kawagishi, T; Kazantsev, A V; Kelly, S; Khachaturov, B; Khanzadeev, A; Kikuchi, J; Kim, D J; Kim, E; Kim, E J; Kim, G -B; Kim, H J; Kim, Y -S; Kinney, E; Kiss, Á; Kistenev, E; Kiyomichi, A; Klein-Boesing, C; Kobayashi, H; Kochenda, L; Kochetkov, V; Kohara, R; Komkov, B; Konno, M; Kotchetkov, D; Kozlov, A; Kroon, P J; Kuberg, C H; Kunde, G J; Kurihara, N; Kurita, K; Kweon, M J; Kwon, Y; Kyle, G S; Lacey, R; Lajoie, J G; Lebedev, A; Bornec, Y Le; Leckey, S; Lee, D M; Lee, M K; Leitch, M J; Leite, M A L; Li, X H; Lim, H; Litvinenko, A; Liu, M X; Maguire, C F; Makdisi, Y I; Malakhov, A; Malik, M D; Manko, V I; Mao, Y; Martinez, G; Masui, H; Matathias, F; Matsumoto, T; McCain, M C; McGaughey, P L; Miake, Y; Miller, T E; Milov, A; Mioduszewski, S; Mishra, G C; Mitchell, J T; Mohanty, A K; Morrison, D P; Moss, J M; Moukhanova, T V; Mukhopadhyay, D; Muniruzzaman, M; Murata, J; Nagamiya, S; Nagata, Y; Nagle, J L; Naglis, M; Nakamura, T; Newby, J; Nguyen, M; Norman, B E; Nyanin, A S; Nystrand, J; O'Brien, E; Ogilvie, C A; Ohnishi, H; Ojha, I D; Okada, K; Omiwade, O O; Oskarsson, A; Otterlund, I; Oyama, K; Ozawa, K; Pal, D; Palounek, A P T; Pantuev, V; Papavassiliou, V; Park, J; Park, W J; Pate, S F; Pei, H; Penev, V; Peng, J -C; Pereira, H; Peresedov, V; Peressounko, D Yu; Pierson, A; Pinkenburg, C; Pisani, R P; Purschke, M L; Purwar, A K; Qu, H; Qualls, J M; Rak, J; Ravinovich, I; Read, K F; Reuter, M; Reygers, K; Riabov, V; Riabov, Y; Roche, G; Romana, A; Rosati, M; Rosendahl, S S E; Rosnet, P; Rukoyatkin, P; Rykov, V L; Ryu, S S; Sahlmueller, B; Saito, N; Sakaguchi, T; Sakai, S; Samsonov, V; Sanfratello, L; Santo, R; Sato, H D; Sato, S; Sawada, S; Schutz, Y; Semenov, V; Seto, R; Sharma, D; Shea, T K; Shein, I; Shibata, T -A; Shigaki, K; Shimomura, M; Shohjoh, T; Shoji, K; Sickles, A; Silva, C L; Silvermyr, D; Sim, K S; Singh, C P; Singh, V; Skutnik, S; Smith, W C; Soldatov, A; Soltz, R A; Sondheim, W E; Sorensen, S P; Sourikova, I V; Staley, F; Stankus, P W; Stenlund, E; Stepanov, M; Ster, A; Stoll, S P; Sugitate, T; Suire, C; Sullivan, J P; Sziklai, J; Tabaru, T; Takagi, S; Takagui, E M; Taketani, A; Tanaka, K H; Tanaka, Y; Tanida, K; Tannenbaum, M J; Taranenko, A; Tarján, P; Thomas, T L; Togawa, M; Tojo, J; Torii, H; Towell, R S; Tram, V-N; Tserruya, I; Tsuchimoto, Y; Tuli, S K; Tydesjö, H; Tyurin, N; Uam, T J; Vale, C; Valle, H; van Hecke, H W; Velkovska, J; Velkovsky, M; Vértesi, R; Veszprémi, V; Vinogradov, A A; Volkov, M A; Vznuzdaev, E; Wagner, M; Wang, X R; Watanabe, Y; Wessels, J; White, S N; Willis, N; Winter, D; Wohn, F K; Woody, C L; Wysocki, M; Xie, W; Yanovich, A; Yokkaichi, S; Young, G R; Younus, I; Yushmanov, I E; Zajc, W A; Zaudtke, O; Zhang, C; Zhou, S; Zimányi, J; Zolin, L; Zong, X 2013-01-01 Measurements of the midrapidity transverse energy distribution, d\\Et/d\\eta, are presented for p$$+$$p, d$$+$Au, and Au$+$Au collisions at$\\sqrt{s_{_{NN}}}=200$GeV and additionally for Au$+$Au collisions at$\\sqrt{s_{_{NN}}}=62.4$and 130 GeV. The$d\\Et/d\\eta$distributions are first compared with the number of nucleon participants$N_{\\rm part}$, number of binary collisions$N_{\\rm coll}$, and number of constituent-quark participants$N_{qp}$calculated from a Glauber model based on the nuclear geometry. For Au$+$Au,$\\mean{d\\Et/d\\eta}/N_{\\rm part}$increases with$N_{\\rm part}$, while$\\mean{d\\Et/d\\eta}/N_{qp}$is approximately constant for all three energies. This indicates that the two component ansatz,$dE_{T}/d\\eta \\propto (1-x) N_{\\rm part}/2 + x N_{\\rm coll}$, which has been used to represent$E_T$distributions, is simply a proxy for$N_{qp}$, and that the$N_{\\rm coll}$term does not represent a hard-scattering component in$E_T$distributions. The$dE_{T}/d\\eta$distributions of Au$+$Au and$...
20. Turbulence-induced bubble collision force modeling and validation in adiabatic two-phase flow using CFD
Energy Technology Data Exchange (ETDEWEB)
Sharma, Subash L., E-mail: [email protected] [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907-1290 (United States); Hibiki, Takashi; Ishii, Mamoru [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907-1290 (United States); Brooks, Caleb S. [Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois, Urbana, IL 61801 (United States); Schlegel, Joshua P. [Nuclear Engineering Program, Missouri University of Science and Technology, Rolla, MO 65409 (United States); Liu, Yang [Nuclear Engineering Program, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States); Buchanan, John R. [Bechtel Marine Propulsion Corporation, Bettis Laboratory, West Mifflin, PA 15122 (United States)
2017-02-15
Highlights: • Void distribution in narrow rectangular channel with various non-uniform inlet conditions. • Modeling of void diffusion due to bubble collision force. • Validation of new modeling in adiabatic air–water two-phase flow in a narrow channel. - Abstract: The prediction capability of the two-fluid model for gas–liquid dispersed two-phase flow depends on the accuracy of the closure relations for the interfacial forces. In previous studies of two-phase flow Computational Fluid Dynamics (CFD), interfacial force models for a single isolated bubble has been extended to disperse two-phase flow assuming the effect in a swarm of bubbles is similar. Limited studies have been performed investigating the effect of the bubble concentration on the lateral phase distribution. Bubbles, while moving through the liquid phase, may undergo turbulence-driven random collision with neighboring bubbles without significant coalescence. The rate of these collisions depends upon the bubble approach velocity and bubble spacing. The bubble collision frequency is expected to be higher in locations with higher bubble concentrations, i.e., volume fraction. This turbulence-driven random collision causes the diffusion of the bubbles from high concentration to low concentration. Based on experimental observations, a phenomenological model has been developed for a “turbulence-induced bubble collision force” for use in the two-fluid model. For testing the validity of the model, two-phase flow data measured at Purdue University are utilized. The geometry is a 10 mm × 200 mm cross section channel. Experimentally, non-uniform inlet boundary conditions are applied with different sparger combinations to vary the volume fraction distribution across the wider dimension. Examining uniform and non-uniform inlet data allows for the influence of the volume fraction to be studied as a separate effect. The turbulence-induced bubble collision force has been implemented in ANSYS CFX. The
1. Binary oscillations in the Kok model of oxygen evolution in oxygenic photosynthesis.
Science.gov (United States)
Shinkarev, V P
1996-06-01
The flash-induced kinetics of various characteristics of Photosystem II (PS II) in the thylakoids of oxygenic plants are modulated by a period of two, due to the function of a two-electron gate in the electron acceptor side, and by a period of four, due to the changes in the state of the oxygen-evolving complex. In the absence of inhibitors of PS II, the assignment of measured signal to the oxygen-evolving complex or to quinone acceptor side has frequently been done on the basis of the periodicity of its flash-induced oscillations, i.e. four or two. However, in some circumstances, the period four oscillatory processes of the donor side of PS II can generate period two oscillations. It is shown here that in the Kok model of oxygen evolution (equal misses and equal double hits), the sum of the concentrations of the S 0 and S 2 states (as well as the sum of concentrations of S 1 and S 3 states) oscillates with period of two: S 0+S 2→S 1+S 3→S 0+S 2→S 1+S 3. Moreover, in the generalized Kok model (with specific miss factors and double hits for each S-state) there always exist such ε0, ε1, ε2, ε3 that the sum ε0[S0] + ε1[S1] + ε2[S2] + ε3[S3] oscillates with period of two as a function of flash number. Any other coefficients which are linearly connected with these coefficients, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiqbew7aLzaaja% aaaa!3917!\$\\hat \\varepsilon \$i = c1εi + c2, also generate binary oscillations of this sum. Therefore, the decomposition of the flash-induced oscillations of some measured parameters into binary oscillations, depending only on the acceptor side of PS II, and quaternary oscillations, depending only on the donor side of PS II, becomes practically impossible when measured with
2. Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes
Directory of Open Access Journals (Sweden)
Steyerberg Ewout W
2011-05-01
Full Text Available Abstract Background Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. Methods We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI enrolled in eight Randomized Controlled Trials (RCTs and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4, Stata (GLLAMM, SAS (GLIMMIX and NLMIXED, MLwiN ([R]IGLS and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC, R package MCMCglmm and SAS experimental procedure MCMC. Three data sets (the full data set and two sub-datasets were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted. Results The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal models for the main study and when based on a relatively large number of level-1 (patient level data compared to the number of level-2 (hospital level data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in
3. Bayesian model comparison for one-dimensional azimuthal correlations in 200GeV AuAu collisions
Science.gov (United States)
Eggers, Hans C.; de Kock, Michiel B.; Trainor, Thomas A.
2016-07-01
In the context of data modeling and comparisons between different fit models, Bayesian analysis calls that model best which has the largest evidence, the prior-weighted integral over model parameters of the likelihood function. Evidence calculations automatically take into account both the usual chi-squared measure and an Occam factor which quantifies the price for adding extra parameters. Applying Bayesian analysis to projections onto azimuth of 2D angular correlations from 200 GeV AuAu collisions, we consider typical model choices including Fourier series and a Gaussian plus combinations of individual cosine components. We find that models including a Gaussian component are consistently preferred over pure Fourier-series parametrizations, sometimes strongly so. For 0-5% central collisions the Gaussian-plus-dipole model performs better than Fourier Series models or any other combination of Gaussian-plus-multipoles.
4. Bayesian model comparison for one-dimensional azimuthal correlations in 200GeV AuAu collisions
CERN Document Server
Eggers, Hans C; Trainor, Thomas A
2015-01-01
In the context of data modeling and comparisons between different fit models, Bayesian analysis calls that model best which has the largest evidence, the prior-weighted integral over model parameters of the likelihood function. Evidence calculations automatically take into account both the usual chi-squared measure and an Occam factor which quantifies the price for adding extra parameters. Applying Bayesian analysis to projections onto azimuth of 2D angular correlations from 200 GeV AuAu collisions, we consider typical model choices including Fourier series and a Gaussian plus combinations of individual cosine components. We find that models including a Gaussian component are consistently preferred over pure Fourier-series parametrizations, sometimes strongly so. For 0-5% central collisions the Gaussian-plus-dipole model performs better than Fourier Series models or any other combination of Gaussian-plus-multipoles.
5. Bayesian model comparison for one-dimensional azimuthal correlations in 200GeV AuAu collisions
Directory of Open Access Journals (Sweden)
Eggers Hans C.
2016-01-01
Full Text Available In the context of data modeling and comparisons between different fit models, Bayesian analysis calls that model best which has the largest evidence, the prior-weighted integral over model parameters of the likelihood function. Evidence calculations automatically take into account both the usual chi-squared measure and an Occam factor which quantifies the price for adding extra parameters. Applying Bayesian analysis to projections onto azimuth of 2D angular correlations from 200 GeV AuAu collisions, we consider typical model choices including Fourier series and a Gaussian plus combinations of individual cosine components. We find that models including a Gaussian component are consistently preferred over pure Fourier-series parametrizations, sometimes strongly so. For 0–5% central collisions the Gaussian-plus-dipole model performs better than Fourier Series models or any other combination of Gaussian-plus-multipoles.
6. Summary goodness-of-fit statistics for binary generalized linear models with noncanonical link functions.
Science.gov (United States)
Canary, Jana D; Blizzard, Leigh; Barry, Ronald P; Hosmer, David W; Quinn, Stephen J
2016-05-01
Generalized linear models (GLM) with a canonical logit link function are the primary modeling technique used to relate a binary outcome to predictor variables. However, noncanonical links can offer more flexibility, producing convenient analytical quantities (e.g., probit GLMs in toxicology) and desired measures of effect (e.g., relative risk from log GLMs). Many summary goodness-of-fit (GOF) statistics exist for logistic GLM. Their properties make the development of GOF statistics relatively straightforward, but it can be more difficult under noncanonical links. Although GOF tests for logistic GLM with continuous covariates (GLMCC) have been applied to GLMCCs with log links, we know of no GOF tests in the literature specifically developed for GLMCCs that can be applied regardless of link function chosen. We generalize the Tsiatis GOF statistic originally developed for logistic GLMCCs, (TG), so that it can be applied under any link function. Further, we show that the algebraically related Hosmer-Lemeshow (HL) and Pigeon-Heyse (J(2) ) statistics can be applied directly. In a simulation study, TG, HL, and J(2) were used to evaluate the fit of probit, log-log, complementary log-log, and log models, all calculated with a common grouping method. The TG statistic consistently maintained Type I error rates, while those of HL and J(2) were often lower than expected if terms with little influence were included. Generally, the statistics had similar power to detect an incorrect model. An exception occurred when a log GLMCC was incorrectly fit to data generated from a logistic GLMCC. In this case, TG had more power than HL or J(2) .
7. 3-D Computational Modelling of Oblique Continental Collision near South Island, New Zealand
Science.gov (United States)
Karatun, L.; Pysklywec, R. N.
2015-12-01
The research explores the highly oblique continental convergence at the South Island of New Zealand, considering the fundamental geodynamic mechanisms of sub-crustal lithospheric deformation during the orogenesis. In addition to the high velocity of along-strike plate motion, the oppositely verging subduction zones bounding the collision make the problem inherently three-dimensional. To study such factors during orogenesis, we conduct 3D computational modelling and present the results of a series of new experiments configured for the oblique South Island collision. The geodynamic modelling uses ASPECT - a robust highly-scalable and extendable geodynamic code featuring adaptive mesh refinement and complex rheologies. The model domain is defined by a box with prescribed velocities on the left and right faces with varied ratio of convergent versus strike-slip components, periodic boundary conditions for the front and back faces, free surface on top, and free slip at the bottom. Two different rheology types are used: brittle (pressure-, strain rate-, and material strength-dependent) for crust and visco-plastic (temperature-, pressure- and strain rate-dependent) for mantle. The obtained results provide insight into the behaviour of the lithosphere under the situation of young oblique convergence. We focus on the development of the mantle lithosphere, considering how the morphology of the sub-crustal orogenic root evolves during the convergent/strike-slip plate motions. The numerical experiments explore the dependence of this process on such factors as ratio of convergent versus strike-slip motion at the plate boundary, and rheological parameters of crust and mantle. The behaviour of the crust is also tracked to determine how the deep 3D tectonics may manifest at the surface.
8. A parallel Discrete Element Method to model collisions between non-convex particles
Science.gov (United States)
Rakotonirina, Andriarimina Daniel; Delenne, Jean-Yves; Wachs, Anthony
2017-06-01
In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called "glued-convex method" (in the sense clumping convex bodies together), as an extension of the popular "glued-spheres" method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor.
9. Novel modelling of ultracompact X-ray binary evolution - stable mass transfer from white dwarfs to neutron stars
Science.gov (United States)
Sengar, Rahul; Tauris, Thomas M.; Langer, Norbert; Istrate, Alina G.
2017-09-01
Tight binaries of helium white dwarfs (He WDs) orbiting millisecond pulsars (MSPs) will eventually merge' due to gravitational damping of the orbit. The outcome has been predicted to be the production of long-lived ultracompact X-ray binaries (UCXBs), in which the WD transfers material to the accreting neutron star (NS). Here we present complete numerical computations, for the first time, of such stable mass transfer from a He WD to a NS. We have calculated a number of complete binary stellar evolution tracks, starting from pre-low-mass X-ray binary systems, and evolved these to detached MSP+WD systems and further on to UCXBs. The minimum orbital period is found to be as short as 5.6 min. We followed the subsequent widening of the systems until the donor stars become planets with a mass of ˜0.005 M⊙ after roughly a Hubble time. Our models are able to explain the properties of observed UCXBs with high helium abundances and we can identify these sources on the ascending or descending branch in a diagram displaying mass-transfer rate versus orbital period.
10. Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals
CERN Document Server
Schmidt, Patricia; Husa, Sascha
2012-01-01
One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional parameter space) can be mapped to only a two-dimensional space of non-precessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-aligned frame, and is extremely accurate (matches $> 0.99$ with parameter biases in the total spin of $\\Delta \\chi \\leq 0.04$), even in the case of transitional precession. In addition, we demonstrate a simple method to construct hybrid post-Newtonian--numerical-relativity precessing-binary waveforms in the quadrupole-aligned frame, and provide evidence that our approximate mapping can be used all the way to the merger. Finally, ...
11. Modeling collision energy transfer in APCI/CID mass spectra of PAHs using thermal-like post-collision internal energy distributions
Science.gov (United States)
Solano, Eduardo A.; Mohamed, Sabria; Mayer, Paul M.
2016-10-01
The internal energy transferred when projectile molecular ions of naphthalene collide with argon gas atoms was extracted from the APCI-CID (atmospheric-pressure chemical ionization collision-induced dissociation) mass spectra acquired as a function of collision energy. Ion abundances were calculated by microcanonical integration of the differential rate equations using the Rice-Ramsperger-Kassel-Marcus rate constants derived from a UB3LYP/6-311G+(3df,2p)//UB3LYP/6-31G(d) fragmentation mechanism and thermal-like vibrational energy distributions p M (" separators=" E , T char ) . The mean vibrational energy excess of the ions was characterized by the parameter Tchar ("characteristic temperature"), determined by fitting the theoretical ion abundances to the experimental breakdown graph (a plot of relative abundances of the ions as a function of kinetic energy) of activated naphthalene ions. According to these results, the APCI ion source produces species below Tchar = 1457 K, corresponding to 3.26 eV above the vibrational ground state. Subsequent collisions heat the ions up further, giving rise to a sigmoid curve of Tchar as a function of Ecom (center-of-mass-frame kinetic energy). The differential internal energy absorption per kinetic energy unit (dEvib/dEcom) changes with Ecom according to a symmetric bell-shaped function with a maximum at 6.38 ± 0.32 eV (corresponding to 6.51 ± 0.27 eV of vibrational energy excess), and a half-height full width of 6.30 ± 1.15 eV. This function imposes restrictions on the amount of energy that can be transferred by collisions, such that a maximum is reached as kinetic energy is increased. This behavior suggests that the collisional energy transfer exhibits a pronounced increase around some specific value of energy. Finally, the model is tested against the CID mass spectra of anthracene and pyrene ions and the corresponding results are discussed.
12. Thermodynamic properties of binary mixtures containing dimethyl carbonate+2-alkanol: Experimental data, correlation and prediction by ERAS model and cubic EOS
Energy Technology Data Exchange (ETDEWEB)
Almasi, Mohammad, E-mail: [email protected] [Department of Chemistry, Science and Research Branch, Islamic Azad University, Khouzestan (Iran, Islamic Republic of)
2013-03-01
Densities and viscosities for binary mixtures of dimethyl carbonate with 2-propanol up to 2-heptanol were measured at various temperatures and ambient pressure. From experimental data, excess molar volumes, V{sub m}{sup E}. were calculated and correlated by the Redlich–Kister equation to obtain the binary coefficients and the standard deviations. Excess molar volumes, V{sub m}{sup E}, are positive for all studied mixtures over the entire range of the mole fraction. The ERAS-model has been applied for describing the binary excess molar volumes and also Peng–Robinson–Stryjek–Vera (PRSV) equation of state (EOS) has been used to predict the binary excess molar volumes and viscosities. Also several semi-empirical models were used to correlate the viscosity of binary mixtures.
13. Tidal heating and mass loss in neutron star binaries - Implications for gamma-ray burst models
Science.gov (United States)
Meszaros, P.; Rees, M. J.
1992-01-01
A neutron star in a close binary orbit around another neutron star (or stellar-mass black hole) spirals inward owing to gravitational radiation. We discuss the effects of tidal dissipation during this process. Tidal energy dissipated in the neutron star's core escapes mainly as neutrinos, but heating of the crust, and outward diffusion of photons, blows off the outer layers of the star. This photon-driven mass loss precedes the final coalescence. The presence of this eject material impedes the escape of gamma-rays created via neutrino interactions. If an e(+) - e(-) fireball, created in the late stages of coalescence, were loaded with (or surrounded by) material with the mean column density of the ejecta, it could not be an efficient source of gamma-rays. Models for cosmologically distant gamma-rays burst that involve neutron stars must therefore be anisotropic, so that the fireball expands preferentially in directions where the column density of previously blown-off material is far below the spherically averaged value which we have calculated. Some possible 'scenarios' along these lines are briefly discussed.
14. The likelihood of achieving quantified road safety targets: a binary logistic regression model for possible factors.
Science.gov (United States)
Sze, N N; Wong, S C; Lee, C Y
2014-12-01
15. Exact Scale Invariance in Mixing of Binary Candidates in Voting Model
Science.gov (United States)
2010-03-01
We introduce a voting model and discuss the scale invariance in the mixing of candidates. The Candidates are classified into two categories μ\\in \\{0,1\\} and are called as “binary” candidates. There are in total N=N0+N1 candidates, and voters vote for them one by one. The probability that a candidate gets a vote is proportional to the number of votes. The initial number of votes (“seed”) of a candidate μ is set to be sμ. After infinite counts of voting, the probability function of the share of votes of the candidate μ obeys gamma distributions with the shape exponent sμ in the thermodynamic limit Z0=N1s1+N0s0\\to ∞. Between the cumulative functions \\{xμ\\} of binary candidates, the power-law relation 1-x1 ˜ (1-x0)α with the critical exponent α=s1/s0 holds in the region 1-x0,1-x1≪ 1. In the double scaling limit (s1,s0)\\to (0,0) and Z0 \\to ∞ with s1/s0=α fixed, the relation 1-x1=(1-x0)α holds exactly over the entire range 0≤ x0,x1 ≤ 1. We study the data on horse races obtained from the Japan Racing Association for the period 1986 to 2006 and confirm scale invariance.
16. Hysteresis and the Cholesterol Dependent Phase Transition in Binary Lipid Mixtures with the Martini Model.
Science.gov (United States)
Arnarez, Clement; Webb, Alexis; Rouvière, Eric; Lyman, Edward
2016-12-29
Extensive Martini simulation data, totaling 5 ms, is presented for binary mixtures of dipalmitoylphosphatidylcholine (DPPC) and cholesterol. Using simulation initiated from both gel (so) and liquid-disordered (Ld) phases, significant and strongly cholesterol-dependent hysteresis in the enthalpy as a function of temperature is observed for cholesterol mole fractions from 0 to 20 mol %. Although the precise phase transition temperature cannot be determined due to the hysteresis, the data are consistent with a first order gel to fluid transition, which increases in temperature with cholesterol. At 30 mol % cholesterol, no hysteresis is observed, and there is no evidence for a continuous transition, in either structural parameters like the area per lipid or in the heat capacity as a function of temperature. The results are consistent with a single uniform phase above a critical cholesterol composition between 20 and 30 mol % in Martini, while highlighting the importance and difficulty of obtaining the equilibrium averages to locate phase boundaries precisely in computational models of lipid bilayers.
17. Tidal heating and mass loss in neutron star binaries - Implications for gamma-ray burst models
Science.gov (United States)
Meszaros, P.; Rees, M. J.
1992-01-01
A neutron star in a close binary orbit around another neutron star (or stellar-mass black hole) spirals inward owing to gravitational radiation. We discuss the effects of tidal dissipation during this process. Tidal energy dissipated in the neutron star's core escapes mainly as neutrinos, but heating of the crust, and outward diffusion of photons, blows off the outer layers of the star. This photon-driven mass loss precedes the final coalescence. The presence of this eject material impedes the escape of gamma-rays created via neutrino interactions. If an e(+) - e(-) fireball, created in the late stages of coalescence, were loaded with (or surrounded by) material with the mean column density of the ejecta, it could not be an efficient source of gamma-rays. Models for cosmologically distant gamma-rays burst that involve neutron stars must therefore be anisotropic, so that the fireball expands preferentially in directions where the column density of previously blown-off material is far below the spherically averaged value which we have calculated. Some possible 'scenarios' along these lines are briefly discussed.
18. A Neutron Star-White Dwarf Binary Model for Repeating Fast Radio Burst 121102
CERN Document Server
Gu, Wei-Min; Liu, Tong; Ma, Renyi; Wang, Junfeng
2016-01-01
We propose a compact binary model for the fast radio burst (FRB) repeaters, where the system consists of a magnetic white dwarf (WD) and a neutron star (NS) with strong bipolar magnetic fields. When the WD fills its Roche lobe, mass transfer will occur from the WD to the NS through the inner Lagrange point. The accreted magnetized materials may trigger magnetic reconnection when they approach the NS surface, and therefore the electrons can be accelerated to an ultra-relativistic speed. In this scenario, the curvature radiation of the electrons moving along the NS magnetic field lines can account for the characteristic frequency and the timescale of an FRB. Owing to the conservation of angular momentum, the WD may be kicked away after a burst, and the next burst may appear when the system becomes semi-detached again through the gravitational radiation. By comparing our analyses with the observations, we show that such an intermittent Roche lobe overflow mechanism can be responsible for the observed repeating b...
19. Model-Driven Verifying Compilation of Synchronous Distributed Applications
Science.gov (United States)
2014-10-01
Portable to different OSes (Windows, Linux, Android etc.) and networking technology (TCP/IP, UDP, DDS etc.) Binary MADARA Middleware Guarantee...0,3) Potential Collision Reservation Contention Resolved based on Node ID. No collision possible if no over- booking . X Y 15 Model
20. Concept of an enhanced V2X pedestrian collision avoidance system with a cost function-based pedestrian model.
Science.gov (United States)
Kotte, Jens; Schmeichel, Carsten; Zlocki, Adrian; Gathmann, Hauke; Eckstein, Lutz
2017-04-03
Objective State-of-the-art collision avoidance and collision mitigation systems predict the behavior of pedestrians based on trivial models that assume a constant acceleration or velocity. New sources of sensor information, for example smart devices (smartphones, tablets, smartwatches, …), can support enhanced pedestrian behavior models. The objective of this paper is the development and implementation of a V2X pedestrian collision avoidance system that uses new information sources. Methods A literature review of existing state-of-the-art pedestrian collision avoidance systems, pedestrian behavior models in Advanced Driver Assistance Systems (ADAS), and traffic simulations is conducted together with an analysis of existing studies on typical pedestrian patterns in traffic. Based on this analysis, possible parameters for predicting pedestrian behavior were investigated. The results led to new requirements from which a concept was developed and implemented. Results The analysis of typical pedestrian behavior patterns in traffic situations showed the complexity of predicting pedestrian behavior. Requirements for an improved behavior prediction were derived. A concept for a V2X collision avoidance system, based on a cost function that predicts pedestrian near future presence, and its implementation, is presented. The concept presented considers several challenges such as information privacy, inaccuracies of the localization, and inaccuracies of the prediction. Conclusion A concept for an enhanced V2X pedestrian collision avoidance system was developed and introduced. The concept uses new information sources such as smart devices to improve the prediction of the pedestrian's presence in the near future and considers challenges that come along with the usage of these information sources. | {"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": 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": 0.8423742055892944, "perplexity": 2637.732892477338}, "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-2018-09/segments/1518891817437.99/warc/CC-MAIN-20180225205820-20180225225820-00022.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcds.2014.34.1747 | # American Institute of Mathematical Sciences
May 2014, 34(5): 1747-1774. doi: 10.3934/dcds.2014.34.1747
## Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary: Interaction with a Hardy-Leray potential
1 Laboratoire D'Analyse Nonlinéaire et Mathématiques Appliquées, Université Aboubekr Belkaïd, Tlemcen, Tlemcen 13000, Algeria 2 Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Università di Roma Sapienza, via Scarpa 16, 00161 Roma, Italy 3 Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid 4 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Received July 2013 Revised August 2013 Published October 2013
In this article we consider the following family of nonlinear elliptic problems,
$-\Delta (u^m) - \lambda \frac{u^m}{|x|^2} = |Du|^q + c f(x).$
We will analyze the interaction between the Hardy-Leray potential and the gradient term getting existence and nonexistence results in bounded domains $\Omega\subset\mathbb{R}^N$, $N\ge 3$, containing the pole of the potential.
