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http://cms.math.ca/cmb/kw/polygon | Canadian Mathematical Society www.cms.math.ca
location: Publications → journals
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Search: All articles in the CMB digital archive with keyword polygon
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1. CMB 2009 (vol 52 pp. 424)
Martini, Horst; Spirova, Margarita
Covering Discs in Minkowski Planes We investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by \$k\$ unit circles. In particular, we study the cases \$k=3\$, \$k=4\$, and \$k=7\$. For \$k=3\$ and \$k=4\$, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, \$d\$-segments, and the monotonicity lemma. Keywords:affine regular polygon, bisector, circle covering problem, circumradius, \$d\$-segment, Minkowski plane, (strictly convex) normed planeCategories:46B20, 52A21, 52C15
2. CMB 2006 (vol 49 pp. 321)
Balser, Andreas
Polygons with Prescribed Gauss Map in Hadamard Spaces and Euclidean Buildings We show that given a stable weighted configuration on the asymptotic boundary of a locally compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration. Moreover, the same result holds for semistable configurations on arbitrary Euclidean buildings. Keywords:Euclidean buildings, Hadamard spaces, polygonsCategory:53C20
3. CMB 2002 (vol 45 pp. 417)
Kamiyama, Yasuhiko; Tsukuda, Shuichi
On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons For an integer \$n \geq 3\$, let \$M_n\$ be the moduli space of spatial polygons with \$n\$ edges. We consider the case of odd \$n\$. Then \$M_n\$ is a Fano manifold of complex dimension \$n-3\$. Let \$\Theta_{M_n}\$ be the sheaf of germs of holomorphic sections of the tangent bundle \$TM_n\$. In this paper, we prove \$H^q (M_n,\Theta_{M_n})=0\$ for all \$q \geq 0\$ and all odd \$n\$. In particular, we see that the moduli space of deformations of the complex structure on \$M_n\$ consists of a point. Thus the complex structure on \$M_n\$ is locally rigid. Keywords:polygon space, complex structureCategories:14D20, 32C35
© Canadian Mathematical Society, 2015 : https://cms.math.ca/ | {"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": 0.9720563292503357, "perplexity": 2946.53117689467}, "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-2015-06/segments/1422122059136.7/warc/CC-MAIN-20150124175419-00174-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/84885-radical-function-no-vertical-asymptote-print.html | # Radical function with no vertical asymptote
• Apr 21st 2009, 05:32 PM
mgannon93
Radical function with no vertical asymptote
Hi,
I need help with a problem. I don't understand it.
Describe the condition that will produce a rational function with a graph that has no vertical asymtote.
Thanks for any help!
Michele
• Apr 21st 2009, 05:39 PM
Reckoner
Quote:
Originally Posted by mgannon93
Hi,
I need help with a problem. I don't understand it.
Describe the condition that will produce a rational function with a graph that has no vertical asymtote.
Where do the vertical asymptotes of a rational function occur? So then what can you do to prevent a vertical asymptote?
• Apr 21st 2009, 05:45 PM
mgannon93
Quote:
Originally Posted by Reckoner
Where do the vertical asymptotes of a rational function occur? So then what can you do to prevent a vertical asymptote?
The vertical asymptotes occur in the denominator, right? When they equal zero?
So if there's no x's in the denominator?
I'm sorry I'm difficult.. it sounds like such an easy problem but I don't get it.
• Apr 21st 2009, 05:50 PM
Reckoner
Quote:
Originally Posted by mgannon93
The vertical asymptotes occur in the denominator, right? When they equal zero?
Right. And what happens if there are no zeroes?
• Apr 21st 2009, 05:55 PM
mgannon93
Quote:
Originally Posted by Reckoner
Right. And what happens if there are no zeroes?
Nothing crosses the x-axis?
• Apr 21st 2009, 06:03 PM
Reckoner
Quote:
Originally Posted by mgannon93
Nothing crosses the x-axis?
I meant in the denominator. If the vertical asymptotes of a rational function only occur when the denominator is zero, then what happens if the denominator has no zeroes?
Although technically, if the numerator and denominator are simultaneously zero at a point, it is possible that there is no vertical asymptote there; it depends on the multiplicity of the factors.
• Apr 21st 2009, 06:14 PM
mgannon93
Quote:
Originally Posted by Reckoner
I meant in the denominator. If the vertical asymptotes of a rational function only occur when the denominator is zero, then what happens if the denominator has no zeroes?
Although technically, if the numerator and denominator are simultaneously zero at a point, it is possible that there is no vertical asymptote there; it depends on the multiplicity of the factors.
Then the denominator has to be just a number, without a variable?
So as long as the denominator doesn't have an x in it, there won't be a vertical asymtote. So an equation like,
(x-2)(x+5)=0 would have no vertical asymtote.
?
• Apr 21st 2009, 06:17 PM
Reckoner
Quote:
Originally Posted by mgannon93
Then the denominator has to be just a number, without a variable?
So as long as the denominator doesn't have an x in it, there won't be a vertical asymtote. So an equation like,
(x-2)(x+5)=0 would have no vertical asymtote.
?
Tell me then, what are the (real) zeroes of $x^2+1?$
• Apr 21st 2009, 06:22 PM
mgannon93
Quote:
Originally Posted by Reckoner
Tell me then, what are the (real) zeroes of $x^2+1?$
OH! So equations that give you imaginary numbers!
Wow I feel like an idiot. Thanks. Is this explained alright?
--
Describe the condition that will produce a rational function with a graph that has no vertical asymptote.
Rational functions with no rational zeroes will have no vertical asymptote, so an equation like x^2+1 would be a rational function with no vertical asymptotes.
Is that right?
• Apr 21st 2009, 06:25 PM
Reckoner
Quote:
Originally Posted by mgannon93
Rational functions with no rational zeroes will have no vertical asymptote, so an equation like x^2+1 would be a rational function with no vertical asymptotes.
Is that right?
No, you aren't quite getting it. Yes, the function $f(x)=x^2+1$ has no vertical asymptotes, and we may consider it a rational function. But what I was trying to get you to see was that you can put it in the denominator, and the denominator will always be nonzero (that is, the denominator doesn't have to be a constant).
$g(x)=\frac1{x^2+1}$
has no vertical asymptotes.
• Apr 21st 2009, 07:04 PM
mgannon93
Quote:
Originally Posted by Reckoner
No, you aren't quite getting it. Yes, the function $f(x)=x^2+1$ has no vertical asymptotes, and we may consider it a rational function. But what I was trying to get you to see was that you can put it in the denominator, and the denominator will always be nonzero (that is, the denominator doesn't have to be a constant).
$g(x)=\frac1{x^2+1}$
has no vertical asymptotes.
Oh! Thank you thank you 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": 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": 0.9898536205291748, "perplexity": 660.9804603642591}, "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-2017-04/segments/1484560280280.6/warc/CC-MAIN-20170116095120-00514-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/55114/how-to-make-a-nongrounded-conductor-have-equipotential | # How to make a nongrounded conductor have equipotential?
I'm studying the Method of Images and I seemed to have come to a conundrum. Method of Images takes advantage of grounded objects, (I am currently studying spheres), to set boundary conditions. However, how would one use the idea of MoI to set the potential of a conducting sphere as constant?
Since $E = \nabla V$, a constant potential would be the electric field inside would be constant? Therefore, a density of charge inside the sphere?
-
I edited your question, to fix $\nabla E = V$, which should be $E=\nabla V$. but perhaps that typo is the source of your equation. – askewchan Feb 26 '13 at 2:04
Also note that conundrum is a noun and not a verb. – Emilio Pisanty Feb 26 '13 at 16:20
Regardless of whether it is grounded, if there were a nonzero electric field inside a conductor, it would push the charge carriers around until there were no longer forces on them.
Thus: A perfect conductor, grounded or isolated, will have a surface (and volume) of equal potential, and the electric field inside will be zero.
If the conductor is not grounded, then there will be some net charge (possibly zero) on the conductor. If it's a symmetric shape (a sphere) then it will have a uniform surface density, namely the total charge over the total surface area ($Q / 4\pi r^2$).
You cannot assume to know $Q$ on the sphere. Whether or not $Q=0$, there will be $E=0$ inside the sphere (Gauss Law), and outside the sphere there will be $E\neq 0$ if $Q\neq0$.
Adding an image charge at the origin would actually create a nonzero $E$ inside the sphere, which you cannot have inside a conductor (I'm assuming the sphere is solid). The charge on the surface of the sphere already cancels its own $E$ field inside the sphere. If you want to cancel the $E$ field outside the sphere, then an image at the origin would do that.
-
So if I were to find the potential outside of a conducting sphere that is not grounded, the potential inside would have to be constant. Therefore that second image charge would have to be placed at the origin to mimic if it were grounded. – julesverne Feb 26 '13 at 17:53
@julesverne you really don't need an image charge to solve this, assuming you're trying to find the potential everywhere, just use Gauss' law. – askewchan Feb 26 '13 at 17:56 | {"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": 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": 0.9254986643791199, "perplexity": 237.8457173867422}, "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/1397609535745.0/warc/CC-MAIN-20140416005215-00621-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/15955/density-of-zeros-of-a-power-series-over-the-reals | # Density of zeros of a power series over the reals
Let $f(x) = \sum_{i =0}^\infty a_i x^i$ be a power series which converges for all real $x$. Assume that $f(x)$ is not identically zero. I'm interested in the density of the zeros of $f(x)$. Let $Z$ be the set of zeros of $f(x)$. Which of the following claims about density of $Z$ are true?
Claim 1: $Z$ is nowhere dense.
Claim 2: $Z$ is countable.
Claim 3: For any $a,b \in \mathbb{R}$ , $Z \cap [a,b]$ is finite.
I believe (correct me if I'm wrong) that claim 3 implies the other two. I suspect all three claims are true.
I suspect that the answers to these questions are well-known, though I was not able to find an obvious reference. Can anyone suggest a reference with a nice treatment of these questions?
-
Claim 3 is true, and it does imply the other 2. It is enough to consider analytic functions, i.e. functions that have a power series expansion in some interval centered at each real number, which in particular holds if you have an everywhere convergent power series. If $[a,b]$ had infinitely many zeros of $f$, then there would be a limit point $c$ of these zeros. By continuity $f(c)=0$. Let $n\gt0$ be the smallest positive integer such that $f^{(n)}(c)\neq0$ (using the assumption that $f$ is not identically $0$). Then $f$ has power series expansion
\begin{align*} f(x)&=\sum_{k=0}^\infty\frac{f^{(k)}(c)}{k!}(x-c)^k =\sum_{k=n}^\infty\frac{f^{(k)}(c)}{k!}(x-c)^k\\ &=(x-c)^n\sum_{k=n}^\infty\frac{f^{(k)}(c)}{k!}(x-c)^{k-n}=(x-c)^ng(x), \end{align*}
where $g(x)$ is a continuous function such that $g(c)\neq0$, and hence $g(x)\neq0$ in some open interval $I$ containing $c$. So the only zero of $f$ in $I$ is $c$, contradicting the fact that $c$ is a limit point of the set of zeros. Hence, unless $f$ is identically zero, the limit point $c$ cannot exist.
For reference you can read any good text on complex analysis. If you prefer to stick to the real case, there is the book A primer of real analytic functions by Krantz and Parks.
-
Actually, what if $f$ is not everywhere convergent? In particular, what if $f$ converges only for $x \in [0,1]$? Are there finitely many zeros of $f$ in $[0,1]$? It seems to me that the answer is yes,and nothing really changes. Right? – srd Dec 31 '10 at 7:40
It is impossible for a power series centered at $0$ to converge only on $[0,1]$. If it converges on $[0,1]$, then its radius of convergence is at least $1$ and it converges on at least $(-1,1]$. Nothing changes on the interior of the interval, where $f$ is analytic, but you have to be more careful at $1$. It is possible that $f$ cannot be extended to an analytic function in an interval at $1$, so the argument above doesn't apply with $c=1$. That means you have to consider the possibility that the function has a sequence of zeros converging to $1$. – Jonas Meyer Dec 31 '10 at 8:20
There are functions that are analytic on (at least) $(-1,1)$ and continuous on $(-1,1]$ with an infinite sequence of zeros converging to $1$, like $f(x)=(1-x)\sin(1/(1-x))$, $f(1)=0$. That may not precisely answer your question, because I'm not sure whether the series expansion for $f$ centered at $0$ converges at $1$. – Jonas Meyer Dec 31 '10 at 8:27
I meant to say "converges on at least $x \in [0,1]$". I think what you say answers my question. I interpret it as follows. If $f$ converges on at least $[0,1]$, then for any $a,b \in (0,1)$ we know $Z \cap [a,b]$ is finite. – srd Dec 31 '10 at 8:53
@shaddin: yes, an analytic function on an open interval can have only finitely many zeros on any compact subinterval of $(a,b)$, for the same reason as for the case where $f$ is defined on all of $\mathbb{R}$. A power series with positive radius of convergence defines an analytic function on the interior of its interval of convergence, which in your example will contain at least $(-1,1)$. – Jonas Meyer Dec 31 '10 at 8:57
All three claims are true. Claim 3 $\Rightarrow$ Claim 2 and Claim 1. The zeros of an analytic function are isolated. This implies Claim 3.
-
I'm not sure I see why the fact that the zeros are isolated implies claim 3. Suppose for example the zeros were $Z=\{1/2^i\}_{i \in \mathbb{N}}$. This set of points is infinite. However, it is isolated, since given any $x\in Z$ I can present you an open interval containing $x$ and no other point in $Z$. Am I misinterpreting the definition of "isolated"? – srd Dec 31 '10 at 3:31
@shaddin: That cannot be the set of all zeros of a continuous function on $\mathbb{R}$; it contains $0$ as a limit point, so $0$ must also be a zero, and it is not isolated. Hence, because analytic functions have isolated zeros, no nonvanishing analytic function can be zero at $1/2^i$ for all $i\in \mathbb{N}$. – Jonas Meyer Dec 31 '10 at 3:41
@Jonas Meyer: I see, thanks! – srd Dec 31 '10 at 3:45
@shaddin: You're welcome. (I didn't mean nonvanishing, I meant not identically zero.) – Jonas Meyer Dec 31 '10 at 3:49 | {"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": 0.9686902165412903, "perplexity": 92.7076571141349}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395560.69/warc/CC-MAIN-20160624154955-00103-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/78265/intuitive-examples-of-r-0-tensors | # Intuitive Examples of (r,0) Tensors
It's easy to find "intuitive" examples of $(0, r)$ tensors or even $(k, r)$ tensors $( k, r > 0)$. For the purposes of this question, I am considering a tensor in the "classical" sense as being represented by a multilinear form. For instance, every inner product space has an associated inner product which is just a $(0, 2)$-tensor that satisfies certain properties. Also, if $V$ is a vector space over a field $\mathbb{F}$ and $V^{*}$ denotes its dual, then the evaluation map $E:V^{*} \times V \rightarrow \mathbb{F}$ given by $E(f,v) = f(v)$ is an example of a $(1, 1)$ tensor. What are some elementary/intuitive examples of $(k,0)$ tensors?
-
Examples of completely contravariant tensors:
• The stress-energy tensor.
• The inverse metric.
Intuitive examples of completely contravariant tensors:
• The angular momentum bivector.
• The torque bivector.
-
It all depends. Unfortunately, because dimension is the only invariant for vectors spaces there are literally more than five equivalent, common, definitions of $V\otimes V$ I can think of. Probably the one that best fits your needs is to think about a $(m,n)$-tensor as just being a multililinear map $T:\text{Hom}(V,F)^m\times V^n\to F$. So, for example, taking $m=0$ gives that a $(0,n)$-tensor is nothing more than a member of $\text{Mult}_m(V,F)$ ($m$-linear maps on $V^m$) and taking $n=0$ gives that $(m,0)$-tensors are just $m$-linear maps on $\text{Hom}(V,F)^m$.
Does that help?
-
I have updated the question to be explicit about the type of tensor I am considering. – ItsNotObvious Nov 2 '11 at 18:21
Well, I think that I went with that definition, so I have no more to add. I hope what I said was helpful. – Alex Youcis Nov 2 '11 at 18:24
You helped me clarify my question and be more explicit about what I was asking, but your examples effectively defined the type of tensors I am considering. Thanks. – ItsNotObvious Nov 2 '11 at 18:32 | {"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": 0.9026816487312317, "perplexity": 405.9179799645039}, "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/1432207930895.96/warc/CC-MAIN-20150521113210-00078-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.ncbi.nlm.nih.gov/pubmed/12317045 | Format
Choose Destination
Maandstat Bevolking. 1991 Sep;39(9):31-9.
# [Uncertainty variants in population forecasts for the Netherlands].
[Article in Dutch]
### Abstract
"Because of the uncertainty of population forecasts the Netherlands Central Bureau of Statistics publishes a Low and a High variant next to the Medium variant.... Variants are obtained by using a deterministic model. Hence the probability that the interval between the variants [covers] the true future values is unknown. Under reasonable assumptions a statistical confidence interval for total population size can be derived. The basic assumption is that the forecast errors of population growth are serially correlated. If a first-order autoregressive model is estimated on the basis of all population forecasts published...since 1950, it turns out that the interval between the Low and High variants corresponds reasonably close to a two-thirds confidence interval in the next two decades." (SUMMARY IN ENG).
PMID:
12317045
[Indexed for MEDLINE] | {"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": 0.9643728137016296, "perplexity": 1534.2927074092622}, "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/1555578532882.36/warc/CC-MAIN-20190421195929-20190421221929-00445.warc.gz"} |
https://en.wikibooks.org/wiki/Electronics/Voltage_Dividers | # Electronics/Voltage Dividers
Jump to navigation Jump to search
### Ideal case
Consider the illustration below. Assume initially that no current is flowing in or out of the terminal marked Vout. In this case, the only path for current is from Vin through R1 and R2 to GND. The equivalent resistance of this configuration is R1+R2 since these are resistors in series. From Ohm's law the current flowing through both resistors is
${\displaystyle I={\frac {V_{in}}{R_{1}+R_{2}}}}$.
Also from Ohm's law, we know that the voltage drops across the resistors are I*R1 and I*R2 respectively. A quick check shows that the sum of the voltage drops across the resistors adds up to Vin. Now we can calculate the voltage at Vout (still assuming that no current flows through the terminal Vout). In this case the voltage is just
${\displaystyle 0V+IR_{2}}$
where the 0V is the voltage at GND. If we substitute what we calculated for I, we obtain
${\displaystyle V_{out}={\frac {R_{2}}{R_{1}+R_{2}}}V_{in}}$.
This is the voltage divider equation for the ideal case where no current flows through the output. Another way of saying that no current flows through the output is that the output has infinite resistance. A quick mental check using ${\displaystyle I=V/R}$ shows that the voltage calculated divided by infinity equals zero
### Non-ideal case - finite resistance outputs
In the non-ideal case, we need to consider the resistance of the output. If we assume that the resistance of the output is R3 (and it is connected only to GND), we need to modify our analysis as follows. Now we have two resistors in parallel from the Vout junction to GND. The equivalent resistance of the parallel reistors then is
${\displaystyle R_{eq}={\frac {R_{2}R_{3}}{R_{2}+R_{3}}}}$
and the equivalent reistance of the entire circuit is
${\displaystyle R_{tot}=R_{1}+{\frac {R_{2}R_{3}}{R_{2}+R_{3}}}}$.
This yields a current of
${\displaystyle I={\frac {V}{R_{tot}}}={\frac {V_{in}}{R_{1}+{\frac {R_{2}R_{3}}{R_{2}+R_{3}}}}}}$.
Now we multiply this by ${\displaystyle R_{eq}}$ calculated above to obtain the output voltage:
${\displaystyle V_{out}=IR_{eq}={\frac {R_{eq}}{R_{tot}}}V={\frac {\frac {R_{2}R_{3}}{R_{2}+R_{3}}}{R_{1}+{\frac {R_{2}R_{3}}{R_{2}+R_{3}}}}}V_{in}}$
Normally R2 will be much smaller than R3 so Req will be approximately equal to R2. Keep in mind that a resistance R3 that is 100 times as large as R2 results in a voltage sag of about 1% and that a reistance R3 that is 10 times as large as R2 results in an almost 10% voltage sag.
### Non-ideal case - complex impedance
Both voltage divider equations hold for complex impedances. Just substitute Z's for R's and do the complex arithmetic. The resulting equations are just the following:
${\displaystyle V_{out}={\frac {Z_{2}}{Z_{1}+Z_{2}}}V_{in}}$ - ideal case
${\displaystyle V_{out}={\frac {\frac {Z_{2}Z_{3}}{Z_{2}+Z_{3}}}{Z_{1}+{\frac {Z_{2}Z_{3}}{Z_{2}+Z_{3}}}}}V_{in}}$ - non-ideal case | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 11, "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": 0.9732212424278259, "perplexity": 459.7125269637938}, "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-2019-22/segments/1558232257432.60/warc/CC-MAIN-20190523224154-20190524010154-00174.warc.gz"} |
https://www.sparrho.com/item/relative-torsion-and-bordism-classes-of-positive-scalar-curvature-metrics-on-manifolds-with-boundary/28d9b7a/ | # Relative torsion and bordism classes of positive scalar curvature metrics on manifolds with boundary
Research paper by Simone Cecchini, Mehran Seyedhosseini, Vito Felice Zenobi
Indexed on: 30 Sep '20Published on: 28 Sep '20Published in: arXiv - Mathematics - Geometric Topology
#### Abstract
In this paper, we define a relative $L^2$-$\rho$-invariant for Dirac operators on odd-dimensional spin manifolds with boundary and show that they are invariants of the bordism classes of positive scalar curvature metrics which are collared near the boundary. As an application, we show that if a $4k+3$-dimensional spin manifold with boundary admits such a metric and if, roughly speaking, there exists a torsion element in the difference of the fundamental groups of the manifold and its boundary, then there are infinitely many bordism classes of such psc metrics on the given manifold. This result in turn implies that the moduli-space of psc metrics on such manifolds has infinitely many path components. We also indicate how to define delocalised $\eta$-invariants for odd-dimensional spin manifolds with boundary, which could then be used to obtain similar results for $4k+1$-dimensional manifolds. | {"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": 0.9648439884185791, "perplexity": 360.7195281048572}, "config": {"markdown_headings": true, "markdown_code": false, "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-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00317.warc.gz"} |
http://mathoverflow.net/questions/103645/cohomology-vanishing-for-formal-completions-of-modules/103674 | Cohomology vanishing for formal completions of modules?
Let $A$ be a ring, Noetherian or even of finite type over a field if necessary. Let $I$ be an ideal in $A$, $\widehat{A}$ the formal completion of $A$ along $I$, $M$ an $A$-module, finitely generated if necessary, and $\widehat{M}$ the formal completion. Then the sheaf cohomology $H^{i}(Spec(A),M)=0$ for $i > 0$.
Is the same true for $\widehat{M}$ on the formal completion? (Clarification based on the below comment: The underlying topological space of the formal completion is $Spec(A/I)$, not $Spec(\widehat{A}))$, thus there is something to prove.)
-
I think you have unnecessarily complicated the question. The cohomology vanishing is true for any (Noetherian) commutative ring and any module. – Mohan Jul 31 '12 at 23:11
My question is not about $\widehat{M}$ on $Spec(\widehat{A})$, which is a quasi-coherent sheaf on an affine scheme, but about $\widehat{M}$ on the formal scheme whose underlying topological space is $Spec(A/I)$. In particular, $\widehat{M}$ is not an $A/I$-module and so I can't just apply the usual vanishing on an affine scheme. – A. Pascal Aug 1 '12 at 8:11
$H^i( X, \lim\limits_\longleftarrow \mathcal{F}_k )$
$\lim\limits_\longleftarrow H^i( X, \mathcal{F}_k)$
for an inverse system $(\mathcal{F}_k)$ of sheaves of abelian groups on a topological space $X$. | {"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": 0.9593479037284851, "perplexity": 150.98422634390576}, "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-2016-22/segments/1464049273643.15/warc/CC-MAIN-20160524002113-00073-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/666493/smallest-non-zero-eigenvalue-of-a-0-1-matrix | # Smallest non-zero eigenvalue of a (0,1) matrix
What's the smallest absolute value possible of a non-zero eigenvalue of an $n$ by $n$ square matrix whose entries are either $0$ or $1$ (all operations are over $\mathbb{R}$)?
-
A square matrix whose values are either $0$ or $1$. – Anush Feb 6 at 20:10
Yes, please elaborate – Dave S Feb 6 at 20:11
Please edit your question to make this clear. Regards – Dave S Feb 6 at 20:12
@Dror: John Habert just showed in his answer that this is wrong. – Andreas H. Feb 6 at 21:14
Cross-posted to mathoverflow.net/questions/157472/… now. – Anush Feb 13 at 11:17
For a $2\times 2$ matrix, the smallest is $\left| \dfrac{1-\sqrt{5}}{2}\right|$ from $\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$ or $\begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix}$.
For a $3\times 3$ matrix, the smallest is $\left|\frac{1}{2}(3-\sqrt{5})\right|$ from $\begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}$ or any other matrix with all entries $1$ except for a single off (main) diagonal $0$.
Best so far - have more calculations to run and check
For a $4\times 4$ matrix, the smallest is $\left|2-\sqrt{3}\right|$ from $\begin{pmatrix} 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{pmatrix}$
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OK, I think your eigenvalues are $\tfrac{1}{2}\left(n\pm\sqrt{n^2-4}\right)$, which is bounded below by $1/n$. Note that this doesn't work for 2x2; my derivation starts with at least a 3x3. – Michael C. Grant Feb 7 at 3:38
@MichaelC.Grant Added best so far for $n=4$ case. I think I've found a smaller but need to double check things. Even with the smaller one, bound of $\frac{1}{n+1}$ seems to be holding so far. – John Habert Feb 7 at 3:42
I verified the correctness of my formula in the previous comment up to $n=1000$, for a matrix with all ones except a single zero in the $(1,2)$ position. That's not to say better matrices do not exist; but for a single off-diagonal nonzero, that's it. – Michael C. Grant Feb 7 at 4:22
@MichaelC.Grant Nice work. I'm going to finish rechecking $n=4$ to see if the better case still exists. Discovered my code wasn't giving correct output. – John Habert Feb 7 at 4:32
Consider the $n\times n$ matrix $$E_n = \vec{1} \vec{1}^T + e_1 e_1^T - I$$ where $\vec{1}$ is the vector of all ones, $e_1$ is the vector with a $1$ in the first element and zeros elsewhere, and $I$ is the identity matrix. In other words, $E_n$ has ones everywhere except the latter $n-1$ elements of the diagonal.
Empirically, I'm finding that the smallest nonzero eigenvalue in absolute value is approximately $-1/n$. I suspect that could be bounded rigorously, and if I can do so, I'll edit this answer. But it would seem clear to me that the smallest non-zero eigenvalue cannot be bounded away from zero.
EDIT: The eigenvalues of $E_n$ for $n>2$ are $-1$ and $$\frac{n-1\pm\sqrt{(n-1)^2+4}}{2}=\frac{n-1}{2}\pm\sqrt{\left(\frac{n-1}{2}\right)^2+1}.$$ The smallest absolute value is therefore $$\sqrt{\left(\frac{n-1}{2}\right)^2+1}-\frac{n-1}{2}\geq \frac{1}{n-1}.$$ Of course, this is not a bound for all $\{0,1\}$ matrices, just for this one.
EDIT: John Habert's 3x3 matrices and 4x4 matrices do better than this. For a matrix will all ones except a single off-diagonal zero, the eigenvalues are 0 (with $n-2$ multiplicty) and $$\frac{n}{2} \pm \sqrt{ \frac{n^2}{4} - 1 } \geq \frac{1}{n}.$$ I verified this numerically up to $n=1000$.
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Why doesn't your formula and my empirical result agree? – John Habert Feb 6 at 22:03
Our matrices are different. Yours has one zero value, mine has $n-1$. – Michael C. Grant Feb 6 at 22:06
Plus it appears I've miscalculated something. Double-checking on my own side shows my 3 by 3 answer is off. Will figure out why. – John Habert Feb 6 at 22:08
Your matrix is $\vec{1}\vec{1}-e_1e_1^T$. Simpler than mine, to be sure. – Michael C. Grant Feb 6 at 22:09
If it can be shown that the smallest absolute value is $1/n$ that would be great. – Anush Feb 6 at 22:12 | {"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": 0.8879421949386597, "perplexity": 662.1996363237854}, "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-2014-10/segments/1394021585790/warc/CC-MAIN-20140305121305-00062-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/38791/relative-entropy-given-two-non-equivalent-sets | # Relative Entropy given two non-equivalent sets
I am trying to calculate the relative entropy given two collections and have a question regarding some issues.
Supposed we have two sets, $Real$ and $Calculated$, and their respective probability mass functions, $P$, and $Q$.
Relative Entropy, or Kullback Leibler Divergence is defined as the following:
$$\sum_{i=0}^{n} P(i)\log \frac{P(i)}{Q(i)}$$
How do we properly handle situations where $|Q| \neq |P|$?
Should we take the intersection of the sets, $Real$ and $Calculated$, and scale their respective probability mass functions to correct the calculation of the relative entropy? Otherwise only calculating over the intersection without scaling the probabilities can lead to negative results, which is not correct.
I am using the following code to calculate R.E.
def kullback_leibler_divergence(real, predicted):
sum = 0.0
for qs, freq in predicted.items():
freq_r = real.get(qs, 0.0)
operand = m.log(freq_r / freq) if freq_r != 0 and freq != 0 else 0
sum += freq_r * operand
return sum
...but I get negative results occasionally, which made me question how I am handling my input parameters.
- | {"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": 0.8740919232368469, "perplexity": 357.17856472998994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443738006925.85/warc/CC-MAIN-20151001222006-00235-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://markkarpov.com/post/category-theory-part-1.html | # Category Theory Basics, Part I
other
Published on September 18, 2016, last updated June 1, 2017
When you do Haskell on daily basis (simply put, earn a living writing Haskell code), sooner or later you start to regret you don’t have background in advanced math (unless you have such background, of course, and in that case the post will be probably uninteresting for you). I think it’s a situation in which people who use Haskell as engineers (not researchers) find themselves at some point.
The most important and relevant math area for a Haskeller is probably category theory, which does look scary at first and Wikipedia articles/videos of lectures seem to be only partially understandable, always leaving you with a bunch of new notions unexplained. There is no problem to understand what Monad means and how it’s useful in functional programming (although the abstraction may take some time to sink in), but the feeling of missing “bigger picture”, full of wonderful ideas may not leave you once you started to use abstractions from category theory.
So, having intuitive understanding of what the word “injective” means and more-or-less proper understanding of what some things like “isomorphism” mean, I decided to read a book that describes all the concepts in order and using simple language.
The book I found is called “Conceptual Mathematics—A First Introduction to Categories” by F. William Lawvere and Stephen H. Schanuel. The book does not assume math background of any sort and anyone can understand concepts described in it. You can give it a try, but the books in not short—376 pages, and it does not even get you to monads (probably will need something else after it if I decide that I haven’t got enough). So this post is the first in a series of blog posts1 that I want to write as a sort of overgrown cheat sheets that highlight important ideas from category theory in a concise form.
I hope that working on the blog posts will help me better organize the ideas from the book in my head, and may be useful for others who may not necessarily have the time to read the book.
Note: here is a somewhat similar post here, but it tries to make the concepts more programmer-friendly by providing examples from “programming world” using pipes, compilers, and circuits. I have no such intention, and in fact I tested this descriptions on people who are neither programmers nor mathematicians, and it worked!
## What is a category?
As everything in math, we need some starting points and definitions to build on. The main definition is of course category itself. Category is defined by objects and maps (synonyms: arrows, morphisms, functions, transformations). There are also a few laws that should hold for the objects and maps in order to form a category, but we will get to them a bit later.
Objects can be pretty much everything. The simplest and most intuitive object is probably finite set (just a collection of things), and it will be discussed in the next section.
Maps have domain (an object), codomain (an object again), and a rule assigning to each element2 $$a$$ in the domain, an element $$b$$ in the codomain. This $$b$$ is denoted by $$f \circ a$$ (or sometimes $$f(a)$$), read “$$f$$ of $$a$$”. Simply put, domain contains all possible arguments of the mapping function and codomain contains output values.
An important thing here is that if we say that object $$A$$ is domain and object $$B$$ is codomain of some map, then the map should be defined for every value $$a$$ in $$A$$ (i.e. it should “use” all input values), but not necessarily it should map to all values in $$B$$. This may seem obvious, but I want to put it here explicitly, because I found this “rule” useful for understanding some conclusions in the book many times.
At this point it should be clear that category theory is a very abstract thing. If we study abstract transformations of abstract objects, then certainly we study something that takes place in every area of science and human knowledge, because human knowledge in general has to do with objects, their relations, and mappings.
There are a couple more things that a category should have, and I’ll describe them in a moment, but first it’s good to introduce category of finite sets and some notation that will be helpful for visualization.
## Category of finite sets, internal and external diagrams
In the category of finite sets objects are finite sets and maps are rules how to go from a value in one set to a value in another set. Due to how our brain works, it’s much easier to reason about collections of values and their mappings, than about abstract categories. We will be using the category of finite sets to explain most concepts here, and to visualize them, we will draw pictures of the sets and maps between them.
The set $$\{John, Mary, Sam\}$$ may be drawn just as:
where a dot represents each element. We can also leave off the labels if they are irrelevant to discussion. Such picture, labelled or not, is called internal diagram of the set.
We can picture a map as collection of arrows that go from elements of one set to element of another set:
There are also external diagrams for the cases when we do not care about concrete elements of objects:
$A \xrightarrow{f} B$
## Endomaps and identity maps
A map in which the domain and codomain are the same object is called an endomap (“endo”, a prefix from Greek ἔνδον endon meaning “within, inner, absorbing, or containing” Wikipedia says). For endomaps we have a special form of internal diagram:
It turns out that in every category, for each object, we have a map that maps elements of an object $$A$$ to themselves. This map is called identity map and is denoted as $$1_\text{A}$$. Here is an example of internal diagram of an identity map (taken from the book, like the pictures above):
The $$1_\text{A}$$ notation will make more sense once we learn about composition of maps in the next section.
Definition: An endomap $$e$$ is called idempotent if $$e \circ e = e$$.
## Composition
The final, fourth (after objects, maps, and identity maps) thing that a category should have (or support) is the ability to compose maps. That’s where all the fun begins.
Composition of two maps $$f$$ and $$g$$, written as $$f \circ g$$ (read as “$$f$$ after $$g$$”) is another map with the same domain as domain of $$g$$ and the same codomain as codomain of $$f$$. To find output value for an input $$a$$ we first “apply” (or follow arrows) of map $$g$$ and then take the result, feed it as input to map $$f$$ and get the final result. Obviously, to feed result of $$g$$ as input to $$f$$, domain of $$f$$ should be the same of codomain of $$g$$.
In a more familiar notation:
$f \circ g = f(g(a))$
That equation also explains why composition “works” from right to left (with respect to the $$f \circ g$$ notation), it’s from the desire to preserve order of functions when we go from a more explicit notation on the right hand side to notation on the left hand side.
Once we have the $$f \circ g$$ map we can forget how we got it and treat it just as an ordinary map, which it is, of course:
$A \xrightarrow{g} B \xrightarrow{f} C = A \xrightarrow{f \circ g} C$
Not only the composition of maps should be possible, but it should satisfy these laws so objects and maps “fit together nicely”:
1. The identity laws:
$A \xrightarrow{1_\text{A}} A \xrightarrow{g} B \Rightarrow A \xrightarrow{g \circ 1_\text{A} = g} B$
and
$A \xrightarrow{f} B \xrightarrow{1_\text{B}} B \Rightarrow A \xrightarrow{1_\text{B} \circ f = f} B$
2. The associative law:
$A \xrightarrow{f} B \xrightarrow{g} C \xrightarrow{h} D \Rightarrow$$A \xrightarrow{h \circ (g \circ f) = (h \circ g) \circ f} D$
These rules make composition of maps work similarly to multiplication of numbers. The identity laws ensure that identity maps work indeed like number 1, so we can easily remove (or add) them without changing anything. We will use that trick a lot. The associative law allows us to move parenthesis. The analogy between multiplication and composition does not extend too far though, because we cannot generally swap order of maps in composition, since their inputs and outputs are sort of “typed” by domain and codomain objects.
## Isomorphisms
One of simplest and ubiquitous things in category theory is isomorphism. A map $$A \xrightarrow{f} B$$ is called an isomorphism, or invertable map, if there is a map $$B \xrightarrow{g} A$$ for which $$g \circ f = 1_\text{A}$$ and $$f \circ g = 1_\text{B}$$. Two objects $$A$$ and $$B$$ are said to be isomorphic if there is at least one isomorphism $$A \xrightarrow{f} B$$.
What does $$g \circ f = 1_\text{A}$$ mean? It means that if we apply $$f$$ to any $$a$$ from $$A$$, feed the result into $$g$$, then we get the same value $$a$$ we started with. Pretty easy, right?
Isomorphisms are cool. They allow to move freely from one representation of object to another. For example, Cartesian system of coordinates is based on the idea that a pair of numbers is isomorphic to a point on plane, then you work from that.
There are a few properties of isomophisms that come directly from the associative and identity laws of maps:
• Reflexive: $$A$$ is isomorphic to $$A$$ (follows from the existence of identity maps).
• Symmetric: if $$A$$ is isomorphic to $$B$$, then $$B$$ is isomorphic to $$A$$. This simply follows from the definition of isomorphism.
• Transitive if $$A$$ is isomorphic to $$B$$, and $$B$$ is isomorphic to $$C$$, then $$A$$ is isomorphic to $$C$$ (see the proof below).
Notation: if $$A \xrightarrow{f} B$$ has an inverse, then the (one and only) inverse for $$f$$ is denoted by the symbol $$f^{-1}$$ (read “$$f$$-inverse”, or “the inverse of $$f$$”). Yes, again we have the analogies with numbers!
$f^{-1} \circ f = 1_\text{A}, f \circ f^{-1} = 1_\text{B}$
Let’s prove the transitive property now as an exercise. We are given that:
$A \xrightarrow{f} B, B \xrightarrow{f^{-1}} A,$$f^{-1} \circ f = 1_\text{A}, f \circ f^{-1} = 1_\text{B}$$B \xrightarrow{k} C, C \xrightarrow{k^{-1}} B,$$k^{-1} \circ k = 1_\text{B}, k \circ k^{-1} = 1_\text{C}$
In order to show that $$A$$ is isomorphic to $$C$$, we need to show that the $$k \circ f$$ map (the only map that takes us from $$A$$ to $$C$$) has an inverse $$g$$. Replacing $$f$$ with $$k \circ f$$ in the definition of isomorphism we have:
$g \circ (k \circ f) = 1_\text{A}$$(k \circ f) \circ g = 1_\text{C}$
To go back from $$C$$ to $$A$$ we have the only way: $$C \xrightarrow{f^{-1} \circ k^{-1}} A$$, let’s show that it actually an inverse for $$k \circ f$$:
$(f^{-1} \circ k^{-1}) \circ (k \circ f) = 1_\text{A}$$f^{-1} \circ (k^{-1} \circ k) \circ f = 1_\text{A}$$f^{-1} \circ 1_\text{B} \circ f = 1_\text{A}$$f^{-1} \circ f = 1_\text{A}$$1_\text{A} = 1_\text{A}$
This makes use of identity laws and associative law we discussed previously. The second equation can be proved the same way.
If $$f$$ has an inverse, then $$f$$ satisfies two cancellation laws:
• If $$f \circ h = f \circ k$$, then $$h = k$$.
• If $$h \circ f = k \circ f$$, then $$h = k$$.
Let prove the first one. We assume that $$f$$ has an inverse and that $$f \circ h = f \circ k$$ and we try to show that $$h = k$$. Since $$f \circ h$$ and $$f \circ k$$ are the same map, $$f^{-1} \circ (f \circ h)$$ and $$f^{-1} \circ (f \circ k)$$ are also the same. But now we can use the rules we already know:
$f^{-1} \circ (f \circ h) = f^{-1} \circ (f \circ k)$$(f^{-1} \circ f) \circ h = (f^{-1} \circ f) \circ k$$1_\text{A} \circ h = 1_\text{A} \circ k$$h = k$
## Sections and retractions
Let’s give names to some special relations of maps that will be very useful to us later. If $$A \xrightarrow{f} B$$, then
• a retraction for $$f$$ is a map $$B \xrightarrow{r} A$$ for which $$r \circ f = 1_\text{A}$$;
• a section for $$f$$ is a map $$B \xrightarrow{s} A$$ for which $$f \circ s = 1_\text{B}$$.
The first thing to note is that we cannot say that some map $$r$$ is a retraction by itself, it only makes sense to say that $$r$$ is retraction for another map $$f$$. The same for sections. So if we have $$r \circ s = 1_\text{A}$$, then $$r$$ is retraction for $$s$$ and $$s$$ is section for $$r$$.
Useful mnemonics for retraction is that it retracts values “back from where they come”. While the name “section” is a little trickier.
We can think of a section $$B \xrightarrow{s} A$$ as a way to select a “B-section” in a (possibly) bigger object $$A$$:
This picture also shows the important idea that in order for $$f$$ to have a section, its domain $$A$$ should be at least as big as codomain $$B$$, not smaller. (Make sure that this makes sense to you now, imagine $$A$$ having only two dots in it and try to travel from dots in $$B$$ to values in $$A$$ and back arriving to the same dots—that’s impossible.)
On the other hand, for $$f$$ to have a retraction, its codomain $$B$$ should be at least as big as its domain $$A$$ (the logic is exactly the same, so I won’t repeat it here).
## Monomorphism and epimorphism
Suppose a map $$A \xrightarrow{f} B$$ has a retraction. Then for any set $$T$$ and for any pair of maps $$T \xrightarrow{x_\text{1}} A$$, $$T \xrightarrow{x_\text{2}} A$$ from $$T$$ to $$A$$.
$\text{if } f \circ x_\text{1} = f \circ x_\text{2} \text{ then } x_\text{1} = x_\text{2}$
Proof: Looking at the definition, we see that the assumption means that we have a map $$r$$ for which $$r \circ f = 1_\text{A}$$. Using the assumption that $$x_\text{1}$$ and $$x_\text{2}$$ are such that $$f$$ composes with them to get the same $$T \to B$$, we can compose further with $$r$$ as follows:
$x_\text{1} = 1_\text{A} \circ x_\text{1} = (r \circ f) \circ x_\text{1}$$= r \circ (f \circ x_\text{1}) = r \circ (f \circ x_\text{2})$$= (r \circ f) \circ x_\text{2} = 1_\text{A} \circ x_\text{2} = x_\text{2}$
Definitions: A map $$f$$ satisfying the conclusion “for any pair of maps $$T \xrightarrow{x_\text{1}} A$$ and $$T \xrightarrow{x_\text{2}} A$$, if $$f \circ x_\text{1} = f \circ x_\text{2}$$ then $$x_\text{1} = x_\text{2}$$” is said to be injective for maps from $$T$$.
If $$f$$ is injective for maps from $$T$$ for every $$T$$, one says that $$f$$ is injective, or is a monomorphism.
What does all this stuff mean anyway? Simply put, if you can “cancel” $$f$$ by having a way (retraction) to go back, then when you apply $$f$$ after other maps and get the same results, then those maps are the same. I.e. you can cancel application of $$f$$ and tell if we were given the same maps or different ones. After application of $$f$$ we can still reason of what happened before the application. That’s the cancellation.
For example, when GHC gets into a situation when it has only result of type-level function application, but it needs to figure out what argument of that function was, it complains that the type-level function may be not injective. Fair enough! (In GHC 8.0, there is a way to annotate type-level functions telling that they are injective.)
Remember that if $$f$$ has a retraction, then $$f$$ satisfies the cancelation law:
• If $$f \circ h = f \circ k$$, then $$h = k$$.
And if $$f$$ has a section, then $$f$$ satisfies another cancelation law:
• If $$h \circ f = k \circ f$$, then $$h = k$$.
(We talked about $$f$$ having an inverse, but if $$f$$ as an inverse, then it happens to be both retraction and section for $$f$$, we will prove this later in the post.)
Suppose a map $$A \xrightarrow{f} B$$ has a section. Then for any set $$T$$ and any pair of maps $$B \xrightarrow{t_\text{1}} T$$, $$B \xrightarrow{t_\text{2}} T$$ from $$B$$ to $$T$$.
$\text{if } t_\text{1} \circ f = t_\text{2} \circ f \text{ then } t_\text{1} = t_\text{2}$
Definition: A map $$f$$ with this cancellation property (if $$t_\text{1} \circ f = t_\text{2} \circ f$$ then $$t_\text{1}=t_\text{2}$$) for every $$T$$ is called epimorphism.
What happens here? Now we apply $$f$$ before some maps $$t_\text{1}$$ and $$t_\text{2}$$, and we conclude that if the results we get are the same, then those $$t_\text{1}$$ and $$t_\text{2}$$ are also the same. Intuitively, given a value $$b$$ from $$B$$ that goes as an input to $$t_\text{1}$$ and $$t_\text{2}$$, we should be able to “cancel” previous application of $$f$$ and tell which value $$a$$ from $$A$$ was given to $$f$$ so that it produced that particular $$b$$. The condition that $$f$$ has a section is exactly the condition that there is a way to go from values from $$B$$ (result of $$f$$) “back” to values from $$A$$ (inputs for $$f$$). Note however that $$A$$ may be “bigger” than $$B$$ and the condition does not forbid $$A$$ from having several $$a$$ going to the same $$b$$.
## Composing sections and retractions
Now we are going to consider two really simple propositions.
Proposition: If $$A \xrightarrow{f} B$$ has a retraction and if $$B \xrightarrow{g} C$$ has a retraction, then $$A \xrightarrow{g \circ f} C$$ has a retraction.
Proof: Let $$r_\text{1} \circ f = 1_\text{A}$$ and $$r_\text{2} \circ g = 1_\text{B}$$. Then a good guess for a retraction of the composite would be the composite of the retractions in the opposite order (which is anyway the only order in which they can be composed).
Using the familiar tricks:
$r \circ (g \circ f) = (r_\text{1} \circ r_\text{2}) \circ (g \circ f)$$= r_\text{1} \circ (r_\text{2} \circ g) \circ f = r_\text{1} \circ 1_\text{B} \circ f$$= r_\text{1} \circ f = 1_\text{A}$
This proves that $$r$$ is a retraction for $$g \circ f$$.
Proving that the composite of two maps each having sections, has itself a section is left as an exercise for the reader.
## Theorem of uniqueness of inverses
Theorem (uniqueness of inverses): If $$f$$ has both a retraction $$r$$ and a section $$s$$, then $$r = s$$.
Proof: From the definition we have, if $$A \xrightarrow{f} B$$, both of the equations
$r \circ f = 1_\text{A} \text{ and } f \circ s = 1_\text{B}$
Then by identity and associative law
$r = r \circ 1_\text{B} = r \circ (f \circ s)$$= (r \circ f) \circ s = 1_\text{A} \circ s = s$
## Another definition of isomorphism, automorphism
Using the notions of “section” and “retraction” we can rephrase the definition of “isomorphism”.
Definitions: A map $$f$$ is called an isomorphism if there exists another map $$f^{-1}$$ which is both a retraction and a section for $$f$$:
$A \xrightarrow{f} B, f \circ f^{-1} = 1_\text{B}$$A \xleftarrow{f^{-1}} B, f^{-1} \circ f = 1_\text{A}$
Such a map $$f^{-1}$$ is called the inverse map for $$f$$; since both of the two equations are required, the theorem of uniqueness of inverses shows that there is only one inverse.
Definition: A map that is an endomap and at the same time an isomorphism is usually called by the one word automorphism.
1. Sorry, I must admit I’ve abandoned the series as of 1st of July, 2017.
2. OK, as one my friend noticed, from now on we rather discuss category of sets, not category theory (which is more abstract, there are no elemenets in objects for example). Too late for me to rewrite everything, though! | {"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": 0.9032001495361328, "perplexity": 418.8427639645501}, "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-2021-25/segments/1623488249738.50/warc/CC-MAIN-20210620144819-20210620174819-00606.warc.gz"} |
http://mathoverflow.net/questions/137841/could-a-non-algebraically-closed-pac-field-be-a-finite-extension-of-an-ordered-f | # Could a non-algebraically closed PAC field be a finite extension of an ordered field?
Is there such an example? Or it is known that a pseudo algebraically closed field which is a finite extension of a formally real field is algebraically closed?
-
As far as I can tell, you can take your formally real field to be the field $\mathbb{Q}^{tr}$ of totally real algebraic numbers (see this paper for a description of its Galois group). Then (according to Wikipedia), adjoining a square root of $-1$ gives you a pseudo algebraically closed field. | {"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": 0.9470018744468689, "perplexity": 119.72038188966326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395679.92/warc/CC-MAIN-20160624154955-00174-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://talkstats.com/threads/why-do-we-use-sample-sd-to-estimate-pop-sd-in-nhst.76625/ | # Why Do We Use Sample SD to Estimate Pop SD in NHST?
#### sosbo
##### New Member
Hello. I'm trying understand how we derive the properties of a null distribution in null hypothesis significance testing. A one-sample z-test scenario (seeing if a sample mean is significantly different from a population where µ and σ are known) makes sense to me. My understanding is that the central limit theorem states that the sampling distribution of the mean will have a mean of µ and SD of σ/√n (i.e., standard error), so those are the properties of the null in that scenario. Once I've established the mean and SE of the null distribution, I understand how to work out the probability associated with a sample mean at least as extreme as the observed one.
But if we take the same scenario, except that σ is unknown, the reasoning starts breaking down for me. My understanding is that we estimate σ using the sample standard deviation (s). That means the properties of the null distribution will be mean = µ and SE = s/√n, and you can work out the probability value from the t distribution. I can do the calculations, but what I don't understand is why s is taken as a trustworthy estimate of the σ to plug into the SE formula in the first place. If the sample is representative of the population, then it makes perfect sense to me that s could estimate σ. But isn't the whole idea of a one-sample t-test that perhaps the sample doesn't belong to the population we're comparing it to? And if it doesn't, then why would s is a good estimate of σ? The reasoning only seems to make sense when the null is true.
I've looked through several intro stats books, but none give a justification for this. I've also tried Googling and searching this forum, but I don't see where this specific question has been posed. I would appreciate any insights on this! Is it just a limitation of the analysis, or am I misunderstanding how it works? Thanks! | {"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": 0.9646308422088623, "perplexity": 211.92782163805202}, "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/1614178363782.40/warc/CC-MAIN-20210302065019-20210302095019-00236.warc.gz"} |
https://worldwidescience.org/topicpages/m/magnetospheres+stellar.html | #### Sample records for magnetospheres stellar
1. A SEARCH FOR X-RAY EMISSION FROM COLLIDING MAGNETOSPHERES IN YOUNG ECCENTRIC STELLAR BINARIES
Energy Technology Data Exchange (ETDEWEB)
Getman, Konstantin V.; Broos, Patrick S. [Department of Astronomy and Astrophysics, 525 Davey Laboratory, Pennsylvania State University, University Park, PA 16802 (United States); Kóspál, Ágnes [Konkoly Observatory, Research Center for Astronomy and Earth Sciences, Hungarian Academy of Sciences, P.O. Box 67, 1525 Budapest (Hungary); Salter, Demerese M. [Department of Astronomy and Laboratory for Millimeter-Wave Astronomy, University of Maryland, College Park, MD 20742 (United States); Garmire, Gordon P. [Huntingdon Institute for X-ray Astronomy, LLC, 10677 Franks Road, Huntingdon, PA 16652 (United States)
2016-12-01
Among young binary stars whose magnetospheres are expected to collide, only two systems have been observed near periastron in the X-ray band: the low-mass DQ Tau and the older and more massive HD 152404. Both exhibit elevated levels of X-ray emission at periastron. Our goal is to determine whether colliding magnetospheres in young high-eccentricity binaries commonly produce elevated average levels of X-ray activity. This work is based on Chandra snapshots of multiple periastron and non-periastron passages in four nearby young eccentric binaries (Parenago 523, RX J1622.7-2325 Nw, UZ Tau E, and HD 152404). We find that for the merged sample of all four binaries the current X-ray data show an increasing average X-ray flux near periastron (at a ∼2.5-sigma level). Further comparison of these data with the X-ray properties of hundreds of young stars in the Orion Nebula Cluster, produced by the Chandra Orion Ultradeep Project (COUP), indicates that the X-ray emission from the merged sample of our binaries cannot be explained within the framework of the COUP-like X-ray activity. However, due to the inhomogeneities of the merged binary sample and the relatively low statistical significance of the detected flux increase, these findings are regarded as tentative only. More data are needed to prove that the flux increase is real and is related to the processes of colliding magnetospheres.
2. Time monitoring of radio jets and magnetospheres in the nearby young stellar cluster R Coronae Australis
International Nuclear Information System (INIS)
Liu, Hauyu Baobab; Takami, Michihiro; Yan, Chi-Hung; Karr, Jennifer; Chou, Mei-Yin; Ho, Paul T.-P.; Galván-Madrid, Roberto; Costigan, Gráinne; Manara, Carlo Felice; Forbrich, Jan; Rodríguez, Luis F.; Zhang, Qizhou
2014-01-01
We report Karl G. Jansky Very Large Array 8-10 GHz (λ = 3.0-3.7 cm) monitoring observations toward the young stellar object (YSO) cluster R Coronae Australis (R CrA), taken from 2012 March 15 to 2012 September 12. These observations were planned to measure the radio flux variabilities in timescales from 0.5 hr to several days, to tens of days, and up to ∼200 days. We found that among the YSOs detectable in individual epochs, in general, the most reddened objects in the Spitzer observations show the highest mean 3.5 cm Stokes I emission, and the lowest fractional variabilities on <200 day timescales. The brightest radio flux emitters in our observations are the two reddest sources IRS7W and IRS7E. In addition, by comparing our observations with observations taken from 1996 to 1998 and 2005, we found that the radio fluxes of these two sources have increased by a factor of ∼1.5. The mean 3.5 cm fluxes of the three Class I/II sources, IRSI, IRS2, and IRS6, appear to be correlated with their accretion rates derived by a previous near-infrared line survey. The weakly accreting Class I/II YSOs, or those in later evolutionary stages, present radio flux variability on <0.5 hr timescales. Some YSOs were detected only during occasional flaring events. The source R CrA went below our detection limit during a few fading events.
3. Planetary magnetospheres
International Nuclear Information System (INIS)
Hill, T.W.; Michel, F.C.
1975-01-01
Recent planetary probes have resulted in the realization of the generality of magnetospheric interactions between the solar wind and the planets. The three categories of planetary magnetospheres are discussed: intrinsic slowly rotating magnetospheres, intrinsic rapidly rotating magnetospheres, and induced magnetospheres. (BJG)
4. The magnetosphere
International Nuclear Information System (INIS)
Ratcliffe, J.A.
1977-01-01
The structure of the magnetosphere, deduced from observations in space craft, is described, together with some of the phenomena that occur in it. A simple non-mathematical outline is given of some of the processes involved. The effects of the magnetosphere on the aurora, and on the magnetic field observed at the ground, are described, and the way they change during magnetospheric storms is discussed. (author)
5. Magnetospheric substorm
International Nuclear Information System (INIS)
1974-01-01
The results of observation of electric field, magnetic field, high energy particles, plasma and aurora on the ground and with artificial satellites during magnetospheric substorm are reviewed, and the problems are mentioned. A new image of magnetospheric substorm is described. The whole description is divided into eight parts. The first part describes the ionospheric electric current and plasma convection accompanying magnetospheric substorm. The variation of geomagnetism during the magnetospheric substorm, the ionospheric equivalent current during the growth and expansion period of substorm, and the relationship between the high energy proton flux of equatorial zone current and peripheral plasma density are illustrated. The second part describes auroral storm. The time variation of aurora observed with a whole sky camera is illustrated. The third part describes the structure of magnetosphere tail. The variation of electron spectrum parameters when the inner edge of plasma sheet passes is illustrated. The fourth part describes the auroral zone of the plasma sheet. The fifth part describes the magnetospheric substorm in magnetosphere tail. The sixth part describes the electric connection of magnetosphere with high latitudinal ionosphere. The seventh part describes interplanet magnetic field and magnetospheric substorm. The eighth part is summary. The ''SC- triggered bay'' accompanied by rapid decrease of X- or H-component occurred frequently immediately after SC in the night side of auroral zone when the rapidstart type magnetic storm at mid- and low-latitudes occurred. The correlation between the Dsub(st) at low latitude and the DS at high latitude during magnetic storm should be reexamined. (Iwakiri, K.)
6. Venus magnetosphere
International Nuclear Information System (INIS)
Podgornyj, I.M.
1983-01-01
Some peculiarities of the structure of the Venus magnetosphere are considered. A Swedish scientist H. Alfven supposes that nebular bodies with ionospheric shelles of the type of Venus atmosphere possess induced magnetospheres with dragged magnetic tails. In the Institute of Space Research of the USSR Academy of Sciences experiments on the modelling of such magnetosphere are performed. The possibility of formation of the shock wave in the body with plasma shell in the absence of the proper magnetic shell is proved. The cosmic ''Pioneer-Venus'' equipment is used to obtain such a distribution of the magnetic field depending on the distance to Venus as it was predicted by the laboratory model
7. Outer magnetosphere
International Nuclear Information System (INIS)
Schardt, A.W.; Behannon, K.W.; Lepping, R.P.; Carbary, J.F.; Eviatar, A.; Siscoe, G.L.
1984-01-01
Similarities between the Saturnian and terrestrial outer magnetosphere are examined. Saturn, like earth, has a fully developed magnetic tail, 80 to 100 RS in diameter. One major difference between the two outer magnetospheres is the hydrogen and nitrogen torus produced by Titan. This plasma is, in general, convected in the corotation direction at nearly the rigid corotation speed. Energies of magnetospheric particles extend to above 500 keV. In contrast, interplanetary protons and ions above 2 MeV have free access to the outer magnetosphere to distances well below the Stormer cutoff. This access presumably occurs through the magnetotail. In addition to the H+, H2+, and H3+ ions primarily of local origin, energetic He, C, N, and O ions are found with solar composition. Their flux can be substantially enhanced over that of interplanetary ions at energies of 0.2 to 0.4 MeV/nuc
8. Terrestrial magnetosphere
International Nuclear Information System (INIS)
Pande, D.C.; Agarwal, D.C.
1982-01-01
This paper presents a review about terrestrial magnetosphere. During the last few years considerable investigation have been carried out about the properties of Solar Wind and its interaction with planetary magnetic fields. It is therefore of high importance to accumulate all the investigations in a comprehensive form. The paper reviews the property of earth's magnetosphere, magnetosheath, magneto pause, polar cusps, bow shook and plasma sheath. (author)
9. Pulsar magnetospheres
International Nuclear Information System (INIS)
Kennel, C.F.; Fujimura, F.S.; Pellat, R.
1979-01-01
The structure of both the interior and exterior pulsar magnetospehere depends upon the strength of its plasma source near the surface of the star. We review magnetospheric models in the light of a vacuum pair-production source model proposed by Sturrock, and Ruderman and Sutherland. This model predicts the existence of a cutoff, determined by the neutron star's spin rate and magnetic field strength, beyond which coherent radio emission is no longer possible. The observed distribution of pulsar spin periods and period derivates, and the distribution of pulsars with missing radio pulses, is quantitatively consistent with the pair production threshold, when its variation of neutron star radius and moment of interia with mass is taken into account. All neutron stars observed as pulsars can have relativistic magneto-hydrodynamic wind exterior magnetospheres. The properties of the wind can be directly related to those of the pair production source. Radio pulsars cannot have relativistic plasma wave exterior magnetospheres. On the other hand, most erstwhile pulsars in the galaxy are probably halo objects that emit weak fluxes of energetic photons that can have relativistic wave exterior magnetospheres. Extinct pulsars have not been yet observed. (orig.)
10. Pulsars Magnetospheres
Science.gov (United States)
Timokhin, Andrey
2012-01-01
Current density determines the plasma flow regime. Cascades are non-stationary. ALWAYS. All flow regimes look different: multiple components (?) Return current regions should have particle accelerating zones in the outer magnetosphere: y-ray pulsars (?) Plasma oscillations in discharges: direct radio emission (?)
11. Theories of magnetospheres around accreting compact objects
International Nuclear Information System (INIS)
Vasyliunas, V.M.
1979-01-01
A wide class of galactic X-ray sources are believed to be binary systems where mass is flowing from a normal star to a companion that is a compact object, such as a neutron star. The strong magnetic fields of the compact object create a magnetosphere around it. We review the theoretical models developed to describe the properties of magnetospheres in such accreting binary systems. The size of the magnetosphere can be estimated from pressure balance arguments and is found to be small compared to the over-all size of the accretion region but large compared object if the latter is a neutron star. In the early models the magnetosphere was assumed to have open funnels in the polar regions, through which accreting plasma could pour in. Later, magnetically closed models were developed, with plasma entry made possible by instabilities at the magnetosphere boundary. The theory of plasma flow inside the magnetosphere has been formulated in analogy to a stellar wind with reversed flow; a complicating factor is the instability of the Alfven critical point for inflow. In the case of accretion via a well-defined disk, new problems if magnetospheric structure appear, in particular the question to what extent and by what process the magnetic fields from the compact object can penetrate into the acretion disk. Since the X-ray emission is powered by the gravitational energy released in the accretion process, mass transfer into the magnetosphere is of fundamental importance; the various proposed mechanisms are critically examined. (orig.)
12. Magnetohydrodynamic calculations on pulsar magnetospheres
International Nuclear Information System (INIS)
Brinkmann, W.
1976-01-01
In this paper, the relativistic magnetohydrodynamic is presented in covariant form and applied to some problems in the field of pulsar magnetospheres. In addition, numerical methods to solve the resulting equations of motion are investigated. The theory of relativistic magnetohydrodynamic presented here is valid in the framework of the theory of general relativity, describing the interaction of electromagnetic fields with an ideal fluid. In the two-dimensional case, a Lax-Wendroff method is studied which should be optimally stable with the operator splitting of Strang. In the framework of relativistic magnetohydrodynamic also the model of a stationary aequatorial stellar pulsar wind as well as the parallel rotator is investigated. (orig.) [de
13. Mercury's Dynamic Magnetosphere
Science.gov (United States)
Imber, S. M.
2018-05-01
The global dynamics of Mercury's magnetosphere will be discussed, focussing on observed asymmetries in the magnetotail and on the precipitation of particles of magnetospheric origin onto the nightside planetary surface.
14. Dynamics of magnetospheric plasmas
International Nuclear Information System (INIS)
Horwitz, J.L.