Recall that $Λ_N = (\frac{N-2}{2})^2$ is the optimal constant in the Hardy-Leray inequality.
1.For $0 < m \le 2$ we prove the existence of a critical exponent $q_+ \le 2$ such that for $q > q_+$, the above equation has no positive distributional solution. If $q < q_+$ we find solutions by using different alternative arguments.
Moreover if $q = q_+ > 1$ we get the following alternative results.
(a) If $m < 2$ and $q=q_+$ there is no solution.
(b) If $m = 2$, then $q_+=2$ for all $\lambda$. We prove that there exists solution if and only if $2\lambda\leq\Lambda_N$ and, moreover, we find infinitely many positive solutions.
2. If $m > 2$ we obtain some partial results on existence and nonexistence.
We emphasize that if $q(\frac{1}{m}-1)<-1$ and $1 < q \le 2$, there exists positive solutions for any $f \in L^1(Ω)$.
Citation: Boumediene Abdellaoui, Daniela Giachetti, Ireneo Peral, Magdalena Walias. Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary: Interaction with a Hardy-Leray potential. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 1747-1774. doi: 10.3934/dcds.2014.34.1747
##### References:
[1] B. Abdellaoui, A. Dall'Aglio and I. Peral, Some Remarks on Elliptic Problems with Critical Growth in the Gradient, J. Diff. Eq., 222 (2006), 21-62. doi: 10.1016/j.jde.2005.02.009. Google Scholar [2] B. Abdellaoui, D. Giachetti, I. Peral and M. Walias, Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary, Nonlinear Analysis, 74 (2011), 1355-1371. doi: 10.1016/j.na.2010.10.008. Google Scholar [3] B. Abdellaoui and I. Peral, Nonexistence results for quasilinear elliptic equations related to Caffarelli-Kohn-Nirenberg inequalities, Communications in Pure and Applied Analysis, 2 (2003), 539-566. doi: 10.3934/cpaa.2003.2.539. Google Scholar [4] B. Abdellaoui and I. Peral, The Equation $-\Delta u - \lambda \frac u{|x|^2} = |D u|^p + c f(x)$, the optimal power, Ann. Scuola Norm. Sup. Pisa, VI, (2007), 159-183. Google Scholar [5] B. Abdellaoui and I. Peral, Existence and nonexistence results for quasilinear elliptic equations involving the p-Laplacian with a critical potential, Annali di Matematica Pura e Applicata, 182 (2003), 247-270. doi: 10.1007/s10231-002-0064-y. Google Scholar [6] B. Abdellaoui and I. Peral, A note on a critical problem with natural growth in the gradient, J. Eur. Math. Soc., 8 (2006), 157-170. doi: 10.4171/JEMS/43. Google Scholar [7] N. E. Alaa and M. Pierre, Weak solutions of some quasilinear elliptic equations with data measures, SIAM J. Math. Anal., 24 (1993), 23-35. doi: 10.1137/0524002. Google Scholar [8] D. Arcoya, L. Boccardo, T. Leonori and A. Porretta, Some elliptic problems with singular natural growth lower order terms, J.diff. equation, 249 (2010), 2771-2795. doi: 10.1016/j.jde.2010.05.009. Google Scholar [9] P. Baras and M. Pierre, Singularités éliminables pour des équations semi-linéaires, Ann. Inst. Fourier, 34 (1984), 185-206. doi: 10.5802/aif.956. Google Scholar [10] L. Boccardo, Dirichlet problems with singular and gradient quadratic lower order terms, ESAIM - Control, Optimisation and Calculus of Variations, 14 (2008), 411-426. doi: 10.1051/cocv:2008031. Google Scholar [11] L.Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal., 19 (1992), 581-597. doi: 10.1016/0362-546X(92)90023-8. Google Scholar [12] L. Boccardo, L. Orsina and I. Peral, A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential, Discrete Contin. Dyn. Syst., 16 (2006), 513-523. doi: 10.3934/dcds.2006.16.513. Google Scholar [13] H. Brezis and X. Cabré, Some simple nonlinear PDE's without solution, Boll. Unione. Mat. Ital. Sez. B, 8 (1998), 223-262. Google Scholar [14] H. Brezis and S. Kamin, Sublinear elliptic equations in $\mathbbR^N$, Manuscripta Math., 74 (1992), 87-106. doi: 10.1007/BF02567660. Google Scholar [15] H. Brezis and A. Ponce, Kato's inequality when $\Delta u$ is a measure, C.R. Math. Acad. Sci. Paris, 338 (2004), 599-604. doi: 10.1016/j.crma.2003.12.032. Google Scholar [16] L. Caffarelli, R. Kohn and L. Nirenberg, First Order Interpolation Inequality with Weights, Compositio Math., 53 (1984), 259-275. Google Scholar [17] G. Dal Maso, F. Murat, L. Orsina, Luigi and A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28 (1999), 741-808. Google Scholar [18] D. Giachetti and F. Murat, An elliptic problem with a lower order term having singular behavior, Boll. Unione Mat. Ital., 2 (2009), 349-370. Google Scholar [19] T. Kato, Schrödinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148. doi: 10.1007/BF02760233. Google Scholar [20] F. Murat, L'injection du cone positif de $H^{-1}$ dans $W^{-1,q}$ est compacte pour tout $q<2$, J. Math. Pures Appl., 60 (1981), 309-322. Google Scholar
show all references
##### References:
[1] B. Abdellaoui, A. Dall'Aglio and I. Peral, Some Remarks on Elliptic Problems with Critical Growth in the Gradient, J. Diff. Eq., 222 (2006), 21-62. doi: 10.1016/j.jde.2005.02.009. Google Scholar [2] B. Abdellaoui, D. Giachetti, I. Peral and M. Walias, Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary, Nonlinear Analysis, 74 (2011), 1355-1371. doi: 10.1016/j.na.2010.10.008. Google Scholar [3] B. Abdellaoui and I. Peral, Nonexistence results for quasilinear elliptic equations related to Caffarelli-Kohn-Nirenberg inequalities, Communications in Pure and Applied Analysis, 2 (2003), 539-566. doi: 10.3934/cpaa.2003.2.539. Google Scholar [4] B. Abdellaoui and I. Peral, The Equation $-\Delta u - \lambda \frac u{|x|^2} = |D u|^p + c f(x)$, the optimal power, Ann. Scuola Norm. Sup. Pisa, VI, (2007), 159-183. Google Scholar [5] B. Abdellaoui and I. Peral, Existence and nonexistence results for quasilinear elliptic equations involving the p-Laplacian with a critical potential, Annali di Matematica Pura e Applicata, 182 (2003), 247-270. doi: 10.1007/s10231-002-0064-y. Google Scholar [6] B. Abdellaoui and I. Peral, A note on a critical problem with natural growth in the gradient, J. Eur. Math. Soc., 8 (2006), 157-170. doi: 10.4171/JEMS/43. Google Scholar [7] N. E. Alaa and M. Pierre, Weak solutions of some quasilinear elliptic equations with data measures, SIAM J. Math. Anal., 24 (1993), 23-35. doi: 10.1137/0524002. Google Scholar [8] D. Arcoya, L. Boccardo, T. Leonori and A. Porretta, Some elliptic problems with singular natural growth lower order terms, J.diff. equation, 249 (2010), 2771-2795. doi: 10.1016/j.jde.2010.05.009. Google Scholar [9] P. Baras and M. Pierre, Singularités éliminables pour des équations semi-linéaires, Ann. Inst. Fourier, 34 (1984), 185-206. doi: 10.5802/aif.956. Google Scholar [10] L. Boccardo, Dirichlet problems with singular and gradient quadratic lower order terms, ESAIM - Control, Optimisation and Calculus of Variations, 14 (2008), 411-426. doi: 10.1051/cocv:2008031. Google Scholar [11] L.Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal., 19 (1992), 581-597. doi: 10.1016/0362-546X(92)90023-8. Google Scholar [12] L. Boccardo, L. Orsina and I. Peral, A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential, Discrete Contin. Dyn. Syst., 16 (2006), 513-523. doi: 10.3934/dcds.2006.16.513. Google Scholar [13] H. Brezis and X. Cabré, Some simple nonlinear PDE's without solution, Boll. Unione. Mat. Ital. Sez. B, 8 (1998), 223-262. Google Scholar [14] H. Brezis and S. Kamin, Sublinear elliptic equations in $\mathbbR^N$, Manuscripta Math., 74 (1992), 87-106. doi: 10.1007/BF02567660. Google Scholar [15] H. Brezis and A. Ponce, Kato's inequality when $\Delta u$ is a measure, C.R. Math. Acad. Sci. Paris, 338 (2004), 599-604. doi: 10.1016/j.crma.2003.12.032. Google Scholar [16] L. Caffarelli, R. Kohn and L. Nirenberg, First Order Interpolation Inequality with Weights, Compositio Math., 53 (1984), 259-275. Google Scholar [17] G. Dal Maso, F. Murat, L. Orsina, Luigi and A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28 (1999), 741-808. Google Scholar [18] D. Giachetti and F. Murat, An elliptic problem with a lower order term having singular behavior, Boll. Unione Mat. Ital., 2 (2009), 349-370. Google Scholar [19] T. Kato, Schrödinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148. doi: 10.1007/BF02760233. Google Scholar [20] F. Murat, L'injection du cone positif de $H^{-1}$ dans $W^{-1,q}$ est compacte pour tout $q<2$, J. Math. Pures Appl., 60 (1981), 309-322. Google Scholar
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2020 Impact Factor: 1.392 | {"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": 0.9175460338592529, "perplexity": 4445.450847292789}, "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/1634323585215.14/warc/CC-MAIN-20211018221501-20211019011501-00666.warc.gz"} |
http://mathhelpforum.com/calculus/205820-3-related-rate-problems-i-am-truly-lost.html | # Thread: 3 related rate problems, I am truly lost.
1. ## 3 related rate problems, I am truly lost.
Hi, i have no idea where to begin on these three related rate problems.
A water-f lled spherical tank with a radius of 1 meter empties from a hole in the bottom in
such a way that the water level decreases at a constant rate of 3 centimeters per second. How fast
is the volume of water in the tank changing when the tank is half full?
A girl blows up a spherical balloon with a face drawn on it. She blows 100 cubic centime-
ters of air into the balloon every second. When t = 2 seconds, the eyes of the face on the balloon
are 4 centimeters apart, measured along the surface of the balloon. How far apart are the eyes after
5 seconds, measured along the surface of the balloon? You may assume that the balloon stretches
uniformly.
A flying saucer circles the earth from pole to pole at a height of 500 miles and a speed of
10,000 miles per hour. A boy lying on his back on the ice at the north pole watches it
How fast is the
flying saucer moving away from the boy when it passes over the horizon? (Hint:
you will need to know the radius of the Earth.)
You do not need to answer all of the problems if you do not wish to.
I greatly appreciate any help provided.
2. ## Re: 3 related rate problems, I am truly lost.
i think i got the answer to number 1, i calculated 6pi
3. ## Re: 3 related rate problems, I am truly lost.
Originally Posted by gosbor6
i think i got the answer to number 1, i calculated 6pi
don't think so ...
let $\displaystyle x^2 + y^2 = 1$ be the side view of the spherical tank.
let $\displaystyle h$ = water level in the tank , $\displaystyle -1 \le h \le 1$
Water volume in the tank can be modeled by the accumulation function ...
$\displaystyle V = \pi \int_{-1}^h \left(1 - y^2 \right) \, dy$
using the FTC ...
$\displaystyle \frac{dV}{dt} = \pi \left(1 - h^2 \right) \cdot \frac{dh}{dt}$
... sub in your given values and determine $\displaystyle \frac{dh}{dt}$ .
Note that these are not what I would call "basic" related rates problems ...
4. ## Re: 3 related rate problems, I am truly lost.
Hi skeeter, thanks for your quick response! sorry for my not so quick response i was at work today.
I am currently enrolled in calculus 1 and we have yet to start doing integrals and i was wondering if there was a simpler way to get the answer, such as:
since you want to find the rate its draining at halfway. i would just take pi r^2 and use that.
2pi r (in this case r is 1) dh/dt(3).
is there something im missing?
thank you. | {"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": 0.8610262870788574, "perplexity": 711.6670674563385}, "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-2018-26/segments/1529267868237.89/warc/CC-MAIN-20180625170045-20180625190045-00277.warc.gz"} |
https://codepunk.io/adding-powershell-core-to-the-hyper-terminal/ | A lot of programmers are aware of the split in .NET between Framework and Core, but unless you live in the Windows scripting environment, you might not realize that PowerShell has also experienced this Renaissance. In one fell swoop, Microsoft has decided to open source the latest PowerShell (6), while also making it cross-platform. This version of PowerShell is being referred to as PowerShell Core, and it not only continues the fantastic development of PowerShell as a Windows scripting environment, but also brings that power to Linux.
As many of you know, I've been using the Hyper terminal as a terminal emulator, and in particular, I'm using it for its ability to have a tabbed interface, and along with the HyperStart script, I can choose my command line. Recently, I installed PowerShell Core on my work computer, and I added it as an option in HyperStart. Here's what you would need to do.
You'll notice some changes in the above gist from the last one (and again, this code was originally forked from another programmer). It's very easy to add another potential command line to the terminal emulator. We've added a couple of lines, and then edited the numbering.
First we add PowerShell Core as an option:
``````ECHO [4] PowerShell Core
``````
We make sure to update the choices:
``````CHOICE /N /C:1234567 /M "> "
``````
We then add the path to the PowerShell Core executable:
``````IF ERRORLEVEL ==4 "C:\Program Files\PowerShell\6.0.2\pwsh.exe"
``````
It's that simple, and because PowerShell and PowerShell Core can be run in parallel, you can have each as an option in your HyperStart file. | {"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": 0.9029160141944885, "perplexity": 2447.530559727039}, "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-2019-04/segments/1547583658901.41/warc/CC-MAIN-20190117082302-20190117104302-00290.warc.gz"} |
http://clay6.com/qa/15073/two-particles-of-mass-1-kg-and-3-kg-have-position-vectors-2-overrightarrow- | Comment
Share
Q)
Two particles of mass 1 kg and 3 kg have position vectors $2 \overrightarrow i + 3\overrightarrow j+4\overrightarrow k \: and \: -2\overrightarrow i+3\overrightarrow j-4\overrightarrow k$ respectively. The position vector of centre of mass of the system is
$\begin {array} {1 1} (1)\;- \overrightarrow i +3\overrightarrow j -2\overrightarrow k & \quad (2)\;- \overrightarrow i +3\overrightarrow j+2\overrightarrow k \\ (3)\;- \overrightarrow i -3\overrightarrow j -2\overrightarrow k & \quad (4)\;\overrightarrow i +3\overrightarrow j-2\overrightarrow k \end {array}$
(1) $-\overrightarrow i+3 \overrightarrow j-2\overrightarrow k$ | {"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": 0.8013738989830017, "perplexity": 308.7435599319748}, "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-2019-51/segments/1575540523790.58/warc/CC-MAIN-20191209201914-20191209225914-00055.warc.gz"} |
http://mathhelpforum.com/algebra/50719-sum-2-squares-print.html | # Sum of 2 Squares
• September 26th 2008, 09:03 AM
ViperRobK
Sum of 2 Squares
How do you express x^2 + xy + y^2 as the sum of two squares
Any help much appreciated.
ViperRobK
• September 26th 2008, 11:03 AM
Soroban
Hello, ViperRobK!
Quote:
How do you express $x^2 + xy + y^2$ as the sum of two squares?
There is a way . . . but it's not "pleasant".
Subtract and add $3xy\!:\quad x^2 + xy \:{\color{red}-\;3xy} + y^2 \;{\color{red}+\; 3xy}$
. . . . . .and we have: . $x^2 - 2xy + y^2 + 3xy$
. . . . . . . and finally: . $(x-y)^2 + (\sqrt{3xy})^2$ | {"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": 0.9332912564277649, "perplexity": 765.309644485354}, "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-2014-10/segments/1394678705901/warc/CC-MAIN-20140313024505-00073-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://neuronaldynamics.epfl.ch/online/Pt3.html | # Part III Networks of Neurons and Population Activity
The organization of this book follows a path of successive simplifications so as to ultimately bridge scales from micrometers to centimeters, from single cells to cognition. The first two parts focused on isolated neurons. In Part I, we took as our starting point a rather detailed biophysical description of a neuron, exemplified by the Hodgkin-Huxley model and variants thereof. Working along from Part I to Part II, this description of a neuron was simplified to a point neuron of the integrate-and-fire type.
Part III is the cornerstone for the transition from single neurons to macroscopic phenomena and, ultimately, forms the basis of the cognitive phenomena discussed in Part IV. Chapter 12 starts the transition from single neurons to populations of neurons; the mathematical methods for this transition and the major dynamic phenomena in populations of neurons are explained in Chapter 13 and 14. Because of their complexity, the mathematical equations for the dynamics of populations of neurons are often simplified to so-called rate models. The limitations of the simplification step are highlighted in Chapter 15. The simplified rate equations will then be used for the analysis of a few selected large-scale phenomena in Part IV. | {"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": 0.8754218220710754, "perplexity": 789.3781187106026}, "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-2017-34/segments/1502886109670.98/warc/CC-MAIN-20170821211752-20170821231752-00494.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/represent-sqrt35-sqrt94-sqrt105-real-number-line-representing-real-numbers-number-line_24192 | # Represent Sqrt3.5, Sqrt9.4, Sqrt10.5 on the Real Number Line. - Mathematics
Represent sqrt3.5, sqrt9.4, sqrt10.5 on the real number line.
#### SolutionShow Solution
We are asked to represent the real numbers sqrt3.5, sqrt9.4 and sqrt10.5on the real number line
We will follow a certain algorithm to represent these numbers on real number line
(a) sqrt3.5
We will take A as reference point to measure the distance
(1) Draw a sufficiently large line and mark a point A on it
(2) Take a point B on the line such that AB = 3.5 cm
(3) Mark a point C on the line such that BC = 1 cm
(4) Find mid point of AB and let it be O
(5) Take O as center and OC as radius and draw a semi circle. Draw a perpendicular BD which cuts the semi circle at D
(6) Take B as the center and BD as radius, draw an arc which cuts the horizontal line at E
(7) Point E is the representation of sqrt3.5
(b) sqrt9.4
We will take A as reference point to measure the distance. We will follow the same figure in the part (a)
(1) Draw a sufficiently large line and mark a point A on it
(2) Take a point B on the line such that AB = 9.4 cm
(3) Mark a point C on the line such that BC = 1 cm
(4) Find mid point of AB and let it be O
(5) Take O as center and OC as radius and draw a semi circle. Draw a perpendicular BC which cuts the semi circle at D
(6) Take B as the center and BD as radius, draw an arc which cuts the horizontal line at E
(7) Point E is the representation of sqrt9.4
(c) sqrt10.5
We will take A as reference point to measure the distance. We will follow the same figure in the part (a)
(1) Draw a sufficiently large line and mark a point A on
(2) Take a point B on the line such that AB = 10.5 cm
(3) Mark a point C on the line such that BC = 1 cm
(4) Find mid point of AB and let it be O
(5) Take O as center and OC as radius and draw a semi circle. Draw a perpendicular BC which cuts the semi circle at D
(6) Take B as the center and BD as radius, draw an arc which cuts the horizontal line at E
(7) Point E is the representation of sqrt10.5
Concept: Representing Real Numbers on the Number Line
Is there an error in this question or solution?
#### APPEARS IN
RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.5 | Q 4 | Page 36 | {"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": 0.9060181379318237, "perplexity": 1100.5419012253287}, "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/1652662509990.19/warc/CC-MAIN-20220516041337-20220516071337-00780.warc.gz"} |
http://blog.gmane.org/gmane.comp.tex.macosx/month=20111001 | 1 Oct 05:14 2011
### Re: how make cocoAspell recognize LaTeX commands?
On Sep 30, 2011, at 3:50 PM, Murray Eisenberg wrote:
> I'm using TeXShop 2.43 under OS X 10.6.8 and installed cocoAspell 2.1.
>
> As the docs say, I then:
>
> - in System Preferences, Spelling preferences panel selected "English
> (United States) as the Dictionary and checked the Filter for TeX/LaTeX; and
>
> - in System Preferences, Language & Text, Text pane, chose what I believe
> is the corresponding dictionary for the Spelling choice: "English (United
> States} [w_accents] (Aspell) -- this is the only Aspell entry I see in that
> drop-down for Spelling.
>
> Nonetheless, in TeXShop, every LaTeX command that is not an ordinary English
> word is still getting flagged as misspelled. E.g.:
>
> documentclass, usepackages, textbf, displaystyle, emph, frac
>
> (Only such command as \section, \begin, \end, \item formed from actual words
> are left unflagged)
>
> What's wrong and how does one fix this?
Howdy,
Take a look in the TeX/LaTeX Tab under the Filters Tab to see the list of commands that are understood.
In TeXShop under Edit->Show Spelling and Grammar make sure that the English(Aspell) dictionary is
1 Oct 05:20 2011
### Re: how enable smart quotes of LaTeX kind
On Sep 30, 2011, at 5:25 PM, Murray Eisenberg wrote:
> In TeXShop 2.43, I don't understand how to use the Edit > Substitutions dialog so that if I type, say
>
> "hello world"
>
> it will automatically be changed to the LaTeX markup:
>
> hello world''
>
> I don't see any choice to get the latter.
>
Howdy,
I assume you want two at the beginning and two ' at the end. Don't use substitutions but turn on Key Bindings
(Check TeXShop->Preferences->Source->Editor->Key Bindings) and the pressing " (dumb double quote)
will produce then any selection and the cursor and the ''.
Good Luck,
Herb Schulz
(herbs at wideopenwest dot com)
----------- Please Consult the Following Before Posting -----------
TeX FAQ: http://www.tex.ac.uk/faq
List Reminders and Etiquette: http://email.esm.psu.edu/mac-tex/
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1 Oct 18:29 2011
### TeXShop and Cloud Computing
I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had some
problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The
recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex
files from the iPad while traveling, and in particular I have started using DropBox instead of
synchronization to have access from different computers to a single set of files. This seems to work a lot
better than synchronizing.
Which brings me to my questions.
1.I have several .sty files with a mass of custom macros that I use in all of my work. On my laptop and on my iMac,
these reside in my user ->Library->texmf->tex (or bibtex)->latex folder. I understand that these are
now hidden in Lion; if I use the search function (the magnifying glass on my tool bar) I can find about 15
different files with the correct name, but can't find the pathname to any of them. Obviously there is only
one I want to use, and that is the one which TeXShop calls up. How do I find it?
2. Even more to the point, I want to put these files in DropBox so that again I have only one copy to modify when I
need to. Where do I put them in Drop Box so that TeXShop will find them when I \usepackage them? (of course,
TeXShop resides in two copies, one on my laptop and one on my iMac).
And can that be designed so that these files get used when I am using TeXShop on a file that didn't come from
Drop Box as well?
Zbigniew Nitecki
Department of Mathematics
Tufts University
Medford, MA 02155
telephones:
Office (617)627-3843
Dept. (617)627-3234
Dept. fax (617)627-3966
1 Oct 19:01 2011
### Re: TeXShop and Cloud Computing
On Oct 1, 2011, at 12:29 PM, Nitecki, Zbigniew H. wrote:
> I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had
some problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The
recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex
files from the iPad while traveling, and in particular I have started using DropBox instead of
synchronization to have access from different computers to a single set of files. This seems to work a lot
better than synchronizing.
>
> Which brings me to my questions.
>
> 1.I have several .sty files with a mass of custom macros that I use in all of my work. On my laptop and on my
iMac, these reside in my user ->Library->texmf->tex (or bibtex)->latex folder. I understand that these
are now hidden in Lion; if I use the search function (the magnifying glass on my tool bar) I can find about 15
different files with the correct name, but can't find the pathname to any of them. Obviously there is only
one I want to use, and that is the one which TeXShop calls up. How do I find it?
If you open a Terminal window, and type
kpsewhich foo.sty
it will return the actual path that TeX uses to find that particular file. So for example, on my machine
kpsewhich article.cls
returns /usr/local/texlive/2011/texmf-dist/tex/latex/base/article.cls
while
kpsewhich Statweave.sty
1 Oct 19:12 2011
### Re: TeXShop and Cloud Computing
The way I work, I have the current document in a folder in Dropbox.
This folder contains all the source files, illustrations, and a current copy of my style file:
lattice.sty.
This is the folder I archive when I am done.
1. Whichever computer I use, it has the current version of all my files.
2. Say, in 10 years time, I want to use parts of this article, so first I typeset it. Since lattice.sty
is in the archived folder, no problem.
In 10 years time, lattice.sty will evolve. But since for the old papers I always have the lattice.sty
from that time, I am OK.
I have 260 versions of lattice sty stored in my computer…
GG
On 2011-10-01, at 12:29 PM, Nitecki, Zbigniew H. wrote:
> I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had
some problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The
recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex
files from the iPad while traveling, and in particular I have started using DropBox instead of
synchronization to have access from different computers to a single set of files. This seems to work a lot
better than synchronizing.
1 Oct 19:14 2011
### Re: TeXShop and Cloud Computing
On 2011-10-01, at 6:29 PM, Nitecki, Zbigniew H. wrote:
> I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had
some problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The
recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex
files from the iPad while traveling, and in particular I have started using DropBox instead of
synchronization to have access from different computers to a single set of files. This seems to work a lot
better than synchronizing.
>
> Which brings me to my questions.
>
> 1.I have several .sty files with a mass of custom macros that I use in all of my work. On my laptop and on my
iMac, these reside in my user ->Library->texmf->tex (or bibtex)->latex folder. I understand that these
are now hidden in Lion; if I use the search function (the magnifying glass on my tool bar) I can find about 15
different files with the correct name, but can't find the pathname to any of them. Obviously there is only
one I want to use, and that is the one which TeXShop calls up. How do I find it?
The files are stored in their usual place where you put them: ~/Library->texmf->...
If you want to have your Library folder back, simply open the terminal and run
chflags nohidden ~/Library/
and you will have your ~/Library folder back.
> 2. Even more to the point, I want to put these files in DropBox so that again I have only one copy to modify when
I need to. Where do I put them in Drop Box so that TeXShop will find them when I \usepackage them? (of course,
TeXShop resides in two copies, one on my laptop and one on my iMac).
> And can that be designed so that these files get used when I am using TeXShop on a file that didn't come from
Drop Box as well?
1 Oct 19:16 2011
### Re: TeXShop and Cloud Computing
Thanks---I will try that. I am not that experienced in using command lines in Terminal: is your suggestion
in response to question 2 a command to enter in Terminal, or is it a command to put in a file in the folder you
suggest (and in the latter case, what should that folder be called)?