1985-01-01
The dynamical behavior of the magnetospheric plasmas which control the electrostatic charging of spacecraft is the result of the complex interaction of a variety of production, loss, transport, and energization mechanisms in the magnetosphere. This paper is intended to provide the spacecraft engineer with a foundation in the basic morphology and controlling processes pertaining to magnetospheric plasma dynamics in the inner magnetosphere, including the synchronous orbit region. 32 references
15. Inner Magnetospheric Physics
Science.gov (United States)
Gallagher, Dennis
2018-01-01
Outline - Inner Magnetosphere Effects: Historical Background; Main regions and transport processes: Ionosphere, Plasmasphere, Plasma sheet, Ring current, Radiation belt; Geomagnetic Activity: Storms, Substorm; Models.
16. Concepts of magnetospheric convection
International Nuclear Information System (INIS)
Vasyliunas, V.M.
1975-01-01
Magnetospheric physics, which grew out of attempts to understand the space environment of the Earth, is becoming increasingly applicable to other systems in the Universe. Among the planets, in addition to the Earth, Jupiter, Mercury, Mars and (in a somewhat different way) Venus are now known to have magnetospheres. The magnetospheres of pulsars have been regarded as an essential part of the pulsar phenomenon. Other astrophysical systems, such as supernova remnant shells or magnetic stars and binary star systems, may be describable as magnetospheres. The major concepts of magnetospheric physics thus need to be formulated in a general way not restricted to the geophysical context in which they may have originated. Magnetospheric convection has been one of the most important and fruitful concepts in the study of the Earth's magnetosphere. This paper describes the basic theoretical notions of convection in a manner applicable to magnetospheres generally and discusses the relative importance of convective corotational motions, with particular reference to the comparison of the Earth and Jupiter. (Auth.)
17. MESSENGER: Exploring Mercury's Magnetosphere
Science.gov (United States)
Slavin, James A.
2008-01-01
The MESSENGER mission to Mercury offers our first opportunity to explore this planet's miniature magnetosphere since Mariner 10's brief fly-bys in 1974-5. Mercury's magnetosphere is unique in many respects. The magnetosphere of Mercury is the smallest in the solar system with its magnetic field typically standing off the solar wind only - 1000 to 2000 km above the surface. For this reason there are no closed dri-fi paths for energetic particles and, hence, no radiation belts; the characteristic time scales for wave propagation and convective transport are short possibly coupling kinetic and fluid modes; magnetic reconnection at the dayside magnetopause may erode the subsolar magnetosphere allowing solar wind ions to directly impact the dayside regolith; inductive currents in Mercury's interior should act to modify the solar In addition, Mercury's magnetosphere is the only one with its defining magnetic flux tubes rooted in a planetary regolith as opposed to an atmosphere with a conductive ionosphere. This lack of an ionosphere is thought to be the underlying reason for the brevity of the very intense, but short lived, approx. 1-2 min, substorm-like energetic particle events observed by Mariner 10 in Mercury's magnetic tail. In this seminar, we review what we think we know about Mercury's magnetosphere and describe the MESSENGER science team's strategy for obtaining answers to the outstanding science questions surrounding the interaction of the solar wind with Mercury and its small, but dynamic magnetosphere.
18. Planets, stars and stellar systems
CERN Document Server
Bond, Howard; McLean, Ian; Barstow, Martin; Gilmore, Gerard; Keel, William; French, Linda
2013-01-01
This is volume 3 of Planets, Stars and Stellar Systems, a six-volume compendium of modern astronomical research covering subjects of key interest to the main fields of contemporary astronomy. This volume on “Solar and Stellar Planetary Systems” edited by Linda French and Paul Kalas presents accessible review chapters From Disks to Planets, Dynamical Evolution of Planetary Systems, The Terrestrial Planets, Gas and Ice Giant Interiors, Atmospheres of Jovian Planets, Planetary Magnetospheres, Planetary Rings, An Overview of the Asteroids and Meteorites, Dusty Planetary Systems and Exoplanet Detection Methods. All chapters of the handbook were written by practicing professionals. They include sufficient background material and references to the current literature to allow readers to learn enough about a specialty within astronomy, astrophysics and cosmology to get started on their own practical research projects. In the spirit of the series Stars and Stellar Systems published by Chicago University Press in...
19. Saturn's outer magnetosphere
Science.gov (United States)
Schardt, A. W.; Behannon, K. W.; Carbary, J. F.; Eviatar, A.; Lepping, R. P.; Siscoe, G. L.
1983-01-01
Similarities between the Saturnian and terrestrial outer magnetosphere are examined. Saturn, like Earth, has a fully developed magnetic tail, 80 to 100 RS in diameter. One major difference between the two outer magnetospheres is the hydrogen and nitrogen torus produced by Titan. This plasma is, in general, convected in the corotation direction at nearly the rigid corotation speed. Energies of magnetospheric particles extend to above 500 keV. In contrast, interplanetary protons and ions above 2 MeV have free access to the outer magnetosphere to distances well below the Stormer cutoff. This access presumably occurs through the magnetotail. In addition to the H+, H2+, and H3+ ions primarily of local origin, energetic He, C, N, and O ions are found with solar composition. Their flux can be substantially enhanced over that of interplanetary ions at energies of 0.2 to 0.4 MeV/nuc.
20. Magnetospheric plasma physics
International Nuclear Information System (INIS)
Bingham, R.
1989-09-01
The discovery of the earth's radiation belts in 1957 by Van Allen marked the beginning of what is now known as magnetospheric physics. In this study of plasma physics in the magnetosphere, we shall take the magnetosphere to be that part of the earth's ionized atmosphere which is formed by the interaction of the solar wind with the earth's dipole-like magnetic field. It extends from approximately 100km above the earth's surface where the proton-neutral atom collision frequency is equal to the proton gyrofrequency to about ten earth radii (R E ∼ 6380km) in the sunward direction and to several hundred earth radii in the anti-sunward direction. The collision dominated region is called the ionosphere and is sometimes considered separate from the collisionless plasma region. In the ionosphere ion-neutral collisions are dominant and one may think of the ionosphere as a frictional boundary layer ∼ 1000km thick. Other planets are also considered. (author)
1. Stellar formation
CERN Document Server
Reddish, V C
1978-01-01
Stellar Formation brings together knowledge about the formation of stars. In seeking to determine the conditions necessary for star formation, this book examines questions such as how, where, and why stars form, and at what rate and with what properties. This text also considers whether the formation of a star is an accident or an integral part of the physical properties of matter. This book consists of 13 chapters divided into two sections and begins with an overview of theories that explain star formation as well as the state of knowledge of star formation in comparison to stellar structure
2. Magnetospheric plasma waves
International Nuclear Information System (INIS)
Shawhan, S.D.
1977-01-01
A brief history of plasma wave observations in the Earth's magnetosphere is recounted and a classification of the identified plasma wave phenomena is presented. The existence of plasma waves is discussed in terms of the characteristic frequencies of the plasma, the energetic particle populations and the proposed generation mechanisms. Examples are given for which plasmas waves have provided information about the plasma parameters and particle characteristics once a reasonable theory has been developed. Observational evidence and arguments by analogy to the observed Earth plasma wave processes are used to identify plasma waves that may be significant in other planetary magnetospheres. The similarities between the observed characteristics of the terrestrial kilometric radiation and radio bursts from Jupiter, Saturn and possibly Uranus are stressed. Important scientific problems concerning plasma wave processes in the solar system and beyond are identified and discussed. Models for solar flares, flare star radio outbursts and pulsars include elements which are also common to the models for magnetospheric radio bursts. Finally, a listing of the research and development in terms of instruments, missions, laboratory experiments, theory and computer simulations needed to make meaningful progress on the outstanding scientific problems of plasma wave research is given. (Auth.)
3. Stellar remnants
CERN Document Server
Kawaler, S D; Srinivasan, G
1997-01-01
This volume examines the internal structure, origin and evolution of white dwarfs, neutron stars and black holes, all objects at the final stage of stellar evolution. It covers topics such as: pulsation of white dwarfs; millisecond pulsars; and the dynamics around black holes.
4. Stellar winds
International Nuclear Information System (INIS)
Weymann, R.J.
1978-01-01
It is known that a steady outflow of material at comparable rates of mass loss but vastly different speeds is now known to be ubiquitous phenomenon among both the luminous hot stars and the luminous but cool red giants. The flows are probably massive enough in both cases to give rise to significant effects on stellar evolution and the mass balance between stars and the interstellar medium. The possible mechanisms for these phenomena as well as the methods of observation used are described. In particular, the mass-loss processes in stars other than the sun that also involve a steady flow of matter are considered. The evidence for their existence is described, and then the question of whether the process thought to produce the solar wind is also responsible for producing these stellar winds is explored
5. Stellarator physics
International Nuclear Information System (INIS)
1990-07-01
This document consists of the proceedings of the Seventh International Workshop on Stellarators, held in Oak Ridge, Tennessee, USA, 10-14 April, 1989. The document consists of a summary of presentations, an overview of experimental results, and papers presented at the workshop on transport, impurities and divertors, diagnostics, ECH confinement experiments, equilibrium and stability studies, RF heating, confinement, magnetic configurations, and new experiments. Refs, figs and tabs
6. Pulsar Magnetospheres and Pulsar Winds
OpenAIRE
Beskin, Vasily S.
2016-01-01
Surprisingly, the chronology of nearly 50 years of the pulsar magnetosphere and pulsar wind research is quite similar to the history of our civilization. Using this analogy, I have tried to outline the main results obtained in this field. In addition to my talk, the possibility of particle acceleration due to different processes in the pulsar magnetosphere is discussed in more detail.
7. Stellar evolution
CERN Document Server
2013-01-01
Stellar Evolution, Second Edition covers the significant advances in the understanding of birth, life, and death of stars.This book is divided into nine chapters and begins with a description of the characteristics of stars according to their brightness, distance, size, mass, age, and chemical composition. The next chapters deal with the families, structure, and birth of stars. These topics are followed by discussions of the chemical composition and the evolution of main-sequence stars. A chapter focuses on the unique features of the sun as a star, including its evolution, magnetic fields, act
8. Globally Imaging the Magnetosphere
Science.gov (United States)
Sibeck, D. G.
2017-12-01
Over the past two decades, a host of missions have provided the multipoint in situ measurementsneeded to understand the meso- and micro-scale physics governing the solar wind-magnetosphereinteraction. Observations by the ISTP missions, Cluster, THEMIS, Double Star, and most recentlyMMS, have enabled us to identify the occurrence of some of the many proposed models for magneticreconnection and particle acceleration in a wide range of accessible magnetospheric contexts. However, todetermine which of these processes are most important to the overall interaction, we need globalobservations, from both ground-based instrumentation and imaging spacecraft. This talk outlinessome of the the global puzzles that remain to be solved and some of the very novel means that are availableto address them, including soft X-ray, energetic neutral atom, far and extreme ultraviolet imaging andenhanced arrays of ground observatories.
9. The Extended Pulsar Magnetosphere
Science.gov (United States)
Constantinos, Kalapotharakos; Demosthenes, Kazanas; Ioannis, Contopoulos
2012-01-01
We present the structure of the 3D ideal MHD pulsar magnetosphere to a radius ten times that of the light cylinder, a distance about an order of magnitude larger than any previous such numerical treatment. Its overall structure exhibits a stable, smooth, well-defined undulating current sheet which approaches the kinematic split monopole solution of Bogovalov 1999 only after a careful introduction of diffusivity even in the highest resolution simulations. It also exhibits an intriguing spiral region at the crossing of two zero charge surfaces on the current sheet, which shows a destabilizing behavior more prominent in higher resolution simulations. We discuss the possibility that this region is physically (and not numerically) unstable. Finally, we present the spiral pulsar antenna radiation pattern.
10. Upper ionosphere and magnetospheric-ionospheric coupling
International Nuclear Information System (INIS)
Manzano, J.R.
1989-02-01
After a presentation of the ionospheric physics and of the earth magnetosphere morphology, generation and dynamics, the magnetosphere-ionosphere coupling in quiet and perturbed conditions is discussed. Some summary information about other planetary magnetospheres, particularly Venus and Jupiter magnetospheres, are finally given. 41 refs, 24 figs
11. The Magnetospheric Multiscale Mission
Science.gov (United States)
Burch, James
Magnetospheric Multiscale (MMS), a NASA four-spacecraft mission scheduled for launch in November 2014, will investigate magnetic reconnection in the boundary regions of the Earth’s magnetosphere, particularly along its dayside boundary with the solar wind and the neutral sheet in the magnetic tail. Among the important questions about reconnection that will be addressed are the following: Under what conditions can magnetic-field energy be converted to plasma energy by the annihilation of magnetic field through reconnection? How does reconnection vary with time, and what factors influence its temporal behavior? What microscale processes are responsible for reconnection? What determines the rate of reconnection? In order to accomplish its goals the MMS spacecraft must probe both those regions in which the magnetic fields are very nearly antiparallel and regions where a significant guide field exists. From previous missions we know the approximate speeds with which reconnection layers move through space to be from tens to hundreds of km/s. For electron skin depths of 5 to 10 km, the full 3D electron population (10 eV to above 20 keV) has to be sampled at rates greater than 10/s. The MMS Fast-Plasma Instrument (FPI) will sample electrons at greater than 30/s. Because the ion skin depth is larger, FPI will make full ion measurements at rates of greater than 6/s. 3D E-field measurements will be made by MMS once every ms. MMS will use an Active Spacecraft Potential Control device (ASPOC), which emits indium ions to neutralize the photoelectron current and keep the spacecraft from charging to more than +4 V. Because ion dynamics in Hall reconnection depend sensitively on ion mass, MMS includes a new-generation Hot Plasma Composition Analyzer (HPCA) that corrects problems with high proton fluxes that have prevented accurate ion-composition measurements near the dayside magnetospheric boundary. Finally, Energetic Particle Detector (EPD) measurements of electrons and
12. Jupiter's magnetosphere and radiation belts
Science.gov (United States)
Kennel, C. F.; Coroniti, F. V.
1979-01-01
Radioastronomy and Pioneer data reveal the Jovian magnetosphere as a rotating magnetized source of relativistic particles and radio emission, comparable to astrophysical cosmic ray and radio sources, such as pulsars. According to Pioneer data, the magnetic field in the outer magnetosphere is radially extended into a highly time variable disk-shaped configuration which differs fundamentally from the earth's magnetosphere. The outer disk region, and the energetic particles confined in it, are modulated by Jupiter's 10 hr rotation period. The entire outer magnetosphere appears to change drastically on time scales of a few days to a week. In addition to its known modulation of the Jovian decametric radio bursts, Io was found to absorb some radiation belt particles and to accelerate others, and most importantly, to be a source of neutral atoms, and by inference, a heavy ion plasma which may significantly affect the hydrodynamic flow in the magnetosphere. Another important Pioneer finding is that the Jovian outer magnetosphere generates, or permits to escape, fluxes of relativistic electrons of such intensities that Jupiter may be regarded as the dominant source of 1 to 30 MeV cosmic ray electrons in the heliosphere.
13. The Magnetospheric Multiscale Magnetometers
Science.gov (United States)
Russell, C. T.; Anderson, B. J.; Baumjohann, W.; Bromund, K. R.; Dearborn, D.; Fischer, D.; Le, G.; Leinweber, H. K.; Leneman, D.; Magnes, W.;
2014-01-01
The success of the Magnetospheric Multiscale mission depends on the accurate measurement of the magnetic field on all four spacecraft. To ensure this success, two independently designed and built fluxgate magnetometers were developed, avoiding single-point failures. The magnetometers were dubbed the digital fluxgate (DFG), which uses an ASIC implementation and was supplied by the Space Research Institute of the Austrian Academy of Sciences and the analogue magnetometer (AFG) with a more traditional circuit board design supplied by the University of California, Los Angeles. A stringent magnetic cleanliness program was executed under the supervision of the Johns Hopkins University,s Applied Physics Laboratory. To achieve mission objectives, the calibration determined on the ground will be refined in space to ensure all eight magnetometers are precisely inter-calibrated. Near real-time data plays a key role in the transmission of high-resolution observations stored onboard so rapid processing of the low-resolution data is required. This article describes these instruments, the magnetic cleanliness program, and the instrument pre-launch calibrations, the planned in-flight calibration program, and the information flow that provides the data on the rapid time scale needed for mission success.
14. International Nuclear Information System (INIS)
Van Allen, J.A.
1983-01-01
The history of the scientific investigation of the earth magnetosphere during the period 1946-1960 is reviewed, with a focus on satellite missions leading to the discovery of the inner and outer radiation belts. Chapters are devoted to ground-based studies of the earth magnetic field through the 1930s, the first U.S. rocket flights carrying scientific instruments, the rockoon flights from the polar regions (1952-1957), U.S. planning for scientific use of artificial satellites (1956), the launch of Sputnik I (1957), the discovery of the inner belt by Explorers I and III (1958), the Argus high-altitude atomic-explosion tests (1958), the confirmation of the inner belt and discovery of the outer belt by Explorer IV and Pioneers I-V, related studies by Sputniks II and III and Luniks I-III, and the observational and theoretical advances of 1959-1961. Photographs, drawings, diagrams, graphs, and copies of original notes and research proposals are provided. 227 references
15. Stellar astrophysics
International Nuclear Information System (INIS)
1988-01-01
Enhanced mass loss occurs at critical stages in the evolution of stars over a wide range of stellar mass. Observationally, these stages are difficult to identify because of their short duration and because the star is often obscured by dust which condenses in the ejecta. A study of a G-type star, of which only the outer envelope was directly visible, was undertaken by the South African Astronomical Observatory (SAAO). The star itself was obscured by dust clouds and its light was only feebly seen by reflection from some of these clouds. Other studies of the galaxy undertaken by the SAAO include observations of the following: the extreme carbon star IRAS 15194-5115; RV Tauri and T Tauri stars; pre-main sequence stars; the properties of circumstellar dust; rotational modulation and flares on RS CVn and BY Dra stars; heavy-element stars; hydrogen-deficient stars; the open cluster NGC6192; stars in Omega Centauri, and lunar occulations of stars. Simultaneous x-ray, radio and optical data of the flare star YZ CMi were also obtained. 1 fig
International Nuclear Information System (INIS)
Ondoh, Tadanori; Nakamura, Yoshikatsu; Koseki, Teruo; Watanabe, Sigeaki; Murakami, Toshimitsu
1977-01-01
Radio sounding of the plasmapause from a geostationary satellite has been investigated to observe time variations of the plasmapause structure and effects of the plasma convection. In the equatorial plane, the plasmapause is located, on the average, at 4 R sub(E) (R sub(E); Earth radius), and the plasma density drops outwards from 10 2 -10 3 /cm 3 to 1-10/cm 3 in the plasmapause width of about 600 km. Plasmagrams showing a relation between the virtual range and sounding frequencies are computed by ray tracing of LF-VLF waves transmitted from a geostationary satellite, using model distributions of the electron density in the vicinity of the plasmapause. The general features of the plasmagrams are similar to the topside ionograms. The plasmagram has no penetration frequency such as f 0 F 2 , but the virtual range of the plasmagram increases rapidly with frequency above 100 kHz, since the distance between a satellite and wave reflection point increases rapidly with increasing the electron density inside the plasmapause. The plasmapause sounder on a geostationary satellite has been designed by taking account of an average propagation distance of 2 x 2.6 R sub(E) between a satellite (6.6 R sub(E)) and the plasmapause (4.0 R sub(E)), background noise, range resolution, power consumption, and receiver S/N of 10 dB. The 13-bit Barker coded pulses of baud length of 0.5 msec should be transmitted in direction parallel to the orbital plane at frequencies for 10 kHz-2MHz in a pulse interval of 0.5 sec. The transmitter peak power of 70 watts and 700 watts are required respectively in geomagnetically quiet and disturbed (strong nonthermal continuum emissions) conditions for a 400 meter cylindrical dipole of 1.2 cm diameter on the geostationary satellite. This technique will open new area of radio sounding in the magnetosphere. (auth.)
17. Electric fields in the magnetosphere
International Nuclear Information System (INIS)
Faelthammar, C.G.
1989-12-01
The electric field plays an important role in the complex plasma system called the magnetosphere. In spite of this, direct measurement of this quantity are still scarce except in its lowest-altitude part, i.e. the ionosphere. The large scale ionospheric electric field has been determined from measurement on the ground and in low satellite orbit. For most of the magnetosphere, our concepts of the electric field have mostly been based on theoretical considerations and extrapolations of the ionspheric electric field. Direct, in situ, electric field measurements in the outer parts of the magnetosphere have been made only relatively recently. A few satellite missions. most recently the Viking mission, have extended the direct empirical knowledge so as to include major parts of the magnetosphere. These measurements have revealed a number of unexpected features. The actual electric field has been found to have unexpectedly strong space and time variations, which reflect the dynamic nature of the system. Examples are give of measured electric fields in the plasmasphere, the plasmasheet, the neutral sheet, the magnetotail, the flanks of the magnetosphere, the dayside magnetopause and the auroral acceleration region. (author)
18. A novel look at the pulsar force-free magnetosphere
Science.gov (United States)
Petrova, S. A.; Flanchik, A. B.
2018-03-01
The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, B_{new}0=3.3×10^{-4}B/P, where P is the pulsar period. Then the 7-order scatter of the magnetic field derived from the rotational characteristics of the pulsars observed appears consistent with the \\cotχ-law, where χ is a random quantity uniformly distributed in the interval [0,π/2]. Our result is suggestive of a unique actual magnetic field strength of the neutron stars along with a random angle between the magnetic and rotational axes and gives insight into the neutron star unification on the geometrical basis.
19. Research in magnetospheric wave phenomena
International Nuclear Information System (INIS)
Barfield, J.N.
1975-01-01
During the last 4 years a number of developments have occurred which have led to an increased understanding of the role of wave phenomena in the physical processes of the magnetosphere. While the studies span the frequency regime from millihertz to the electron gyrofrequency, the developments to be discussed in this paper have in common that they have added substantially to the understanding of the controlling processes, regions, and boundaries in the magnetosphere. The topics discussed are the increased awareness and documentation of the role of the plasmapause in micropulsation generation and propagation; the establishment of the role of ion cyclotron waves in the wave-particle interactions at the plasmapause; the discovery of magnetospheric electrostatic waves with ω = (3/2)Ω/sub -/; the discovery and preliminary identification of the source of plasmaspheric hiss; and the analysis of storm time Pc 5 waves as observed on the satellites ATS 1 and Explorer 45. (auth)
20. Substorms in the earth's magnetosphere
International Nuclear Information System (INIS)
Baker, D.N.
1984-01-01
Magnetospheres are plasma regions of large scale in space dominated by magnetic field effects. The earth, and many planets in our solar system, are known to have magnetospheric regions around them. Magnetospheric substorms represent the intense, rapid dissipation of energy that has been extracted from the solar wind and stored temporarily in the terrestrial magnetotail. In this paper a widely, but not universally, accepted model of substorms is described. The energy budgets, time scales, and conversion efficiencies for substorms are presented. The primary forms of substorm energy dissipation are given along with the average levels of the dissipation. Aspects of particle acceleration and precipitation, Joule heating mechanisms, ring current formation, and plasmoid escape are illustrated based on in situ observations taken from the large available data base. A brief description is given of possible analogues of substorm-like behavior in other astrophysical systems. 27 references, 12 figures
1. Stellar Metamorphosis:
Science.gov (United States)
2002-01-01
[TOP LEFT AND RIGHT] The Hubble Space Telescope's Wide Field and Planetary Camera 2 has captured images of the birth of two planetary nebulae as they emerge from wrappings of gas and dust, like butterflies breaking out of their cocoons. These images highlight a fleeting phase in the stellar burnout process, occurring just before dying stars are transformed into planetary nebulae. The left-hand image is the Cotton Candy nebula, IRAS 17150-3224; the right-hand image, the Silkworm nebula, IRAS 17441-2411. Called proto-planetary nebulae, these dying stars have been caught in a transition phase between a red giant and a planetary nebula. This phase is only about 1,000 years long, very short in comparison to the 1 billion-year lifetime of a star. These images provide the earliest snapshots of the transition process. Studying images of proto-planetary nebulae is important to understanding the process of star death. A star begins to die when it has exhausted its thermonuclear fuel - hydrogen and helium. The star then becomes bright and cool (red giant phase) and swells to several tens of times its normal size. It begins puffing thin shells of gas off into space. These shells become the star's cocoon. In the Hubble images, the shells are the concentric rings seen around each nebula. But the images also reveal the nebulae breaking out from those shells. The butterfly-like wings of gas and dust are a common shape of planetary nebulae. Such butterfly shapes are created by the 'interacting winds' process, in which a more recent 'fast wind' - material propelled by radiation from the hot central star - punches a hole in the cocoon, allowing the nebula to emerge. (This 'interacting wind' theory was first proposed by Dr. Sun Kwok to explain the origin of planetary nebulae, and has been subsequently proven successful in explaining their shapes.) The nebulae are being illuminated by light from the invisible central star, which is then reflected toward us. We are viewing the nebulae
2. The inner magnetosphere imager mission
International Nuclear Information System (INIS)
Johnson, L.; Herrmann, M.
1993-01-01
After 30 years of in situ measurements of the Earth's magnetosphere, scientists have assembled an incomplete picture of its global composition and dynamics. Imaging the magnetosphere from space will enable scientists to better understand the global shape of the inner magnetosphere, its components and processes. The proposed inner magnetosphere imager (IMI) mission will obtain the first simultaneous images of the component regions of the inner magnetosphere and will enable scientists to relate these global images to internal and external influences as well as local observations. To obtain simultaneous images of component regions of the inner magnetosphere, measurements will comprise: the ring current and inner plasma sheet using energetic neutral atoms; the plasmasphere using extreme ultraviolet; the electron and proton auroras using far ultraviolet (FUV) and x rays; and the geocorona using FUV. The George C. Marshall Space Flight Center (MSFC) is performing a concept definition study of the proposed mission. NASA's Office of Space Science and Applications has placed the IMI third in its queue of intermediate-class missions for launch in the 1990's. An instrument complement of approximately seven imagers will fly in an elliptical Earth orbit with a seven Earth Radii (R E ) altitude apogee and approximately 4,800-kin altitude perigee. Several spacecraft concepts were examined for the mission. The first concept utilizes a spinning spacecraft with a despun platform. The second concept splits the instruments onto a spin-stabilized spacecraft and a complementary three-axis stabilized spacecraft. Launch options being assessed for the spacecraft range from a Delta 11 for the single and dual spacecraft concepts to dual Taurus launches for the two smaller spacecraft. This paper will address the mission objectives, the spacecraft design considerations, the results of the MSFC concept definition study, and future mission plans
3. Investigating the Magnetospheres of Rapidly Rotating B-type Stars
Science.gov (United States)
Fletcher, C. L.; Petit, V.; Nazé, Y.; Wade, G. A.; Townsend, R. H.; Owocki, S. P.; Cohen, D. H.; David-Uraz, A.; Shultz, M.
2017-11-01
Recent spectropolarimetric surveys of bright, hot stars have found that ~10% of OB-type stars contain strong (mostly dipolar) surface magnetic fields (~kG). The prominent paradigm describing the interaction between the stellar winds and the surface magnetic field is the magnetically confined wind shock (MCWS) model. In this model, the stellar wind plasma is forced to move along the closed field loops of the magnetic field, colliding at the magnetic equator, and creating a shock. As the shocked material cools radiatively it will emit X-rays. Therefore, X-ray spectroscopy is a key tool in detecting and characterizing the hot wind material confined by the magnetic fields of these stars. Some B-type stars are found to have very short rotational periods. The effects of the rapid rotation on the X-ray production within the magnetosphere have yet to be explored in detail. The added centrifugal force due to rapid rotation is predicted to cause faster wind outflows along the field lines, leading to higher shock temperatures and harder X-rays. However, this is not observed in all rapidly rotating magnetic B-type stars. In order to address this from a theoretical point of view, we use the X-ray Analytical Dynamical Magnetosphere (XADM) model, originally developed for slow rotators, with an implementation of new rapid rotational physics. Using X-ray spectroscopy from ESA's XMM-Newton space telescope, we observed 5 rapidly rotating B-types stars to add to the previous list of observations. Comparing the observed X-ray luminosity and hardness ratio to that predicted by the XADM allows us to determine the role the added centrifugal force plays in the magnetospheric X-ray emission of these stars.
4. General-relativistic pulsar magnetospheric emission
Science.gov (United States)
Pétri, J.
2018-06-01
Most current pulsar emission models assume photon production and emission within the magnetosphere. Low-frequency radiation is preferentially produced in the vicinity of the polar caps, whereas the high-energy tail is shifted to regions closer but still inside the light cylinder. We conducted a systematic study of the merit of several popular radiation sites like the polar cap, the outer gap, and the slot gap. We computed sky maps emanating from each emission site according to a prescribed distribution function for the emitting particles made of an electron/positron mixture. Calculations are performed using a three-dimensional integration of the plasma emissivity in the vacuum electromagnetic field of a rotating and centred general-relativistic dipole. We compare Newtonian electromagnetic fields to their general-relativistic counterpart. In the latter case, light bending is also taken into account. As a typical example, light curves and sky maps are plotted for several power-law indices of the particle distribution function. The detailed pulse profiles strongly depend on the underlying assumption about the fluid motion subject to strong electromagnetic fields. This electromagnetic topology enforces the photon propagation direction directly, or indirectly, from aberration effects. We also discuss the implication of a net stellar electric charge on to sky maps. Taking into account, the electric field strongly affects the light curves originating close to the light cylinder, where the electric field strength becomes comparable to the magnetic field strength.
International Nuclear Information System (INIS)
Miller, R.L.
1994-01-01
The stellarator is a class of helical/toroidal magnetic fusion devices. Recent international progress in stellarator power plant conceptual design is reviewed and comparisons in the areas of physics, engineering, and economics are made with recent tokamak design studies
6. Magnetosphere imager science definition team: Executive summary
Science.gov (United States)
Armstrong, T. P.; Gallagher, D. L.; Johnson, C. L.
1995-01-01
For three decades, magnetospheric field and plasma measurements have been made by diverse instruments flown on spacecraft in many different orbits, widely separated in space and time, and under various solar and magnetospheric conditions. Scientists have used this information to piece together an intricate, yet incomplete view of the magnetosphere. A simultaneous global view, using various light wavelengths and energetic neutral atoms, could reveal exciting new data and help explain complex magnetospheric processes, thus providing a clear picture of this region of space. This report summarizes the scientific rationale for such a magnetospheric imaging mission and outlines a mission concept for its implementation.
7. Magnetosphere imager science definition team interim report
Science.gov (United States)
Armstrong, T. P.; Johnson, C. L.
1995-01-01
For three decades, magnetospheric field and plasma measurements have been made by diverse instruments flown on spacecraft in may different orbits, widely separated in space and time, and under various solar and magnetospheric conditions. Scientists have used this information to piece together an intricate, yet incomplete view of the magnetosphere. A simultaneous global view, using various light wavelengths and energetic neutral atoms, could reveal exciting new data nd help explain complex magnetospheric processes, thus providing a clear picture of this region of space. This report documents the scientific rational for such a magnetospheric imaging mission and provides a mission concept for its implementation.
8. GAMERA - The New Magnetospheric Code
Science.gov (United States)
Lyon, J.; Sorathia, K.; Zhang, B.; Merkin, V. G.; Wiltberger, M. J.; Daldorff, L. K. S.
2017-12-01
The Lyon-Fedder-Mobarry (LFM) code has been a main-line magnetospheric simulation code for 30 years. The code base, designed in the age of memory to memory vector ma- chines,is still in wide use for science production but needs upgrading to ensure the long term sustainability. In this presentation, we will discuss our recent efforts to update and improve that code base and also highlight some recent results. The new project GAM- ERA, Grid Agnostic MHD for Extended Research Applications, has kept the original design characteristics of the LFM and made significant improvements. The original de- sign included high order numerical differencing with very aggressive limiting, the ability to use arbitrary, but logically rectangular, grids, and maintenance of div B = 0 through the use of the Yee grid. Significant improvements include high-order upwinding and a non-clipping limiter. One other improvement with wider applicability is an im- proved averaging technique for the singularities in polar and spherical grids. The new code adopts a hybrid structure - multi-threaded OpenMP with an overarching MPI layer for large scale and coupled applications. The MPI layer uses a combination of standard MPI and the Global Array Toolkit from PNL to provide a lightweight mechanism for coupling codes together concurrently. The single processor code is highly efficient and can run magnetospheric simulations at the default CCMC resolution faster than real time on a MacBook pro. We have run the new code through the Athena suite of tests, and the results compare favorably with the codes available to the astrophysics community. LFM/GAMERA has been applied to many different situations ranging from the inner and outer heliosphere and magnetospheres of Venus, the Earth, Jupiter and Saturn. We present example results the Earth's magnetosphere including a coupled ring current (RCM), the magnetospheres of Jupiter and Saturn, and the inner heliosphere.
9. Report of the magnetospheric physics panel
International Nuclear Information System (INIS)
Burch, J.L.; Potemra, T.A.; Ashourabdalla, M.; Baker, D.N.; Cattell, C.A.; Chang, A.F.; Frank, L.A.; Goertz, C.K.; Kivelson, M.G.; Lee, Lou-Chuang
1991-01-01
Magnetospheric research is a relatively new area in the study of the Earth's environment. The present report attempts to overview past and future research on this topic. The goals of magnetospheric research are numerous, and include: understanding large scale magnetospheres of the Earth and other planets; understanding the plasma physical processes operating within the various magnetospheres; to understand how mass, energy and momentum are transmitted from the solar wind; to understand quantitatively the coupling between magnetospheres and their ionospheres; and to understand the magnetospheric mechanisms which accelerate particles to high energies, as well as the ultimate fate of these particles. The report continues on to summarize a number of proposed space missions aimed at data acquisition. Finally, there is a brief discussion of the theory and modeling of magnetospheres
10. Boundary layers of the earth's outer magnetosphere
Science.gov (United States)
Eastman, T. E.; Frank, L. A.
1984-01-01
The magnetospheric boundary layer and the plasma-sheet boundary layer are the primary boundary layers of the earth's outer magnetosphere. Recent satellite observations indicate that they provide for more than 50 percent of the plasma and energy transport in the outer magnetosphere although they constitute less than 5 percent by volume. Relative to the energy density in the source regions, plasma in the magnetospheric boundary layer is predominantly deenergized whereas plasma in the plasma-sheet boundary layer has been accelerated. The reconnection hypothesis continues to provide a useful framework for comparing data sampled in the highly dynamic magnetospheric environment. Observations of 'flux transfer events' and other detailed features near the boundaries have been recently interpreted in terms of nonsteady-state reconnection. Alternative hypotheses are also being investigated. More work needs to be done, both in theory and observation, to determine whether reconnection actually occurs in the magnetosphere and, if so, whether it is important for overall magnetospheric dynamics.
11. Boundary layers of the earth's outer magnetosphere
International Nuclear Information System (INIS)
Eastman, T.E.; Frank, L.A.
1984-01-01
The magnetospheric boundary layer and the plasma-sheet boundary layer are the primary boundary layers of the earth's outer magnetosphere. Recent satellite observations indicate that they provide for more than 50 percent of the plasma and energy transport in the outer magnetosphere although they constitute less than 5 percent by volume. Relative to the energy density in the source regions, plasma in the magnetospheric boundary layer is predominantly deenergized whereas plasma in the plasma-sheet boundary layer has been accelerated. The reconnection hypothesis continues to provide a useful framework for comparing data sampled in the highly dynamic magnetospheric environment. Observations of flux transfer events and other detailed features near the boundaries have been recently interpreted in terms of nonsteady-state reconnection. Alternative hypotheses are also being investigated. More work needs to be done, both in theory and observation, to determine whether reconnection actually occurs in the magnetosphere and, if so, whether it is important for overall magnetospheric dynamics. 30 references
12. Outer Magnetospheric Boundaries Cluster Results
CERN Document Server
Paschmann, Goetz; Schwartz, S J
2006-01-01
When the stream of plasma emitted from the Sun (the solar wind) encounters Earth's magnetic field, it slows down and flows around it, leaving behind a cavity, the magnetosphere. The magnetopause is the surface that separates the solar wind on the outside from the Earth's magnetic field on the inside. Because the solar wind moves at supersonic speed, a bow shock must form ahead of the magnetopause that acts to slow the solar wind to subsonic speeds. Magnetopause, bow shock and their environs are rich in exciting processes in collisionless plasmas, such as shock formation, magnetic reconnection, particle acceleration and wave-particle interactions. They are interesting in their own right, as part of Earth's environment, but also because they are prototypes of similar structures and phenomena that are ubiquitous in the universe, having the unique advantage that they are accessible to in situ measurements. The boundaries of the magnetosphere have been the target of direct in-situ measurements since the beginning ...
13. Particle acceleration in pulsar magnetospheres
International Nuclear Information System (INIS)
Baker, K.B.
1978-10-01
The structure of pulsar magnetospheres and the acceleration mechanism for charged particles in the magnetosphere was studied, using a pulsar model which required large acceleration of the particles near the surface of the star. A theorem was developed which showed that particle acceleration cannot be expected when the angle between the magnetic field lines and the rotation axis is constant (e.g. radial field lines). If this angle is not constant, however, acceleration must occur. The more realistic model of an axisymmetric neutron star with a strong dipole magnetic field aligned with the rotation axis was investigated. In this case, acceleration occurred at large distances from the surface of the star. The magnitude of the current can be determined using the model presented. In the case of nonaxisymmetric systems, the acceleration is expected to occur nearer to the surface of the star
14. Discontinuities and the magnetospheric phenomena
International Nuclear Information System (INIS)
Rajaram, R.; Kalra, G.L.; Tandon, J.N.
1978-01-01
Wave coupling at contact discontinuities has an important bearing on the transmission of waves from the solar wind into the magnetosphere across the cusp region of the solar wind-magnetosphere boundary and on the propagation of geomagnetic pulsations in the polar exosphere. Keeping this in view, the problems of wave coupling across a contact discontinuity in a collisionless plasma, described by a set of double adiabatic fluid equations, is examined. The magnetic field is taken normal to the interface and it is shown that total reflection is not possible for any angle of incidence. The Alfven and the magneto-acoustic waves are not coupled. The transmission is most efficient for small density discontinuities. Inhibition of the transmission of the Alfven wave by the sharp density gradients above the F2-peak in the polar exosphere appears to account for the decrease in the pulsation amplitude, on the ground, as the poles are approached from the auroral zone. (author)
15. Magnetosphere as an Alfven maser
International Nuclear Information System (INIS)
Trakhtengerts, V.Yu.
1979-01-01
The Earth magnetosphere is considered as an Alfven maser. The operation mechanism of such a maser is duscussed. The main fact of this mechanism is ''overpopulation'' of the Earth radiation belt with particles moving with cross velocities. The cross velocity particles excess results in the excitation of cyclotron instability in the radiation belt and in the self-arbitrary increase of Alfven waves. At late the theory of cyclotron instability of radiation belts has been universally developed. On the basis of ideas on magnetosphere maser on cyclotron resonance it was possible to explain many geophysical phenomena such as periodical spillings out of particles from the radiation belts, pulsing polar lights, oscillations of magnetic force tubes etc. It is proposed to carry out active cosmic experiments to understand deeper the processes occuring in radiation belts
16. Electric fields in the magnetosphere
International Nuclear Information System (INIS)
Falthammar, C.G.
1989-01-01
Electric field measurements on the satellites GEOS-1, GEOS-2, ISEE-1, and Viking have extended the empirical knowledge of electric fields in space so as to include the outer regions of the magnetosphere. While the measurements confirm some of the theoretically expected properties of the electric fields, they also reveal unexpected features and a high degree of complexity and variability. The existence of a magnetospheric dawn-to-dusk electric field, as expected on the basis of extrapolation from low altitude measurements, is confirmed in an average sense. However, the actual field exhibits large spatial and temporal variations, including strong fields of inductive origin. At the magnetopause, the average (dawn-to-dusk directed) tangential electric field component is typically obscured by irregular fluctuations of larger amplitude. The magnetic-field aligned component of the electric field, which is of particular importance for ionosphere-magnetosphere coupling and for auroral acceleration, is even now very difficult to measure directly. However, the data from electric field measurements provide further support for the conclusion, based on a variety of evidence, that a non-vanishing magnetic-field aligned electric field exists in the auroral acceleration region
17. Does the Magnetosphere go to Sleep?
Science.gov (United States)
Hesse, M.; Moretto, T.; Friis-Christensen, E. A.; Kuznetsova, M.; Østgaard, N.; Tenfjord, P.; Opgenoorth, H. J.
2017-12-01
An interesting question in magnetospheric research is related to the transition between magnetospheric configurations under substantial solar wind driving, and a putative relaxed state after the driving ceases. While it is conceivable that the latter state may be unique and only dependent on residual solar wind driving, a more likely scenario has magnetospheric memory playing a key role. Memory processes may be manifold: constraints from conservation of flux tube entropy to neutral wind inertia in the upper atmosphere may all contribute. In this presentation, we use high-resolution, global, MHD simulations to begin to shed light on this transition, as well as on the concept of a quiet state of the magnetosphere. We will discuss key elements of magnetospheric memory, and demonstrate their influence, as well as the actual memory time scale, through simulations and analytical estimates. Finally, we will point out processes with the potential to effect magnetospheric memory loss.
18. Modeling Magnetospheric Fields in the Jupiter System
OpenAIRE
Saur, Joachim; Chané, Emmanuel; Hartkorn, Oliver
2018-01-01
The various processes which generate magnetic fields within the Jupiter system are exemplary for a large class of similar processes occurring at other planets in the solar system, but also around extrasolar planets. Jupiter’s large internal dynamo magnetic field generates a gigantic magnetosphere, which in contrast to Earth’s magnetosphere is strongly rotational driven and possesses large plasma sources located deeply within the magnetosphere. The combination of the latter two effects is the ...
19. Stellar structure and evolution
International Nuclear Information System (INIS)
Kippernhahn, R.; Weigert, A.
1990-01-01
This book introduces the theory of the internal structure of stars and their evolution in time. It presents the basic physics of stellar interiors, methods for solving the underlying equations, and the most important results necessary for understanding the wide variety of stellar types and phenomena. The evolution of stars is discussed from their birth through normal evolution to possibly spectacular final stages. Chapters on stellar oscillations and rotation are included
20. Global Vlasov simulation on magnetospheres of astronomical objects
International Nuclear Information System (INIS)
Umeda, Takayuki; Ito, Yosuke; Fukazawa, Keiichiro
2013-01-01
Space plasma is a collisionless, multi-scale, and highly nonlinear medium. There are various types of self-consistent computer simulations that treat space plasma according to various approximations. We develop numerical schemes for solving the Vlasov (collisionless Boltzmann) equation, which is the first-principle kinetic equation for collisionless plasma. The weak-scaling benchmark test shows that our parallel Vlasov code achieves a high performance and a high scalability. Currently, we use more than 1000 cores for parallel computations and apply the present parallel Vlasov code to various cross-scale processes in space plasma, such as a global simulation on the interaction between solar/stellar wind and magnetospheres of astronomical objects
1. Models for stellar flares
International Nuclear Information System (INIS)
Cram, L.E.; Woods, D.T.
1982-01-01
We study the response of certain spectral signatures of stellar flares (such as Balmer line profiles and the broad-band continuum) to changes in atmospheric structure which might result from physical processes akin to those thought to occur in solar flares. While each physical process does not have a unique signature, we can show that some of the observed properties of stellar flares can be explained by a model which involves increased pressures and temperatures in the flaring stellar chromosphere. We suggest that changes in stellar flare area, both with time and with depth in the atmosphere, may play an important role in producing the observed flare spectrum
2. Stellar Physics 2: Stellar Evolution and Stability
CERN Document Server
2011-01-01
"Stellar Physics" is a an outstanding book in the growing body of literature on star formation and evolution. Not only does the author, a leading expert in the field, very thoroughly present the current state of knowledge on stellar physics, but he handles with equal care the many problems that this field of research still faces. A bibliography with well over 1000 entries makes this book an unparalleled reference source. "Stellar Evolution and Stability" is the second of two volumes and can be read, as can the first volume "Fundamental Concepts and Stellar Equilibrium," as a largely independent work. It traces in great detail the evolution of protostars towards the main sequence and beyond this to the last stage of stellar evolution, with the corresponding vast range from white dwarfs to supernovae explosions, gamma-ray bursts and black hole formation. The book concludes with special chapters on the dynamical, thermal and pulsing stability of stars. This second edition is carefully updated in the areas of pre...
3. A New Standard Pulsar Magnetosphere
Science.gov (United States)
Contopoulos, Ioannis; Kalapotharakos, Constantinos; Kazanas, Demosthenes
2014-01-01
In view of recent efforts to probe the physical conditions in the pulsar current sheet, we revisit the standard solution that describes the main elements of the ideal force-free pulsar magnetosphere. The simple physical requirement that the electric current contained in the current layer consists of the local electric charge moving outward at close to the speed of light yields a new solution for the pulsar magnetosphere everywhere that is ideal force-free except in the current layer. The main elements of the new solution are as follows: (1) the pulsar spindown rate of the aligned rotator is 23% larger than that of the orthogonal vacuum rotator; (2) only 60% of the magnetic flux that crosses the light cylinder opens up to infinity; (3) the electric current closes along the other 40%, which gradually converges to the equator; (4) this transfers 40% of the total pulsar spindown energy flux in the equatorial current sheet, which is then dissipated in the acceleration of particles and in high-energy electromagnetic radiation; and (5) there is no separatrix current layer. Our solution is a minimum free-parameter solution in that the equatorial current layer is electrostatically supported against collapse and thus does not require a thermal particle population. In this respect, it is one more step toward the development of a new standard solution. We discuss the implications for intermittent pulsars and long-duration gamma-ray bursts. We conclude that the physical conditions in the equatorial current layer determine the global structure of the pulsar magnetosphere.
4. Pulsar magnetospheres in binary systems
Science.gov (United States)
Ershkovich, A. I.; Dolan, J. F.
1985-01-01
The criterion for stability of a tangential discontinuity interface in a magnetized, perfectly conducting inviscid plasma is investigated by deriving the dispersion equation including the effects of both gravitational and centrifugal acceleration. The results are applied to neutron star magnetospheres in X-ray binaries. The Kelvin-Helmholtz instability appears to be important in determining whether MHD waves of large amplitude generated by instability may intermix the plasma effectively, resulting in accretion onto the whole star as suggested by Arons and Lea and leading to no X-ray pulsar behavior.
5. X-ray pulsar magnetosphere
International Nuclear Information System (INIS)
Lipunov, V.
1981-01-01
A pulsar consists of a close binary star system whose one component is a neutron star and the other a normal star. This supplies the neutron star with fuel in form of star wind or a gas stream. A hot plasma-like matter falls onto the neutron star, penetrates in its magnetic field and interacts with it. The matter coming from the normal star has a great rotational moment and forms a hot diamagnetic disk around the neutron star. The plasma penetrates in the internal parts of the magnetosphere where hard x radiation is formed as a result of the plasma impingement on the neutron star surface. (M.D.)
6. The magnetosphere in relativistic physics
International Nuclear Information System (INIS)
Zapffe, C.A.
1982-01-01
The present paper takes off from the author's earlier epistemological analysis and criticism of the Special Theory of Relativity, identifies the problem as lying in Einstein's choice of the inertial frame of Newtonian mechanics rather than the electromagnetic frame of the locally embedding Maxwellian field when discussing electrodynamics, then proposes this Maxwellian field of the magnetosphere as the specific rest frame proper to all experimentation of optical or electromagnetic sort conducted within its bounds. The result is shown to remove all paradoxes from relativistic physics. (author)
7. Magnetospheric structure and atmospheric Joule heating of habitable planets orbiting M-dwarf stars
Energy Technology Data Exchange (ETDEWEB)
Cohen, O.; Drake, J. J.; Garraffo, C.; Poppenhaeger, K. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Glocer, A. [NASA/GSFC, Code 673, Greenbelt, MD 20771 (United States); Bell, J. M. [Center for Planetary Atmospheres and Flight Sciences, National Institute of Aerospace, Hampton, VA 23666 (United States); Ridley, A. J.; Gombosi, T. I. [Center for Space Environment Modeling, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 (United States)
2014-07-20
We study the magnetospheric structure and the ionospheric Joule Heating of planets orbiting M-dwarf stars in the habitable zone using a set of magnetohydrodynamic models. The stellar wind solution is used to drive a model for the planetary magnetosphere, which is coupled with a model for the planetary ionosphere. Our simulations reveal that the space environment around close-in habitable planets is extreme, and the stellar wind plasma conditions change from sub- to super-Alfvénic along the planetary orbit. As a result, the magnetospheric structure changes dramatically with a bow shock forming in the super-Alfvénic sectors, while no bow shock forms in the sub-Alfvénic sectors. The planets reside most of the time in the sub-Alfvénic sectors with poor atmospheric protection. A significant amount of Joule Heating is provided at the top of the atmosphere as a result of the intense stellar wind. For the steady-state solution, the heating is about 0.1%-3% of the total incoming stellar irradiation, and it is enhanced by 50% for the time-dependent case. The significant Joule Heating obtained here should be considered in models for the atmospheres of habitable planets in terms of the thickness of the atmosphere, the top-side temperature and density, the boundary conditions for the atmospheric pressure, and particle radiation and transport. Here we assume constant ionospheric Pedersen conductance similar to that of the Earth. The conductance could be greater due to the intense EUV radiation leading to smaller heating rates. We plan to quantify the ionospheric conductance in future study.
8. Stellar photometry and polarimetry
International Nuclear Information System (INIS)
Golay, M.; Serkowski, K.
1976-01-01
A critical review of progress made in stellar photometry and polarimetry over the period 1973-1975 is presented. Reports of photometric measurements from various observatories throughout the world are summarized. The summary of work on stellar polarimetry lists the review papers, the catalogues and lists of standard stars, and descriptions of new observing techniques. (B.R.H.)
9. Magnetic absorption of VHE photons in the magnetosphere of the Crab pulsar
Science.gov (United States)
Bogovalov, S. V.; Contopoulos, I.; Prosekin, A.; Tronin, I.; Aharonian, F. A.
2018-05-01
The detection of the pulsed ˜1 TeV gamma-ray emission from the Crab pulsar reported by MAGIC and VERITAS collaborations demands a substantial revision of existing models of particle acceleration in the pulsar magnetosphere. In this regard model independent restrictions on the possible production site of the very high energy (VHE) photons become an important issue. In this paper, we consider limitations imposed by the process of conversion of VHE gamma-rays into e± pairs in the magnetic field of the pulsar magnetosphere. Photons with energies exceeding 1 TeV are effectively absorbed even at large distances from the surface of the neutron star. Our calculations of magnetic absorption in the force-free magnetosphere show that the twisting of the magnetic field due to the pulsar rotation makes the magnetosphere more transparent compared to the dipole magnetosphere. The gamma-ray absorption appears stronger for photons emitted in the direction of rotation than in the opposite direction. There is a small angular cone inside which the magnetosphere is relatively transparent and photons with energy 1.5 TeV can escape from distances beyond 0.1 light cylinder radius (Rlc). The emission surface from where photons can be emitted in the observer's direction further restricts the sites of VHE gamma-ray production. For the observation angle 57° relative to the Crab pulsar axis of rotation and the orthogonal rotation, the emission surface in the open field line region is located as close as 0.4 Rlc from the stellar surface for a dipole magnetic field, and 0.1 Rlc for a force-free magnetic field.
10. Compact stellarators as reactors
International Nuclear Information System (INIS)
Lyon, J.F.; Valanju, P.; Zarnstorff, M.C.; Hirshman, S.; Spong, D.A.; Strickler, D.; Williamson, D.E.; Ware, A.
2001-01-01
Two types of compact stellarators are examined as reactors: two- and three-field-period (M=2 and 3) quasi-axisymmetric devices with volume-average =4-5% and M=2 and 3 quasi-poloidal devices with =10-15%. These low-aspect-ratio stellarator-tokamak hybrids differ from conventional stellarators in their use of the plasma-generated bootstrap current to supplement the poloidal field from external coils. Using the ARIES-AT model with B max =12T on the coils gives Compact Stellarator reactors with R=7.3-8.2m, a factor of 2-3 smaller R than other stellarator reactors for the same assumptions, and neutron wall loadings up to 3.7MWm -2 . (author)
11. Terrestrial magnetosphere and comparison with Jupiter's
International Nuclear Information System (INIS)
Michel, F.C.
1974-01-01
A review of the characteristics of Jupiter's magnetosphere, with comparisons to the earth's is given. Radio observations of Jupiter indicate that energetic electrons are trapped in its magnetic field. The interaction of the trapped radiation with the satellite Io and the centrifugal instability of Jupiter's magnetosphere are discussed. Jupiter's outer magnetosphere is constantly accreting plasma at an uncertain rate. Various mechanisms for supplying ions to the outer magnetosphere are discussed, including: gravitational and centrifugal forces acting on corotating particles; field-line diffusion; photoelectron injection; excitation by Io or other satellites; and viscous interaction with the solar wind. The over-all morphology of the Jovian magnetosphere seems to be highly distorted by centrifugal forces and is easily compressed or deflected by the solar wind
12. Pulsar magnetosphere-wind or wave
International Nuclear Information System (INIS)
Kennel, C.F.
1979-01-01
The structure of both the interior and exterior pulsar magnetosphere depends upon the strength of its plasma source near the surface of the star. We review wave models of exterior pulsar magnetospheres in the light of a vacuum pair-production source model proposed by Sturrock, and Ruderman and Sutherland. This model predicts the existence of a cutoff, determined by the neutron star's spin rate and magnetic field strenght, beyond which coherent radio emission is no longer possible. Since the observed distribution of pulsar spin periods and period derivatives, and the distribution of pulsars with missing radio pulses, is consistent with the pair production threshold, those neutron stars observed as radio pulsars can have relativistic magnetohydrodynamic wind exterior magnetospheres, and cannot have relativistic plasma wave exterior magnetospheres. On the other hand, most erstwhile pulsars in the galaxy are probably halo objects that emit weak fluxes of energetic photons that can have relativistic wave exterior magnetospheres. Extinct pulsars have not been yet observed
13. Stellarator-Spheromak
International Nuclear Information System (INIS)
Moroz, P.E.
1997-03-01
A novel concept for magnetic plasma confinement, Stellarator-Spheromak (SSP), is proposed. Numerical analysis with the classical-stellarator-type outboard stellarator windings demonstrates a number of potential advantages of SSP for controlled nuclear fusion. Among the main ones are: simple and compact magnet coil configuration, absence of material structures (e.g. magnet coils or conducting walls) in the center of the torus, high rotational transform, and a possibility of MHD equilibria with very high β (pressure/magnetic pressure) of the confined plasma
14. Double-helix stellarator
International Nuclear Information System (INIS)
Moroz, P.E.
1997-09-01
A new stellarator configuration, the Double-Helix Stellarator (DHS), is introduced. This novel configuration features a double-helix center post as the only helical element of the stellarator coil system. The DHS configuration has many unique characteristics. One of them is the extreme low plasma aspect ratio, A ∼ 1--1.2. Other advantages include a high enclosed volume, appreciable rotational transform, and a possibility of extreme-high-β MHD equilibria. Moreover, the DHS features improved transport characteristics caused by the absence of the magnetic field ripple on the outboard of the torus. Compactness, simplicity and modularity of the coil system add to the DHS advantages for fusion applications
15. A combined multiwavelength VLA/ALMA/Chandra study unveils the complex magnetosphere of the B-type star HR5907
Science.gov (United States)
Leto, P.; Trigilio, C.; Oskinova, L. M.; Ignace, R.; Buemi, C. S.; Umana, G.; Ingallinera, A.; Leone, F.; Phillips, N. M.; Agliozzo, C.; Todt, H.; Cerrigone, L.
2018-05-01
We present new radio/millimeter measurements of the hot magnetic star HR 5907 obtained with the VLA and ALMA interferometers. We find that HR 5907 is the most radio luminous early type star in the cm-mm band among those presently known. Its multi-wavelength radio light curves are strongly variable with an amplitude that increases with radio frequency. The radio emission can be explained by the populations of the non-thermal electrons accelerated in the current sheets on the outer border of the magnetosphere of this fast-rotating magnetic star. We classify HR 5907 as another member of the growing class of strongly magnetic fast-rotating hot stars where the gyro-synchrotron emission mechanism efficiently operates in their magnetospheres. The new radio observations of HR 5907 are combined with archival X-ray data to study the physical condition of its magnetosphere. The X-ray spectra of HR 5907 show tentative evidence for the presence of non-thermal spectral component. We suggest that non-thermal X-rays originate a stellar X-ray aurora due to streams of non-thermal electrons impacting on the stellar surface. Taking advantage of the relation between the spectral indices of the X-ray power-law spectrum and the non-thermal electron energy distributions, we perform 3-D modelling of the radio emission for HR 5907. The wavelength-dependent radio light curves probe magnetospheric layers at different heights above the stellar surface. A detailed comparison between simulated and observed radio light curves leads us to conclude that the stellar magnetic field of HR 5907 is likely non-dipolar, providing further indirect evidence of the complex magnetic field topology of HR 5907.
16. Ionospheric control of the magnetosphere: conductance
Directory of Open Access Journals (Sweden)
A. J. Ridley
2004-01-01
Full Text Available It is well known that the ionosphere plays a role in determining the global state of the magnetosphere. The ionosphere allows magnetospheric currents to close, thereby allowing magnetospheric convection to occur. The amount of current which can be carried through the ionosphere is mainly determined by the ionospheric conductivity. This paper starts to quantify the nonlinear relationship between the ionospheric conductivity and the global state of the magnetosphere. It is found that the steady-state magnetosphere acts neither as a current nor as a voltage generator; a uniform Hall conductance can influence the potential pattern at low latitudes, but not at high latitude; the EUV generated conductance forces the currents to close in the sunlight, while the potential is large on the nightside; the solar generated Hall conductances cause a large asymmetry between the dawn and dusk potential, which effects the pressure distribution in the magnetosphere; a uniform polar cap potential removes some of this asymmetry; the potential difference between solar minimum and maximum is ∼11%; and the auroral precipitation can be related to the local field-aligned current through an exponential function. Key words. Ionosphere (ionosphere-magnetosphere interactions; modelling and forecasting; polar ionosphere
17. Ionospheric control of the magnetosphere: conductance
Directory of Open Access Journals (Sweden)
A. J. Ridley
2004-01-01
Full Text Available It is well known that the ionosphere plays a role in determining the global state of the magnetosphere. The ionosphere allows magnetospheric currents to close, thereby allowing magnetospheric convection to occur. The amount of current which can be carried through the ionosphere is mainly determined by the ionospheric conductivity. This paper starts to quantify the nonlinear relationship between the ionospheric conductivity and the global state of the magnetosphere. It is found that the steady-state magnetosphere acts neither as a current nor as a voltage generator; a uniform Hall conductance can influence the potential pattern at low latitudes, but not at high latitude; the EUV generated conductance forces the currents to close in the sunlight, while the potential is large on the nightside; the solar generated Hall conductances cause a large asymmetry between the dawn and dusk potential, which effects the pressure distribution in the magnetosphere; a uniform polar cap potential removes some of this asymmetry; the potential difference between solar minimum and maximum is ∼11%; and the auroral precipitation can be related to the local field-aligned current through an exponential function.
Key words. Ionosphere (ionosphere-magnetosphere interactions; modelling and forecasting; polar ionosphere
18. Synchronous x-ray and radio mode switches: a rapid global transformation of the pulsar magnetosphere.
Science.gov (United States)
Hermsen, W; Hessels, J W T; Kuiper, L; van Leeuwen, J; Mitra, D; de Plaa, J; Rankin, J M; Stappers, B W; Wright, G A E; Basu, R; Alexov, A; Coenen, T; Grießmeier, J-M; Hassall, T E; Karastergiou, A; Keane, E; Kondratiev, V I; Kramer, M; Kuniyoshi, M; Noutsos, A; Serylak, M; Pilia, M; Sobey, C; Weltevrede, P; Zagkouris, K; Asgekar, A; Avruch, I M; Batejat, F; Bell, M E; Bell, M R; Bentum, M J; Bernardi, G; Best, P; Bîrzan, L; Bonafede, A; Breitling, F; Broderick, J; Brüggen, M; Butcher, H R; Ciardi, B; Duscha, S; Eislöffel, J; Falcke, H; Fender, R; Ferrari, C; Frieswijk, W; Garrett, M A; de Gasperin, F; de Geus, E; Gunst, A W; Heald, G; Hoeft, M; Horneffer, A; Iacobelli, M; Kuper, G; Maat, P; Macario, G; Markoff, S; McKean, J P; Mevius, M; Miller-Jones, J C A; Morganti, R; Munk, H; Orrú, E; Paas, H; Pandey-Pommier, M; Pandey, V N; Pizzo, R; Polatidis, A G; Rawlings, S; Reich, W; Röttgering, H; Scaife, A M M; Schoenmakers, A; Shulevski, A; Sluman, J; Steinmetz, M; Tagger, M; Tang, Y; Tasse, C; ter Veen, S; Vermeulen, R; van de Brink, R H; van Weeren, R J; Wijers, R A M J; Wise, M W; Wucknitz, O; Yatawatta, S; Zarka, P
2013-01-25
Pulsars emit from low-frequency radio waves up to high-energy gamma-rays, generated anywhere from the stellar surface out to the edge of the magnetosphere. Detecting correlated mode changes across the electromagnetic spectrum is therefore key to understanding the physical relationship among the emission sites. Through simultaneous observations, we detected synchronous switching in the radio and x-ray emission properties of PSR B0943+10. When the pulsar is in a sustained radio-"bright" mode, the x-rays show only an unpulsed, nonthermal component. Conversely, when the pulsar is in a radio-"quiet" mode, the x-ray luminosity more than doubles and a 100% pulsed thermal component is observed along with the nonthermal component. This indicates rapid, global changes to the conditions in the magnetosphere, which challenge all proposed pulsar emission theories.
19. Double-reconnected magnetic structures driven by Kelvin-Helmholtz vortices at the Earth's magnetosphere
Science.gov (United States)
Faganello, Matteo; Borgogno, Dario; Califano, Francesco; Pegoraro, Francesco
2015-11-01
In an almost collisionless MagnetoHydrodynamic plasma in a relatively strong magnetic field, stresses can be conveyed far from the region where they are exerted e.g., through the propagation of Alfvèn waves. The forced dynamics of line-tied magnetic structures in solar and stellar coronae is a paradigmatic case. We investigate how this action at a distance develops from the equatorial region of the Kelvin-Helmholtz unstable flanks of the Earth's magnetosphere leading to the onset, at mid latitude in both hemispheres, of correlated double magnetic field line reconnection events that can allow the solar wind plasma to enter the Earth's magnetosphere. This mid-latitude double reconnection process, first investigated in, has been confirmed here by following a large set of individual field lines using a method similar to a Poincarè map.
20. Theory of neutron star magnetospheres
CERN Document Server
Curtis Michel, F
1990-01-01
An incomparable reference for astrophysicists studying pulsars and other kinds of neutron stars, "Theory of Neutron Star Magnetospheres" sums up two decades of astrophysical research. It provides in one volume the most important findings to date on this topic, essential to astrophysicists faced with a huge and widely scattered literature. F. Curtis Michel, who was among the first theorists to propose a neutron star model for radio pulsars, analyzes competing models of pulsars, radio emission models, winds and jets from pulsars, pulsating X-ray sources, gamma-ray burst sources, and other neutron-star driven phenomena. Although the book places primary emphasis on theoretical essentials, it also provides a considerable introduction to the observational data and its organization. Michel emphasizes the problems and uncertainties that have arisen in the research as well as the considerable progress that has been made to date.
1. Electric current model of magnetosphere
International Nuclear Information System (INIS)
Alfen, H.
1979-05-01
A dualism between the field and the particle approach exists also in plasma physics. A number of phenomena, such as the formation of double layers and the energy transport form one region to another, can be understood only by the particle (electric current) description. Hence a translation of the traditional field description into a particle (electric current) description is essential. Such a translation has earlier been made for the heliosphere. The purpose of this paper is to outline a similar application to the magnetosphere, focussing on the energy transfer from the solar wind. As a first approximation a magnetic field consisting of a dipole field and homogeneous magnetic field is used whereas in a second approximation the configuration is more realistic. (author)
2. Wimps and stellar structure
International Nuclear Information System (INIS)
Bouquet, A.; Salati, P.
1988-01-01
We present the results of an analytic approximation to compute the effects of WIMPs on stellar structures in a self-consistent way. We examine in particular the case of the Sun and of horizontal branch stars
3. Principles of Stellar Interferometry
CERN Document Server
Glindemann, Andreas
2011-01-01
Over the last decade, stellar interferometry has developed from a specialist tool to a mainstream observing technique, attracting scientists whose research benefits from milliarcsecond angular resolution. Stellar interferometry has become part of the astronomer’s toolbox, complementing single-telescope observations by providing unique capabilities that will advance astronomical research. This carefully written book is intended to provide a solid understanding of the principles of stellar interferometry to students starting an astronomical research project in this field or to develop instruments and to astronomers using interferometry but who are not interferometrists per se. Illustrated by excellent drawings and calculated graphs the imaging process in stellar interferometers is explained starting from first principles on light propagation and diffraction wave propagation through turbulence is described in detail using Kolmogorov statistics the impact of turbulence on the imaging process is discussed both f...
4. Convection and stellar oscillations
DEFF Research Database (Denmark)
Aarslev, Magnus Johan
2017-01-01
for asteroseismology, because of the challenges inherent in modelling turbulent convection in 1D stellar models. As a result of oversimplifying the physics near the surface, theoretical calculations systematically overestimate the oscillation frequencies. This has become known as the asteroseismic surface effect. Due...... to lacking better options, this frequency difference is typically corrected for with ad-hoc formulae. The topic of this thesis is the improvement of 1D stellar convection models and the effects this has on asteroseismic properties. The source of improvements is 3D simulations of radiation...... atmospheres to replace the outer layers of stellar models. The additional turbulent pressure and asymmetrical opacity effects in the atmosphere model, compared to convection in stellar evolution models, serve to expand the atmosphere. The enlarged acoustic cavity lowers the pulsation frequencies bringing them...
5. Oscillations in stellar atmospheres
International Nuclear Information System (INIS)
Costa, A.; Ringuelet, A.E.; Fontenla, J.M.
1989-01-01
Atmospheric excitation and propagation of oscillations are analyzed for typical pulsating stars. The linear, plane-parallel approach for the pulsating atmosphere gives a local description of the phenomenon. From the local analysis of oscillations, the minimum frequencies are obtained for radially propagating waves. The comparison of the minimum frequencies obtained for a variety of stellar types is in good agreement with the observed periods of the oscillations. The role of the atmosphere in the globar stellar pulsations is thus emphasized. 7 refs
6. Interaction of Titan's atmosphere with Saturn's magnetosphere
International Nuclear Information System (INIS)
Hartle, R.E.
1985-01-01
The Voyager 1 measurements made during the Titan flyby reveal that Saturn's rotating magnetospheric plasma interacts directly with Titan's neutral atmosphere and ionosphere. This results from the lack of an intrinsic magnetic field at Titan. The interaction induces a magnetosphere which deflects the flowing plasma around Titan and forms a plasma wake downstream. Within the tail of the induced magnetosphere, ions of ionospheric origin flow away from Titan. Just outside Titan's magnetosphere, a substantial ion-exosphere forms from an extensive hydrogen-nitrogen exosphere. The exospheric ions are picked up and carried downstream into the wake by the plasma flowing around Titan. Mass loading produced by the addition of exospheric ions slows the wake plasma down considerably in the vicinity of the magnetopause. 36 references
7. Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates
Science.gov (United States)
Wilson, F.; Neukirch, T.
2018-01-01
We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.
8. The Magnetospheric Cusps Structure and Dynamics
CERN Document Server
Fritz, Theodore A
2005-01-01
This collection of papers will address the question "What is the Magnetospheric Cusp?" and what is its role in the coupling of the solar wind to the magnetosphere as well as its role in the processes of particle transport and energization within the magnetosphere. The cusps have traditionally been described as narrow funnel-shaped regions that provide a focus of the Chapman-Ferraro currents that flow on the magnetopause, a boundary between the cavity dominated by the geomagnetic field (i.e., the magnetosphere) and the external region of the interplanetary medium. Measurements from a number of recent satellite programs have shown that the cusp is not confined to a narrow region near local noon but appears to encompass a large portion of the dayside high-latitude magnetosphere and it appears that the cusp is a major source region for the production of energetic charged particles for the magnetosphere. Audience: This book will be of interest to space science research organizations in governments and industries, ...
9. Pair plasma in pulsar magnetospheres
International Nuclear Information System (INIS)
Asseo, Estelle
2003-01-01
The main features of radiation received from pulsars imply that they are neutron stars which contain an extremely intense magnetic field and emit coherently in the radio domain. Most recent studies attribute the origin of the coherence to plasma instabilities arising in pulsar magnetospheres; they mainly concern the linear, or the nonlinear, character of the involved unstable waves. We briefly introduce radio pulsars and specify physical conditions in pulsar emission regions: geometrical properties, magnetic field, pair creation processes and repartition of relativistic charged particles. We point to the main ingredients of the linear theory, extensively explored since the 1970s: (i) a dispersion relation specific to the pulsar case; (ii) the characteristics of the waves able to propagate in relativistic pulsar plasmas; (iii) the different ways in which a two-humped distribution of particles may arise in a pulsar magnetosphere and favour the development of a two-stream instability. We sum up recent improvements of the linear theory: (i) the determination of a 'coupling function' responsible for high values of the wave field components and electromagnetic energy available; (ii) the obtention of new dispersion relations for actually anisotropic pulsar plasmas with relativistic motions and temperatures; (iii) the interaction between a plasma and a beam, both with relativistic motions and temperatures; (iv) the interpretation of observed 'coral' and 'conal' features, associated with the presence of boundaries and curved magnetic field lines in the emission region; (v) the detailed topology of the magnetic field in the different parts of the emission region and its relation to models recently proposed to interpret drifting subpulses observed from PSR 0943+10, showing 20 sub-beams of emission. We relate the nonlinear evolution of the two-stream instability and development of strong turbulence in relativistic pulsar plasmas to the emergence of relativistic solitons, able
10. PREFACE: A Stellar Journey A Stellar Journey
Science.gov (United States)
Asplund, M.
2008-10-01
The conference A Stellar Journey was held in Uppsala, Sweden, 23 27June 2008, in honour of Professor Bengt Gustafsson's 65th birthday. The choice of Uppsala as the location for this event was obvious given Bengt's long-standing association with the city stemming back to his school days. With the exception of a two-year postdoc stint in Copenhagen, five years as professor at Stockholm University and two years as director of the Sigtuna foundation, Bengt has forged his illustrious professional career at Uppsala University. The symposium venue was Museum Gustavianum, once the main building of the oldest university in Scandinavia. The title of the symposium is a paraphrasing of Bengt's popular astronomy book Kosmisk Resa (in English: Cosmic Journey) written in the early eighties. I think this aptly symbolizes his career that has been an astronomical voyage from near to far, from the distant past to the present. The original book title was modified slightly to reflect that most of his work to date has dealt with stars in one way or another. In addition it also gives credit to Bengt's important role as a guiding light for a very large number of students, colleagues and collaborators, indeed for several generations of astronomers. For me personally, the book Kosmisk Resa bears particular significance as it has shaped my life rather profoundly. Although I had already decided to become an astronomer, when I first read the book as a 14-year-old I made up my mind then and there that I would study under Bengt Gustafsson and work on stars. Indeed I have remained true to this somewhat audacious resolution. I suspect that a great number of us have similar stories how Bengt has had a major influence on our lives, whether on the professional or personal level. Perhaps Bengt's most outstanding characteristic is his enthralling enthusiasm. This is equally true whether he is pondering some scientific conundrum, supervising students or performing in front of an audience, be it an
11. Stellar magnetic activity
International Nuclear Information System (INIS)
Schrijver, C.J.
1986-01-01
The stellar emission in the chromospheric Ca II H+K lines is compared with the coronal soft X-ray emission, measuring the effects of non-radiative heating in the outer atmosphere at temperatures differing two orders of magnitude. The comparison of stellar flux densities in Ca II H+K and X-rays is extended to fluxes from the transition-region and the high-temperature chromosphere. The stellar magnetic field is probably generated in the differentially rotating convective envelope. The relation between rotation rate and the stellar level of activity measured in chromospheric, transition-region, and coronal radiative diagnostics is discovered. X-ray observations of the binary λ Andromedae are discussed. The departure of M-type dwarfs from the main relations, and the implications for the structure of the chromospheres of these stars are discussed. Variations of the average surface flux densities of the Sun during the 11-year activity cycle agree with flux-flux relations derived for other cool stars, suggesting that the interpretation of the stellar relations may be furthered by studying the solar analogue in more detail. (Auth.)
12. Charged dust in saturn's magnetosphere
International Nuclear Information System (INIS)
Mendis, D.A.; Hill, J.R.; Houpis, H.L.F.
1983-01-01
Gravito-electrodynamic theory of charged dust grains is used to explain a variety of phenomena in those portions of the Saturnian ring system that are known to be dominated by fine (micron- and submicron-sized) dust, and in which collisional forces and Coulomb drag can be neglected. Among the phenomena discussed are the formation and evolution of the rotating near-radial spokes in the B-ring, the formation of waves in the F-ring, the cause of eccentricities of certain isolated ringlets, and the origin and morphology of the broad diffuse E-ring. Several novel processes predicted by the gravitoelectrodynamic theory, including 'magneto-gravitational capture' of exogenic dust by the magnetosphere, '1:1 magneto-gravitational orbital resonances' of charged dust with nearby satellites, and 'gyro-orbital resonances,' are used to explain individual observations. The effect of a ring current associated with this charged dust is also evaluated. Finally, the cosmogonic implications of the magneto-gravitational theory are briefly discussed. While several (although not all) of these processes have been discussed by one or more of the present authors elsewhere, the purpose of this paper is to synthesize all these processes within the framework of gravito-electrodynamics, and also to show its range of applicability within Saturn's ring system
13. Mercury's magnetosphere and magnetotial revisited
International Nuclear Information System (INIS)
Bergan, S.; Engle, I.M.
1981-01-01
Magnetic observations which are not complicated by currents of trapped plasma are a good test of geomagnetopause and geomagnetotail predictions. Recent attempts to model the Hermean magnetospheric field based on a planet-centered magnetic multipole field with a quadrupole moment in addition to the planetary dipole field or a dipole field linearly displaced from planet center and no quadrupole moment have produced reasonably good fits to the Mercury magnetic field measurements. In this work we find a better fit for a dipole displacement from the planet center by making use of an improved representation of the magnetic field in the magnetotail, where many of the Mercury measurements were made. The rms deviation of the data was reduced from 10. or 11. γ to 9.3 γ by employing this new tail field representation. Also, by making use of this new tail field representation, we find a best fit for a dipole displacement of -0.0285 R/sub M/ (earlier, 0.026 R/sub M/) toward the dawn in the magnetic equatorial plane and 0.17 R/sub M/ (earlier, 0.189 R/sub M/ (earlier 0.189 R/sub M/) northward along the magnetic dipole axis, where R/sub M/ is the planet radius. Thus with only minor adjustments in the displacement vector of the dipole from the planet center we achieve a measurable improvement in the fit of the data by using the improved magnetotail field representation
14. Introduction to stellar structure
CERN Document Server
Maciel, Walter J
2016-01-01
In the first part of this book, the author presents the basic properties of the stellar interior and describes them thoroughly, along with deriving the main stellar structure equations of temperature, density, pressure and luminosity, among others. The process and application of solving these equations is explained, as well as linking these results with actual observations. The second part of the text describes what happens to a star over time, and how to determine this by solving the same equations at different points during a star’s lifetime. The fate of various stars is quite different depending on their masses, and this is described in the final parts of the book. This text can be used for an upper level undergraduate course or an introductory graduate course on stellar physics.
15. On the paleo-magnetospheres of Earth and Mars
Science.gov (United States)
Scherf, Manuel; Khodachenko, Maxim; Alexeev, Igor; Belenkaya, Elena; Blokhina, Marina; Johnstone, Colin; Tarduno, John; Lammer, Helmut; Tu, Lin; Guedel, Manuel
2017-04-01
The intrinsic magnetic field of a terrestrial planet is considered to be an important factor for the evolution of terrestrial atmospheres. This is in particular relevant for early stages of the solar system, in which the solar wind as well as the EUV flux from the young Sun were significantly stronger than at present-day. We therefore will present simulations of the paleo-magnetospheres of ancient Earth and Mars, which were performed for ˜4.1 billion years ago, i.e. the Earth's late Hadean eon and Mars' early Noachian. These simulations were performed with specifically adapted versions of the Paraboloid Magnetospheric Model (PMM) of the Skobeltsyn Institute of Nuclear Physics of the Moscow State University, which serves as ISO-standard for the Earth's magnetic field (see e.g. Alexeev et al., 2003). One of the input parameters into our model is the ancient solar wind pressure. This is derived from a newly developed solar/stellar wind evolution model, which is strongly dependent on the initial rotation rate of the early Sun (Johnstone et al., 2015). Another input parameter is the ancient magnetic dipole field. In case of Earth this is derived from measurements of the paleomagnetic field strength by Tarduno et al., 2015. These data from zircons are varying between 0.12 and 1.0 of today's magnetic field strength. For Mars the ancient magnetic field is derived from the remanent magnetization in the Martian crust as measured by the Mars Global Surveyor MAG/ER experiment. These data together with dynamo theory are indicating an ancient Martian dipole field strength in the range of 0.1 to 1.0 of the present-day terrestrial dipole field. For the Earth our simulations show that the paleo-magnetosphere during the late Hadean eon was significantly smaller than today, with a standoff-distance rs ranging from ˜3.4 to 8 Re, depending on the input parameters. These results also have implications for the early terrestrial atmosphere. Due to the significantly higher EUV flux, the
16. The Galactic stellar disc
International Nuclear Information System (INIS)
Feltzing, S; Bensby, T
2008-01-01
The study of the Milky Way stellar discs in the context of galaxy formation is discussed. In particular, we explore the properties of the Milky Way disc using a new sample of about 550 dwarf stars for which we have recently obtained elemental abundances and ages based on high-resolution spectroscopy. For all the stars we also have full kinematic information as well as information about their stellar orbits. We confirm results from previous studies that the thin and the thick discs have distinct abundance patterns. But we also explore a larger range of orbital parameters than what has been possible in our previous studies. Several new results are presented. We find that stars that reach high above the Galactic plane and have eccentric orbits show remarkably tight abundance trends. This implies that these stars formed out of well-mixed gas that had been homogenized over large volumes. We find some evidence that suggest that the event that most likely caused the heating of this stellar population happened a few billion years ago. Through a simple, kinematic exploration of stars with super-solar [Fe/H], we show that the solar neighbourhood contains metal-rich, high velocity stars that are very likely associated with the thick disc. Additionally, the HR1614 moving group and the Hercules and Arcturus stellar streams are discussed and it is concluded that, probably, a large fraction of the groups and streams so far identified in the disc are the result of evolution and interactions within the stellar disc rather than being dissolved stellar clusters or engulfed dwarf galaxies.
17. Stellar activity for every TESS star in the Southern sky
Science.gov (United States)
Howard, Ward S.; Law, Nicholas; Fors, Octavi; Corbett, Henry T.; Ratzloff, Jeff; del Ser, Daniel
2018-01-01
Although TESS will search for Earths around more than 200,000 nearby stars, the life-impacting superflare occurrence of these stars remains poorly characterized. We monitor long-term stellar flare occurrence for every TESS star in the accessible sky at 2-minute cadence with the CTIO-based Evryscope, a combination of twenty-four telescopes, together giving instantaneous sky coverage of 8000 square degrees. In collaboration with Owens Valley Long Wavelength Array (LWA) all-sky monitoring, Evryscope also provides optical counterparts to radio flare, CME, and exoplanet-magnetosphere stellar activity searches. A Northern Evryscope will be installed at Mount Laguna Observatory, CA in collaboration with SDSU later this year, enabling stellar activity characterization for the full TESS target list and both continuous viewing zones, as well as providing 100% overlap with LWA radio activity. Targets of interest (e.g. Proxima Cen, TRAPPIST-1) are given special focus. We are currently sensitive to stellar activity down to 1% precision at g' ~ 10 and about 0.2 of a magnitude at g' ~ 15. With 2-minute cadence and a projected 5-year timeline, with 2+ years already recorded, we present preliminary results from an activity characterization of every Southern TESS target.
18. Transport in stellarators
International Nuclear Information System (INIS)
Maassberg, H.; Brakel, R.; Burhenn, R.; Gasparino, U.; Grigull, P.; Kick, M.; Kuehner, G.; Ringler, H.; Sardei, F.; Stroth, U.; Weller, A.
1993-01-01
The local electron and ion heat transport as well as the particle and impurity transport properties in stellarators are reviewed. In this context, neoclassical theory is used as a guideline for the comparison of the experimental results of the quite different confinement concepts. At sufficiently high temperatures depending on the specific magnetic configuration, neoclassical predictions are confirmed by experimental findings. The confinement properties in the LMFP collisionality regime are discussed with respect to the next stellarator generation, for which at higher temperatures the neoclassical transport is expected to become more important. (orig.)
19. Solar and stellar oscillations
International Nuclear Information System (INIS)
Fossat, E.
1981-01-01
We try to explain in simple words what a stellar oscillation is, what kind of restoring forces and excitation mechanisms can be responsible for its occurence, what kind of questions the theoretician asks to the observer and what kind of tools the latter is using to look for the answers. A selected review of the most striking results obtained in the last few years in solar seismology and the present status of their consequences on solar models is presented. A brief discussion on the expected extension towards stellar seismology will end the paper. A selected bibliography on theory as well as observations and recent papers is also included. (orig.)
20. 3-D Force-balanced Magnetospheric Configurations
International Nuclear Information System (INIS)
Sorin Zaharia; Cheng, C.Z.; Maezawa, K.
2003-01-01
The knowledge of plasma pressure is essential for many physics applications in the magnetosphere, such as computing magnetospheric currents and deriving magnetosphere-ionosphere coupling. A thorough knowledge of the 3-D pressure distribution has however eluded the community, as most in-situ pressure observations are either in the ionosphere or the equatorial region of the magnetosphere. With the assumption of pressure isotropy there have been attempts to obtain the pressure at different locations by either (a) mapping observed data (e.g., in the ionosphere) along the field lines of an empirical magnetospheric field model or (b) computing a pressure profile in the equatorial plane (in 2-D) or along the Sun-Earth axis (in 1-D) that is in force balance with the magnetic stresses of an empirical model. However, the pressure distributions obtained through these methods are not in force balance with the empirical magnetic field at all locations. In order to find a global 3-D plasma pressure distribution in force balance with the magnetospheric magnetic field, we have developed the MAG-3D code, that solves the 3-D force balance equation J x B = (upside-down delta) P computationally. Our calculation is performed in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials as B = (upside-down delta) psi x (upside-down delta) alpha. The pressure distribution, P = P(psi,alpha), is prescribed in the equatorial plane and is based on satellite measurements. In addition, computational boundary conditions for y surfaces are imposed using empirical field models. Our results provide 3-D distributions of magnetic field and plasma pressure as well as parallel and transverse currents for both quiet-time and disturbed magnetospheric conditions
1. Magnetosphere Modeling: From Cartoons to Simulations
Science.gov (United States)
Gombosi, T. I.
2017-12-01
Over the last half a century physics-based global computer simulations became a bridge between experiment and basic theory and now it represents the "third pillar" of geospace research. Today, many of our scientific publications utilize large-scale simulations to interpret observations, test new ideas, plan campaigns, or design new instruments. Realistic simulations of the complex Sun-Earth system have been made possible by the dramatically increased power of both computing hardware and numerical algorithms. Early magnetosphere models were based on simple E&M concepts (like the Chapman-Ferraro cavity) and hydrodynamic analogies (bow shock). At the beginning of the space age current system models were developed culminating in the sophisticated Tsyganenko-type description of the magnetic configuration. The first 3D MHD simulations of the magnetosphere were published in the early 1980s. A decade later there were several competing global models that were able to reproduce many fundamental properties of the magnetosphere. The leading models included the impact of the ionosphere by using a height-integrated electric potential description. Dynamic coupling of global and regional models started in the early 2000s by integrating a ring current and a global magnetosphere model. It has been recognized for quite some time that plasma kinetic effects play an important role. Presently, global hybrid simulations of the dynamic magnetosphere are expected to be possible on exascale supercomputers, while fully kinetic simulations with realistic mass ratios are still decades away. In the 2010s several groups started to experiment with PIC simulations embedded in large-scale 3D MHD models. Presently this integrated MHD-PIC approach is at the forefront of magnetosphere simulations and this technique is expected to lead to some important advances in our understanding of magnetosheric physics. This talk will review the evolution of magnetosphere modeling from cartoons to current systems
2. Closed model of the earth's magnetosphere
International Nuclear Information System (INIS)
Piddington, J.H.
1979-01-01
The existence of large-scale motions within the earth's magnetosphere and that of a long magnetotail were predicted in 1960 as results of a hypothetical frictional interaction between the solar wind and the geomagnetic field. The boundary layer model of this interaction involves the flow of magnetosheath plasma in a magnetospheric boundary layer. The flow is across magnetic field lines, and so the layer must be polarized, with a space charge field nearly balancing the induction field V x B. The space charge tends to discharge through the ionosphere, thus providing some magnetic and related activity as well as the Lorentz frictional force. This closed magnetosphere model has been largely neglected in favor of the reconnection model but is now strongly supported by observational results and their interpretation as follows. (1) The evidence for the reconnection model, increasing activity with a southward interplanetary field and invasion of the polar caps by flare particles, is shown to be equally compatible with the closed field model. (2) The magnetotail grows by the motions of closed flux tubes through the dawn and dusk meridians, a process which depends on the nature of the boundary between magnetosphere and magnetosheath plasmas and perhaps also on the solar wind dynamo. Both of these features depend, in turn, on the direction of the interplanetary magnetic field. (3) Closed field lines entering the tail may be stretched to a few tens of earth radii and then contract back to the corotating magnetosphere. Others enter the long tail and are stretched to hundreds of earth radii and so are pervious to fast solar particles. (4) A new model of the magnetospheric substorm involves the entry of closed field lines into the tail and their rapid return to the corotating magnetosphere. The return is due, first, to the release of their trapped plasma as it becomes electrically polarized and, second, to mounting magnetic and plasma stresses in the inflated magnetotail
3. The fundamentals of stellar astrophysics
International Nuclear Information System (INIS)
Collins, G.W. II.
1989-01-01
A broad overview of theoretical stellar astrophysics is presented in a textbook intended for graduate students. Chapters are devoted to fundamental principles, assumptions, theorems, and polytropes; energy sources and sinks; the flow of energy through the star and the construction of stellar models; the theory of stellar evolution; relativistic stellar structure; the structure of distorted stars; stellar pulsation and oscillation. Also discussed are the flow of radiation through the stellar atmosphere, the solution of the radiative-transfer equation, the environment of the radiation field, the construction of a stellar model atmosphere, the formation and shape of spectral lines, LTE breakdown, illuminated and extended stellar atmospheres, and the transfer of polarized radiation. Diagrams, graphs, and sample problems are provided. 164 refs
4. Observations of Heavy Ions in the Magnetosphere
Science.gov (United States)
Kistler, L. M.
2017-12-01
There are two sources for the hot ions in the magnetosphere: the solar wind and the ionosphere. The solar wind is predominantly protons, with about 4% He++ and less than 1% other high charge state heavy ions. The ionospheric outflow is also predominantly H+, but can contain a significant fraction of heavy ions including O+, N+, He+, O++, and molecular ions (NO+, N2+, O2+). The ionospheric outflow composition varies significantly both with geomagnetic activity and with solar EUV. The variability in the contribution of the two sources, the variability in the ionospheric source itself, and the transport paths of the different species are all important in determining the ion composition at a given location in the magnetosphere. In addition to the source variations, loss processes within the magnetosphere can be mass dependent, changing the composition. In particular, charge exchange is strongly species dependent, and can lead to heavy ion dominance at some energies in the inner magnetosphere. In this talk we will review the current state of our understanding of the composition of the magnetosphere and the processes that determine it.
5. Auroral kilometric radiation and magnetospheric substorm
International Nuclear Information System (INIS)
Morioka, Akira; Oya, Hiroshi
1980-01-01
The auroral kilometric radiation (AKR) and its relation to the development of the magnetospheric substorm have been studied based on the data obtained by JIKIKEN (EXOS-B) satellite. The occurrence of AKR is closely correlated to the intense UHR emission outside the plasmapause at the satellite position; the evidence clearly suggests that the development of the field aligned current system is associated with AKR generated at the upward current region and with the UHR emission at the downward current region. The drifting plasma due to the electric field that is generated in the magnetosphere at the moment of the magnetospheric substorm is derived from the frequency change of the plasma waves. The enhancement of the westward electric field in the duskside magnetosphere is detected simultaneously with the appearence of AKR. The altitude of the center of the AKR source region varies with intimate relation to the substorm activity suggesting that the generation of AKR is taking place in the region where the polar ionosphere and the magnetosphere are predominantly coupling through the precipitating or up going particles. From the fine structure of the dynamic spectra of AKR, it is suggested that the source of AKR might be closely related to the double layer type electric field along the magnetic field. (author)
6. Progress Toward Attractive Stellarators
International Nuclear Information System (INIS)
Neilson, G.H.; Bromberg, L.; Brown, T.G.; Gates, D.A.; Ku, L.P.; Zarnstorff, M.C.; Boozer, A.H.; Harris, J.H.; Meneghini, O.; Mynick, H.E.; Pomphrey, N.; Reiman, A.H.; Xanthopoulos, P.
2011-01-01
The quasi-axisymmetric stellarator (QAS) concept offers a promising path to a more compact stellarator reactor, closer in linear dimensions to tokamak reactors than previous stellarator designs. Concept improvements are needed, however, to make it more maintainable and more compatible with high plant availability. Using the ARIES-CS design as a starting point, compact stellarator designs with improved maintenance characteristics have been developed. While the ARIES-CS features a through-the-port maintenance scheme, we have investigated configuration changes to enable a sector-maintenance approach, as envisioned for example in ARIES AT. Three approaches are reported. The first is to make tradeoffs within the QAS design space, giving greater emphasis to maintainability criteria. The second approach is to improve the optimization tools to more accurately and efficiently target the physics properties of importance. The third is to employ a hybrid coil topology, so that the plasma shaping functions of the main coils are shared more optimally, either with passive conductors made of high-temperature superconductor or with local compensation coils, allowing the main coils to become simpler. Optimization tools are being improved to test these approaches.
7. Stellar population synthesis
International Nuclear Information System (INIS)
Pickles, A.J.
1989-01-01
The techniques used to derive astrophysically useful information from observations of the integrated light of composite stellar systems are briefly reviewed. A synthesis technique, designed to separate and describe on a standard system the competing effects of age and metallicity variations is introduced, and illustrated by its application to the study of the history of star formation in bright elliptical galaxies in clusters. (author)
8. Relativistic stellar dynamics
International Nuclear Information System (INIS)
Contopoulos, G.
1983-01-01
In this paper, three main areas of relativistic stellar dynamics are reviewed: (a) The dynamics of clusters, or nuclei of galaxies, of very high density; (b) The dynamics of systems containing a massive black hole; and (c) The dynamics of particles (and photons) in an expanding Universe. The emphasis is on the use of orbit perturbations. (Auth.)
9. Compact stellarator coils
International Nuclear Information System (INIS)
Pomphrey, N.; Berry, L.A.; Boozer, A.H.
2001-01-01
Experimental devices to study the physics of high-beta (β>∼4%), low aspect ratio (A<∼4.5) stellarator plasmas require coils that will produce plasmas satisfying a set of physics goals, provide experimental flexibility, and be practical to construct. In the course of designing a flexible coil set for the National Compact Stellarator Experiment, we have made several innovations that may be useful in future stellarator design efforts. These include: the use of Singular Value Decomposition methods for obtaining families of smooth current potentials on distant coil winding surfaces from which low current density solutions may be identified; the use of a Control Matrix Method for identifying which few of the many detailed elements of the stellarator boundary must be targeted if a coil set is to provide fields to control the essential physics of the plasma; the use of Genetic Algorithms for choosing an optimal set of discrete coils from a continuum of potential contours; the evaluation of alternate coil topologies for balancing the tradeoff between physics objective and engineering constraints; the development of a new coil optimization code for designing modular coils, and the identification of a 'natural' basis for describing current sheet distributions. (author)
10. Stellar Structure and Evolution
CERN Document Server
Kippenhahn, Rudolf; Weiss, Achim
2013-01-01
This long-awaited second edition of the classical textbook on Stellar Structure and Evolution by Kippenhahn and Weigert is a thoroughly revised version of the original text. Taking into account modern observational constraints as well as additional physical effects such as mass loss and diffusion, Achim Weiss and Rudolf Kippenhahn have succeeded in bringing the book up to the state-of-the-art with respect to both the presentation of stellar physics and the presentation and interpretation of current sophisticated stellar models. The well-received and proven pedagogical approach of the first edition has been retained. The book provides a comprehensive treatment of the physics of the stellar interior and the underlying fundamental processes and parameters. The models developed to explain the stability, dynamics and evolution of the stars are presented and great care is taken to detail the various stages in a star’s life. Just as the first edition, which remained a standard work for more than 20 years after its...
11. 8. stellarator workshop
International Nuclear Information System (INIS)
1991-07-01
The technical reports in this collection of papers were presented at the 8th International Workshop on Stellarators, and International Atomic Energy Agency Technical Committee Meeting. They include presentations on transport, magnetic configurations, fluctuations, equilibrium, stability, edge plasma and wall aspects, heating, diagnostics, new concepts and reactor studies. Refs, figs and tabs
12. Stellar wind theory
International Nuclear Information System (INIS)
Summers, D.
1980-01-01
The theory of stellar winds as given by the equations of classical fluid dynamics is considered. The equations of momentum and energy describing a steady, spherically symmetric, heat-conducting, viscous stellar wind are cast in a dimensionless form which involves a thermal conduction parameter E and a viscosity parameter γ. An asymptotic analysis is carried out, for fixed γ, in the cases E→O and E→infinity (corresponding to small and large thermal conductivity, respectively), and it is found that it is possible to construct critical solutions for the wind velocity and temperature over the entire flow. The E→O solution represents a wind which emanates from the star at low, subsonic speeds, accelerates through a sonic point, and then approaches a constant asymptotic speed, with its temperature varying as r/sup -4/3/ at large distances r from the star; the E→infinity solution represents a wind which, after reaching an approximately constant speed, with temperature varying as r/sup -2/7/, decelerates through a diffuse shock and approaches a finite pressure at infinity. A categorization is made of all critical stellar wind solutions for given values of γ and E, and actual numerical examples are given. Numerical solutions are obtained by integrating upstream 'from infinity' from initial values of the flow parameters given by appropriate asymptotic expansions. The role of viscosity in stellar wind theory is discussed, viscous and inviscid stellar wind solutions are compared, and it is suggested that with certain limitations, the theory presented may be useful in analyzing winds from solar-type stars
13. Identifying Cassini's Magnetospheric Location Using Magnetospheric Imaging Instrument (MIMI) Data and Machine Learning
Science.gov (United States)
Vandegriff, J. D.; Smith, G. L.; Edenbaum, H.; Peachey, J. M.; Mitchell, D. G.
2017-12-01
We analyzed data from Cassini's Magnetospheric Imaging Instrument (MIMI) and Magnetometer (MAG) and attempted to identify the region of Saturn's magnetosphere that Cassini was in at a given time using machine learning. MIMI data are from the Charge-Energy-Mass Spectrometer (CHEMS) instrument and the Low-Energy Magnetospheric Measurement System (LEMMS). We trained on data where the region is known based on a previous analysis of Cassini Plasma Spectrometer (CAPS) plasma data. Three magnetospheric regions are considered: Magnetosphere, Magnetosheath, and Solar Wind. MIMI particle intensities, magnetic field values, and spacecraft position are used as input attributes, and the output is the CAPS-based region, which is available from 2004 to 2012. We then use the trained classifier to identify Cassini's magnetospheric regions for times after 2012, when CAPS data is no longer available. Training accuracy is evaluated by testing the classifier performance on a time range of known regions that the classifier has never seen. Preliminary results indicate a 68% accuracy on such test data. Other techniques are being tested that may increase this performance. We present the data and algorithms used, and will describe the latest results, including the magnetospheric regions post-2012 identified by the algorithm.
14. Advances in magnetospheric physics, 1971--1974: energetic particles
International Nuclear Information System (INIS)
West, H.I. Jr.
1974-12-01
An account is given of energetic particle research in magnetospheric physics for the time period 1971--1974. Emphasis is on relating the various aspects of energetic particles to magnetospheric processes. 458 refs. (U.S.)
15. Magnetospheric structure of rotation powered pulsars
Energy Technology Data Exchange (ETDEWEB)
Arons, J. (California Univ., Berkeley, CA (USA) California Univ., Livermore, CA (USA). Inst. of Geophysics and Planetary Physics)
1991-01-07
I survey recent theoretical work on the structure of the magnetospheres of rotation powered pulsars, within the observational constraints set by their observed spindown, their ability to power synchrotron nebulae and their ability to produce beamed collective radio emission, while putting only a small fraction of their energy into incoherent X- and gamma radiation. I find no single theory has yet given a consistent description of the magnetosphere, but I conclude that models based on a dense outflow of pairs from the polar caps, permeated by a lower density flow of heavy ions, are the most promising avenue for future research. 106 refs., 4 figs., 2 tabs.
16. Theory of imperfect magnetosphere-ionosphere coupling
International Nuclear Information System (INIS)
Kan, J.R.; Lee, L.C.
1980-01-01
Atheory of magnetosphere-ionosphere coupling in the presence of field-aligned potential drops is formulated within the framework of magnetohydrodynamic equations. Our formulation allows the magnetosphere as well as the ionosphere to respond self-consistently to the parallel potential drop along auroral field lines. Equipotential contours are distorted into a V-shaped structure near the convection reversal boundary and S-shaped on the equatorward side, each gives rise to an inverted V precipitation band. The loading effect of the imperfect coupling results in a valley in the electric field profile which occurs equatorward of the convection reversal boundary
17. Magnetosphere, exosphere, and surface of Mercury
International Nuclear Information System (INIS)
Cheng, A.F.; Krimigis, S.M.; Johnson, R.E.; Lanzerotti, L.J.
1987-01-01
It is presently suggested in light of the atomic Na exosphere discovered for Mercury that this planet, like the Jupiter moon Io, is capable of maintaining a heavy ion magnetosphere. Na(+) ions from the exosphere are in this scenario accelerated to keV energies en route to making substantial contributions to the mass and energy budgets of the magnetosphere. Since Mercury's Na supply to the exosphere is primarily internal, it would appear that Mercury is losing its semivolatiles and that this process will proceed by way of photosputtering, which maintains an adequate Na-ejection rate from the planet's surface. 39 references
18. Magnetic reconnection in the terrestrial magnetosphere
International Nuclear Information System (INIS)
Feldman, W.C.
1984-01-01
An overview is given of quantitative comparisons between measured phenomena in the terrestrial magnetosphere thought to be associated with magnetic reconnection, and related theoretical predictions based on Petschek's simple model. Although such a comparison cannot be comprehensive because of the extended nature of the process and the relatively few in situ multipoint measurements made to date, the agreement is impressive where comparisons have been possible. This result leaves little doubt that magnetic reconnection does indeed occur in the terrestrial magnetosphere. The maximum reconnection rate, expressed in terms of the inflow Mach number, M/sub A/, is measured to be M/sub A/ = 0.2 +- 0.1
19. Time-dependent Models of Magnetospheric Accretion onto Young Stars
Energy Technology Data Exchange (ETDEWEB)
Robinson, C. E.; Espaillat, C. C. [Department of Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215 (United States); Owen, J. E. [Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States); Adams, F. C., E-mail: [email protected] [Physics Department, University of Michigan, Ann Arbor, MI 48109 (United States)
2017-04-01
Accretion onto Classical T Tauri stars is thought to take place through the action of magnetospheric processes, with gas in the inner disk being channeled onto the star’s surface by the stellar magnetic field lines. Young stars are known to accrete material in a time-variable manner, and the source of this variability remains an open problem, particularly on the shortest (∼day) timescales. Using one-dimensional time-dependent numerical simulations that follow the field line geometry, we find that for plausibly realistic young stars, steady-state transonic accretion occurs naturally in the absence of any other source of variability. However, we show that if the density in the inner disk varies smoothly in time with ∼day-long timescales (e.g., due to turbulence), this complication can lead to the development of shocks in the accretion column. These shocks propagate along the accretion column and ultimately hit the star, leading to rapid, large amplitude changes in the accretion rate. We argue that when these shocks hit the star, the observed time dependence will be a rapid increase in accretion luminosity, followed by a slower decline, and could be an explanation for some of the short-period variability observed in accreting young stars. Our one-dimensional approach bridges previous analytic work to more complicated multi-dimensional simulations and observations.
20. Time-dependent Models of Magnetospheric Accretion onto Young Stars
International Nuclear Information System (INIS)
Robinson, C. E.; Espaillat, C. C.; Owen, J. E.; Adams, F. C.
2017-01-01
Accretion onto Classical T Tauri stars is thought to take place through the action of magnetospheric processes, with gas in the inner disk being channeled onto the star’s surface by the stellar magnetic field lines. Young stars are known to accrete material in a time-variable manner, and the source of this variability remains an open problem, particularly on the shortest (∼day) timescales. Using one-dimensional time-dependent numerical simulations that follow the field line geometry, we find that for plausibly realistic young stars, steady-state transonic accretion occurs naturally in the absence of any other source of variability. However, we show that if the density in the inner disk varies smoothly in time with ∼day-long timescales (e.g., due to turbulence), this complication can lead to the development of shocks in the accretion column. These shocks propagate along the accretion column and ultimately hit the star, leading to rapid, large amplitude changes in the accretion rate. We argue that when these shocks hit the star, the observed time dependence will be a rapid increase in accretion luminosity, followed by a slower decline, and could be an explanation for some of the short-period variability observed in accreting young stars. Our one-dimensional approach bridges previous analytic work to more complicated multi-dimensional simulations and observations.
1. Ion transport in stellarators
International Nuclear Information System (INIS)
Ho, D.D.M.; Kulsrud, R.M.
1985-09-01
Stellarator ion transport in the low-collisionality regime with a radial electric field is calculated by a systematic expansion of the drift-Boltzmann equation. The shape of the helical well is taken into account in this calculation. It is found that the barely trapped ions with three to four times the thermal energy give the dominant contribution to the diffusion. Expressions for the ion particle and energy fluxes are derived
2. Status of stellarator research
International Nuclear Information System (INIS)
Wobig, H.
1985-01-01
In recent years main activities in stellarator research were focussed on production and investigation of currentless plasmas. Several heating methods have been applied: electron cyclotron heating, ion cyclotron heating and neutral beam injection. The parameters achieved in HELIOTRON E and W VII-A are: antin 20 m 3 , Tsub(i) <= 1 keV. The confinement is improved as compared with ohmically heated discharges. By ECRH (P = 200 kW) it is possible to heat electrons up to 1.4 keV, confinement in this regime is dominated already by trapped particle effects. Toroidal currents up to 2 kA - either bootstrap currents or externally driven currents - were observed. High β-values (antiβ = 2%) have been obtained in HELIOTRON E, in this regime already pressure driven MHD-modes were observed. Future experiments (ATF-1 and W VII-AS) will extend the parameter regime to temperatures of several keV. These experiments will give important information about critical problems of the stellarator line (β-limit, neoclassical confinement impurity transport). A few reactor studies of stellarators exist, attention is mainly concentrated on technical problems of the modular coil system
3. Propagation of microwaves in pulsar magnetospheres
Energy Technology Data Exchange (ETDEWEB)
Bodo, G; Ferrari, A [Turin Univ. (Italy). Ist. di Fisica Generale; Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica); Massaglia, S [Turin Univ. (Italy). Ist. di Fisica Generale; Cambridge Univ. (UK). Inst. of Astronomy)
1981-12-01
We discuss the dispersion relation of linearly-polarized waves, propagating along a strong background magnetic field embedded in an electron-positron plasma. The results are then applied to the study of the propagation conditions of coherent curvature radio radiation inside neutron stars magnetospheres, as produced by electric discharges following current pulsar models.
4. Polarized curvature radiation in pulsar magnetosphere
Science.gov (United States)
Wang, P. F.; Wang, C.; Han, J. L.
2014-07-01
The propagation of polarized emission in pulsar magnetosphere is investigated in this paper. The polarized waves are generated through curvature radiation from the relativistic particles streaming along curved magnetic field lines and corotating with the pulsar magnetosphere. Within the 1/γ emission cone, the waves can be divided into two natural wave-mode components, the ordinary (O) mode and the extraordinary (X) mode, with comparable intensities. Both components propagate separately in magnetosphere, and are aligned within the cone by adiabatic walking. The refraction of O mode makes the two components separated and incoherent. The detectable emission at a given height and a given rotation phase consists of incoherent X-mode and O-mode components coming from discrete emission regions. For four particle-density models in the form of uniformity, cone, core and patches, we calculate the intensities for each mode numerically within the entire pulsar beam. If the corotation of relativistic particles with magnetosphere is not considered, the intensity distributions for the X-mode and O-mode components are quite similar within the pulsar beam, which causes serious depolarization. However, if the corotation of relativistic particles is considered, the intensity distributions of the two modes are very different, and the net polarization of outcoming emission should be significant. Our numerical results are compared with observations, and can naturally explain the orthogonal polarization modes of some pulsars. Strong linear polarizations of some parts of pulsar profile can be reproduced by curvature radiation and subsequent propagation effect.
5. Whistler instability in a magnetospheric duct
International Nuclear Information System (INIS)
Talukdar, I.; Tripathi, V.K.; Jain, V.K.
1989-01-01
A whistler wave propagating through a preformed magnetospheric duct is susceptible to growth/amplification by an electron beam. The interaction is non-local and could be of Cerenkov or slow-cyclotron type. First-order perturbation theory is employed to obtain the growth rate for flat and Gaussian beam densities. (author)
6. The Magnetospheric Boundary in Cataclysmic Variables
Directory of Open Access Journals (Sweden)
Hellier Coel
2014-01-01
During outbursts, when the accretion flow increases by orders of magnitude, the disk pushes the magnetosphere inwards, and appears to feed field lines over a much greater range of magnetic azimuth. The non-equilibrium outburst behaviour shows an even richer phenomenology than in quiescence, adding DNOs and QPOs into the mix.
7. Impulsive Alfven coupling between the magnetosphere and ionosphere
International Nuclear Information System (INIS)
Reddy, R.V.; Watanabe, K.; Sato, T.; Watanabe, T.H.
1994-04-01
Basic properties of the impulsive Alfven interaction between the magnetosphere and ionosphere have been studied by means of a three-dimensional self-consistent simulation of the coupled magnetosphere and ionosphere system. It is found that the duration time of an impulsive perturbation at the magnetospheric equator, the latitudinal distribution of the Alfven propagation time along the field lines, and the ratio between the magnetospheric impedance and the ionospheric resistance is the main key factors that determine the propagation dynamics and the ionospheric responses for an impulsive MHD perturbation in the magnetosphere. (author)
8. A New Approach to Modeling Jupiter's Magnetosphere
Science.gov (United States)
Fukazawa, K.; Katoh, Y.; Walker, R. J.; Kimura, T.; Tsuchiya, F.; Murakami, G.; Kita, H.; Tao, C.; Murata, K. T.
2017-12-01
The scales in planetary magnetospheres range from 10s of planetary radii to kilometers. For a number of years we have studied the magnetospheres of Jupiter and Saturn by using 3-dimensional magnetohydrodynamic (MHD) simulations. However, we have not been able to reach even the limits of the MHD approximation because of the large amount of computer resources required. Recently thanks to the progress in supercomputer systems, we have obtained the capability to simulate Jupiter's magnetosphere with 1000 times the number of grid points used in our previous simulations. This has allowed us to combine the high resolution global simulation with a micro-scale simulation of the Jovian magnetosphere. In particular we can combine a hybrid (kinetic ions and fluid electrons) simulation with the MHD simulation. In addition, the new capability enables us to run multi-parameter survey simulations of the Jupiter-solar wind system. In this study we performed a high-resolution simulation of Jovian magnetosphere to connect with the hybrid simulation, and lower resolution simulations under the various solar wind conditions to compare with Hisaki and Juno observations. In the high-resolution simulation we used a regular Cartesian gird with 0.15 RJ grid spacing and placed the inner boundary at 7 RJ. From these simulation settings, we provide the magnetic field out to around 20 RJ from Jupiter as a background field for the hybrid simulation. For the first time we have been able to resolve Kelvin Helmholtz waves on the magnetopause. We have investigated solar wind dynamic pressures between 0.01 and 0.09 nPa for a number of IMF values. These simulation data are open for the registered users to download the raw data. We have compared the results of these simulations with Hisaki auroral observations.
9. Hydromagnetic wave coupling in the magnetosphere
International Nuclear Information System (INIS)
Lee, D.
1990-01-01
The hydromagnetic wave phenomena in the magnetosphere has been an area of space physics and plasma physics where theory has been successful in explaining many features in satellite experiments and ground-based observations. Magnetohydrodynamic (MHD) waves, which are composed of transverse Alven waves and compressional waves, are usually coupled in space due to an inhomogeneous plasma density and curved magnetic field lines. In addition to these effects, hot temperature plasmas invoke various ultra low frequency (ULF) wave phenomena via macroscopic wave instabilities or wave particle resonant interactions. These properties of the coupling between the two different MHD waves were analytically and numerically studied in a simplified model such as the box model with straight field lines. However, the real magnetosphere is rather close to a dipole field, even though the night side of the magnetosphere is significantly distorted from dipole geometry. The curvature of field lines plays an important role in understanding hydromagnetic wave coupling in the magnetosphere since the MHD wave propagation depends strongly on the curved magnetic fields. The study of the hydromagnetic wave properties on an inhomogeneous and curved magnetic field system by considering realistic geometry is emphasized. Most of the current theories are reviewed and a number of observations are introduced according to the wave excitation mechanism. Studies are also performed with the development of numerical models such as the two and three dimensional MHD dipole models. An attempt is made to understand and classify the hydromagnetic wave behavior in inhomogeneous and hot plasmas with respect to the energy sources and their frequency band in the magnetosphere. Therefore, various excitation mechanisms for hydromagnetic waves are examined to compare analytical and numerical results with the observations
10. Particle Acceleration in Dissipative Pulsar Magnetospheres
Science.gov (United States)
Kazanas, Z.; Kalapotharakos, C.; Harding, A.; Contopoulos, I.
2012-01-01
Pulsar magnetospheres represent unipolar inductor-type electrical circuits at which an EM potential across the polar cap (due to the rotation of their magnetic field) drives currents that run in and out of the polar cap and close at infinity. An estimate ofthe magnitude of this current can be obtained by dividing the potential induced across the polar cap V approx = B(sub O) R(sub O)(Omega R(sub O)/c)(exp 2) by the impedance of free space Z approx eq 4 pi/c; the resulting polar cap current density is close to $n {GJ} c$ where $n_{GJ}$ is the Goldreich-Julian (GJ) charge density. This argument suggests that even at current densities close to the GJ one, pulsar magnetospheres have a significant component of electric field $E_{parallel}$, parallel to the magnetic field, a condition necessary for particle acceleration and the production of radiation. We present the magnetic and electric field structures as well as the currents, charge densities, spin down rates and potential drops along the magnetic field lines of pulsar magnetospheres which do not obey the ideal MHD condition $E cdot B = 0$. By relating the current density along the poloidal field lines to the parallel electric field via a kind of Ohm's law $J = sigma E_{parallel}$ we study the structure of these magnetospheres as a function of the conductivity $sigma$. We find that for $sigma gg OmegaS the solution tends to the (ideal) Force-Free one and to the Vacuum one for$sigma 11 OmegaS. Finally, we present dissipative magnetospheric solutions with spatially variable $sigma$ that supports various microphysical properties and are compatible with the observations.
11. Double-reconnected magnetic structures driven by Kelvin-Helmholtz vortices at the Earth's magnetosphere
International Nuclear Information System (INIS)
Borgogno, D.; Califano, F.; Pegoraro, F.; Faganello, M.
2015-01-01
In an almost collisionless magnetohydrodynamic plasma in a relatively strong magnetic field, stresses can be conveyed far from the region where they are exerted, e.g., through the propagation of Alfvèn waves. The forced dynamics of line-tied magnetic structures in solar and stellar coronae (see, e.g., A. F. Rappazzo and E. N. Parker, Astrophys. J. 773, L2 (2013) and references therein) is a paradigmatic case. Here, we investigate how this action at a distance develops from the equatorial region of the Kelvin-Helmholtz unstable flanks of the Earth's magnetosphere leading to the onset, at mid latitude in both hemispheres, of correlated double magnetic field line reconnection events that can allow the solar wind plasma to enter the Earth's magnetosphere
DEFF Research Database (Denmark)
Jørgensen, John Leif; Liebe, Carl Christian
1997-01-01
The science objective of the Danish Geomagnetic Research Satellite "Ørsted" is to map the magnetic field of the Earth, with a vector precision of a fraction of a nanotesla. This necessitates an attitude reference instrument with a precision of a few arcseconds onboard the satellite. To meet...... this demand the Advanced Stellar Compass (ASC), a fully autonomous miniature star tracker, was developed. This ASC is capable of both solving the "lost in space" problem and determine the attitude with arcseconds precision. The development, principles of operation and instrument autonomy of the ASC...
13. Physics of Stellar Convection
Science.gov (United States)
Arnett, W. David
2009-05-01
We review recent progress using numerical simulations as a testbed for development of a theory of stellar convection, much as envisaged by John von Newmann. Necessary features of the theory, non-locality and fluctuations, are illustrated by computer movies. It is found that the common approximation of convection as a diffusive process presents the wrong physical picture, and improvements are suggested. New observational results discussed at the conference are gratifying in their validation of some of our theoretical ideas, especially the idea that SNIb and SNIc events are related to the explosion of massive star cores which have been stripped by mass loss and binary interactions [1
14. Stellar axion models
Energy Technology Data Exchange (ETDEWEB)
Nowakowski, Daniel; Kuster, Markus; Meister, Claudia V.; Fuelbert, Florian; Hoffmann, Dieter H.H. [TU Darmstadt (Germany). Institut fuer Kernphysik; Weiss, Achim [Max-Planck-Institut fuer Astrophysik, Garching (Germany)
2010-07-01
An axion helioscope is typically operated to observe the sun as an axion source. Additional pointings at celestial sources, e.g. stars in other galaxies, result in possible detections of axions from distant galactic objects. For the observation of supplementary axion sources we therefore calculate the thereotical axion flux from distant stars by extending axionic flux models for the axion Primakoff effect in the sun to other main sequence stars. The main sequence star models used for our calculations are based on full stellar structure calculations. To deduce the effective axion flux of stellar objects incident on the Earth the All-Sky catalogue was used to obtain the spectral class and distance of the stars treated. Our calculations of the axion flux in the galactic plane show that for a zero age main sequence star an maximum axion flux of {phi}{sub a}=303.43 cm{sup -2}s{sup -1} could be expected. Furthermore we present estimates of axion fluxes from time-evolved stars.
15. The DEMO Quasisymmetric Stellarator
Directory of Open Access Journals (Sweden)
2010-02-01
Full Text Available The NSTAB nonlinear stability code solves differential equations in conservation form, and the TRAN Monte Carlo test particle code tracks guiding center orbits in a fixed background, to provide simulations of equilibrium, stability, and transport in tokamaks and stellarators. These codes are well correlated with experimental observations and have been validated by convergence studies. Bifurcated 3D solutions of the 2D tokamak problem have been calculated that model persistent disruptions, neoclassical tearing modes (NTMs and edge localized modes (ELMs occurring in the International Thermonuclear Experimental Reactor (ITER, which does not pass the NSTAB simulation test for nonlinear stability. So we have designed a quasiaxially symmetric (QAS stellarator with similar proportions as a candidate for the demonstration (DEMO fusion reactor that does pass the test [1]. The configuration has two field periods and an exceptionally accurate 2D symmetry that furnishes excellent thermal confinement and good control of the prompt loss of alpha particles. Robust coils are found from a filtered form of the Biot-Savart law based on a distribution of current over a control surface for the coils and the current in the plasma defined by the equilibrium calculation. Computational science has addressed the issues of equilibrium, stability, and transport, so it remains to develop an effective plan to construct the coils and build a diverter.
16. Magnetosphere - Ionosphere - Thermosphere (MIT) Coupling at Jupiter
Science.gov (United States)
Yates, J. N.; Ray, L. C.; Achilleos, N.
2017-12-01
Jupiter's upper atmospheric temperature is considerably higher than that predicted by Solar Extreme Ultraviolet (EUV) heating alone. Simulations incorporating magnetosphere-ionosphere coupling effects into general circulation models have, to date, struggled to reproduce the observed atmospheric temperatures under simplifying assumptions such as azimuthal symmetry and a spin-aligned dipole magnetic field. Here we present the development of a full three-dimensional thermosphere model coupled in both hemispheres to an axisymmetric magnetosphere model. This new coupled model is based on the two-dimensional MIT model presented in Yates et al., 2014. This coupled model is a critical step towards to the development of a fully coupled 3D MIT model. We discuss and compare the resulting thermospheric flows, energy balance and MI coupling currents to those presented in previous 2D MIT models.
17. Electromagnetic field for an open magnetosphere
International Nuclear Information System (INIS)
Heikkila, W.J.
1984-01-01
The boundary-layer-dominated models of the earth EM field developed by Heikkila (1975, 1978, 1982, and 1983) and Heikkila et al. (1979) to account for deficiencies in the electric-field descriptions of quasi-steady-state magnetic-field-reconnection models (such as that of Cowley, 1980) are characterized, reviewing the arguments and indicating the most important implications. The mechanisms of boundary-layer formation and field direction reversal are explained and illustrated with diagrams, and it is inferred that boundary-layer phenomena rather than magnetic reconnection may be the cause of large-scale magnetospheric circulation, convection, plasma-sheet formation and sunward convection, and auroras, the boundary layer acting basically as a viscous process mediating solar-wind/magnetosphere interactions. 23 references
18. Two-stream instability in pulsar magnetospheres
International Nuclear Information System (INIS)
Usov, V.V.
1987-01-01
If the electron-positron plasma flow from the pulsar environment is stationary, the two-stream instability does not have enough time to develop in the pulsar magnetosphere. In that case the outflowing electron-positron plasma gathers into separate clouds. The clouds move along magnetic field lines and disperse as they go farther from the pulsar. At a distance of about 10 to the 8th cm from the pulsar surface, the high-energy particles of a given cloud catch up with the low-energy particles that belong to the cloud going ahead of it. In this region of a pulsar magnetosphere, the energy distribution of plasma particles is two-humped, and a two-stream instability may develop. The growth rate of the instability is quite sufficient for its development. 17 references
19. The electromagnetic field for an open magnetosphere
Science.gov (United States)
Heikkila, W. J.
1984-01-01
The boundary-layer-dominated models of the earth EM field developed by Heikkila (1975, 1978, 1982, and 1983) and Heikkila et al. (1979) to account for deficiencies in the electric-field descriptions of quasi-steady-state magnetic-field-reconnection models (such as that of Cowley, 1980) are characterized, reviewing the arguments and indicating the most important implications. The mechanisms of boundary-layer formation and field direction reversal are explained and illustrated with diagrams, and it is inferred that boundary-layer phenomena rather than magnetic reconnection may be the cause of large-scale magnetospheric circulation, convection, plasma-sheet formation and sunward convection, and auroras, the boundary layer acting basically as a viscous process mediating solar-wind/magnetosphere interactions.
20. Modeling Jovian Magnetospheres Beyond the Solar System
Science.gov (United States)
Williams, Peter K. G.
2018-06-01
Low-frequency radio observations are believed to represent one of the few means of directly probing the magnetic fields of extrasolar planets. However, a half-century of low-frequency planetary observations within the Solar System demonstrate that detailed, physically-motivated magnetospheric models are needed to properly interpret the radio data. I will present recent work in this area focusing on the current state of the art: relatively high-frequency observations of relatively massive objects, which are now understood to have magnetospheres that are largely planetary in nature. I will highlight the key challenges that will arise in future space-based observations of lower-mass objects at lower frequencies.
1. Terrestrial VLF transmitter injection into the magnetosphere
Science.gov (United States)
Cohen, M. B.; Inan, U. S.
2012-08-01
Very Low Frequency (VLF, 3-30 kHz) radio waves emitted from ground sources (transmitters and lightning) strongly impact the radiation belts, driving electron precipitation via whistler-electron gyroresonance, and contributing to the formation of the slot region. However, calculations of the global impacts of VLF waves are based on models of trans-ionospheric propagation to calculate the VLF energy reaching the magnetosphere. Limited comparisons of these models to individual satellite passes have found that the models may significantly (by >20 dB) overestimate amplitudes of ground based VLF transmitters in the magnetosphere. To form a much more complete empirical picture of VLF transmitter energy reaching the magnetosphere, we present observations of the radiation pattern from a number of ground-based VLF transmitters by averaging six years of data from the DEMETER satellite. We divide the slice at ˜700 km altitude above a transmitter into pixels and calculate the average field for all satellite passes through each pixel. There are enough data to see 25 km features in the radiation pattern, including the modal interference of the subionospheric signal mapped upwards. Using these data, we deduce the first empirical measure of the radiated power into the magnetosphere from these transmitters, for both daytime and nighttime, and at both the overhead and geomagnetically conjugate region. We find no detectable variation of signal intensity with geomagnetic conditions at low and mid latitudes (L ionospheric heating by one VLF transmitter which modifies the trans-ionospheric absorption of signals from other transmitters passing through the heated region.
2. The magnetosphere under weak solar wind forcing
Directory of Open Access Journals (Sweden)
C. J. Farrugia
2007-02-01
Full Text Available The Earth's magnetosphere was very strongly disturbed during the passage of the strong shock and the following interacting ejecta on 21–25 October 2001. These disturbances included two intense storms (Dst*≈−250 and −180 nT, respectively. The cessation of this activity at the start of 24 October ushered in a peculiar state of the magnetosphere which lasted for about 28 h and which we discuss in this paper. The interplanetary field was dominated by the sunward component [B=(4.29±0.77, −0.30±0.71, 0.49±0.45 nT]. We analyze global indicators of geomagnetic disturbances, polar cap precipitation, ground magnetometer records, and ionospheric convection as obtained from SuperDARN radars. The state of the magnetosphere is characterized by the following features: (i generally weak and patchy (in time low-latitude dayside reconnection or reconnection poleward of the cusps; (ii absence of substorms; (iii a monotonic recovery from the previous storm activity (Dst corrected for magnetopause currents decreasing from ~−65 to ~−35 nT, giving an unforced decreased of ~1.1 nT/h; (iv the probable absence of viscous-type interaction originating from the Kelvin-Helmholtz (KH instability; (v a cross-polar cap potential of just 20–30 kV; (vi a persistent, polar cap region containing (vii very weak, and sometimes absent, electron precipitation and no systematic inter-hemisphere asymmetry. Whereas we therefore infer the presence of a moderate amount of open flux, the convection is generally weak and patchy, which we ascribe to the lack of solar wind driver. This magnetospheric state approaches that predicted by Cowley and Lockwood (1992 but has never yet been observed.
3. A catalog of stellar spectrophotometry
Science.gov (United States)
Adelman, S. J.; Pyper, D. M.; Shore, S. N.; White, R. E.; Warren, W. H., Jr.
1989-01-01
A machine-readable catalog of stellar spectrophotometric measurements made with rotating grating scanner is introduced. Consideration is given to the processes by which the stellar data were collected and calibrated with the fluxes of Vega (Hayes and Latham, 1975). A sample page from the spectrophotometric catalog is presented.
4. Quasisymmetry equations for conventional stellarators
International Nuclear Information System (INIS)
Pustovitov, V.D.
1994-11-01
General quasisymmetry condition, which demands the independence of B 2 on one of the angular Boozer coordinates, is reduced to two equations containing only geometrical characteristics and helical field of a stellarator. The analysis is performed for conventional stellarators with a planar circular axis using standard stellarator expansion. As a basis, the invariant quasisymmetry condition is used. The quasisymmetry equations for stellarators are obtained from this condition also in an invariant form. Simplified analogs of these equations are given for the case when averaged magnetic surfaces are circular shifted torii. It is shown that quasisymmetry condition can be satisfied, in principle, in a conventional stellarator by a proper choice of two satellite harmonics of the helical field in addition to the main harmonic. Besides, there appears a restriction on the shift of magnetic surfaces. Thus, in general, the problem is closely related with that of self-consistent description of a configuration. (author)
5. Nucleosynthesis in stellar explosions
Energy Technology Data Exchange (ETDEWEB)
Woosley, S.E.; Axelrod, T.S.; Weaver, T.A.
1983-01-01
The final evolution and explosion of stars from 10 M/sub solar/ to 10/sup 6/ M/sub solar/ are reviewed with emphasis on factors affecting the expected nucleosynthesis. We order our paper in a sequence of decreasing mass. If, as many suspect, the stellar birth function was peaked towards larger masses at earlier times (see e.g., Silk 1977; but also see Palla, Salpeter, and Stahler 1983), this sequence of masses might also be regarded as a temporal sequence. At each stage of Galactic chemical evolution stars form from the ashes of preceding generations which typically had greater mass. A wide variety of Type I supernova models, most based upon accreting white dwarf stars, are also explored using the expected light curves, spectra, and nucleosynthesis as diagnostics. No clearly favored Type I model emerges that is capable of simultaneously satisfying all three constraints.