Zbigniew Nitecki
Department of Mathematics
Tufts University
Medford, MA 02155
telephones:
Office (617)627-3843
Dept. (617)627-3234
Dept. fax (617)627-3966
http://www.tufts.edu/~znitecki/
On Oct 1, 2011, at 13:01, Alan Munn wrote:
On Oct 1, 2011, at 12:29 PM, Nitecki, Zbigniew H. wrote:
I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had some
problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The
recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex
files from the iPad while traveling, and in particular I have started using DropBox instead of
synchronization to have access from different computers to a single set of files. This seems to work a lot
better than synchronizing.
Which brings me to my questions.
1.I have several .sty files with a mass of custom macros that I use in all of my work. On my laptop and on my iMac,
these reside in my user ->Library->texmf->tex (or bibtex)->latex folder. I understand that these are
1 Oct 19:29 2011
### Re: TeXShop and Cloud Computing
Minor correction, type
sudo chflags nohidden ~/Library/
--
M. Tamer Özsu
University of Waterloo
(Currently on sabbatical leave at ETH Zürich)
On 2011-10-01, at 7:14 PM, M. Tamer Özsu wrote:
> On 2011-10-01, at 6:29 PM, Nitecki, Zbigniew H. wrote:
>
>> I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had
some problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The
recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex
files from the iPad while traveling, and in particular I have started using DropBox instead of
synchronization to have access from different computers to a single set of files. This seems to work a lot
better than synchronizing.
>>
>> Which brings me to my questions.
>>
>> 1.I have several .sty files with a mass of custom macros that I use in all of my work. On my laptop and on my
iMac, these reside in my user ->Library->texmf->tex (or bibtex)->latex folder. I understand that these
are now hidden in Lion; if I use the search function (the magnifying glass on my tool bar) I can find about 15
different files with the correct name, but can't find the pathname to any of them. Obviously there is only
one I want to use, and that is the one which TeXShop calls up. How do I find it?
1 Oct 19:44 2011
### Re: TeXShop and Cloud Computing
TeX will always use the .sty, .bib, etc. files that are in the same folder as the tex source file. Hence I suggest you put your corresponding files in the dropbox (sub)folder where your source files are residing.
To use the same files when your source file isn't stored in the dropbox folder but somewhere on your local computer create symbolic links to any of these helper files in the proper subfolders of ~/Library/texmf.
Consult the man pages for the command ln to get it right.
Claus
On Oct 1, 2011, at 19:16, Nitecki, Zbigniew H. wrote:
Thanks---I will try that. I am not that experienced in using command lines in Terminal: is your suggestion in response to question 2 a command to enter in Terminal, or is it a command to put in a file in the folder you suggest (and in the latter case, what should that folder be called)?
Zbigniew Nitecki
Department of Mathematics
Tufts University
Medford, MA 02155
telephones:
Office (617)627-3843
Dept. (617)627-3234
Dept. fax (617)627-3966
http://www.tufts.edu/~znitecki/
On Oct 1, 2011, at 13:01, Alan Munn wrote:
On Oct 1, 2011, at 12:29 PM, Nitecki, Zbigniew H. wrote:
I use Texshop on two different computers---a home laptop (MacBook Pro) and an office iMac, and have had some problems trying to use Folders Synchronizer to avoid carrying my laptop when I walk to my office. The recent purchase of an iPad 2 prompted me to investigate using Tex Touch and Tex Timer to be able to work on tex files from the iPad while traveling, and in particular I have started using DropBox instead of synchronization to have access from different computers to a single set of files. This seems to work a lot better than synchronizing.
Which brings me to my questions.
1.I have several .sty files with a mass of custom macros that I use in all of my work. On my laptop and on my iMac, these reside in my user ->Library->texmf->tex (or bibtex)->latex folder. I understand that these are now hidden in Lion; if I use the search function (the magnifying glass on my tool bar) I can find about 15 different files with the correct name, but can't find the pathname to any of them. Obviously there is only one I want to use, and that is the one which TeXShop calls up. How do I find it?
If you open a Terminal window, and type
kpsewhich foo.sty
it will return the actual path that TeX uses to find that particular file. So for example, on my machine
kpsewhich article.cls
returns /usr/local/texlive/2011/texmf-dist/tex/latex/base/article.cls
while
kpsewhich Statweave.sty
returns
/Users/alan/Library/texmf/tex/latex/Statweave/Statweave.sty
which is in my local texmf folder.
2. Even more to the point, I want to put these files in DropBox so that again I have only one copy to modify when I need to. Where do I put them in Drop Box so that TeXShop will find them when I \usepackage them? (of course, TeXShop resides in two copies, one on my laptop and one on my iMac).
And can that be designed so that these files get used when I am using TeXShop on a file that didn't come from Drop Box as well?
I don't know much about Drop Box, but I would suggest putting them a single folder inside your dropbox, and then creating a symbolic link inside the local texmf folder on each of the macs to that dropbox folder. Then the dropbox folder will appear as if it is in the local texmf folder.
Assuming that your files are just of one type (e.g. latex packages) you would make the link inside ~/Library/texmf/tex/latex
ln -s <path-to-dropbox-dir> ~/Library/texmf/tex/latex/<local-dir-name>
Alan
--
Alan Munn
[email protected]<mailto:[email protected]>
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List Info: http://email.esm.psu.edu/mailman/listinfo/macosx-tex
1 Oct 20:05 2011
### Re: TeXShop and Cloud Computing
On Oct 1, 2011, at 1:12 PM, George Gratzer wrote:
> The way I work, I have the current document in a folder in Dropbox.
>
> This folder contains all the source files, illustrations, and a current copy of my style file:
>
> lattice.sty.
>
> This is the folder I archive when I am done.
>
> This has the following advantages:
>
> 1. Whichever computer I use, it has the current version of all my files.
>
> 2. Say, in 10 years time, I want to use parts of this article, so first I typeset it. Since lattice.sty
> is in the archived folder, no problem.
>
> In 10 years time, lattice.sty will evolve. But since for the old papers I always have the lattice.sty
> from that time, I am OK.
>
> I have 260 versions of lattice sty stored in my computer…
I'm not sure this should be listed under "Advantages"
Just out of curiosity, how often are you likely to need to recompile an old file (rather than just use its
preexisting pdf?)
Alan
--
--
Alan Munn
amunn@...
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`
Gmane | {"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": 0.9054853916168213, "perplexity": 4364.363679193492}, "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-2015-11/segments/1424936461359.90/warc/CC-MAIN-20150226074101-00317-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/lightning-series-question.195900/ | # Lightning SERIES question
1. Nov 4, 2007
### frasifrasi
can anyone explain why the summation from 0 to infinity of
(-2)^(n)/3^(n+1) diverges?
- Is it simply because the terms bounce between - and +?
2. Nov 4, 2007
### P3X-018
Are you sure you wrote it correct? Because the series
$$\sum_{n=0}^{\infty} \frac{(-2)^n}{3^{n+1}}$$
does converge...
3. Nov 4, 2007
### frasifrasi
I have in the answer that it diverges...could you explain how you arrived at that?
4. Nov 4, 2007
### Dick
It's (1/3)*(-2/3)^n. It's a geometric series. You can even sum it.
5. Nov 4, 2007
### frasifrasi
I see the light! I guess the answer key was wrong. But hey,
What if had the SEQUENCE (-2)^(n)/3^(n+1) , how could I show that it converges to 0?
could I also "simplify" it to (1/3)*(-2/3)^n and say that since r > -1, it converges to 0?
(by the fact that for a sequence r^n , the sequence converges for -1 < r <= 1)
6. Nov 4, 2007
### Dick
If you mean |r|<1, then yes, the sequence converges to zero. | {"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": 0.9893743991851807, "perplexity": 2589.9248140806153}, "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/1480698540915.89/warc/CC-MAIN-20161202170900-00030-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://www.vernier.com/experiment/msb-wind-e-1_energy-transformation/ | ### Introduction
Energy can be transferred between objects, and sometime, it is also transformed. For example, when you stretch a rubber band, you transfer energy into the rubber band, which we then call elastic potential energy. Elastic because it is related to the stretchiness of the rubber band and potential energy because, as long as the rubber band remains stretched, the energy is stored and available for use. Releasing the rubber band allows the elastic potential energy to transform into kinetic energy (the energy associated with motion), as the rubber band flies through the air.
When you stretched the rubber band, you applied a force to the rubber band and moved one part of the rubber band a certain distance. Whenever a force moves an object some distance, we say that mechanical work is done. Mechanical work, like energy, is measured in joules (J). Work is one way to transfer or transform energy.
Just as you can do work to stretch a rubber band, you can also do work to lift a weight. In order to lift an object from a lower position to a higher position, a force must be applied vertically. In this case, the work done gives the object moved upward gravitational potential energy, because instead of pulling against a stretchy material, the object is moved against the direction of the force of gravity.
Power is defined as the rate at which energy is used or transformed. It is also the rate at which work is done. More power is used when the same amount of work is done at a faster rate. For example, imagine an elevator that takes 100 seconds to be lifted from the first floor to the fourth floor. If you want the elevator to reach the fourth floor in 80 seconds, the lifting mechanism needs more power. The unit of power is the watt (W). Power can be calculated using the following equation:
${\text{power}} = {\frac{\text{amount of work done}}{\text{how long it took}}}$
In this experiment, you will use a wind turbine to do the work of lifting an object (a bucket of washers).
### Objectives
• Understand that energy can be transformed and transferred between objects.
• Describe the relationship between power and work.
• Do work with energy produced from a wind turbine. | {"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": 1, "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": 0.8098132014274597, "perplexity": 261.3034301302585}, "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-2021-43/segments/1634323585242.44/warc/CC-MAIN-20211019043325-20211019073325-00593.warc.gz"} |
https://mathoverflow.net/questions/346013/theorems-of-zf-through-countable-transitive-models?noredirect=1 | # Theorems of ZF through countable transitive models
Let $$T$$ be a finite collection of axioms of $$\mathrm{ZF}$$, let $$\sigma$$ be a sentence in the language of $$\mathrm{ZF}$$ and consider the statement
$$\tau$$: “any transitive countable model of $$T$$ satisfies $$\sigma$$”.
Then $$\mathrm{ZFC}\vdash\tau$$ implies $$\mathrm{ZFC}\vdash\sigma$$, by the classical argument using Reflection, Downward Löwenheim–Skolem and Mostowki’s collapse to get a countable transitive model where finitely many sentences are absolute.
My question is: does $$\mathrm{ZF}\vdash\tau$$ imply $$\mathrm{ZF}\vdash\sigma$$? This may look trivial but, without choice, Downward Löwenheim–Skolem can’t be used as above. On the other hand, it could be argued that $$\mathrm{ZF}\vdash$$ “there is a proof of $$\sigma$$ from $$T$$”, but this does not mean that such a proof can be found in the meta-theory.
Thank you for your help with this (possibly trivial) matter.
• I don’t know about the rest, but ZF certainly proves reflection in the form “if there is a proof of $\sigma$ in $T$, then $\sigma$”. This holds for any sequential theory that proves induction for all formulas in its language, see mathoverflow.net/a/87249 . Nov 14, 2019 at 15:06
• @WillBrian Work inside ZFC, and assume $\neg\sigma$. By Jech’s remark, there exists a countable transitive model of $T+\neg\sigma$. But by assumption, all countable transitive models of $T$ satisfy $\sigma$, a contradiction. Thus, $\sigma$. (By the way, this actually shows the stronger statement $\mathrm{ZFC}\vdash\tau\to\sigma$.) Nov 14, 2019 at 15:53
• @WillBrian That’s not what the OP is claiming. The claim is absolutely clear: $\mathrm{ZFC}\vdash\tau$ implies $\mathrm{ZFC}\vdash\sigma$. I have shown that even $\mathrm{ZFC}\vdash(\tau\to\sigma)$. Your interpretation is $\mathrm{ZFC}\vdash(\tau\to\mathrm{Pr}_{\mathrm{ZFC}}(\sigma))$, which may be false. Nov 14, 2019 at 16:16
• Nov 14, 2019 at 21:34
• @ElliotGlazer The answer to the post you suggested indicates a way to answer my question affirmatively. Thank you. Nov 14, 2019 at 23:34 | {"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": 14, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.922184407711029, "perplexity": 244.02691358737417}, "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-2022-27/segments/1656103355949.26/warc/CC-MAIN-20220628050721-20220628080721-00705.warc.gz"} |
http://mathhelpforum.com/trigonometry/152446-trigonometric-equality.html | # Math Help - trigonometric equality
1. ## trigonometric equality
$
\begin{array}{l}
\frac{{\sin x + \sin y + \sin z}}{{\sin (x + y + z)}} = \frac{{\cos x + \cos y + \cos z}}{{\cos (x + y + z)}} = 2 \\
\\
find \\
\sin x\sin y + \sin y\sin z + \sin x\sin z \\
\end{array}
$
2. This is a very interesting problem. It has either too much symmetry, or not enough, depending on how you're looking at it.
One thing I would highly recommend: abbreviate! I'm going to abbreviate as follows:
$\sin(x)=s(x)$
$\cos(x)=c(x).$
If you square both equations and add together in the appropriate way, you can get it down to
$\displaystyle{s(x)s(y)+s(x)s(z)+s(y)s(z)+c(x)c(y)+ c(x)c(z)+c(y)c(z)=\frac{1}{2}}.$
Unfortunately, if you plug in a test case, you find out that the sin terms do not necessarily make up half of the sum. Here's one test case:
$x=0.1$
$y=1.011189$
$z=-1.07805,$
approximately. All of these are in radians. The sin terms add up to $-0.75$, and the cosine terms add up to $1.25.$
So there's a specific case, plus some general information about the problem. Nothing more is coming to mind at the moment. Your result should be -3/4. But now you have to prove it!
3. Hello, fxs12!
Askbeet has an excellent game plan,
. . but I can't finish the problem.
$\dfrac{{\sin x + \sin y + \sin z}}{{\sin (x + y + z)}} \;=\; \dfrac{{\cos x + \cos y + \cos z}}{{\cos (x + y + z)}} \;=\; 2$
$\text{Find: }\,\sin x\sin y + \sin y\sin z + \sin x\sin z$
We have: . $\begin{array}{cccc}
\sin x + \sin y + \sin z &=& 2\sin(x+y+z) & [1] \\
\cos x + \cos y + \cos z &=& 2\cos(x+y+z) & [2] \end{array}$
$\begin{array}{ccccc}\text{Square [1]:} & (\sin x + \sin y + \sin z)^2 &=& 4\sin^2(x+y+z) & [3] \\
\text{Square [2]:} & (\cos x + \cos y + \cos z)^2 &=& 4\cos^2(x+y+z) & [4]\end{array}$
$\underbrace{\begin{Bmatrix}\sin^2x \\ \cos^2x\end{Bmatrix}}_{\text{This is 1}} + \underbrace{\begin{Bmatrix}\sin^2y \\ \cos^2y\end{Bmatrix}}_{\text{This is 1}} + \underbrace{\begin{Bmatrix}\sin^2z \\ \cos^2z\end{Bmatrix}}_{\text{This is 1}} + 2\begin{Bmatrix}\sin x\sin y + \sin y\sin z + \sin x\sin z \\ \cos x\cos y + \cos y\cos z + \cos x\cos z \end{Bmatrix}$
. . . . . . . $=\; 4\underbrace{\bigg[\sin^2(x+y+z) + \cos^2(x+y+z)\bigg]}_{\text{This is 1}}$
We have:
. . $1 + 1 + 1 + 2\begin{Bmatrix}\sin x\sin y +\sin y\sin z + \sin x\sin z \\ \cos x\cos y + \cos y\cos z + \cos x\cos z\end{Bmatrix} \;=\;4$
. . $\begin{Bmatrix}\sin x\sin y + \sin y\sin z + \sin x\sin z \\ \cos x\cos y + \cos y\cos z + \cos x\cos z\end{Bmatrix} \;=\;\frac{1}{2}$
And I can't go any further . . .
4. ...
cos(x-y)+cos(y-z)+cos(x-z)=1/2
5. I also have proved:
sin(x-y)/sinx siny + sin(y-z)/siny sinz + sin(x-z)/sinx sinz = 0
$sinx=a$
$siny=b$
$sinz=c$
$cosx=\sqrt{1-a^2}$
$cosy=\sqrt{1-b^2}$
$cosz=\sqrt{1-c^2}$
$tan(x+y+z)=\frac{tanx+tany+tanz-tanxtanytanz}{1-tanxtany-tanytanz-tanztanx}
$
$tanx=\frac{a}{\sqrt{1-a^2}}$
$tany=\frac{b}{\sqrt{1-b^2}}$
$tanx=\frac{c}{\sqrt{1-c^2}}$
Hence:
$\dfrac{{\sin x + \sin y + \sin z}}{{\sin (x + y + z)}} \;=\; \dfrac{{\cos x + \cos y + \cos z}}{{\cos (x + y + z)}} \;=\; 2$
becomes:
$\frac{a+b+c}{\sqrt{1-a^2}+\sqrt{1-b^2}+\sqrt{1-c^2}}=tan(x+y+z)=2$
when we need to find: $ab+bc+ac$ | {"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": 30, "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": 0.8967518210411072, "perplexity": 664.4864034257648}, "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/1432207929023.5/warc/CC-MAIN-20150521113209-00308-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/107554/convergence-in-mean-square-longrightarrow-convergence-in-probability | # Convergence in Mean Square $\Longrightarrow$ Convergence in Probability
I'm reading through some notes on Probability, and the statement is made that:
If random variables $X_1, \ldots, X_n$ converge to $X$ in mean square, then they also converge in probability.
Can someone please explain why this is the case? Regards.
-
Fix $\delta>0$. Then $$\delta^2 P(|X_n-X|\geq \delta)=\delta^2 P(|X_n-X|^2\geq \delta^2)\leq \int_{\Omega}|X_n-X|^2dP,$$ so $P(|X_n-X|\geq \delta)\leq \frac 1{\delta^2}\int_{\Omega}|X_n-X|^2dP$ and we can conclude since the las integral converges to $0$.
Many thanks. What rule are you invoking to say that $\delta^2 P(|X_n-X|^2\geq \delta^2)\leq \int_{\Omega}|X_n-X|^2dP$? – Mathmo Feb 9 '12 at 19:18
You integrate over the set $\{|X_n-X|\geq \delta\}$ the constant $\delta^2$. On this set it's smaller than $|X_n-X|^2$, and the integral over this set is small than the integral on $\Omega$. – Davide Giraudo Feb 9 '12 at 19:21 | {"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": 0.9957285523414612, "perplexity": 262.98062239793865}, "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-2016-22/segments/1464049277286.54/warc/CC-MAIN-20160524002117-00077-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/contracted-epsilon-identity.834083/ | # Contracted Epsilon Identity
• Start date
• #1
555
19
Hi,
I am confused about how I arrive at the contracted epsilon identity. $$\epsilon_{ijk} \epsilon_{imn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$$
1. Homework Statement
Show that $$\epsilon_{ijk} \epsilon_{imn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$$
## The Attempt at a Solution
[/B]
From the relation between the Levi-civita symbol and the Kronecker delta, I compute $\epsilon_{ijk} \epsilon_{imn}$ by finding the determinant of the following matrix.
$\epsilon_{ijk} \epsilon_{imn} = det \left[ \begin{array}{cccc} \delta_{ii} & \delta_{im} & \delta_{in} \\ \delta_{ji} & \delta_{jm} & \delta_{jn} \\ \delta_{ki} & \delta_{km} & \delta_{kn} \end{array} \right]$ which yields
$\epsilon_{ijk} \epsilon_{imn} = \delta_{ii} (\delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}) - \delta_{im} (\delta_{ji} \delta_{kn} - \delta_{jn} \delta_{ki}) + \delta_{in} (\delta_{ji} \delta_{km} - \delta_{jm} \delta_{ki})$
I am confused about how to progress.
Related Calculus and Beyond Homework Help News on Phys.org
• #2
Geofleur
Gold Member
423
176
For starters, what does $\delta_{ii}$ equal? Note that you need to sum over repeated indices.
• #3
555
19
For starters, what does $\delta_{ii}$ equal? Note that you need to sum over repeated indices.
$$\delta_{ii} = 3$$
This seems to be the only repeated indice.
• #4
RUber
Homework Helper
1,687
344
Hi,
I am confused about how I arrive at the contracted epsilon identity. $$\epsilon_{ijk} \epsilon_{imn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$$
1. Homework Statement
Show that $$\epsilon_{ijk} \epsilon_{imn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$$
3. The Attempt at a Solution
$\epsilon_{ijk} \epsilon_{imn} = \delta_{ii} (\delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}) - \delta_{im} (\delta_{ji} \delta_{kn} - \delta_{jn} \delta_{ki}) + \delta_{in} (\delta_{ji} \delta_{km} - \delta_{jm} \delta_{ki})$
I am confused about how to progress.
Note that your first term in the expansion: $\delta_{ii} (\delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km})$ looks a lot like the final result you are looking for.
Then, the challenge should be to show that $- \delta_{im} (\delta_{ji} \delta_{kn} - \delta_{jn} \delta_{ki}) + \delta_{in} (\delta_{ji} \delta_{km} - \delta_{jm} \delta_{ki}) = 0$ in all cases. To do this, think about what must be true for any term to not be zero, and show that it implies another opposite term must also not be zero.
• #5
RUber
Homework Helper
1,687
344
$$\delta_{ii} = 3$$
This seems to be the only repeated indice.
You seem to be using a different definition of the Kronecker delta? Usually the only possible outcomes are 0 or 1.
• #6
555
19
You seem to be using a different definition of the Kronecker delta? Usually the only possible outcomes are 0 or 1.
I thought the idea was that $\delta_{ii}$ implied the summation of $\delta_{11}, \delta_{22}, and \delta_{33}$, which are each respectively equal to 1.
• #7
Geofleur
Gold Member
423
176
That's right, $\delta_{ii} = \delta_{11} + \delta_{22} + \delta_{33} = 3$. Now eliminate the $\delta$'s in front of the other two terms and see what happens.
• #8
RUber
Homework Helper
1,687
344
I see. I was thinking one term at a time, rather than the sum over the terms.
In that case, I get the same result as Geofleur.
• #9
555
19
That's right, $\delta_{ii} = \delta_{11} + \delta_{22} + \delta_{33} = 3$. Now eliminate the $\delta$'s in front of the other two terms and see what happens.
I am unsure of how to evaluate these deltas.
$\delta_{im} = 0$ unless $i = m$ so do they both just vanish?
• #10
Geofleur
Gold Member
423
176
They do vanish unless $i = m$. In that case, the $\delta$'s in front become ones, and the $i$'s inside the parenthesized terms become $m$'s.
• #11
Geofleur
Gold Member
423
176
Note that the $i$'s are repeated and thus being summed over.
• #12
555
19
They do vanish unless $i = m$. In that case, the $\delta$'s in front become ones, and the $i$'s inside the parenthesized terms become $m$'s.
ahh, I see.
so I have that $\epsilon_{ijk} \epsilon_{imn} = 3 \delta_{jm} \delta_{kn} - 3 \delta_{jn} \delta_{km} - \delta_{jm} \delta_{kn} + \delta_{jn} \delta_{km} + \delta_{jn} \delta_{km} - \delta_{jm} \delta_{kn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$
Thank you very much for your help!
• #13
Ray Vickson
Homework Helper
Dearly Missed
10,705
1,722
Hi,
I am confused about how I arrive at the contracted epsilon identity. $$\epsilon_{ijk} \epsilon_{imn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$$
1. Homework Statement
Show that $$\epsilon_{ijk} \epsilon_{imn} = \delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$$
## The Attempt at a Solution
[/B]
The factor $\epsilon_{ijk}$ vanishes unless $ijk$ is a permutation of $123$, so for any pair $j \neq k$ the required $i$ is uniquely determined. Then, for that $i$, $\epsilon_{imn}$ vanishes unless $mn$ is a permutation of $jk$. Thus, for a nonzero term on the left, we need either $j = m$ and $k = n$ (in which case the left-hand-side is $(\pm1 )^2 = +1$, or $j = n$ and $k = m$ (in which case the left-hand-side is $(-1)(+1) = -1$). That is, the nonzero values of the left-hand-side are the same as the nonzero values of $\delta_{jm} \delta_{kn} - \delta_{jn} \delta_{km}$. The same is true of the zero values, so the two sides must be equal.
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http://www.physicsforums.com/showpost.php?p=134531&postcount=24 | View Single Post
P: 1 Why does no body even try to explain the phenomenon from beginning to end? I'm quite ignorent, studied physics 25 years ago and hardly even remember Snellius law. My daughter wanted to make a schoolthesis on the subject and found no literature describing it in detail. We only red a popular but nice text from Minnaert. Now we are so ignorent/arrogant that after quite some discussion we think we understand it all and then we found this (a bit disappointing)discussion so we give it a try: 1- Mirage concerns a virtual image as a result of a vertical temperature gradiënt and thus a density and thus a n-gradiënt (diffraction index). 2- Light propagating through this gradiënt wil curve towards the higher n-side. 3- Because off the gradiënt no critical angle can be identified (or asymptotic to 90degr.), the medium can be seen as a multi layer with infinetesimal small differences off n. 4- The curving process continues until the light propagation is asymptoticly horrizontal. 5 Then we have a problem. With the preassumption off a ideal medium (exact horrizontal isotherms an consequently exact vertical n-gradiënt the beam is captured in the horrizontal plane because it propagates perpendicular to the n-gradiënt. 6 Up to this point we can draw a first conclusion. From Snellius it follows that for a multi layer medium, diffraction depends only from n of the first and the last layer. Consider a point object at a certain level where n=n1 and angel Q1 of the departing beam, and consider n=n2 at the level at which the beam is appr. horrizontal.(Q2=90degr) Then we CONCLUDE that: On the MICRO LEVEL the beam curves increasingly from layer to layer (with infinetisemal small differences of n) until horrizontal, so no critical angle can be identified and no total reflection takes place. On a MACRO LEVEL the relation between Q1, n1 and n2 is described just AS IF Q1 is the crical angel. (However if we consider the same point object from which departs a beam with a smaller Q, this Q can also be considered as a Critical angle, be it in a other macro system: the horrizontal will be reached at a lower point with a smaller n. The smallest possible Q is from the beam which reaches horrizontal at ground level.) 7 The first escape from this capture to the horrizontal is to take in account the curving off the earth and thus the curving of isotherms etc. In this forum this is correctly rejected, it only works with upward bending (positive upward n-gradiënt). With downward curving (in the case of inversion = negative n-gradiënt) the beam will be captured in the horrizontal isotherm and curve with the rounding of the earth but not curve back to the earth.(It also cannot escape upward because pushed backward by the negative n-gradiënt;would it go in circles around the earth for ever?) 8 The second escape from the horrizontal capture is to take in account the imperfection of the medium. In real life isotherms are not perfect horrizontal. The temperature gradiënt results in turbulations of the air and fluctuating isotherms. Consider the isotherm as (slightly) sinusoïdal, then also the horrizontal beam meets a gradiënt and tends to bent towards the positive of the n-gradiënt. So it can escape from the horrizontal and then curves further upward. Consequently bending backwards can be explained in both situations: warm earth/cold air as well as in the case of inversion. 8 We can conclude that air turbulations can explain curving back, which then still is a refraction phenomenon. 9 This model of continuïng curving also explains the compression of the virtual image which often takes place. If the observer is at a lower altitude then the object the Qin is smaller then Qout (Qin is the departing beam angle at the top of the object where Qout is the angel at which this refracted beam is observed). In fact the difference between Qin and Qout depends on the difference between n at the level of the object and n at the observers level. If n at the upper part of the object is (about) the same as n at the observer, the bending of the downward curve is (about) the same as the bending of the upward curve, Qin equals (about) Qout and the image is not compressed. | {"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": 0.9133662581443787, "perplexity": 1136.3108677345358}, "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-2014-23/segments/1405997889314.41/warc/CC-MAIN-20140722025809-00011-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://marocstreetfood.com/manitoba/what-is-an-example-of-a-linear-equation.php | What is the definition of a nonlinear equation? Quora. Linear algebra/systems of linear equations. from wikibooks, open books for an open world < linear algebra. some examples of linear equations are as follows:, linear equations. system of linear equations. 55 min 7 examples. what is linear algebra? what is a matrix? and what is a linear equation? example of determining.