6. Nucleosynthesis in stellar explosions
International Nuclear Information System (INIS)
Woosley, S.E.; Axelrod, T.S.; Weaver, T.A.
1983-01-01
The final evolution and explosion of stars from 10 M/sub solar/ to 10 6 M/sub solar/ are reviewed with emphasis on factors affecting the expected nucleosynthesis. We order our paper in a sequence of decreasing mass. If, as many suspect, the stellar birth function was peaked towards larger masses at earlier times (see e.g., Silk 1977; but also see Palla, Salpeter, and Stahler 1983), this sequence of masses might also be regarded as a temporal sequence. At each stage of Galactic chemical evolution stars form from the ashes of preceding generations which typically had greater mass. A wide variety of Type I supernova models, most based upon accreting white dwarf stars, are also explored using the expected light curves, spectra, and nucleosynthesis as diagnostics. No clearly favored Type I model emerges that is capable of simultaneously satisfying all three constraints
7. Remarks on stellar clusters
International Nuclear Information System (INIS)
Teller, E.
1985-01-01
In the following, a few simple remarks on the evolution and properties of stellar clusters will be collected. In particular, globular clusters will be considered. Though details of such clusters are often not known, a few questions can be clarified with the help of primitive arguments. These are:- why are spherical clusters spherical, why do they have high densities, why do they consist of approximately a million stars, how may a black hole of great mass form within them, may they be the origin of gamma-ray bursts, may their invisible remnants account for the missing mass of our galaxy. The available data do not warrant a detailed evaluation. However, it is remarkable that exceedingly simple models can shed some light on the questions enumerated above. (author)
8. L = ± 1 stellarator
International Nuclear Information System (INIS)
Kikuchi, T.; Shiina, S.; Saito, K.; Gesso, H.; Aizawa, M.; Kawakami, I.
1985-01-01
We report the magnetic field configuration of helical magnetic axis stellarator. The magnetic field configuration is composed of large l=1 field and small l=-1 and l=0(bumpy) fields. The large l=1 field (combined with the small l=-1 field) is used to form helical magnetic axis with the helical curvature much larger than the toroidal curvature, which provides the high limiting values of β. The small l=-1 field, furthermore, as well as the large l=1 field reduces the Pfirsch-Schlueter currents by combining with l=0 field. Therefore, the large l=1 field and the combination of three field components may be favourable for the increase of limiting β value
9. The role of scientific ballooning for exploration of the magnetosphere
International Nuclear Information System (INIS)
Block, L.P.; Lazutin, L.L.; Riedler, W.
1984-11-01
The magnetosphere is explored in situ by satellites, but measurements near the low altitude magnetospheric boundary by rockets, balloons and groundbased instruments play a very significant role. The geomagnetic field provides a frame with anisotropic wave and particle propagation effects, enabling remote sensing of the distant magnetosphere by means of balloon-borne and groundbased instruments. Examples will be given of successful studies, with coordinated satellite and balloon observations, of substorm, pulsation and other phenomena propagating both along and across the geomagnetic field. Continued efforts with sophisticated balloon-borne instrumentations should contribute substantially to our understanding of magnetospheric physics. (Author)
10. Magnetic field in the magnetosphere. Numerical simulation of the magnetospheric magnetic field
International Nuclear Information System (INIS)
Mal'kov, M.V.
1993-01-01
The last version of the empirical model of the magnetospheric magnetic field (Tsyganenko, 1989) is considered. Total number of data used for construction of the model contains 36682 average vector values of the field. This number of data is obtained by satellite measurements at distances of r=4-66 R e (R e is the Earth radius). 5 figs., 2 tabs
11. Actions of magnetospheres on planetary atmospheres
International Nuclear Information System (INIS)
Hultqvist, Bengt.
1989-12-01
Planet Earth is rather special in terms of transfer of magnetospheric energy to the atmosphere (apart from Jupiter, which is extreme in almost all respects). The auroral particle energy input rate to the atmosphere per unit area, and therefore the resulting auroral emission intensity, is second only to that of Jupiter. The contribution of the Joule heating to the heating of the upper atmosphere, measured in terms of the energetic particle precipitation power, is probably larger on Earth than on all the other planets, possibly with the exception of Uranus (and perhaps Neptune, which we know nothing of when this is written). For all those planets which have a corotating plasmasphere extending to the magnetopause, the Joule heating power is small compared with the precipitating particle power. The extremely successful Pioneer and Voyager missions have provided us with most impressive sets of data from the outer planets and Phobos has recently added unique new data from Mars. Still, the conclusion that the observational basis for our understanding of the physics of the magnetosphere-atmosphere interactions at all the planets other than Earth is very limited, is a self-evident one. Even at Earth many aspects of this interaction are frontline areas of research. The grand tour of the Voyagers has demonstrated very clearly how different the magnetospheres and atmospheres of the various planets are and the very high degree of complexity of the plasma systems around the planets. Most questions of physics are still unanswered; those related to source and sink processes of the plasma and energetic particles being one set of examples. The Galileo and Cassini-Huygens missions will certainly contribute in very important ways to the answering of many open questions. (147 refs.)
12. Origins Of Magnetospheric Physics An Expanded Edition
CERN Document Server
Van Allen, James A
2004-01-01
Early in 1958, instruments on the space satellites Explorer I and Explorer III revealed the presence of radiation belts, enormous populations of energetic particles trapped in the magnetic field of the earth. Originally published in 1983 but long out of print until now, Origins of Magnetospheric Physics tells the story of this dramatic and hugely transformative period in scientific and Cold War history. Writing in an accessible style and drawing on personal journals, correspondence, published papers, and the recollections of colleagues, James Van Allen documents a trail-blazing era in space hi
13. The art of mapping the magnetosphere
International Nuclear Information System (INIS)
Stern, D.P.
1994-01-01
A comprehensive review is presented of the mathematical methods used to represent magnetic fields in the Earth's magnetosphere, of the way existing data-based models use these methods and of the associated problems and concepts. The magnetic field has five main components: the internal field, the magnetopause, the ring current, the tail and Birkeland currents. Methods of representing separately each of these are discussed, as is the deformation of magnetic fields; Appendix B traces the connection between deformations and the Cauchy integral. A summary section lists the uses of data-based models and their likely evolution, and Appendix A supplements the text with a set of problems. 55 refs., 20 figs
14. Evolution of stellar systems
International Nuclear Information System (INIS)
1981-01-01
The stellar systems of which the evolution will be considered in this thesis, are either galaxies, which contain about 10 11 stars, or binary systems, which consist of only two stars. It is seen that binary systems can give us some insight into the relative age of the nucleus of M31. The positive correlation between the metal content of a galaxy and its mass, first noted for elliptical galaxies, seems to be a general property of galaxies of all types. The observed increase of metallicity with galaxy mass is too large to be accounted for by differences in the evolutionary stage of galaxies. To explain the observed correlation it is proposed that a relatively larger proportion of massive stars is formed in more massive galaxies. The physical basis is that the formation of massive stars seems to be tied to the enhanced gas-dynamical activity in more massive galaxies. A specific aspect of the production of heavy elements by massive stars is investigated in some detail. In 1979 a cluster of 18 point X-ray sources within 400 pc of the centre of M31 was detected with the Einstein satellite. This is a remarkable result since no equivalent of this cluster has been observed in the nucleus of our own Galaxy, which otherwise is very similar to that of M31. An explanation for this phenomenon is proposed, suggesting that X-ray binaries are the products of the long-term evolution of nova systems. (Auth.)
15. Stellar extreme ultraviolet astronomy
International Nuclear Information System (INIS)
Cash, W.C. Jr.
1978-01-01
The design, calibration, and launch of a rocket-borne imaging telescope for extreme ultraviolet astronomy are described. The telescope, which employed diamond-turned grazing incidence optics and a ranicon detector, was launched November 19, 1976, from the White Sands Missile Range. The telescope performed well and returned data on several potential stellar sources of extreme ultraviolet radiation. Upper limits ten to twenty times more sensitive than previously available were obtained for the extreme ultraviolet flux from the white dwarf Sirius B. These limits fall a factor of seven below the flux predicted for the star and demonstrate that the temperature of Sirius B is not 32,000 K as previously measured, but is below 30,000 K. The new upper limits also rule out the photosphere of the white dwarf as the source of the recently reported soft x-rays from Sirius. Two other white dwarf stars, Feige 24 and G191-B2B, were observed. Upper limits on the flux at 300 A were interpreted as lower limits on the interstellar hydrogen column densities to these stars. The lower limits indicate interstellar hydrogen densitites of greater than .02 cm -3 . Four nearby stars (Sirius, Procyon, Capella, and Mirzam) were observed in a search for intense low temperature coronae or extended chromospheres. No extreme ultraviolet radiation from these stars was detected, and upper limits to their coronal emisson measures are derived
16. Mapping stellar surface features
International Nuclear Information System (INIS)
Noah, P.V.
1987-01-01
New photometric and spectroscopic observations of the RS Canum Venaticorum binaries Sigma Geminorum and UX Arietis are reported along with details of the Doppler-imaging program SPOTPROF. The observations suggest that the starspot activity on Sigma Gem has decreased to 0.05 magnitude in two years. A photometric spot model for September 1984 to January 1985 found that a single spot covering 2% of the surface and 1000 K cooler than the surrounding photosphere could model the light variations. Equivalent-width observations contemporaneous with the photometric observations did not show any significant variations. Line-profile models from SPOTPROF predict that the variation of the equivalent width of the 6393 A Fe I line should be ∼ 1mA. Photometric observations of UX Ari from January 1984 to March 1985 show an 0.3 magnitude variation indicating a large spot group must cover the surface. Contemporaneous spectroscopic observations show asymmetric line profiles. The Doppler imaging and the photometric light-curve models were used in an iterative method to describe the stellar surface-spot distribution and successfully model both the photometric and the spectroscopic variations
17. SI: The Stellar Imager
Science.gov (United States)
Carpenter, Kenneth G.; Schrijver, Carolus J.; Karovska, Margarita
2006-01-01
The ultra-sharp images of the Stellar Imager (SI) will revolutionize our view of many dynamic astrophysical processes: The 0.1 milliarcsec resolution of this deep-space telescope will transform point sources into extended sources, and simple snapshots into spellbinding evolving views. SI s science focuses on the role of magnetism in the Universe, particularly on magnetic activity on the surfaces of stars like the Sun. SI s prime goal is to enable long-term forecasting of solar activity and the space weather that it drives in support of the Living With a Star program in the Exploration Era by imaging a sample of magnetically active stars with enough resolution to map their evolving dynamo patterns and their internal flows. By exploring the Universe at ultra-high resolution, SI will also revolutionize our understanding of the formation of planetary systems, of the habitability and climatology of distant planets, and of many magnetohydrodynamically controlled structures and processes in the Universe.
18. Stellar Presentations (Abstract)
Science.gov (United States)
Young, D.
2015-12-01
(Abstract only) The AAVSO is in the process of expanding its education, outreach and speakers bureau program. powerpoint presentations prepared for specific target audiences such as AAVSO members, educators, students, the general public, and Science Olympiad teams, coaches, event supervisors, and state directors will be available online for members to use. The presentations range from specific and general content relating to stellar evolution and variable stars to specific activities for a workshop environment. A presentation—even with a general topic—that works for high school students will not work for educators, Science Olympiad teams, or the general public. Each audience is unique and requires a different approach. The current environment necessitates presentations that are captivating for a younger generation that is embedded in a highly visual and sound-bite world of social media, twitter and U-Tube, and mobile devices. For educators, presentations and workshops for themselves and their students must support the Next Generation Science Standards (NGSS), the Common Core Content Standards, and the Science Technology, Engineering and Mathematics (STEM) initiative. Current best practices for developing relevant and engaging powerpoint presentations to deliver information to a variety of targeted audiences will be presented along with several examples.
19. Turbulence optimisation in stellarator experiments
Energy Technology Data Exchange (ETDEWEB)
Proll, Josefine H.E. [Max-Planck/Princeton Center for Plasma Physics (Germany); Max-Planck-Institut fuer Plasmaphysik, Wendelsteinstr. 1, 17491 Greifswald (Germany); Faber, Benjamin J. [HSX Plasma Laboratory, University of Wisconsin-Madison, Madison, WI 53706 (United States); Helander, Per; Xanthopoulos, Pavlos [Max-Planck/Princeton Center for Plasma Physics (Germany); Lazerson, Samuel A.; Mynick, Harry E. [Plasma Physics Laboratory, Princeton University, P.O. Box 451 Princeton, New Jersey 08543-0451 (United States)
2015-05-01
Stellarators, the twisted siblings of the axisymmetric fusion experiments called tokamaks, have historically suffered from confining the heat of the plasma insufficiently compared with tokamaks and were therefore considered to be less promising candidates for a fusion reactor. This has changed, however, with the advent of stellarators in which the laminar transport is reduced to levels below that of tokamaks by shaping the magnetic field accordingly. As in tokamaks, the turbulent transport remains as the now dominant transport channel. Recent analytical theory suggests that the large configuration space of stellarators allows for an additional optimisation of the magnetic field to also reduce the turbulent transport. In this talk, the idea behind the turbulence optimisation is explained. We also present how an optimised equilibrium is obtained and how it might differ from the equilibrium field of an already existing device, and we compare experimental turbulence measurements in different configurations of the HSX stellarator in order to test the optimisation procedure.
20. Optimizing Stellarators for Turbulent Transport
International Nuclear Information System (INIS)
Mynick, H.E.; Pomphrey, N.; Xanthopoulos, P.
2010-01-01
Up to now, the term 'transport-optimized' stellarators has meant optimized to minimize neoclassical transport, while the task of also mitigating turbulent transport, usually the dominant transport channel in such designs, has not been addressed, due to the complexity of plasma turbulence in stellarators. Here, we demonstrate that stellarators can also be designed to mitigate their turbulent transport, by making use of two powerful numerical tools not available until recently, namely gyrokinetic codes valid for 3D nonlinear simulations, and stellarator optimization codes. A first proof-of-principle configuration is obtained, reducing the level of ion temperature gradient turbulent transport from the NCSX baseline design by a factor of about 2.5.
1. Stellar magnetic activity and exoplanets
Directory of Open Access Journals (Sweden)
Vidotto A.A.
2017-01-01
Full Text Available It has been proposed that magnetic activity could be enhanced due to interactions between close-in massive planets and their host stars. In this article, I present a brief overview of the connection between stellar magnetic activity and exoplanets. Stellar activity can be probed in chromospheric lines, coronal emission, surface spot coverage, etc. Since these are manifestations of stellar magnetism, these measurements are often used as proxies for the magnetic field of stars. Here, instead of focusing on the magnetic proxies, I overview some recent results of magnetic field measurements using spectropolarimetric observations. Firstly, I discuss the general trends found between large-scale magnetism, stellar rotation, and coronal emission and show that magnetism seems to be correlated to the internal structure of the star. Secondly, I overview some works that show evidence that exoplanets could (or not act as to enhance the activity of their host stars.
2. Terrestrial aurora: astrophysical laboratory for anomalous abundances in stellar systems
Directory of Open Access Journals (Sweden)
I. Roth
2014-02-01
Full Text Available The unique magnetic structure of the terrestrial aurora as a conduit of information between the ionosphere and magnetosphere can be utilized as a laboratory for physical processes at similar magnetic configurations and applied to various evolutionary phases of the solar (stellar system. The most spectacular heliospheric abundance enhancement involves the 3He isotope and selective heavy elements in impulsive solar flares. In situ observations of electromagnetic waves on active aurora are extrapolated to flaring corona in an analysis of solar acceleration processes of 3He, the only element that may resonate strongly with the waves, as well as heavy ions with specific charge-to-mass ratios, which may resonate weaker via their higher gyroharmonics. These results are applied to two observed anomalous astrophysical abundances: (1 enhanced abundance of 3He and possibly 13C in the late stellar evolutionary stages of planetary nebulae; and (2 enhanced abundance of the observed fossil element 26Mg in meteorites as a decay product of radioactive 26Al isotope due to interaction with the flare-energized 3He in the early solar system.
3. Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
4. On origin of stellar clusters
International Nuclear Information System (INIS)
Tovmasyan, G.M.
1977-01-01
The ratios of the gas component of the mass of young stellar clusters to their stellar mass are considered. They change by more than four orders from one cluster to another. The results are in direct contradiction with the hypothesis of formation of cluster stars from a preliminarily existing gas cloud by its condensation, and they favour the Ambartsumian hypothesis of the joint origin of stars and gas clouds from superdense protostellar matter
5. Solar wind conditions for a quiet magnetosphere
International Nuclear Information System (INIS)
Kerns, K.J.; Gussenhoven, M.S.
1990-01-01
The conditions of the solar wind that lead to a quiet magnetosphere are determined under the assumption that the quiet or baseline magnetosphere can be identified by prolonged periods of low values of the am index. The authors analyzed solar wind data from 1978 to 1984 (7 years) during periods in which am ≤ 3 nT to identify those solar wind parameters that deviate significantly from average values. Parallel studies were also performed for prolonged periods of Kp = 0, 0+ and AE z ) show distinctive variations from average values. They independently varied these solar wind parameters and the length of time the conditions must persist to minimize am. This was done with the additional requirement that the conditions yield a reasonable number of occurrences (5% of the data set). The resulting baseline conditions are V ≤ 390 km/s; 180 degree - arctan |B y /B z | ≤ 101 degree, when b z ≤ 0 (no restriction on B z positive); B ≤ 6.5 nT; and persistence of these conditions for at least 5 hours. Minimizing the am index does not require a clear upper limit on the value of B z as might be anticipated from the work of Gussenhoven (1988) and Berthelier (1980). Apparently, this is a result of the requirement that the conditions must occur 5% of the time. When the requirement is lowered to 1% occurrence, an upper limit to B z emerges
6. Fast Plasma Investigation for Magnetospheric Multiscale
Science.gov (United States)
Pollock, C.; Moore, T.; Coffey, V.; Dorelli J.; Giles, B.; Adrian, M.; Chandler, M.; Duncan, C.; Figueroa-Vinas, A.; Garcia, K.;
2016-01-01
The Fast Plasma Investigation (FPI) was developed for flight on the Magnetospheric Multiscale (MMS) mission to measure the differential directional flux of magnetospheric electrons and ions with unprecedented time resolution to resolve kinetic-scale plasma dynamics. This increased resolution has been accomplished by placing four dual 180-degree top hat spectrometers for electrons and four dual 180-degree top hat spectrometers for ions around the periphery of each of four MMS spacecraft. Using electrostatic field-of-view deflection, the eight spectrometers for each species together provide 4pi-sr-field-of-view with, at worst, 11.25-degree sample spacing. Energy/charge sampling is provided by swept electrostatic energy/charge selection over the range from 10 eVq to 30000 eVq. The eight dual spectrometers on each spacecraft are controlled and interrogated by a single block redundant Instrument Data Processing Unit, which in turn interfaces to the observatory's Instrument Suite Central Instrument Data processor. This paper described the design of FPI, its ground and in-flight calibration, its operational concept, and its data products.
7. Directory of Open Access Journals (Sweden)
M. A. Shukhtina
2004-03-01
Full Text Available Quantitative relationships allowing one to compute the lobe magnetic field, flaring angle and tail radius, and to evaluate magnetic flux based on solar wind/IMF parameters and spacecraft position are obtained for the middle magnetotail, X=(–15,–35RE, using 3.5 years of simultaneous Geotail and Wind spacecraft observations. For the first time it was done separately for different states of magnetotail including the substorm onset (SO epoch, the steady magnetospheric convection (SMC and quiet periods (Q. In the explored distance range the magnetotail parameters appeared to be similar (within the error bar for Q and SMC states, whereas at SO their values are considerably larger. In particular, the tail radius is larger by 1–3 RE at substorm onset than during Q and SMC states, for which the radius value is close to previous magnetopause model values. The calculated lobe magnetic flux value at substorm onset is ~1GWb, exceeding that at Q (SMC states by ~50%. The model magnetic flux values at substorm onset and SMC show little dependence on the solar wind dynamic pressure and distance in the tail, so the magnetic flux value can serve as an important discriminator of the state of the middle magnetotail. Key words. Magnetospheric physics (solar windmagnetosphere- interactions, magnetotail, storms and substorms
8. Quantitative magnetotail characteristics of different magnetospheric states
Directory of Open Access Journals (Sweden)
M. A. Shukhtina
2004-03-01
Full Text Available Quantitative relationships allowing one to compute the lobe magnetic field, flaring angle and tail radius, and to evaluate magnetic flux based on solar wind/IMF parameters and spacecraft position are obtained for the middle magnetotail, X=(–15,–35RE, using 3.5 years of simultaneous Geotail and Wind spacecraft observations. For the first time it was done separately for different states of magnetotail including the substorm onset (SO epoch, the steady magnetospheric convection (SMC and quiet periods (Q. In the explored distance range the magnetotail parameters appeared to be similar (within the error bar for Q and SMC states, whereas at SO their values are considerably larger. In particular, the tail radius is larger by 1–3 RE at substorm onset than during Q and SMC states, for which the radius value is close to previous magnetopause model values. The calculated lobe magnetic flux value at substorm onset is ~1GWb, exceeding that at Q (SMC states by ~50%. The model magnetic flux values at substorm onset and SMC show little dependence on the solar wind dynamic pressure and distance in the tail, so the magnetic flux value can serve as an important discriminator of the state of the middle magnetotail.
Key words. Magnetospheric physics (solar windmagnetosphere- interactions, magnetotail, storms and substorms
9. Cosmogony as an extrapolation of magnetospheric research
International Nuclear Information System (INIS)
Alfven, H.
1984-03-01
A theory of the origin and evolution of the Solar System (Alfven and Arrhenius, 1975: 1976) which considered electromagnetic forces and plasma effects is revised in the light of new information supplied by space research. In situ measurements in the magnetospheres and solar wind have changed our views of basic properties of cosmic plasmas. These results can be extrapolated both outwards in space, to interstellar clouds, backwards in time, to the formation of the solar system. The first extrapolation leads to a revision of some cloud properties which are essential for the early phases in the formation of stars and solar nebule. The latter extrapolation makes possible to approach the cosmogonic processes by extrapolation of (rather) well-known magnetospheric phenomena. Pioneer-Voyager observations of the Saturnian rings indicate that essential parts of their structure are fossils from cosmogonic times. By using detailed information from these space missions, it seems possible to reconstruct certain events 4-5 billion years ago with an accuracy of a few percent. This will cause a change in our views of the evolution of the solar system.(author)
10. A kinetic approach to magnetospheric modeling
International Nuclear Information System (INIS)
Whipple, E.C. Jr.
1979-01-01
The earth's magnetosphere is caused by the interaction between the flowing solar wind and the earth's magnetic dipole, with the distorted magnetic field in the outer parts of the magnetosphere due to the current systems resulting from this interaction. It is surprising that even the conceptually simple problem of the collisionless interaction of a flowing plasma with a dipole magnetic field has not been solved. A kinetic approach is essential if one is to take into account the dispersion of particles with different energies and pitch angles and the fact that particles on different trajectories have different histories and may come from different sources. Solving the interaction problem involves finding the various types of possible trajectories, populating them with particles appropriately, and then treating the electric and magnetic fields self-consistently with the resulting particle densities and currents. This approach is illustrated by formulating a procedure for solving the collisionless interaction problem on open field lines in the case of a slowly flowing magnetized plasma interacting with a magnetic dipole
11. A kinetic approach to magnetospheric modeling
Science.gov (United States)
Whipple, E. C., Jr.
1979-01-01
The earth's magnetosphere is caused by the interaction between the flowing solar wind and the earth's magnetic dipole, with the distorted magnetic field in the outer parts of the magnetosphere due to the current systems resulting from this interaction. It is surprising that even the conceptually simple problem of the collisionless interaction of a flowing plasma with a dipole magnetic field has not been solved. A kinetic approach is essential if one is to take into account the dispersion of particles with different energies and pitch angles and the fact that particles on different trajectories have different histories and may come from different sources. Solving the interaction problem involves finding the various types of possible trajectories, populating them with particles appropriately, and then treating the electric and magnetic fields self-consistently with the resulting particle densities and currents. This approach is illustrated by formulating a procedure for solving the collisionless interaction problem on open field lines in the case of a slowly flowing magnetized plasma interacting with a magnetic dipole.
12. The Comprehensive Inner Magnetosphere-Ionosphere Model
Science.gov (United States)
Fok, M.-C.; Buzulukova, N. Y.; Chen, S.-H.; Glocer, A.; Nagai, T.; Valek, P.; Perez, J. D.
2014-01-01
Simulation studies of the Earth's radiation belts and ring current are very useful in understanding the acceleration, transport, and loss of energetic particles. Recently, the Comprehensive Ring Current Model (CRCM) and the Radiation Belt Environment (RBE) model were merged to form a Comprehensive Inner Magnetosphere-Ionosphere (CIMI) model. CIMI solves for many essential quantities in the inner magnetosphere, including ion and electron distributions in the ring current and radiation belts, plasmaspheric density, Region 2 currents, convection potential, and precipitation in the ionosphere. It incorporates whistler mode chorus and hiss wave diffusion of energetic electrons in energy, pitch angle, and cross terms. CIMI thus represents a comprehensive model that considers the effects of the ring current and plasmasphere on the radiation belts. We have performed a CIMI simulation for the storm on 5-9 April 2010 and then compared our results with data from the Two Wide-angle Imaging Neutral-atom Spectrometers and Akebono satellites. We identify the dominant energization and loss processes for the ring current and radiation belts. We find that the interactions with the whistler mode chorus waves are the main cause of the flux increase of MeV electrons during the recovery phase of this particular storm. When a self-consistent electric field from the CRCM is used, the enhancement of MeV electrons is higher than when an empirical convection model is applied. We also demonstrate how CIMI can be a powerful tool for analyzing and interpreting data from the new Van Allen Probes mission.
13. Magnetospheric MultiScale (MMS) System Manager
Science.gov (United States)
Schiff, Conrad; Maher, Francis Alfred; Henely, Sean Philip; Rand, David
2014-01-01
The Magnetospheric MultiScale (MMS) mission is an ambitious NASA space science mission in which 4 spacecraft are flown in tight formation about a highly elliptical orbit. Each spacecraft has multiple instruments that measure particle and field compositions in the Earths magnetosphere. By controlling the members relative motion, MMS can distinguish temporal and spatial fluctuations in a way that a single spacecraft cannot.To achieve this control, 2 sets of four maneuvers, distributed evenly across the spacecraft must be performed approximately every 14 days. Performing a single maneuver on an individual spacecraft is usually labor intensive and the complexity becomes clearly increases with four. As a result, the MMS flight dynamics team turned to the System Manager to put the routine or error-prone under machine control freeing the analysts for activities that require human judgment.The System Manager is an expert system that is capable of handling operations activities associated with performing MMS maneuvers. As an expert system, it can work off a known schedule, launching jobs based on a one-time occurrence or on a set reoccurring schedule. It is also able to detect situational changes and use event-driven programming to change schedules, adapt activities, or call for help.
14. Engineering aspects of compact stellarators
International Nuclear Information System (INIS)
Nelson, B.E.; Benson, R.D.; Brooks, A.
2003-01-01
Compact stellarators could combine the good confinement and high beta of a tokamak with the inherently steady state, disruption-free characteristics of a stellarator. Two U.S. compact stellarator facilities are now in the conceptual design phase: the National Compact Stellarator Experiment (NCSX) and the Quasi- Poloidal Stellarator (QPS). NCSX has a major radius of 1.4 m and a toroidal field up to 2 T. The primary feature of both NCSX and QPS is the set of modular coils that provide the basic magnetic configuration. These coils represent a major engineering challenge due to the complex shape, precise geometric accuracy, and high current density of the windings. The winding geometry is too complex for conventional hollow copper conductor construction. Instead, the modular coils will be wound with flexible, multi strand cable conductor that has been compacted to a 75% copper packing fraction. Inside the NCSX coil set and surrounding the plasma is a highly contoured vacuum vessel. The vessel consists of three identical, 120 deg. segments that are bolted together at double sealed joints. The QPS device has a major radius of 0.9 m, a toroidal field of 1 T, and an aspect ratio of only 2.7. Instead of an internal vacuum vessel, the QPS modular coils will operate in an external vacuum tank. (author)
15. Stellar Oxygen Abundances
Science.gov (United States)
King, Jeremy
1994-04-01
This dissertation addresses several issues concerning stellar oxygen abundances. The 7774 {\\AA} O I triplet equivalent widths of Abia & Rebolo [1989, AJ, 347, 186] for metal-poor dwarfs are found to be systematically too high. I also argue that current effective temperatures used in halo star abundance studies may be ~150 K too low. New color-Teff relations are derived for metal-poor stars. Using the revised Teff values and improved equivalent widths for the 7774A O I triplet, the mean [O/Fe] ratio for a handful of halo stars is found to be +0.52 with no dependence on Teff or [Fe/H]. Possible cosmological implications of the hotter Teff scale are discussed along with additional evidence supporting the need for a higher temperature scale for metal-poor stars. Our Teff scale leads to a Spite Li plateau value of N(Li)=2.28 +/- 0.09. A conservative minimal primordial value of N(Li)=2.35 is inferred. If errors in the observations and models are considered, consistency with standard models of Big Bang nucleosynthesis is still achieved with this larger Li abundance. The revised Teff scale raises the observed B/Be ratio of HD 140283 from 10 to 12, making its value more comfortably consistent with the production of the observed B and Be by ordinary spallation. Our Teff values are found to be in good agreement with values predicted from both the Victoria and Yale isochrone color-Teff relations. Thus, it appears likely that no changes in globular cluster ages would result. Next, we examine the location of the break in the [O/Fe] versus [Fe/H] plane in a quantitative fashion. Analysis of a relatively homogeneous data set does not favor any unique break point in the range -1.7 /= -3), in agreement with the new results for halo dwarfs. We find that the gap in the observed [O/H] distribution, noted by Wheeler et al. [1989, ARAA, 27, 279], persists despite the addition of more O data and may betray the occurrence of a hiatus in star formation between the end of halo formation and
16. On the mapping of ionospheric convection into the magnetosphere
International Nuclear Information System (INIS)
Hesse, M.; Birn, J.; Hoffman, R.A.
1997-01-01
Under steady state conditions and in the absence of parallel electric fields, ionospheric convection is a direct map of plasma and magnetic flux convection in the magnetosphere, and quantitative estimates can be obtained from the mapping along magnetic field lines of electrostatic ionospheric electric fields. The resulting magnetospheric electrostatic potential distribution then provides the convection electric field in various magnetospheric regions. We present a quantitative framework for the investigation of the applicability and limitations of this approach based on an analytical theory derived from first principles. Particular emphasis is on the role of parallel electric field regions and on inductive effects, such as expected during the growth and expansive phases of magnetospheric substorms. We derive quantitative estimates for the limits in which either effect leads to a significant decoupling between ionospheric and magnetospheric convection and provide an interpretation of ionospheric convection which is independent of the presence of inductive electric fields elsewhere in the magnetosphere. Finally, we present a study of the relation between average and instantaneous convection, using two periodic dynamical models. The models demonstrate and quantify the potential mismatch between the average electric fields in the ionosphere and the magnetosphere in strongly time-dependent cases that may exist even when they are governed entirely by ideal MHD
17. The earth's palaeomagnetosphere as the third type of planetary magnetosphere
International Nuclear Information System (INIS)
Saito, T; Sakurai, T.; Yumoto, K.
1978-01-01
From the viewpoint of dynamical topology, planetary magnetospheres are classified into three: Types 1,2 and 3. When the rotation vector and dipole moment of a planet and the velocity vector of the solar wind are denoted as Ω,M, and V, respectively, the planetary magnetosphere with Ωparallel to M perpendicular to V is called Type 1. The magnetospheres of the present Earth, Jupiter, and Uranus at its equinoctial points belong to this type. The magnetosphere with Ωparallel to M parallel to V is called Type 2, which includes the Uranium magnetosphere at its solstitial points. The magnetosphere with Ωperpendicular M and perpendicular V is called Type 3. The Earth's palaeomagnetosphere is considered to have experienced Type 3 during excursions and transition stages of palaeomagnetic polarity reversals. In the Type 3 magnetosphere, drastic variations are expected in configurations of the dayside cusps, tail axis, neutral sheet, polar caps, and so on. A possible relation between the Type 3 palaeomagnetosphere and palaeoclimate of the Earth during polarity reversals and geomagnetic excursions is suggested. It is also suggested that the heliomagnetosphere during polarity reversals of the general field of the Sun exhibits a drastic configuration change similar to the Type 3 palaeomagnetosphere of the Earth. A relation between the perpendicular condition Ω perpendicular to M and magnetic variable stars and pulsars is briefly discussed. (author)
18. The solar wind-magentosphere energy coupling and magnetospheric disturbances
International Nuclear Information System (INIS)
Akasofu, S.I.
1980-01-01
The recent finding of the solar wind-magnetosphere energy coupling function epsilon has advanced significantly our understanding of magnetosphere disturbances. It is shown that the magnetosphere-ionosphere coupling system responds somewhat differently to three different input energy flux levels of epsilon. As epsilon increases from 17 erg s -1 to >10 19 erg s -1 , typical responses of the magnetosphere-ionosphere coupling system are: (1) epsilon 17 erg s -1 : an enhancement of the Ssub(q)sup(p), etc. (2) epsilon approximately 10 18 erg s -1 : substorm onset. (3) 10 18 erg s -1 19 erg s -1 : a typical substorm. (4) epsilon >10 19 erg s -1 : an abnormal growth of the ring current belt, resulting in a magnetospheric storm. It is stressed that the magnetospheric substorm results as a direct response of the magnetosphere to a rise and fall of epsilon above approximately 10 18 erg s -1 , so that it is not caused by a sudden conversion of magnetic energy accumulated prior to substorm onset. The variety of the development of the main phase of geomagnetic storms is also primarily controlled by epsilon. (author)
19. Recent advances in magnetospheric substorm research
International Nuclear Information System (INIS)
Fairfield, D.H.
1990-01-01
More than two decades of magnetospheric exploration have led to a reasonably clear morphological picture of geomagnetic substorms, which is often summarized in terms of the near-Earth neutral line (NENL) model of substorms. Although this qualitative theory is quite comprehensive and explains a great many observations, it is hard pressed to explain both recent observations of consistently earthward flow within 19 R E and also the prompt onset of magnetic turbulence at 8 R E at the time of substorm onset. Other theories have recently been proposed which tend to be more quantitative, but which explain a more limited number of substorm observations. The challenge seems to be to understand the essential physics of these various quantitative theories and integrate them into a large structure such as is provided by the near-Earth neutral line model. (author)
20. Ground observations of magnetospheric boundary layer phenomena
International Nuclear Information System (INIS)
McHenry, M.A.; Clauer, C.R.; Friis-Christensen, E.; Newell, P.T.; Kelly, J.D.
1990-01-01
Several classes of traveling vortices in the dayside ionospheric convection have been detected and tracked using the Greenland magnetometer chain (Friis-Christensen et al., 1988, McHenry et al., 1989). One class observed during quiet times consists of a continuous series of vortices moving generally anti-sunward for several hours at a time. The vortices strength is seen to be approximately steady and neighboring vortices rotate in opposite directions. Sondrestrom radar observations show that the vortices are located at the ionospheric convection reversal boundary. Low altitude DMSP observations indicate the vortices are on field lines which map to the inner edge of the low latitude boundary layer. Because the vortices are conjugate to the boundary layer, repeat in a regular fashion and travel antisunward, the authors argue that this class of vortices is caused by the Kelvin-Helmholtz instability of the inner edge of the magnetospheric boundary layer
1. Kinetic Theory of the Inner Magnetospheric Plasma
CERN Document Server
Khazanov, George V
2011-01-01
This book provides a broad introduction to the kinetic theory of space plasma physics with the major focus on the inner magnetospheric plasma. It is designed to provide a comprehensive description of the different kinds of transport equations for both plasma particles and waves with an emphasis on the applicability and limitations of each set of equations. The major topics are: Kinetic Theory of Superthermal Electrons, Kinetic Foundation of the Hydrodynamic Description of Space Plasmas (including wave-particle interaction processes), and Kinetic Theory of the Terrestrial Ring Current. Distinguishable features of this book are the analytical solutions of simplified transport equations. Approximate analytic solutions of transport phenomena are very useful because they help us gain physical insight into how the system responds to varying sources of mass, momentum and energy and also to various external boundary conditions. They also provide us a convenient method to test the validity of complicated numerical mod...
2. Global Particle-in-Cell Simulations of Mercury's Magnetosphere
Science.gov (United States)
Schriver, D.; Travnicek, P. M.; Lapenta, G.; Amaya, J.; Gonzalez, D.; Richard, R. L.; Berchem, J.; Hellinger, P.
2017-12-01
Spacecraft observations of Mercury's magnetosphere have shown that kinetic ion and electron particle effects play a major role in the transport, acceleration, and loss of plasma within the magnetospheric system. Kinetic processes include reconnection, the breakdown of particle adiabaticity and wave-particle interactions. Because of the vast range in spatial scales involved in magnetospheric dynamics, from local electron Debye length scales ( meters) to solar wind/planetary magnetic scale lengths (tens to hundreds of planetary radii), fully self-consistent kinetic simulations of a global planetary magnetosphere remain challenging. Most global simulations of Earth's and other planet's magnetosphere are carried out using MHD, enhanced MHD (e.g., Hall MHD), hybrid, or a combination of MHD and particle in cell (PIC) simulations. Here, 3D kinetic self-consistent hybrid (ion particle, electron fluid) and full PIC (ion and electron particle) simulations of the solar wind interaction with Mercury's magnetosphere are carried out. Using the implicit PIC and hybrid simulations, Mercury's relatively small, but highly kinetic magnetosphere will be examined to determine how the self-consistent inclusion of electrons affects magnetic reconnection, particle transport and acceleration of plasma at Mercury. Also the spatial and energy profiles of precipitating magnetospheric ions and electrons onto Mercury's surface, which can strongly affect the regolith in terms of space weathering and particle outflow, will be examined with the PIC and hybrid codes. MESSENGER spacecraft observations are used both to initiate and validate the global kinetic simulations to achieve a deeper understanding of the role kinetic physics play in magnetospheric dynamics.
3. Impulsive ion acceleration in earth's outer magnetosphere
International Nuclear Information System (INIS)
Baker, D.N.; Belian, R.D.
1985-01-01
Considerable observational evidence is found that ions are accelerated to high energies in the outer magnetosphere during geomagnetic disturbances. The acceleration often appears to be quite impulsive causing temporally brief (10's of seconds), very intense bursts of ions in the distant plasma sheet as well as in the near-tail region. These ion bursts extend in energy from 10's of keV to over 1 MeV and are closely associated with substorm expansive phase onsets. Although the very energetic ions are not of dominant importance for magnetotail plasma dynamics, they serve as an important tracer population. Their absolute intensity and brief temporal appearance bespeaks a strong and rapid acceleration process in the near-tail, very probably involving large induced electric fields substantially greater than those associated with cross-tail potential drops. Subsequent to their impulsive acceleration, these ions are injected into the outer trapping regions forming ion ''drift echo'' events, as well as streaming tailward away from their acceleration site in the near-earth plasma sheet. Most auroral ion acceleration processes occur (or are greatly enhanced) during the time that these global magnetospheric events are occurring in the magnetotail. A qualitative model relating energetic ion populations to near-tail magnetic reconnection at substorm onset followed by global redistribution is quite successful in explaining the primary observational features. Recent measurements of the elemental composition and charge-states have proven valuable for showing the source (solar wind or ionosphere) of the original plasma population from which the ions were accelerated
4. Investigation of Magnetospheric Line Radiation above China
Science.gov (United States)
Sheng, X.; Wu, J.; Pu, X.
2017-12-01
Magnetospheric Line Radiation (MLR) is a kind of VLF emission that is considered by some researchers to be related with the power system on ground, and in frequency-time spectrograms of electromagnetic field, it has a line structure with large frequency bandwidth. These emission waves propagate through the magnetosphere and strongly interact with energetic electrons trapped in the earth's magnetic field. Such a wave-particle interaction amplifies the radiation and scatters energetic electrons, which may trigger new radiations. We detected 328 MLR events by analyzing the electric field data observed by DEMETER satellite in the space above China from the year of 2008 to 2010. Their characteristics and possible cause have been investigated systematically. There were more MLR events in daytime than in nighttime and more in winter than in summer. Such diurnal and seasonal differences were closely associated with whistlers and ionosphere conditions. Comparing Kp indices at the occurring time of MLR events and nationwide Kp indices through the analyzed years, we found these MLR events were not significantly dependent on geomagnetic activity. Most of events were distributed in the low latitude, while their peak intensities in frequency-time spectrograms seemed to be independent of latitude. The frequency intervals of MLR events were between 50 to 95Hz, and the frequency drifts were mostly in 0 0.4Hz/s. The above characteristics of MLR events were similar to those of Power Line Harmonic Radiation (PLHR) events observed in the space above China, therefore we inferred that these two emissions have close relation.
5. Motion of charged particles in the magnetosphere
International Nuclear Information System (INIS)
Mukherjee, G.K.; Rajaram, R.
1981-01-01
The adiabatic motion of charged particles in the magnetosphere has been investigated using Mead-Fairfield magnetospheric field model (Mead and Fairfield, 1975). Since the motion of charged particles in a dipolar field geometry is well understood, we bring out in this paper some important features in characteristic motion due to non-dipolar distortions in the field geometry. We look at the tilt averaged picture of the field configuration and estimate theoretically the parameters like bounce period, longitudinal invariant and the bounce averaged drift velocities of the charged particle in the Mead-Fairfield field geometry. These parameters are evaluated as a function of pitch angle and azimuthal position in the region of ring current (5 to 7 Earth radii from the centre of the Earth) for four ranges of magnetic activity. At different longitudes the non-dipolar contribution as a percentage of dipole value in bounce period and longitudinal invariant shows maximum variation for particles close to 90 0 pitch angles. For any low pitch angle, these effects maximize at the midnight meridian. The radial component of the bounce averaged drift velocity is found to be greatest at the dawn-dusk meridians and the contribution vanishes at the day and midnight meridians for all pitch angles. In the absence of tilt-dependent terms in the model, the latitudinal component of the drift velocity vanishes. On the other hand, the relative non-dipolar contribution to bounce averaged azimuthal drift velocity is very high as compared to similar contribution in other characteristic parameters of particle motion. It is also shown that non-dipolar contribution in bounce period, longitudinal invariant and bounce averaged drift velocities increases in magnitude with increase in distance and magnetic activity. (orig.)
6. Substorms - Future of magnetospheric substorm-storm research
International Nuclear Information System (INIS)
Akasofu, S.I.
1989-01-01
Seven approaches and/or areas of magnetospheric substorm and storm science which should be emphasized in future research are briefly discussed. They are: the combining of groups of researchers who study magnetic storms and substorms in terms of magnetic reconnection with those that do not, the possible use of a magnetosphere-ionosphere coupling model to merge the groups, the development of improved input-output relationships, the complementing of satellite and ground-based observations, the need for global imaging of the magnetosphere, the complementing of observations with computer simulations, and the need to study the causes of changes in the north-south component of the IMF. 36 refs
7. A MODEL FOR (QUASI-)PERIODIC MULTIWAVELENGTH PHOTOMETRIC VARIABILITY IN YOUNG STELLAR OBJECTS
Energy Technology Data Exchange (ETDEWEB)
Kesseli, Aurora Y. [Boston University, 725 Commonwealth Ave, Boston, MA 02215 (United States); Petkova, Maya A.; Wood, Kenneth; Gregory, Scott G. [SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9AD (United Kingdom); Whitney, Barbara A. [Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter St, Madison, WI 53706 (United States); Hillenbrand, L. A. [Astronomy Department, California Institute of Technology, Pasadena, CA 91125 (United States); Stauffer, J. R.; Morales-Calderon, M.; Rebull, L. [Spitzer Science Center, California Institute of Technology, CA 91125 (United States); Alencar, S. H. P., E-mail: [email protected] [Departamento de Física—ICEx—UFMG, Av. Antônio Carlos, 6627, 30270-901, Belo Horizonte, MG (Brazil)
2016-09-01
We present radiation transfer models of rotating young stellar objects (YSOs) with hot spots in their atmospheres, inner disk warps, and other three-dimensional effects in the nearby circumstellar environment. Our models are based on the geometry expected from magneto-accretion theory, where material moving inward in the disk flows along magnetic field lines to the star and creates stellar hot spots upon impact. Due to rotation of the star and magnetosphere, the disk is variably illuminated. We compare our model light curves to data from the Spitzer YSOVAR project to determine if these processes can explain the variability observed at optical and mid-infrared wavelengths in young stars. We focus on those variables exhibiting “dipper” behavior that may be periodic, quasi-periodic, or aperiodic. We find that the stellar hot-spot size and temperature affects the optical and near-infrared light curves, while the shape and vertical extent of the inner disk warp affects the mid-IR light curve variations. Clumpy disk distributions with non-uniform fractal density structure produce more stochastic light curves. We conclude that magneto-accretion theory is consistent with certain aspects of the multiwavelength photometric variability exhibited by low-mass YSOs. More detailed modeling of individual sources can be used to better determine the stellar hot-spot and inner disk geometries of particular sources.
8. Stellar CME candidates: towards a stellar CME-flare relation
Science.gov (United States)
Paraskevi Moschou, Sofia; Drake, Jeremy J.; Cohen, Ofer; Alvarado-Gomez, Julian D.; Garraffo, Cecilia
2018-06-01
For decades the Sun has been the only star that allowed for direct CME observations. Recently, with the discovery of multiple extrasolar systems, it has become imperative that the role of stellar CMEs be assessed in the context of exoplanetary habitability. Solar CMEs and flares show a higher association with increasing flaring energy, with strong flares corresponding to large and fast CMEs. As argued in earlier studies, extrasolar environments around active stars are potentially dominated by CMEs, as a result of their extreme flaring activity. This has strong implications for the energy budget of the system and the atmospheric erosion of orbiting planets.Nevertheless, with current instrumentation we are unable to directly observe CMEs in even the closest stars, and thus we have to look for indirect techniques and observational evidence and signatures for the eruption of stellar CMEs. There are three major observational techniques for tracing CME signatures in other stellar systems, namely measuring Type II radio bursts, Doppler shifts in UV/optical lines or transient absorption in the X-ray spectrum. We present observations of the most probable stellar CME candidates captured so far and examine the different observational techniques used together with their levels of uncertainty. Assuming that they were CMEs, we try to asses their kinematic and energetic characteristics and place them in an extension of the well-established solar CME-flare energy scaling law. We finish by discussing future observations for direct measurements.
9. Nonlinear dynamics of the magnetosphere and space weather
Science.gov (United States)
Sharma, A. Surjalal
1996-01-01
The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.
10. Problems related to macroscopic electric fields in the magnetosphere
International Nuclear Information System (INIS)
Faelthammar, C.
1977-01-01
The macroscopic electric fields in the magnetosphere originate from internal as well as external sources. The fields are intimately coupled with the dynamics of magnetospheric plasma convection. They also depend on the complicated electrical properties of the hot collisionless plasma. Macroscopic electric fields are responsible for some important kinds of energization of charged particles that take place in the magnetosphere and affect not only particles of auroral energy but also, by multistep processes, trapped high-energy particles. A particularly interesting feature of magnetospheric electric fields is that they can have substantial components along the geomagnetic field, as has recently been confirmed by observations. Several physical mechanisms have been identified by which such electric fields can be supported even when collisions between particles are negligible. Comments are made on the magnetic mirror effect, anomalous resistivity, the collisionless thermoelectric effect, and electric double layers, emphasizing key features and differences and their significance in the light of recent observational data
11. From the Solar Wind to the Magnetospheric Substorm
Institute of Scientific and Technical Information of China (English)
E.A. Ponomarev; P.A. Sedykh; O.V. Mager
2005-01-01
This paper gives a brief outline of the progression from the first substorm model developed in Ref.[4] and [8] based on Kennel's ideas[3], to the present views about the mechanism by which solar wind kinetic energy is converted to electromagnetic energy at the Bow Shock and by which this energy is transferred to the magnetosphere in the form of current; about the transformation of the energy of this current to gas kinetic energy of convecting plasma tubes, and, finally, the back transformation of gas kinetic energy to electromagnetic energy in secondary magnetospheric MHD generators. The questions of the formation of the magnetospheric convection system, the nature of substorm break-up, and of the matching of currents in the magnetosphere-ionosphere system are discussed.
12. Echo 7: Magnetospheric properties determined by artificial electron beams
International Nuclear Information System (INIS)
Nemzek, R.J.
1990-01-01
The sounding rocket Echo 7 was launched from the Poker Flat Research Range. An on-board accelerator injected high-power electron beams into the magnetospheric tail near L = 6.5. After mirroring at the southern conjugate point, about 20 percent of the initial beam electrons returned to the North as Conjugate Echoes, where detectors (scintillators and spectrometers) on four subpayloads measured their energy and bounce time. The other 80 percent of the beam was pitch angle diffused by wave near the equatorial plane either into the conjugate atmosphere or up to mirror points above the payload. Comparison of measured values to calculations showed that the actual magnetosphere during the flight was well-described by the Tsyganenko-Usmanov model magnetosphere with a Kp value of 2- or 2+. Analysis of echo energies yielded values for the highly variable magnetospheric convection electric field
13. The outer magnetosphere. [composition and comparison with earth
Science.gov (United States)
Schardt, A. W.; Behannon, K. W.; Lepping, R. P.; Carbary, J. F.; Eviatar, A.; Siscoe, G. L.
1984-01-01
Similarities between the Saturnian and terrestrial outer magnetosphere are examined. Saturn, like earth, has a fully developed magnetic tail, 80 to 100 RS in diameter. One major difference between the two outer magnetospheres is the hydrogen and nitrogen torus produced by Titan. This plasma is, in general, convected in the corotation direction at nearly the rigid corotation speed. Energies of magnetospheric particles extend to above 500 keV. In contrast, interplanetary protons and ions above 2 MeV have free access to the outer magnetosphere to distances well below the Stormer cutoff. This access presumably occurs through the magnetotail. In addition to the H+, H2+, and H3+ ions primarily of local origin, energetic He, C, N, and O ions are found with solar composition. Their flux can be substantially enhanced over that of interplanetary ions at energies of 0.2 to 0.4 MeV/nuc.
14. Interactions of planetary magnetospheres with icy satellite surfaces
International Nuclear Information System (INIS)
Cheng, A.F.; Haff, P.K.; Johnson, R.E.; Lanzerotti, L.J.
1986-01-01
When natural satellites and ring particles are embedded within magnetospheric plasmas, the charged particles interact with the surfaces of these solid bodies. These interactions have important implications for the surface, the atmosphere of the parent body, and the magnetosphere as a whole. Significant erosion of the surface by sputtering, as well as redeposition of sputter ejecta, can occur over geologic time. The surface can also be chemically modified. Sputter ejecta can make important contributions to the atmosphere; sputtering provides a lower limit to the atmospheric column density even for arbitrarily cold satellite surfaces. Sputter ejecta escaping from the parent body can form extensive neutral clouds within the magnetosphere. Ionization and dissociation within these neutral clouds can be dominant sources of low-energy plasma. The importance of these processes is discussed for the satellites and magnetospheres of Jupiter, Saturn and Uranus
15. Overview of Mercury Magnetospheric Orbiter (MMO) for BepiColombo
Science.gov (United States)
Murakami, G.; Hayakawa, H.; Fujimoto, M.; BepiColombo Project Team
2018-05-01
The next Mercury exploration mission BepiColombo will be launched in October 2018 and will arrive at Mercury in December 2025. We present the current status, science goals, and observation plans of JAXA's Mercury Magnetospheric Orbiter (MMO).
16. Coupled rotational dynamics of Jupiter's thermosphere and magnetosphere
Directory of Open Access Journals (Sweden)
C. G. A. Smith
2009-01-01
Full Text Available We describe an axisymmetric model of the coupled rotational dynamics of the thermosphere and magnetosphere of Jupiter that incorporates self-consistent physical descriptions of angular momentum transfer in both systems. The thermospheric component of the model is a numerical general circulation model. The middle magnetosphere is described by a simple physical model of angular momentum transfer that incorporates self-consistently the effects of variations in the ionospheric conductivity. The outer magnetosphere is described by a model that assumes the existence of a Dungey cycle type interaction with the solar wind, producing at the planet a largely stagnant plasma flow poleward of the main auroral oval. We neglect any decoupling between the plasma flows in the magnetosphere and ionosphere due to the formation of parallel electric fields in the magnetosphere. The model shows that the principle mechanism by which angular momentum is supplied to the polar thermosphere is meridional advection and that mean-field Joule heating and ion drag at high latitudes are not responsible for the high thermospheric temperatures at low latitudes on Jupiter. The rotational dynamics of the magnetosphere at radial distances beyond ~30 RJ in the equatorial plane are qualitatively unaffected by including the detailed dynamics of the thermosphere, but within this radial distance the rotation of the magnetosphere is very sensitive to the rotation velocity of the thermosphere and the value of the Pedersen conductivity. In particular, the thermosphere connected to the inner magnetosphere is found to super-corotate, such that true Pedersen conductivities smaller than previously predicted are required to enforce the observed rotation of the magnetosphere within ~30 RJ. We find that increasing the Joule heating at high latitudes by adding a component due to rapidly fluctuating electric fields is unable to explain the high equatorial temperatures. Adding a component of Joule
17. Energetic Nitrogen Ions within the Inner Magnetosphere of Saturn
Science.gov (United States)
Sittler, E. C.; Johnson, R. E.; Richardson, J. D.; Jurac, S.; Moore, M.; Cooper, J. F.; Mauk, B. H.; Smith, H. T.; Michael, M.; Paranicus, C.; Armstrong, T. P.; Tsurutani, B.; Connerney, J. E. P.
2003-05-01
Titan's interaction with Saturn's magnetosphere will result in the energetic ejection of atomic nitrogen atoms into Saturn's magnetosphere due to dissociation of N2 by electrons, ions, and UV photons. The ejection of N atoms into Saturn's magnetosphere will form a nitrogen torus around Saturn with mean density of about 4 atoms/cm3 with source strength of 4.5x1025 atoms/sec. These nitrogen atoms are ionized by photoionization, electron impact ionization and charge exchange reactions producing an N+ torus of 1-4 keV suprathermal ions centered on Titan's orbital position. We will show Voyager plasma observations that demonstrate presence of a suprathermal ion component within Saturn's outer magnetosphere. The Voyager LECP data also reported the presence of inward diffusing energetic ions from the outer magnetosphere of Saturn, which could have an N+ contribution. If so, when one conserves the first and second adiabatic invariant the N+ ions will have energies in excess of 100 keV at Dione's L shell and greater than 400 keV at Enceladus' L shell. Energetic charged particle radial diffusion coefficients are also used to constrain the model results. But, one must also consider the solar wind as another important source of keV ions, in the form of protons and alpha particles, for Saturn's outer magnetosphere. Initial estimates indicate that a solar wind source could dominate in the outer magnetosphere, but various required parameters for this estimate are highly uncertain and will have to await Cassini results for confirmation. We show that satellite sweeping and charged particle precipitation within the middle and outer magnetosphere will tend to enrich N+ ions relative to protons within Saturn's inner magnetosphere as they diffuse radially inward for radial diffusion coefficients that do not violate observations. Charge exchange reactions within the inner magnetosphere can be an important loss mechanism for O+ ions, but to a lesser degree for N+ ions. Initial LECP
18. Science with Synthetic Stellar Surveys
Science.gov (United States)
Sanderson, Robyn Ellyn
2018-04-01
A new generation of observational projects is poised to revolutionize our understanding of the resolved stellar populations of Milky-Way-like galaxies at an unprecedented level of detail, ushering in an era of precision studies of galaxy formation. In the Milky Way itself, astrometric, spectroscopic and photometric surveys will measure three-dimensional positions and velocities and numerous chemical abundances for stars from the disk to the halo, as well as for many satellite dwarf galaxies. In the Local Group and beyond, HST, JWST and eventually WFIRST will deliver pristine views of resolved stars. The groundbreaking scale and dimensionality of this new view of resolved stellar populations in galaxies challenge us to develop new theoretical tools to robustly compare these surveys to simulated galaxies, in order to take full advantage of our new ability to make detailed predictions for stellar populations within a cosmological context. I will describe a framework for generating realistic synthetic star catalogs and mock surveys from state-of-the-art cosmological-hydrodynamical simulations, and present several early scientific results from, and predictions for, resolved stellar surveys of our Galaxy and its neighbors.
19. Maximum stellar iron core mass
An analytical method of estimating the mass of a stellar iron core, just prior to core collapse, is described in this paper. The method employed depends, in part, upon an estimate of the true relativistic mass increase experienced by electrons within a highly compressed iron core, just prior to core collapse, and is significantly ...
20. Maximum stellar iron core mass
60, No. 3. — journal of. March 2003 physics pp. 415–422. Maximum stellar iron core mass. F W GIACOBBE. Chicago Research Center/American Air Liquide ... iron core compression due to the weight of non-ferrous matter overlying the iron cores within large .... thermal equilibrium velocities will tend to be non-relativistic.
1. Integrated Circuit Stellar Magnitude Simulator
Science.gov (United States)
Blackburn, James A.
1978-01-01
Describes an electronic circuit which can be used to demonstrate the stellar magnitude scale. Six rectangular light-emitting diodes with independently adjustable duty cycles represent stars of magnitudes 1 through 6. Experimentally verifies the logarithmic response of the eye. (Author/GA)
2. Stellar dynamics and black holes
Chandrasekhar's most important contribution to stellar dynamics was the concept of dynamical friction. I briefly review that work, then discuss some implications of Chandrasekhar's theory of gravitational encounters for motion in galactic nuclei. Author Affiliations. David Merritt1. Department of Physics, Rochester Institute ...
3. TEM turbulence optimisation in stellarators
Science.gov (United States)
Proll, J. H. E.; Mynick, H. E.; Xanthopoulos, P.; Lazerson, S. A.; Faber, B. J.
2016-01-01
With the advent of neoclassically optimised stellarators, optimising stellarators for turbulent transport is an important next step. The reduction of ion-temperature-gradient-driven turbulence has been achieved via shaping of the magnetic field, and the reduction of trapped-electron mode (TEM) turbulence is addressed in the present paper. Recent analytical and numerical findings suggest TEMs are stabilised when a large fraction of trapped particles experiences favourable bounce-averaged curvature. This is the case for example in Wendelstein 7-X (Beidler et al 1990 Fusion Technol. 17 148) and other Helias-type stellarators. Using this knowledge, a proxy function was designed to estimate the TEM dynamics, allowing optimal configurations for TEM stability to be determined with the STELLOPT (Spong et al 2001 Nucl. Fusion 41 711) code without extensive turbulence simulations. A first proof-of-principle optimised equilibrium stemming from the TEM-dominated stellarator experiment HSX (Anderson et al 1995 Fusion Technol. 27 273) is presented for which a reduction of the linear growth rates is achieved over a broad range of the operational parameter space. As an important consequence of this property, the turbulent heat flux levels are reduced compared with the initial configuration.
4. Investigating dynamical complexity in the magnetosphere using various entropy measures
Science.gov (United States)
Balasis, Georgios; Daglis, Ioannis A.; Papadimitriou, Constantinos; Kalimeri, Maria; Anastasiadis, Anastasios; Eftaxias, Konstantinos
2009-09-01
The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather
5. Nonlinear dynamical modeling and prediction of the terrestrial magnetospheric activity
International Nuclear Information System (INIS)
1992-01-01
The irregular activity of the magnetosphere results from its complex internal dynamics as well as the external influence of the solar wind. The dominating self-organization of the magnetospheric plasma gives rise to repetitive, large-scale coherent behavior manifested in phenomena such as the magnetic substorm. Based on the nonlinearity of the global dynamics this dissertation examines the magnetosphere as a nonlinear dynamical system using time series analysis techniques. Initially the magnetospheric activity is modeled in terms of an autonomous system. A dimension study shows that its observed time series is self-similar, but the correlation dimension is high. The implication of a large number of degrees of freedom is confirmed by other state space techniques such as Poincare sections and search for unstable periodic orbits. At the same time a stability study of the time series in terms of Lyapunov exponents suggests that the series is not chaotic. The absence of deterministic chaos is supported by the low predictive capability of the autonomous model. Rather than chaos, it is an external input which is largely responsible for the irregularity of the magnetospheric activity. In fact, the external driving is so strong that the above state space techniques give results for magnetospheric and solar wind time series that are at least qualitatively similar. Therefore the solar wind input has to be included in a low-dimensional nonautonomous model. Indeed it is shown that such a model can reproduce the observed magnetospheric behavior up to 80-90 percent. The characteristic coefficients of the model show little variation depending on the external disturbance. The impulse response is consistent with earlier results of linear prediction filters. The model can be easily extended to contain nonlinear features of the magnetospheric activity and in particular the loading-unloading behavior of substorms
6. Mission Concept to Connect Magnetospheric Physical Processes to Ionospheric Phenomena
Science.gov (United States)
Dors, E. E.; MacDonald, E.; Kepko, L.; Borovsky, J.; Reeves, G. D.; Delzanno, G. L.; Thomsen, M. F.; Sanchez, E. R.; Henderson, M. G.; Nguyen, D. C.; Vaith, H.; Gilchrist, B. E.; Spanswick, E.; Marshall, R. A.; Donovan, E.; Neilson, J.; Carlsten, B. E.
2017-12-01
On the Earth's nightside the magnetic connections between the ionosphere and the dynamic magnetosphere have a great deal of uncertainty: this uncertainty prevents us from scientifically understanding what physical processes in the magnetosphere are driving the various phenomena in the ionosphere. Since the 1990s, the space plasma physics group at Los Alamos National Laboratory has been working on a concept to connect magnetospheric physical processes to auroral phenomena in the ionosphere by firing an electron beam from a magnetospheric spacecraft and optically imaging the beam spot in the ionosphere. The magnetospheric spacecraft will carry a steerable electron accelerator, a power-storage system, a plasma contactor, and instruments to measure magnetic and electric fields, plasma, and energetic particles. The spacecraft orbit will be coordinated with a ground-based network of cameras to (a) locate the electron beam spot in the upper atmosphere and (b) monitor the aurora. An overview of the mission concept will be presented, including recent enabling advancements based on (1) a new understanding of the dynamic spacecraft charging of the accelerator and plasma-contactor system in the tenuous magnetosphere based on ion emission rather than electron collection, (2) a new understanding of the propagation properties of pulsed MeV-class beams in the magnetosphere, and (3) the design of a compact high-power 1-MeV electron accelerator and power-storage system. This strategy to (a) determine the magnetosphere-to-ionosphere connections and (b) reduce accelerator- platform charging responds to one of the six emerging-technology needs called out in the most-recent National Academies Decadal Survey for Solar and Space Physics. [LA-UR-17-23614
7. Advances in magnetospheric storm and substorm research: 1989-1991
International Nuclear Information System (INIS)
Fairfield, D.H.