## Linear Algebra/Systems of linear equations Wikibooks
What is a Linear Equation? Video & Lesson Transcript. To determine if an equation is a linear function without graphing, it is not a linear equation. in the example, if an equation is a linear function without, students learn about the different forms of linear equations. copyright. (the y-intercept), then you can write the equation of the line. for example,.
Get an answer for 'how do i determine if this equation is a linear function or a nonlinear function?' and find homework an example of a linear equation would be introduction. in general linear equations are found in most calculations in science.in chemistry for example,linear equations are used in balancing chemical equations
To determine if an equation is a linear function without graphing, it is not a linear equation. in the example, if an equation is a linear function without the simple linear regression equation is graphed as a straight line. examples: the least squares
The point slope form of a linear equation is written as . for example when we need to find the equation of a line when given a point and the slope. the simple linear regression equation is graphed as a straight line. examples: the least squares
Identity an identity is an equation that is always true. every real number is a solution of an identity, so it has infinite solutions. the solution of a linear identity an identity is an equation that is always true. every real number is a solution of an identity, so it has infinite solutions. the solution of a linear
Examples of how to solve of linear equations with one variable like 3x + 5 = 10 . also discusses when there is no solution or infinitely many solutions. get an answer for 'how do i determine if this equation is a linear function or a nonlinear function?' and find homework an example of a linear equation would be
The point slope form of a linear equation is written as . for example when we need to find the equation of a line when given a point and the slope. combinations of linear equations. linear equations can be added together, multiplied or divided. a simple example of addition of linear equations
These are examples of linear equations which is a first degree algebraic expression with one, two or more variables equated to a constant. . students learn about the different forms of linear equations. copyright. (the y-intercept), then you can write the equation of the line. for example,
Eighth grade Lesson Introduction to Linear Equations in. Linear functions and equations, the formula 0 = ax + by + c is said to be the 'general form' for the equation of a line. a, b, a simple example., video: what is a linear equation? most cars won't be able to run for more than 250,000 miles, examples of linear equations in slope-intercept form.
## What is the definition of a nonlinear equation? Quora
Rearranging and solving linear equations The Learning. What is a linear equation? an equation which involves only one variable whose highest power is 1 is known as a linear equation in that variable. (a) x + 4 = 19, (b) y, solutions of algebraic equations. for example, if x = 3 then the an equation like 2x + 3 = 7 is a simple type called a linear equation in one variable..
Graphing Linear Equations Calcworkshop. Solutions of algebraic equations. for example, if x = 3 then the an equation like 2x + 3 = 7 is a simple type called a linear equation in one variable., combinations of linear equations. linear equations can be added together, multiplied or divided. a simple example of addition of linear equations.
## Linear Equations Introduction to Statistics
Linear Equation What is a Linear Equation? How to. Linear algebra/systems of linear equations. from wikibooks, open books for an open world < linear algebra. some examples of linear equations are as follows: A linear equation is a polynomial of degree 1. in order to solve for the unknown variable, you must isolate the variable. in the order of operation, multiplication.
What is an example of a linear equation in two variables? 2. what does introduction to linear equations in two unknowns homework page.pdf. previous lesson. home в» graphing linear equations. graphing linear equations. coordinate plane. 1 hr 6 min 23 examples. what is a solution to a linear equation? examples #1-6:
Solve the following system of equations: x + z = 1 x + y + z = 2 x вђ“ y + z = 1. you should be getting the hang of things by now, so i'll just show the steps that example. solve the following system of linear equations: \left\ solving systems of equations in two variables; mathplanet is licensed by
What is an example of a linear equation in two variables? 2. what does introduction to linear equations in two unknowns homework page.pdf. previous lesson. identity an identity is an equation that is always true. every real number is a solution of an identity, so it has infinite solutions. the solution of a linear
Or to draw the graph of a linear equation such as y =2x+1, economics is another area that makes use of linear equations a lot. think, for example, linear algebra/systems of linear equations. from wikibooks, open books for an open world < linear algebra. some examples of linear equations are as follows:
Linear equation. mathematically, a example 2: a linear relationship can also be found in the equation distance = rate x time. because distance is a positive linear equations. system of linear equations. 55 min 7 examples. what is linear algebra? what is a matrix? and what is a linear equation? example of determining
Linear equations can have any number of variables. here is an example of a linear equation with 2 variables: 3x - 7y = 5 what makes it linear is the each term with a the point slope form of a linear equation is written as . for example when we need to find the equation of a line when given a point and the slope.
Get an answer for 'how do i determine if this equation is a linear function or a nonlinear function?' and find homework an example of a linear equation would be in this section we solve linear first order differential equations, since this is the same differential equation as we looked at in example 1, we already have | {"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": 0.8255928158760071, "perplexity": 270.0189935891233}, "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-2020-45/segments/1603107918164.98/warc/CC-MAIN-20201031121940-20201031151940-00088.warc.gz"} |
https://mathcenter.ru/en/higgs-bundles-and-related-topics-2022-05-03 | # «Donaldson Invariants and Hitchin Moduli Space. Part II. Higgs bundles and related topics»
Lecturer Dr. Qiongling Li Chern Institute of Mathematics, Nankai University Bio: Qiongling Li got her Ph.D. from Rice University in 2014. She is currently a research fellow at Chern Institute of Mathematics, Nankai University. Her main research fields are Higgs bundles, harmonic maps, and higher Teichmuller theory. Her recent works have been focused on understanding the non-abelian Hodge correspondence over Riemann surfaces.
Higgs bundles over a complex manifold is a natural generalization of holomorphic vector bundles and variation of Hodge structures. The main goal in this short course is to introduce Higgs bundles and associated research topics. Firstly, the non-abelian Hodge correspondence gives a homeomorphism between the representation variety of the surface group into a noncompact Lie group and the moduli space of Higgs bundles. In this way, Higgs bundles plays an important role in the study of higher Teichmuller theory as the generalization of classical Teichmuller theory into higher rank Lie groups. Secondly, the Hitchin fibration on the moduli space of Higgs bundles shows it is a classical integrable system which links with geometric Langlands correspondence.
This short course consists of two parts. In the first part, I will introduce Higgs bundles, moduli spaces, Hitchin integrable system, spectral curve, non-abelian Hodge correspondence, higher Teichmuller theory, etc. I will show some lower rank examples to link Higgs bundles with explicit geometry. In the second part, I will explain current developments on several selected research topics such as Hitchin WKB problem, harmonic maps for Hitchin representations, algebraic structures of the nilpotent cone, and the Hitchin-Kobayashi correspondence over non-compact surfaces.
The lecture will be held in English in the form of a webinar on the Zoom platform.
20:00 - 21:30 Beijing time（15:00 - 16:30 Moscow time)
Join Zoom Meeting:
Meeting ID：862 7775 8883
Passcode：837467
(link may change closer to the event) | {"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": 0.8306904435157776, "perplexity": 615.5716701166577}, "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/1669446710909.66/warc/CC-MAIN-20221202150823-20221202180823-00635.warc.gz"} |
https://arxiv.org/abs/1904.05627 | cs.DC
# Title:Locality of not-so-weak coloring
Abstract: Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes:
- "Easy": solvable in $O(\log^* n)$ rounds with both deterministic and randomized distributed algorithms.
- "Hard": requires at least $\Omega(\log n)$ rounds with deterministic and $\Omega(\log \log n)$ rounds with randomized distributed algorithms.
Hence for any parameterized LCL problem, when we move from local problems towards global problems, there is some point at which complexity suddenly jumps from easy to hard. For example, for vertex coloring in $d$-regular graphs it is now known that this jump is at precisely $d$ colors: coloring with $d+1$ colors is easy, while coloring with $d$ colors is hard.
However, it is currently poorly understood where this jump takes place when one looks at defective colorings. To study this question, we define $k$-partial $c$-coloring as follows: nodes are labeled with numbers between $1$ and $c$, and every node is incident to at least $k$ properly colored edges.
It is known that $1$-partial $2$-coloring (a.k.a. weak $2$-coloring) is easy for any $d \ge 1$. As our main result, we show that $k$-partial $2$-coloring becomes hard as soon as $k \ge 2$, no matter how large a $d$ we have.
We also show that this is fundamentally different from $k$-partial $3$-coloring: no matter which $k \ge 3$ we choose, the problem is always hard for $d = k$ but it becomes easy when $d \gg k$. The same was known previously for partial $c$-coloring with $c \ge 4$, but the case of $c < 4$ was open.
Subjects: Distributed, Parallel, and Cluster Computing (cs.DC); Computational Complexity (cs.CC) Cite as: arXiv:1904.05627 [cs.DC] (or arXiv:1904.05627v1 [cs.DC] for this version)
## Submission history
From: Jukka Suomela [view email]
[v1] Thu, 11 Apr 2019 11:11:02 UTC (110 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": 0.9139582514762878, "perplexity": 1114.0541482071333}, "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-2019-35/segments/1566027315809.69/warc/CC-MAIN-20190821043107-20190821065107-00102.warc.gz"} |
http://www.computer.org/csdl/trans/td/2006/07/l0656-abs.html | Subscribe
Issue No.07 - July (2006 vol.17)
pp: 656-666
ABSTRACT
<p><b>Abstract</b>—Leader-based protocols rest on a primitive able to provide the processes with the same unique leader. Such protocols are very common in distributed computing to solve synchronization or coordination problems. Unfortunately, providing such a primitive is far from being trivial in asynchronous distributed systems prone to process crashes. (It is even impossible in fault-prone purely asynchronous systems.) To circumvent this difficulty, several protocols have been proposed that build a leader facility on top of an asynchronous distributed system enriched with additional assumptions. The protocols proposed so far consider either additional assumptions based on synchrony or additional assumptions on the pattern of the messages that are exchanged. Considering systems with <tmath>n</tmath> processes and up to <tmath>f</tmath> process crashes, <tmath>1\leq f <n</tmath>, this paper investigates the combination of a time-free assumption on the message pattern with a synchrony assumption on process speed and message delay. It shows that both types of assumptions can be combined to obtain a hybrid eventual leader protocol benefiting from the best of both worlds. This combined assumption considers a star communication structure involving <tmath>f+1</tmath> processes. Its noteworthy feature lies in the level of combination of both types of assumption that is "as fine as possible” in the sense that each of the <tmath>f</tmath> channels of the star has to satisfy a property independently of the property satisfied by each of the <tmath>f-1</tmath> other channels (the <tmath>f</tmath> channels do not have to satisfy the same assumption). More precisely, this combined assumption is the following: There is a correct process <tmath>p</tmath> (center of the star) and a set <tmath>Q</tmath> of <tmath>f</tmath> processes <tmath>q</tmath> (<tmath>p \notin Q</tmath>) such that, eventually, either 1) each time it broadcasts a query, <tmath>q</tmath> receives a response from <tmath>p</tmath> among the <tmath>(n-f)</tmath> first responses to that query, or 2) the channel from <tmath>p</tmath> to <tmath>q</tmath> is timely. (The processes in the set <tmath>Q</tmath> can crash.) A surprisingly simple eventual leader protocol based on this fine grain hybrid assumption is proposed and proved correct. An improvement is also presented.</p>
INDEX TERMS
Asynchronous system, distributed algorithm, fault tolerance, hybrid protocol, leader election, process crash, time-free assumption, timer-based assumption.
CITATION
Achour Mostefaoui, Michel Raynal, Corentin Travers, "Time-Free and Timer-Based Assumptions Can Be Combined to Obtain Eventual Leadership", IEEE Transactions on Parallel & Distributed Systems, vol.17, no. 7, pp. 656-666, July 2006, doi:10.1109/TPDS.2006.95 | {"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": 0.8818297982215881, "perplexity": 2441.9893360515744}, "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/1432207926828.58/warc/CC-MAIN-20150521113206-00141-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=1996_AHSME_Problems/Problem_30&diff=prev&oldid=41729 | # Difference between revisions of "1996 AHSME Problems/Problem 30"
## Problem
A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to , where and are relatively prime positive integers. Find .
## Solution
All angle measures are in degrees. Let the first trapezoid be , where . Then the second trapezoid is , where . We look for .
Since is an isosceles trapezoid, we know that and, since , if we drew , we would see . Anyway, ( means arc AB). Using similar reasoning, .
Let and . Since (add up the angles), and thus . Therefore, . as well.
Now I focus on triangle . By the Law of Cosines, , so . Seeing and , we can now use the Law of Sines to get:
Now I focus on triangle . and , and we are given that , so We know , but we need to find . Using various identities, we see Returning to finding , we remember Plugging in and solving, we see . Thus, the answer is , which is answer choice .
1996 AHSME (Problems • Answer Key • Resources) Preceded byProblem 29 Followed byLast Problem 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions | {"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": 0.952703058719635, "perplexity": 1300.1249916648953}, "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/1606141176922.14/warc/CC-MAIN-20201124170142-20201124200142-00458.warc.gz"} |
https://www.graduate.technion.ac.il/Theses/Abstracts.asp?Id=25110 | M.Sc Student M.Sc Thesis Hess Green Rachel A Probabilistic Approach to Bounded Solutions of the Schrodinger Equation Department of Mathematics PROF. Ross Pinsky
Abstract
In this work we present three results. The first two concern the operator on with a potential V : [0;1) -> R which is non-negative, piecewise continuous and compactly supported. Extend V to all of R by V (x) = 0, x < 0.
We define where , and we investigate the behavior of the critical value , i.e. the value at which becomes a critical operator.
The second result, called the localization of binding, determines for what values of t; s > 0 the operator will be subcritical where the potentials V1, V2 are non-negative, piecewise continuous, compactly supported and not identically zero.
In the third result we consider the equation (1) where . It is known that there exists a solution to (1) if and only if (2) a.s. where X(s) is a Brownian motion. One would like to have an analytic condition for the existence of solutions to (1) rather than just a probabilistic one. We show that under certain restrictions, a necessary and suffcient analytic condition can be given. | {"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": 0.966386079788208, "perplexity": 433.1844064124565}, "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-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00262.warc.gz"} |
http://math.stackexchange.com/questions/115999/bounding-vert-m-1-vert-and-eigenvalues-of-m | # Bounding $\Vert M^{-1} \Vert$ and eigenvalues of $M$.
We work in $\mathbb{R}^n$. Let $M$ be an $n\times n$ matrix with $$x^TMx \geq k\Vert x\Vert^2$$ for all $x \in \mathbb{R}^n$, where $k>0$.
I want to show that $\Vert M^{-1} \Vert \leq \frac{1}{k}$ and that the real parts of the (possibly complex) eigenvalues of $M$ are at least $k$.
Attempt so far: It is easy to see that $M$ is invertible since otherwise there would be an $x\neq 0$ with $Mx=0$ and hence $x^TMx = 0$ which would violate the condition above.
Furthermore if $\lambda$ is an eigenvalue, then $|\lambda| \geq k$ by similar reasoning. I don't see how to deal with the complex eigenvalues at all though, since this bound doesn't ignore the imaginary part.
I know that $\Vert M^{-1} \Vert = \sqrt{\rho((M^{-1})^T(M^{-1})}$ is the square root of the norm of the maximum eigenvalue of $(M^{-1})^TM^{-1}$. But since $M$ isn't necessarily symmetric I don't know how much help that will be.
Any help would be greatly appreciated.
-
I suppose that $\alpha$ and $k$ are meant to be the same here. – Geoff Robinson Mar 3 '12 at 16:34
Yes, thank you. I changed it. – nullUser Mar 3 '12 at 16:41
(Oops. Wrong comment removed. The software won't let med delete it.) – Harald Hanche-Olsen Mar 3 '12 at 16:59
We have writing the hypothesis for $M^{-1}x$ that $x^TM^{-1}x\geq k\lVert M^{-1}x\rVert^2$ so $$k\lVert M^{-1}x\rVert^2\leq x^TM^{-1}x=\langle x,M^{—1}x\rangle\leq \lVert x\rVert \cdot\lVert M^{—1}x\rVert$$ so for $x\neq 0$ $\lVert M^{—1}x\rVert\leq \frac{\lVert x\rVert}k$ which gives the result.
I was so close to this in my scratchwork! What can I do about the complex eigenvalues? Say an eigenvalue is $c+di$, the real part of $x^*Mx$ is $c\Vert x\Vert^2$, can I somehow extract a real vector $v$ for which $v^TMv = c\Vert v \Vert^2$? – nullUser Mar 3 '12 at 17:41 | {"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": 0.977462649345398, "perplexity": 141.1457529899606}, "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/1432207926924.76/warc/CC-MAIN-20150521113206-00325-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.cfd-online.com/Forums/openfoam/94093-morph-mesh-given-displacement-boundary-points-print.html | CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
- OpenFOAM (https://www.cfd-online.com/Forums/openfoam/)
- - Morph mesh given displacement of boundary points (https://www.cfd-online.com/Forums/openfoam/94093-morph-mesh-given-displacement-boundary-points.html)
praveen November 5, 2011 02:12
Morph mesh given displacement of boundary points
Hello
Is there anything in openfoam which allows me to morph the interior mesh, given the displacement of the boundary mesh nodes ?
praveen
wyldckat November 5, 2011 04:04
Hi Praveen,
Does this tutorial suit your requirements: "tutorials/mesh/moveDynamicMesh/simpleHarmonicMotion"
Best regards,
Bruno
praveen November 5, 2011 07:05
Thanks. That seems relevant to me. I will check it out. Is it possible to specify the displacement of each individual boundary mesh point ?
ngj November 5, 2011 08:33
Hi Praveen,
Yes, it is possible to specify the displacement on the point level. This type of boundary condition can be put into two categories:
1. You know the motion by an algebraic equation, hence you loop over every boundary point and specify the displacement (Note: Some solvers use the boundary velocity, thus differentiate your algebraric equation with respect to time and evaluate it). Furthermore, if you are using tet-decomposition (available in 1.6-ext), you specify both the motion on the points and in the centers of the boundary faces. On the boundary, they are ordered as [<points> <face centers>].
2. You move the mesh based on results from the state of your simulation. Typically you can compute the motion in the face centers, and then you perform an interpolation to the points on the boundary. Again, be aware when you are using displacement or velocity solvers for the mesh motion.
With respect to the interpolation methods you can either look through the forum, or so-forth you have 1.6-ext installed, you can see an example of the implementation in the file "freeSurface.C" located somewhere in the "applications/solvers" directory.
A final comment: If the boundary you are moving also has a very fine boundary layer resolution, then my experience is that laplaceFaceDecomposition (1.6-ext) is the most robust combined with a very stiff mesh diffusivity next to that boundary. The diffusivity is the term in the following Laplace equation for the velocity of the mesh motion:
The diffusivity is specified in the dynamicMeshDict in <rootCase>/constant.
Good luck and kind regards,
Niels
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https://socratic.org/questions/hcl-is-a-strong-acid-what-is-the-ph-of-200-ml-of-0-002-m-hcl | Chemistry
Topics
# HCl is a strong acid. What is the pH of 200 mL of 0.002 M HCl?
##### 1 Answer
Feb 6, 2017
$p H = - {\log}_{10} \left[{H}_{3} {O}^{+}\right]$
#### Explanation:
$\text{Hydrochloric acid}$, as a strong acid, is stoichiometric in ${H}_{3} {O}^{+}$. And thus:
$p H = - {\log}_{10} \left[{H}_{3} {O}^{+}\right] = - {\log}_{10} \left(0.002\right) = - \left(- 2.70\right) = 2.70$
Note that the $p H$ thus depends on concentration solely. And thus what would be the $p H$ of a $2 \cdot L$ volume of $2 \times {10}^{-} 3 \cdot m o l \cdot {L}^{-} 1$ $\text{hydrochloric acid}$?
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http://physics.stackexchange.com/questions/21111/whats-the-difference-between-boundary-value-problems-and-initial-value-probl | # What's the difference between “boundary value problems” and “initial value problems”?
Mathematically speaking, is there any essential difference between initial value problems and boundary value problems?
The specification of the values of a function $f$ and the "velocities" $\frac{\partial f}{\partial t}$ at an initial time $t=0$ can also be seen, I think, as the specification of boundary values, since the boundaries of the variable $t$ are, usually, at $t=0$ and $t<\infty$.
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In many cases, there really is no difference. Think of the specification of initial values as boundary values on a "time slice." (Incidentally, I addressed a question tangentially related to this the other day: Differentiating Propagator, Greens function, Correlation function, etc) However, sometimes the specificity of calling something an initial value question might indicate something useful about the boundary, e.g. that it is a Cauchy surface and all of the rest of space lies in its causal future/past if the problem is relativistic.
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When there is only one spatial variable then mathematically the two are indistinguishable. But often boundary value problems are solved over a higher dimensional domain. For example, a common problem in physics is to solve Laplace's equation over a spatial region of three dimensions, with a two dimensional surface providing the boundary conditions. If the boundary condition specifies the value of the solution on the surface, then it is called a Dirichlet boundary condition. However, sometimes the boundary condition specifies the normal derivative of the solution at the surface, and then it is called a Neumann boundary condition. Boundary value problems over multi-dimensional domains are necessarily tied to partial differential equations rather than ordinary differential equations, and so they are more complicated than ordinary differential equations with a single initial value specified.
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Seems to me the difference is semantic:
It is implicit that one is seeking a specific solution to a problem in time and space given the initial values.
The boundary conditions bound the solutions but do not pick up a specific solution, unless the initial values are used.
Initial values pick up a specific solution from the family of solutions allowed/defined by the boundary conditions.
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https://proofwiki.org/wiki/Definition:Uncountable_Set | # Definition:Uncountable Set
## Definition
An infinite set which is not countable is described as uncountable.
## Also known as
An uncountable set is also sometimes seen referred to as non-countable or non-denumerable.
## Also see
• Results about uncountable sets can be found here. | {"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": 0.9854184985160828, "perplexity": 2486.8424472133115}, "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-2019-18/segments/1555578655155.88/warc/CC-MAIN-20190424174425-20190424200425-00182.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-vertical-horizontal-or-slant-asymptotes-for-f-x-2x-8-3x-24 | Precalculus
Topics
How do you find the vertical, horizontal or slant asymptotes for f(x) = (2x-8) / (3x-24)?
Jul 20, 2016
Answer:
vertical asymptote x = 8
horizontal asymptote $y = \frac{2}{3}$
Explanation:
The denominator of f(x) cannot be zero as this is undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.
solve: 3x - 24 = 0 → x = 8 is the asymptote
Horizontal asymptotes occur as
${\lim}_{x \to \pm \infty} , f \left(x\right) \to c \text{ (a constant)}$
divide terms on numerator/denominator by x
$\frac{\frac{2 x}{x} - \frac{8}{x}}{\frac{3 x}{x} - \frac{24}{x}} = \frac{2 - \frac{8}{x}}{3 - \frac{24}{x}}$
as $x \to \pm \infty , f \left(x\right) \to \frac{2 - 0}{3 - 0}$
$\Rightarrow y = \frac{2}{3} \text{ is the asymptote}$
Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case her ( both degree 1 ) Hence there are no slant asymptotes.
graph{(2x-8)/(3x-24) [-20, 20, -10, 10]}
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http://brian2.readthedocs.io/en/2.0beta/introduction/known_issues.html | Known issues¶
List of known issues
Cannot find msvcr90d.dll¶
If you see this message coming up, find the file PythonDir\Lib\site-packages\numpy\distutils\mingw32ccompiler.py and modify the line msvcr_dbg_success = build_msvcr_library(debug=True) to read msvcr_dbg_success = False (you can comment out the existing line and add the new line immediately after).
Problems with numerical integration¶
If the beginning of a run takes a long time, the reason might be the automatic determination of a suitable numerical integration algorithm. This can in particular happen for complicated equations where sympy’s solvers take a long time trying to solve the equations symbolically (typically failing in the end). We try to improve this situation (see #351) but until then, chose a numerical integration algorithm explicitly (Numerical integration). | {"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": 0.8406402468681335, "perplexity": 1837.3734033117423}, "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-2017-47/segments/1510934806258.88/warc/CC-MAIN-20171120223020-20171121003020-00671.warc.gz"} |
http://www.nag.com/numeric/MB/manual64_24_1/html/D03/d03phf.html | Integer type: int32 int64 nag_int show int32 show int32 show int64 show int64 show nag_int show nag_int
Chapter Contents
Chapter Introduction
NAG Toolbox
# NAG Toolbox: nag_pde_1d_parab_dae_fd (d03ph)
## Purpose
nag_pde_1d_parab_dae_fd (d03ph) integrates a system of linear or nonlinear parabolic partial differential equations (PDEs) in one space variable, with scope for coupled ordinary differential equations (ODEs). The spatial discretization is performed using finite differences, and the method of lines is employed to reduce the PDEs to a system of ODEs. The resulting system is solved using a backward differentiation formula method or a Theta method (switching between Newton's method and functional iteration).
## Syntax
[ts, u, rsave, isave, ind, user, cwsav, lwsav, iwsav, rwsav, ifail] = d03ph(npde, m, ts, tout, pdedef, bndary, u, x, ncode, odedef, xi, rtol, atol, itol, norm_p, laopt, algopt, rsave, isave, itask, itrace, ind, cwsav, lwsav, iwsav, rwsav, 'npts', npts, 'nxi', nxi, 'neqn', neqn, 'lisave', lisave, 'user', user)
[ts, u, rsave, isave, ind, user, cwsav, lwsav, iwsav, rwsav, ifail] = nag_pde_1d_parab_dae_fd(npde, m, ts, tout, pdedef, bndary, u, x, ncode, odedef, xi, rtol, atol, itol, norm_p, laopt, algopt, rsave, isave, itask, itrace, ind, cwsav, lwsav, iwsav, rwsav, 'npts', npts, 'nxi', nxi, 'neqn', neqn, 'lisave', lisave, 'user', user)
Note: the interface to this routine has changed since earlier releases of the toolbox:
Mark 22: lrsave has been removed from the interface
.
## Description
nag_pde_1d_parab_dae_fd (d03ph) integrates the system of parabolic-elliptic equations and coupled ODEs
npde ∑ Pi,j( ∂ Uj)/( ∂ t) + Qi = x − m( ∂ )/( ∂ x)(xmRi), i = 1,2, … ,npde, a ≤ x ≤ b, t ≥ t0, j = 1
$∑j=1npdePi,j ∂Uj ∂t +Qi=x-m ∂∂x (xmRi), i=1,2,…,npde, a≤x≤b, t≥t0,$
(1)
Fi(t,V,V.,ξ,U*,Ux * ,R*,Ut * ,Uxt * ) = 0, i = 1,2, … ,ncode, $Fi(t,V,V.,ξ,U*,Ux*,R*,Ut*,Uxt*)=0, i=1,2,…,ncode,$ (2)
where (1) defines the PDE part and (2) generalizes the coupled ODE part of the problem.
In (1), Pi,j${P}_{i,j}$ and Ri${R}_{i}$ depend on x$x$, t$t$, U$U$, Ux${U}_{x}$ and V$V$; Qi${Q}_{i}$ depends on x$x$, t$t$, U$U$, Ux${U}_{x}$, V$V$ and linearly on V.$\stackrel{.}{V}$. The vector U$U$ is the set of PDE solution values
U (x,t) = [ U1 (x,t) , … , Unpde (x,t) ]T , $U (x,t) = [ U 1 (x,t) ,…, U npde (x,t) ] T ,$
and the vector Ux${U}_{x}$ is the partial derivative with respect to x$x$. The vector V$V$ is the set of ODE solution values
V (t) = [ V1 (t) , … , (t) ]T , $V (t) = [ V 1 ( t ) ,…, V ncode ( t ) ] T ,$
and V.$\stackrel{.}{V}$ denotes its derivative with respect to time.
In (2), ξ$\xi$ represents a vector of nξ${n}_{\xi }$ spatial coupling points at which the ODEs are coupled to the PDEs. These points may or may not be equal to some of the PDE spatial mesh points. U*${U}^{*}$, Ux * ${U}_{x}^{*}$, R*${R}^{*}$, Ut * ${U}_{t}^{*}$ and Uxt * ${U}_{xt}^{*}$ are the functions U$U$, Ux${U}_{x}$, R$R$, Ut${U}_{t}$ and Uxt${U}_{xt}$ evaluated at these coupling points. Each Fi${F}_{i}$ may only depend linearly on time derivatives. Hence the equation (2) may be written more precisely as
F = GAV.B
( Ut * ) Uxt *
,
$F=G-AV.-B Ut* Uxt* ,$
(3)
where F = [F1,,]T$F={\left[{F}_{1},\dots ,{F}_{{\mathbf{ncode}}}\right]}^{\mathrm{T}}$, G$G$ is a vector of length ncode, A$A$ is an ncode by ncode matrix, B$B$ is an ncode by (nξ × npde)$\left({n}_{\xi }×{\mathbf{npde}}\right)$ matrix and the entries in G$G$, A$A$ and B$B$ may depend on t$t$, ξ$\xi$, U*${U}^{*}$, Ux * ${U}_{x}^{*}$ and V$V$. In practice you only need to supply a vector of information to define the ODEs and not the matrices A$A$ and B$B$. (See Section [Parameters] for the specification of odedef.)
The integration in time is from t0${t}_{0}$ to tout${t}_{\mathrm{out}}$, over the space interval axb$a\le x\le b$, where a = x1$a={x}_{1}$ and b = xnpts$b={x}_{{\mathbf{npts}}}$ are the leftmost and rightmost points of a user-defined mesh x1,x2,,xnpts${x}_{1},{x}_{2},\dots ,{x}_{{\mathbf{npts}}}$. The coordinate system in space is defined by the values of m$m$; m = 0$m=0$ for Cartesian coordinates, m = 1$m=1$ for cylindrical polar coordinates and m = 2$m=2$ for spherical polar coordinates.
The PDE system which is defined by the functions Pi,j${P}_{i,j}$, Qi${Q}_{i}$ and Ri${R}_{i}$ must be specified in pdedef.
The initial values of the functions U(x,t)$U\left(x,t\right)$ and V(t)$V\left(t\right)$ must be given at t = t0$t={t}_{0}$.
The functions Ri${R}_{i}$ which may be thought of as fluxes, are also used in the definition of the boundary conditions. The boundary conditions must have the form
βi(x,t)Ri(x,t,U,Ux,V) = γi(x,t,U,Ux,V,V.), i = 1,2, … ,npde, $βi(x,t)Ri(x,t,U,Ux,V)=γi(x,t,U,Ux,V,V.), i=1,2,…,npde,$ (4)
where x = a$x=a$ or x = b$x=b$.
The boundary conditions must be specified in bndary. The function γi${\gamma }_{i}$ may depend linearly on V.$\stackrel{.}{V}$.
The problem is subject to the following restrictions:
(i) In (1), V.j(t)${\stackrel{.}{V}}_{\mathit{j}}\left(t\right)$, for j = 1,2, … ,ncode$\mathit{j}=1,2,\dots ,{\mathbf{ncode}}$, may only appear linearly in the functions Qi${Q}_{\mathit{i}}$, for i = 1,2, … ,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$, with a similar restriction for γ$\gamma$; (ii) Pi,j${P}_{\mathit{i},j}$ and the flux Ri${R}_{\mathit{i}}$ must not depend on any time derivatives; (iii) t0 < tout${t}_{0}<{t}_{\mathrm{out}}$, so that integration is in the forward direction; (iv) the evaluation of the terms Pi,j${P}_{\mathit{i},j}$, Qi${Q}_{\mathit{i}}$ and Ri${R}_{\mathit{i}}$ is done approximately at the mid-points of the mesh x(i)${\mathbf{x}}\left(\mathit{i}\right)$, for i = 1,2, … ,npts$\mathit{i}=1,2,\dots ,{\mathbf{npts}}$, by calling the pdedef for each mid-point in turn. Any discontinuities in these functions must therefore be at one or more of the mesh points x1,x2, … ,xnpts${x}_{1},{x}_{2},\dots ,{x}_{{\mathbf{npts}}}$; (v) at least one of the functions Pi,j${P}_{i,j}$ must be nonzero so that there is a time derivative present in the PDE problem; (vi) if m > 0$m>0$ and x1 = 0.0${x}_{1}=0.0$, which is the left boundary point, then it must be ensured that the PDE solution is bounded at this point. This can be done by either specifying the solution at x = 0.0$x=0.0$ or by specifying a zero flux there, that is βi = 1.0${\beta }_{i}=1.0$ and γi = 0.0${\gamma }_{i}=0.0$. See also Section [Further Comments] below.
The algebraic-differential equation system which is defined by the functions Fi${F}_{i}$ must be specified in odedef. You must also specify the coupling points ξ$\xi$ in the array xi.
The parabolic equations are approximated by a system of ODEs in time for the values of Ui${U}_{i}$ at mesh points. For simple problems in Cartesian coordinates, this system is obtained by replacing the space derivatives by the usual central, three-point finite difference formula. However, for polar and spherical problems, or problems with nonlinear coefficients, the space derivatives are replaced by a modified three-point formula which maintains second order accuracy. In total there are ${\mathbf{npde}}×{\mathbf{npts}}+{\mathbf{ncode}}$ ODEs in the time direction. This system is then integrated forwards in time using a backward differentiation formula (BDF) or a Theta method.
## References
Berzins M (1990) Developments in the NAG Library software for parabolic equations Scientific Software Systems (eds J C Mason and M G Cox) 59–72 Chapman and Hall
Berzins M, Dew P M and Furzeland R M (1989) Developing software for time-dependent problems using the method of lines and differential-algebraic integrators Appl. Numer. Math. 5 375–397
Berzins M and Furzeland R M (1992) An adaptive theta method for the solution of stiff and nonstiff differential equations Appl. Numer. Math. 9 1–19
Skeel R D and Berzins M (1990) A method for the spatial discretization of parabolic equations in one space variable SIAM J. Sci. Statist. Comput. 11(1) 1–32
## Parameters
### Compulsory Input Parameters
1: npde – int64int32nag_int scalar
The number of PDEs to be solved.
Constraint: npde1${\mathbf{npde}}\ge 1$.
2: m – int64int32nag_int scalar
The coordinate system used:
m = 0${\mathbf{m}}=0$
Indicates Cartesian coordinates.
m = 1${\mathbf{m}}=1$
Indicates cylindrical polar coordinates.
m = 2${\mathbf{m}}=2$
Indicates spherical polar coordinates.
Constraint: m = 0${\mathbf{m}}=0$, 1$1$ or 2$2$.
3: ts – double scalar
The initial value of the independent variable t$t$.
Constraint: ${\mathbf{ts}}<{\mathbf{tout}}$.
4: tout – double scalar
The final value of t$t$ to which the integration is to be carried out.
5: pdedef – function handle or string containing name of m-file
pdedef must evaluate the functions Pi,j${P}_{i,j}$, Qi${Q}_{i}$ and Ri${R}_{i}$ which define the system of PDEs. The functions may depend on x$x$, t$t$, U$U$, Ux${U}_{x}$ and V$V$. Qi${Q}_{i}$ may depend linearly on V.$\stackrel{.}{V}$. pdedef is called approximately midway between each pair of mesh points in turn by nag_pde_1d_parab_dae_fd (d03ph).
[p, q, r, ires, user] = pdedef(npde, t, x, u, ux, ncode, v, vdot, ires, user)
Input Parameters
1: npde – int64int32nag_int scalar
The number of PDEs in the system.
2: t – double scalar
The current value of the independent variable t$t$.
3: x – double scalar
The current value of the space variable x$x$.
4: u(npde) – double array
u(i)${\mathbf{u}}\left(\mathit{i}\right)$ contains the value of the component Ui(x,t)${U}_{\mathit{i}}\left(x,t\right)$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
5: ux(npde) – double array
ux(i)${\mathbf{ux}}\left(\mathit{i}\right)$ contains the value of the component (Ui(x,t))/(x) $\frac{\partial {U}_{\mathit{i}}\left(x,t\right)}{\partial x}$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
6: ncode – int64int32nag_int scalar
The number of coupled ODEs in the system.
7: v(ncode) – double array
If ncode > 0${\mathbf{ncode}}>0$, v(i)${\mathbf{v}}\left(\mathit{i}\right)$ contains the value of the component Vi(t)${V}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
8: vdot(ncode) – double array
If ncode > 0${\mathbf{ncode}}>0$, vdot(i)${\mathbf{vdot}}\left(\mathit{i}\right)$ contains the value of component V.i(t)${\stackrel{.}{V}}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
Note: V.i(t)${\stackrel{.}{V}}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$, may only appear linearly in Qj${Q}_{\mathit{j}}$, for j = 1,2,,npde$\mathit{j}=1,2,\dots ,{\mathbf{npde}}$.
9: ires – int64int32nag_int scalar
Set to 1 or 1$-1\text{ or }1$.
10: user – Any MATLAB object
pdedef is called from nag_pde_1d_parab_dae_fd (d03ph) with the object supplied to nag_pde_1d_parab_dae_fd (d03ph).
Output Parameters
1: p(npde,npde) – double array
p(i,j)${\mathbf{p}}\left(\mathit{i},\mathit{j}\right)$ must be set to the value of Pi,j(x,t,U,Ux,V)${P}_{\mathit{i},\mathit{j}}\left(x,t,U,{U}_{x},V\right)$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,npde$\mathit{j}=1,2,\dots ,{\mathbf{npde}}$.
2: q(npde) – double array
q(i)${\mathbf{q}}\left(\mathit{i}\right)$ must be set to the value of Qi(x,t,U,Ux,V,V.)${Q}_{\mathit{i}}\left(x,t,U,{U}_{x},V,\stackrel{.}{V}\right)$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
3: r(npde) – double array
r(i)${\mathbf{r}}\left(\mathit{i}\right)$ must be set to the value of Ri(x,t,U,Ux,V)${R}_{\mathit{i}}\left(x,t,U,{U}_{x},V\right)$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
4: ires – int64int32nag_int scalar
Should usually remain unchanged. However, you may set ires to force the integration function to take certain actions as described below:
ires = 2${\mathbf{ires}}=2$
Indicates to the integrator that control should be passed back immediately to the calling (sub)routine with the error indicator set to ${\mathbf{ifail}}={\mathbf{6}}$.
ires = 3${\mathbf{ires}}=3$
Indicates to the integrator that the current time step should be abandoned and a smaller time step used instead. You may wish to set ires = 3${\mathbf{ires}}=3$ when a physically meaningless input or output value has been generated. If you consecutively set ires = 3${\mathbf{ires}}=3$, then nag_pde_1d_parab_dae_fd (d03ph) returns to the calling function with the error indicator set to ${\mathbf{ifail}}={\mathbf{4}}$.
5: user – Any MATLAB object
6: bndary – function handle or string containing name of m-file
bndary must evaluate the functions βi${\beta }_{i}$ and γi${\gamma }_{i}$ which describe the boundary conditions, as given in (4).
[beta, gamma, ires, user] = bndary(npde, t, u, ux, ncode, v, vdot, ibnd, ires, user)
Input Parameters
1: npde – int64int32nag_int scalar
The number of PDEs in the system.
2: t – double scalar
The current value of the independent variable t$t$.
3: u(npde) – double array
u(i)${\mathbf{u}}\left(\mathit{i}\right)$ contains the value of the component Ui(x,t)${U}_{\mathit{i}}\left(x,t\right)$ at the boundary specified by ibnd, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
4: ux(npde) – double array
ux(i)${\mathbf{ux}}\left(\mathit{i}\right)$ contains the value of the component (Ui(x,t))/(x) $\frac{\partial {U}_{\mathit{i}}\left(x,t\right)}{\partial x}$ at the boundary specified by ibnd, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
5: ncode – int64int32nag_int scalar
The number of coupled ODEs in the system.
6: v(ncode) – double array
If ncode > 0${\mathbf{ncode}}>0$, v(i)${\mathbf{v}}\left(\mathit{i}\right)$ contains the value of the component Vi(t)${V}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
7: vdot(ncode) – double array
If ncode > 0${\mathbf{ncode}}>0$, vdot(i)${\mathbf{vdot}}\left(\mathit{i}\right)$ contains the value of component V.i(t)${\stackrel{.}{V}}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
Note: V.i(t)${\stackrel{.}{V}}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$, may only appear linearly in Qj${Q}_{\mathit{j}}$, for j = 1,2,,npde$\mathit{j}=1,2,\dots ,{\mathbf{npde}}$.
8: ibnd – int64int32nag_int scalar
Specifies which boundary conditions are to be evaluated.
ibnd = 0${\mathbf{ibnd}}=0$
bndary must set up the coefficients of the left-hand boundary, x = a$x=a$.
ibnd0${\mathbf{ibnd}}\ne 0$
bndary must set up the coefficients of the right-hand boundary, x = b$x=b$.
9: ires – int64int32nag_int scalar
Set to 1 or 1$-1\text{ or }1$.
10: user – Any MATLAB object
bndary is called from nag_pde_1d_parab_dae_fd (d03ph) with the object supplied to nag_pde_1d_parab_dae_fd (d03ph).
Output Parameters
1: beta(npde) – double array
beta(i)${\mathbf{beta}}\left(\mathit{i}\right)$ must be set to the value of βi(x,t)${\beta }_{\mathit{i}}\left(x,t\right)$ at the boundary specified by ibnd, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
2: gamma(npde) – double array
gamma(i)${\mathbf{gamma}}\left(\mathit{i}\right)$ must be set to the value of γi(x,t,U,Ux,V,V.)${\gamma }_{\mathit{i}}\left(x,t,U,{U}_{x},V,\stackrel{.}{V}\right)$ at the boundary specified by ibnd, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$.
3: ires – int64int32nag_int scalar
Should usually remain unchanged. However, you may set ires to force the integration function to take certain actions as described below:
ires = 2${\mathbf{ires}}=2$
Indicates to the integrator that control should be passed back immediately to the calling (sub)routine with the error indicator set to ${\mathbf{ifail}}={\mathbf{6}}$.
ires = 3${\mathbf{ires}}=3$
Indicates to the integrator that the current time step should be abandoned and a smaller time step used instead. You may wish to set ires = 3${\mathbf{ires}}=3$ when a physically meaningless input or output value has been generated. If you consecutively set ires = 3${\mathbf{ires}}=3$, then nag_pde_1d_parab_dae_fd (d03ph) returns to the calling function with the error indicator set to ${\mathbf{ifail}}={\mathbf{4}}$.
4: user – Any MATLAB object
7: u(neqn) – double array
neqn, the dimension of the array, must satisfy the constraint ${\mathbf{neqn}}={\mathbf{npde}}×{\mathbf{npts}}+{\mathbf{ncode}}$.
The initial values of the dependent variables defined as follows:
• u(npde × (j1) + i)${\mathbf{u}}\left({\mathbf{npde}}×\left(\mathit{j}-1\right)+\mathit{i}\right)$ contain Ui(xj,t0)${U}_{\mathit{i}}\left({x}_{\mathit{j}},{t}_{0}\right)$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,npts$\mathit{j}=1,2,\dots ,{\mathbf{npts}}$, and
• u(npts × npde + i)${\mathbf{u}}\left({\mathbf{npts}}×{\mathbf{npde}}+\mathit{i}\right)$ contain Vi(t0)${V}_{\mathit{i}}\left({t}_{0}\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
8: x(npts) – double array
npts, the dimension of the array, must satisfy the constraint npts3${\mathbf{npts}}\ge 3$.
The mesh points in the space direction. x(1)${\mathbf{x}}\left(1\right)$ must specify the left-hand boundary, a$a$, and x(npts)${\mathbf{x}}\left({\mathbf{npts}}\right)$ must specify the right-hand boundary, b$b$.
Constraint: x(1) < x(2) < < x(npts)${\mathbf{x}}\left(1\right)<{\mathbf{x}}\left(2\right)<\cdots <{\mathbf{x}}\left({\mathbf{npts}}\right)$.
9: ncode – int64int32nag_int scalar
The number of coupled ODE components.
Constraint: ncode0${\mathbf{ncode}}\ge 0$.
10: odedef – function handle or string containing name of m-file
odedef must evaluate the functions F$F$, which define the system of ODEs, as given in (3).
[f, ires, user] = odedef(npde, t, ncode, v, vdot, nxi, xi, ucp, ucpx, rcp, ucpt, ucptx, ires, user)
Input Parameters
1: npde – int64int32nag_int scalar
The number of PDEs in the system.
2: t – double scalar
The current value of the independent variable t$t$.
3: ncode – int64int32nag_int scalar
The number of coupled ODEs in the system.
4: v(ncode) – double array
If ncode > 0${\mathbf{ncode}}>0$, v(i)${\mathbf{v}}\left(\mathit{i}\right)$ contains the value of the component Vi(t)${V}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
5: vdot(ncode) – double array
If ncode > 0${\mathbf{ncode}}>0$, vdot(i)${\mathbf{vdot}}\left(\mathit{i}\right)$ contains the value of component V.i(t)${\stackrel{.}{V}}_{\mathit{i}}\left(t\right)$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$.
6: nxi – int64int32nag_int scalar
The number of ODE/PDE coupling points.
7: xi(nxi) – double array
If nxi > 0${\mathbf{nxi}}>0$, xi(i)${\mathbf{xi}}\left(\mathit{i}\right)$ contains the ODE/PDE coupling points, ξi${\xi }_{\mathit{i}}$, for i = 1,2,,nxi$\mathit{i}=1,2,\dots ,{\mathbf{nxi}}$.
8: ucp(npde, : $:$) – double array
The second dimension of the array must be at least max (1,nxi)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nxi}}\right)$
If nxi > 0${\mathbf{nxi}}>0$, ucp(i,j)${\mathbf{ucp}}\left(\mathit{i},\mathit{j}\right)$ contains the value of Ui(x,t)${U}_{\mathit{i}}\left(x,t\right)$ at the coupling point x = ξj$x={\xi }_{\mathit{j}}$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,nxi$\mathit{j}=1,2,\dots ,{\mathbf{nxi}}$.
9: ucpx(npde, : $:$) – double array
The second dimension of the array must be at least max (1,nxi)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nxi}}\right)$
If nxi > 0${\mathbf{nxi}}>0$, ucpx(i,j)${\mathbf{ucpx}}\left(\mathit{i},\mathit{j}\right)$ contains the value of (Ui(x,t))/(x) $\frac{\partial {U}_{\mathit{i}}\left(x,t\right)}{\partial x}$ at the coupling point x = ξj$x={\xi }_{\mathit{j}}$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,nxi$\mathit{j}=1,2,\dots ,{\mathbf{nxi}}$.
10: rcp(npde, : $:$) – double array
The second dimension of the array must be at least max (1,nxi)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nxi}}\right)$
rcp(i,j)${\mathbf{rcp}}\left(\mathit{i},\mathit{j}\right)$ contains the value of the flux Ri${R}_{\mathit{i}}$ at the coupling point x = ξj$x={\xi }_{\mathit{j}}$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,nxi$\mathit{j}=1,2,\dots ,{\mathbf{nxi}}$.
11: ucpt(npde, : $:$) – double array
The second dimension of the array must be at least max (1,nxi)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nxi}}\right)$
If nxi > 0${\mathbf{nxi}}>0$, ucpt(i,j)${\mathbf{ucpt}}\left(\mathit{i},\mathit{j}\right)$ contains the value of (Ui)/(t) $\frac{\partial {U}_{\mathit{i}}}{\partial t}$ at the coupling point x = ξj$x={\xi }_{\mathit{j}}$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,nxi$\mathit{j}=1,2,\dots ,{\mathbf{nxi}}$.
12: ucptx(npde, : $:$) – double array
The second dimension of the array must be at least max (1,nxi)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nxi}}\right)$
ucptx(i,j)${\mathbf{ucptx}}\left(\mathit{i},\mathit{j}\right)$ contains the value of (2Ui)/( x t ) $\frac{{\partial }^{2}{U}_{\mathit{i}}}{\partial x\partial t}$ at the coupling point x = ξj$x={\xi }_{\mathit{j}}$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,nxi$\mathit{j}=1,2,\dots ,{\mathbf{nxi}}$.
13: ires – int64int32nag_int scalar
The form of F$F$ that must be returned in the array f.
ires = 1${\mathbf{ires}}=1$
Equation (5) must be used.
ires = 1${\mathbf{ires}}=-1$
Equation (6) must be used.
14: user – Any MATLAB object
odedef is called from nag_pde_1d_parab_dae_fd (d03ph) with the object supplied to nag_pde_1d_parab_dae_fd (d03ph).
Output Parameters
1: f(ncode) – double array
f(i)${\mathbf{f}}\left(\mathit{i}\right)$ must contain the i$\mathit{i}$th component of F$F$, for i = 1,2,,ncode$\mathit{i}=1,2,\dots ,{\mathbf{ncode}}$, where F$F$ is defined as
F = GAV.B
( Ut * ) Uxt *
,
$F=G-AV.-B Ut* Uxt* ,$
(5)
or
F = AV.B
( Ut * ) Uxt *
.
$F=-AV.-B Ut* Uxt* .$
(6)
The definition of F$F$ is determined by the input value of ires.
2: ires – int64int32nag_int scalar
Should usually remain unchanged. However, you may reset ires to force the integration function to take certain actions as described below:
ires = 2${\mathbf{ires}}=2$
Indicates to the integrator that control should be passed back immediately to the calling (sub)routine with the error indicator set to ${\mathbf{ifail}}={\mathbf{6}}$.
ires = 3${\mathbf{ires}}=3$
Indicates to the integrator that the current time step should be abandoned and a smaller time step used instead. You may wish to set ires = 3${\mathbf{ires}}=3$ when a physically meaningless input or output value has been generated. If you consecutively set ires = 3${\mathbf{ires}}=3$, then nag_pde_1d_parab_dae_fd (d03ph) returns to the calling function with the error indicator set to ${\mathbf{ifail}}={\mathbf{4}}$.
3: user – Any MATLAB object
11: xi(nxi) – double array
nxi, the dimension of the array, must satisfy the constraint
• if ncode = 0${\mathbf{ncode}}=0$, nxi = 0${\mathbf{nxi}}=0$;
• if ncode > 0${\mathbf{ncode}}>0$, nxi0${\mathbf{nxi}}\ge 0$.
If nxi > 0${\mathbf{nxi}}>0$, xi(i)${\mathbf{xi}}\left(\mathit{i}\right)$, for i = 1,2,,nxi$\mathit{i}=1,2,\dots ,{\mathbf{nxi}}$, must be set to the ODE/PDE coupling points.
Constraint: x(1)xi(1) < xi(2) < < xi(nxi)x(npts)${\mathbf{x}}\left(1\right)\le {\mathbf{xi}}\left(1\right)<{\mathbf{xi}}\left(2\right)<\cdots <{\mathbf{xi}}\left({\mathbf{nxi}}\right)\le {\mathbf{x}}\left({\mathbf{npts}}\right)$.
12: rtol( : $:$) – double array
Note: the dimension of the array rtol must be at least 1$1$ if itol = 1${\mathbf{itol}}=1$ or 2$2$ and at least neqn${\mathbf{neqn}}$ if itol = 3${\mathbf{itol}}=3$ or 4$4$.
The relative local error tolerance.
Constraint: rtol(i)0.0${\mathbf{rtol}}\left(i\right)\ge 0.0$ for all relevant i$i$.
13: atol( : $:$) – double array
Note: the dimension of the array atol must be at least 1$1$ if itol = 1${\mathbf{itol}}=1$ or 3$3$ and at least neqn${\mathbf{neqn}}$ if itol = 2${\mathbf{itol}}=2$ or 4$4$.
The absolute local error tolerance.
Constraint: atol(i)0.0${\mathbf{atol}}\left(i\right)\ge 0.0$ for all relevant i$i$.
Note: corresponding elements of rtol and atol cannot both be 0.0$0.0$.
14: itol – int64int32nag_int scalar
A value to indicate the form of the local error test. itol indicates to nag_pde_1d_parab_dae_fd (d03ph) whether to interpret either or both of rtol or atol as a vector or scalar. The error test to be satisfied is ei / wi < 1.0$‖{e}_{i}/{w}_{i}‖<1.0$, where wi${w}_{i}$ is defined as follows:
itol rtol atol wi${w}_{i}$ 1 scalar scalar rtol(1) × |Ui| + atol(1)${\mathbf{rtol}}\left(1\right)×|{U}_{i}|+{\mathbf{atol}}\left(1\right)$ 2 scalar vector rtol(1) × |Ui| + atol(i)${\mathbf{rtol}}\left(1\right)×|{U}_{i}|+{\mathbf{atol}}\left(i\right)$ 3 vector scalar rtol(i) × |Ui| + atol(1)${\mathbf{rtol}}\left(i\right)×|{U}_{i}|+{\mathbf{atol}}\left(1\right)$ 4 vector vector rtol(i) × |Ui| + atol(i)${\mathbf{rtol}}\left(i\right)×|{U}_{i}|+{\mathbf{atol}}\left(i\right)$
In the above, ei${e}_{\mathit{i}}$ denotes the estimated local error for the i$\mathit{i}$th component of the coupled PDE/ODE system in time, u(i)${\mathbf{u}}\left(\mathit{i}\right)$, for i = 1,2,,neqn$\mathit{i}=1,2,\dots ,{\mathbf{neqn}}$.
The choice of norm used is defined by the parameter norm_p.
Constraint: 1itol4$1\le {\mathbf{itol}}\le 4$.
15: norm_p – string (length ≥ 1)
The type of norm to be used.
norm = 'M'${\mathbf{norm}}=\text{'M'}$
Maximum norm.
norm = 'A'${\mathbf{norm}}=\text{'A'}$
Averaged L2${L}_{2}$ norm.
If unorm${{\mathbf{u}}}_{\mathrm{norm}}$ denotes the norm of the vector u of length neqn, then for the averaged L2${L}_{2}$ norm
unorm = sqrt(1/(neqn) ∑ i = 1neqn(u(i) / wi)2), $unorm=1neqn∑i=1neqn(ui/wi)2,$
while for the maximum norm
unorm = maxi |u(i) / wi| . $u norm = maxi| ui / wi | .$
See the description of itol for the formulation of the weight vector w$w$.
Constraint: norm = 'M'${\mathbf{norm}}=\text{'M'}$ or 'A'$\text{'A'}$.
16: laopt – string (length ≥ 1)
The type of matrix algebra required.
laopt = 'F'${\mathbf{laopt}}=\text{'F'}$
Full matrix methods to be used.
laopt = 'B'${\mathbf{laopt}}=\text{'B'}$
Banded matrix methods to be used.
laopt = 'S'${\mathbf{laopt}}=\text{'S'}$
Sparse matrix methods to be used.
Constraint: laopt = 'F'${\mathbf{laopt}}=\text{'F'}$, 'B'$\text{'B'}$ or 'S'$\text{'S'}$.
Note: you are recommended to use the banded option when no coupled ODEs are present (i.e., ncode = 0${\mathbf{ncode}}=0$).
17: algopt(30$30$) – double array
May be set to control various options available in the integrator. If you wish to employ all the default options, then algopt(1)${\mathbf{algopt}}\left(1\right)$ should be set to 0.0$0.0$. Default values will also be used for any other elements of algopt set to zero. The permissible values, default values, and meanings are as follows:
algopt(1)${\mathbf{algopt}}\left(1\right)$
Selects the ODE integration method to be used. If algopt(1) = 1.0${\mathbf{algopt}}\left(1\right)=1.0$, a BDF method is used and if algopt(1) = 2.0${\mathbf{algopt}}\left(1\right)=2.0$, a Theta method is used. The default value is algopt(1) = 1.0${\mathbf{algopt}}\left(1\right)=1.0$.