1992-01-01
Geomagnetic storms represent the magnetospheric response to fast solar wind and unusually large southward interplanetary magnetic fields that are caused by solar processes and resulting dynamics in the interplanetary medium. The solar wind/magnetosphere interaction is, however, more commonly studied via smaller, more common, magnetospheric substorms. Accumulating evidence suggests that two separate magnetospheric current systems are important during magnetospheric substorms. Currents directly driven by the solar wind/magnetosphere interaction produce magnetic field variations that make important contributions to the AE index but have little relation to the many effects traditionally associated with sudden substorm onsets. Currents driven by energy unloaded from the magnetotail form the nightside current wedge and are associated with onset effects such as auroral breakup, field dipolarization, and particle acceleration. Observations are gradually leading to a coherent picture of the interrelations among these various onset phenomena, but their cause remains a controversial question. The abrupt nature of substorm onsets suggests a magnetospheric instability, but doubt remains as to its nature and place of origin. Measurements increasingly suggest the region of 7-10 R E near midnight as the likely point of origin, but it is not clear that the long-popular tearing mode can go unstable this close to the Earth, where it may be stabilized by a small northward field component. Also the tailward flows that would be expected tailward of a near-Earth neutral line are seldom seen inside of 19 R E . The changing magnetic field configuration during substorms means that existing static models cannot be used to map phenomena between the magnetosphere and the ground at these interesting times
8. Radiation Belts of Antiparticles in Planetary Magnetospheres
Science.gov (United States)
Pugacheva, G. I.; Gusev, A. A.; Jayanthi, U. B.; Martin, I. M.; Spjeldvik, W. N.
2007-05-01
The Earth's radiation belts could be populated, besides with electrons and protons, also by antiparticles, such as positrons (Basilova et al., 1982) and antiprotons (pbar). Positrons are born in the decay of pions that are directly produced in nuclear reactions of trapped relativistic inner zone protons with the residual atmosphere at altitudes in the range of about 500 to 3000 km over the Earth's surface. Antiprotons are born by high energy (E > 6 GeV) cosmic rays in p+p - p+p+p+ pbar and in p+p - p+p+n+nbar reactions. The trapping and storage of these charged anti-particles in the magnetosphere result in radiation belts similar to the classical Van Allen belts of protons and electrons. We describe the mathematical techniques used for numerical simulation of the trapped positron and antiproton belt fluxes. The pion and antiproton yields were simulated on the basis of the Russian nuclear reaction computer code MSDM, a Multy Stage Dynamical Model, Monte Carlo code, (i.e., Dementyev and Sobolevsky, 1999). For estimates of positron flux there we have accounted for ionisation, bremsstrahlung, and synchrotron energy losses. The resulting numerical estimates show that the positron flux with energy >100 MeV trapped into the radiation belt at L=1.2 is of the order ~1000 m-2 s-1 sr-1, and that it is very sensitive to the shape of the trapped proton spectrum. This confined positron flux is found to be greater than that albedo, not trapped, mixed electron/positron flux of about 50 m-2 s-1 sr-1 produced by CR in the same region at the top of the geomagnetic field line at L=1.2. As we show in report, this albedo flux also consists mostly of positrons. The trapped antiproton fluxes produced by CR in the Earth's upper rarified atmosphere were calculated in the energy range from 10 MeV to several GeV. In the simulations we included a mathematic consideration of the radial diffusion process, both an inner and an outer antiproton source, losses of particles due to ionization process
9. Global Current Circuit Structure in a Resistive Pulsar Magnetosphere Model
Science.gov (United States)
Kato, Yugo. E.
2017-12-01
Pulsar magnetospheres have strong magnetic fields and large amounts of plasma. The structures of these magnetospheres are studied using force-free electrodynamics. To understand pulsar magnetospheres, discussions must include their outer region. However, force-free electrodynamics is limited in it does not handle dissipation. Therefore, a resistive pulsar magnetic field model is needed. To break the ideal magnetohydrodynamic (MHD) condition E\\cdot B=0, Ohm’s law is used. This work introduces resistivity depending upon the distance from the star and obtain a self-consistent steady state by time integration. Poloidal current circuits form in the magnetosphere while the toroidal magnetic field region expands beyond the light cylinder and the Poynting flux radiation appears. High electric resistivity causes a large space scale poloidal current circuit and the magnetosphere radiates a larger Poynting flux than the linear increase outside of the light cylinder radius. The formed poloidal-current circuit has width, which grows with the electric conductivity. This result contributes to a more concrete dissipative pulsar magnetosphere model.
10. Possibility of detecting magnetospheric radio bursts from Uranus and Neptune
International Nuclear Information System (INIS)
Kennel, C.F.; Maggs, J.E.
1976-01-01
It is known that Earth, Jupiter and Saturn are sources of intense sporadic bursts of electromagnetic radiation, known as magnetospheric radio bursts. These bursts are here described. It is thought that the similarities in the power flux spectra, together with the burst occurrence patterns, suggest a common physical origin for these bursts in all three planets. The common mechanism may be noise amplification by field aligned currents, since it has been shown that the Earth's MRBs are associated with bright auroral arcs that involve intense field aligned currents. Such currents result from the interaction of the solar wind with the magnetosphere and should be a general feature of the interaction between the solar wind and planetary magnetospheres. If MRBs are produced by solar wind-magnetosphere interaction their total radiated power might scale with the solar wind input into the magnetosphere, and it has been suggested that the frequency of emission scales with the polar magnetic field strength of a planet. The intensity of MRBs is here scaled to the solar wind input and the frequency of emission to the polar field strength with a view to estimating the possibility of detecting MRBs from Uranus and Neptune. It is found that scaling of MRB power to the solar wind-magnetosphere dissipation power is probably a reasonable hypothesis. It is suggested that detection of MRB bursts from Uranus and Neptune might be a reasonable radioastronomy objective on future missions to the outer Solar System. (U.K.)
11. Stellar Parameters for Trappist-1
Science.gov (United States)
Van Grootel, Valérie; Fernandes, Catarina S.; Gillon, Michael; Jehin, Emmanuel; Manfroid, Jean; Scuflaire, Richard; Burgasser, Adam J.; Barkaoui, Khalid; Benkhaldoun, Zouhair; Burdanov, Artem; Delrez, Laetitia; Demory, Brice-Olivier; de Wit, Julien; Queloz, Didier; Triaud, Amaury H. M. J.
2018-01-01
TRAPPIST-1 is an ultracool dwarf star transited by seven Earth-sized planets, for which thorough characterization of atmospheric properties, surface conditions encompassing habitability, and internal compositions is possible with current and next-generation telescopes. Accurate modeling of the star is essential to achieve this goal. We aim to obtain updated stellar parameters for TRAPPIST-1 based on new measurements and evolutionary models, compared to those used in discovery studies. We present a new measurement for the parallax of TRAPPIST-1, 82.4 ± 0.8 mas, based on 188 epochs of observations with the TRAPPIST and Liverpool Telescopes from 2013 to 2016. This revised parallax yields an updated luminosity of {L}* =(5.22+/- 0.19)× {10}-4 {L}ȯ , which is very close to the previous estimate but almost two times more precise. We next present an updated estimate for TRAPPIST-1 stellar mass, based on two approaches: mass from stellar evolution modeling, and empirical mass derived from dynamical masses of equivalently classified ultracool dwarfs in astrometric binaries. We combine them using a Monte-Carlo approach to derive a semi-empirical estimate for the mass of TRAPPIST-1. We also derive estimate for the radius by combining this mass with stellar density inferred from transits, as well as an estimate for the effective temperature from our revised luminosity and radius. Our final results are {M}* =0.089+/- 0.006 {M}ȯ , {R}* =0.121+/- 0.003 {R}ȯ , and {T}{eff} = 2516 ± 41 K. Considering the degree to which the TRAPPIST-1 system will be scrutinized in coming years, these revised and more precise stellar parameters should be considered when assessing the properties of TRAPPIST-1 planets.
12. Targeted Optimization of Quasi-Symmetric Stellarators
International Nuclear Information System (INIS)
Hegna, Chris C.; Talmadge, J. N.
2016-01-01
The proposed research focuses on targeted areas of plasma physics dedicated to improving the stellarator concept. Research was pursued in the technical areas of edge/divertor physics in 3D configurations, magnetic island physics in stellarators, the role of 3D shaping on microinstabilities and turbulent transport and energetic ion confinement in stellarators.
13. Targeted Optimization of Quasi-Symmetric Stellarators
Energy Technology Data Exchange (ETDEWEB)
Hegna, Chris C. [Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics; Anderson, D. T. [Univ. of Wisconsin, Madison, WI (United States); Talmadge, J. N. [Univ. of Wisconsin, Madison, WI (United States)
2016-10-06
The proposed research focuses on targeted areas of plasma physics dedicated to improving the stellarator concept. Research was pursued in the technical areas of edge/divertor physics in 3D configurations, magnetic island physics in stellarators, the role of 3D shaping on microinstabilities and turbulent transport and energetic ion confinement in stellarators.
14. Plasma sources of solar system magnetospheres
CERN Document Server
Blanc, Michel; Chappell, Charles; Krupp, Norbert
2016-01-01
This volume reviews what we know of the corresponding plasma source for each intrinsically magnetized planet. Plasma sources fall essentially in three categories: the solar wind, the ionosphere (both prevalent on Earth), and the satellite-related sources. Throughout the text, the case of each planet is described, including the characteristics, chemical composition and intensity of each source. The authors also describe how the plasma generated at the source regions is transported to populate the magnetosphere, and how it is later lost. To summarize, the dominant sources are found to be the solar wind and sputtered surface ions at Mercury, the solar wind and ionosphere at Earth (the relative importance of the two being discussed in a specific introductory chapter), Io at Jupiter and – a big surprise of the Cassini findings – Enceladus at Saturn. The situation for Uranus and Neptune, which were investigated by only one fly-by each, is still open and requires further studies and exploration. In the final cha...
15. Lunar biological effects and the magnetosphere.
Science.gov (United States)
Bevington, Michael
2015-12-01
The debate about how far the Moon causes biological effects has continued for two millennia. Pliny the Elder argued for lunar power "penetrating all things", including plants, fish, animals and humans. He also linked the Moon with tides, confirmed mathematically by Newton. A review of modern studies of biological effects, especially from plants and animals, confirms the pervasive nature of this lunar force. However calculations from physics and other arguments refute the supposed mechanisms of gravity and light. Recent space exploration allows a new approach with evidence of electromagnetic fields associated with the Earth's magnetotail at full moon during the night, and similar, but more limited, effects from the Moon's wake on the magnetosphere at new moon during the day. The disturbance of the magnetotail is perhaps shown by measurements of electric fields of up to 16V/m compared with the usual lunar biological effects, such as acute myocardial infarction, could help the development of strategies to reduce adverse effects for people sensitive to geomagnetic disturbance. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
16. Wave propagation in the magnetosphere of Jupiter
Science.gov (United States)
Liemohn, H. B.
1972-01-01
A systematic procedure is developed for identifying the spatial regimes of various modes of wave propagation in the Jupiter magnetosphere that may be encountered by flyby missions. The Clemmow-Mullaly-Allis (CMA) diagram of plasma physics is utilized to identify the frequency regimes in which different modes of propagation occur in the magnetoplasma. The Gledhill model and the Ioannidis and Brice model of the magnetoplasma are summarized, and configuration-space CMA diagrams are constructed for each model for frequencies from 10 Hz to 1 MHz. The distinctive propagation features, the radio noise regimes, and the wave-particle interactions are discussed. It is concluded that the concentration of plasma in the equatorial plane makes this region of vital importance for radio observations with flyby missions. Local radio noise around the electron cyclotron frequency will probably differ appreciably from its terrestrial counterpart due to the lack of field-line guidance. Hydromagnetic wave properties at frequencies near the ion cyclotron frequency and below will probably be similar to the terrestrial case.
17. Electron acoustic nonlinear structures in planetary magnetospheres
Science.gov (United States)
Shah, K. H.; Qureshi, M. N. S.; Masood, W.; Shah, H. A.
2018-04-01
In this paper, we have studied linear and nonlinear propagation of electron acoustic waves (EAWs) comprising cold and hot populations in which the ions form the neutralizing background. The hot electrons have been assumed to follow the generalized ( r , q ) distribution which has the advantage that it mimics most of the distribution functions observed in space plasmas. Interestingly, it has been found that unlike Maxwellian and kappa distributions, the electron acoustic waves admit not only rarefactive structures but also allow the formation of compressive solitary structures for generalized ( r , q ) distribution. It has been found that the flatness parameter r , tail parameter q , and the nonlinear propagation velocity u affect the propagation characteristics of nonlinear EAWs. Using the plasmas parameters, typically found in Saturn's magnetosphere and the Earth's auroral region, where two populations of electrons and electron acoustic solitary waves (EASWs) have been observed, we have given an estimate of the scale lengths over which these nonlinear waves are expected to form and how the size of these structures would vary with the change in the shape of the distribution function and with the change of the plasma parameters.
18. Density Variations in the Earth's Magnetospheric Cusps
Science.gov (United States)
Walsh, B. M.; Niehof, J.; Collier, M. R.; Welling, D. T.; Sibeck, D. G.; Mozer, F. S.; Fritz, T. A.; Kuntz, K. D.
2016-01-01
Seven years of measurements from the Polar spacecraft are surveyed to monitor the variations of plasma density within the magnetospheric cusps. The spacecraft's orbital precession from 1998 through 2005 allows for coverage of both the northern and southern cusps from low altitude out to the magnetopause. In the mid- and high- altitude cusps, plasma density scales well with the solar wind density (n(sub cusp)/n(sub sw) approximately 0.8). This trend is fairly steady for radial distances greater then 4 R(sub E). At low altitudes (r less than 4R(sub E)) the density increases with decreasing altitude and even exceeds the solar wind density due to contributions from the ionosphere. The density of high charge state oxygen (O(greater +2) also displays a positive trend with solar wind density within the cusp. A multifluid simulation with the Block-Adaptive-Tree Solar Wind Roe-Type Upwind Scheme MHD model was run to monitor the relative contributions of the ionosphere and solar wind plasma within the cusp. The simulation provides similar results to the statistical measurements from Polar and confirms the presence of ionospheric plasma at low altitudes.
19. Energetic Particles Dynamics in Mercury's Magnetosphere
Science.gov (United States)
Walsh, Brian M.; Ryou, A.S.; Sibeck, D. G.; Alexeev, I. I.
2013-01-01
We investigate the drift paths of energetic particles in Mercury's magnetosphere by tracing their motion through a model magnetic field. Test particle simulations solving the full Lorentz force show a quasi-trapped energetic particle population that gradient and curvature drift around the planet via "Shabansky" orbits, passing though high latitudes in the compressed dayside by equatorial latitudes on the nightside. Due to their large gyroradii, energetic H+ and Na+ ions will typically collide with the planet or the magnetopause and will not be able to complete a full drift orbit. These simulations provide direct comparison for recent spacecraft measurements from MESSENGER. Mercury's offset dipole results in an asymmetric loss cone and therefore an asymmetry in particle precipitation with more particles precipitating in the southern hemisphere. Since the planet lacks an atmosphere, precipitating particles will collide directly with the surface of the planet. The incident charged particles can kick up neutrals from the surface and have implications for the formation of the exosphere and weathering of the surface
20. EXTENDED MAGNETOSPHERES IN PRE-MAIN-SEQUENCE EVOLUTION: FROM T TAURI STARS TO THE BROWN DWARF LIMIT
Energy Technology Data Exchange (ETDEWEB)
Gomez de Castro, Ana I.; Marcos-Arenal, Pablo [Grupo de Investigacion Complutense AEGORA, Universidad Complutense de Madrid, 28040 Madrid (Spain)
2012-04-20
Low-mass pre-main-sequence stars, i.e., T Tauri stars (TTSs), strongly radiate at high energies, from X-rays to the ultraviolet (UV). This excess radiation with respect to main-sequence cool stars (MSCSs) is associated with the accretion process, i.e., it is produced in the extended magnetospheres, in the accretion shocks on the stellar surface, and in the outflows. Although evidence of accretion shocks and outflow contribution to the high-energy excess have been recently addressed, there is not an updated revision of the magnetospheric contribution. This article addresses this issue. The UV observations of the TTSs in the well-known Taurus region have been analyzed together with the XMM-Newton observations compiled in the XEST survey. For the first time the high sensitivity of the Hubble Space Telescope UV instrumentation has allowed measurement of the UV line fluxes of TTSs to M8 type. UV- and X-ray-normalized fluxes have been determined to study the extent and properties of the TTS magnetospheres as a class. They have been compared with the atmospheres of the MSCSs. The main results from this analysis are (1) the normalized fluxes of all the tracers are correlated; this correlation is independent of the broad mass range and the hardness of the X-ray radiation field; (2) the TTS correlations are different than the MSCS correlations; (3) there is a very significant excess emission in O I in the TTSs compared with MSCSs that seems to be caused by recombination radiation from the disk atmosphere after photoionization by extreme UV radiation; the Fe II/Mg II recombination continuum has also been detected in several TTSs and most prominently in AA Tau; and (4) the normalized flux of the UV tracers anticorrelates with the strength of the X-ray flux, i.e., the stronger the X-ray surface flux is, the weaker the observed UV flux. This last behavior is counterintuitive within the framework of stellar dynamo theory and suggests that UV emission can be produced in the
1. Characterizing stellar and exoplanetary environments
CERN Document Server
Khodachenko, Maxim
2015-01-01
In this book an international group of specialists discusses studies of exoplanets subjected to extreme stellar radiation and plasma conditions. It is shown that such studies will help us to understand how terrestrial planets and their atmospheres, including the early Venus, Earth and Mars, evolved during the host star’s active early phase. The book presents an analysis of findings from Hubble Space Telescope observations of transiting exoplanets, as well as applications of advanced numerical models for characterizing the upper atmosphere structure and stellar environments of exoplanets. The authors also address detections of atoms and molecules in the atmosphere of “hot Jupiters” by NASA’s Spitzer telescope. The observational and theoretical investigations and discoveries presented are both timely and important in the context of the next generation of space telescopes.
The book is divided into four main parts, grouping chapters on exoplanet host star radiation and plasma environments, exoplanet u...
2. Modular Stellarator Fusion Reactor concept
International Nuclear Information System (INIS)
Miller, R.L.; Krakowski, R.A.
1981-08-01
A preliminary conceptual study is made of the Modular Stellarator Reactor (MSR). A steady-state ignited, DT-fueled, magnetic fusion reactor is proposed for use as a central electric-power station. The MSR concept combines the physics of the classic stellarator confinement topology with an innovative, modular-coil design. Parametric tradeoff calculations are described, leading to the selection of an interim design point for a 4-GWt plant based on Alcator transport scaling and an average beta value of 0.04 in an l = 2 system with a plasma aspect ratio of 11. The physics basis of the design point is described together with supporting magnetics, coil-force, and stress computations. The approach and results presented herein will be modified in the course of ongoing work to form a firmer basis for a detailed conceptual design of the MSR
3. Hydromagnetic instability in a stellarator
Energy Technology Data Exchange (ETDEWEB)
Kruskal, M D; Gottlieb, M B; Johnson, J L; Goldman, L M [Project Matterhorn, Princeton University, Princeton, NJ (United States)
1958-07-01
It was noted that when there is a uniform externally imposed longitudinal field much larger than the field of the discharge current, one should expect instabilities in the form of a lateral displacement of the plasma column into a helix of large pitch. At the wavelength of fastest growth the e-folding time approximates the time it takes a sound wave in the plasma to traverse the radius of the plasma column. This problem has been re-examines under the conditions which might be expected to occur in the stellarator during ohmic heating, including the presence of external conductors. The theory is applied to the stellarator; and it is shown that the external conductors are in fact unimportant. The important effects due to the finite length of the Machine are discussed and the effects of more general current distributions are considered. The results from the experiments are given.
4. ACCELERATED FITTING OF STELLAR SPECTRA
Energy Technology Data Exchange (ETDEWEB)
Ting, Yuan-Sen; Conroy, Charlie [Harvard–Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Rix, Hans-Walter [Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg (Germany)
2016-07-20
Stellar spectra are often modeled and fitted by interpolating within a rectilinear grid of synthetic spectra to derive the stars’ labels: stellar parameters and elemental abundances. However, the number of synthetic spectra needed for a rectilinear grid grows exponentially with the label space dimensions, precluding the simultaneous and self-consistent fitting of more than a few elemental abundances. Shortcuts such as fitting subsets of labels separately can introduce unknown systematics and do not produce correct error covariances in the derived labels. In this paper we present a new approach—Convex Hull Adaptive Tessellation (chat)—which includes several new ideas for inexpensively generating a sufficient stellar synthetic library, using linear algebra and the concept of an adaptive, data-driven grid. A convex hull approximates the region where the data lie in the label space. A variety of tests with mock data sets demonstrate that chat can reduce the number of required synthetic model calculations by three orders of magnitude in an eight-dimensional label space. The reduction will be even larger for higher dimensional label spaces. In chat the computational effort increases only linearly with the number of labels that are fit simultaneously. Around each of these grid points in the label space an approximate synthetic spectrum can be generated through linear expansion using a set of “gradient spectra” that represent flux derivatives at every wavelength point with respect to all labels. These techniques provide new opportunities to fit the full stellar spectra from large surveys with 15–30 labels simultaneously.
5. Grigori Kuzmin and Stellar Dynamics
Directory of Open Access Journals (Sweden)
Zeeuw P. Tim de
2011-06-01
Full Text Available Grigori Kuzmin was a very gifted dynamicist and one of the towering figures in the distinguished history of the Tartu Observatory. He obtained a number of important results in relative isolation which were later rediscovered in the West. This work laid the foundation for further advances in the theory of stellar systems in dynamical equilibrium, thereby substantially increasing our understanding of galaxy dynamics.
6. Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes
7. The High-Energy Polarization-Limiting Radius of Neutron Star Magnetospheres 1, Slowly Rotating Neutron Stars
CERN Document Server
Heyl, J S; Lloyd, D; CERN. Geneva; Heyl, Jeremy S.; Shaviv, Nir J.; Lloyd, Don
2003-01-01
In the presence of strong magnetic fields, the vacuum becomes a birefringent medium. We show that this QED effect decouples the polarization modes of photons leaving the NS surface. Both the total intensity and the intensity in each of the two modes is preserved along a ray's path through the neutron-star magnetosphere. We analyze the consequences that this effect has on aligning the observed polarization vectors across the image of the stellar surface to generate large net polarizations. Counter to previous predictions, we show that the thermal radiation of NSs should be highly polarized even in the optical. When detected, this polarization will be the first demonstration of vacuum birefringence. It could be used as a tool to prove the high magnetic field nature of AXPs and it could also be used to constrain physical NS parameters, such as $R/M$, to which the net polarization is sensitive.
8. Models of hot stellar systems
International Nuclear Information System (INIS)
1986-01-01
Elliptical galaxies consist almost entirely of stars. Sites of recent star formation are rare, and most stars are believed to be several billion years old, perhaps as old as the Universe itself (--10/sup 10/ yrs). Stellar motions in ellipticals show a modest amount of circulation about the center of the system, but most support against the force of gravity is provided by random motions; for this reason ellipticals are called 'hot' stellar systems. Spiral galaxies usually also contain an appreciable amount of gas (--10%, mainly atomic hydrogen) and new stars are continually being formed out of this gas, especially in the spiral arms. In contrast to ellipticals, support against gravity in spiral galaxies comes almost entirely from rotation; random motions of the stars with respect to rotation are small. Consequently, spiral galaxies are called 'cold' stellar systems. Other than in hot systems, in cold systems the collective response of stars to variations in the force field is an essential part of the dynamics. The present overview is limited to mathematical models of hot systems. Computational methods are also discussed
9. Hot plasma parameters in Neptune's magnetosphere
International Nuclear Information System (INIS)
Krimigis, S.M.; Mauk, B.H.; Cheng, A.F.; Keath, E.P.; Kane, M.; Armstrong, T.P.; Gloeckler, G.; Lanzerotti, L.J.
1990-01-01
Energy spectra of energetic protons and electrons (E p approx-gt 28 keV, E e approx-gt 22 keV, respectively) obtained with the Low Energy Charged Particle (LECP) instrument during the Voyager 2 encounter with Neptune on August 24-25, 1989 are presented. The proton spectral form was a power law (dj/dE = KE -γ ), outside the orbit of Triton (∼14.3 R N ); inside that distance, it was found to be a hot (kT ≅ 60 keV) Maxwellian distribution. Such distributions, observed in other planets as well, have yet to be explained theoretically. Similarly, the electron spectral form changed from a simple power law outside Triton to a two-slope power law with a high energy tail inside. Intensity and spectral features in both proton and electron fluxes were identified in association with the crossings of the Triton and 1989 N1 L-shells, but these features do not occur simultaneously in both species. Such signatures were manifested by relative peaks in both kT and γ spectral indices. Peak proton pressures of ∼2x10 -9 dynes cm -2 , and β ∼ 0.2 were measured at successive magnetic equatorial crossings, both inbound and outbound. These parameters show Neptune's magnetosphere to be relatively undistorted by hot plasma loading, similar to that of Uranus and unlike those of Saturn and Jupiter. Trapped electron fluxes at Neptune, as at Uranus, exceed the whistler mode stably trapped flux limit. Whistler-induced pitch angle scattering of energetic electrons in the radiation belts can yield a precipitating energy flux sufficient to drive Neptune's aurora
10. First results from the Magnetospheric Multiscale mission
Science.gov (United States)
Lavraud, B.
2017-12-01
Since its launch in March 2015, NASA's Magnetospheric Multiscale mission (MMS) provides a wealth of unprecedented high resolution measurements of space plasma properties and dynamics in the near-Earth environment. MMS was designed in the first place to study the fundamental process of collision-less magnetic reconnection. The two first results reviewed here pertain to this topic and highlight how the extremely high resolution MMS data (electrons, in particular, with full three dimensional measurements at 30 ms in burst mode) have permitted to tackle electron dynamics in unprecedented details. The first result demonstrates how electrons become demagnetized and scattered near the magnetic reconnection X line as a result of increased magnetic field curvature, together with a decrease in its magnitude. The second result demonstrates that electrons form crescent-shaped, agyrotropic distribution functions very near the X line, suggestive of the existence of a perpendicular current aligned with the local electric field and consistent with the energy conversion expected in magnetic reconnection (such that J\\cdot E > 0). Aside from magnetic reconnection, we show how MMS contributes to topics such as wave properties and their interaction with particles. Thanks again to extremely high resolution measurements, the lossless and periodical energy exchange between wave electromagnetic fields and particles, as expected in the case of kinetic Alfvén waves, was confirmed. Although not discussed, MMS has the potential to solve many other outstanding issues in collision-less plasma physics, for example regarding shock or turbulence acceleration, with obvious broader impacts in astrophysics in general.
11. Charged particle periodicity in the Saturnian magnetosphere
International Nuclear Information System (INIS)
Carbary, J.F.; Krimigis, S.M.
1982-01-01
The low energy charged particles (LECP) experiments on the Voyager 1 and 2 spacecraft performed measurements of electrons (approx.22 keV to approx.20 MeV) and ions (approx.28 keV to approx.150 MeV) during the Saturn encounters in 1980 and 1981. Count rate ratios of two of the low energy electron (22 to 35 keV and 183 to 500 keV) and ion (43 to 80 keV and 137 to 215 keV) channels exhibit an approximation 10 hour periodicity in the outer Saturnian magnetosphere beyond the orbit of Titan. Electron ratios vary from approx.50 to approx.300; ion ratios vary from approx.3 to approx.20. Similar but less pronounced periodicities are observed for higher and lower energy electron and ion spectral indices. Three complete cycles were observed during the Voyager 2 outbound portion of the encounter from which were determined an electron ratio period of 10/sup h/21/sup m/ +- 48/sup m/ and an ion ratio period of 9/sup h/49/sup m/ +- 59/sup m/. Using Saturn Kilometric Radiation (SKR) and Saturn Electrostatic Discharge (SED) periods, extrapolation backward from Voyager 2 to Voyager 1 suggests that the periodicities are Saturnian rather than Jovian in nature, and that they persist in phase for time intervals at least as long as 287 days. Ratio minima, or spectral hardenings, occur in the same hemisphere as do auroral brightenings, SKR activity, and spoke enhanement. We interpret the observations as prima facie evidence of an asymmetry in the Saturian magnetic field and the root cause of the observed SKR periodicity
12. Jupiter's Magnetosphere: Plasma Description from the Ulysses Flyby.
Science.gov (United States)
Bame, S J; Barraclough, B L; Feldman, W C; Gisler, G R; Gosling, J T; McComas, D J; Phillips, J L; Thomsen, M F; Goldstein, B E; Neugebauer, M
1992-09-11
Plasma observations at Jupiter show that the outer regions of the Jovian magnetosphere are remarkably similar to those of Earth. Bow-shock precursor electrons and ions were detected in the upstream solar wind, as at Earth. Plasma changes across the bow shock and properties of the magnetosheath electrons were much like those at Earth, indicating that similar processes are operating. A boundary layer populated by a varying mixture of solar wind and magnetospheric plasmas was found inside the magnetopause, again as at Earth. In the middle magnetosphere, large electron density excursions were detected with a 10-hour periodicity as planetary rotation carried the tilted plasma sheet past Ulysses. Deep in the magnetosphere, Ulysses crossed a region, tentatively described as magnetically connected to the Jovian polar cap on one end and to the interplanetary magnetic field on the other. In the inner magnetosphere and lo torus, where corotation plays a dominant role, measurements could not be made because of extreme background rates from penetrating radiation belt particles.
13. Solar wind and its interaction with the Earth magnetosphere
International Nuclear Information System (INIS)
Grib, S.A.
1978-01-01
A critical review is given regarding the research of the stationary and non-stationary interaction of the solar wind with the Earth magnetosphere. Highlighted is the significance of the interplanetary magnetic field in the non-stationary movement of the solar wind flux. The problem of the solar wind shock waves interaction with the ''bow wave-Earth's magnetosphere'' system is being solved. Considered are the secondary phenomena, as a result of which the depression-type wave occurs, that lowers the pressure on the Earth's maanetosphere. The law, governing the movement of the magnetosphere subsolar point during the abrupt start of a geomagnetic storm has been discovered. Stationary circumvention of the magnetosphere by the solar wind flux is well described by the gas dynamic theory of the hypersonic flux. Non-stationary interaction of the solar wind shock waves with the magnetosphere is magnetohydrodynamic. It is pointed out, that the problems under consideration are important for the forecasting of strong geomagnetic perturbations on the basis of cosmic observations
14. Wave--particle interactions in the magnetosphere and ionosphere
International Nuclear Information System (INIS)
Thorne, R.M.
1975-01-01
Two distinct aspects of the interaction between waves and particles in the earth's magnetosphere and ionosphere were discussed at the Yosemite Conference on Magnetosphere-Ionosphere Coupling; these will be briefly reviewed. Intense field-aligned currents flow between the ionosphere and magnetosphere at auroral latitudes. Under certain conditions these currents can become unstable, permitting potential drops to be established along the field lines. The present status of experimental evidence favoring such parallel electric fields is somewhat controversial. Theoretical models for their origin invoke regions of anomalous resistivity or electrostatic double layers. To date it is impossible to distinguish between these alternatives on the basis of experimental data. The nonadiabatic behavior of magnetospheric ring current particles during geomagnetic storms is largely controlled by wave-particle processes. During the storm main phase, intense fluctuating convection electric fields are responsible for injecting trapped particles into the outer radiation zone. The outer radiation zone also moves in closer to the earth following the storm time compression of the plasmapause. Simultaneous pitch angle scattering by higher-frequency plasma turbulence causes precipitation loss near the strong diffusion limit throughout the outer magnetosphere. During the storm recov []ry phase the plasmapause slowly moves out toward its prestorm location; energetic particle loss at such times appears to be dominated by cyclotron resonant scattering from electromagnetic turbulence. (auth)
15. Evaluation of recent quantitative magnetospheric magnetic field models
International Nuclear Information System (INIS)
Walker, R.J.
1976-01-01
Recent quantitative magnetospheric field models contain many features not found in earlier models. Magnetopause models which include the effects of the dipole tilt were presented. More realistic models of the tail field include tail currents which close on the magnetopause, cross-tail currents of finite thickness, and cross-tail current models which model the position of the neutral sheet as a function of tilt. Finally, models have attempted to calculate the field of currents distributed in the inner magnetosphere. As the purpose of a magnetospheric model is to provide a mathematical description of the field that reasonably reproduces the observed magnetospheric field, several recent models were compared with the observed ΔB(B/sub observed/--B/sub main field/) contours. Models containing only contributions from magnetopause and tail current systems are able to reproduce the observed quiet time field only in an extremely qualitative way. The best quantitative agreement between models and observations occurs when currents distributed in the inner magnetosphere are added to the magnetopause and tail current systems. However, the distributed current models are valid only for zero tilt. Even the models which reproduce the average observed field reasonably well may not give physically reasonable field gradients. Three of the models evaluated contain regions in the near tail in which the field gradient reverses direction. One region in which all the models fall short is that around the polar cusp, though most can be used to calculate the position of the last closed field line reasonably well
16. Observations & modeling of solar-wind/magnetospheric interactions
Science.gov (United States)
Hoilijoki, Sanni; Von Alfthan, Sebastian; Pfau-Kempf, Yann; Palmroth, Minna; Ganse, Urs
2016-07-01
The majority of the global magnetospheric dynamics is driven by magnetic reconnection, indicating the need to understand and predict reconnection processes and their global consequences. So far, global magnetospheric dynamics has been simulated using mainly magnetohydrodynamic (MHD) models, which are approximate but fast enough to be executed in real time or near-real time. Due to their fast computation times, MHD models are currently the only possible frameworks for space weather predictions. However, in MHD models reconnection is not treated kinetically. In this presentation we will compare the results from global kinetic (hybrid-Vlasov) and global MHD simulations. Both simulations are compared with in-situ measurements. We will show that the kinetic processes at the bow shock, in the magnetosheath and at the magnetopause affect global dynamics even during steady solar wind conditions. Foreshock processes cause an asymmetry in the magnetosheath plasma, indicating that the plasma entering the magnetosphere is not symmetrical on different sides of the magnetosphere. Behind the bow shock in the magnetosheath kinetic wave modes appear. Some of these waves propagate to the magnetopause and have an effect on the magnetopause reconnection. Therefore we find that kinetic phenomena have a significant role in the interaction between the solar wind and the magnetosphere. While kinetic models cannot be executed in real time currently, they could be used to extract heuristics to be added in the faster MHD models.
17. Results of Compact Stellarator Engineering Trade Studies
International Nuclear Information System (INIS)
Brown, Tom; Bromberg, L.; Cole, M.
2009-01-01
A number of technical requirements and performance criteria can drive stellarator costs, e.g., tight tolerances, accurate coil positioning, low aspect ratio (compactness), choice of assembly strategy, metrology, and complexity of the stellarator coil geometry. With the completion of a seven-year design and construction effort of the National Compact Stellarator Experiment (NCSX) it is useful to interject the NCSX experience along with the collective experiences of the NCSX stellarator community to improving the stellarator configuration. Can improvements in maintenance be achieved by altering the stellarator magnet configuration with changes in the coil shape or with the combination of trim coils? Can a mechanical configuration be identified that incorporates a partial set of shaped fixed stellarator coils along with some removable coil set to enhance the overall machine maintenance? Are there other approaches that will simplify the concepts, improve access for maintenance, reduce overall cost and improve the reliability of a stellarator based power plant? Using ARIES-CS and NCSX as reference cases, alternative approaches have been studied and developed to show how these modifications would favorably impact the stellarator power plant and experimental projects. The current status of the alternate stellarator configurations being developed will be described and a comparison made to the recently designed and partially built NCSX device and the ARIES-CS reactor design study
18. Results of Compact Stellarator Engineering Trade Studies
International Nuclear Information System (INIS)
Brown, T.; Bromberg, L.; Cole, M.
2009-01-01
A number of technical requirements and performance criteria can drive stellarator costs, e.g., tight tolerances, accurate coil positioning, low aspect ratio (compactness), choice of assembly strategy, metrology, and complexity of the stellarator coil geometry. With the completion of a seven-year design and construction effort of the National Compact Stellarator Experiment (NCSX) it is useful to interject the NCSX experience along with the collective experiences of the NCSX stellarator community to improving the stellarator configuration. Can improvements in maintenance be achieved by altering the stellarator magnet configuration with changes in the coil shape or with the combination of trim coils? Can a mechanical configuration be identified that incorporates a partial set of shaped fixed stellarator coils along with some removable coil set to enhance the overall machine maintenance? Are there other approaches that will simplify the concepts, improve access for maintenance, reduce overall cost and improve the reliability of a stellarator based power plant? Using ARIES-CS and NCSX as reference cases, alternative approaches have been studied and developed to show how these modifications would favorably impact the stellarator power plant and experimental projects. The current status of the alternate stellarator configurations being developed will be described and a comparison made to the recently designed and partially built NCSX device and the ARIES-CS reactor design study.
19. Corotating Magnetic Reconnection Site in Saturn’s Magnetosphere
Energy Technology Data Exchange (ETDEWEB)
Yao, Z. H.; Coates, A. J.; Ray, L. C.; Rae, I. J.; Jones, G. H.; Owen, C. J.; Dunn, W. R.; Lewis, G. R. [UCL Mullard Space Science Laboratory, Dorking RH5 6NT (United Kingdom); Grodent, D.; Radioti, A.; Gérard, J.-C. [Laboratoire de Physique Atmosphérique et Planétaire, STAR institute, Université de Liège, B-4000 Liège (Belgium); Dougherty, M. K. [Imperial College of Science, Technology and Medicine, Space and Atmospheric Physics Group, Department of Physics, London SW7 2BW (United Kingdom); Guo, R. L. [Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing (China); Pu, Z. Y. [School of Earth and Space Sciences, Peking University, Beijing (China); Waite, J. H., E-mail: [email protected] [Southwest Research Institute, San Antonio, TX (United States)
2017-09-10
Using measurements from the Cassini spacecraft in Saturn’s magnetosphere, we propose a 3D physical picture of a corotating reconnection site, which can only be driven by an internally generated source. Our results demonstrate that the corotating magnetic reconnection can drive an expansion of the current sheet in Saturn’s magnetosphere and, consequently, can produce Fermi acceleration of electrons. This reconnection site lasted for longer than one of Saturn’s rotation period. The long-lasting and corotating natures of the magnetic reconnection site at Saturn suggest fundamentally different roles of magnetic reconnection in driving magnetospheric dynamics (e.g., the auroral precipitation) from the Earth. Our corotating reconnection picture could also potentially shed light on the fast rotating magnetized plasma environments in the solar system and beyond.
20. Electromagnetic ion cyclotron waves stimulated by modest magnetospheric compressions
Science.gov (United States)
Anderson, B. J.; Hamilton, D. C.
1993-01-01
AMPTE/CCE magnetic field and particle data are used to test the suggestion that increased hot proton temperature anisotropy resulting from convection during magnetospheric compression is responsible for the enhancement in Pc 1 emission via generation of electromagnetic ion cyclotron (EMIC) waves in the dayside outer equatorial magnetosphere. The relative increase in magnetic field is used to gauge the strength of the compression, and an image dipole model is used to estimate the motion of the plasma during compression. Proton data are used to analyze the evolution of the proton distribution and the corresponding changes in EMIC wave activity expected during the compression. It is suggested that enhancements in dynamic pressure pump the energetic proton distributions in the outer magnetosphere, driving EMIC waves. Waves are expected to be generated most readily close to the magnetopause, and transient pressure pulses may be associated with bursts of EMIC waves, which would be observed on the ground in association with ionospheric transient signatures.
1. Improving magnetosphere in situ observations using solar sails
Science.gov (United States)
Parsay, Khashayar; Schaub, Hanspeter; Schiff, Conrad; Williams, Trevor
2018-01-01
Past and current magnetosphere missions employ conventional spacecraft formations for in situ observations of the geomagnetic tail. Conventional spacecraft flying in inertially fixed Keplerian orbits are only aligned with the geomagnetic tail once per year, since the geomagnetic tail is always aligned with the Earth-Sun line, and therefore, rotates annually. Solar sails are able to artificially create sun-synchronous orbits such that the orbit apse line remains aligned with the geomagnetic tail line throughout the entire year. This continuous presence in the geomagnetic tail can significantly increase the science phase for magnetosphere missions. In this paper, the problem of solar sail formation design is explored using nonlinear programming to design optimal two-craft, triangle, and tetrahedron solar sail formations, in terms of formation quality and formation stability. The designed formations are directly compared to the formations used in NASA's Magnetospheric Multi-Scale mission.
2. On the penetration of solar wind inhomogeneities into the magnetosphere
International Nuclear Information System (INIS)
Maksimov, V.P.; Senatorov, V.N.
1980-01-01
Laboratory experiments were used as a basis to study the process of interaction between solar wind inhomogeneities and the Earth's magnetosphere. The given inhomogeneity represents a lump of plasma characterized by an increased concentration of particles (nsub(e) approximately 20-30 cm -3 ), a discrete form (characteristic dimensions of the lump are inferior to the magnetosphere diameter) and the velocity v approximately 350 km/s. It is shown that there is the possibility of penetration of solar wind inhomogeneities inside the Earth's magnetosphere because of the appearance in the inhomogeneity of an electric field of transverse polarization. The said process is a possible mechanism of the formation of the magnetopshere entrance layer
3. Magnetospheric storm dynamics in terms of energy output rate
International Nuclear Information System (INIS)
Prigancova, A.; Feldstein, Ya.I.
1992-01-01
Using hourly values of both the global magnetospheric disturbance characteristic DR, and AE index of auroral ionospheric currents during magnetic storm intervals, the energy output rate dynamics is evaluated for a magnetic storm main/recovery phase and a whole storm interval. The magnetospheric response to the solar wind energy input rate under varying interplanetary and magnetospheric conditions is considered from the temporal variability point of view. The peculiarities of the response are traced separately. As far as quantitative characteristics of energy output rate are concerned, the time dependence pattern of the ring current decay parameter is emphasized to be fairly important. It is pointed out that more insight into the plasma processes, especially at L = 3 - 5, is needed for adequate evidence of the dependence. (Author)
4. On the significance of magnetospheric research for progress in astrophysics
International Nuclear Information System (INIS)
Faelthammar, C-G.; Akasofu, S-I.; Alfen, H.
1978-04-01
Recent discoveries by means of in situ measurements have led to a substantial revision of our picture of the magnetosphere and parts of the heliosphere. This concerns such essential aspects as the character and distribution of electric fields and currents, the ways in which charged particles are energized, and the chemical composition of the magnetospheric plasma. This revision reflects the fact that even in fundamental respects, real cosmical plasmas behave in different ways than predicted by the idealized models that have traditionally been used in magnetospheric physics as well as in astrophysics. The new understanding of the general properties of cosmical plasma that has been, and continues to be, provided by in situ measurements gives us a much improved basis on which to interpret astrophysical observations
5. Stellarator fusion neutronics research in Australia
International Nuclear Information System (INIS)
Zimin, S.; Cross, R.C.
1997-01-01
The new status of the H-INF Heliac Stellaralor as a National Facility and the signed international Implementing Agreement on 'Collaboration in the Development of the Stellarator Concept' represents a significant encouragement for further fusion research in Australia. In this report the future of fusion research in Australia is discussed with special attention being paid to the importance of Stellarator power plant studies and in particular stellarator fusion neutronics. The main differences between tokamak and stellarator neutronics analyses are identified, namely the neutron wall loading, geometrical modelling and total heating in in-vessel reactor components including toroidal field (TF) coils. Due to the more complicated nature of stellarator neutronics analyses, simplified approaches to fusion neutronics already developed for tokamaks are expected to be even more important and widely used for designing a Conceptual Stellarator Power Plant
6. On the universal stellar law
Science.gov (United States)
Krot, Alexander
In this work, we consider a statistical theory of gravitating spheroidal bodies to derive and develop the universal stellar law for extrasolar systems. Previously, the statistical theory for a cosmogonic body forming (so-called spheroidal body)has been proposed [1-3]. This theory starts from the conception for forming a spheroidal body inside a gas-dust protoplanetary nebula; it permits us to derive the form of distribution functions, mass density, gravitational potentials and strengths both for immovable and rotating spheroidal bodies as well as to find the distribution function of specific angular momentum[1-3]. If we start from the conception for forming a spheroidal body as a protostar (in particular, proto-Sun) inside a prestellar (presolar) nebula then the derived distribution functions of particle (as well as the mass density of an immovable spheroidal body) characterizes the first stage of evolution: from a prestellar molecular cloud (the presolar nebula) to the forming core of protostar (the proto-Sun) together with its shell as a stellar nebula (the solar nebula). This work derives the equation of state of an ideal stellar substance based on conception of gravitating spheroidal body. Using this equation, we obtain the universal stellar law (USL) for the planetary systems connecting temperature, size and mass of each of stars. This work also considers the Solar corona in the connection with USL. Then it is accounting under calculation of the ratio of temperature of the Solar corona to effective temperature of the Sun’ surfaceand modification of USL. To test justice of the modified USLfor different types of stars, the temperature of stellar corona is estimated. The prediction of parameters of stars is carrying out by means of the modified USL,as well as the Hertzsprung-Russell’s dependence [5-7]is derivedby means of USL directly. This paper also shows that knowledge of some characteristics for multi-planet extrasolar systems refines own parameters of
7. Some recent results from European sounding rocket and satellite observations of the hot magnetospheric plasma
International Nuclear Information System (INIS)
Hultqvist, B.
1979-03-01
A brief summary of some recent results from European studies of the hot magnetospheric plasma is presented. The material is organized in four main sections: 1) Observations of keV auroral electrons. 2) Observation of the hot ion component of the magnetospheric plasma. 3) Sudden changes of the distribution of the hot plasma in the dayside magnetosphere. 4) Banded electron cyclotron harmonic instability in the magnetosphere - a first comparison of theory and experiment. (E.R.)
8. Auroral phenomenology and magnetospheric processes earth and other planets
CERN Document Server
Keiling, Andreas; Bagenal, Fran; Karlsson, Tomas
2013-01-01
Published by the American Geophysical Union as part of the Geophysical Monograph Series. Many of the most basic aspects of the aurora remain unexplained. While in the past terrestrial and planetary auroras have been largely treated in separate books, Auroral Phenomenology and Magnetospheric Processes: Earth and Other Planets takes a holistic approach, treating the aurora as a fundamental process and discussing the phenomenology, physics, and relationship with the respective planetary magnetospheres in one volume. While there are some behaviors common in auroras of the diffe
9. Outstanding Issues and Future Directions of Inner Magnetospheric Research (Invited)
Science.gov (United States)
Brandt, P. C.
2009-12-01
Several research areas of the inner magnetosphere and ionosphere (MI) system have reached a state, where the coupling mechanisms can no longer be treated as boundary conditions or ad-hoc assumptions in our physical models. It is nothing new that our community has become increasingly aware of the necessity to use global measurements from multiple observation platforms and missions, in order to understand both the system as a whole as well as its individual subsystems. In this presentation we briefly review the current status and outstanding issues of inner MI research. We attempt to establish a working definition of the term "Systems Approach", then present observational tools and techniques that enable such an approach. Physical modeling plays a central role not only in understanding the mechanisms at work, but also in determining the key quantities to be measured. We conclude by discussing questions relevant to future directions. Are there new techniques that need more attention? Should multi-platform observations be included as a default component already at the mission-level in the future? Is solar minimum uninteresting from an MI perspective? Should we actively compare to magnetospheres of other planets? Examples of outstanding issues in inner MI research include the circulation of ionospheric plasma from low to high latitudes and its escape to the magnetosphere, where it is energized by magnetospheric processes and becomes a part of the plasma pressure that in turn affects the ionospheric and magnetospheric electric field. The electric field, in turn, plays a controlling role in the transport of both magnetospheric and ionospheric plasma, which is intimately linked with ionospheric conductance. The conductance, in turn, is controlled by thermospheric chemistry coupled with plasma flow and heating and magnetospheric precipitation and Joule heating. Several techniques have emerged as important tools: auroral imaging, inversions of ENA images to retrieve the
10. Dynamics of electrons and heavy ions in Mercury's magnetosphere
International Nuclear Information System (INIS)
Ip, W.H.
1987-01-01
The present investigation of Mercury magnetosphere processes employs simple models for the adiabatic acceleration and convection of equatorially mirroring charged particles, as well as the current sheet acceleration effect and the acceleration of such exospheric ions as that of Na(+) by both electric and magnetic magnetospheric fields near Mercury's surface. The large gyroradii of such heavy ions as those of Na allow surface reimpact as well as magnetopause-interception losses to occur; gyromotion-derived kinetic energy could in the case of the latter process account for the loss of as many as half of the planet's exospheric ions. 27 references
11. Modelling Mercury's magnetosphere and plasma entry through the dayside magnetopause
Science.gov (United States)
Massetti, S.; Orsini, S.; Milillo, A.; Mura, A.
2007-09-01
Owing to the next space mission Messenger (NASA) and BepiColombo (ESA/JAXA), there is a renewed interest in modelling the Mercury's environment. The geometry of the Mercury's magnetosphere, as well as its response to the solar wind conditions, is one of the major issues. The weak magnetic field of the planet and the increasing weight of the IMF BX component at Mercury's orbit, introduce critical differences with respect to the Earth's case, such as a strong north-south asymmetry and a significant solar wind precipitation into the dayside magnetosphere even for non-negative IMF BZ. With the aim of analysing the interaction between the solar wind and Mercury's magnetosphere, we have developed an empirical-analytical magnetospheric model starting from the Toffoletto-Hill TH93 code. Our model has been tuned to reproduce the key features of the Mariner 10 magnetic data, and to mimic the magnetic field topology obtained by the self-consistent hybrid simulation developed by Kallio and Janhunen [Solar wind and magnetospheric ion impact on Mercury's magnetosphere. Geophys. Res. Lett. 30, 1877, doi: 10.1029/2003GL017842]. The new model has then been used to study the effect of the magnetic reconnection on the magnetosheath plasma entry through the open areas of the dayside magnetosphere (cusps), which are expected to be one of the main sources of charged particles circulating inside the magnetosphere. We show that, depending on the Alfvén speeds on both sides of the magnetopause discontinuity, the reconnection process would be able to accelerate solar wind protons up to few tens of keV: part of these ions can hit the surface and then trigger, via ion-sputtering, the refilling of the planetary exosphere. Finally, we show that non-adiabatic effects are expected to develop in the cusp regions as the energy gained by injected particles increases. The extent of these non-adiabatic regions is shown to be also modulated by upstream IMF condition.
12. Energy coupling function and solar wind-magnetosphere dynamo
International Nuclear Information System (INIS)
Kan, J.R.; Lee, L.C.
1979-01-01
The power delivered by the solar wind dynamo to the open magnetosphere is calculated based on the concept of field line reconnection, independent of the MHD steady reconnection theories. By recognizing a previously overlooked geometrical relationship between the reconnection electric field and the magnetic field, the calculated power is shown to be approximately proportional to the Akasofu-Perreault energy coupling function for the magnetospheric substorm. In addition to the polar cap potential, field line reconnection also gives rise to parallel electric fields on open field lines in the high-latitude cusp and the polar cap reions
13. Expected Navigation Flight Performance for the Magnetospheric Multiscale (MMS) Mission
Science.gov (United States)
Olson, Corwin; Wright, Cinnamon; Long, Anne
2012-01-01
The Magnetospheric Multiscale (MMS) mission consists of four formation-flying spacecraft placed in highly eccentric elliptical orbits about the Earth. The primary scientific mission objective is to study magnetic reconnection within the Earth s magnetosphere. The baseline navigation concept is the independent estimation of each spacecraft state using GPS pseudorange measurements (referenced to an onboard Ultra Stable Oscillator) and accelerometer measurements during maneuvers. State estimation for the MMS spacecraft is performed onboard each vehicle using the Goddard Enhanced Onboard Navigation System, which is embedded in the Navigator GPS receiver. This paper describes the latest efforts to characterize expected navigation flight performance using upgraded simulation models derived from recent analyses.
14. Movement of a charged particle beam in the Earth magnetosphere
International Nuclear Information System (INIS)
Veselovskij, I.S.
1977-01-01
The motion of a charged particle beam injected into the Earth magnetosphere in a dipole magnetic field was investigated. Examined were the simplest stationary distributions of particles. The evolution of the distribution function after pulse injection of the beam into the magnetosphere was studied. It was shown that the pulse shape depends on its starting duration. A long pulse spreads on the base and narrows on the flat top with the distance away from the point of injection. A short pulse spreads both on the base and along the height. The flat top is not present. An analytical expression for the pulse shape as a time function is given
15. Multiplicity in Early Stellar Evolution
Science.gov (United States)
Reipurth, B.; Clarke, C. J.; Boss, A. P.; Goodwin, S. P.; Rodríguez, L. F.; Stassun, K. G.; Tokovinin, A.; Zinnecker, H.
Observations from optical to centimeter wavelengths have demonstrated that multiple systems of two or more bodies is the norm at all stellar evolutionary stages. Multiple systems are widely agreed to result from the collapse and fragmentation of cloud cores, despite the inhibiting influence of magnetic fields. Surveys of class 0 protostars with millimeter interferometers have revealed a very high multiplicity frequency of about 2/3, even though there are observational difficulties in resolving close protobinaries, thus supporting the possibility that all stars could be born in multiple systems. Near-infrared adaptive optics observations of class I protostars show a lower binary frequency relative to the class 0 phase, a declining trend that continues through the class II/III stages to the field population. This loss of companions is a natural consequence of dynamical interplay in small multiple systems, leading to ejection of members. We discuss observational consequences of this dynamical evolution, and its influence on circumstellar disks, and we review the evolution of circumbinary disks and their role in defining binary mass ratios. Special attention is paid to eclipsing PMS binaries, which allow for observational tests of evolutionary models of early stellar evolution. Many stars are born in clusters and small groups, and we discuss how interactions in dense stellar environments can significantly alter the distribution of binary separations through dissolution of wider binaries. The binaries and multiples we find in the field are the survivors of these internal and external destructive processes, and we provide a detailed overview of the multiplicity statistics of the field, which form a boundary condition for all models of binary evolution. Finally, we discuss various formation mechanisms for massive binaries, and the properties of massive trapezia.
16. Physics of Compact Advanced Stellarators
International Nuclear Information System (INIS)
Zarnstorff, M.C.; Berry, L.A.; Brooks, A.; Fredrickson, E.; Fu, G.-Y.; Hirshman, S.; Hudson, S.; Ku, L.-P.; Lazarus, E.; Mikkelsen, D.; Monticello, D.; Neilson, G.H.; Pomphrey, N.; Reiman, A.; Spong, D.; Strickler, D.; Boozer, A.; Cooper, W.A.; Goldston, R.; Hatcher, R.; Isaev, M.; Kessel, C.; Lewandowski, J.; Lyon, J.; Merkel, P.; Mynick, H.; Nelson, B.E.; Nuehrenberg, C.; Redi, M.; Reiersen, W.; Rutherford, P.; Sanchez, R.; Schmidt, J.; White, R.B.
2001-01-01
Compact optimized stellarators offer novel solutions for confining high-beta plasmas and developing magnetic confinement fusion. The 3-D plasma shape can be designed to enhance the MHD stability without feedback or nearby conducting structures and provide drift-orbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low-aspect ratio, high beta-limit, and good confinement of advanced tokamaks. Quasi-axisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation of approximately 1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for beta > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at beta = 4% (the rest is from the coils), thus the equilibrium is much less nonlinear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of ''reversed'' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties
17. STELLAR MASS DEPENDENT DISK DISPERSAL
International Nuclear Information System (INIS)
Kennedy, Grant M.; Kenyon, Scott J.
2009-01-01
We use published optical spectral and infrared (IR) excess data from nine young clusters and associations to study the stellar mass dependent dispersal of circumstellar disks. All clusters older than ∼3 Myr show a decrease in disk fraction with increasing stellar mass for solar to higher mass stars. This result is significant at about the 1σ level in each cluster. For the complete set of clusters we reject the null hypothesis-that solar and intermediate-mass stars lose their disks at the same rate-with 95%-99.9% confidence. To interpret this behavior, we investigate the impact of grain growth, binary companions, and photoevaporation on the evolution of disk signatures. Changes in grain growth timescales at fixed disk temperature may explain why early-type stars with IR excesses appear to evolve faster than their later-type counterparts. Little evidence that binary companions affect disk evolution suggests that photoevaporation is the more likely mechanism for disk dispersal. A simple photoevaporation model provides a good fit to the observed disk fractions for solar and intermediate-mass stars. Although the current mass-dependent disk dispersal signal is not strong, larger and more complete samples of clusters with ages of 3-5 Myr can improve the significance and provide better tests of theoretical models. In addition, the orbits of extra-solar planets can constrain models of disk dispersal and migration. We suggest that the signature of stellar mass dependent disk dispersal due to photoevaporation may be present in the orbits of observed extra-solar planets. Planets orbiting hosts more massive than ∼1.6 M sun may have larger orbits because the disks in which they formed were dispersed before they could migrate.
18. Radiation transfer and stellar atmospheres
Science.gov (United States)
Swihart, T. L.
This is a revised and expanded version of the author's Basic Physics of Stellar Atmospheres, published in 1971. The equation of transfer is considered, taking into account the intensity and derived quantities, the absorption coefficient, the emission coefficient, the source function, and special integrals for plane media. The gray atmosphere is discussed along with the nongray atmosphere, and aspects of line formation. Topics related to polarization are explored, giving attention to pure polarized radiation, general polarized radiation, transfer in a magnetic plasma, and Rayleigh scattering and the sunlit sky. Physical and astronomical constants, and a number of problems related to the subjects of the book are presented in an appendix.
19. Drift waves in a stellarator
International Nuclear Information System (INIS)
Bhattacharjee, A.; Sedlak, J.E.; Similon, P.L.; Rosenbluth, M.N.; Ross, D.W.
1982-11-01
We investigate the eigenmode structure of drift waves in a straight stellarator using the ballooning mode formalism. The electrons are assumed to be adiabatic and the ions constitute a cold, magnetized fluid. The effective potential has an overall parabolic envelope but is modulated strongly by helical ripples along B. We have found two classes of solutions: those that are strongly localized in local helical wells, and those that are weakly localized and have broad spatial extent. The weakly localized modes decay spatially due to the existence of Mathieu resonances between the periods of the eigenfunction and the effective potential
20. Helical axis stellarator equilibrium model
International Nuclear Information System (INIS)
Koniges, A.E.; Johnson, J.L.
1985-02-01
An asymptotic model is developed to study MHD equilibria in toroidal systems with a helical magnetic axis. Using a characteristic coordinate system based on the vacuum field lines, the equilibrium problem is reduced to a two-dimensional generalized partial differential equation of the Grad-Shafranov type. A stellarator-expansion free-boundary equilibrium code is modified to solve the helical-axis equations. The expansion model is used to predict the equilibrium properties of Asperators NP-3 and NP-4. Numerically determined flux surfaces, magnetic well, transform, and shear are presented. The equilibria show a toroidal Shafranov shift
1. Neutrino transport in stellar matter
International Nuclear Information System (INIS)
Basdevant, J.L.
1985-09-01
We reconsider the neutrino transport problem in dense stellar matter which has a variety of applications among which the participation of neutrinos to the dynamics of type II supernova explosions. We describe the position of the problem and make some critiscism of previously used approximation methods. We then propose a method which is capable of handling simultaneously the optically thick, optically thin, and intermediate regimes, which is of crucial importance in such problems. The method consists in a simulation of the transport process and can be considered exact within numerical accuracy. We, finally exhibit some sample calculations which show the efficiency of the method, and present interesting qualitative physical features
2. Characterizing Convection in Stellar Atmospheres
International Nuclear Information System (INIS)
Tanner, Joel; Basu, Sarbani; Demarque, Pierre; Robinson, Frank
2011-01-01
We perform 3D radiative hydrodynamic simulations to study the properties of convection in the superadiabatic layer of stars. The simulations show differences in both the stratification and turbulent quantities for different types of stars. We extract turbulent pressure and eddy sizes, as well as the T-τ relation for different stars and find that they are sensitive to the energy flux and gravity. We also show that contrary to what is usually assumed in the field of stellar atmospheres, the structure and gas dynamics of simulations of turbulent atmospheres cannot be parameterized with T eff and log(g) alone.
3. On modular stellarator reactor coils
International Nuclear Information System (INIS)
Rau, F.; Harmeyer, E.; Kisslinger, J.; Wobig, H.
1985-01-01
Modular twisted coils are discussed which produce magnetic fields of the Advanced Stellarator WENDELSTEIN VII-AS type. Reducing the number coils/FP offers advantage for maintenance of coils, but increases the magnetic ripple and B m /B o . Computation of force densities within the coils of ASR and ASB yield local maximum values of about 80 and 180 MN/m 3 , respectively. A system of mutual coil support is being developed. Twisted coils in helical arrangement provide a reactor-sized HELIAC system. In order to reduce the magnetic ripple, a large number of 14 coils/FP in special arrangement is used
4. Stellar orbits around Sgr A*
International Nuclear Information System (INIS)
Trippe, S; Gillessen, S; Ott, T; Eisenhauer, F; Paumard, T; Martins, F; Genzel, R; Schoedel, R; Eckart, A; Alexander, T
2006-01-01
In this article we present and discuss the latest results from the observations of stars (''S-stars'') orbiting Sgr A* . With improving data quality the number of observed S-stars has increased substantially in the last years. The combination of radial velocity and proper motion information allows an ever more precise determination of orbital parameters and of the mass of and the distance to the supermassive black hole in the centre of the Milky Way. Additionally, the orbital solutions allow us to verify an agreement between the NIR source Sgr A* and the dynamical centre of the stellar orbits to within 2 mas
5. Recent advances in stellarator optimization
Science.gov (United States)
Gates, D. A.; Boozer, A. H.; Brown, T.; Breslau, J.; Curreli, D.; Landreman, M.; Lazerson, S. A.; Lore, J.; Mynick, H.; Neilson, G. H.; Pomphrey, N.; Xanthopoulos, P.; Zolfaghari, A.
2017-12-01
Computational optimization has revolutionized the field of stellarator design. To date, optimizations have focused primarily on optimization of neoclassical confinement and ideal MHD stability, although limited optimization of other parameters has also been performed. The purpose of this paper is to outline a select set of new concepts for stellarator optimization that, when taken as a group, present a significant step forward in the stellarator concept. One of the criticisms that has been leveled at existing methods of design is the complexity of the resultant field coils. Recently, a new coil optimization code—COILOPT++, which uses a spline instead of a Fourier representation of the coils,—was written and included in the STELLOPT suite of codes. The advantage of this method is that it allows the addition of real space constraints on the locations of the coils. The code has been tested by generating coil designs for optimized quasi-axisymmetric stellarator plasma configurations of different aspect ratios. As an initial exercise, a constraint that the windings be vertical was placed on large major radius half of the non-planar coils. Further constraints were also imposed that guaranteed that sector blanket modules could be removed from between the coils, enabling a sector maintenance scheme. Results of this exercise will be presented. New ideas on methods for the optimization of turbulent transport have garnered much attention since these methods have led to design concepts that are calculated to have reduced turbulent heat loss. We have explored possibilities for generating an experimental database to test whether the reduction in transport that is predicted is consistent with experimental observations. To this end, a series of equilibria that can be made in the now latent QUASAR experiment have been identified that will test the predicted transport scalings. Fast particle confinement studies aimed at developing a generalized optimization algorithm are also
6. Inclined Pulsar Magnetospheres in General Relativity: Polar Caps for the Dipole, Quadrudipole, and Beyond
Science.gov (United States)
Gralla, Samuel E.; Lupsasca, Alexandru; Philippov, Alexander
2017-12-01
In the canonical model of a pulsar, rotational energy is transmitted through the surrounding plasma via two electrical circuits, each connecting to the star over a small region known as a “polar cap.” For a dipole-magnetized star, the polar caps coincide with the magnetic poles (hence the name), but in general, they can occur at any place and take any shape. In light of their crucial importance to most models of pulsar emission (from radio to X-ray to wind), we develop a general technique for determining polar cap properties. We consider a perfectly conducting star surrounded by a force-free magnetosphere and include the effects of general relativity. Using a combined numerical-analytical technique that leverages the rotation rate as a small parameter, we derive a general analytic formula for the polar cap shape and charge-current distribution as a function of the stellar mass, radius, rotation rate, moment of inertia, and magnetic field. We present results for dipole and quadrudipole fields (superposed dipole and quadrupole) inclined relative to the axis of rotation. The inclined dipole polar cap results are the first to include general relativity, and they confirm its essential role in the pulsar problem. The quadrudipole pulsar illustrates the phenomenon of thin annular polar caps. More generally, our method lays a foundation for detailed modeling of pulsar emission with realistic magnetic fields.
7. Ab-initio Pulsar Magnetosphere: Particle Acceleration in Oblique Rotators and High-energy Emission Modeling
Science.gov (United States)
Philippov, Alexander A.; Spitkovsky, Anatoly
2018-03-01
We perform global particle-in-cell simulations of pulsar magnetospheres, including pair production, ion extraction from the surface, frame-dragging corrections, and high-energy photon emission and propagation. In the case of oblique rotators, the effects of general relativity increase the fraction of the open field lines that support active pair discharge. We find that the plasma density and particle energy flux in the pulsar wind are highly non-uniform with latitude. A significant fraction of the outgoing particle energy flux is carried by energetic ions, which are extracted from the stellar surface. Their energies may extend up to a large fraction of the open field line voltage, making them interesting candidates for ultra-high-energy cosmic rays. We show that pulsar gamma-ray radiation is dominated by synchrotron emission, produced by particles that are energized by relativistic magnetic reconnection close to the Y-point and in the equatorial current sheet. In most cases, the calculated light curves contain two strong peaks, which is in general agreement with Fermi observations. The radiative efficiency decreases with increasing pulsar inclination and increasing efficiency of pair production in the current sheet, which explains the observed scatter in L γ versus \\dot{E}. We find that the high-frequency cutoff in the spectra is regulated by the pair-loading of the current sheet. Our findings lay the foundation for quantitative interpretation of Fermi observations of gamma-ray pulsars.
8. Introduction to stellar astrophysics. V. 1
International Nuclear Information System (INIS)
Boehm-Vitense, E.
1989-01-01
This textbook introduces basic elements of fundamental astronomy and astrophysics which serve as a foundation for understanding the structure, evolution, and observed properties of stars. The first half of the book explains how stellar motions, distances, luminosities, colours, radii, masses and temperatures are measured or derived. The author then shows how data of these sorts can be arranged to classify stars through their spectra. Stellar rotation and stellar magnetic fields are introduced. Stars with peculiar spectra and pulsating stars also merit special attention. The endpoints of stellar evolutions are briefly described. There is a separate chapter on the Sun and a final one on interstellar absorption. (author)
9. Magnetohydrodynamic instabilities in a stellarator
International Nuclear Information System (INIS)
Matsuoka, K.; Miyamoto, K.; Ohasa, K.; Wakatani, M.
1977-05-01
Numerical studies of stability on kink and resistive tearing modes in a linear stellarator are presented for various current profiles and helical fields. In the case of an l = 2 helical field, a magnetic shear vanishes and the stability diagram is given by the straight lines with iota sup(σ) + iota sup(delta) = const., where iota sup(σ) is a rotational transform due to the plasma current and iota sup(delta) is due to the helical field. In the l = 2 stellarator with chi sup(delta) > 0.5, the m.h.d. stability against kink and tearing modes is improved compared with that in tokamaks. While an l = 3 helical component exists, the magnetic shear plays an important role in the stability properties. The stability diagrams become fairly complex; however, they can be explained by properties of the Euler equation. It should be noted that the internal kink modes become more unstable than in tokamaks by the l = 3 helical field. (auth.)
10. Neoclassical transport simulations for stellarators
International Nuclear Information System (INIS)
Turkin, Y.; Beidler, C. D.; Maassberg, H.; Murakami, S.; Wakasa, A.; Tribaldos, V.
2011-01-01
The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the monoenergetic coefficients obtained by direct interpolation or neural network techniques from the databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution, although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations. Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.
11. Terrestrial magnetospheric imaging: Numerical modeling of low energy neutral atoms
International Nuclear Information System (INIS)
Moore, K.R.; Funsten, H.O.; McComas, D.J.; Scime, E.E.; Thomsen, M.F.
1993-01-01
Imaging of the terrestrial magnetosphere can be performed by detection of low energy neutral atoms (LENAs) that are produced by charge exchange between magnetospheric plasma ions and cold neutral atoms of the Earth's geocorona. As a result of recent instrumentation advances it is now feasible to make energy-resolved measurements of LENAs from less than I key to greater than 30 key. To model expected LENA fluxes at a spacecraft, we initially used a simplistic, spherically symmetric magnetospheric plasma model. 6 We now present improved calculations of both hydrogen and oxygen line-of-sight LENA fluxes expected on orbit for various plasma regimes as predicted by the Rice University Magnetospheric Specification Model. We also estimate expected image count rates based on realistic instrument geometric factors, energy passbands, and image accumulation intervals. The results indicate that presently proposed LENA instruments are capable of imaging of storm time ring current and potentially even quiet time ring current fluxes, and that phenomena such as ion injections from the tail and subsequent drifts toward the dayside magnetopause may also be deduced
12. Hydromagnetic Waves in the Magnetosphere and the Ionosphere
CERN Document Server
Alperovich, Leonid S
2007-01-01
The book deals with Ultra-Low-Frequency (ULF)-electromagnetic waves observed on Earth and in Space. These are so-called geomagnetic variations or pulsations. Alfvén's discovery related to the influence of the strong magnetic field on the conducting fluids (magnetohydrodynamics) led to development of the concept that the ULF-waves are magnetospheric magnetohydrodynamic (MHD)-waves. MHD-waves at their propagation gather information about the magnetosphere, ionosphere, and the ground. There are two applied aspects based on using the ULF electromagnetic oscillations. The first one is the ground-based diagnostics of the magnetosphere. This is an attempt to monitor in the real time the magnetosphere size, distance to the last closed field-lines, distribution of the cold plasma, etc. The second one is the deep electromagnetic sounding of the Earth. The basis for these studies is the capability of any electromagnetic wave to penetrate a conductor to a finite depth. The ULF-waves can reach the depth of a few hundred ...
13. Energetic charged particles in the magnetosphere of Neptune
International Nuclear Information System (INIS)
Stone, E.C.; Cummings, A.C.; Looper, M.D.; Selesnick, R.S.; Lal, N.; McDonald, F.B.; Trainor, J.H.; Chenette, D.L.
1989-01-01
The Voyager 2 cosmic ray system (CRS) measured significant fluxes of energetic [approx-lt 1 megaelectron volt (MeV)] trapped electrons and protons in the magnetosphere of Neptune. The intensities at maximum near a magnetic L shell of 7, decreasing closer to the planet because of absorption by satellites and rings. In the region of the inner satellites of Neptune, the radiation belts have a complicated structure, which provides some constraints on the magnetic field geometry of the inner magnetosphere. Electron phase-space densities have a positive radial gradient, indicating that they diffuse inward from a source in the outer magnetosphere. Electron spectra from 1 to 5 MeV are generally well represented by power laws with indices near 6, which harden in the region of peak flux to power law indices of 4 to 5. Protons have significantly lower fluxes than electrons throughout the magnetosphere, with large anisotropies due to radial intensity gradients. The radiation belts resemble those of Uranus to the extent allowed by the different locations of the satellites, which limit the flux at each planet
14. Global Scale Periodic Responses in Saturn’s Magnetosphere
Science.gov (United States)
Jia, Xianzhe; Kivelson, Margaret G.
2017-10-01
Despite having an axisymmetric internal magnetic field, Saturn’s magnetosphere exhibits periodic modulations in a variety of properties at periods close to the planetary rotation period. While the source of the periodicity remains unidentified, it is evident from Cassini observations that much of Saturn’s magnetospheric structure and dynamics is dominated by global-scale responses to the driving source of the periodicity. We have developed a global MHD model in which a rotating field-aligned current system is introduced by imposing vortical flows in the high-latitude ionosphere in order to simulate the magnetospheric periodicities. The model has been utilized to quantitatively characterize various periodic responses in the magnetosphere, such as the displacement of the magnetopause and bow shock and flapping of the tail plasma sheet, all of which show quantitative agreement with Cassini observations. One of our model predictions is periodic release of plasmoids in the tail that occurs preferentially in the midnight-to-dawn local time sector during each rotation cycle. Here we present detailed analysis of the periodic responses seen in our simulations focusing on the properties of plasmoids predicted by the model, including their spatial distribution, occurrence frequency, and mass loss rate. We will compare these modeled parameters with published Cassini observations, and discuss their implications for interpreting in-situ measurements.
15. Magnetospheric Control of Density and Composition in the Polar Ionosphere
Science.gov (United States)
2015-06-24
verified calculation of three-dimensional plasma continuity at the geomagnetic pole [Dahlgren et al., 2012a; Perry et al., 2015; Semeter et al., 2014...variations in a camera system. This data flow describes a forward model, which may be reversed to reconstruct the magnetospheric drivers, in this case
16. Recent investigation at INPE in magnetospheric physics and geomagnetism
International Nuclear Information System (INIS)
Gonzales, W.D.; Trivedi, N.B.
1984-01-01
During recent years the following research activities related to the earth's magnetosphere have been intensified: a) studies on electric field and energy transfer from the solar wind to the magnetosphere; b) studies on high latitude magnetospheric electric fields and on their penetration into the plasmasphere; c) measurements of atmospheric-large scale-electric fields, related to the low latitude magnetospheric-ionospheric coupling and to the local atmospheric electrodynamics, using detectors on board stratospheric balloons; and d) measurements of atmospheric X-rays, related to the process of energetic particle precipitation at the South Atlantic Magnetic Anomaly, using detectors also on board stratospheric balloons. Similarly, the following research activities related to geomagnetism are being pursued: a) studies on the variability of the geomagnetic field and on the dynamics of the equatorial electrojet from local geomagnetic field measurements; b) studies on terrestrial electromagnetic induction through local measurements of the geo-electromagnetic field; and c) studies on the influence of geomagnetic activity on particle precipitation at the South Atlantic Magnetic Anomaly. (Author) [pt
17. Magnetospheric and atmospheric physics at the University of Natal
International Nuclear Information System (INIS)
Walker, A.D.M.
1982-01-01
A historical outline of geophysical work done at the University of Natal from 1938-1982 is given. Mention is also made of experimental work concerning whistlers and VLF, low-light level TV and geomagnetic pulsations. Current work on the magnetosphere, namely plasma convection in plasmasphere, auroral features, geomagnetic pulsations and the measuring of plasma properties is discussed
18. Modelling of the ring current in Saturn's magnetosphere
Directory of Open Access Journals (Sweden)
G. Giampieri
2004-01-01
Full Text Available The existence of a ring current inside Saturn's magnetosphere was first suggested by Smith et al. (1980 and Ness et al. (1981, 1982, in order to explain various features in the magnetic field observations from the Pioneer 11 and Voyager 1 and 2 spacecraft. Connerney et al. (1983 formalized the equatorial current model, based on previous modelling work of Jupiter's current sheet and estimated its parameters from the two Voyager data sets. Here, we investigate the model further, by reconsidering the data from the two Voyager spacecraft, as well as including the Pioneer 11 flyby data set. First, we obtain, in closed form, an analytic expression for the magnetic field produced by the ring current. We then fit the model to the external field, that is the difference between the observed field and the internal magnetic field, considering all the available data. In general, through our global fit we obtain more accurate parameters, compared to previous models. We point out differences between the model's parameters for the three flybys, and also investigate possible deviations from the axial and planar symmetries assumed in the model. We conclude that an accurate modelling of the Saturnian disk current will require taking into account both of the temporal variations related to the condition of the magnetosphere, as well as non-axisymmetric contributions due to local time effects. Key words. Magnetospheric physics (current systems; planetary magnetospheres; plasma sheet
19. Magnetosphere of Uranus: plasma sources, convection, and field configuration
International Nuclear Information System (INIS)
Voigt, G.; Hill, T.W.; Dessler, A.J.
1983-01-01
At the time of the Voyager 2 flyby of Uranus, the planetary rotational axis will be roughly antiparallel to the solar wind flow. If Uranus has a magnetic dipole moment that is approximately aligned with its spin axis, and if the heliospheric shock has not been encountered, we will have the rare opportunity to observe a ''pole-on'' magnetosphere as discussed qualitatively by Siscoe. Qualitative arguments based on analogy with Earth, Jupiter, and Saturn suggest that the magnetosphere of Uranus may lack a source of plasma adequate to produce significant internal currents, internal convection, and associated effects. In order to provide a test of this hypothesis with the forthcoming Voyager measurements, we have constructed a class of approximately self-consistent quantitative magnetohydrostatic equilibrium configurations for a pole-on magnetosphere with variable plasma pressure parameters. Given a few simplifying assumptions, the geometries of the magnetic field and of the tail current sheet can be computed for a given distribution of trapped plasma pressure. The configurations have a single funnel-shaped polar cusp that points directly into the solar wind and a cylindrical tail plasma sheet whose currents close within the tail rather than on the tail magnetopause, and whose length depends on the rate of decrease of thermal plasma pressure down the tail. Interconnection between magnetospheric and interplanetary fields results in a highly asymmetric tail-field configuration. These features were predicted qualtitatively by Siscoe; the quantitative models presented here may be useful in the interpretation of Voyager encounter results
20. A new method of diagnostics for the magnetospheric plasma
International Nuclear Information System (INIS)
Etcheto, Jacqueline; Petit, Michel
1977-01-01
A new diagnostic technique for magnetospheric plasma, based on in situ excitation of the plasma resonances, has been used for the first time on board the Geos satellite. The preliminary results are very gratifying: electron density and magnetic field intensity are derived reliably and accurately from the resonances observed; hopefully, temperature and electric field will be deduced from the data as well [fr
1. ON THE GLOBAL STRUCTURE OF PULSAR FORCE-FREE MAGNETOSPHERE
International Nuclear Information System (INIS)
Petrova, S. A.
2013-01-01
The dipolar magnetic field structure of a neutron star is modified by the plasma originating in the pulsar magnetosphere. In the simplest case of a stationary axisymmetric force-free magnetosphere, a self-consistent description of the fields and currents is given by the well-known pulsar equation. Here we revise the commonly used boundary conditions of the problem in order to incorporate the plasma-producing gaps and to provide a framework for a truly self-consistent treatment of the pulsar magnetosphere. A generalized multipolar solution of the pulsar equation is found, which, as compared to the customary split monopole solution, is suggested to better represent the character of the dipolar force-free field at large distances. In particular, the outer gap location entirely inside the light cylinder implies that beyond the light cylinder the null and critical lines should be aligned and become parallel to the equator at a certain altitude. Our scheme of the pulsar force-free magnetosphere, which will hopefully be followed by extensive analytic and numerical studies, may have numerous implications for different fields of pulsar research.
2. Quasiperiodic ULF-pulsations in Saturn's magnetosphere
Directory of Open Access Journals (Sweden)
G. Kleindienst
2009-02-01
Full Text Available Recent magnetic field investigations made onboard the Cassini spacecraft in the magnetosphere of Saturn show the existence of a variety of ultra low frequency plasma waves. Their frequencies suggest that they are presumably not eigenoscillations of the entire magnetospheric system, but excitations confined to selected regions of the magnetosphere. While the main magnetic field of Saturn shows a distinct large scale modulation of approximately 2 nT with a periodicity close to Saturn's rotation period, these ULF pulsations are less obvious superimposed oscillations with an amplitude generally not larger than 3 nT and show a package-like structure. We have analyzed these wave packages and found that they are correlated to a certain extent with the large scale modulation of the main magnetic field. The spatial localization of the ULF wave activity is represented with respect to local time and Kronographic coordinates. For this purpose we introduce a method to correct the Kronographic longitude with respect to a rotation period different from its IAU definition. The observed wave packages occur in all magnetospheric regions independent of local time, elevation, or radial distance. Independent of the longitude correction applied the wave packages do not occur in an accentuated Kronographic longitude range, which implies that the waves are not excited or confined in the same selected longitude ranges at all times or that their lifetime leads to a variable phase with respect to the longitudes where they have been exited.
3. Energetic magnetospheric protons in the plasma depletion layer
International Nuclear Information System (INIS)
Fuselier, S.A.
1992-01-01
Interplanetary magnetic field draping against the Earth's dayside subsolar magnetopause creates a region of reduced plasma density and increased magnetic field called the plasma depletion layer. In this region, leakage of energetic ions from the Earth's magnetosphere onto magnetic field lines in the plasma depletion layer can be studied without interference from ions accelerated at the Earth's quasi-parallel bow shock. Active Magnetospheric Particle Tracer Experiment/Charge Composition Explorer (AMPTE/CCE) observations for 13 plasma depletion layer events are used to determine the characteristics of energetic protons between a few keV/e and ∼100keV/e leaked from the magnetosphere. Results indicate that the leaked proton distributions resemble those in the magnetosphere except that they have lower densities and temperatures and much higher velocities parallel (or antiparallel) and perpendicular to the magnetic field. Compared to the low-energy magnetosheath proton distributions present in the depletion layer, the leaked energetic proton distributions typically have substantially higher flow velocities along the magnetic field indicate that the leaked energetic proton distributions to contribute to the energetic proton population seen upstream and downstream from the quasi-parallel bow shock. However, their contribution is small compared to the contribution from acceleration of protons at the bow shock because the leaked proton densities are on the order of 10 times smaller than the energetic proton densities typically observed in the vicinity of the quasi-parallel bow shock
4. Coupling between the solar wind and the magnetosphere: CDAW 6
International Nuclear Information System (INIS)
Tsurutani, B.T.; Slavin, J.A.; Kamide, Y.; Zwickl, R.D.; King, J.H.; Russell, C.T.
1985-01-01
Interplanetary conditions (VB 3 , V 2 B 3 and epsilon-c) are derived from ISEE 3 and IMP 8 field and plasma data for the two Coordinated Data Analysis Workshop (CDAW 6) intervals of study and are compared with various aspects of geomagnetic activity (AE, U/sub T/, derived Joule heating, electric potential, westward eastward and total electrojet currents). The March 22 (day 81), 1979, interval contains two distinct periods of geomagnetic activity, both highly correlated with interplanetary features. The start of the first active interval is caused by a southward turning of the interplanetary magnetic field (IMF) associated with the passage of a heliospheric current sheet. The start of the second interval is related to a second IMF southward turning. The geomagnetic activity intensifies when the second crossing of the current sheet, and a ram pressure increase of 4 to 6, impinges on the magnetosphere. Because the interplanetary parameters VB 3 , V 2 B 3 and epsilon-c decrease across the discontinuity, it is concluded that either additional energy is injected into the magnetosphere from the conversion of ram energy into magnetospheric substorm energy or some feature associated with current sheet crossing ''triggers'' the release of previously stored magnetosphere/magnetotail energy. It is not possible at this time to distinguish between these two possibilities. For day 81, VB 3 , V 2 4 3 , and epsilon-c were highly correlated with AL, AE, westward and equivalent currents with coefficients ranging from approx.0.75 to 0.90
5. Magnetosonic resonance in a dipole-like magnetosphere
Directory of Open Access Journals (Sweden)
A. S. Leonovich
2006-09-01
Full Text Available A theory of resonant conversion of fast magnetosonic (FMS waves into slow magnetosonic (SMS oscillations in a magnetosphere with dipole-like magnetic field has been constructed. Monochromatic FMS waves are shown to drive standing (along magnetic field lines SMS oscillations, narrowly localized across magnetic shells. The longitudinal and transverse structures, as well as spectrum of resonant SMS waves are determined. Frequencies of fundamental harmonics of standing SMS waves lie in the range of 0.1–1 mHz, and are about two orders of magnitude lower than frequencies of similar Alfvén field line resonance harmonics. This difference makes an effective interaction between these MHD modes impossible. The amplitude of SMS oscillations rapidly decreases along the field lines from the magnetospheric equator towards the ionosphere. In this context, magnetospheric SMS oscillations cannot be observed on the ground, and the ionosphere does not play any role either in their generation or dissipation. The theory developed can be used to interpret the occurrence of compressional Pc5 waves in a quiet magnetosphere with a weak ring current.
6. Laboratory simulation of energetic flows of magnetospheric planetary plasma
International Nuclear Information System (INIS)
Shaikhislamov, I F; Posukh, V G; Melekhov, A V; Boyarintsev, E L; Zakharov, Yu P; Prokopov, P A; Ponomarenko, A G
2017-01-01
Dynamic interaction of super-sonic counter-streaming plasmas moving in dipole magnetic dipole is studied in laboratory experiment. First, a quasi-stationary flow is produced by plasma gun which forms a magnetosphere around the magnetic dipole. Second, explosive plasma expanding from inner dipole region outward is launch by laser beams focused at the surface of the dipole cover. Laser plasma is energetic enough to disrupt magnetic field and to sweep through the background plasma for large distances. Probe measurements showed that far from the initially formed magnetosphere laser plasma carries within itself a magnetic field of the same direction but order of magnitude larger in value than the vacuum dipole field at considered distances. Because no compression of magnetic field at the front of laser plasma was observed, the realized interaction is different from previous experiments and theoretical models of laser plasma expansion into uniform magnetized background. It was deduced based on the obtained data that laser plasma while expanding through inner magnetosphere picks up a magnetized shell formed by background plasma and carries it for large distances beyond previously existing magnetosphere. (paper)
7. Stellar Spectral Classification with Locality Preserving Projections ...
With the help of computer tools and algorithms, automatic stellar spectral classification has become an area of current interest. The process of stellar spectral classification mainly includes two steps: dimension reduction and classification. As a popular dimensionality reduction technique, Principal Component Analysis (PCA) ...
8. Enhanced-confinement class of stellarators
International Nuclear Information System (INIS)
Mynick, H.E.; Chu, T.K.; Boozer, A.H.
1981-08-01
A class of stellarators has been found in which the transport is reduced by an order of magnitude from transport in conventional stellarators, by localizing the helical ripple to the inside of the torus. The reduction is observed in numerical experiments and explained theoretically
9. Theories for convection in stellar atmospheres
International Nuclear Information System (INIS)
Nordlund, Aa.
1976-02-01
A discussion of the fundamental differences between laboratory convection in a stellar atmosphere is presented. The shortcomings of laterally homogeneous model atmospheres are analysed, and the extent to which these shortcoming are avoided in the two-component representation is discussed. Finally a qualitative discussion on the scaling properties of stellar granulation is presented. (Auth.)
10. Structure of stellar hydroxyl masers
International Nuclear Information System (INIS)
Reid, M.J.; Muhleman, D.O.; Moran, J.M.; Johnston, K.J.; Schwartz, P.R.
1977-01-01
This paper presents the results of two spectral-line very long baseline (VLB) interferometric experiments on stellar OH masers. These masers are usually associated with long-period variable stars, and exhibit a characteristic double-peaked 1612 MHz OH spectrum. The sources IRC +10011, R Aql, and U Ori were carefully studied in order to determine the spatial structure of their masers. Maser components in these sources exhibited a complex structure which can be interpreted in terms of ''core-halo'' models. For these sources, the emission at any velocity appears to originate from a small (approximately-less-than0.''03) region of brightness approximately-greater-than10 9 K, and from a large (approximately-greater-than0.''5) region of brightness approximately-less-than10 8 K. In IRC+10011, ''core'' components in the two OH peaks probably are separated by less than the apparent size of the ''halos.'' A map of the low-velocity emission of U Ori with a resolution of 0.''01 indicates that the ''cores'' are distributed over a region of only 0.''2. This region is smaller than the apparent sizes of the ''halos.'' Other sources surveyed to determine apparent maser sizes include IRC+50137, OH 1821--12, OH 1837--05, OH 26.5+0.6, W43 A, and VX Sgr at 1612 MHz; and W Hya, R Aql, and IRC--10529 at 1667 MHz. The results of all VLB observations of 1612 MHz stellar OH masers are summarized.The apparent sizes of the strongest components (''halos'') of stellar OH masers typically are approximately-greater-than0.''5, corresponding to linear dimensions of approximately-greater-than3 x 10 15 cm. These surprisingly large sizes imply brightness temperatures much lower than those observed in most other types of astronomical masers. The large sizes rule out models of the 1612 MHz OH masers that require contracting or rotating circumstellar envelopes to explain the double-peaked OH spectra, or that try to explain the apparent maser sizes in terms of interstellar or interplanetary scattering
11. Artificial Neural Network L* from different magnetospheric field models
Science.gov (United States)
Yu, Y.; Koller, J.; Zaharia, S. G.; Jordanova, V. K.
2011-12-01
The third adiabatic invariant L* plays an important role in modeling and understanding the radiation belt dynamics. The popular way to numerically obtain the L* value follows the recipe described by Roederer [1970], which is, however, slow and computational expensive. This work focuses on a new technique, which can compute the L* value in microseconds without losing much accuracy: artificial neural networks. Since L* is related to the magnetic flux enclosed by a particle drift shell, global magnetic field information needed to trace the drift shell is required. A series of currently popular empirical magnetic field models are applied to create the L* data pool using 1 million data samples which are randomly selected within a solar cycle and within the global magnetosphere. The networks, trained from the above L* data pool, can thereby be used for fairly efficient L* calculation given input parameters valid within the trained temporal and spatial range. Besides the empirical magnetospheric models, a physics-based self-consistent inner magnetosphere model (RAM-SCB) developed at LANL is also utilized to calculate L* values and then to train the L* neural network. This model better predicts the magnetospheric configuration and therefore can significantly improve the L*. The above neural network L* technique will enable, for the first time, comprehensive solar-cycle long studies of radiation belt processes. However, neural networks trained from different magnetic field models can result in different L* values, which could cause mis-interpretation of radiation belt dynamics, such as where the source of the radiation belt charged particle is and which mechanism is dominant in accelerating the particles. Such a fact calls for attention to cautiously choose a magnetospheric field model for the L* calculation.
12. Wisconsin torsatron/stellarator program, FY 1989
International Nuclear Information System (INIS)
Shohet, J.L.; Anderson, D.T.; Anderson, F.S.B.; Talmadge, J.N.
1988-07-01
This proposal documents recent activities within the University of Wisconsin-Madison Torsatron/Stellarator Laboratory and presents plans for future research activities for a three year period. Research efforts have focused on fundamental stellarator physics issues through experimental investigations on the Interchangeable Module Stellarator (IMS) and the Proto-Cleo Stellarator. Theoretical activities and studies of new configurations are being undertaken to support and broaden the experimental program. Experimental research at the Torsatron Stellarator Laboratory has been primarily concerned with effects induced through electron-cyclotron resonant frequency plasma production and heating in the IMS device. Plasma electric fields have been shown to play a major role in particle transport and confinement in IMS. ECRF heating at 6 kG has produced electron tail populations in agreement with Monte-Carlo models. Electric and magnetic fields have been shown to alter the particle flows to the IMS modular divertors. 48 refs
13. Astrospheres and Solar-like Stellar Winds
Directory of Open Access Journals (Sweden)
Wood Brian E.
2004-07-01
Full Text Available Stellar analogs for the solar wind have proven to be frustratingly difficult to detect directly. However, these stellar winds can be studied indirectly by observing the interaction regions carved out by the collisions between these winds and the interstellar medium (ISM. These interaction regions are called "astrospheres", analogous to the "heliosphere" surrounding the Sun. The heliosphere and astrospheres contain a population of hydrogen heated by charge exchange processes that can produce enough H I Ly alpha absorption to be detectable in UV spectra of nearby stars from the Hubble Space Telescope (HST. The amount of astrospheric absorption is a diagnostic for the strength of the stellar wind, so these observations have provided the first measurements of solar-like stellar winds. Results from these stellar wind studies and their implications for our understanding of the solar wind are reviewed here. Of particular interest are results concerning the past history of the solar wind and its impact on planetary atmospheres.
14. The aurora and the magnetosphere - The Chapman Memorial Lecture. [dynamo theory development, 1600-present
Science.gov (United States)
Akasofu, S.-I.
1974-01-01
Review of recent progress in magnetospheric physics, in particular, in understanding the magnetospheric substorm. It is shown that a number of magnetospheric phenomena can now be understood by viewing the solar wind-magnetosphere interaction as an MHD dynamo; auroral phenomena are powered by the dynamo. Also, magnetospheric responses to variations of the north-south and east-west components of the interplanetary magnetic field have been identified. The magnetospheric substorm is entirely different from the responses of the magnetosphere to the southward component of the interplanetary magnetic field. It may be associated with the formation of a neutral line within the plasma sheet and with an enhanced reconnection along the line. A number of substorm-associated phenomena can be understood by noting that the new neutral line formation is caused by a short-circuiting of a part of the magnetotail current.
15. Stellarmak a hybrid stellarator: Spheromak
International Nuclear Information System (INIS)
Hartman, C.W.
1980-01-01
This paper discusses hybridization of modified Stellarator-like transform windings (T-windings) with a Spheromak or Field-Reversed-Mirror configuration. This configuration, Stellarmak, retains the important topological advantage of the Spheromak or FRM of having no plasma linking conductors or blankets. The T-windings provide rotational transformation in toroidal angle of the outer poloidal field lines, in effect creating a reversed B/sub Toroidal/ Spheromak or adding average B/sub T/ to the FRM producing higher shear, increased limiting β, and possibly greater stability to kinks and tilt. The presence of field ripple in the toroidal direction may be sufficient to inhibit cancellation of directed ion current by electron drag to allow steady state operation with the toroidal as well as poloidal current maintained by neutral beams
16. Stellar Equilibrium in Semiclassical Gravity.
Science.gov (United States)
Carballo-Rubio, Raúl
2018-02-09
The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its backreaction on the dynamics of spacetime are practically nonexistent outside of the specific context of homogeneous cosmologies. Building on previous results of quantum field theory in curved spacetimes, in this Letter we first derive the semiclassical equations of stellar equilibrium in the s-wave Polyakov approximation. It is highlighted that incorporating the polarization of the quantum vacuum leads to a generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite the complexity of the resulting field equations, it is possible to find exact solutions. Aside from being the first known exact solutions that describe relativistic stars including the nonperturbative backreaction of semiclassical effects, these are identified as a nontrivial combination of the black star and gravastar proposals.
17. On rapid rotation in stellarators
International Nuclear Information System (INIS)
Helander, Per
2008-01-01
The conditions under which rapid plasma rotation may occur in a three-dimensional magnetic field, such as that of a stellarator, are investigated. Rotation velocities comparable to the ion thermal speed are found to be attainable only in magnetic fields which are approximately isometric. In an isometric magnetic field the dependence of the magnetic field strength B on the arc length l along the field is the same for all field lines on each flux surface ψ. Only in fields where the departure from exact isometry, B=B(ψ,l), is of the order of the ion gyroradius divided by the macroscopic length scale are rotation speeds comparable to the ion thermal speed possible. Moreover, it is shown that the rotation must be in the direction of the vector ∇ψx∇B. (author)
18. Magnetohydodynamics stability of compact stellarators
International Nuclear Information System (INIS)
Fu, G.Y.; Ku, L.P.; Cooper, W.A.; Hirshman, S.H.
2000-01-01
Recent stability results of external kink modes and vertical modes in compact stellarators are presented. The vertical mode is found to be stabilized by externally generated poloidal flux. A simple stability criterion is derived in the limit of large aspect ratio and constant current density. For a wall at infinite distance from the plasma, the amount of external flux needed for stabilization is given by Fi = (k2 minus k)=(k2 + 1), where k is the axisymmetric elongation and Fi is the fraction of the external rotational transform. A systematic parameter study shows that the external kink mode in QAS can be stabilized at high beta (approximately 5%) without a conducting wall by magnetic shear via 3D shaping. It is found that external kinks are driven by both parallel current and pressure gradient. The pressure contributes significantly to the overall drive through the curvature term and the Pfirsch-Schluter current
19. NEMO: A Stellar Dynamics Toolbox
Science.gov (United States)
Barnes, Joshua; Hut, Piet; Teuben, Peter
2010-10-01
NEMO is an extendible Stellar Dynamics Toolbox, following an Open-Source Software model. It has various programs to create, integrate, analyze and visualize N-body and SPH like systems, following the pipe and filter architecture. In addition there are various tools to operate on images, tables and orbits, including FITS files to export/import to/from other astronomical data reduction packages. A large growing fraction of NEMO has been contributed by a growing list of authors. The source code consist of a little over 4000 files and a little under 1,000,000 lines of code and documentation, mostly C, and some C++ and Fortran. NEMO development started in 1986 in Princeton (USA) by Barnes, Hut and Teuben. See also ZENO (ascl:1102.027) for the version that Barnes maintains.
20. Neoclassical transport in stellarators - a comparison of conventional stellarator/torsatrons with the advanced stellarator, Wendelstein 7X
Energy Technology Data Exchange (ETDEWEB)
Beidler, C D [Max-Planck-Institut fuer Plasmaphysik, Garching (Germany)
1991-01-01
A general expression for the magnitude of a stellarator's magnetic field, in terms of a Fourier decomposition, is too complicated to lend itself easily to analytic transport calculations. The great majority of stellarator-type devices, however, may be accurately described if one retains only those harmonics with m=0 and m=1. In the long-mean-free-path regime an analytical approximation to the particle's bounce-averaged kinetic equation can then be found. Using a numerical solution of this equation, it is possible to calculate the particle and heat fluxes due to helical-ripple transport in stellarators throughout the entire long-mean-free-path regime. 3 figs.
1. Hydrodynamics and stellar winds an introduction
CERN Document Server
Maciel, Walter J
2014-01-01
Stellar winds are a common phenomenon in the life of stars, from the dwarfs like the Sun to the red giants and hot supergiants, constituting one of the basic aspects of modern astrophysics. Stellar winds are a hydrodynamic phenomenon in which circumstellar gases expand towards the interstellar medium. This book presents an elementary introduction to the fundamentals of hydrodynamics with an application to the study of stellar winds. The principles of hydrodynamics have many other applications, so that the book can be used as an introduction to hydrodynamics for students of physics, astrophysics and other related areas.
2. Ultraviolet photometry of stellar populations in galaxies
International Nuclear Information System (INIS)
Deharveng, J.M.
1981-01-01
The UV flux of stellar populations, which is essentially emitted by young stars, conveys information on the process of star formation and its recent history. However, the evaluation of the flux arising from the young stellar component may be difficult. In the case of late type galaxies it is hampered by the extinction and the effect of scattered stellar radiation. In the case of early type galaxies, the star formation, if any, has to be disentangled from the contribution of hot evolved stars and of a possible 'active' phenomenon. A review of observations and results relevant two cases is presented [fr
3. Helical post stellarator. Part 1: Vacuum configuration
International Nuclear Information System (INIS)
Moroz, P.E.
1997-08-01
Results on a novel type of stellarator configuration, the Helical Post Stellarator (HPS), are presented. This configuration is different significantly from all previously known stellarators due to its unique geometrical characteristics and unique physical properties. Among those are: the magnetic field has only one toroidal period (M = 1), the plasma has an extremely low aspect ratio, A ∼ 1, and the variation of the magnetic field, B, along field lines features a helical ripple on the inside of the torus. Among the main advantages of a HPS for a fusion program are extremely compact, modular, and simple design compatible with significant rotational transform, large plasma volume, and improved particle transport characteristics
4. Electron-positron plasma generation in a pulsar magnetosphere
International Nuclear Information System (INIS)
Gurevich, A.V.; Istomin, Ya.N.
1985-01-01
The generation of an electron-positron plasma in vacuum (vacuum ''breakdown'') in the presence of an inhomogeneous electric field and strong curvilinear magnetic field is considered. A situation of this type may occur in the magnetosphere of a rotating neutron star. A general set of kinetic equations for electrons, positrons and γ quanta in a curvilinear magnetic field is derived by taking into account electron-positron pair production and emission of curvicur and synchrotron photons. The conditions for appearance of ''breakdown'' are determined and the threshold value of the elec tric field discontinuity at the surface of the star is found. Multiplication of particles in the magnetosphere is investigated and the electron, positron and γ quantum distribution functions are found. The extinction limit of pulsars is determined. The theory is shown to be in accordance with the observation results
5. Acceleration processes in the magnetospheric plasma: a review
Energy Technology Data Exchange (ETDEWEB)
Nishida, A [Tokyo Univ. (Japan). Inst. of Space and Aeronautical Science
1975-01-01
Our present knowledge on the acceleration process in the magnetospheric plasma is reviewed and major problems are summarized. Acceleration processes can be classified into three categories. First, acceleration can be made by the reconnection process in the magnetotail. The occurrence of reconnection during substorm expansion phases has been confirmed, but details of the energy conversion mechanism need be clarified. Second, acceleration by the electric potential drop along magnetic field lines has been strongly suggested from observations of precipitating particles. The position and structure of the potential layer, however, have not been clarified, and theoretical understanding of the process is still in the early stage of development. Third, particles can be adiabatically heated as they are driven toward the earth in the course of their convective motion. Spatial structure and dynamical development of the auroral precipitation pattern represent both challenge and clue to the understanding of the magnetospheric acceleration process.
6. Magnetospheres of accreting compact objects in binary systems
International Nuclear Information System (INIS)
Aly, J.J.
1985-09-01
Bright pulsating X-ray sources (X-ray pulsars, AM Her stars,...) have been identified as strongly magnetized compact objects accreting matter from a binary companion. We give here a summary of some of the work which has been recently done to try to understand the interaction between the magnetic field of the compact object and the matter around. We examine in turn the models describing the interaction of the field with: i) a spherically symmetric accretion flow; ii) a thin keplerian accretion disk; iii) the companion itself. In all these cases, we pay particular attention to the following problems: i) how the external plasma interacting with the magnetosphere can get mixed with the field; ii) by which mechanism the magnetic field controls the mass-momentum-energy exchanges between the two stars. In conclusion, we compare the magnetosphere of an accreting compact object with that one of a planet [fr
7. MESSENGER observations of magnetic reconnection in Mercury's magnetosphere.
Science.gov (United States)
Slavin, James A; Acuña, Mario H; Anderson, Brian J; Baker, Daniel N; Benna, Mehdi; Boardsen, Scott A; Gloeckler, George; Gold, Robert E; Ho, George C; Korth, Haje; Krimigis, Stamatios M; McNutt, Ralph L; Raines, Jim M; Sarantos, Menelaos; Schriver, David; Solomon, Sean C; Trávnícek, Pavel; Zurbuchen, Thomas H
2009-05-01
Solar wind energy transfer to planetary magnetospheres and ionospheres is controlled by magnetic reconnection, a process that determines the degree of connectivity between the interplanetary magnetic field (IMF) and a planet's magnetic field. During MESSENGER's second flyby of Mercury, a steady southward IMF was observed and the magnetopause was threaded by a strong magnetic field, indicating a reconnection rate ~10 times that typical at Earth. Moreover, a large flux transfer event was observed in the magnetosheath, and a plasmoid and multiple traveling compression regions were observed in Mercury's magnetotail, all products of reconnection. These observations indicate that Mercury's magnetosphere is much more responsive to IMF direction and dominated by the effects of reconnection than that of Earth or the other magnetized planets.
8. Massive-Star Magnetospheres: Now in 3-D!
Science.gov (United States)
Townsend, Richard
Magnetic fields are unexpected in massive stars, due to the absence of a dynamo convection zone beneath their surface layers. Nevertheless, kilogauss-strength, ordered fields were detected in a small subset of these stars over three decades ago, and the intervening years have witnessed the steady expansion of this subset. A distinctive feature of magnetic massive stars is that they harbor magnetospheres --- circumstellar environments where the magnetic field interacts strongly with the star's radiation-driven wind, confining it and channelling it into energetic shocks. A wide range of observational signatures are associated with these magnetospheres, in diagnostics ranging from X-rays all the way through to radio emission. Moreover, these magnetospheres can play an important role in massive-star evolution, by amplifying angular momentum loss in the wind. Recent progress in understanding massive-star magnetospheres has largely been driven by magnetohydrodynamical (MHD) simulations. However, these have been restricted to two- dimensional axisymmetric configurations, with three-dimensional configurations possible only in certain special cases. These restrictions are limiting further progress; we therefore propose to develop completely general three-dimensional models for the magnetospheres of massive stars, on the one hand to understand their observational properties and exploit them as plasma-physics laboratories, and on the other to gain a comprehensive understanding of how they influence the evolution of their host star. For weak- and intermediate-field stars, the models will be based on 3-D MHD simulations using a modified version of the ZEUS-MP code. For strong-field stars, we will extend our existing Rigid Field Hydrodynamics (RFHD) code to handle completely arbitrary field topologies. To explore a putative 'photoionization-moderated mass loss' mechanism for massive-star magnetospheres, we will also further develop a photoionization code we have recently
9. The force-free magnetosphere of a rotating black hole
Directory of Open Access Journals (Sweden)
Contopoulos Ioannis
2013-12-01
Full Text Available We explore the analogy with pulsars and investigate the structure of the force-free magnetosphere around a Kerr black hole. We propose that the source of the black hole magnetic field is the Poynting-Robertson effect on the plasma electrons at the inner edge of the surrounding accretion disk, the so called Cosmic Battery. The magnetospheric solution is characterized by the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem, the inner ‘light surface’ located inside the ergosphere, and the outer ‘light surface’ which is the generalization of the pulsar light cylinder. The black hole forms a relativistic jet only if it is surrounded by a thick disk and/or extended disk outflows.
10. Enhanced ionosphere-magnetosphere data from the DMSP satellites
International Nuclear Information System (INIS)
Rich, F.J.; Hardy, D.A.; Gussenhoven, M.S.
1985-01-01
The satellites of the Defense Meteorological Satellite Program (DMSP) represent a series of low-altitude (835 km) polar-orbiting satellites. Their primary objective is related to the observation of the tropospheric weather with a high-resolution white light and infrared imaging system. It is also possible to make images of auroras. On a daily basis, information about auroras is used to assist various communication systems which are affected by the ionospheric disturbances associated with auroras. In the past few years, there have been several improvements in the ionospheric monitoring instrumentation. Since the high-latitude ionosphere is connected to the magnetosphere, the DMSP data are used to monitor magnetospheric processes. The instrumentation of the DMSP satellites is discussed, taking into account the data provided by them. 7 references
11. New Understanding of Mercury's Magnetosphere from MESSENGER'S First Flyby
Science.gov (United States)
Slavin, James A.; Acuna, Mario H.; Anderson, Brian J.; Baker, Daniel N.; Benna, Mehdi; Gloeckler, George; Gold, Robert E.; Ho, George C.; Killen, M.; Korth, Haje;
2008-01-01
Observations by the MESSENGER spacecraft on 14 January 2008 have revealed new features of the solar system's smallest planetary magnetosphere. The interplanetary magnetic field orientation was unfavorable for large inputs of energy from the solar wind and no evidence of magnetic substorms, internal magnetic reconnection, or energetic particle acceleration was detected. Large-scale rotations of the magnetic field were measured along the dusk flank of the magnetosphere and ultra-tow frequency waves were frequently observed beginning near closest approach. Outbound the spacecraft encountered two current-sheet boundaries across which the magnetic field intensity decreased in a step-like manner. The outer current sheet is the magnetopause boundary. The inner current sheet is similar in structure, but weaker and -1000 km closer to the planet. Between these two current sheets the magnetic field intensity is depressed by the diamagnetic effect of planetary ions created by the photo-ionization of Mercury's exosphere.
12. Science.gov (United States)
Slavin, James A.; Anderson, Brian J.; Baker, Daniel N.; Benna, Mehdi; Johnson, Catherine L.; Gloeckler, George; Killen, Rosemary M.; Krimigis, Stamatios M.; McClintock, William; McNutt, Ralph L., Jr.;
2009-01-01
MESSENGER's third flyby of Mercury en route to orbit insertion about the innermost planet took place on 29 September 2009. The earlier 14 January and 6 October 2008 encounters revealed that Mercury's magnetic field is highly dipolar and stable over the 35 years since its discovery by Mariner 10; that a structured, temporally variable exosphere extends to great altitudes on the dayside and forms a long tail in the anti-sunward direction; a cloud of planetary ions encompasses the magnetosphere from the dayside bow shock to the downstream magnetosheath and magnetotail; and that the magnetosphere undergoes extremely intense magnetic reconnect ion in response to variations in the interplanetary magnetic field. Here we report on new results derived from observations from MESSENGER's Mercury Atmospheric and Surface Composition Spectrometer (MASCS), Magnetometer (MAG), and Energetic Particle and Plasma Spectrometer (EPPS) taken during the third flyby.
13. CERN Document Server
Dorman, Lev
2009-01-01
This monograph describes the behaviour of cosmic rays in the magnetosphere of the Earth and of some other planets. Recently this has become an important topic both theoretically, because it is closely connected with the physics of the Earth’s magnetosphere, and practically, since cosmic rays determine a significant part of space weather effects on satellites and aircraft. The book contains eight chapters, dealing with – The history of the discovery of geomagnetic effects caused by cosmic rays and their importance for the determination of the nature of cosmic rays or gamma rays – The first explanations of geomagnetic effects within the framework of the dipole approximation of the Earth’s magnetic field – Trajectory computations of cutoff rigidities, transmittance functions, asymptotic directions, and acceptance cones in the real geomagnetic field taking into account higher harmonics – Cosmic ray latitude-longitude surveys on ships, trains, tracks, planes, balloons and satellites for determining the...
14. Magnetospheric pulsations: Models and observations of compressional waves
International Nuclear Information System (INIS)
Zhu, Xiaoming.
1989-01-01
The first part of the dissertation models ultralow frequency (ULF) waves in a simplified geometry in order to understand the physics of the mode coupling between the compressional and shear Alfven waves in an inhomogeneous magnetized plasma. Wave mode coupling occurs when a field line resonant frequency (defined by the shear Alfven mode) matches the global mode frequency (defined by the compressional mode). Large wave amplitudes occur near the resonant field line. Although the wave amplitude of the global mode is small away from resonant field lines, significant wave energy is stored in the wave mode due to its large scale nature. It serves as a reservoir to continuously feed energy to resonant field lines. This mechanism may explain why some field line resonances can last for times longer than that predicted from the ionospheric Joule dissipation. A nonmonotonic Alfven velocity divides the magnetosphere into two or more cavities by the local maxima of the Alfven velocity. The global mode is typically localized in one of the cavities except at some preferred frequencies, the global mode can extend through more than one cavity. This may explain ULF wave excitations in the low latitude magnetosphere. The second part of the dissertation is devoted to study compressional waves in the outer magnetosphere using magnetic field and plasma data. Statistical information on the distribution of compressional Pc 5 waves in the outer magnetosphere is obtained. Large amplitude, long period compressional Pc 5 pulsations are found very common near the magnetic equator. They are polarized mainly in a meridian plane with comparable compressional and transverse amplitudes. Close correlation between compressional wave amplitude and plasma β is also found. Several case studies show that compressional waves are quenched in the region where β < 1
15. Effects of Energetic Ion Outflow on Magnetospheric Dynamics
Science.gov (United States)
Kistler, L. M.; Mouikis, C.; Lund, E. J.; Menz, A.; Nowrouzi, N.
2016-12-01
There are two dominant regions of energetic ion outflow: the nightside auroral region and the dayside cusp. Processes in these regions can accelerate ions up to keV energies. Outflow from the nightside has direct access to the plasma sheet, while outflow from the cusp is convected over the polar cap and into the lobes. The cusp population can enter the plasma sheet from the lobe, with higher energy ions entering further down the tail than lower energy ions. During storm times, the O+ enhanced plasma sheet population is convected into the inner magnetosphere. The plasma that does not get trapped in the inner magnetosphere convects to the magnetopause where reconnection is taking place. An enhanced O+ population can change the plasma mass density, which may have the effect of decreasing the reconnection rate. In addition O+ has a larger gyroradius than H+ at the same velocity or energy. Because of this, there are larger regions where the O+ is demagnetized, which can lead to larger acceleration because the O+ can move farther in the direction of the electric field. In this talk we will review results from Cluster, Van Allen Probes, and MMS, on how outflow from the two locations affects magnetospheric dynamics. We will discuss whether enhanced O+ from either population has an effect on the reconnection rate in the tail or at the magnetopause. We will discuss how the two populations impact the inner magnetosphere during storm times. And finally, we will discuss whether either population plays a role in triggering substorms, particularly during sawtooth events.
16. Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
Directory of Open Access Journals (Sweden)
V. A. Sergeev
2015-12-01
Full Text Available Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms spacecraft during February–March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6–9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites to the equatorial magnetosphere (to find the projected isotropy boundary, PIB and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1–2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32, with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.
17. Magnetospheric signature of some F layer positive storms
International Nuclear Information System (INIS)
Miller, N.J.; Mayr, H.G.; Grebowsky, J.M.; Harris, I.; Tulunay, Y.K.
1981-01-01
Calculations using a self-consistent model of the global thermosphere-ionosphere system perturbed by high-latitude thermospheric heating show that the resultant electron density disturbances within the mid-latitude F layer can propagate upward along magnetic field lines to the equator. The F layer disturbances described by the model calculations correspond to the evolution of enhancements or reductions in electron density that is called the positive or negative phase of an F layer storm. We deduce that the positive phase of dayside F layer storms is initiated when high-latitude thermospheric heating generates equatorward winds. These winds raise the mid-latitude F layer along the geomagnetic field B through momentum transfer from neutral atoms to F layer ons that pull electrons with them. For Lapprox.3 or less the upward movement of ionospheric plasma results in ionization increases at all altitudes along B from the F2 maximum to the equator. An increase in the average magnitude of the equatorial dawn-dusk magnetospheric electric field retards the dayside development of a positive storm phase by drifting plasma away from mid-latitude field lines along which the electron density is increasing. During an F layer storm in June 1972, instruments on Explorer 45 and Ariel 4 detected dayside electron density enhancements simultaneously at 550 km over mid-latitudes and near the equatorial plane in the magnetosphere. These in situ measurements support the model prediction that disturbances in the magnetospheric plasma near the equator can arise through interactions occuring at lower altitudes along a magnetic field line. Our study demonstrates that some storm time enhancements of dayside magnetospheric plasma near Lapprox.2--3 may be signatures of the positive phase of an F layer storm
18. MAVEN Observations of Magnetic Reconnection on the Dayside Martian Magnetosphere
Science.gov (United States)
DiBraccio, Gina A.; Espley, Jared R.; Connerney, John E. P.; Brain, David A.; Halekas, Jasper S.; Mitchell, David L.; Harada, Yuki; Hara, Takuya
2015-04-01
The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission offers a unique opportunity to investigate the complex solar wind-planetary interaction at Mars. The Martian magnetosphere is formed as the interplanetary magnetic field (IMF) drapes around the planet's ionosphere and localized crustal magnetic fields. As the solar wind interacts with this induced magnetosphere, magnetic reconnection can occur at any location where a magnetic shear is present. Reconnection between the IMF and the induced and crustal fields facilitates a direct plasma exchange between the solar wind and the Martian ionosphere. Here we address the occurrence of magnetic reconnection on the dayside magnetosphere of Mars using MAVEN magnetic field and plasma data. When reconnection occurs on the dayside, a non-zero magnetic field component normal to the obstacle, B_N, will result. Using minimum variance analysis, we measure BN by transforming Magnetometer data into boundary-normal coordinates. Selected events are then further examined to identify plasma heating and energization, in the form of Alfvénic outflow jets, using Solar Wind Ion Analyzer measurements. Additionally, the topology of the crustal fields is validated from electron pitch angle distributions provided by the Solar Wind Electron Analyzer. To understand which parameters are responsible for the onset of reconnection, we test the dependency of the dimensionless reconnection rate, calculated from BN measurements, on magnetic field shear angle and plasma beta (the ratio of plasma pressure to magnetic pressure). We assess the global impact of reconnection on Mars' induced magnetosphere by combining analytical models with MAVEN observations to predict the regions where reconnection may occur. Using this approach we examine how IMF orientation and magnetosheath parameters affect reconnection on a global scale. With the aid of analytical models we are able to assess the role of reconnection on a global scale to better understand which
19. Stellar X-Ray Polarimetry
Science.gov (United States)
Swank, J.
2011-01-01
Most of the stellar end-state black holes, pulsars, and white dwarfs that are X-ray sources should have polarized X-ray fluxes. The degree will depend on the relative contributions of the unresolved structures. Fluxes from accretion disks and accretion disk corona may be polarized by scattering. Beams and jets may have contributions of polarized emission in strong magnetic fields. The Gravity and Extreme Magnetism Small Explorer (GEMS) will study the effects on polarization of strong gravity of black holes and strong magnetism of neutron stars. Some part of the flux from compact stars accreting from companion stars has been reflected from the companion, its wind, or accretion streams. Polarization of this component is a potential tool for studying the structure of the gas in these binary systems. Polarization due to scattering can also be present in X-ray emission from white dwarf binaries and binary normal stars such as RS CVn stars and colliding wind sources like Eta Car. Normal late type stars may have polarized flux from coronal flares. But X-ray polarization sensitivity is not at the level needed for single early type stars.
20. Stellar recipes for axion hunters
Energy Technology Data Exchange (ETDEWEB)
Giannotti, Maurizio [Physical Sciences, Barry University, 11300 NE 2nd Ave., Miami Shores, FL 33161 (United States); Irastorza, Igor G.; Redondo, Javier [Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009, Zaragoza (Spain); Ringwald, Andreas; Saikawa, Ken' ichi, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Theory Group, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg (Germany)
2017-10-01
There are a number of observational hints from astrophysics which point to the existence of stellar energy losses beyond the ones accounted for by neutrino emission. These excessive energy losses may be explained by the existence of a new sub-keV mass pseudoscalar Nambu-Goldstone boson with tiny couplings to photons, electrons, and nucleons. An attractive possibility is to identify this particle with the axion—the hypothetical pseudo Nambu-Goldstone boson predicted by the Peccei-Quinn solution to the strong CP problem. We explore this possibility in terms of a DFSZ-type axion and of a KSVZ-type axion/majoron, respectively. Both models allow a good global fit to the data, prefering an axion mass around 10 meV. We show that future axion experiments—the fifth force experiment ARIADNE and the helioscope IAXO—can attack the preferred mass range from the lower and higher end, respectively. An axion in this mass range can also be the main constituent of dark matter.
1. Stellar recipes for axion hunters
Energy Technology Data Exchange (ETDEWEB)
Giannotti, Maurizio [Barry Univ., Miami Shores, FL (United States). Physical Sciences; Irastorza, Igor G. [Zaragoza Univ. (Spain). Dept. de Fisica Teorica; Redondo, Javier [Zaragoza Univ. (Spain). Dept. de Fisica Teorica; Max-Planck-Institut fuer Physik, Muenchen (Germany); Ringwald, Andreas; Saikawa, Ken' ichi [DESY, Hamburg (Germany). Theory Group
2017-08-15
There are a number of observational hints from astrophysics which point to the existence of stellar energy losses beyond the ones accounted for by neutrino emission. These excessive energy losses may be explained by the existence of a new sub-keV mass pseudoscalar Nambu-Goldstone boson with tiny couplings to photons, electrons, and nucleons. An attractive possibility is to identify this particle with the axion - the hypothetical pseudo Nambu-Goldstone boson predicted by the Peccei-Quinn solution to the strong CP problem. We explore this possibility in terms of a DFSZ-type axion and of a KSVZ-type axion/majoron, respectively. Both models allow a good global fit to the data, prefering an axion mass around 10 meV. We show that future axion experiments - the fifth force experiment ARIADNE and the helioscope IAXO - can attack the preferred mass range from the lower and higher end, respectively. An axion in this mass range can also be the main constituent of dark matter.
2. Stellar recipes for axion hunters
International Nuclear Information System (INIS)
Giannotti, Maurizio; Ringwald, Andreas; Saikawa, Ken'ichi
2017-08-01
There are a number of observational hints from astrophysics which point to the existence of stellar energy losses beyond the ones accounted for by neutrino emission. These excessive energy losses may be explained by the existence of a new sub-keV mass pseudoscalar Nambu-Goldstone boson with tiny couplings to photons, electrons, and nucleons. An attractive possibility is to identify this particle with the axion - the hypothetical pseudo Nambu-Goldstone boson predicted by the Peccei-Quinn solution to the strong CP problem. We explore this possibility in terms of a DFSZ-type axion and of a KSVZ-type axion/majoron, respectively. Both models allow a good global fit to the data, prefering an axion mass around 10 meV. We show that future axion experiments - the fifth force experiment ARIADNE and the helioscope IAXO - can attack the preferred mass range from the lower and higher end, respectively. An axion in this mass range can also be the main constituent of dark matter.
3. Stellar core collapse and supernova
International Nuclear Information System (INIS)
Wilson, J.R.; Mayle, R.; Woosley, S.E.; Weaver, T.
1985-04-01
Massive stars that end their stable evolution as their iron cores collapse to a neutron star or black hole long been considered good candidates for producing Type II supernovae. For many years the outward propagation of the shock wave produced by the bounce of these iron cores has been studied as a possible mechanism for the explosion. For the most part, the results of these studies have not been particularly encouraging, except, perhaps, in the case of very low mass iron cores or very soft nuclear equations of state. The shock stalls, overwhelmed by photodisintegration and neutrino losses, and the star does not explode. More recently, slow late time heating of the envelope of the incipient neutron star has been found to be capable of rejuvenating the stalled shock and producing an explosion after all. The present paper discusses this late time heating and presents results from numerical calculations of the evolution, core collapse, and subsequent explosion of a number of recent stellar models. For the first time they all, except perhaps the most massive, explode with reasonable choices of input physics. 39 refs., 17 figs., 1 tab
4. Stellar convection and dynamo theory
Energy Technology Data Exchange (ETDEWEB)
Jennings, R L
1989-10-01
In considering the large scale stellar convection problem the outer layers of a star are modelled as two co-rotating plane layers coupled at a fluid/fluid interface. Heating from below causes only the upper fluid to convect, although this convection can penetrate into the lower fluid. Stability analysis is then used to find the most unstable mode of convection. With parameters appropriate to the Sun the most unstable mode is steady convection in thin cells (aspect ratio {approx equal} 0.2) filling the convection zone. There is negligible vertical motion in the lower fluid, but considerable thermal penetration, and a large jump in helicity at the interface, which has implications for dynamo theory. An {alpha}{omega} dynamo is investigated in isolation from the convection problem. Complexity is included by allowing both latitudinal and time dependence in the magnetic fields. The nonlinear dynamics of the resulting partial differential equations are analysed in considerable detail. On varying the main control parameter D (the dynamo number), many transitions of behaviour are found involving many forms of time dependence, but not chaos. Further, solutions which break equatorial symmetry are common and provide a theoretical explanation of solar observations which have this symmetry. Overall the behaviour was more complicated than expected. In particular, there were multiple stable solutions at fixed D, meaning that similar stars can have very different magnetic patterns, depending upon their history. (author).
5. Collapsing stellar cores and supernovae
Energy Technology Data Exchange (ETDEWEB)
Epstein, R J [Nordisk Inst. for Teoretisk Atomfysik, Copenhagen (Denmark); Noorgaard, H [Nordisk Inst. for Teoretisk Atomfysik, Copenhagen (Denmark); Chicago Univ., IL (USA). Enrico Fermi Inst.); Bond, J R [Niels Bohr Institutet, Copenhagen (Denmark); California Inst. of Tech., Pasadena (USA). W.K. Kellogg Radiation Lab.)
1979-05-01
The evolution of a stellar core is studied during its final quasi-hydrostatic contraction. The core structure and the (poorly known) properties of neutron rich matter are parametrized to include most plausible cases. It is found that the density-temperature trajectory of the material in the central part of the core (the core-center) is insensitive to nearly all reasonable parameter variations. The central density at the onset of the dynamic phase of the collapse (when the core-center begins to fall away from the rest of the star) and the fraction of the emitted neutrinos which are trapped in the collapsing core-center depend quite sensitively on the properties of neutron rich matter. We estimate that the amount of energy Ecm which is imparted to the core-mantle by the neutrinos which escape from the imploded core-center can span a large range of values. For plausible choices of nuclear and model parameters Ecm can be large enough to yield a supernova event.
6. Low-energy neutral atom emission from the Earth's magnetosphere
International Nuclear Information System (INIS)
Moore, K.R.; Scime, E.E.; Funsten, H.O.; McComas, D.J.; Thomsen, M.F.