If algopt(1) = 2.0${\mathbf{algopt}}\left(1\right)=2.0$, then algopt(i)${\mathbf{algopt}}\left(\mathit{i}\right)$, for i = 2,3,4$\mathit{i}=2,3,4$ are not used.
algopt(2)${\mathbf{algopt}}\left(2\right)$
Specifies the maximum order of the BDF integration formula to be used. algopt(2)${\mathbf{algopt}}\left(2\right)$ may be 1.0$1.0$, 2.0$2.0$, 3.0$3.0$, 4.0$4.0$ or 5.0$5.0$. The default value is algopt(2) = 5.0${\mathbf{algopt}}\left(2\right)=5.0$.
algopt(3)${\mathbf{algopt}}\left(3\right)$
Specifies what method is to be used to solve the system of nonlinear equations arising on each step of the BDF method. If algopt(3) = 1.0${\mathbf{algopt}}\left(3\right)=1.0$ a modified Newton iteration is used and if algopt(3) = 2.0${\mathbf{algopt}}\left(3\right)=2.0$ a functional iteration method is used. If functional iteration is selected and the integrator encounters difficulty, then there is an automatic switch to the modified Newton iteration. The default value is algopt(3) = 1.0${\mathbf{algopt}}\left(3\right)=1.0$.
algopt(4)${\mathbf{algopt}}\left(4\right)$
Specifies whether or not the Petzold error test is to be employed. The Petzold error test results in extra overhead but is more suitable when algebraic equations are present, such as Pi,j = 0.0${P}_{i,\mathit{j}}=0.0$, for j = 1,2,,npde$\mathit{j}=1,2,\dots ,{\mathbf{npde}}$, for some i$i$ or when there is no V.i(t)${\stackrel{.}{V}}_{i}\left(t\right)$ dependence in the coupled ODE system. If algopt(4) = 1.0${\mathbf{algopt}}\left(4\right)=1.0$, then the Petzold test is used. If algopt(4) = 2.0${\mathbf{algopt}}\left(4\right)=2.0$, then the Petzold test is not used. The default value is algopt(4) = 1.0${\mathbf{algopt}}\left(4\right)=1.0$.
If algopt(1) = 1.0${\mathbf{algopt}}\left(1\right)=1.0$, then algopt(i)${\mathbf{algopt}}\left(\mathit{i}\right)$, for i = 5,6,7$\mathit{i}=5,6,7$, are not used.
algopt(5)${\mathbf{algopt}}\left(5\right)$
Specifies the value of Theta to be used in the Theta integration method. 0.51algopt(5)0.99$0.51\le {\mathbf{algopt}}\left(5\right)\le 0.99$. The default value is algopt(5) = 0.55${\mathbf{algopt}}\left(5\right)=0.55$.
algopt(6)${\mathbf{algopt}}\left(6\right)$
Specifies what method is to be used to solve the system of nonlinear equations arising on each step of the Theta method. If algopt(6) = 1.0${\mathbf{algopt}}\left(6\right)=1.0$, a modified Newton iteration is used and if algopt(6) = 2.0${\mathbf{algopt}}\left(6\right)=2.0$, a functional iteration method is used. The default value is algopt(6) = 1.0${\mathbf{algopt}}\left(6\right)=1.0$.
algopt(7)${\mathbf{algopt}}\left(7\right)$
Specifies whether or not the integrator is allowed to switch automatically between modified Newton and functional iteration methods in order to be more efficient. If algopt(7) = 1.0${\mathbf{algopt}}\left(7\right)=1.0$, then switching is allowed and if algopt(7) = 2.0${\mathbf{algopt}}\left(7\right)=2.0$, then switching is not allowed. The default value is algopt(7) = 1.0${\mathbf{algopt}}\left(7\right)=1.0$.
algopt(11)${\mathbf{algopt}}\left(11\right)$
Specifies a point in the time direction, tcrit${t}_{\mathrm{crit}}$, beyond which integration must not be attempted. The use of tcrit${t}_{\mathrm{crit}}$ is described under the parameter itask. If algopt(1)0.0${\mathbf{algopt}}\left(1\right)\ne 0.0$, a value of 0.0$0.0$ for algopt(11)${\mathbf{algopt}}\left(11\right)$, say, should be specified even if itask subsequently specifies that tcrit${t}_{\mathrm{crit}}$ will not be used.
algopt(12)${\mathbf{algopt}}\left(12\right)$
Specifies the minimum absolute step size to be allowed in the time integration. If this option is not required, algopt(12)${\mathbf{algopt}}\left(12\right)$ should be set to 0.0$0.0$.
algopt(13)${\mathbf{algopt}}\left(13\right)$
Specifies the maximum absolute step size to be allowed in the time integration. If this option is not required, algopt(13)${\mathbf{algopt}}\left(13\right)$ should be set to 0.0$0.0$.
algopt(14)${\mathbf{algopt}}\left(14\right)$
Specifies the initial step size to be attempted by the integrator. If algopt(14) = 0.0${\mathbf{algopt}}\left(14\right)=0.0$, then the initial step size is calculated internally.
algopt(15)${\mathbf{algopt}}\left(15\right)$
Specifies the maximum number of steps to be attempted by the integrator in any one call. If algopt(15) = 0.0${\mathbf{algopt}}\left(15\right)=0.0$, then no limit is imposed.
algopt(23)${\mathbf{algopt}}\left(23\right)$
Specifies what method is to be used to solve the nonlinear equations at the initial point to initialize the values of U$U$, Ut${U}_{t}$, V$V$ and V.$\stackrel{.}{V}$. If algopt(23) = 1.0${\mathbf{algopt}}\left(23\right)=1.0$, a modified Newton iteration is used and if algopt(23) = 2.0${\mathbf{algopt}}\left(23\right)=2.0$, functional iteration is used. The default value is algopt(23) = 1.0${\mathbf{algopt}}\left(23\right)=1.0$.
algopt(29)${\mathbf{algopt}}\left(29\right)$ and algopt(30)${\mathbf{algopt}}\left(30\right)$ are used only for the sparse matrix algebra option, laopt = 'S'${\mathbf{laopt}}=\text{'S'}$.
algopt(29)${\mathbf{algopt}}\left(29\right)$
Governs the choice of pivots during the decomposition of the first Jacobian matrix. It should lie in the range 0.0 < algopt(29) < 1.0$0.0<{\mathbf{algopt}}\left(29\right)<1.0$, with smaller values biasing the algorithm towards maintaining sparsity at the expense of numerical stability. If algopt(29)${\mathbf{algopt}}\left(29\right)$ lies outside this range then the default value is used. If the functions regard the Jacobian matrix as numerically singular then increasing algopt(29)${\mathbf{algopt}}\left(29\right)$ towards 1.0$1.0$ may help, but at the cost of increased fill-in. The default value is algopt(29) = 0.1${\mathbf{algopt}}\left(29\right)=0.1$.
algopt(30)${\mathbf{algopt}}\left(30\right)$
Is used as a relative pivot threshold during subsequent Jacobian decompositions (see algopt(29)${\mathbf{algopt}}\left(29\right)$) below which an internal error is invoked. If algopt(30)${\mathbf{algopt}}\left(30\right)$ is greater than 1.0$1.0$ no check is made on the pivot size, and this may be a necessary option if the Jacobian is found to be numerically singular (see algopt(29)${\mathbf{algopt}}\left(29\right)$). The default value is algopt(30) = 0.0001${\mathbf{algopt}}\left(30\right)=0.0001$.
18: rsave(lrsave) – double array
lrsave, the dimension of the array, must satisfy the constraint
If laopt = 'F'${\mathbf{laopt}}=\text{'F'}$, lrsaveneqn × neqn + neqn + nwkres + lenode$\mathit{lrsave}\ge {\mathbf{neqn}}×{\mathbf{neqn}}+{\mathbf{neqn}}+\mathit{nwkres}+\mathit{lenode}$.
If laopt = 'B'${\mathbf{laopt}}=\text{'B'}$, lrsave(3 × mlu + 1) × neqn + nwkres + lenode$\mathit{lrsave}\ge \left(3×\mathit{mlu}+1\right)×{\mathbf{neqn}}+\mathit{nwkres}+\mathit{lenode}$.
If laopt = 'S'${\mathbf{laopt}}=\text{'S'}$, lrsave4 × neqn + 11 × neqn / 2 + 1 + nwkres + lenode$\mathit{lrsave}\ge 4×{\mathbf{neqn}}+11×{\mathbf{neqn}}/2+1+\mathit{nwkres}+\mathit{lenode}$.
Note: when laopt = 'S'${\mathbf{laopt}}=\text{'S'}$, the value of lrsave may be too small when supplied to the integrator. An estimate of the minimum size of lrsave is printed on the current error message unit if itrace > 0${\mathbf{itrace}}>0$ and the function returns with ${\mathbf{ifail}}={\mathbf{15}}$.
.
If ind = 0${\mathbf{ind}}=0$, rsave need not be set on entry.
If ind = 1${\mathbf{ind}}=1$, rsave must be unchanged from the previous call to the function because it contains required information about the iteration.
19: isave(lisave) – int64int32nag_int array
If ind = 0${\mathbf{ind}}=0$, isave need not be set on entry.
If ind = 1${\mathbf{ind}}=1$, isave must be unchanged from the previous call to the function because it contains required information about the iteration. In particular:
isave(1)${\mathbf{isave}}\left(1\right)$
Contains the number of steps taken in time.
isave(2)${\mathbf{isave}}\left(2\right)$
Contains the number of residual evaluations of the resulting ODE system used. One such evaluation involves computing the PDE functions at all the mesh points, as well as one evaluation of the functions in the boundary conditions.
isave(3)${\mathbf{isave}}\left(3\right)$
Contains the number of Jacobian evaluations performed by the time integrator.
isave(4)${\mathbf{isave}}\left(4\right)$
Contains the order of the last backward differentiation formula method used.
isave(5)${\mathbf{isave}}\left(5\right)$
Contains the number of Newton iterations performed by the time integrator. Each iteration involves an ODE residual evaluation followed by a back-substitution using the LU$LU$ decomposition of the Jacobian matrix.
Specifies the task to be performed by the ODE integrator.
itask = 1${\mathbf{itask}}=1$
Normal computation of output values u at t = tout$t={\mathbf{tout}}$.
itask = 2${\mathbf{itask}}=2$
One step and return.
itask = 3${\mathbf{itask}}=3$
Stop at first internal integration point at or beyond t = tout$t={\mathbf{tout}}$.
itask = 4${\mathbf{itask}}=4$
Normal computation of output values u at t = tout$t={\mathbf{tout}}$ but without overshooting t = tcrit$t={t}_{\mathrm{crit}}$ where tcrit${t}_{\mathrm{crit}}$ is described under the parameter algopt.
itask = 5${\mathbf{itask}}=5$
Take one step in the time direction and return, without passing tcrit${t}_{\mathrm{crit}}$, where tcrit${t}_{\mathrm{crit}}$ is described under the parameter algopt.
Constraint: itask = 1${\mathbf{itask}}=1$, 2$2$, 3$3$, 4$4$ or 5$5$.
21: itrace – int64int32nag_int scalar
The level of trace information required from nag_pde_1d_parab_dae_fd (d03ph) and the underlying ODE solver. itrace may take the value 1$-1$, 0$0$, 1$1$, 2$2$ or 3$3$.
itrace = 1${\mathbf{itrace}}=-1$
No output is generated.
itrace = 0${\mathbf{itrace}}=0$
Only warning messages from the PDE solver are printed on the current error message unit (see nag_file_set_unit_error (x04aa)).
itrace > 0${\mathbf{itrace}}>0$
Output from the underlying ODE solver is printed on the current advisory message unit (see nag_file_set_unit_advisory (x04ab)). This output contains details of Jacobian entries, the nonlinear iteration and the time integration during the computation of the ODE system.
If itrace < 1${\mathbf{itrace}}<-1$, then 1$-1$ is assumed and similarly if itrace > 3${\mathbf{itrace}}>3$, then 3$3$ is assumed.
The advisory messages are given in greater detail as itrace increases. You are advised to set itrace = 0${\mathbf{itrace}}=0$, unless you are experienced with sub-chapter D02M–N.
22: ind – int64int32nag_int scalar
Indicates whether this is a continuation call or a new integration.
ind = 0${\mathbf{ind}}=0$
Starts or restarts the integration in time.
ind = 1${\mathbf{ind}}=1$
Continues the integration after an earlier exit from the function. In this case, only the parameters tout and ifail should be reset between calls to nag_pde_1d_parab_dae_fd (d03ph).
Constraint: ind = 0${\mathbf{ind}}=0$ or 1$1$.
23: cwsav(10$10$) – cell array of strings
24: lwsav(100$100$) – logical array
25: iwsav(505$505$) – int64int32nag_int array
26: rwsav(1100$1100$) – double array
### Optional Input Parameters
1: npts – int64int32nag_int scalar
Default: The dimension of the array x.
The number of mesh points in the interval [a,b]$\left[a,b\right]$.
Constraint: npts3${\mathbf{npts}}\ge 3$.
2: nxi – int64int32nag_int scalar
Default: The dimension of the array xi.
The number of ODE/PDE coupling points.
Constraints:
• if ncode = 0${\mathbf{ncode}}=0$, nxi = 0${\mathbf{nxi}}=0$;
• if ncode > 0${\mathbf{ncode}}>0$, nxi0${\mathbf{nxi}}\ge 0$.
3: neqn – int64int32nag_int scalar
Default: The dimension of the array u.
The number of ODEs in the time direction.
Constraint: ${\mathbf{neqn}}={\mathbf{npde}}×{\mathbf{npts}}+{\mathbf{ncode}}$.
4: lisave – int64int32nag_int scalar
Default: The dimension of the array isave.
The dimension of the array isave as declared in the (sub)program from which nag_pde_1d_parab_dae_fd (d03ph) is called. Its size depends on the type of matrix algebra selected:
• if laopt = 'F'${\mathbf{laopt}}=\text{'F'}$, lisave24${\mathbf{lisave}}\ge 24$;
• if laopt = 'B'${\mathbf{laopt}}=\text{'B'}$, lisaveneqn + 24${\mathbf{lisave}}\ge {\mathbf{neqn}}+24$;
• if laopt = 'S'${\mathbf{laopt}}=\text{'S'}$, lisave25 × neqn + 24${\mathbf{lisave}}\ge 25×{\mathbf{neqn}}+24$.
Note: when using the sparse option, the value of lisave may be too small when supplied to the integrator. An estimate of the minimum size of lisave is printed on the current error message unit if itrace > 0${\mathbf{itrace}}>0$ and the function returns with ${\mathbf{ifail}}={\mathbf{15}}$.
5: user – Any MATLAB object
user is not used by nag_pde_1d_parab_dae_fd (d03ph), but is passed to pdedef, bndary and odedef. Note that for large objects it may be more efficient to use a global variable which is accessible from the m-files than to use user.
### Input Parameters Omitted from the MATLAB Interface
lrsave iuser ruser
### Output Parameters
1: ts – double scalar
The value of t$t$ corresponding to the solution values in u. Normally ${\mathbf{ts}}={\mathbf{tout}}$.
2: u(neqn) – double array
The computed solution Ui(xj,t)${U}_{\mathit{i}}\left({x}_{\mathit{j}},t\right)$, for i = 1,2,,npde$\mathit{i}=1,2,\dots ,{\mathbf{npde}}$ and j = 1,2,,npts$\mathit{j}=1,2,\dots ,{\mathbf{npts}}$, and Vk(t)${V}_{\mathit{k}}\left(t\right)$, for k = 1,2,,ncode$\mathit{k}=1,2,\dots ,{\mathbf{ncode}}$, evaluated at t = ts$t={\mathbf{ts}}$.
3: rsave(lrsave) – double array
If ind = 1${\mathbf{ind}}=1$, rsave must be unchanged from the previous call to the function because it contains required information about the iteration.
4: isave(lisave) – int64int32nag_int array
If ind = 1${\mathbf{ind}}=1$, isave must be unchanged from the previous call to the function because it contains required information about the iteration. In particular:
isave(1)${\mathbf{isave}}\left(1\right)$
Contains the number of steps taken in time.
isave(2)${\mathbf{isave}}\left(2\right)$
Contains the number of residual evaluations of the resulting ODE system used. One such evaluation involves computing the PDE functions at all the mesh points, as well as one evaluation of the functions in the boundary conditions.
isave(3)${\mathbf{isave}}\left(3\right)$
Contains the number of Jacobian evaluations performed by the time integrator.
isave(4)${\mathbf{isave}}\left(4\right)$
Contains the order of the last backward differentiation formula method used.
isave(5)${\mathbf{isave}}\left(5\right)$
Contains the number of Newton iterations performed by the time integrator. Each iteration involves an ODE residual evaluation followed by a back-substitution using the LU$LU$ decomposition of the Jacobian matrix.
5: ind – int64int32nag_int scalar
ind = 1${\mathbf{ind}}=1$.
6: user – Any MATLAB object
7: cwsav(10$10$) – cell array of strings
8: lwsav(100$100$) – logical array
9: iwsav(505$505$) – int64int32nag_int array
10: rwsav(1100$1100$) – double array
11: ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).
## Error Indicators and Warnings
Errors or warnings detected by the function:
Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.
ifail = 1${\mathbf{ifail}}=1$
On entry, ${\mathbf{tout}}-{\mathbf{ts}}$ is too small, or itask ≠ 1${\mathbf{itask}}\ne 1$, 2$2$, 3$3$, 4$4$ or 5$5$, or m ≠ 0${\mathbf{m}}\ne 0$, 1$1$ or 2$2$, or at least one of the coupling points defined in array xi is outside the interval [x(1),x(npts)${\mathbf{x}}\left(1\right),{\mathbf{x}}\left({\mathbf{npts}}\right)$], or m > 0${\mathbf{m}}>0$ and x(1) < 0.0${\mathbf{x}}\left(1\right)<0.0$, or npts < 3${\mathbf{npts}}<3$, or npde < 1${\mathbf{npde}}<1$, or norm ≠ 'A'${\mathbf{norm}}\ne \text{'A'}$ or 'M'$\text{'M'}$, or laopt ≠ 'F'${\mathbf{laopt}}\ne \text{'F'}$, 'B'$\text{'B'}$ or 'S'$\text{'S'}$, or itol ≠ 1${\mathbf{itol}}\ne 1$, 2$2$, 3$3$ or 4$4$, or ind ≠ 0${\mathbf{ind}}\ne 0$ or 1$1$, or mesh points x(i)${\mathbf{x}}\left(i\right)$ are badly ordered, or lrsave is too small, or lisave is too small, or ncode and nxi are incorrectly defined, or ${\mathbf{neqn}}\ne {\mathbf{npde}}×{\mathbf{npts}}+{\mathbf{ncode}}$, or either an element of rtol or atol < 0.0${\mathbf{atol}}<0.0$, or all the elements of rtol and atol are zero.
W ifail = 2${\mathbf{ifail}}=2$
The underlying ODE solver cannot make any further progress, with the values of atol and rtol, across the integration range from the current point t = ts$t={\mathbf{ts}}$. The components of u contain the computed values at the current point t = ts$t={\mathbf{ts}}$.
W ifail = 3${\mathbf{ifail}}=3$
In the underlying ODE solver, there were repeated error test failures on an attempted step, before completing the requested task, but the integration was successful as far as t = ts$t={\mathbf{ts}}$. The problem may have a singularity, or the error requirement may be inappropriate.
ifail = 4${\mathbf{ifail}}=4$
In setting up the ODE system, the internal initialization function was unable to initialize the derivative of the ODE system. This could be due to the fact that ires was repeatedly set to 3$3$ in at least pdedef, bndary or odedef, when the residual in the underlying ODE solver was being evaluated.
ifail = 5${\mathbf{ifail}}=5$
In solving the ODE system, a singular Jacobian has been encountered. You should check your problem formulation.
W ifail = 6${\mathbf{ifail}}=6$
When evaluating the residual in solving the ODE system, ires was set to 2$2$ in at least pdedef, bndary or odedef. Integration was successful as far as t = ts$t={\mathbf{ts}}$.
ifail = 7${\mathbf{ifail}}=7$
The values of atol and rtol are so small that the function is unable to start the integration in time.
ifail = 8${\mathbf{ifail}}=8$
In one of pdedef, bndary or odedef, ires was set to an invalid value.
ifail = 9${\mathbf{ifail}}=9$ (nag_ode_ivp_stiff_imp_revcom (d02nn))
A serious error has occurred in an internal call to the specified function. Check the problem specification and all parameters and array dimensions. Setting itrace = 1${\mathbf{itrace}}=1$ may provide more information. If the problem persists, contact NAG.
W ifail = 10${\mathbf{ifail}}=10$
The required task has been completed, but it is estimated that a small change in atol and rtol is unlikely to produce any change in the computed solution. (Only applies when you are not operating in one step mode, that is when itask2${\mathbf{itask}}\ne 2$ or 5$5$.)
ifail = 11${\mathbf{ifail}}=11$
An error occurred during Jacobian formulation of the ODE system (a more detailed error description may be directed to the current error message unit). If using the sparse matrix algebra option, the values of algopt(29)${\mathbf{algopt}}\left(29\right)$ and algopt(30)${\mathbf{algopt}}\left(30\right)$ may be inappropriate.
ifail = 12${\mathbf{ifail}}=12$
In solving the ODE system, the maximum number of steps specified in algopt(15)${\mathbf{algopt}}\left(15\right)$ have been taken.
W ifail = 13${\mathbf{ifail}}=13$
Some error weights wi${w}_{i}$ became zero during the time integration (see the description of itol). Pure relative error control (atol(i) = 0.0${\mathbf{atol}}\left(i\right)=0.0$) was requested on a variable (the i$i$th) which has become zero. The integration was successful as far as t = ts$t={\mathbf{ts}}$.
ifail = 14${\mathbf{ifail}}=14$
The flux function Ri${R}_{i}$ was detected as depending on time derivatives, which is not permissible.
ifail = 15${\mathbf{ifail}}=15$
When using the sparse option, the value of lisave or lrsave was not sufficient (more detailed information may be directed to the current error message unit).
## Accuracy
nag_pde_1d_parab_dae_fd (d03ph) controls the accuracy of the integration in the time direction but not the accuracy of the approximation in space. The spatial accuracy depends on both the number of mesh points and on their distribution in space. In the time integration only the local error over a single step is controlled and so the accuracy over a number of steps cannot be guaranteed. You should therefore test the effect of varying the accuracy parameters atol and rtol.
The parameter specification allows you to include equations with only first-order derivatives in the space direction but there is no guarantee that the method of integration will be satisfactory for such systems. The position and nature of the boundary conditions in particular are critical in defining a stable problem. It may be advisable in such cases to reduce the whole system to first-order and to use the Keller box scheme function nag_pde_1d_parab_dae_keller (d03pk).
The time taken depends on the complexity of the parabolic system and on the accuracy requested. For a given system and a fixed accuracy it is approximately proportional to neqn.
## Example
```function nag_pde_1d_parab_dae_fd_example
npde = int64(1);
m = int64(0);
ts = 0.0001;
tout = 0.2;
u = [0.0001000050001666708;
9.500451264289925e-05;
9.000405012150273e-05;
8.500361260235637e-05;
8.000320008533506e-05;
7.500281257031378e-05;
7.000245005716764e-05;
6.500211254577162e-05;
6.000180003600051e-05;
5.500151252772951e-05;
5.000125002083361e-05;
4.50010125151877e-05;
4.000080001066676e-05;
3.50006125071459e-05;
3.00004500045e-05;
2.500031250260415e-05;
2.000020000133336e-05;
1.500011250056251e-05;
1.000005000016669e-05;
5.000012500020888e-06;
0;
0.0001];
x = [0;
0.05;
0.1;
0.15;
0.2;
0.25;
0.3;
0.35;
0.4;
0.45;
0.5;
0.55;
0.6;
0.65;
0.7;
0.75;
0.8;
0.85;
0.9;
0.95;
1];
ncode = int64(1);
xi = [1];
rtol = [0.0001];
atol = [0.0001];
itol = int64(1);
normtype = 'A';
laopt = 'F';
algopt = [0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0];
rsave = zeros(994, 1);
isave = zeros(24, 1, 'int64');
itrace = int64(0);
ind = int64(0);
cwsav = {''; ''; ''; ''; ''; ''; ''; ''; ''; ''};
lwsav = false(100, 1);
iwsav = zeros(505, 1, 'int64');
rwsav = zeros(1100, 1);
[tsOut, uOut, rsaveOut, isaveOut, indOut, user, ...
cwsavOut, lwsavOut, iwsavOut, rwsavOut, ifail] = ...
nag_pde_1d_parab_dae_fd(npde, m, ts, tout, @pdedef, @bndary, u, x, ncode, ...
@odedef, xi, rtol, atol, itol, normtype, laopt, algopt, ...
rsave, isave, itask, itrace, ind, cwsav, lwsav, iwsav, rwsav);
tsOut, uOut, indOut, ifail
function [p, q, r, ires, user] = pdedef(npde, t, x, u, ux, ncode, v, vdot, ires, user)
p = zeros(npde, npde);
q = zeros(npde, 1);
r = zeros(npde, 1);
p(1,1) = v(1)*v(1);
r(1) = ux(1);
q(1) = -x*ux(1)*v(1)*vdot(1);
function [beta, gamma, ires, user] = ...
bndary(npde, t, u, ux, ncode, v, vdot, ibnd, ires, user)
beta = zeros(npde, 1);
gamma = zeros(npde, 1);
beta(1) = 1.0d0;
if (ibnd == 0)
gamma(1) = -v(1)*exp(t);
else
gamma(1) = -v(1)*vdot(1);
end
function [f, ires, user] = ...
odedef(npde, t, ncode, v, vdot, nxi, xi, ucp, ucpx, rcp, ucpt, ucptx, ires, user)
f = zeros(ncode,1);
if (ires == 1)
f(1) = vdot(1) - v(1)*ucp(1,1) - ucpx(1,1) - 1.0d0 - t;
elseif (ires == -1)
f(1) = vdot(1);
end
```
```
tsOut =
0.2000
uOut =
0.2221
0.2099
0.1979
0.1860
0.1742
0.1625
0.1510
0.1396
0.1282
0.1170
0.1059
0.0949
0.0840
0.0733
0.0626
0.0520
0.0416
0.0312
0.0210
0.0109
0.0008
0.2000
indOut =
1
ifail =
0
```
```function d03ph_example
npde = int64(1);
m = int64(0);
ts = 0.0001;
tout = 0.2;
u = [0.0001000050001666708;
9.500451264289925e-05;
9.000405012150273e-05;
8.500361260235637e-05;
8.000320008533506e-05;
7.500281257031378e-05;
7.000245005716764e-05;
6.500211254577162e-05;
6.000180003600051e-05;
5.500151252772951e-05;
5.000125002083361e-05;
4.50010125151877e-05;
4.000080001066676e-05;
3.50006125071459e-05;
3.00004500045e-05;
2.500031250260415e-05;
2.000020000133336e-05;
1.500011250056251e-05;
1.000005000016669e-05;
5.000012500020888e-06;
0;
0.0001];
x = [0;
0.05;
0.1;
0.15;
0.2;
0.25;
0.3;
0.35;
0.4;
0.45;
0.5;
0.55;
0.6;
0.65;
0.7;
0.75;
0.8;
0.85;
0.9;
0.95;
1];
ncode = int64(1);
xi = [1];
rtol = [0.0001];
atol = [0.0001];
itol = int64(1);
normtype = 'A';
laopt = 'F';
algopt = [0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0];
rsave = zeros(994, 1);
isave = zeros(24, 1, 'int64');
itrace = int64(0);
ind = int64(0);
cwsav = {''; ''; ''; ''; ''; ''; ''; ''; ''; ''};
lwsav = false(100, 1);
iwsav = zeros(505, 1, 'int64');
rwsav = zeros(1100, 1);
[tsOut, uOut, rsaveOut, isaveOut, indOut, user, ...
cwsavOut, lwsavOut, iwsavOut, rwsavOut, ifail] = ...
d03ph(npde, m, ts, tout, @pdedef, @bndary, u, x, ncode, ...
@odedef, xi, rtol, atol, itol, normtype, laopt, algopt, ...
rsave, isave, itask, itrace, ind, cwsav, lwsav, iwsav, rwsav);
tsOut, uOut, indOut, ifail
function [p, q, r, ires, user] = pdedef(npde, t, x, u, ux, ncode, v, vdot, ires, user)
p = zeros(npde, npde);
q = zeros(npde, 1);
r = zeros(npde, 1);
p(1,1) = v(1)*v(1);
r(1) = ux(1);
q(1) = -x*ux(1)*v(1)*vdot(1);
function [beta, gamma, ires, user] = ...
bndary(npde, t, u, ux, ncode, v, vdot, ibnd, ires, user)
beta = zeros(npde, 1);
gamma = zeros(npde, 1);
beta(1) = 1.0d0;
if (ibnd == 0)
gamma(1) = -v(1)*exp(t);
else
gamma(1) = -v(1)*vdot(1);
end
function [f, ires, user] = ...
odedef(npde, t, ncode, v, vdot, nxi, xi, ucp, ucpx, rcp, ucpt, ucptx, ires, user)
f = zeros(ncode,1);
if (ires == 1)
f(1) = vdot(1) - v(1)*ucp(1,1) - ucpx(1,1) - 1.0d0 - t;
elseif (ires == -1)
f(1) = vdot(1);
end
```
```
tsOut =
0.2000
uOut =
0.2221
0.2099
0.1979
0.1860
0.1742
0.1625
0.1510
0.1396
0.1282
0.1170
0.1059
0.0949
0.0840
0.0733
0.0626
0.0520
0.0416
0.0312
0.0210
0.0109
0.0008
0.2000
indOut =
1
ifail =
0
``` | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 571, "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": 0.9161684513092041, "perplexity": 4858.348242341265}, "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-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00646-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://mathhelpforum.com/higher-math/201362-integration-product-e-variable-exponent-trigonometric-function.html | # Thread: Integration of Product of e, with variable exponent, and a trigonometric function
1. ## Integration of Product of e, with variable exponent, and a trigonometric function
I have been asked to find the definite integral, as described above, of a product of e, with a variable exponent, and a trigonometric function; an example would be the integral of e^x.cos(x). I have tried to use the integration by parts, or integration by reverse product rule differentiation (integral of udv/dx = uv - integral of vdu/dx), but have almost immediately realised that because both the differentiation and integration either of e with a variable exponent, or a trigonomnetric function, does not gradually cancel out the variables but increases the complexity of the function, the integral will simply increase to an infinite length. I therefore assumed this technique to be incorrect, and I want to ask if anyone can help me with the proper technique? Any help would be much appreciated!
2. ## Re: Integration of Product of e, with variable exponent, and a trigonometric function
Hello, Chuzzle!
I have been asked to find the definite integral, as described above, of a product of e, with a variable exponent,
and a trigonometric function. .An example would be: . $\int\!e^x\cos x\,dx$
Evidently, you have not been shown the procedure for this type of problem.
We have: . $I \:=\:\int\!e^x\cos x\,dx$
By parts: . $\begin{Bmatrix} u &=& e^x && dv &=& \cos x\,dx \\ du &=& e^x\,dx && v &=& \sin x \end{Bmatrix}$
Then: . $I \;=\;e^x\sinx - \int\!e^x\sin x\,dx$
This integral is as "bad" as the original integral, but watch this!
By parts again: . $\begin{Bmatrix}u &=& e^x && dv &=& \sin x\,dx \\ du &=& e^x\,dx && v &=&\text{-}\cos x \end{Bmatrix}$
We have: . . $I \;=\;e^x\sin x - \left[\text{-}e^x\cos x + \int\!e^x\cos x\,dx\right]$
. . . . . . . . . $I \;=\;e^x\sin x + e^x\cos x - \underbrace{\int\!e^x\cos x\,dx}_{\text{This is }I} \,+\;C$
. . . . . . . . . $I \;=\;e^x(\sin x + \cos x) - I + C$
. . . . . . . . $2I \;=\;e^x(\sin x + \cos x) + C$
Therefore: . $I \;=\;\tfrac{1}{2}e^x(\sin x + \cos x) + C$
3. ## Re: Integration of Product of e, with variable exponent, and a trigonometric function
Thanks so much Soroban! I would never have considered that if the integral is expanded out to produce extra terms, the second integral of v(du/dx) in the supposedly infinite chain - if you follow me - would be a cosine and therefore the original integral or a factor of it, which can then be substituted; however, I would also never have used v = - cos x for that second integration of v(du/dx), that was true genius. Thanks again for taking the time to help me out, I really appreciate it, you are a true legend made of win. Peace.
4. ## Re: Integration of Product of e, with variable exponent, and a trigonometric function
Scratch that, only just remembered that the integral of sin x is - cos x . Derp derp derp, that tends to happen at 1 AM. Thanks again! | {"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": 10, "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": 0.9872445464134216, "perplexity": 500.5760940066192}, "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-2017-26/segments/1498128320362.97/warc/CC-MAIN-20170624221310-20170625001310-00345.warc.gz"} |
http://www.physicsforums.com/showpost.php?p=1146663&postcount=8 | View Single Post
we already know the length of the arm (5m). Yeah the weights represent forces vertically down one at the end of the arm (the mass) and the other half way through the arm (weight of the arm). but i still down understand how to work out the weather its cos or sin | {"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": 0.8355530500411987, "perplexity": 502.8696336423957}, "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/1368707436332/warc/CC-MAIN-20130516123036-00047-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://techie-buzz.com/science/negative-temperature-quantum-gas.html | # Achieved: Negative Temperature For A Quantum Gas!
There exists nothing as negative temperature (in Kelvin scale), at least not in ‘normal’ systems; this is something we learn in physics. This is a scale devised by Lord Kelvin (and hence the name of the unit) and according to this scale, there can be no negative value of temperature. Temperature was thought to be the measure of the energy of the particles in a system. While this isn’t untrue, the modern definition of temperature is broader.
For a system with energy levels, temperature is a measure of the probability of the occupation of an energy level with respect to energy. As we access more and more energetic states, the probability of occupation generally decreases and this leads to a positive temperature state. Now, imagine a system having the reverse configuration, like the higher energy states being more populated than the lower energy states. This kind of system will then have a negative temperature.
Try and note that negative temperature states are extremely rare and do not occur in our day-to-day lives. Particles will always like to occupy the lower energy states first and then go for the higher energy ones. In a room of air, you’ll always find more molecules with very low energies than molecules with very high energies. This is because the energy has a lower limit, viz E=0. The lowest energy possible is if the molecule were completely static. However, there is no upper limit.
### Interesting systems
But if you did have an upper limit, things would be interesting! Say there is an upper limit of the energy spectrum, meaning that no particle can have any energy beyond this limit (just like no particle could go below the lower limit). Now, under certain conditions, the system would occupy the upper energy levels more than the lower ones! This causes an inversion of the sign of temperature, according to the modern definition. Thus, we have negative temperature!
So what’s the big deal, you ask? Negative temperatures have been known for magnetic systems (which have an upper and a lower limit), but we haven’t known of any system with motional degrees of freedom (like an atom free to move in 3 dimensions) to have such an energy spectrum.
### The Experiment
Ulrich Schneider, a physicist at the Ludwig Maximilian University in Munich, Germany and his team created an ultra-cold quantum gas made up of potassium atoms and they confined these atoms to a lattice (i.e. a crystal like arrangement). At positive temperatures, the atoms repelled each other, but the team was able to flip the magnetic field fast enough for the atoms to start attracting each other. This also flips the sign of the temperature. Explains Prof. Schneider:
This suddenly shifts the atoms from their most stable, lowest-energy state to the highest possible energy state, before they can react. It’s like walking through a valley, then instantly finding yourself on the mountain peak.
The temperature measured was a billionths of a degree below absolute zero! Wolfgang Ketterle, Nobel Laureate, called this an ‘experimental Tour de Force’. It truly is! | {"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": 0.8805939555168152, "perplexity": 530.9145815850568}, "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/1575540527010.70/warc/CC-MAIN-20191210070602-20191210094602-00265.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/117651-hypergeometric-distribution.html | ## Hypergeometric distribution!
Hello guys,
I've been working on this problem for a while, but it'd be a lot easier if I had an equation to work with.
Here's the deal; the problem is hypergeometric.
pop=N=400
#of successes within pop=X=40
N-X=360
sample=n=64
# of successes within samples=x
The question asks the probability that p-hat (of sample successes) exceeds 0.20
I just don't have the right formulas for this... I was able to get that for p-hat to equal 20, x=12.8; and I could find the probability for that specific value using the combinations formula... but the question is asking for the probability that p-hat is greater than or equal to .2, not just equal to. Also, I'm pretty sure that this is the same as the probability that x is greater than or equal to 12.8.
Any help would be much appreciated as I've hit a brick wall! | {"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": 0.8037598729133606, "perplexity": 310.65932829219656}, "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-2018-17/segments/1524125945272.41/warc/CC-MAIN-20180421164646-20180421184646-00473.warc.gz"} |
http://www.newton.ac.uk/programmes/RMA/seminars/2004062811001.html | # RMA
## Seminar
### Long time propagation of coherent states under perturbed cat map dynamics
De Bievre, S (Lille)
Monday 28 June 2004, 11:00-11:40
Seminar Room 1, Newton Institute
#### Abstract
I will describe recent work with J.M. Bouclet (Lille) on the propagation of coherent states up to times logarithmic in hbar under quantized perturbed cat maps. We show that, for long enough times, the quantum evolution equidistributes the coherent states throughout phase space. The proof requires a good control on the error term in the Egorov theorem on the one hand and on the classical rate of mixing on the other. This generalizes to perturbed cat maps a result obtained previously with F. Bonechi. | {"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": 0.9097702503204346, "perplexity": 2092.7540342670072}, "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-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00522-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://www.ni.com/documentation/en/labview-comms/1.0/mrd-node-ref/sine-and-cosine/ | Computes both the sine and cosine of a specified value (x), where x is in radians.
Use this node only when you need both results.
x
An input to this operation.
This input supports scalar numbers and fixed-size 1-dimensional arrays of numbers.
Data Type Changes on FPGA
sin
Result of the operation.
This output assumes the same numeric representation as x. When x is of the form x = a + b i, that is, when x is complex, the following equation defines sin:
$\mathrm{sin}\left(x\right)=\mathrm{sin}\left(a\right)*\mathrm{cosh}\left(b\right)+i\left(\mathrm{cos}\left(a\right)*\mathrm{sinh}\left(b\right)\right)$
Data Type Changes on FPGA
cos
Result of the operation.
This output assumes the same numeric representation as x. When x is of the form x = a + b i, that is, when x is complex, the following equation defines cos:
$\mathrm{cos}\left(x\right)=\mathrm{cos}\left(a\right)*\mathrm{cosh}\left(b\right)+i\left(-\mathrm{sin}\left(a\right)*\mathrm{sinh}\left(b\right)\right)$
Data Type Changes on FPGA | {"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": 0.9697117805480957, "perplexity": 1164.623061161733}, "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-2018-47/segments/1542039745015.71/warc/CC-MAIN-20181119023120-20181119045120-00274.warc.gz"} |
http://math.stackexchange.com/questions/456744/can-pq-1-equiv-1-pmod-q3-for-primes-pq | # Can $p^{q-1}\equiv 1 \pmod {q^3}$ for primes $p<q$?
For prime $q$ can it be that $$p^{q-1}\equiv 1 \pmod{q^k}$$ for some prime $p<q$ and for $k\ge 3$?
There doesn't seem to be a case with $k=3$ and $q<90000$, and I also checked for small solutions with $3<k\le 20$ and found none.
If we remove the condition $p<q$ then there are always solutions, e.g. $15441^{16}\equiv 1 \pmod{17^5}$. Also for $k=2$ there are many, e.g. $71^{330} \equiv 1 \pmod {331^2}$.
-
I don't know. Agree about removal of condition $p\lt q$, use Hensel lifting and the Dirichlet theorem on primes in arithmetic progressions. – André Nicolas Jul 31 '13 at 21:29
Short Pari/GP command line for probing more $q$ (adjust the range for $q$): k=3;forprime(q=3,1000,g=znprimroot(q^k)^(q^(k-1));h=g;for(j=1,q-2,p=lift(h);if(p<q && ispseudoprime(p), print(p," ",q));h*=g)) – ccorn Aug 1 '13 at 1:23
@Zander: Do you really mean $3< k\leq 20$ or $3< p \leq 20$? Testing higher $k$ when nothing is found for $k=3$ seems to make no sense to me. – ccorn Aug 1 '13 at 2:01
If the requirement "$p$ prime" is dropped, there is precisely one $1<p<q\leq 100000$ with prime $q$, namely $(p,q)=(68,113)$ with $k=3$. – ccorn Aug 1 '13 at 2:24
Assuming (without proof) the heuristics associated with Daniel Fischers argument, I figure that, given $q^k$, the probabilistic density of suitable $p$ is about $\frac{1}{q^{k-2}\log q}$. For fixed $k>3$ this indicates that the number of suitable $(p,q^k)$ pairs should be finite. For $k=3$ an infinite number of solutions seems "not implausible". Still searching, yet nothing found for $q$ up to $347000$. – ccorn Aug 1 '13 at 12:34
Let $w>1$ be any integer and let $q$ be an odd prime and $w^{q-1}$ $\equiv 1 \pmod {q^3}$. Let v be a primitive root mod $q^3$ where $v^h$ $\equiv w \pmod {q^3}$. So $v^{h(q-1)}$ $\equiv 1\pmod {q^3}$. Therefore h=$q^2 k$ ; k >= 1. Assume k> 1 , then $w^{(q-1)/k}$ $\equiv 1\pmod {q^3}$ ; $v^{q^2 k-k}$ $\equiv(w/v^k) \pmod {q^3}$ , so $v^{(q^2 k -k)(q^2)}$ $\equiv 1 \pmod {q^3}$ ,therefore $(w/v^k)^{q^2}$ $\equiv 1\pmod {q^3}$. If the order of w mod $q^3$ is M then given $(w/v)^{q^2 M}$ $\equiv 1 \pmod {q^3}$ ; $v^{q^2 M}$ $\equiv 1 \pmod {q^3}$. Yet this implies M = (q-1). Then the order of w mod $q^3$ is not <(q-1) contradiction. So k = 1. And $v^{q^2}$ $\equiv w \pmod q^3$. The order of w mod $q^3$ is (q-1). If w = p a prime < q then $p^{q-1}$ $\equiv 1 \pmod {q^3}$ where (q-1) is the order of p. p = (q-v); $(q-v)^q$ $\equiv(q-v)\pmod {q^3}$. So ($q^2$ $v^{q-1}$ -$v^q$) $\equiv(q-v)\pmod {q^3}$. Therefore $v^{q-1}$ ($q^2$-v) $\equiv (q-v)\pmod{q^3}$ ; $(-v q)\equiv (q^2-v q)\pmod{q^3}$ ; $q^2 \equiv 0 \pmod{q^3}$ Contradiction , so if p < q the order of p mod $q^3$ can not be (q-1)
Moreover, where did $w^{(q^4+1)/(w+1)}$ come from? You aren't asserting $$q^4+1=(q+1)(q^3-q^2+q-1)$$ are you? – Gerry Myerson Aug 17 '14 at 2:17
Firstly, I think you mean $\frac{q^5+1}{q+1}$, not $\frac{q^5+1}{w+1}$. Secondly, I think you mean $q^4-q^3+q^2-q+1=T$, since that is $\frac{q^5+1}{q+1}$. Thirdly, $w^T\equiv w$ mod $q^3$: how do you get that to be $\equiv 1$? Lastly, how are $u,v,y$ relevant? – whacka Aug 22 '14 at 5:56 | {"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": 0.9708738327026367, "perplexity": 449.24169039232436}, "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/1454701171770.2/warc/CC-MAIN-20160205193931-00073-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://connection.ebscohost.com/c/articles/47955915/new-extremal-domains-first-eigenvalue-laplacian-flat-tori | TITLE
# New extremal domains for the first eigenvalue of the Laplacian in flat tori
AUTHOR(S)
Sicbaldi, Pieralberto
PUB. DATE
March 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Mar2010, Vol. 37 Issue 3/4, p329
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We prove the existence of nontrivial compact extremal domains for the first eigenvalue of the Laplacian in manifolds $${\mathbb{R}^{n}\times \mathbb{R}{/}T\, \mathbb{Z}}$$ with flat metric, for some T > 0. These domains are close to the cylinder-type domain $${B_1 \times \mathbb{R}{/}T\, \mathbb{Z}}$$, where B1 is the unit ball in $${\mathbb{R}^{n}}$$, they are invariant by rotation with respect to the vertical axe, and are not invariant by vertical translations. Such domains can be extended by periodicity to nontrivial and noncompact domains in Euclidean spaces whose first eigenfunction of the Laplacian with 0 Dirichlet boundary condition has also constant Neumann data at the boundary.
ACCESSION #
47955915
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Share | {"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": 0.9458357691764832, "perplexity": 1665.4714213532125}, "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-2017-43/segments/1508187823168.74/warc/CC-MAIN-20171018233539-20171019013539-00492.warc.gz"} |
https://joshnguyen.net/publication/2021-08-FedAA | Accelerating Federated Edge Learning
Published in IEEE Communications Letters, 2021
Recommended citation: Tuan Dung Nguyen, Amir R. Balef, Canh T. Dinh, Nguyen H. Tran, Duy T. Ngo, Tuan Anh Le, and Phuong L. Vo. 2021. Accelerating Federated Edge Learning. IEEE Communications Letters, 25(10):3282–3286.
[Paper]
Abstract: Transferring large models in federated learning (FL) networks is often hindered by clients’ limited bandwidth. We propose FedAA , an FL algorithm which achieves fast convergence by exploiting the regularized Anderson acceleration (AA) on the global level. First, we demonstrate that FL can benefit from acceleration methods in numerical analysis. Second, FedAA improves the convergence rate for quadratic losses and improves the empirical performance for smooth and strongly convex objectives, compared to FedAvg, an FL algorithm using gradient descent (GD) local updates. Experimental results demonstrate that employing AA can significantly improve the performance of FedAvg, even when the objective is non-convex. | {"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": 0.9354042410850525, "perplexity": 4085.588523595724}, "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-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00221.warc.gz"} |
https://www.physicsforums.com/threads/legrendre-integral-using-rodriquez-formula.836824/ | # Legrendre integral using Rodriquez' formula
1. Oct 9, 2015
### ognik
1. The problem statement, all variables and given/known data
Show that $$\int_{-1}^{1}{x}^{n}P_n(x) \,dx= \frac{2^{n+1}n!n!}{(2n+1)}!$$
(Side question: this is the orthogonality integral= 0 when the functions inside the integrand are orthogonal; but I have seen hints that sometimes the Integral is NOT=0 even though the functions are orthogonal - would appreciate confirmation and understanding of that please?)
2. Relevant equations
Hint: Use Rodriquez formula $$P_n(x)=\frac{1}{2n}\frac{1}{n!} \frac{d ^{n}({x}^{2}-1)^n} {dx^{n}}$$
3. The attempt at a solution
(NB: this section is new to me, my aim is to do & fully understand every problem in the book, but I have deadlines -so need some help where I get a bit bogged down. Please be vigilant as to where I might have understood some theory wrong or missed something)
------------
To simplify the workings, the limits are [-1,1] throughout, I kept aside this term in n for now: $$\frac{1}{2n}\frac{1}{n!}; \:and\:also\:let\: (x^2-1) = f$$
Then, by parts, $$\int {x}^{n} \frac{ d{^{n}{f}^n}} {{dx}^{n}} dx = {x}^{n} \frac{ d{^{n-1}{f}^n}} {{dx}^{n-1}} |^{1}_{-1} - \int n{x}^{n-1} \frac{ d{^{n-1}{f}^n}} {{dx}^{n-1}} dx$$ - and repeating by parts n times. I then argue as follows (and would appreciate improvements/corrections as appropriate)
1st term (outside integral): After doing 3 Successive differentiations of $$\frac{ d{^{n-1}{f}^n}} {{dx}^{n-1}}, - \: ALL \:have \:a \: ({x}^{2}-1) \: term \:in \:them =(x+1)(x-1)$$
Therefore I claim all the following terms over [-1,1] will vanish, ie $$\frac{d{^{i}{f}^n}}{{x}^{i}} =0$$
I also claim that further integration by parts will always produce a 1st term (outside the integral) which will include $$\frac{d{^{i}{f}^n}}{{x}^{i}}$$, and to which the above claim applies. So, comfortable that the 1st(outer terms) will always vanish through repeated integration by parts, the problem is simplified to the sequence of the integral part only.
---------------------
The Integrand will always have 2 parts, A) and B):
$$A) x^n$$ This part is repeatedly differentiated with each integration (always making it the 'u' term for parts). Therefore after n integrations it becomes $$n!x^{0}=n!$$
$$B) \frac {d{^{n}{f^n}}} {{dx}^{n}}$$ Because this is always 'dv' by parts, each successive integral just produces a reduced derivative, until finally we are left with just $$f^n$$
-----------------------
So putting it all together, I can find $$\frac{1}{2n}\frac{1}{n!} n! \int_{-1}^{1}f^n \,dx = \frac{1}{2n} \frac{{(x^2-1)}^{n}}{n(n+1)}|^1_{-1}$$
Tantalisingly close, but after checking a few times, I still can't see what I have done wrong above?
2. Oct 10, 2015
### MisterX
Your anti-derivative does not seem correct to me. For example $$\int f^1dx = \int (x^2 - 1)dx = \frac{1}{3}x^3 - x + C$$ Unless I am missing something, anti-derivative of $f^n$ cannot be written as $(x^2 -1)^n*g(n)$ the way you seem to have done.
3. Oct 11, 2015
### ognik
Probably not, I think I used parts, something like splitting the integrand into $$(x^2-1)^{n-1}(x^2-1)$$
Anyway, I have subsequently stumbled upon the 'beta function' with which I made more progress, rewriting my eqtn as $$\frac{1}{2n} [2\int_0^1(1-x^2)^n dx$$
Then the part inside the [] should = $$B(\frac{1}{2}, n+1)$$
But, not having encountered Bet fanction before, I am struggling to turn this Beta function into $$\frac {2^{n+1}n!n!}{(2n+1)!}$$
(PS: Is there a way to write latex inline? ie not using ) | {"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": 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": 0.9329401254653931, "perplexity": 1119.8941601716292}, "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-2017-51/segments/1512948587496.62/warc/CC-MAIN-20171216084601-20171216110601-00091.warc.gz"} |
https://www.physicsforums.com/threads/capacitor-charging.890713/ | # Homework Help: Capacitor charging
1. Oct 25, 2016
### Biker
1. The problem statement, all variables and given/known data
In the following diagram, The voltmeter reading is 5 volts when the switch K is open and C1 is not charged.
When you close K calculate the following:
2- Charge of each capacitor
3- Voltage of each capacitor
2. Relevant equations
Usual electronics equation
3. The attempt at a solution
Well, I was looking through my friend's private tutor papers and I found this question. My solution is different that his so I thought I could bring it here so someone can check it and see if I am missing something.
C1 is not charged thus it doesn't contribute to the voltage of the voltmeter (assuming actual current flowing or assuming it is negligible) so the voltage reading is purely C2's voltage
Now instead of assuming Q as transferred charged, you could choose a much simpler way.
C1 and C3 (it didnt say if C3 is charged so I assumed it is not) are in series then the resultant is parallel with C2
So
$\frac{Q_t}{C_{eq}} = V_{after~opening~ the switch}$
you get $V = 4.25 volts$
The Charge for any of C1 and C3 capacitors is the voltage times the equivalent capacitance of C1 and C3 which is in series
$V ~ ( \frac{1}{C_1} + \frac{1}{C_3} ) = Q_{3 ~ or ~ 1}$
$Q = 9 uC$
the charge for C2 is simply
$Q_2 = C_2 V$
$Q_2 = 51 uC$
Now the first requirement needs the voltmeter reading which is:
$V = V_{C_2} - V_{C_1}$
$V = 4.25 - Q/C_1$
$V = 4.25 - 2.25$
$V = 2$ which he found to be the same
the rest is straight forward.
For the charges and voltages, he got it different because he assumed that C2 and C1 are connected in series which is wrong because they definitely don't have the same charge
2. Oct 25, 2016
### TSny
Your method of solution looks correct to me. Your answers agree with what I got by first solving for the charge q that leaves C2 when the switch is closed. Your solution gets to the answer quicker!
3. Oct 25, 2016
### Biker
Thank you TSny :).
I usually use that method to derive if I could treat those capacitor is a parallel or series way. Sometimes it can get complicated so I just use the Q method :D
Anyway, Thank you again. Much appreciated
4. Oct 25, 2016
### haruspex
I would have thought that either the diagram is labelled wrongly or the given statement that C1 starts uncharged is a typo; should say C3. A voltmeter works by allowing a trickle current, so the two in series must both be charged.
On that basis, the two in series have combined capacitance of 3uF, and including the one in parallel we get 7.5uF. The final voltage is therefore (3/7.5)5=2. I think that was your argument, but I did not find it very clear.
5. Oct 25, 2016
### TSny
I worried about the effect of the voltmeter, too. I ended up assuming that the voltmeter had no influence. I interpreted it as just a way to say that the total potential difference in going from the left side of C2 to the right side of C1 is 5 V when C1 is uncharged and the switch is open. That's a weird way to just say that initially C2 has 5 V while the other two caps are uncharged.
6. Oct 26, 2016
### Biker
Doesn't the ideal voltmeter have infinite resistance? Which means a negligible amount of charges gets transfered from C2 to C1
I don't know about C1 being charged or no but I clearly remember that the question statement said C1 is not charged but It didnt mention C3
Even if we assume C1 is charged with certain charge Q and C3 isn't, we can't be sure that $Q_2 = Q_1$ so that we can take it as series unless the question states that they perhaps were connected to the same voltage source initially or providing that they have the same charge
Last edited: Oct 26, 2016
7. Oct 26, 2016
### haruspex
No real voltmeter has infinite resistance, just very high, which means the current will be very small. How much charge is transferred depends on how long the voltmeter is connected. That said, I think we have to assume no significant charge is leaking through, otherwise it would eventually be reading 0. The two capacitors would have equal and opposite voltages.
I don't think it matters. All we need to know is that the initial voltage reading is 5V. How the charge is arranged on those two capacitors is unimportant.
I suggest the question should be saying that the third capacitor starts with no charge; it's a misprint in either the text or the diagram.
8. Oct 26, 2016
### Biker
Yea I get that no real voltmeter has infinite resistance that is why I said ideal. Also it would be a bit difficult to calculate at least for my level.
Yes, I derived that just few secs ago. Assuming Q charge transfer method or Using the method you gave me above they both yield in the same variables.
But just a question, We can't find the B and C part of the question because we have no knowledge of Q1 and Q2 right?
9. Oct 26, 2016
### Biker
Can anyone confirm the last question in the comment above?
10. Oct 26, 2016
### Staff: Mentor
The question does say that C1 is initially uncharged. So that's not an issue. The only possible impediment to finding all the steady-state charges is that no mention was made of an initial charge for C3. But you would be justified in assuming it to be initially uncharged and proceeding; Just state your assumption as part of your answer. Alternatively, assume some unknown initial charge and give the answers as expressions (symbolically). That would be more work, and probably not what the question author intended. | {"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": 0.9024274349212646, "perplexity": 729.5348305370838}, "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-2018-30/segments/1531676590866.65/warc/CC-MAIN-20180719105750-20180719125750-00131.warc.gz"} |
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# formula for calculating type 2 error Prince Frederick, Maryland
share|improve this answer answered Feb 21 '11 at 6:37 Jeromy Anglim 27.7k1394196 add a comment| up vote 0 down vote Try this: http://en.wikipedia.org/wiki/Type_I_and_type_II_errors share|improve this answer answered Feb 19 '11 at The former may be rephrased as given that a person is healthy, the probability that he is diagnosed as diseased; or the probability that a person is diseased, conditioned on that Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the Diese Funktion ist zurzeit nicht verfügbar.
It's that first point that leads us to what is called the power function of the hypothesis test. Can I buy my plane ticket to exit the US to Mexico? probability power-analysis type-ii-errors share|improve this question edited Feb 21 '11 at 5:55 Jeromy Anglim 27.7k1394196 asked Feb 19 '11 at 20:56 Beatrice 240248 1 See Wikipedia article 'Statistical power' –onestop In order to determine a sample size for a given hypothesis test, you need to specify: (1) The desired α level, that is, your willingness to commit a Type I error.
Solution We begin with computing the standard error estimate, SE. > n = 35 # sample size > s = 2.5 # sample standard deviation > SE = s/sqrt(n); SE # standard error estimate [1] 0.42258 We next compute the lower and upper bounds of sample means for which the null hypothesis μ = 15.4 would more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation Science Cyclically sort lists of mixed element types? What is the probability that a randomly chosen coin which weighs more than 475 grains is genuine?
Assume, a bit unrealistically, thatXis normally distributed with unknown meanμand standard deviation 16. The probability of a type II error is denoted by *beta*. Hence P(AD)=P(D|A)P(A)=.0122 × .9 = .0110. Doing so, we get: So, calculating the engineer's probability of committing a Type II error again reduces to making a normal probability calculation.