1994-01-01
Imaging of the terrestrial magnetosphere is possible through the detection of low-energy neutral atoms (LENAs) produced by charge exchange between magnetospheric plasma ions and neutral atoms of the Earth's geocorona. The authors present calculations of both hydrogen and oxygen line-of-sight LENA fluxes expected on orbit for various plasma regimes as predicted by the Rice University Magnetospheric Specification Model. To decrease the required computation time, they are in the process of adapting their code for massively parallel computers. The speed gains achieved from parallel algorithms are substantial, and they present results from computational runs on the Connection Machine CM-2 data parallel supercomputer. They also estimate expected image count rates and image quality based on realistic instrument geometric factors, energy passbands, neutral atom scattering in the instrument, and image accumulation intervals. The results indicate that LENA imaging instruments will need a geometric factor (G) on the order of 0.1 cm 2 sr eV/eV to be capable of imaging storm time ring currents, and a G of 1.0 cm 2 sr eV/eV in order to image the quiet time ring current fluxes, ion injections from the tail, and subsequent ion drifts toward the dayside magnetopause
7. Electron and ion Bernstein waves in Saturnian Magnetosphere
Science.gov (United States)
Bashir, M. F.; Waheed, A.; Ilie, R.; Naeem, I.; Maqsood, U.; Yoon, P. H.
2017-12-01
The study of Bernstein mode is presented in order to interpret the observed micro-structures (MIS) and banded emission (BEM) in the Saturnian magnetosphere. The general dispersion relation of Bernstein wave is derived using the Lerche-NewBerger sum rule for the kappa distribution function and further analyzed the both electron Bernstein (EB) and ion Bernstein (IB) waves. The observational data of particle measurements is obtained from the electron spectrometer (ELS) and the ion mass spectrometer (IMS), which are part of the Cassini Plasma Spectrometer (CAPS) instrument suite on board the Cassini spacecraft. For additional electron data, the measurements of Low Energy Magnetospheric Measurements System of the Magnetospheric Imaging Instrument (LEMMS /MIMI) are also utilized. The effect of kappa spectral index, density ratio (nohe/noce for EB and nohe/noi for IB) and the temperature ratio (The/Tce for EB and The/T(h,c)i for IB) on the dispersion properties are discussed employing the exact numerical analysis to explain the appearing of additional maxima/minima (points where the perpendicular group velocity vanishes, i.e., ∂w/∂k = 0) above/below the lower (for IB) and upper hybrid (EB) bands in the observation and their relation to the MIS and BED. The results of these waves may also be compared with the simulation results of Space Weather Modeling Framework (SWMF) .
8. Different magnetospheric modes: solar wind driving and coupling efficiency
Directory of Open Access Journals (Sweden)
N. Partamies
2009-11-01
Full Text Available This study describes a systematic statistical comparison of isolated non-storm substorms, steady magnetospheric convection (SMC intervals and sawtooth events. The number of events is approximately the same in each group and the data are taken from about the same years to avoid biasing by different solar cycle phase. The very same superposed epoch analysis is performed for each event group to show the characteristics of ground-based indices (AL, PCN, PC potential, particle injection at the geostationary orbit and the solar wind and IMF parameters. We show that the monthly occurrence of sawtooth events and isolated non-stormtime substorms closely follows maxima of the geomagnetic activity at (or close to the equinoxes. The most strongly solar wind driven event type, sawtooth events, is the least efficient in coupling the solar wind energy to the auroral ionosphere, while SMC periods are associated with the highest coupling ratio (AL/EY. Furthermore, solar wind speed seems to play a key role in determining the type of activity in the magnetosphere. Slow solar wind is capable of maintaining steady convection. During fast solar wind streams the magnetosphere responds with loading–unloading cycles, represented by substorms during moderately active conditions and sawtooth events (or other storm-time activations during geomagnetically active conditions.
9. Physics of the diffusion region in the Magnetospheric Multiscale era
Science.gov (United States)
Chen, L. J.; Hesse, M.; Wang, S.; Ergun, R.; Bessho, N.; Burch, J. L.; Giles, B. L.; Torbert, R. B.; Gershman, D. J.; Wilson, L. B., III; Dorelli, J.; Pollock, C. J.; Moore, T. E.; Lavraud, B.; Strangeway, R. J.; Russell, C. T.; Khotyaintsev, Y. V.; Le Contel, O.; Avanov, L. A.
2016-12-01
Encounters of reconnection diffusion regions by the Magnetospheric Multiscale (MMS) mission during its first magnetopause scan are studied in combination with theories and simulations. The goal is to understand by first-principles how stored magnetic energy is converted into plasma thermal and bulk flow energies via particle energization, mixing and interaction with waves. The magnetosheath population having much higher density than the magnetospheric plasma is an outstanding narrator for and participant in the magnetospheric part of the diffusion region. For reconnection with negligible guide fields, the accelerated magnetosheath population (for both electrons and ions) is cyclotron turned by the reconnected magnetic field to form outflow jets, and then gyrotropized downstream. Wave fluctuations are reduced in the central electron diffusion region (EDR) and do not dominate the energy conversion there. For an event with a significant guide field to magnetize the electrons, wave fluctuations at the lower hybrid frequency dominate the energy conversion in the EDR, and the fastest electron outflow is established dominantly by a strong perpendicular electric field via the ExB flow in one exhaust and by time-of-flight effects along with parallel electric field acceleration in the other. Whether the above features are common threads to magnetopause reconnection diffusion regions is a question to be further examined.
10. Trajectory traces of charged particles in the magnetosphere
International Nuclear Information System (INIS)
Ejiri, M.
1978-01-01
The characteristic enhancements of ring current particles with energies of about 1--1000keV, associated with magnetospheric substorms, were observed by Explorer 45 (S 3 -A) around the plasmapause in the afternoon to midnight region and showed the characteristic structure called a 'noise' in the proton spectrograms. This paper examines the time developing characteristics of newly injected particles in the magnetosphere under a recently proposed convection electric field and a dipole magnetic field. Approximate equations of a bounce period, a second adiabatic invariant, and a bounce-averaged azimuthal velocity are given with an error of less than about 10 -3 for all pitch angles. The complete set of flow patterns of 90 0 pitch angles is also described by means of inflection lines through whicch radial and/or azimuthal drifts change their directions and where particle velocities show their local minima, i.e., the flow becomes sluggish. These particle tracings in the magnetosphere, from which time dependent particle fronts can be constructed, give the basic concept and mechanics to explain the complex and dynamical properties of the magnetic storm time particle enhancements
11. Crafoord Symposium on Magnetospheric Physics : Achievements and Prospects
CERN Document Server
Fälthammar, C-G
1990-01-01
This book contains the proceedings of the 1989 Crafoord Symposium organized by the Royal Swedish Academy of Sciences. The scientific field for the Crafoord Prize of 1989 was decided in 1988 by the Academy to be Magnetospheric Physics. On September 27,1989 the Academy awarded the 1989 Crafoord Prize to Professor J. A. Van Allen, Iowa City, USA "for his pioneer work in space research, in particular for the discovery of the high energy charged particles that are trapped in the Earth's magnetic field and form the radiation belts -often called the Van Allen belts - around the Earth". The subject for the Crafoord Symposium, which was held on September 28-29 at the Royal Swedish Academy of Sciences in Stockholm, was Magnetospheric Physics, Achievements and Prospects. Some seventy of the world's leading scientists in magnetospheric physics (see list of participants) were invited to the Symposium. The program contained only invited papers. After the ?resentation of the Crafoord Prize Laureate, Prof. J . A. Van Allen, ...
12. Results of investigation of magnetohydrodynamic flow round the magnetosphere
International Nuclear Information System (INIS)
Erkaev, N.V.
1988-01-01
Review of the main results of the study on the Earth magnetosphere quasi-stationary magnetohydrodynamic flow-around by the solar wind is given. The principle attenuation is paid to the problem of magnetic and electric fields calculation in the transition layer and at the magnetosphere boundary. Analysis of kinematic approximation and linear diffusion model is conducted. Existence condition for the magnetic barrier region, where kinematic approximation is inapplicable, is determined. Main properties of the solution - gasokinetic pressure decrease and magnetic pressure increase up to maximum at the numerical integration results of magnetohydrodynamic equations within the magnetic barrier range. Calculation problem of reconnection field at the magnetic barrier background is considered as the next step. It is shown, that the introduction of Petchek reconnection model into the problem solution general diagram allows to obtain at the magnetosphere boundary the values of electric and magnetic fields, compatible with the experiment. Problems, linked with choice of reconnection line direction and Petchek condition generalization for the case of the crossed field reconnection, are considered
13. Three-dimensional magnetospheric equilibrium with isotropic pressure
International Nuclear Information System (INIS)
Cheng, C.Z.
1995-05-01
In the absence of the toroidal flux, two coupled quasi two-dimensional elliptic equilibrium equations have been derived to describe self-consistent three-dimensional static magnetospheric equilibria with isotropic pressure in an optimal (Ψ,α,χ) flux coordinate system, where Ψ is the magnetic flux function, χ is a generalized poloidal angle, α is the toroidal angle, α = φ - δ(Ψ,φ,χ) is the toroidal angle, δ(Ψ,φ,χ) is periodic in φ, and the magnetic field is represented as rvec B = ∇Ψ x ∇α. A three-dimensional magnetospheric equilibrium code, the MAG-3D code, has been developed by employing an iterative metric method. The main difference between the three-dimensional and the two-dimensional axisymmetric solutions is that the field-aligned current and the toroidal magnetic field are finite for the three-dimensional case, but vanish for the two-dimensional axisymmetric case. With the same boundary flux surface shape, the two-dimensional axisymmetric results are similar to the three-dimensional magnetosphere at each local time cross section
14. On the electric field model for an open magnetosphere
Science.gov (United States)
Wang, Zhi; Ashour-Abdalla, Maha; Walker, Raymond J.
1993-01-01
We have developed a new canonical separator line type magnetospheric magnetic field and electric field model for use in magnetospheric calculations, we determine the magnetic and electric field by controlling the reconnection rate at the subsolar magnetopause. The model is applicable only for purely southward interplanetary magnetic field (IMF). We have obtained a more realistic magnetotail configuration by applying a stretch transformation to an axially symmetric field solution. We also discuss the Stern singularity in which there is an electric field singlarity in the canonical separate line models for B(sub y) not = to 0 by using a new technique that solves for the electric field along a field line directly instead of determining it by a potential mapping. The singularity not only causes an infinite electric field on the polar cap, but also causes the boundary conditions at plus infinity and minus infinity in the solar wind to contradict each other. This means that the canonical separator line models do not represent the open magnetosphere well, except for the case of purely southward IMF.
15. A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
International Nuclear Information System (INIS)
Johnson, Jay R.; Wing, Simon
2004-01-01
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach
16. Solar wind dynamic pressure variations and transient magnetospheric signatures
International Nuclear Information System (INIS)
Sibeck, D.G.; Baumjohann, W.
1989-01-01
Contrary to the prevailing popular view, we find some transient ground events with bipolar north-south signatures are related to variations in solar wind dynamic pressure and not necessarily to magnetic merging. We present simultaneous solar wind plasma observations for two previously reported transient ground events observed at dayside auroral latitudes. During the first event, originally reported by Lanzerotti et al. [1987], conjugate ground magnetometers recorded north-south magetic field deflections in the east-west and vertical directions. The second event was reported by Todd et al. [1986], we noted ground rader observations indicating strong northward then southward ionospheric flows. The events were associated with the postulated signatures of patchy, sporadic, merging of magnetosheath and magnetospheric magnetic field lines at the dayside magnetospause, known as flux transfer events. Conversely, we demonstrate that the event reported by Lanzerotti et al. was accompanied by a sharp increase in solar wind dynamic pressure, a magnetospheric compression, and a consequent ringing of the magnetospheric magnetic field. The event reported by Todd et al. was associated with a brief but sharp increase in the solar wind dynamic pressure. copyright American Geophysical Union 1989
17. Side-band mutual interactions in the magnetosphere
Science.gov (United States)
Chang, D. C. D.; Helliwell, R. A.; Bell, T. F.
1980-01-01
Sideband mutual interactions between VLF waves in the magnetosphere are investigated. Results of an experimental program involving the generation of sidebands by means of frequency shift keying are presented which indicate that the energetic electrons in the magnetosphere can interact only with sidebands generated by signals with short modulation periods. Using the value of the memory time during which electrons interact with the waves implied by the above result, it is estimated that the length of the electron interaction region in the magnetosphere is between 4000 and 2000 km. Sideband interactions are found to be similar to those between constant-frequency signals, exhibiting suppression and energy coupling. Results from a second sideband transmitting program show that for most cases the coherence bandwidth of sidebands is about 50 Hz. Sideband mutual interactions are then explained by the overlap of the ranges of the parallel velocity of the electrons which the sidebands organize, and the wave intensity in the interaction region is estimated to be 2.5-10 milli-gamma, in agreement with satellite measurements.
18. Diagnostics for the National Compact Stellarator Experiment
International Nuclear Information System (INIS)
Stratton, B.C.; Johnson, D.; Feder, R.; Fredrickson, E.; Neilson, H.; Takahashi, H.; Zarnstorf, M.; Cole, M.; Goranson, P.; Lazarus, E.; Nelson, B.
2003-01-01
The status of planning of the National Compact Stellarator Experiment (NCSX) diagnostics is presented, with the emphasis on resolution of diagnostics access issues and on diagnostics required for the early phases of operation
19. Stellar Spectral Classification with Locality Preserving Projections ...
School of Computer and Control Engineering, North University of China,. Taiyuan 030051 ... (2013) was used to mine the association rules of a stellar ... of the graph, we then compute a transformation matrix which maps the data points to.
20. The relation between stellar evolution and cosmology
International Nuclear Information System (INIS)
Tayler, R.J.
1984-01-01
Observations of star clusters combined with the theory of stellar evolution enable us to estimate the ages of stars while cosmological observations and theories give us a value for the age of the Universe. This is the most important interaction between cosmology and stellar evolution because it is clearly necessary that stars are younger than the Universe. Stellar evolution also plays an important role in relating the present chemical composition of the Universe to its original composition. The author restricts the review to a discussion of the relation between stellar evolution and the big bang cosmological theory because there is such a good qualitative agreement between the hot big bang theory and observations. (Auth.)
1. Evaluating Stellarator Divertor Designs with EMC3
Science.gov (United States)
Bader, Aaron; Anderson, D. T.; Feng, Y.; Hegna, C. C.; Talmadge, J. N.
2013-10-01
In this paper various improvements of stellarator divertor design are explored. Next step stellarator devices require innovative divertor solutions to handle heat flux loads and impurity control. One avenue is to enhance magnetic flux expansion near strike points, somewhat akin to the X-Divertor concept in Tokamaks. The effect of judiciously placed external coils on flux deposition is calculated for configurations based on the HSX stellarator. In addition, we attempt to optimize divertor plate location to facilitate the external coil placement. Alternate areas of focus involve altering edge island size to elucidate the driving physics in the edge. The 3-D nature of stellarators complicates design and necessitates analysis of new divertor structures with appropriate simulation tools. We evaluate the various configurations with the coupled codes EMC3-EIRENE, allowing us to benchmark configurations based on target heat flux, impurity behavior, radiated power, and transitions to high recycling and detached regimes. Work supported by DOE-SC0006103.
2. Development of the stellarator/heliotron research
International Nuclear Information System (INIS)
Iiyoshi, A.
1991-05-01
The author reviewed the history of the development of the stellarator/heliotron system, and pointed out the important role of the radial electric field in plasma transport in helical devices. (J.P.N.)
3. Radiative otacity tables for 40 stellar mixtures
International Nuclear Information System (INIS)
Cox, A.N.; Tabor, J.E.
1976-01-01
Using improved methods, radiative opacities for 40 mixtures of elements are given for use in calculations of stellar structure, stellar evolution, and stellar pulsation. The major improvements over previous Los Alamos data are increased iron abundance in the composition, better allowance for the continuum depression for bound electrons, and corrections in some bound-electron energy levels. These opacities have already been widely used, and represent a relatively homogeneous set of data for stellar structures. Further improvements to include more bound-bound (line) transitions by a smearing technique and to include molecular absorptions are becoming available, and in a few years these tables, as well as all previous tables, will be outdated. At high densities the conduction of energy will dominate radiation flow, and this effect must be added separately
4. STELLAR ATMOSPHERES, ATMOSPHERIC EXTENSION, AND FUNDAMENTAL PARAMETERS: WEIGHING STARS USING THE STELLAR MASS INDEX
Energy Technology Data Exchange (ETDEWEB)
Neilson, Hilding R.; Lester, John B. [Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON, M5S 3H4 (Canada); Baron, Fabien; Norris, Ryan; Kloppenborg, Brian, E-mail: [email protected] [Center for High Angular Resolution Astronomy, Department of Physics and Astronomy, Georgia State University, P.O. Box 5060, Atlanta, GA 30302-5060 (United States)
2016-10-20
One of the great challenges of understanding stars is measuring their masses. The best methods for measuring stellar masses include binary interaction, asteroseismology, and stellar evolution models, but these methods are not ideal for red giant and supergiant stars. In this work, we propose a novel method for inferring stellar masses of evolved red giant and supergiant stars using interferometric and spectrophotometric observations combined with spherical model stellar atmospheres to measure what we call the stellar mass index, defined as the ratio between the stellar radius and mass. The method is based on the correlation between different measurements of angular diameter, used as a proxy for atmospheric extension, and fundamental stellar parameters. For a given star, spectrophotometry measures the Rosseland angular diameter while interferometric observations generally probe a larger limb-darkened angular diameter. The ratio of these two angular diameters is proportional to the relative extension of the stellar atmosphere, which is strongly correlated to the star’s effective temperature, radius, and mass. We show that these correlations are strong and can lead to precise measurements of stellar masses.
5. Does the stellar distribution flare? A comparison of stellar scale heights with LAB H I data
Energy Technology Data Exchange (ETDEWEB)
Kalberla, P. M. W.; Kerp, J.; Dedes, L. [Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn (Germany); Haud, U., E-mail: [email protected] [Tartu Observatory, 61602 Tõravere (Estonia)
2014-10-10
The question of whether the stellar populations in the Milky Way take part in the flaring of scale heights as observed for the H I gas is a matter of debate. Standard mass models for the Milky Way assume a constant scale height for each of the different stellar distributions. However, there is mounting evidence that at least some of the stellar distributions reach, at large galactocentric distances, high altitudes, which are incompatible with a constant scale height. We discuss recent observational evidence for stellar flaring and compare it with H I data from the Leiden/Argentine/Bonn survey. Within the systemic and statistical uncertainties we find a good agreement between both.
6. The WEGA Stellarator: Results and Prospects
International Nuclear Information System (INIS)
Otte, M.; Andruczyk, D.; Koenig, R.; Laqua, H. P.; Lischtschenko, O.; Marsen, S.; Schacht, J.; Podoba, Y. Y.; Wagner, F.; Warr, G. B.; Holzhauer, E.; Howard, J.; Krupnik, L.; Zhezhera, A.; Urban, J.; Preinhalter, J.
2008-01-01
In this article an overview is given on results from magnetic flux surface measurements, applied ECR heating scenarios for 2.45 GHz and 28 GHz, fluctuation and transport studies and plasma edge biasing experiments performed in the WEGA stellarator. Examples for the development of new diagnostics and the machine control system are given that will be used at Wendelstein 7-X stellarator, which is currently under construction in Greifswald
7. Cosmic abundances: The impact of stellar duplicity
OpenAIRE
Jorissen, A.; Van Eck, S.
2004-01-01
The mass-transfer scenario links chemical peculiarities with stellar duplicity for an increasing number of stellar classes (classical and dwarf barium stars, subgiant and giant CH stars, S stars without technetium, yellow symbiotic stars, WIRRING stars, Abell-35-like nuclei of planetary nebulae...). Despite these successes, the mass-transfer scenario still faces several problems: What is the mass-transfer mode? Why orbital elements of dwarf barium stars do not fully match those of the classic...
8. The Stellar-Dynamical Oeuvre James Binney
tribpo
of the eigenvalues of M. The variation of the stellar density from point to point .... of Σ,(ΔΕ)2 , where ∆ Ε is the change in energy that a star suffers during a binary ... could use these results to calculate the relaxation time in a stellar system if he .... the region of enhanced density that tails behind it like a wake behind a ship. By.
9. Weakly interacting massive particles and stellar structure
International Nuclear Information System (INIS)
Bouquet, A.
1988-01-01
The existence of weakly interacting massive particles (WIMPs) may solve both the dark matter problem and the solar neutrino problem. Such particles affect the energy transport in the stellar cores and change the stellar structure. We present the results of an analytic approximation to compute these effects in a self-consistent way. These results can be applied to many different stars, but we focus on the decrease of the 8 B neutrino flux in the case of the Sun
10. Close stellar encounters in globular clusters
International Nuclear Information System (INIS)
Bailyn, C.D.
1989-01-01
Stellar encounters are expected to produce a variety of interesting objects in the cores of globular clusters, either through the formation of binaries by tidal capture, or direct collisions. Here, I describe several attempts to observe the products of stellar encounters. In particular, the use of color maps has demonstrated the existence of a color gradient in the core of M15, which seems to be caused by a population of faint blue objects concentrated towards the cluster center. (author)
11. On plasma radiative properties in stellar conditions
International Nuclear Information System (INIS)
Turck-Chieze, S.; Delahaye, F.; Gilles, D.; Loisel, G.; Piau, L.; Loisel, G.
2009-01-01
The knowledge of stellar evolution is evolving quickly thanks to an increased number of opportunities to scrutinize the stellar internal plasma properties by stellar seismology and by 1D and 3D simulations. These new tools help us to introduce the internal dynamical phenomena in stellar modeling. A proper inclusion of these processes supposes a real confidence in the microscopic physics used, partly checked by solar or stellar acoustic modes. In the present paper we first recall which fundamental physics has been recently verified by helioseismology. Then we recall that opacity is an important ingredient of the secular evolution of stars and we point out why it is necessary to measure absorption coefficients and degrees of ionization in the laboratory for some well identified astrophysical conditions. We examine two specific experimental conditions which are accessible to large laser facilities and are suitable to solve some interesting questions of the stellar community: are the solar internal radiative interactions properly estimated and what is the proper role of the opacity in the excitation of the non-radial modes in the envelop of the β Cepheids and the Be stars? At the end of the paper we point out the difficulties of the experimental approach that we need to overcome. (authors)
12. Comparative studies of stellarator and tokamak transport
Energy Technology Data Exchange (ETDEWEB)
Stroth, U; Burhenn, R; Geiger, J; Giannone, L.; Hartfuss, H J; Kuehner, G; Ledl, L; Simmet, E E; Walter, H [Max-Planck-Inst. fuer Plasmaphysik, IPP-Euratom Association, Garching (Germany); ECRH Team; W7-AS Team
1997-09-01
Transport properties in the W7-AS stellarator and in tokamaks are compared. The parameter dependences and the absolute values of the energy confinement time are similar. Indications are found that the density dependence, which is usually observed in stellarator confinement, can vanish above a critical density. The density dependence in stellarators seems to be similar to that in the linear ohmic confinement regime, which, in small tokamaks, extends to high density values, too. Because of the similarity in the gross confinement properties, transport in stellarators and tokamaks should not be dominated by the parameters which are very different in the two concepts, i.e. magnetic shear, major rational values of the rotational transform and plasma current. A difference in confinement is that there exists evidence for pinches in the particle and, possibly, energy transport channels in tokamaks whereas in stellarators no pinches have been observed, so far. In order to study the effect of plasma current and toroidal electric fields, stellarator discharges were carried out with an increasing amount of plasma current. From these experiments, no clear evidence of a connection of pinches with these parameters is found. The transient response in W7-AS plasmas can be described in terms of a non-local model. As in tokamaks, also cold pulse experiments in W7-AS indicate the importance of non-local transport. (author). 8 refs, 5 figs.
13. Magnetosphere-ionosphere coupling currents in Jupiter's middle magnetosphere: effect of magnetosphere-ionosphere decoupling by field-aligned auroral voltages
Directory of Open Access Journals (Sweden)
J. D. Nichols
2005-03-01
Full Text Available We consider the effect of field-aligned voltages on the magnetosphere-ionosphere coupling current system associated with the breakdown of rigid corotation of equatorial plasma in Jupiter's middle magnetosphere. Previous analyses have assumed perfect mapping of the electric field and flow along equipotential field lines between the equatorial plane and the ionosphere, whereas it has been shown that substantial field-aligned voltages must exist to drive the field-aligned currents associated with the main auroral oval. The effect of these field-aligned voltages is to decouple the flow of the equatorial and ionospheric plasma, such that their angular velocities are in general different from each other. In this paper we self-consistently include the field-aligned voltages in computing the plasma flows and currents in the system. A third order differential equation is derived for the ionospheric plasma angular velocity, and a power series solution obtained which reduces to previous solutions in the limit that the field-aligned voltage is small. Results are obtained to second order in the power series, and are compared to the original zeroth order results with no parallel voltage. We find that for system parameters appropriate to Jupiter the effect of the field-aligned voltages on the solutions is small, thus validating the results of previously-published analyses.
14. Electromagnetic and Radiative Properties of Neutron Star Magnetospheres
Science.gov (United States)
Li, Jason G.
2014-05-01
Magnetospheres of neutron stars are commonly modeled as either devoid of plasma in "vacuum'' models or filled with perfectly conducting plasma with negligible inertia in "force-free'' models. While numerically tractable, neither of these idealized limits can simultaneously account for both the plasma currents and the accelerating electric fields that are needed to explain the morphology and spectra of high-energy emission from pulsars. In this work we improve upon these models by considering the structure of magnetospheres filled with resistive plasma. We formulate Ohm's Law in the minimal velocity fluid frame and implement a time-dependent numerical code to construct a family of resistive solutions that smoothly bridges the gap between the vacuum and force-free magnetosphere solutions. We further apply our method to create a self-consistent model for the recently discovered intermittent pulsars that switch between two distinct states: an "on'', radio-loud state, and an "off'', radio-quiet state with lower spin-down luminosity. Essentially, we allow plasma to leak off open field lines in the absence of pair production in the "off'' state, reproducing observed differences in spin-down rates. Next, we examine models in which the high-energy emission from gamma-ray pulsars comes from reconnecting current sheets and layers near and beyond the light cylinder. The reconnected magnetic field provides a reservoir of energy that heats particles and can power high-energy synchrotron radiation. Emitting particles confined to the sheet naturally result in a strong caustic on the skymap and double peaked light curves for a broad range of observer angles. Interpulse bridge emission likely arises from interior to the light cylinder, along last open field lines that traverse the space between the polar caps and the current sheet. Finally, we apply our code to solve for the magnetospheric structure of merging neutron star binaries. We find that the scaling of electromagnetic
15. Geometric corrections due to inhomogeneous field in the magnetospheric double current layer
International Nuclear Information System (INIS)
Callebaut, D.K.; Van den Buys, A.M.
1985-01-01
The case of oblique incidence and of a slope in the magnetic field for plane parallel models of the magnetospheric double layer is considered. The two models are the Magnetospheric Double Layer (MDL) and the Magnetospheric Double Current Layer (MDCL). The latter is more appropriate but due to some approximations it gives sometimes incorrect results. An improved model uses a triple current layer. (R.P.)
16. Particle-in-Cell Simulations of the Twisted Magnetospheres of Magnetars. I.
Science.gov (United States)
Chen, Alexander Y.; Beloborodov, Andrei M.
2017-08-01
The magnetospheres of magnetars are believed to be filled with electron-positron plasma generated by electric discharge. We present a first numerical experiment demonstrating this process in an axisymmetric magnetosphere with a simple threshold prescription for pair creation, which is applicable to the inner magnetosphere with an ultrastrong field. The {e}+/- discharge occurs in response to the twisting of the closed magnetic field lines by a shear deformation of the magnetar surface, which launches electric currents into the magnetosphere. The simulation shows the formation of an electric “gap” with an unscreened electric field ({\\boldsymbol{E}}\\cdot {\\boldsymbol{B}}\
17. The AMPTE program's contribution to studies of the solar wind-magnetosphere-ionosphere interaction
International Nuclear Information System (INIS)
Sibeck, D.G.
1990-01-01
The Active Magnetospheric Particle Tracer Explorers (AMPTE) program provided important information on the behavior of clouds of plasma artificially injected into the solar wind and the earth's magnetosphere. Now that the releases are over, data from the satellites are being analyzed to investigate the processes by which the ambient solar wind mass, momentum, and energy are transferred to the magnetosphere. Work in progress at APL indicates that the solar wind is much more inhomogeneous than previously believed, that the solar wind constantly buffets the magnetosphere, and that ground observers may remotely sense these interactions as geomagnetic pulsations. 8 refs
18. Corotation-driven magnetosphere-ionosphere coupling currents in Saturn’s magnetosphere and their relation to the auroras
Directory of Open Access Journals (Sweden)
S. W. H. Cowley
2003-08-01
Full Text Available We calculate the latitude profile of the equatorward-directed ionospheric Pedersen currents that are driven in Saturn’s ionosphere by partial corotation of the magnetospheric plasma. The calculation incorporates the flattened figure of the planet, a model of Saturn’s magnetic field derived from spacecraft flyby data, and angular velocity models derived from Voyager plasma data. We also employ an effective height-integrated ionospheric Pedersen conductivity of 1 mho, suggested by a related analysis of Voyager magnetic field data. The Voyager plasma data suggest that on the largest spatial scales, the plasma angular velocity declines from near-rigid corotation with the planet in the inner magnetosphere, to values of about half of rigid corotation at the outer boundary of the region considered. The latter extends to ~ 15–20 Saturn radii (RS in the equatorial plane, mapping along magnetic field lines to ~ 15° co-latitude in the ionosphere. We find in this case that the ionospheric Pedersen current peaks near the poleward (outer boundary of this region, and falls toward zero over ~ 5°–10° equator-ward of the boundary as the plasma approaches rigid corotation. The peak current near the poleward boundary, integrated in azimuth, is ~ 6 MA. The field-aligned current required for continuity is directed out of the ionosphere into the magnetosphere essentially throughout the region, with the current density peaking at ~ 10 nA m-2 at ~ 20° co-latitude. We estimate that such current densities are well below the limit requiring field-aligned acceleration of magnetospheric electrons in Saturn’s environment ( ~ 70 nAm-2, so that no significant auroral features associated with this ring of upward current is anticipated. The observed ultraviolet auroras at Saturn are also found to occur significantly closer to the pole (at ~ 10°–15° co-latitude, and show considerable temporal and local time variability, contrary to expectations for corotation
19. Use of the stellarator expansion to investigate plasma equilibrium in modular stellarators
International Nuclear Information System (INIS)
Anania, G.; Johnson, J.L.; Weimer, K.E.
1982-11-01
A numerical code utilizing a large-aspect ratio, small-helical-distortion expansion is developed and used to investigate the effect of plasma currents on stellarator equilibrium. Application to modular stellarator configurations shows that a large rotational transform, and hence large coil deformation, is needed to achieve high-beta equilibria
20. Stellar Firework in a Whirlwind
Science.gov (United States)
2007-09-01
VLT Image of Supernova in Beautiful Spiral Galaxy NGC 1288 Stars do not like to be alone. Indeed, most stars are members of a binary system, in which two stars circle around each other in an apparently never-ending cosmic ballet. But sometimes, things can go wrong. When the dancing stars are too close to each other, one of them can start devouring its partner. If the vampire star is a white dwarf - a burned-out star that was once like our Sun - this greed can lead to a cosmic catastrophe: the white dwarf explodes as a Type Ia supernova. In July 2006, ESO's Very Large Telescope took images of such a stellar firework in the galaxy NGC 1288. The supernova - designated SN 2006dr - was at its peak brightness, shining as bright as the entire galaxy itself, bearing witness to the amount of energy released. ESO PR Photo 39/07 ESO PR Photo 39/07 SN 2006dr in NGC 1288 NGC 1288 is a rather spectacular spiral galaxy, seen almost face-on and showing multiple spiral arms pirouetting around the centre. Bearing a strong resemblance to the beautiful spiral galaxy NGC 1232, it is located 200 million light-years away from our home Galaxy, the Milky Way. Two main arms emerge from the central regions and then progressively split into other arms when moving further away. A small bar of stars and gas runs across the centre of the galaxy. The first images of NGC 1288, obtained during the commissioning period of the FORS instrument on ESO's VLT in 1998, were of such high quality that they have allowed astronomers [1] to carry out a quantitative analysis of the morphology of the galaxy. They found that NGC 1288 is most probably surrounded by a large dark matter halo. The appearance and number of spiral arms are indeed directly related to the amount of dark matter in the galaxy's halo. The supernova was first spotted by amateur astronomer Berto Monard. On the night of 17 July 2006, Monard used his 30-cm telescope in the suburbs of Pretoria in South Africa and discovered the supernova as an
1. sunstardb: A Database for the Study of Stellar Magnetism and the Solar-stellar Connection
Science.gov (United States)
Egeland, Ricky
2018-05-01
The “solar-stellar connection” began as a relatively small field of research focused on understanding the processes that generate magnetic fields in stars and sometimes lead to a cyclic pattern of long-term variability in activity, as demonstrated by our Sun. This area of study has recently become more broadly pertinent to questions of exoplanet habitability and exo-space weather, as well as stellar evolution. In contrast to other areas of stellar research, individual stars in the solar-stellar connection often have a distinct identity and character in the literature, due primarily to the rarity of the decades-long time-series that are necessary for studying stellar activity cycles. Furthermore, the underlying stellar dynamo is not well understood theoretically, and is thought to be sensitive to several stellar properties, e.g., luminosity, differential rotation, and the depth of the convection zone, which in turn are often parameterized by other more readily available properties. Relevant observations are scattered throughout the literature and existing stellar databases, and consolidating information for new studies is a tedious and laborious exercise. To accelerate research in this area I developed sunstardb, a relational database of stellar properties and magnetic activity proxy time-series keyed by individual named stars. The organization of the data eliminates the need for the problematic catalog cross-matching operations inherent when building an analysis data set from heterogeneous sources. In this article I describe the principles behind sunstardb, the data structures and programming interfaces, as well as use cases from solar-stellar connection research.
2. Indicators of Mass in Spherical Stellar Atmospheres
Science.gov (United States)
Lester, John B.; Dinshaw, Rayomond; Neilson, Hilding R.
2013-04-01
Mass is the most important stellar parameter, but it is not directly observable for a single star. Spherical model stellar atmospheres are explicitly characterized by their luminosity ( L⋆), mass ( M⋆), and radius ( R⋆), and observations can now determine directly L⋆ and R⋆. We computed spherical model atmospheres for red giants and for red supergiants holding L⋆ and R⋆ constant at characteristic values for each type of star but varying M⋆, and we searched the predicted flux spectra and surface-brightness distributions for features that changed with mass. For both stellar classes we found similar signatures of the stars’ mass in both the surface-brightness distribution and the flux spectrum. The spectral features have been use previously to determine log 10(g), and now that the luminosity and radius of a non-binary red giant or red supergiant can be observed, spherical model stellar atmospheres can be used to determine a star’s mass from currently achievable spectroscopy. The surface-brightness variations of mass are slightly smaller than can be resolved by current stellar imaging, but they offer the advantage of being less sensitive to the detailed chemical composition of the atmosphere.
3. Stellarator Coil Design and Plasma Sensitivity
International Nuclear Information System (INIS)
Ku, Long-Poe; Boozer, Allen H.
2010-01-01
The rich information contained in the plasma response to external magnetic perturbations can be used to help design stellarator coils more effectively. We demonstrate the feasibility by first devel oping a simple, direct method to study perturbations in stellarators that do not break stellarator symmetry and periodicity. The method applies a small perturbation to the plasma boundary and evaluates the resulting perturbed free-boundary equilibrium to build up a sensitivity matrix for the important physics attributes of the underlying configuration. Using this sensitivity information, design methods for better stellarator coils are then developed. The procedure and a proof-of-principle application are given that (1) determine the spatial distributions of external normal magnetic field at the location of the unperturbed plasma boundary to which the plasma properties are most sen- sitive, (2) determine the distributions of external normal magnetic field that can be produced most efficiently by distant coils, (3) choose the ratios of the magnitudes of the the efficiently produced magnetic distributions so the sensitive plasma properties can be controlled. Using these methods, sets of modular coils are found for the National Compact Stellarator Experiment (NCSX) that are either smoother or can be located much farther from the plasma boundary than those of the present design.
4. Development of code PRETOR for stellarator simulation
International Nuclear Information System (INIS)
Dies, J.; Fontanet, J.; Fontdecaba, J.M.; Castejon, F.; Alejandre, C.
1998-01-01
The Department de Fisica i Enginyeria Nuclear (DFEN) of the UPC has some experience in the development of the transport code PRETOR. This code has been validated with shots of DIII-D, JET and TFTR, it has also been used in the simulation of operational scenarios of ITER fast burnt termination. Recently, the association EURATOM-CIEMAT has started the operation of the TJ-II stellarator. Due to the need of validating the results given by others transport codes applied to stellarators and because all of them made some approximations, as a averaging magnitudes in each magnetic surface, it was thought suitable to adapt the PRETOR code to devices without axial symmetry, like stellarators, which is very suitable for the specific needs of the study of TJ-II. Several modifications are required in PRETOR; the main concerns to the models of: magnetic equilibrium, geometry and transport of energy and particles. In order to solve the complex magnetic equilibrium geometry the powerful numerical code VMEC has been used. This code gives the magnetic surface shape as a Fourier series in terms of the harmonics (m,n). Most of the geometric magnitudes are also obtained from the VMEC results file. The energy and particle transport models will be replaced by other phenomenological models that are better adapted to stellarator simulation. Using the proposed models, it is pretended to reproduce experimental data available from present stellarators, given especial attention to the TJ-II of the association EURATOM-CIEMAT. (Author)
5. ON THE ORIGIN OF STELLAR MASSES
International Nuclear Information System (INIS)
Krumholz, Mark R.
2011-01-01
It has been a longstanding problem to determine, as far as possible, the characteristic masses of stars in terms of fundamental constants; the almost complete invariance of this mass as a function of the star-forming environment suggests that this should be possible. Here I provide such a calculation. The typical stellar mass is set by the characteristic fragment mass in a star-forming cloud, which depends on the cloud's density and temperature structure. Except in the very early universe, the latter is determined mainly by the radiation released as matter falls onto seed protostars. The energy yield from this process is ultimately set by the properties of deuterium burning in protostellar cores, which determines the stars' radii. I show that it is possible to combine these considerations to compute a characteristic stellar mass almost entirely in terms of fundamental constants, with an extremely weak residual dependence on the interstellar pressure and metallicity. This result not only explains the invariance of stellar masses, it resolves a second mystery: why fragmentation of a cold, low-density interstellar cloud, a process with no obvious dependence on the properties of nuclear reactions, happens to select a stellar mass scale such that stellar cores can ignite hydrogen. Finally, the weak residual dependence on the interstellar pressure and metallicity may explain recent observational hints of a smaller characteristic mass in the high-pressure, high-metallicity cores of giant elliptical galaxies.
6. Collisionless microinstabilities in stellarators. II. Numerical simulations
International Nuclear Information System (INIS)
Proll, J. H. E.; Xanthopoulos, P.; Helander, P.
2013-01-01
Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here, the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes, and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations
7. Review of stellarator research world wide
International Nuclear Information System (INIS)
Shonet, J.L.
1987-01-01
The world-wide effort in stellarators has evolved considerably during the past few years. Stellarator facilities are located in the Australia, Federal Republic of Germany, Japan, the Soviet Union, Spain, the United Kingdom and the United States. Dimensions of stellarators range from less than 20 centimeters in major radius to more than 2 meters, and magnetic field values between 0.2 Tesla to more than 3.0 Tesla. Stellarators are made in a variety of magnetic configurations with wide ranges of toroidal aspect ratios and methods of generating the stellarator magnetic surfaces. In particular, continuous helical coils, twisted modular coils, or twisted vacuum chambers all provide different means to generate nested toroidal magnetic surfaces without the need for currents flowing in the plasma. The goal of present day experiments is to accumulate a physics data base. This is being done by increasing electron and ion temperatures with non-ohmic heating, by transport and scaling studies considering neoclassical scaling, global scaling, effects of electric fields, the bootstrap current and magnetic islands. Higher betas are being attempted by designing suitable magnetic configurations, pellet injection and/or minimizing transport losses. Plasma-wall interactions and particle control are being examined by divertor, pumped-limiter and carbonization experiments
8. The Stellar Imager (SI)"Vision Mission"
Science.gov (United States)
Carpenter, Ken; Danchi, W.; Leitner, J.; Liu, A.; Lyon, R.; Mazzuca, L.; Moe, R.; Chenette, D.; Karovska, M.; Allen, R.
2004-01-01
The Stellar Imager (SI) is a "Vision" mission in the Sun-Earth Connection (SEC) Roadmap, conceived for the purpose of understanding the effects of stellar magnetic fields, the dynamos that generate them, and the internal structure and dynamics of the stars in which they exist. The ultimate goal is to achieve the best possible forecasting of solar/stellar magnetic activity and its impact on life in the Universe. The science goals of SI require an ultra-high angular resolution, at ultraviolet wavelengths, on the order of 100 micro-arcsec and thus baselines on the order of 0.5 km. These requirements call for a large, multi-spacecraft (less than 20) imaging interferometer, utilizing precision formation flying in a stable environment, such as in a Lissajous orbit around the Sun-Earth L2 point. SI's resolution will make it an invaluable resource for many other areas of astrophysics, including studies of AGN s, supernovae, cataclysmic variables, young stellar objects, QSO's, and stellar black holes. ongoing mission concept and technology development studies for SI. These studies are designed to refine the mission requirements for the science goals, define a Design Reference Mission, perform trade studies of selected major technical and architectural issues, improve the existing technology roadmap, and explore the details of deployment and operations, as well as the possible roles of astronauts and/or robots in construction and servicing of the facility.
9. Geometric phase modulation for stellar interferometry
International Nuclear Information System (INIS)
Roy, M.; Boschung, B.; Tango, W.J.; Davis, J.
2002-01-01
Full text: In a long baseline optical interferometer, the fringe visibility is normally measured by modulation of the optical path difference between the two arms of the instruments. To obtain accurate measurements, the spectral bandwidth must be narrow, limiting the sensitivity of the technique. The application of geometric phase modulation technique to stellar interferometry has been proposed by Tango and Davis. Modulation of the geometric phase has the potential for improving the sensitivity of optical interferometers, and specially the Sydney University Stellar Interferometer (SUSI), by allowing broad band modulation of the light signals. This is because a modulator that changes the geometric phase of the signal is, in principle, achromatic. Another advantage of using such a phase modulator is that it can be placed in the common path traversed by the two orthogonally polarized beams emerging from the beam combiner in a stellar interferometer. Thus the optical components of the modulator do not have to be interferometric quality and could be relatively easily introduced into SUSI. We have investigated the proposed application in a laboratory-based experiment using a Mach-Zehnder interferometer with white-light source. This can be seen as a small model of an amplitude stellar interferometer where the light source takes the place of the distant star and two corner mirrors replaces the entrance pupils of the stellar interferometer
10. Geomagnetic response to sudden expansions of the magnetosphere
International Nuclear Information System (INIS)
Araki, Tohru; Nagano, Hiroshi
1988-01-01
The geomagnetic response to five successive sudden expansions of the magnetosphere was examined by the use of magnetic data observed on the ground and by satellites. At the geosynchronous orbit between 0800 and 1100 LT the magnetic field component parallel to Earth's rotation axis decreased successively. The amplitude and the fall time of each decrease were 20-30 nT and 2.5-3.5 min, respectively. The decrease was propagated about 10 min later to the distance of about 31 R E from Earth in the antisunward direction, indicating propagation speed of about 300 km/s. The H component of ground magnetograms from low-latitude stations showed decreases with waveform similar to that at the geosynchronous orbit, but each decrease at the dayside equator was greatly enhanced and preceded by a short small positive impulse. Each of the corresponding geomagnetic variations at high latitude stations consisted of two successive sharp pulses of opposite sense with 2-3 min duration. The dominant component and the sense of these high-latitude pulses were highly dependent upon local time and latitude. The distribution of equivalent ionospheric current arrows for each high-latitude pulse showed clear twin vortices centered at 70-76 degree geomagnetic latitude in the dayside and was approximately symmetric with respect to the noon meridian. The current direction of the vortices was reversed from the first pulse to the second. it suggests successive appearance of a dawn-to-dusk and then a dusk-to-dawn electric field, both of which were transmitted from the magnetosphere to the polar ionosphere. The effect of ionospheric currents due to these polar electric fields was superposed on the simple magnetic decrease produced by an expansion of the whole magnetosphere and produced the complex waveform distribution on the ground
11. Fast hisslers: a form of magnetospheric radio emissions
International Nuclear Information System (INIS)
Siren, J.C.
1974-01-01
Auroral radio hiss bursts in the frequency range 2-18 kHz have been observed, with rise or turn-on-times of 20-50 ms, and fall or turn-off times of 20-80 ms. These time scales are too brief to reconcile with the Cerenkov radiation emission mechanism often proposed as the transducer that converts precipitating auroral electron kinetic energy into very-low-frequency radio wave energy. The auroral hiss bursts, called here ''fast hisslers,'' are observed to be ''dispersed,', that is, their arrival time at the receiving site is not simultaneous at all frequencies, but depends on frequency in a way that is consistent with propagation in the whistler mode of electromagnetic wave propagation. Since whistler mode wave propagation at these frequencies occurs only in the earth' magnetosphere, it is inferred that these fast hisslers are of magnetospheric origin. On the assumption that all the observed dispersion results from whistler mode dispersion at high latitudes, altitudes of origin of 1800 km to 30,000 km are calculated for these emissions. Fine details of some of the amplitude spectra of fast hisslers have been examined. Potential double layers have been investigated as a highly localized region of acceleration of the auroral electrons that are believed to be the source of energy of the fast hisslers. Evidence is strong that a plasma instability exists which rapidly converts electron kinetic energies into whistler-mode wave energy traveling in the same direction relative to the rest frame of the thermal magnetospheric plasma
12. Particle tracing in the magnetosphere: New algorithms and results
International Nuclear Information System (INIS)
Sheldon, R.B.; Gaffey, J.D. Jr.
1993-01-01
The authors present new algorithms for calculating charged-particle trajectories in realistic magnetospheric fields in fast and efficient manners. The scheme is based on a hamiltonian energy conservation principle. It requires that particles conserve the first two adiabatic invariants, and thus also conserve energy. It is applicable for particles ranging in energy from 0.01 to 100 keV, having arbitrary charge, and pitch angle. In addition to rapid particle trajectory calculations, it allows topological boundaries to be located efficiently. The results can be combined with fluid models to provide quantitative models of the time development of the whole convecting plasma model
13. Obervations of low energy magnetospheric plasma outside the plasmasphere
International Nuclear Information System (INIS)
Hultqvist, B.
1985-01-01
After some introductory discussions about morphological concepts and limitations of various measurement techniques, existing low energy plasma data, orginating primarily from the GEOS, Dynamics Explorer, and Prognoz spacecraft, is described and discussed. The plasmasphere measurements are not included (but for some observations of plasmasphere refilling). It is finally concluded that we are very far from a complete picture of the low-energy plasma component in the magnetosphere and that this problem has to be given high priority in planning payloads of future space plasma physics missions. (Author)
14. Physical processes for the onset of magnetospheric substorms
International Nuclear Information System (INIS)
Kan, J.R.; Akasofu, S-I.; Lee, L.C.
1980-01-01
There are at least three important advances in observational as well as theoretical understanding of substorm processes during the last several years; they are: (i) the 'V-shaped' potential structure for auroral acceleration, (ii) deflation as the cause of thinning of the distant plasma sheet, and (iii) interruption and subsequent diversion of the cross-tail current during the expansive phase of magnetospheric substorms. A possible chain of processes is suggested, including (i), (ii) and (iii) as vital parts, which leads to substorm onset. (Auth.)
15. Artificial electron beams in the magnetosphere and ionosphere
International Nuclear Information System (INIS)
Winckler, J.R.
1990-01-01
The Plasma Diagnostics Payload of the Echo 7 satellite carried TV cameras and photometers by means of which the luminosity around an electron beam in the polar ionosphere could be studied. It was found that, while the beam Larmor spiral could be clearly seen near 100 km, above this only a column due to suprathermal electrons was observable. At high altitudes, the emission of neutral gas both generated powerful luminosity and substantially reduced accelerator potentials. An analysis of conjugate echoes indicates that inferred magnetospheric electric fields do not map well into the ionosphere, as well as the presence of strong pitch-angle scattering. 11 refs
16. Earth's magnetosphere formed by the low-latitude boundary layer
CERN Document Server
Heikkila, W J
2011-01-01
The author argues that, after five decades of debate about the interactive of solar wind with the magnetosphere, it is time to get back to basics. Starting with Newton's law, this book also examines Maxwell's equations and subsidiary equations such as continuity, constitutive relations and the Lorentz transformation; Helmholtz' theorem, and Poynting's theorem, among other methods for understanding this interaction. Includes chapters on prompt particle acceleration to high energies, plasma transfer event, and the low latitude boundary layer More than 200 figures illustrate the text Includes a color insert.
17. Stellar Wakes from Dark Matter Subhalos.
Science.gov (United States)
Buschmann, Malte; Kopp, Joachim; Safdi, Benjamin R; Wu, Chih-Liang
2018-05-25
We propose a novel method utilizing stellar kinematic data to detect low-mass substructure in the Milky Way's dark matter halo. By probing characteristic wakes that a passing dark matter subhalo leaves in the phase-space distribution of ambient halo stars, we estimate sensitivities down to subhalo masses of ∼10^{7} M_{⊙} or below. The detection of such subhalos would have implications for dark matter and cosmological models that predict modifications to the halo-mass function at low halo masses. We develop an analytic formalism for describing the perturbed stellar phase-space distributions, and we demonstrate through idealized simulations the ability to detect subhalos using the phase-space model and a likelihood framework. Our method complements existing methods for low-mass subhalo searches, such as searches for gaps in stellar streams, in that we can localize the positions and velocities of the subhalos today.
18. Stellar Wakes from Dark Matter Subhalos
Science.gov (United States)
Buschmann, Malte; Kopp, Joachim; Safdi, Benjamin R.; Wu, Chih-Liang
2018-05-01
We propose a novel method utilizing stellar kinematic data to detect low-mass substructure in the Milky Way's dark matter halo. By probing characteristic wakes that a passing dark matter subhalo leaves in the phase-space distribution of ambient halo stars, we estimate sensitivities down to subhalo masses of ˜107 M⊙ or below. The detection of such subhalos would have implications for dark matter and cosmological models that predict modifications to the halo-mass function at low halo masses. We develop an analytic formalism for describing the perturbed stellar phase-space distributions, and we demonstrate through idealized simulations the ability to detect subhalos using the phase-space model and a likelihood framework. Our method complements existing methods for low-mass subhalo searches, such as searches for gaps in stellar streams, in that we can localize the positions and velocities of the subhalos today.
19. Effect of finite β on stellarator transport
International Nuclear Information System (INIS)
Mynick, H.E.
1984-04-01
A theory of the modification of stellarator transport due to the presence of finite plasma pressure is developed, and applied to a range of stellarator configurations. For many configurations of interest, plasma transport can change by more than an order of magnitude in the progression from zero pressure to the equilibrium β limit of the device. Thus, a stellarator with transport-optimized vacuum fields can have poor confinement at the desired operating β. Without an external compensating field, increasing β tends to degrade confinement, unless the initial field structure is very carefully chosen. The theory permits one to correctly determine this vacuum structure, in terms of the desired structure of the field at a prescribed operating β. With a compensating external field, the deleterious effect of finite β on transport can be partially eliminated
20. Recent advances in modeling stellar interiors (u)
Energy Technology Data Exchange (ETDEWEB)
Guzik, Joyce Ann [Los Alamos National Laboratory
2010-01-01
Advances in stellar interior modeling are being driven by new data from large-scale surveys and high-precision photometric and spectroscopic observations. Here we focus on single stars in normal evolutionary phases; we will not discuss the many advances in modeling star formation, interacting binaries, supernovae, or neutron stars. We review briefly: (1) updates to input physics of stellar models; (2) progress in two and three-dimensional evolution and hydrodynamic models; (3) insights from oscillation data used to infer stellar interior structure and validate model predictions (asteroseismology). We close by highlighting a few outstanding problems, e.g., the driving mechanisms for hybrid {gamma} Dor/{delta} Sct star pulsations, the cause of giant eruptions seen in luminous blue variables such as {eta} Car and P Cyg, and the solar abundance problem.
1. Electron Capture Cross Sections for Stellar Nucleosynthesis
Directory of Open Access Journals (Sweden)
P. G. Giannaka
2015-01-01
Full Text Available In the first stage of this work, we perform detailed calculations for the cross sections of the electron capture on nuclei under laboratory conditions. Towards this aim we exploit the advantages of a refined version of the proton-neutron quasiparticle random-phase approximation (pn-QRPA and carry out state-by-state evaluations of the rates of exclusive processes that lead to any of the accessible transitions within the chosen model space. In the second stage of our present study, we translate the abovementioned e--capture cross sections to the stellar environment ones by inserting the temperature dependence through a Maxwell-Boltzmann distribution describing the stellar electron gas. As a concrete nuclear target we use the 66Zn isotope, which belongs to the iron group nuclei and plays prominent role in stellar nucleosynthesis at core collapse supernovae environment.
2. Equilibrium reconstruction in stellarators: V3FIT
Energy Technology Data Exchange (ETDEWEB)
Hanson, J.D.; Knowlton, S.F. [Physics Department, Auburn University, Auburn, AL (United States); Hirshman, S.P.; Lazarus, E.A. [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Lao, L.L. [General Atomics, San Diego, CA (United States)
2003-07-01
The first section describes a general response function formalism for computing stellarator magnetic diagnostic signals, which is the first step in developing a reconstruction capability. The approach parallels that used in the EFIT two-dimensional (2-D) equilibrium reconstruction code. The second section describes the two codes we have written, V3RFUN and V3POST. V3RFUN computes the response functions for a specified magnetic diagnostic coil, and V3POST uses the response functions calculated by V3RFUN, along with the plasma current information supplied by the equilibrium code VMEC, to compute the expected magnetic diagnostic signals. These two codes are currently being used to design magnetic diagnostic for the NCSX stellarator (at PPPL) and the CTH toroidal hybrid stellarator (at Auburn University). The last section of the paper describes plans for the V3FIT code. (orig.)
3. The low-luminosity stellar mass function
International Nuclear Information System (INIS)
Kroupa, Pavel; Tout, C.A.; Gilmore, Gerard
1990-01-01
The stellar mass function for low-mass stars is constrained using the stellar luminosity function and the slope of the mass-luminosity relation. We investigate the range of mass functions for stars with absolute visual magnitude fainter than M V ≅ +5 which are consistent with both the local luminosity function and the rather poorly determined mass-absolute visual magnitude relation. Points of inflexion in the mass-luminosity relation exist because of the effects of H - , H 2 and of other molecules on the opacity and equation of state. The first two of these correspond to absolute magnitudes M V ≅ +7 and M V ≅ +12, respectively, at which structure is evident in the stellar luminosity function (a flattening and a maximum, respectively). Combining the mass-luminosity relation which shows these inflexion points with a peaked luminosity function, we test smooth mass functions in the mass range 0.9-0.1 the solar mass. (author)
4. Young and Exotic Stellar Zoo
Science.gov (United States)
2005-03-01
Summary Super star clusters are groups of hundreds of thousands of very young stars packed into an unbelievably small volume. They represent the most extreme environments in which stars and planets can form. Until now, super star clusters were only known to exist very far away, mostly in pairs or groups of interacting galaxies. Now, however, a team of European astronomers [1] have used ESO's telescopes to uncover such a monster object within our own Galaxy, the Milky Way, almost, but not quite, in our own backyard! The newly found massive structure is hidden behind a large cloud of dust and gas and this is why it took so long to unveil its true nature. It is known as "Westerlund 1" and is a thousand times closer than any other super star cluster known so far. It is close enough that astronomers may now probe its structure in some detail. Westerlund 1 contains hundreds of very massive stars, some shining with a brilliance of almost one million suns and some two-thousand times larger than the Sun (as large as the orbit of Saturn)! Indeed, if the Sun were located at the heart of this remarkable cluster, our sky would be full of hundreds of stars as bright as the full Moon. Westerlund 1 is a most unique natural laboratory for the study of extreme stellar physics, helping astronomers to find out how the most massive stars in our Galaxy live and die. From their observations, the astronomers conclude that this extreme cluster most probably contains no less than 100,000 times the mass of the Sun, and all of its stars are located within a region less than 6 light-years across. Westerlund 1 thus appears to be the most massive compact young cluster yet identified in the Milky Way Galaxy. PR Photo 09a/05: The Super Star Cluster Westerlund 1 (2.2m MPG/ESO + WFI) PR Photo 09b/05: Properties of Young Massive Clusters Super Star Clusters Stars are generally born in small groups, mostly in so-called "open clusters" that typically contain a few hundred stars. From a wide range of
5. The Stellar IMF from Isothermal MHD Turbulence
Science.gov (United States)
Haugbølle, Troels; Padoan, Paolo; Nordlund, Åke
2018-02-01
We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwarfs to massive stars. Our simulations represent a generic 4 pc region within a typical Galactic molecular cloud, with a mass of 3000 M ⊙ and an rms velocity 10 times the isothermal sound speed and 5 times the average Alfvén velocity, in agreement with observations. We achieve a maximum resolution of 50 au and a maximum duration of star formation of 4.0 Myr, forming up to a thousand sink particles whose mass distribution closely matches the observed stellar IMF. A large set of medium-size simulations is used to test the sink particle algorithm, while larger simulations are used to test the numerical convergence of the IMF and the dependence of the IMF turnover on physical parameters predicted by the turbulent fragmentation model. We find a clear trend toward numerical convergence and strong support for the model predictions, including the initial time evolution of the IMF. We conclude that the physics of isothermal MHD turbulence is sufficient to explain the origin of the IMF.
6. Students Excited by Stellar Discovery
Science.gov (United States)
2011-02-01
In the constellation of Ophiuchus, above the disk of our Milky Way Galaxy, there lurks a stellar corpse spinning 30 times per second -- an exotic star known as a radio pulsar. This object was unknown until it was discovered last week by three high school students. These students are part of the Pulsar Search Collaboratory (PSC) project, run by the National Radio Astronomy Observatory (NRAO) in Green Bank, WV, and West Virginia University (WVU). The pulsar, which may be a rare kind of neutron star called a recycled pulsar, was discovered independently by Virginia students Alexander Snider and Casey Thompson, on January 20, and a day later by Kentucky student Hannah Mabry. "Every day, I told myself, 'I have to find a pulsar. I better find a pulsar before this class ends,'" said Mabry. When she actually made the discovery, she could barely contain her excitement. "I started screaming and jumping up and down." Thompson was similarly expressive. "After three years of searching, I hadn't found a single thing," he said, "but when I did, I threw my hands up in the air and said, 'Yes!'." Snider said, "It actually feels really neat to be the first person to ever see something like that. It's an uplifting feeling." As part of the PSC, the students analyze real data from NRAO's Robert C. Byrd Green Bank Telescope (GBT) to find pulsars. The students' teachers -- Debra Edwards of Sherando High School, Leah Lorton of James River High School, and Jennifer Carter of Rowan County Senior High School -- all introduced the PSC in their classes, and interested students formed teams to continue the work. Even before the discovery, Mabry simply enjoyed the search. "It just feels like you're actually doing something," she said. "It's a good feeling." Once the pulsar candidate was reported to NRAO, Project Director Rachel Rosen took a look and agreed with the young scientists. A followup observing session was scheduled on the GBT. Snider and Mabry traveled to West Virginia to assist in the
7. On the detection of magnetospheric radio bursts from Uranus and Neptune
International Nuclear Information System (INIS)
Kennel, C.F.; Maggs, J.E.
1975-11-01
Earth, Jupiter, and Saturn are sources of intense but sporadic bursts of electromagnetic radiation or magnetospheric radio bursts (MRB). The similarity of the differential power flux spectra of the MRB from all three planets is examined. The intensity of the MRB is scaled for the solar wind power input into a planetary magnetosphere. The possibility of detecting MRB from Uranus and Neptune is considered
8. Experimental aspects of ion acceleration and transport in the Earth's magnetosphere
International Nuclear Information System (INIS)
Young, D.T.
1985-01-01
Major particle population within the Earth's magnetosphere have been studied via ion acceleration processes. Experimental advances over the past ten to fifteen years have demonstrated the complexity of the processes. A review is given here for areas where composition experiments have expanded perception on magnetospheric phenomena. 64 refs., 6 figs., 1 tab
9. Interplanetary Magnetic Field Control of the Entry of Solar Energetic Particles into the Magnetosphere
Science.gov (United States)
Richard, R. L.; El-Alaoui, M.; Ashour-Abdalla, M.; Walker, R. J.
2002-01-01
We have investigated the entry of energetic ions of solar origin into the magnetosphere as a function of the interplanetary magnetic field orientation. We have modeled this entry by following high energy particles (protons and 3 He ions) ranging from 0.1 to 50 MeV in electric and magnetic fields from a global magnetohydrodynamic (MHD) model of the magnetosphere and its interaction with the solar wind. For the most part these particles entered the magnetosphere on or near open field lines except for some above 10 MeV that could enter directly by crossing field lines due to their large gyroradii. The MHD simulation was driven by a series of idealized solar wind and interplanetary magnetic field (IMF) conditions. It was found that the flux of particles in the magnetosphere and transport into the inner magnetosphere varied widely according to the IMF orientation for a constant upstream particle source, with the most efficient entry occurring under southward IMF conditions. The flux inside the magnetosphere could approach that in the solar wind implying that SEPs can contribute significantly to the magnetospheric energetic particle population during typical SEP events depending on the state of the magnetosphere.
10. Jupiter's magnetosphere and aurorae observed by the Juno spacecraft during its first polar orbits
DEFF Research Database (Denmark)
Connerney, J. E. P.; Adriani, Alberto; Allegrini, F.
2017-01-01
The Juno spacecraft acquired direct observations of the jovian magnetosphere and auroral emissions from a vantage point above the poles. Juno's capture orbit spanned the jovian magnetosphere from bow shock to the planet, providing magnetic field, charged particle, and wave phenomena context...
11. Generation mechanisms for magnetic-field-aligned electric fields in the magnetosphere
International Nuclear Information System (INIS)
Faelthammar, C.-G.