In this example: Ho: μ0 = 500 Ha: μ > 500 μ = 524 Draw a normal curve with population mean μ = 524, and sample mean found which is x We've illustrated several sample size calculations. Melde dich bei YouTube an, damit dein Feedback gezählt wird. Melde dich an, um unangemessene Inhalte zu melden.
Assume (unrealistically) that X is normally distributed with unknown mean μ and standard deviation σ = 6. That is, rather than considering the probability that the engineer commits an error, perhaps we could consider the probability that the engineer makes the correct decision. Perhaps there is no better way to see this than graphically by plotting the two power functions simultaneously, one when n = 16 and the other when n = 64: As Die Bewertungsfunktion ist nach Ausleihen des Videos verfügbar.
Related 64Is there a way to remember the definitions of Type I and Type II Errors?1How to interpret type-II error probability while doing A/B testing?2Computing type II error $\beta$0How to compute z=(225-180)/20=2.25; the corresponding tail area is .0122, which is the probability of a type I error. Suppose the medical researcher rejected the null hypothesis, because the mean was 201. We have two(asterisked (**))equations and two unknowns!
What are MLSAG's, and what is their significance for Monero and/or RingCT? Wird verarbeitet... Example (continued) LetXdenote the IQ of a randomly selected adult American. Take a random sample ofn= 16 students, so that, after setting the probability of committing a Type I error atα= 0.01,we can test the null hypothesisH0:μ= 100 against the alternative hypothesis
Wähle deine Sprache aus. A Type II error occurs if we fail to reject the null hypothesisH0when the alternative hypothesisHAis true.We denote β =P(Type II Error). Solution.In this case, the engineer makes the correct decision if his observed sample mean falls in the rejection region, that is, if it is greater than 172, when the true (unknown) Solution.
Formula: Example : Suppose the mean weight of King Penguins found in an Antarctic colony last year was 5.2 kg. Generated Sun, 16 Oct 2016 00:17:11 GMT by s_ac15 (squid/3.5.20) The probability of a type I error is the level of significance of the test of hypothesis, and is denoted by *alpha*. Is 'if there's any' grammatical in this sentence?
Wird geladen... Definition of Power Let's start our discussion of statistical power by recalling two definitions we learned when we first introduced to hypothesis testing: A Type I error occurs if we reject One way of quantifying the quality of a hypothesis test is to ensure that it is a "powerful" test. That, is minimize α = P(Type I Error).
Let's return to our engineer's problem to see if we can instead look at the glass as being half full! All we need to do is equate the equations, and solve for n. Truth in numbers What is the difference between a crosscut sled and a table saw boat? Therefore, he is interested in testing, at the α = 0.05 level,the null hypothesis H0:μ= 40 against the alternative hypothesis thatHA:μ> 40.Find the sample size n that is necessary to achieve
In the above, example, the power of the hypothesis test depends on the value of the mean μ. (2) As the actual meanμmoves further away from the value of the meanμ assist. Assume 90% of the population are healthy (hence 10% predisposed). | {"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": 0.8629651069641113, "perplexity": 1214.927396829318}, "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-2019-04/segments/1547583730728.68/warc/CC-MAIN-20190120184253-20190120210253-00048.warc.gz"} |
https://experts.arizona.edu/en/publications/self-avoiding-walks-in-a-rectangle-2 | # Self-avoiding walks in a rectangle
Anthony J. Guttmann, Tom Kennedy
Research output: Contribution to journalArticlepeer-review
3 Scopus citations
## Abstract
A celebrated problem in numerical analysis is to consider Brownian motion originating at the centre of a (Formula presented.) rectangle and to evaluate the probability of a Brownian path hitting the short ends of the rectangle before hitting one of the long sides. For Brownian motion this probability can be calculated exactly (The SIAM 100-digit challenge: a study in high-accuracy numerical computing. SIAM, Philadelphia, 2004). Here we consider instead the more difficult problem of a self-avoiding walk (SAW) in the scaling limit and pose the same question. Assuming that the scaling limit of SAW is conformally invariant, we evaluate, asymptotically, the same probability. For the SAW case we find the probability is approximately 200 times greater than for Brownian motion.
Original language English (US) 201-208 8 Journal of Engineering Mathematics 84 1 https://doi.org/10.1007/s10665-013-9622-0 Published - Feb 1 2014
## Keywords
• Brownian motion
• Conformal invariance
• SLE
• Scaling limit
• Self-avoiding walks
## ASJC Scopus subject areas
• Mathematics(all)
• Engineering(all)
## Fingerprint
Dive into the research topics of 'Self-avoiding walks in a rectangle'. Together they form a unique fingerprint. | {"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": 0.9612159132957458, "perplexity": 2704.71201794751}, "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-2022-27/segments/1656103920118.49/warc/CC-MAIN-20220701034437-20220701064437-00352.warc.gz"} |
https://www.physicsforums.com/threads/bonding-etc.127547/ | # Bonding etc.
1. Jul 30, 2006
### broegger
Hi. I need help with (part of) this exercise:
c) By considering the differences in bonding determine which of the combustion reactions (in part a) I have written combustion reactions for the following hydrides: B2H6, CH4, NH3 and H2S) must be expected to have the lowest energy of activation.
f) Hydrogen bonding is the strongest intermolecular interaction, and it is of enormous importance in chemistry. Two important hydrogen bondings is O-H---O and N-H---H. Which of these two hydrogen bonds must be expected to be strongest (explain)?
I'm lost again... Any hints?
2. Jul 30, 2006
### Gokul43201
Staff Emeritus
You know the rules - we need to some some thought process from you first.
3. Jul 30, 2006
### end3r7
c) Think intermolecular forces.
f) Think electronegativity.
4. Jul 30, 2006
### broegger
c) Still in the dark. Can't relate these things to the activation energy... sorry.
f) Oxygen is more electronegative than nitrogen, so the OH-molecule has a greater dipole strength than the NH-molecule and therefore the hydrogen bond is stronger in the former case (O-H---O). Right?
Thanks for helping.
5. Jul 31, 2006
### Mattara
c) What is it that is keeping the atoms in the molecules from just breaking loose? What is needed to break bonds between atoms?
Similar Discussions: Bonding etc. | {"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": 0.8919097781181335, "perplexity": 4581.243892590223}, "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-2017-39/segments/1505818690376.61/warc/CC-MAIN-20170925074036-20170925094036-00261.warc.gz"} |
http://en.wikipedia.org/wiki/Goldbeter-Koshland_kinetics | # Goldbeter–Koshland kinetics
(Redirected from Goldbeter-Koshland kinetics)
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A kinase Y and a phosphatase X that act on a protein Z; one possible application for the Goldbeter–Koshland kinetics
The Goldbeter–Koshland kinetics describe a steady-state solution for a 2-state biological system. In this system, the interconversion between these two states is performed by two enzymes with opposing effect. One example would be a protein Z that exists in a phosphorylated form ZP and in an unphosphorylated form Z; the corresponding kinase Y and phosphatase X interconvert the two forms. In this case we would be interested in the equilibrium concentration of the protein Z (Goldbeter–Koshland kinetics only describe equilibrium properties, thus no dynamics can be modeled). It has many applications in the description of biological systems.
The Goldbeter–Koshland kinetics is described by the Goldbeter–Koshland function:
\begin{align} z = \frac{[Z]}{[Z]_0 } = G(v_1, v_2, J_1, J_2) &= \frac{ 2 v_1 J_2}{B + \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}\\ \end{align}
with the constants
\begin{align} v_1 = k_1 [X] ; \ v_2 &= k_2 [Y] ; \ J_1 = \frac{K_{M1}}{[Z]_0 } ; \ J_2 = \frac{K_{M2}}{[Z]_0 }; \ B = v_2 - v_1 + J_1 v_2 + J_2 v_1 \end{align}
Graphically the function takes values between 0 and 1 and has a sigmoid behavior. The smaller the parameters J1 and J2 the steeper the function gets and the more of a switch-like behavior is observed. Goldbeter–Koshland kinetics is an example of ultrasensitivity.
## Derivation
Since we are looking at equilibrium properties we can write
\begin{align} \frac{d[Z]}{dt} \ \stackrel{!}{=}\ 0 \end{align}
From Michaelis–Menten kinetics we know that the rate at which ZP is dephosphorylated is $r_1 = \frac{k_1 [X] [Z_P]}{K_{M1}+ [Z_P]}$ and the rate at which Z is phosphorylated is $r_2 = \frac{k_2 [Y] [Z]}{K_{M2}+ [Z]}$. Here the KM stand for the Michaelis–Menten constant which describes how well the enzymes X and Y bind and catalyze the conversion whereas the kinetic parameters k1 and k2 denote the rate constants for the catalyzed reactions. Assuming that the total concentration of Z is constant we can additionally write that [Z]0 = [ZP] + [Z] and we thus get:
\begin{align} \frac{d[Z]}{dt} = r_1 - r_2 = \frac{k_1 [X] ([Z]_0 - [Z])}{K_{M1}+ ([Z]_0 - [Z])} &-\frac{k_2 [Y] [Z]}{K_{M2}+ [Z]} = 0 \\ \frac{k_1 [X] ([Z]_0 - [Z])}{K_{M1}+ ([Z]_0 - [Z])} &= \frac{k_2 [Y] [Z]}{K_{M2}+ [Z]} \\ \frac{k_1 [X] (1- \frac{[Z]}{[Z]_0 })}{\frac{K_{M1}}{[Z]_0 }+ (1 - \frac{[Z]}{[Z]_0 })} &= \frac{k_2 [Y] \frac{[Z]}{[Z]_0 }}{\frac{K_{M2}}{[Z]_0 }+ \frac{[Z]}{[Z]_0 }} \\ \frac{v_1 (1- z)}{J_1+ (1 - z)} &= \frac{v_2 z}{J_2+ z} \qquad \qquad (1) \end{align}
with the constants
\begin{align} z = \frac{[Z]}{[Z]_0 } ; \ v_1 = k_1 [X] ; \ v_2 &= k_2 [Y] ; \ J_1 = \frac{K_{M1}}{[Z]_0 } ; \ J_2 = \frac{K_{M2}}{[Z]_0 }; \ \qquad \qquad (2) \end{align}
If we thus solve the quadratic equation (1) for z we get:
\begin{align} \frac{v_1 (1- z)}{J_1+ (1 - z)} &= \frac{v_2 z}{J_2+ z} \\ J_2 v_1+ z v_1 - J_2 v_1 z - z^2 v_1 &= z v_2 J_1+ v_2 z - z^2 v_2\\ z^2 (v_2 - v_1) - z \underbrace{(v_2 - v_1 + J_1 v_2 + J_2 v_1)}_{B} + v_1 J_2 &= 0\\ z = \frac{B - \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}{2 (v_2 - v_1)} &= \frac{B - \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}{2 (v_2 - v_1)} \cdot \frac{B + \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}{B + \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}\\ z &= \frac{ 4 (v_2 - v_1) v_1 J_2}{2 (v_2 - v_1)} \cdot \frac{1}{B + \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}\\ z &= \frac{ 2 v_1 J_2}{B + \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}. \qquad \qquad (3) \end{align}
Thus (3) is a solution to the initial equilibrium problem and describes the equilibrium concentration of [Z] and [ZP] as a function of the kinetic parameters of the phoshorylation and dephoshorylation reaction and the concentrations of the kinase and phosphotase. The solution is the Goldbeter–Koshland function with the constants from (2):
\begin{align} z = \frac{[Z]}{[Z]_0 } = G(v_1, v_2, J_1, J_2) &= \frac{ 2 v_1 J_2}{B + \sqrt{B^2 - 4 (v_2 - v_1) v_1 J_2}}.\\ \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": 9, "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": 0.9994151592254639, "perplexity": 4205.050305480548}, "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-2014-23/segments/1404776420526.72/warc/CC-MAIN-20140707234020-00085-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://learn.careers360.com/ncert/question-solve-each-of-the-following-equations-minus-x-power-2-plus-x-minus-2-equals-0/ | Q
# Solve each of the following equations: (4) -x^2+x-2=0
Solve each of the following equations:
Q: 4 $-x^2+x-2=0$
Views
Given equation is
$-x^2+x-2=0$
Now, we know that the roots of the quadratic equation is given by the formula
$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
In this case value of a = -1 , b = 1 and c = -2
Therefore,
$\frac{-1\pm \sqrt{1^2-4.(-1).(-2)}}{2.(-1)}= \frac{-1\pm\sqrt{1-8}}{-2} = \frac{-1\pm\sqrt{-7}}{-2}=\frac{-1\pm\sqrt7i}{-2}$
Therefore, the solutions of equation are
$\frac{-1\pm\sqrt7i}{-2}$
Exams
Articles
Questions | {"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": 5, "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": 0.968341588973999, "perplexity": 714.2054308883174}, "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-2020-10/segments/1581875143505.60/warc/CC-MAIN-20200218025323-20200218055323-00408.warc.gz"} |
https://math.libretexts.org/TextMaps/Calculus_TextMaps/Map%3A_Calculus_(Guichard)/12%3A_Three_Dimensions/12.6%3A_Other_Coordinate_Systems | $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
In two dimensions you may already be familiar with an alternative, called polar coordinates. In this system, each point in the plane is identified by a pair of numbers $$(r,\theta)$$. The number $$\theta$$ measures the angle between the positive $$x$$-axis and a vector with tail at the origin and head at the point, as shown in Figure $$\PageIndex{1}$$; the number $$r$$ measures the distance from the origin to the point. Either of these may be negative; a negative $$\theta$$ indicates the angle is measured clockwise from the positive $$x$$-axis instead of counter-clockwise, and a negative $$r$$ indicates the point at distance $$|r|$$ in the opposite of the direction given by $$\theta$$. Figure $$\PageIndex{1}$$ also shows the point with rectangular coordinates $$(1,\sqrt3)$$ and polar coordinates $$(2,\pi/3)$$, 2 units from the origin and $$\pi/3$$ radians from the positive $$x$$-axis. | {"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": 0.970187783241272, "perplexity": 66.43227500338203}, "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-2018-13/segments/1521257647649.70/warc/CC-MAIN-20180321121805-20180321141805-00237.warc.gz"} |
https://physics.stackexchange.com/questions/396642/understanding-the-behaviour-of-an-interacting-bose-gas | # Understanding the behaviour of an interacting Bose gas
From the Bose-Einstein distribution it follows that a non-interacting Bose gas condenses into the Bose-Einstein condensate below a certain critical temperature. What happens when interactions are introduced in a Bose gas is not dealt with in introductory Statistical mechanics courses. Hence my questions are pretty naive and basic.
How is(are) the interaction(s) quantitatively modelled in a Bose gas and how does it change the behaviour (compared to the noninteracting Bose gas) when the temperature is lowered? Is there a way to physical understand the change in the behaviour, if any?
As a minor comment, I have been informed that in case of Fermi gases, the role of interactions shifts the effective mass from $m\to m^*$ and the energy levels (effectively mapping the interacting system to a system of quasiparticles that still obey FD statistics). Does the similar thing happen here too?
• So, should the title of this question then be "Understanding the behaviour of an interacting Bose gas"? – Rococo Mar 30 '18 at 16:16
1) First note that a non-interacting Bose gas is an idealization. If the gas was truly non-interacting, then it would be impossible to cool by evaporative cooling (or any other method that removes energy and requires the gas to re-equilibrate).
2) In a Bose gas the short range part of the interaction has to be repulsive (otherwise the gas will collape at low temperature). A typical model is a repulsive delta function $$V(x_1,x_2)=\frac{4\pi a}{m} \delta(x_1-x_2)$$ controlled by the s-wave scattering length $a$. Indeed, for a dilute gas this is not a model but a systematic description of the low energy properties.
3) In a non-interacting gas Bose condensation takes place at the Einstein temperature $$T_c = \frac{2\pi}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}.$$ The leading shift due to (repulsive, $a>0$) interactions is $$\Delta T_c \simeq 1.3 an^{1/3} T_c$$ which, even in a strongly interacting gas like helium, is not a large shift.
4) The systematic study of perturbation theory in $a$ goes back to Bogoliubov. He found, for example, that the dispersion relation of quasi-particle in a Bose condensed fluid is $$\epsilon_p = \frac{1}{2m}\sqrt{(p^2+8\pi an)^2-(8\pi an)^2}$$ which smoothly interpolates between a Goldstone mode at low $p$, and non-interacting atoms at large $p$.
5) And indeed, as remarked below, you can take the interaction in (2) and treat in a mean field approximation. This leads to a non-linear Schroedinger equation (the Gross-Pitaevski equation) for the condensate wave function. This equation can be used to study cloud profiles, collective modes, etc.
• Shouldn't there must also be an attraction (at least) at long-range because once a degenerate ground state is occupied there is an enhanced affinity for the other bosons to occupy the already filled state? @Thomas – SRS Mar 30 '18 at 16:28
• Bose statistics is of course taken into account in the calculation. What we mean by "interaction" is the interaction Hamiltonian for two particles in free space. It is indeed true that the long range part of the interaction of two neutral particles is almost always attractive (the Casimir-Polder-van-der-Waals force). What matters to the (dilute) Bose condensed gas is the short range s-wave interaction, which has to be repulsive. – Thomas Mar 30 '18 at 16:51
• Let me just say that taking the potential $V(x_1,x_2)$ leads to the Gross-Pitaevskii equation, which is the quantum mechanical starting point in the study of interacting Bose gases: $$i\hbar \frac{\partial \psi}{\partial t} = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\vec{r}) + gN|\psi|^2 \right]\psi$$ – Matteo Mar 30 '18 at 23:59 | {"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": 0.9003313183784485, "perplexity": 508.9206982951322}, "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-2019-22/segments/1558232255536.6/warc/CC-MAIN-20190520021654-20190520043654-00188.warc.gz"} |
https://www.physicsforums.com/threads/help-with-oscillations-problem.303113/ | # Help with Oscillations Problem
1. Mar 27, 2009
### nweis84
1. The problem statement, all variables and given/known data
A 253 g oscillator has a speed of 89.28 cm/s when the displacement is 2.79 cm and a speed of 70.95 cm/s when the displacement is 6.56 cm. What is the oscillator's maximum speed?
2. Relevant equations
3. The attempt at a solution
well, I haven't really attempted a solution because I'm totally confused on where to start with this problem. I've read the entire chapter and can't come up with any similar examples or formulas that would help solve this because it just doesn't give me enough information.
2. Mar 27, 2009
### Dr.D
Re: oscillations
Presumably this is a mechanical oscillator executing simple harmonic motion?
If that is the case, assume the displacement looks like
x(t) = A*cos(omega*t) + B*sin(omega*t)
and see what you can do to fit the given information.
3. Mar 27, 2009
### nweis84
Re: oscillations
Sorry I'm still very confused,
how can we find omega or t or A or B from any of the given information?
my book just doesn't explain at all how to handle this type of problem
and also thats the first time I've seen an equation written that way
I have seen the x(t) = Acos(w*t) and the one with the phase constant phi
Similar Discussions: Help with Oscillations 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": 0.9165332317352295, "perplexity": 984.5192616947618}, "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-2017-51/segments/1512948581033.57/warc/CC-MAIN-20171216010725-20171216032725-00201.warc.gz"} |
https://mathshistory.st-andrews.ac.uk/OfTheDay/oftheday-01-07/ | ## Mathematicians Of The Day
### 7th January
#### Quotation of the day
##### From Émile Borel
Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation.
Probabilities and Life | {"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": 0.8953471779823303, "perplexity": 2289.937773638835}, "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-2022-05/segments/1642320306301.52/warc/CC-MAIN-20220128152530-20220128182530-00150.warc.gz"} |
https://en.wikiversity.org/wiki/Risk_Literacy | # Risk Literacy
Risk Literacy is understood as the ability to perceive the risk individuals, communities and environment is exposed to and a derive appropriate decision from the awarness about the risk. The term's meaning has been expanded to include the ability to use detect actively the risk, identify risk mitigation resources and other means to understand and use these resources. Risk perception is the subjective judgment people make about the severity and/or probability of a risk, and may vary person to person. Any human endeavor carries some risk, but some are much riskier than others.[1]
## Risk and Response
Basic Risk and Response Cycle
Risk Literacy is understood as the ability to
• (Risk) perceive and process risks (Risk Awareness)and
• (Response) perform activities of risk mitigation.
If we consider risk as:
${\displaystyle Risk=Probability\times Impact}$
risk awareness might refer to the probability and/or the impact of events for the exposed population. Citizens might regard a risk as not high because the probability is not high (e.g. accident in an atomic power plant) or they might be very afraid of the risk because they aware of the huge impact on society, long-term contamination of areas and the impact on public health. Scientific assessment of risk literacy involves both
• the comprehension about the probability and
• the comprehension about the impact. | {"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": 0.8037499785423279, "perplexity": 3369.1822806318755}, "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-2018-17/segments/1524125947803.66/warc/CC-MAIN-20180425115743-20180425135743-00292.warc.gz"} |
http://mathhelpforum.com/latex-help/26563-underbraces-inside-array.html | # Math Help - underbraces inside array
1. ## underbraces inside array
Hi,
I have the following expression:
$
\begin{array}{cclclclclcl}
= & & 2^{k-2} \\
& + & 2^{k-3} & + & 2^{k-3} \\
& + & 2^{k-4} & + & 2^{k-4} & + & 2^{k-4} \\
& \vdots \\
& + & 2^1 & + & 2^1 & + & \dots & + & 2^1 \\
& + & 2^0 & + & 2^0 & + & \dots & + & 2^0 & + & 2^0 \\
\end{array}
$
It is set inside an array because of the + alignment. I would like to add underbraces under the two bottom rows, such as this:
$
$
$
$
However, I would still like to retain the vertical alignment of all the + signs in all rows, so I need to somehow put these underbraces inside the array. (Or use array inside an array, but I can't figure exactly how.)
Do you know any way to do this? Thanks!
2. Hello,
maybe this reply http://www.mathhelpforum.com/math-help/94284-post2.html helps a little bit further.
3. Originally Posted by earboth
Hello,
maybe this reply http://www.mathhelpforum.com/math-help/94284-post2.html helps a little bit further.
It doesn't
I could do the bottom brace that way, but there would still be a problem with the inner one.
Also, I could put all the stuff above the inner brace into an array and then put the brace under this array, and the whole thing would be in a bigger array with the second brace under itself, but one problem still remains - the +'s in the bottom line (which is outside the inner array, but inside the outer one) would not be aligned with the +'s in the inner array (which they are out of).
$\begin{split}
&= 2^{k-2} \\
& \quad + 2^{k-3} + 2^{k-3} \\
& \quad+ 2^{k-4} + 2^{k-4} + 2^{k-4} \\
& \quad + \underbrace{2^1 + 2^1 + \cdots + 2^1}_{k-2} \\
& \quad + \underbrace{2^0 + 2^0 + \cdots + 2^0 + 2^0}_{k-1}.
\end{split}$
¿?
5. $\begin{array}{ccl}
= & {} & 2^{k-2}\\
{} & + & 2^{k-3}\ +\ 2^{k-3}\\
{} & + & 2^{k-4}\ +\ 2^{k-4}\ +\ 2^{k-4}\\
{} & {} & \vdots\\
\end{array}$
6. Originally Posted by Krizalid
$\begin{split}
&= 2^{k-2} \\
& \quad + 2^{k-3} + 2^{k-3} \\
& \quad+ 2^{k-4} + 2^{k-4} + 2^{k-4} \\
& \quad + \underbrace{2^1 + 2^1 + \cdots + 2^1}_{k-2} \\
& \quad + \underbrace{2^0 + 2^0 + \cdots + 2^0 + 2^0}_{k-1}.
\end{split}$
¿?
Thanks, but it doesn't keep the vertical alignment of +'s, so not exactly what I needed.
Originally Posted by JaneBennet
$\begin{array}{ccl}
= & {} & 2^{k-2}\\
{} & + & 2^{k-3}\ +\ 2^{k-3}\\
{} & + & 2^{k-4}\ +\ 2^{k-4}\ +\ 2^{k-4}\\
{} & {} & \vdots\\
\end{array}$
Thanks, this looks pretty much like what I needed - but as I understand it, you just approximated the spaces to keep the alignment, so if I add/change something, I would have to approximate and change the spaces in all rows, so it is kind of unpractical if I want to use it more often. Also, I think the alignment is not 100% precise.
7. Originally Posted by johny
Thanks, this looks pretty much like what I needed - but as I understand it, you just approximated the spaces to keep the alignment, so if I add/change something, I would have to approximate and change the spaces in all rows, so it is kind of unpractical if I want to use it more often. Also, I think the alignment is not 100% precise.
If you really want 100% precise alignment then you can use TeX's \rlap and \hphantom routines to write a superscript 1 that takes up exactly the same amount of space as k–4. The input looks like this:
Code:
\begin{array}{cl}
= & \hphantom{{}+{}} 2^{k-2}\\
&{} + 2^{k-3} + 2^{k-3}\\
&{} + 2^{k-4} + 2^{k-4} + 2^{k-4}\\
& \hphantom{{}+{}} \vdots\\
&{} + \underbrace{2^{\rlap{$\scriptstyle1$}\hphantom{k-4}} + 2^{\rlap{$\scriptstyle1$}\hphantom{k-4}} + \ldots + 2^1}_{k-2}\vspace{.5ex}\\
&{} + \underbrace{2^{\rlap{$\scriptstyle0$}\hphantom{k-4}} + 2^{\rlap{$\scriptstyle0$}\hphantom{k-4}} + \ldots + 2^0 + 2^0}_{k-1}
\end{array}
I can't show the complete output here, because the LaTeX string is too long for the MathHelpForum's compiler to accept. But it works nicely with the TeX program on my computer. If I leave out a couple of lines to bring it down to MathHelpForum's 400-character limit then it looks like this:
$\begin{array}{cl}
= & \hphantom{{}+{}} 2^{k-2}\\
&{} + 2^{k-4} + 2^{k-4} + 2^{k-4}\\
&{} + \underbrace{2^{\rlap{\scriptstyle1}\hphantom{k-4}} + 2^{\rlap{\scriptstyle1}\hphantom{k-4}} + \ldots + 2^1}_{k-2}\vspace{.5ex}\\
&{} + \underbrace{2^{\rlap{\scriptstyle0}\hphantom{k-4}} + 2^{\rlap{\scriptstyle0}\hphantom{k-4}} + \ldots + 2^0 + 2^0}_{k-1}
\end{array}$ | {"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": 1, "img_math": 0, "codecogs_latex": 8, "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": 0.8935513496398926, "perplexity": 913.9406828199569}, "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/1419447549979.35/warc/CC-MAIN-20141224185909-00091-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/87800-submartingale-help-print.html | # Submartingale help
How do i show that $(B_t^2 -t)^2$ is a submartingale w.r.t. the natural filtration generated by $B_t$ , where $B_t$ is a standard Brownian motion started at zero....
Apply Ito's formula to $f(t,B) = (B_t^2-t)^2$.
$4\int_0^t B^2(u)du$
$E[4\int_0^t B^2(u)du | F(s)] \geq 4\int_0^s B^2(u)du, 0 \leq s \leq t$ and thus f(t,B) is a submartingale. | {"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": 6, "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": 0.9951040744781494, "perplexity": 284.44779792806514}, "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-2014-49/segments/1416400376728.38/warc/CC-MAIN-20141119123256-00039-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://papers.nips.cc/paper/6127-stochastic-three-composite-convex-minimization | # NIPS Proceedingsβ
## Stochastic Three-Composite Convex Minimization
[PDF] [BibTeX] [Supplemental] [Reviews]
### Abstract
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computationally advantageous to process smooth term in the decomposition with its stochastic gradient estimate and the other two functions separately with their proximal operators, such as doubly regularized empirical risk minimization problems. We prove the convergence characterization of the proposed algorithm in expectation under the standard assumptions for the stochastic gradient estimate of the smooth term. Our method operates in the primal space and can be considered as a stochastic extension of the three-operator splitting method. Finally, numerical evidence supports the effectiveness of our method in real-world problems. | {"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": 0.8310674428939819, "perplexity": 257.8735549215846}, "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-2019-04/segments/1547583792338.50/warc/CC-MAIN-20190121111139-20190121133139-00528.warc.gz"} |
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