1977-09-01
Magnetic-field-aligned electric fields in the magnetosphere can be generated in several different ways, and in this review some possible mechanisms are presented. Observational data now available indicates that more than one of the mechanisms mentioned are operative in the magnetosphere but it is not yet possible to evaluate their relative importance. (author)
12. Near-Field Cosmology with Resolved Stellar Populations Around Local Volume LMC Stellar-Mass Galaxies
Science.gov (United States)
Carlin, Jeffrey L.; Sand, David J.; Willman, Beth; Brodie, Jean P.; Crnojevic, Denija; Forbes, Duncan; Hargis, Jonathan R.; Peter, Annika; Pucha, Ragadeepika; Romanowsky, Aaron J.; Spekkens, Kristine; Strader, Jay
2018-06-01
We discuss our ongoing observational program to comprehensively map the entire virial volumes of roughly LMC stellar mass galaxies at distances of ~2-4 Mpc. The MADCASH (Magellanic Analog Dwarf Companions And Stellar Halos) survey will deliver the first census of the dwarf satellite populations and stellar halo properties within LMC-like environments in the Local Volume. Our results will inform our understanding of the recent DES discoveries of dwarf satellites tentatively affiliated with the LMC/SMC system. This program has already yielded the discovery of the faintest known dwarf galaxy satellite of an LMC stellar-mass host beyond the Local Group, based on deep Subaru+HyperSuprimeCam imaging reaching ~2 magnitudes below its TRGB, and at least two additional candidate satellites. We will summarize the survey results and status to date, highlighting some challenges encountered and lessons learned as we process the data for this program through a prototype LSST pipeline. Our program will examine whether LMC stellar mass dwarfs have extended stellar halos, allowing us to assess the relative contributions of in-situ stars vs. merger debris to their stellar populations and halo density profiles. We outline the constraints on galaxy formation models that will be provided by our observations of low-mass galaxy halos and their satellites.
13. Optimisation of stellarator systems: Possible ways
International Nuclear Information System (INIS)
Cooper, W.A.; Isaev, M.; Leneva, A.E.; Mikhailov, M.; Shafranov, V.D.; Subbotin, A.A.
2001-01-01
The results of our search for advanced helical (stellarator) systems with a small number of field periods over the last five years are presented. The comparison of stellarator systems with toroidal (helical or axial) and poloidal directions of the contours with B = constant on the magnetic surface as well as systems with Helias and Heliac-like orientation of the magnetic surfaces cross-sections with respect to the principal normal to the magnetic axis is undertaken. Particular attention is paid to some attractive features of the systems with constant B-lines in the poloidal direction. (author)
14. Optimisation of stellarator systems: Possible ways
International Nuclear Information System (INIS)
Cooper, W.A.; Isaev, M.Yu.; Leneva, A.E.; Mikhailov, M.I.; Sharfranov, V.D.; Subbotin, A.A.
1999-01-01
The results of our search for advanced helical (stellarator) systems with a small number of field periods over the last five years are presented. The comparison of stellarator systems with toroidal (helical or axial) and poloidal directions of the contours with B = constant on the magnetic surface as well as systems with Helias and Heliac-like orientation of the magnetic surfaces cross-sections with respect to the principal normal to the magnetic axis is undertaken. Particular attention is paid to some attractive features of the systems with constant B-lines in the poloidal direction. (author)
15. 3D radiative transfer in stellar atmospheres
International Nuclear Information System (INIS)
Carlsson, M
2008-01-01
Three-dimensional (3D) radiative transfer in stellar atmospheres is reviewed with special emphasis on the atmospheres of cool stars and applications. A short review of methods in 3D radiative transfer shows that mature methods exist, both for taking into account radiation as an energy transport mechanism in 3D (magneto-) hydrodynamical simulations of stellar atmospheres and for the diagnostic problem of calculating the emergent spectrum in more detail from such models, both assuming local thermodynamic equilibrium (LTE) and in non-LTE. Such methods have been implemented in several codes, and examples of applications are given.
16. Stellar compass for the Clementine Mission
Energy Technology Data Exchange (ETDEWEB)
Wilson, B. [Lawrence Livermore National Lab., CA (United States)
1994-11-15
A CCD sensor with 42 x 28 degrees FOV and 576 x 384 pixels was built by the Advanced Technology Program (ATP) in the Physics Department at LLNL. That sensor, called the StarTracker camera, is used on the Clementine Lunar Mapping mission between January and May, 1994. Together with the Stellar Compass software, the StarTracker camera provided a way of identifying its orientation to within about 150 microradians in camera body pitch and yaw. This presentation will be an overview of basically how the Stellar Compass software works, along with showing some of its performance results.
17. Overdense Plasma Operation in the WEGA Stellarator
Czech Academy of Sciences Publication Activity Database
Otte, M.; Laqua, H.P.; Marsen, S.; Podoba, Y.; Preinhaelter, Josef; Stange, T.; Urban, Jakub; Wagner, F.; Zhang, D.
2010-01-01
Roč. 50, č. 8 (2010), s. 785-789 ISSN 0863-1042. [International Stellarator/Heliotron Workshop/17th./. Princeton, 12.10.2009-16.10.2009] R&D Projects: GA ČR GA202/08/0419; GA MŠk 7G09042 Institutional research plan: CEZ:AV0Z20430508 Keywords : Stellarator * Bernstein waves * overdense plasma * supra -thermal electrons Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.006, year: 2010 http://dx.doi.org/10.1002/ctpp.200900053
18. 176Lu: Cosmic clock or stellar thermometer
International Nuclear Information System (INIS)
Ward, R.A.; Beer, H.; Kaeppeler, F.; Wisshak, K.
1980-12-01
We quantitatively examine the various experimental and theoretical aspects of the stellar synthesis of the long-lived ground state of 176 Lu (3.6 x 10 10 y). We discuss the various regimes of stellar temperature and free-neutron density in which either: (i) the internal electromagnetic couplings between 176 Lusup(o) and 176 Lusup(m) (3.68 hours) are sufficiently slow that they may be treated as separate nuclei, or (ii) the internal couplings are rapidly able to establish thermal equilibrium between 176 Lusup(o) and 176 Lusup(m). (orig.)
19. Magnetospheric Response Associated With Multiple Atmospheric Reflections of Precipitated Electrons in Aurora.
Science.gov (United States)
Khazanov, G. V.; Merkin, V. G.; Zesta, E.; Sibeck, D. G.; Grubbs, G. A., II; Chu, M.; Wiltberger, M. J.
2017-12-01
The magnetosphere and ionosphere are strongly coupled by precipitating electrons during storm times. Therefore, first principle simulations of precipitating electron fluxes are required to understand storm time variations of ionospheric conductances and related electric fields. As has been discussed by Khazanov et al. [2015 - 2017], the first step in such simulations is initiation of electron precipitation from the Earth's plasma sheet via wave particle interaction processes into both magnetically conjugate points, and the step 2 is the follow up of multiple atmospheric reflections of electron fluxes formed at the boundary between the ionosphere and magnetosphere of two magnetically conjugate points. To demonstrate this effect on the global magnetospheric response the Lyon-Fedder-Mobarry global magnetosphere model coupled with the Rice Convection Model of the inner magnetosphere has been used and run for the geomagnetic storm of 17 March 2013.
20. Identification of the different magnetic field contributions during a geomagnetic storm in magnetospheric and ground observations
Directory of Open Access Journals (Sweden)
T. Alberti
2016-11-01
Full Text Available We used the empirical mode decomposition (EMD to investigate the time variation of the magnetospheric and ground-based observations of the Earth's magnetic field during both quiet and disturbed periods. We found two timescale variations in magnetospheric data which are associated with different magnetospheric current systems and the characteristic diurnal orbital variation, respectively. On the ground we identified three timescale variations related to the solar-wind–magnetosphere high-frequency interactions, the ionospheric processes, and the internal dynamics of the magnetosphere. This approach is able to identify the different physical processes involved in solar-wind–magnetosphere–ionosphere coupling. In addition, the large-timescale contribution can be used as a local index for the identification of the intensity of a geomagnetic storm on the ground.
1. Magnetospheric Truncation, Tidal Inspiral, and the Creation of Short-period and Ultra-short-period Planets
International Nuclear Information System (INIS)
Lee, Eve J.; Chiang, Eugene
2017-01-01
Sub-Neptunes around FGKM dwarfs are evenly distributed in log orbital period down to ∼10 days, but dwindle in number at shorter periods. Both the break at ∼10 days and the slope of the occurrence rate down to ∼1 day can be attributed to the truncation of protoplanetary disks by their host star magnetospheres at corotation. We demonstrate this by deriving planet occurrence rate profiles from empirical distributions of pre-main-sequence stellar rotation periods. Observed profiles are better reproduced when planets are distributed randomly in disks—as might be expected if planets formed in situ—rather than piled up near disk edges, as would be the case if they migrated in by disk torques. Planets can be brought from disk edges to ultra-short (<1 day) periods by asynchronous equilibrium tides raised on their stars. Tidal migration can account for how ultra-short-period planets are more widely spaced than their longer-period counterparts. Our picture provides a starting point for understanding why the sub-Neptune population drops at ∼10 days regardless of whether the host star is of type FGK or early M. We predict planet occurrence rates around A stars to also break at short periods, but at ∼1 day instead of ∼10 days because A stars rotate faster than stars with lower masses (this prediction presumes that the planetesimal building blocks of planets can drift inside the dust sublimation radius).
2. Magnetospheric Truncation, Tidal Inspiral, and the Creation of Short-period and Ultra-short-period Planets
Energy Technology Data Exchange (ETDEWEB)
Lee, Eve J.; Chiang, Eugene, E-mail: [email protected] [Department of Astronomy, University of California, Berkeley, CA 94720-3411 (United States)
2017-06-10
Sub-Neptunes around FGKM dwarfs are evenly distributed in log orbital period down to ∼10 days, but dwindle in number at shorter periods. Both the break at ∼10 days and the slope of the occurrence rate down to ∼1 day can be attributed to the truncation of protoplanetary disks by their host star magnetospheres at corotation. We demonstrate this by deriving planet occurrence rate profiles from empirical distributions of pre-main-sequence stellar rotation periods. Observed profiles are better reproduced when planets are distributed randomly in disks—as might be expected if planets formed in situ—rather than piled up near disk edges, as would be the case if they migrated in by disk torques. Planets can be brought from disk edges to ultra-short (<1 day) periods by asynchronous equilibrium tides raised on their stars. Tidal migration can account for how ultra-short-period planets are more widely spaced than their longer-period counterparts. Our picture provides a starting point for understanding why the sub-Neptune population drops at ∼10 days regardless of whether the host star is of type FGK or early M. We predict planet occurrence rates around A stars to also break at short periods, but at ∼1 day instead of ∼10 days because A stars rotate faster than stars with lower masses (this prediction presumes that the planetesimal building blocks of planets can drift inside the dust sublimation radius).
3. The Force-Free Magnetosphere of a Rotating Black Hole
Science.gov (United States)
Contopoulos, Ioannis; Kazanas, Demosthenes; Papadopoulos, Demetrios B.
2013-01-01
We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."
4. Magnetospheric particle detection efficiency of a conical telescope
International Nuclear Information System (INIS)
Miah, M.A.; Mitchell, J.W.; Wefel, J.P.
1989-01-01
A semianalytic program has been developed to map the pitch angles of magnetospheric particles onto a detector telescope acceptance cone. The telescope fractional efficiency is defined as the fraction of the pitch angle cone in common with the telescope cone multiplied by the fractional perpendicular component of the exposed detector area, and normalized by 2π. Calculations have been performed as a function of the satellite's location, orbital inclination and the zenith angle of the telescope axis, both in dipole and real geomagnetic field models. At the dipole equator, the peak efficiency occurs at 90 0 pitch angle. In the real geomagnetic field model, the average value of the pitch angle for maximum efficiency is ≅ 88 0 . The efficiency function depends strongly upon latitude and is independent of longitude in a dipole field, but depends on longitude in the real field model. In either field model, altitude, angle of tilt and orbital inclination have little effect upon efficiency. The efficiency function calculated at the dipole equator can be used at the minimum magnetic field equator with little error, but not for points away from the B min position. The results are applied to calculate the absolute flux of magnetospheric particles observed near the equator. (orig.)
5. Field-aligned currents near the magnetosphere boundary
International Nuclear Information System (INIS)
Hones, E.W. Jr.
1984-01-01
This paper describes present thinking about the structure of magnetospheric boundary layers and their roles in the generation of the field-aligned currents that are observed in the polar regions. A principal effect of the momentum loss by magnetosheath plasma to the magnetosphere boundary regions just within the magnetopause, whether it be by a diffusive process or by magnetic reconnection, is the tailward pulling of the surface flux tubes relative to those deeper below the surface. The dayside region 1 currents at low altitudes flow along field lines in the resulting regions of magnetic shear. The direction of the shear and its magnitude, actually measured in the boundary region, confirm that the polarities and intensities of the dayside region 1 currents can be accounted for by this process. The low latitude boundary layer, formerly thought to be threaded entirely by closed field lines, now appears to contain at least some open field lines, newly reconnected, that are in the process of being swept into the high latitude tail to form the plasma mantle. The open flux tubes of the flux transfer events, thought to be the product of patchy reconnection have a spiral magnetic structure whose helicity is such as to suggest currents having the polarities of the region 1 currents. 13 references
6. Controlled VLF phase reversal experiment in the magnetosphere
International Nuclear Information System (INIS)
Koons, H.C.; Dazey, M.H.; Dowden, R.L.; Amon, L.E.S.
1976-01-01
During the 1973 operations of the transportable very low frequency transmitter near Anchorage, Alaska (Lapprox.4), an experiment was performed to determine the effect of controlled phase change of the transmitted wave on the magnetospherically propagated signal received in the conjugate region. At periodic intervals the phase of the driving voltage was changed (essentially instantaneously) by 180degree. The amplitude of the 6.6-kHz signal detected in the conjugate region went to zero and recovered with a characteristic time constant of 33 ms. This is 10 times longer than the antenna current response time and is in fact comparable with characteristic electron interaction times with whistler mode waves. Between the times at which the phase reversals occurred the received signal was amplitude modulated. The period of the modulation was approx.26 ms. An upper side band was present in the spectrum while these pulsations were occurring. These characteristic times are in general agreement with theoretical predictions of bandwidths, growth rates, and particle-trapping frequencies for whistler instabilities in the magnetosphere. Data obtained from the controlled transmissions and from lightning-generated whistlers propagating in the same duct were combined to determine the plasma and wave parameters at the geomagnetic equator. Of particular interest is the level at which the magnetic field of the wave saturated. During the time period for which the data were analyzed this was found to be 3.5 pT (mγ)
7. Plasma Transport at the Magnetospheric Flank Boundary. Final report
International Nuclear Information System (INIS)
Otto, Antonius
2012-01-01
Progress is highlighted in these areas: 1. Model of magnetic reconnection induced by three-dimensional Kelvin Helmholtz (KH) modes at the magnetospheric flank boundary; 2. Quantitative evaluation of mass transport from the magnetosheath onto closed geomagnetic field for northward IMF; 3. Comparison of mass transfer by cusp reconnection and Flank Kelvin Helmholtz modes; 4. Entropy constraint and plasma transport in the magnetotail - a new mechanism for current sheet thinning; 5. Test particle model for mass transport onto closed geomagnetic field for northward IMF; 6. Influence of density asymmetry and magnetic shear on (a) the linear and nonlinear growth of 3D Kelvin Helmholtz (KH) modes, and (b) three-dimensional KH mediated mass transport; 7. Examination of entropy and plasma transport in the magnetotail; 8. Entropy change and plasma transport by KH mediated reconnection - mixing and heating of plasma; 9. Entropy and plasma transport in the magnetotail - tail reconnection; and, 10. Wave coupling at the magnetospheric boundary and generation of kinetic Alfven waves
8. Eigenmode analysis of coupled magnetohydrodynamic oscillations in the magnetosphere
International Nuclear Information System (INIS)
Fujita, S.; Patel, V.L.
1992-01-01
The authors have performed an eigenmode analysis of the coupled magnetohydrodynamic oscillations in the magnetosphere with a dipole magnetic field. To understand the behavior of the spatial structure of the field perturbations with a great accuracy, they use the finite element method. The azimuthal and radial electric field perturbations are assumed to vanish at the ionosphere, and the azimuthal electric field is assumed to be zero on the outer boundary. The global structures of the electromagnetic field perturbations associated with the coupled magnetohydrodynamic oscillations are presented. In addition, the three-dimensional current system associated with the coupled oscillations is numerically calculated and the following characteristics are found: (1) A strong field-aligned current flows along a resonant field line. The current is particularly strong near the ionosphere. (2) The radial current changes its direction on the opposite sides of the resonant L shell. Unlike the field-aligned current, the radial currents exist in the entire magnetosphere. (3) Although the azimuthal and radial currents are intense on the resonant field line, these currents do not form a loop in the plane perpendicular to the ambient magnetic field. Therefore the field-aligned component of the perturbed magnetic field does not have a maximum at the resonant L shell
9. Parabolic heavy ion flow in the polar magnetosphere
International Nuclear Information System (INIS)
Horwitz, J.L.
1987-01-01
Recent observations by the Dynamics Explorer 1 satellite over the dayside polar cap magnetosphere have indicated downward flows of heavy ions (O + , O ++ , N + , N ++ ) with flow velocities of the order 1 km/s (Lockwood et al., 1985b). These downward flows were interpreted as the result of parabolic flow of these heavy ionospheric ions from a source region associated with the polar cleft topside ionosphere. Here the author utilizes a two-dimensional kinetic model to elicit features of the transport of very low energy O + ions from the cleft ionosphere. Bulk parameter (density, flux, thermal energies, etc.) distributions in the noon-midnight meridian plane illustrate the effects of varying convection electric fields and source energies. The results illustrate that particularly under conditions of weak convection electric fields and weak ion heating in the cleft region, much of the intermediate altitude polar cap magnetosphere may be populated by downward flowing heavy ions. It is further shown how two-dimensional transport effects may alter the characteristic vertical profiles of densities and fluxes from ordinary profiles computed in one-dimensional steady state models
10. Field-aligned currents near the magnetosphere boundary
International Nuclear Information System (INIS)
Hones, E.W. Jr.
1983-01-01
This paper reviews present thinking about the structure of magnetospheric boundary layers and their roles in the generation of the field-aligned currents that are observed in the polar regions. A principal effect of the momentum loss by magnetosheath plasma to the magnetosphere boundary regions just within the magnetopause, whether it be by a diffusive process or by magnetic reconnection, is the tailward pulling of surface flux tubes relative to those deeper below the surface. The dayside region 1 currents at low altitudes flow along field lines in the resulting regions of magnetic shear. The direction of the shear and its magnitude, measured in the boundary region, confirm tht the polarities and intensities of the dayside region 1 currents can be accounted for by this process. The low latitude boundary layer, formerly thought to be threaded entirely by closed field lines, now appears to contain at least some open field lines, newly reconnected, that are in the process of being swept into the high latitude tail to form the plasma mantle. The open flux tubes of the flux transfer events, thought to be the product of patchy reconnection have a spiral magnetic structure whose helicity is such as to suggest currents having the polarities of the region 1 currents
11. Electron dynamics during substorm dipolarization in Mercury's magnetosphere
Directory of Open Access Journals (Sweden)
D. C. Delcourt
2005-11-01
Full Text Available We examine the nonlinear dynamics of electrons during the expansion phase of substorms at Mercury using test particle simulations. A simple model of magnetic field line dipolarization is designed by rescaling a magnetic field model of the Earth's magnetosphere. The results of the simulations demonstrate that electrons may be subjected to significant energization on the time scale (several seconds of the magnetic field reconfiguration. In a similar manner to ions in the near-Earth's magnetosphere, it is shown that low-energy (up to several tens of eV electrons may not conserve the second adiabatic invariant during dipolarization, which leads to clusters of bouncing particles in the innermost magnetotail. On the other hand, it is found that, because of the stretching of the magnetic field lines, high-energy electrons (several keVs and above do not behave adiabatically and possibly experience meandering (Speiser-type motion around the midplane. We show that dipolarization of the magnetic field lines may be responsible for significant, though transient, (a few seconds precipitation of energetic (several keVs electrons onto the planet's surface. Prominent injections of energetic trapped electrons toward the planet are also obtained as a result of dipolarization. These injections, however, do not exhibit short-lived temporal modulations, as observed by Mariner-10, which thus appear to follow from a different mechanism than a simple convection surge.
12. Discovery of Suprathermal Fe+ in and near Earth's Magnetosphere
Science.gov (United States)
Christon, S. P.; Hamilton, D. C.; Plane, J. M. C.; Mitchell, D. G.; Grebowsky, J. M.; Spjeldvik, W. N.; Nylund, S. R.
2017-12-01
Suprathermal (87-212 keV/e) singly charged iron, Fe+, has been observed in and near Earth's equatorial magnetosphere using long-term ( 21 years) Geotail/STICS ion composition data. Fe+ is rare compared to dominant suprathermal solar wind and ionospheric origin heavy ions. Earth's suprathermal Fe+ appears to be positively associated with both geomagnetic and solar activity. Three candidate lower-energy sources are examined for relevance: ionospheric outflow of Fe+ escaped from ion layers altitude, charge exchange of nominal solar wind Fe+≥7, and/or solar wind transported inner source pickup Fe+ (likely formed by solar wind Fe+≥7 interaction with near sun interplanetary dust particles, IDPs). Semi-permanent ionospheric Fe+ layers form near 100 km altitude from the tons of IDPs entering Earth's atmosphere daily. Fe+ scattered from these layers is observed up to 1000 km altitude, likely escaping in strong ionospheric outflows. Using 26% of STICS's magnetosphere-dominated data at low-to-moderate geomagnetic activity levels, we demonstrate that solar wind Fe charge exchange secondaries are not an obvious Fe+ source then. Earth flyby and cruise data from Cassini/CHEMS, a nearly identical instrument, show that inner source pickup Fe+ is likely not important at suprathermal energies. Therefore, lacking any other candidate sources, it appears that ionospheric Fe+ constitutes at least an important portion of Earth's suprathermal Fe+, comparable to observations at Saturn where ionospheric origin suprathermal Fe+ has also been observed.
13. Flute instability in the plasma shell of the earth's magnetosphere
International Nuclear Information System (INIS)
Ivanov, V.N.; Pokhotelov, O.A.
1987-01-01
In the plasma shell of the earth's magnetosphere, the surfaces of constant pressure may not coincide with surfaces of constant specific volume. This circumstance forces a reexamination of the theory for the flute instability, in which the pressure has been assumed to remain constant on surfaces of constant specific volume. The MHD equations for flute waves in a curvilinear magnetic field are used to show that an instability of a new type, with a pressure which does not remain constant on surfaces of constant specific volume, can occur in the plasma shell of the magnetosphere. An expression is derived for the growth rate of this instability. Analysis of the equation also shows that perturbations with wavelengths shorter than the ion Larmor radius are stable by virtue of magnetodrift effects. The growth rates of the flute instabilities are calculated for both a dipole magnetic field and an arbitrary magnetic-field configuration. Growth rates calculated for typical values of the characteristics of the earth's plasma shell are reported
14. Magnetosphere energetics during substorm events IMP 8 and Geotail observations
CERN Document Server
Belehaki, A
2001-01-01
Magnetospheric energetics during substorm events is studied in this paper. Three events were selected, a weak substorm, a large isolated one and finally a prolonged period of substorm activity with multiple intensifications. It is assumed that the energy, that entered the magnetosphere due to electromagnetic coupling with the solar wind, is described by the epsilon parameter, proposed by Perreault and Akasofu (1978). High resolution, magnetic field and plasma data from the MGF and LEP experiments on board Geotail were analyzed to determine the timing of plasmoid release, its dimensions, its convection velocity and finally the energy carried by each plasmoid. Plasmoids were defined as structures with rotating magnetic fields and enhanced total pressure. Tailward plasmoid bulk speed in the distant tail varied from 350 to 750 km/s. Their dimensions in the X/sub GSM/ direction was found to be from 4.5 to 28 R/sub E/, and their duration did not exceed 5 min. The average energy carried by each plasmoid in the dista...
15. Sodium Ion Dynamics in the Magnetospheric Flanks of Mercury
Science.gov (United States)
Aizawa, Sae; Delcourt, Dominique; Terada, Naoki
2018-01-01
We investigate the transport of planetary ions in the magnetospheric flanks of Mercury. In situ measurements from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft show evidences of Kelvin-Helmholtz instability development in this region of space, due to the velocity shear between the downtail streaming flow of solar wind originating protons in the magnetosheath and the magnetospheric populations. Ions that originate from the planet exosphere and that gain access to this region of space may be transported across the magnetopause along meandering orbits. We examine this transport using single-particle trajectory calculations in model Magnetohydrodynamics simulations of the Kelvin-Helmholtz instability. We show that heavy ions of planetary origin such as Na+ may experience prominent nonadiabatic energization as they E × B drift across large-scale rolled up vortices. This energization is controlled by the characteristics of the electric field burst encountered along the particle path, the net energy change realized corresponding to the maximum E × B drift energy. This nonadiabatic energization also is responsible for prominent scattering of the particles toward the direction perpendicular to the magnetic field.
16. The Earth's magnetosphere is 165 R(sub E) long: Self-consistent currents, convection, magnetospheric structure, and processes for northward interplanetary magnetic field
Science.gov (United States)
Fedder, J. A.; Lyon, J. G.
1995-01-01
The subject of this paper is a self-consistent, magnetohydrodynamic numerical realization for the Earth's magnetosphere which is in a quasi-steady dynamic equilibrium for a due northward interplanetary magnetic field (IMF). Although a few hours of steady northward IMF are required for this asymptotic state to be set up, it should still be of considerable theoretical interest because it constitutes a 'ground state' for the solar wind-magnetosphere interaction. Moreover, particular features of this ground state magnetosphere should be observable even under less extreme solar wind conditions. Certain characteristics of this magnetosphere, namely, NBZ Birkeland currents, four-cell ionospheric convection, a relatively weak cross-polar potential, and a prominent flow boundary layer, are widely expected. Other characteristics, such as no open tail lobes, no Earth-connected magnetic flux beyond 155 R(sub E) downstream, magnetic merging in a closed topology at the cusps, and a 'tadpole' shaped magnetospheric boundary, might not be expected. In this paper, we will present the evidence for this unusual but interesting magnetospheric equilibrium. We will also discuss our present understanding of this singular state.
17. Ambitious Survey Spots Stellar Nurseries
Science.gov (United States)
2010-08-01
-dimensional geometry of the Magellanic system. Chris Evans from the VMC team adds: "The VISTA images will allow us to extend our studies beyond the inner regions of the Tarantula into the multitude of smaller stellar nurseries nearby, which also harbour a rich population of young and massive stars. Armed with the new, exquisite infrared images, we will be able to probe the cocoons in which massive stars are still forming today, while also looking at their interaction with older stars in the wider region." The wide-field image shows a host of different objects. The bright area above the centre is the Tarantula Nebula itself, with the RMC 136 cluster of massive stars in its core. To the left is the NGC 2100 star cluster. To the right is the tiny remnant of the supernova SN1987A (eso1032). Below the centre are a series of star-forming regions including NGC 2080 - nicknamed the "Ghost Head Nebula" - and the NGC 2083 star cluster. The VISTA Magellanic Cloud Survey is one of six huge near-infrared surveys of the southern sky that will take up most of the first five years of operations of VISTA. Notes [1] VISTA ― the Visible and Infrared Survey Telescope for Astronomy ― is the newest telescope at ESO's Paranal Observatory in northern Chile. VISTA is a survey telescope working at near-infrared wavelengths and is the world's largest survey telescope. Its large mirror, wide field of view and very sensitive detectors will reveal a completely new view of the southern sky. The telescope is housed on the peak adjacent to the one hosting ESO's Very Large Telescope (VLT) and shares the same exceptional observing conditions. VISTA has a main mirror that is 4.1 m across. In photographic terms it can be thought of as a 67-megapixel digital camera with a 13 000 mm f/3.25 mirror lens. More information ESO, the European Southern Observatory, is the foremost intergovernmental astronomy organisation in Europe and the world's most productive astronomical observatory. It is supported by 14 countries
18. The “Building Blocks” of Stellar Halos
Directory of Open Access Journals (Sweden)
Kyle A. Oman
2017-08-01
Full Text Available The stellar halos of galaxies encode their accretion histories. In particular, the median metallicity of a halo is determined primarily by the mass of the most massive accreted object. We use hydrodynamical cosmological simulations from the apostle project to study the connection between the stellar mass, the metallicity distribution, and the stellar age distribution of a halo and the identity of its most massive progenitor. We find that the stellar populations in an accreted halo typically resemble the old stellar populations in a present-day dwarf galaxy with a stellar mass ∼0.2–0.5 dex greater than that of the stellar halo. This suggests that had they not been accreted, the primary progenitors of stellar halos would have evolved to resemble typical nearby dwarf irregulars.
19. Deriving stellar parameters with the SME software package
Science.gov (United States)
Piskunov, N.
2017-09-01
Photometry and spectroscopy are complementary tools for deriving accurate stellar parameters. Here I present one of the popular packages for stellar spectroscopy called SME with the emphasis on the latest developments and error assessment for the derived parameters.
20. Stellar chemical signatures and hierarchical galaxy formation
NARCIS (Netherlands)
Venn, KA; Irwin, M; Shetrone, MD; Tout, CA; Hill, [No Value; Tolstoy, E
To compare the chemistries of stars in the Milky Way dwarf spheroidal (dSph) satellite galaxies with stars in the Galaxy, we have compiled a large sample of Galactic stellar abundances from the literature. When kinematic information is available, we have assigned the stars to standard Galactic
1. Equilibrium 𝛽-limits in classical stellarators
Science.gov (United States)
Loizu, J.; Hudson, S. R.; Nührenberg, C.; Geiger, J.; Helander, P.
2017-12-01
A numerical investigation is carried out to understand the equilibrium -limit in a classical stellarator. The stepped-pressure equilibrium code (Hudson et al., Phys. Plasmas, vol. 19 (11), 2012) is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high . Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed (Taylor, Rev. Mod. Phys., vol. 58 (3), 1986, pp. 741-763), the former is shown to maintain good flux surfaces up to the equilibrium -limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium -limit, is shown to develop regions of magnetic islands and chaos at sufficiently high , thereby providing a `non-ideal -limit'. Perhaps surprisingly, however, the value of at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg (Ideal MHD, 2014, Cambridge University Press) and derive a new prediction for the non-ideal equilibrium -limit above which chaos emerges.
2. Stellar Sources of Gamma-ray Bursts
OpenAIRE
Luchkov, B. I.
2011-01-01
Correlation analysis of Swift gamma-ray burst coordinates and nearby star locations (catalog Gliese) reveals 4 coincidences with good angular accuracy. The random probability is 4\\times 10^{-5}, so evidencing that coincident stars are indeed gamma-ray burst sources. Some additional search of stellar gamma-ray bursts is discussed.
3. Benchmarking the Multidimensional Stellar Implicit Code MUSIC
Science.gov (United States)
Goffrey, T.; Pratt, J.; Viallet, M.; Baraffe, I.; Popov, M. V.; Walder, R.; Folini, D.; Geroux, C.; Constantino, T.
2017-04-01
We present the results of a numerical benchmark study for the MUltidimensional Stellar Implicit Code (MUSIC) based on widely applicable two- and three-dimensional compressible hydrodynamics problems relevant to stellar interiors. MUSIC is an implicit large eddy simulation code that uses implicit time integration, implemented as a Jacobian-free Newton Krylov method. A physics based preconditioning technique which can be adjusted to target varying physics is used to improve the performance of the solver. The problems used for this benchmark study include the Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and the decay of the Taylor-Green vortex. Additionally we show a test of hydrostatic equilibrium, in a stellar environment which is dominated by radiative effects. In this setting the flexibility of the preconditioning technique is demonstrated. This work aims to bridge the gap between the hydrodynamic test problems typically used during development of numerical methods and the complex flows of stellar interiors. A series of multidimensional tests were performed and analysed. Each of these test cases was analysed with a simple, scalar diagnostic, with the aim of enabling direct code comparisons. As the tests performed do not have analytic solutions, we verify MUSIC by comparing it to established codes including ATHENA and the PENCIL code. MUSIC is able to both reproduce behaviour from established and widely-used codes as well as results expected from theoretical predictions. This benchmarking study concludes a series of papers describing the development of the MUSIC code and provides confidence in future applications.
4. Microlensing and the physics of stellar atmospheres
NARCIS (Netherlands)
Sackett, PD; Menzies, JW; Sackett, PD
2001-01-01
The simple physics of microlensing provides a well understood tool with which to probe the atmospheres of distant stars in the Galaxy and Local Group with high magnification and resolution. Recent results in measuring stellar surface structure through broad band photometry and spectroscopy of high
5. Evolution and seismic tools for stellar astrophysics
CERN Document Server
Monteiro, Mario JPFG
2008-01-01
A collection of articles published by the journal "Astrophysics and Space Science, Volume 316, Number 1-4", August 2008. This work covers 10 evolution codes and 9 oscillation codes. It is suitable for researchers and research students working on the modeling of stars and on the implementation of seismic test of stellar models.
6. STELLAR TRANSITS IN ACTIVE GALACTIC NUCLEI
International Nuclear Information System (INIS)
Béky, Bence; Kocsis, Bence
2013-01-01
Supermassive black holes (SMBHs) are typically surrounded by a dense stellar population in galactic nuclei. Stars crossing the line of site in active galactic nuclei (AGNs) produce a characteristic transit light curve, just like extrasolar planets do when they transit their host star. We examine the possibility of finding such AGN transits in deep optical, UV, and X-ray surveys. We calculate transit light curves using the Novikov-Thorne thin accretion disk model, including general relativistic effects. Based on the expected properties of stellar cusps, we find that around 10 6 solar mass SMBHs, transits of red giants are most common for stars on close orbits with transit durations of a few weeks and orbital periods of a few years. We find that detecting AGN transits requires repeated observations of thousands of low-mass AGNs to 1% photometric accuracy in optical, or ∼10% in UV bands or soft X-ray. It may be possible to identify stellar transits in the Pan-STARRS and LSST optical and the eROSITA X-ray surveys. Such observations could be used to constrain black hole mass, spin, inclination, and accretion rate. Transit rates and durations could give valuable information on the circumnuclear stellar clusters as well. Transit light curves could be used to image accretion disks with unprecedented resolution, allowing us to resolve the SMBH silhouette in distant AGNs.
7. Robust Modeling of Stellar Triples in PHOEBE
Science.gov (United States)
Conroy, Kyle E.; Prsa, Andrej; Horvat, Martin; Stassun, Keivan G.
2017-01-01
The number of known mutually-eclipsing stellar triple and multiple systems has increased greatly during the Kepler era. These systems provide significant opportunities to both determine fundamental stellar parameters of benchmark systems to unprecedented precision as well as to study the dynamical interaction and formation mechanisms of stellar and planetary systems. Modeling these systems to their full potential, however, has not been feasible until recently. Most existing available codes are restricted to the two-body binary case and those that do provide N-body support for more components make sacrifices in precision by assuming no stellar surface distortion. We have completely redesigned and rewritten the PHOEBE binary modeling code to incorporate support for triple and higher-order systems while also robustly modeling data with Kepler precision. Here we present our approach, demonstrate several test cases based on real data, and discuss the current status of PHOEBE's support for modeling these types of systems. PHOEBE is funded in part by NSF grant #1517474.
8. On the collapse of iron stellar cores
International Nuclear Information System (INIS)
Barkat, Z.; Rakavy, G.; Reiss, Y.; Wilson, J.R.
1975-01-01
The collapse of iron stellar cores is investigated to see whether the outward shock produced by the bounce at neutron star density is sufficient to burn appreciable amounts of the envelope around the iron core. Several models were tried, and in all cases no appreciable burn took place; hence no explosion results from the collapse of these models
9. Modular Stellarator Reactor conceptual design study
International Nuclear Information System (INIS)
Miller, R.L.; Bathke, C.G.
1983-01-01
A conceptual design study of the Modular Stellarator Reactor is summarized. The physics basis of the approach is elucidated with emphasis on magnetics performance optimization. Key engineering features of the fusion power core are described. Comparisons with an analogous continuous-helical-coil (torsatron) system are made as the basis of a technical and economic assessment
10. Summary of the Advanced Stellar Compass
DEFF Research Database (Denmark)
Jørgensen, John Leif
1997-01-01
The current version of the Advanced Stellar Compass (ASC) is an improved implementation of the instrument developed for the Danish Geomagnetic Research Satellite Ørsted. The Ørsted version was successfully tested in space on the NASA sounding rocket "Thunderstorm III", that was launched September 2...
11. Neutrino confinement in collapsing stellar cores
International Nuclear Information System (INIS)
Chung, K.C.
1987-01-01
Neutrino confinement is expected to occur in the core of highly evolved stars, leading to the formation of a degenerate neutrino gas. The main neutrino sources are briefly reviewed and the neutrino processes relevant to the neutrino opacity in the stellar matter are discussed. Implications for the equation of state of neutrino-trapped matter are examined. (author) [pt
12. Survey of the MAgellanic Stellar History -- SMASH
NARCIS (Netherlands)
Nidever, David; Olsen, Knut; Besla, Gurtina; Gruendl, Robert; Saha, Abhijit; Gallart, Carme; Olszewski, Edward W.; Munoz, Ricardo; Monelli, Matteo; Kunder, Andrea; Kaleida, Catherine; Walker, Alistair; Stringfellow, Guy; Zaritsky, Dennis; van der Marel, Roeland; Blum, Robert; Vivas, Kathy; Chu, You-Hua; Martin, Nicolas; Conn, Blair; Noel, Noelia; Majewski, Steven; Jin, Shoko; Kim, Hwihyun; Cioni, Maria-Rosa; Bell, Eric; Monachesi, Antonela; de Boer, Thomas
Over the last several years, various discoveries have drastically altered our view of the iconic Magellanic Clouds (MCs), the nearest interacting galaxy system. The best evidence is now that they are on first infall into the Milky Way, that their stellar populations extend much further than
13. The evolution of stellar exponential discs
NARCIS (Netherlands)
Ferguson, AMN; Clarke, CJ
2001-01-01
Models of disc galaxies which invoke viscosity-driven radial flows have long been known to provide a natural explanation for the origin of stellar exponential discs, under the assumption that the star formation and viscous time-scales are comparable. We present models which invoke simultaneous star
14. Modular stellarator reactor conceptual design study
International Nuclear Information System (INIS)
Miller, R.L.; Krakowski, R.A.; Bathke, C.G.
1983-01-01
A conceptual design study of the Modular Stellarator Reactor is summarized. The physics basis of the approach is elucidated with emphasis on magnetics performance optimization. Key engineering features of the fusion power core are described. Comparisons with an analogous continuous-helical-coil (torsatron) system are made as the basis of a technical and economic assessment
15. The Stellar Imager (SI) Mission Concept
Science.gov (United States)
Carpenter, Kenneth G.; Schrijver, Carolus J.; Lyon, Richard G.; Mundy, Lee G.; Allen, Ronald J.; Armstrong, Thomas; Danchi, William C.; Karovska, Margarita; Marzouk, Joe; Mazzuca, Lisa M.;
2002-01-01
The Stellar Imager (SI) is envisioned as a space-based, UV-optical interferometer composed of 10 or more one-meter class elements distributed with a maximum baseline of 0.5 km. It is designed to image stars and binaries with sufficient resolution to enable long-term studies of stellar magnetic activity patterns, for comparison with those on the sun. It will also support asteroseismology (acoustic imaging) to probe stellar internal structure, differential rotation, and large-scale circulations. SI will enable us to understand the various effects of the magnetic fields of stars, the dynamos that generate these fields, and the internal structure and dynamics of the stars. The ultimate goal of the mission is to achieve the best-possible forecasting of solar activity as a driver of climate and space weather on time scales ranging from months up to decades, and an understanding of the impact of stellar magnetic activity on life in the Universe. In this paper we describe the scientific goals of the mission, the performance requirements needed to address these goals, the "enabling technology" development efforts being pursued, and the design concepts now under study for the full mission and a possible pathfinder mission.
16. Indian Academy of Sciences (India)
tribpo
detect giant extra solar planets (detectable by spectroscopy from the ground) and determine their albedo. As COROT is devoted to stellar photometry, aiming at both a high precision and a long observation time, the search for exoplanets by the transit method can easily be integrated in the payload and in the mission profile.
17. Teaching stellar interferometry with polymer optical fibers
Science.gov (United States)
Illarramendi, M. A.; Arregui, L.; Zubia, J.; Hueso, R.; Sanchez-Lavega, A.
2017-08-01
In this manuscript we show the design of a simple experiment that reproduces the operation of the Michelson stellar interferometer by using step-index polymer optical fibers. The emission of stellar sources, single or binary stars, has been simulated by the laser light emerging from the output surface of the 2 meter-long polymer optical fiber. This light has an emission pattern that is similar to the emission pattern of stellar sources - circular, uniform, spatially incoherent, and quasi-monochromatic. Light coming from the fiber end faces passes through two identical pinholes located on a lid covering the objective of a small telescope, thus producing interference. Interference fringes have been acquired using a camera that is coupled to a telescope. The experiments have been carried out both outdoors in the daytime and indoors. By measuring the fringe visibilities, we have determined the size of our artificial stellar sources and the distance between them, when placing them at distances of 54 m from the telescope in the indoor measurements and of 75 m in the outdoor ones.
18. Plea for stellarator funding raps tokamaks
International Nuclear Information System (INIS)
Blake, M.
1992-01-01
The funding crunch in magnetic confinement fusion development has moved the editor of a largely technical publication to speak out on a policy issue. James A. Rome, who edits Stellarator News from the Fusion Energy Division at Oak Ridge National Laboratory, wrote an editorial that appeared on the front page of the May 1992 issue. It was titled open-quotes The US Stellarator Program: A Time for Renewal,close quotes and while it focused chiefly on that subject (and lamented the lack of funding for the operation of the existing ATF stellarator at Oak Ridge), it also cited some of the problems inherent in the mainline MCF approach--the tokamak--and stated that if the money can be found for further tokamak design upgrades, it should also be found for stellarators. Rome wrote, open-quotes There is growing recognition in the US, and elsewhere, that the conventional tokamak does not extrapolate to a commercially competitive energy source except with very high field coils ( 1000 MWe).close quotes He pointed up open-quotes the difficulty of simultaneously satisfying conflicting tokamak requirements for efficient current drive, high bootstrap-current fraction, complete avoidance of disruptions, adequate beta limits, and edge-plasma properties compatible with improved (H-mode) confinement and acceptable erosion of divertor plates.close quotes He then called for support for the stellarator as open-quotes the only concept that has performance comparable to that achieved in tokamaks without the plasma-current-related limitations listed above.close quotes
19. The Quasi-Toroidal Stellarator: An Innovative Confinement Experiment
International Nuclear Information System (INIS)
Knowlton, S. F.
2001-01-01
To develop a new class of stellarators that exhibit improved confinement compared to conventional stellarators. This approach generally makes use of a designed symmetry of the magnetic field strength along a particular coordinate axis in the toroidal geometry of the stellarator, and is referred to as quasi-symmetry
20. Constraining the Stellar Mass Function in the Galactic Center via Mass Loss from Stellar Collisions
Directory of Open Access Journals (Sweden)
Douglas Rubin
2011-01-01
Full Text Available The dense concentration of stars and high-velocity dispersions in the Galactic center imply that stellar collisions frequently occur. Stellar collisions could therefore result in significant mass loss rates. We calculate the amount of stellar mass lost due to indirect and direct stellar collisions and find its dependence on the present-day mass function of stars. We find that the total mass loss rate in the Galactic center due to stellar collisions is sensitive to the present-day mass function adopted. We use the observed diffuse X-ray luminosity in the Galactic center to preclude any present-day mass functions that result in mass loss rates >10-5M⨀yr−1 in the vicinity of ~1″. For present-day mass functions of the form, dN/dM∝M-α, we constrain the present-day mass function to have a minimum stellar mass ≲7M⨀ and a power-law slope ≳1.25. We also use this result to constrain the initial mass function in the Galactic center by considering different star formation scenarios.
1. Methane Group Ions in Saturn’s Outer Magnetosphere?
Science.gov (United States)
Sittler, E. C.; Hartle, R. E.; Cooper, J. F.; Johnson, R. E.; Smith, H.; Shappirio, M.; Reisenfeld, D. B.
2009-12-01
Yelle et al. [2008] have estimated from Cassini Ion Neutral Mass Spectrometer (INMS) measurements that methane is escaping from Titan’s upper atmosphere at the rate of 2.5-3.0×109 mol/cm2/s and in order to explain this loss rate Strobel [2008] has proposed a hydrodynamic escape model to explain such high loss rates. This translates to loss of 2.8×1027 methane mol/s. The consequence of this work is the formation of a methane torus around Saturn which will dissociate to CH3 and other fragments of methane. The CH3 will then become ionized to form CH3+ with pickup energies ≈ keV after which it can be detected by the Cassini Plasma Spectrometer (CAPS) Ion Mass Spectrometer (IMS). Up till now the ion composition within Saturn’s outer magnetosphere in the vicinity of Titan’s orbit have yielded negative results with water group ions W+ dominating. The water group ions probably result from the emission of fast neutrals from the Enceladus torus via charge exchange reactions but still gravitationally bound to Saturn [see Johnson et al., 2005 and Sittler et al. 2006] and then become ionized in the outer magnetosphere as ~≈keV pickup ions. The CAPS IMS produces two ion composition data products, one called Straight Through (ST) and the other Linear Electric Field (LEF). The first has a higher sensitivity, while the latter has a greater discrimination in time-of-flight (TOF). For ST data O+ and CH4+ have similar TOF with the primary discriminator being the O- fragment which appears at a different TOF than for mass 16 ions. One can also look for other discriminators called ghost peaks. In case of LEF W+ ions produce TOF peak close to that for atomic O+ and the methane will produce TOF close to that for atomic C+ which has a significantly different(shorter) TOF than O+. We will be reporting on our continual search for methane ions within Saturn’s outer magnetosphere. References: 1. Yelle, R. V., J. Cui and I.C.F. Müller-Wodarg, JGR, 2008. 2. Strobel, D. F., Icarus
2. Rotation Rate of Saturn's Magnetosphere using CAPS Plasma Measurements
Science.gov (United States)
Sittler, E.; Cooper, J.; Simpson, D.; Paterson, W.
2012-01-01
We present the present status of an investigation of the rotation rate of Saturn 's magnetosphere using a 3D velocity moment technique being developed at Goddard which is similar to the 2D version used by Sittler et al. (2005) [1] for SOI and similar to that used by Thomsen et al. (2010). This technique allows one to nearly cover the full energy range of the CAPS IMS from 1 V less than or equal to E/Q less than 50 kV. Since our technique maps the observations into a local inertial frame, it does work during roll manoeuvres. We have made comparisons with Wilson et al. (2008) [2] (2005-358 and 2005-284) who performs a bi-Maxwellian fit to the ion singles data and our results are nearly identical. We will also make comparisons with results by Thomsen et al. (2010) [3]. Our analysis uses ion composition data to weight the non-compositional data, referred to as singles data, to separate H+, H2+ and water group ions (W+) from each other. The ion data set is especially valuable for measuring flow velocities for protons, which are more difficult to derive using singles data within the inner magnetosphere, where the signal is dominated by heavy ions (i.e., proton peak merges with W+ peak as low energy shoulder). Our technique uses a flux function, which is zero in the proper plasma flow frame, to estimate fluid parameter uncertainties. The comparisons investigate the experimental errors and potential for systematic errors in the analyses, including ours. The rolls provide the best data set when it comes to getting 4PI coverage of the plasma but are more susceptible to time aliasing effects. Since our analysis is a velocity moments technique it will work within the inner magnetosphere where pickup ions are important and velocity distributions are non-Maxwellian. So, we will present results inside Enceladus' L shell and determine if mass loading is important. In the future we plan to make comparisons with magnetic field observations, use Saturn ionosphere conductivities as
3. Penetration of magnetosonic waves into the magnetosphere: influence of a transition layer
Directory of Open Access Journals (Sweden)
A. S. Leonovich
2003-05-01
Full Text Available We have constructed a theory for the penetration of magnetosonic waves from the solar wind into the magnetosphere through a transition layer in a plane-stratified model for the medium. In this model the boundary layer is treated as a region, inside of which the parameters of the medium vary from values characteristic for the magnetosphere, to values typical of the solar wind. It is shown that if such a layer has sufficiently sharp boundaries, then magnetosonic eigen-oscillations can be excited inside of it. The boundaries of such a layer are partially permeable for magnetosonic waves. Therefore, if the eigen-oscillations are not sustained by an external source, they will be attenuated, because some of the energy is carried away by the oscillations that penetrate the solar wind and the magnetosphere. It is shown that about 40% of the energy flux of the waves incident on the transition layer in the magnetotail region penetrate to the magnetosphere’s interior. This energy flux suffices to sustain the stationary convection of magnetospheric plasma. The total energy input to the magnetosphere during a time interval of the order of the substorm growth phase time is comparable with the energetics of an average substorm.Key words. Magnetospheric physics (MHD waves and instabilities; solar wind–magnetosphere interactions – Space plasma physics (kinetic and MHD theory
4. Penetration of magnetosonic waves into the magnetosphere: influence of a transition layer
Directory of Open Access Journals (Sweden)
A. S. Leonovich
Full Text Available We have constructed a theory for the penetration of magnetosonic waves from the solar wind into the magnetosphere through a transition layer in a plane-stratified model for the medium. In this model the boundary layer is treated as a region, inside of which the parameters of the medium vary from values characteristic for the magnetosphere, to values typical of the solar wind. It is shown that if such a layer has sufficiently sharp boundaries, then magnetosonic eigen-oscillations can be excited inside of it. The boundaries of such a layer are partially permeable for magnetosonic waves. Therefore, if the eigen-oscillations are not sustained by an external source, they will be attenuated, because some of the energy is carried away by the oscillations that penetrate the solar wind and the magnetosphere. It is shown that about 40% of the energy flux of the waves incident on the transition layer in the magnetotail region penetrate to the magnetosphere’s interior. This energy flux suffices to sustain the stationary convection of magnetospheric plasma. The total energy input to the magnetosphere during a time interval of the order of the substorm growth phase time is comparable with the energetics of an average substorm.
Key words. Magnetospheric physics (MHD waves and instabilities; solar wind–magnetosphere interactions – Space plasma physics (kinetic and MHD theory
5. Surface conductivity of Mercury provides current closure and may affect magnetospheric symmetry
Directory of Open Access Journals (Sweden)
P. Janhunen
2004-04-01
Full Text Available We study what effect a possible surface conductivity of Mercury has on the closure of magnetospheric currents by making six runs with a quasi-neutral hybrid simulation. The runs are otherwise identical but use different synthetic conductivity models: run 1 has a fully conducting planet, run 2 has a poorly conducting planet ( m and runs 3-6 have one of the hemispheres either in the dawn-dusk or day-night directions, conducting well, the other one being conducting poorly. Although the surface conductivity is not known from observations, educated guesses easily give such conductivity values that magnetospheric currents may close partly within the planet, and as the conductivity depends heavily on the mineral composition of the surface, the possibility of significant horizontal variations cannot be easily excluded. The simulation results show that strong horizontal variations may produce modest magnetospheric asymmetries. Beyond the hybrid simulation, we also briefly discuss the possibility that in the nightside there may be a lack of surface electrons to carry downward current, which may act as a further source of surface-related magnetospheric asymmetry. Key words. Magnetospheric physics (planetary magnetospheres; current systems; solar wind-magnetosphere interactions.6
6. Electromagnetic radiation trapped in the magnetosphere above the plasma frequency
Science.gov (United States)
Gurnett, D. A.; Shaw, R. R.
1973-01-01
An electromagnetic noise band is frequently observed in the outer magnetosphere by the Imp 6 spacecraft at frequencies from about 5 to 20 kHz. This noise band generally extends throughout the region from near the plasmapause boundary to near the magnetopause boundary. The noise typically has a broadband field strength of about 5 microvolts/meter. The noise band often has a sharp lower cutoff frequency at about 5 to 10 kHz, and this cutoff has been identified as the local electron plasma frequency. Since the plasma frequency in the plasmasphere and solar wind is usually above 20 kHz, it is concluded that this noise must be trapped in the low-density region between the plasmapause and magnetopause boundaries. The noise bands often contain a harmonic frequency structure which suggests that the radiation is associated with harmonics of the electron cyclotron frequency.
7. On the relaxation of magnetospheric convection when Bz turns northward
Directory of Open Access Journals (Sweden)
M. C. Kelley
2012-06-01
Full Text Available The solar wind inputs considerable energy into the upper atmosphere, particularly when the interplanetary magnetic field (IMF is southward. According to Poynting's theorem (Kelley, 2009, this energy becomes stored as magnetic fields and then is dissipated by Joule heat and by energizing the plasmasheet plasma. If the IMF turns suddenly northward, very little energy is transferred into the system while Joule dissipation continues. In this process, the polar cap potential (PCP decreases. Experimentally, it was shown many years ago that the energy stored in the magnetosphere begins to decay with a time constant of two hours. Here we use Poynting's theorem to calculate this time constant and find a result that is consistent with the data.
8. Proxy studies of energy transfer to the magnetosphere
International Nuclear Information System (INIS)
Scurry, L.; Russell, C.T.
1991-01-01
The transfer of energy into the magnetosphere is studied using as proxy the Am geomagnetic index and multilinear regressions and correlations with solar wind data. In particular, the response of Am to the reconnection mechanism is examined in relation to the orientation of the interplanetary magnetic field as well as the upstream plasma parameters. A functional dependence of Am on clock angle, the orientation of the IMF in the plane perpendicular to the flow, is derived after first correcting the index for nonreconnection effects due to dynamic pressure and velocity. An examination of the effect of upstream magnetosonic Mach number shows the reconnection mechanism to become less efficient at high Mach numbers. The reconnection mechanism is shown to be slightly enhanced by higher dynamic pressures
9. Influence of the IMF azimuthal component on magnetospheric substorm dynamics
International Nuclear Information System (INIS)
Troshichev, O.A.; Kotikov, A.L.; Bolotinskaya, B.D.; Andrezen, V.G.
1986-01-01
The effect of the IMF azimuthal component on magnetospheric substorm dynamics has been studied on the basis of five-minute average values of the IMF B y and B z components and the AL index. The results obtained from case studies and from superposed epoch analysis show the dependence of substorm dynamics on the azimuthal component: the reversal of B y from positive to negative increases the activity with minimum delay time, while the opposite reversal either does not change or only slightly changes the activity level. This effect is more evident in winter. The reversal of the IMF vertical component from south to north after an interval of sustained southward IMF statistically gives rise to magnetic activity, too but this growth is less intense than that produced by the B y negative turning. The role of both vertical and azimuthal IMF components must be considered in future studies of substorm triggering mechanisms. (author)
10. Slow-mode shocks in the earth's magnetosphere
International Nuclear Information System (INIS)
Feldman, W.C.
1987-01-01
The locations and structure of slow-mode shocks in the earth's magnetosphere are reviewed. To date, such shocks have only been identified along the high latitude portions of the lobe-plasma sheet boundary of the geomagnetic tail. Although their intrinsic thickness is of the order of the upstream ion inertial length, they affect the internal state of a relatively much larger volume of surrounding plasma. In particular, they support a well-developed foreshock very similar to that observed upstream of the earth's bow shock, and a turbulent, strongly convecting downstream flow. They also figure importantly in the energy budget of geomagnetic substorms and produce effects which are closely analogous to much of the phenomenology known from solar observations to be associated with two-ribbon flares. 74 refs., 14 figs
11. Beam generated electrostatic electron waves in the magnetosphere
International Nuclear Information System (INIS)
Hultqvist, B.
1986-03-01
The generation of growing electrostatic electron waves by electron beams in the ionosphere and magnetosphere is investigated. The auroral F-region, the high latitude exosphere, the auroral acceleration region around 1 Rsub(e), the outer plasmasphere and the plasmasheet are treated. It is found that auroral electron beams can amplify electrostatic waves in all these regions but in different k-ranges. The growth rate, in terms of ωsub(i)/ω, generally increases outward. The propagation direction range of the waves discussed varies from a narrow cone around the magnetic field lines to all directions except close to perpendicularity. Strong cyclotron resonance effects at propagation angles close to 90 degrees are not dealt with. The method used can easily be applied to any plasma system where free energy is available in the form of an electron beam, including laboratory plasma. (author)
12. Kinetic Simulation and Energetic Neutral Atom Imaging of the Magnetosphere
Science.gov (United States)
Fok, Mei-Ching H.
2011-01-01
Advanced simulation tools and measurement techniques have been developed to study the dynamic magnetosphere and its response to drivers in the solar wind. The Comprehensive Ring Current Model (CRCM) is a kinetic code that solves the 3D distribution in space, energy and pitch-angle information of energetic ions and electrons. Energetic Neutral Atom (ENA) imagers have been carried in past and current satellite missions. Global morphology of energetic ions were revealed by the observed ENA images. We have combined simulation and ENA analysis techniques to study the development of ring current ions during magnetic storms and substorms. We identify the timing and location of particle injection and loss. We examine the evolution of ion energy and pitch-angle distribution during different phases of a storm. In this talk we will discuss the findings from our ring current studies and how our simulation and ENA analysis tools can be applied to the upcoming TRIO-CINAMA mission.
13. Self-consistent equilibria in the pulsar magnetosphere
International Nuclear Information System (INIS)
Endean, V.G.
1976-01-01
For a 'collisionless' pulsar magnetosphere the self-consistent equilibrium particle distribution functions are functions of the constants of the motion ony. Reasons are given for concluding that to a good approximation they will be functions of the rotating frame Hamiltonian only. This is shown to result in a rigid rotation of the plasma, which therefore becomes trapped inside the velocity of light cylinder. The self-consistent field equations are derived, and a method of solving them is illustrated. The axial component of the magnetic field decays to zero at the plasma boundary. In practice, some streaming of particles into the wind zone may occur as a second-order effect. Acceleration of such particles to very high energies is expected when they approach the velocity of light cylinder, but they cannot be accelerated to very high energies near the star. (author)
14. The Titan haze revisted: Magnetospheric energy sorces quantitative tholin yields
Science.gov (United States)
Thompson, W. Reid; Mcdonald, Gene D.; Sagan, Carl
1994-01-01
We present laboratory measurements of the radiation yields of complex organic solids produced from N2/CH4 gas mixtures containing 10 or 0.1% CH4. These tholins are thought to resemble organic aerosols produced in the atmospheres of Titan, Pluto, and Triton. The tholin yields are large compared to the total yield of gaseous products: nominally, 13 (C + N)/100 eV for Titan tholin and 2.1 (C + N)/100 eV for Triton tholin. High-energy magnetospheric electrons responsible for tholin production represents a class distinct from the plasma electrons considered in models of Titan's aiglow. Electrons with E greater than 20 keV provide an energy flux approximately 1 x 10(exp -2) erg/cm/sec, implying from our measured tholin yields a mass flux of 0.5 to 4.0 x 10(exp -14) g/sq cm/sec of tholin. (The corresponding thickness of the tholin sedimentary column accumulated over 4 Gyr on Titan's surface is 4 to 30 m). This figure is in agreement with required mass fluxes computed from recent radiative transfer and sedimentation models. If, however, theses results, derived from experiments at approximately 2 mb, are applied to lower pressure levels toward peak auroral electron energy deposition and scaled with pressure as the gas-phase organic yields, the derived tholin mass flux is at least an order of magnitude less. We attrribute this difference to the fact that tholin synthesis occurs well below the level of maximum electron energy depositon and to possible contributions to tholis from UV-derived C2-hydrocarbons. We conclude that Tita tholin, produced by magnetospheric electrons, is alone sufficient to supply at least a significant fraction of Titan's haze-a result consistent with the fact that the optical properties of Titan tholin, among all proposed material, are best at reproducing Titan's geometric albedo spectrum from near UV to mid-IR in light-scattering models.
15. Adiabatic motion of charged dust grains in rotating magnetospheres
International Nuclear Information System (INIS)
Northrop, T.G.; Hill, J.R.
1983-01-01
Dust grains in the ring systems and rapidly rotating magnetospheres of the outer planets such as Jupiter and Saturn may be sufficiently charged that the magnetic and electric forces on them are comparable with the gravitational force. The adiabatic theory of charged particle motion has previously been applied to electrons and atomic size particles. But it is also applicable to these charged dust grains in the micrometer and smaller size range. We derive here the guiding center equation of motion, drift velocity, and parallel equation of motion for these grains in a rotating magnetosphere. The effects of periodic grain charge-discharge have not been treated previously and have been included in this analysis. Grain charge is affected by the surrounding plasma properties and by the grain plasma velocity (among other factors), both of which may vary over the gyrocircle. The resulting charge-discharge process at the gyrofrequency destroys the invariance of the magnetic moment and causes a grain to move radially. The magnetic moment may increase or decrease, depending on the gyrophase of the charge variation. If it decreases, the motion is always toward synchronous radius for an equatorial grain. But the orbit becomes circular before the grain reaches synchronous radius, a conclusion that follows from an exact constant of the motion. This circularization can be viewed as a consequence of the gradual reduction in the magnetic moment. This circularization also suggests that dust grains leaving Io could not reach the region of the Jovian ring, but several effects could change that conclusion. Excellent qualitative and quantitative agreement is obtained between adiabatic theory and detailed numerical orbit integrations
16. MESSENGER Observations of Magnetic Reconnection in Mercury's Magnetosphere
Science.gov (United States)
Slavin. James A.
2009-01-01
During MESSENGER'S second flyby of Mercury on October 6,2008, very intense reconnection was observed between the planet's magnetic field and a steady southward interplanetary magnetic field (IMF). The dawn magnetopause was threaded by a strong magnetic field normal to its surface, approx.14 nT, that implies a rate of reconnection approx.10 times the typical rate at Earth and a cross-magnetospheric electric potential drop of approx.30 kV. The highest magnetic field observed during this second flyby, approx.160 nT, was found at the core of a large dayside flux transfer event (FTE). This FTE is estimated to contain magnetic flux equal to approx.5% that of Mercury's magnetic tail or approximately one order of magnitude higher fraction of the tail flux than is typically found for FTEs at Earth. Plasmoid and traveling compression region (TCR) signatures were observed throughout MESSENGER'S traversal of Mercury's magnetotail with a repetition rate comparable to the Dungey cycle time of approx.2 min. The TCR signatures changed from south-north, indicating tailward motion, to north-south, indicating sunward motion, at a distance approx.2.6 RM (where RM is Mercury's radius) behind the terminator indicating that the near-Mercury magnetotail neutral line was crossed at that point. Overall, these new MESSENGER observations suggest that magnetic reconnection at the dayside magnetopause is very intense relative to what is found at Earth and other planets, while reconnection in Mercury's tail is similar to that in other planetary magnetospheres, but with a very short Dungey cycle time.
17. Characteristics of the magnetohydrodynamic waves observed in the earth's magnetosphere and on the ground
International Nuclear Information System (INIS)
Kuwashima, M.; Fujita, S.
1989-01-01
Current research topics on MHD waves in the earth's magnetosphere and on the ground are summarized. Upstream waves in the earth's foreshock region and their transmission into and propagation through the magnetosphere are discussed in the context of relationships of Pc3 magnetic pulsations on the ground. The characteristics of ssc-associated magnetic pulsations are considered, and instabilities with the hot plasma in the ring current in the magnetosphere are addressed in the context of the relationships of compressional Pc 4-5 waves. The characteristics of Pi2 magnetic pulsations are examined, and the role of the ionosphere on the modifications of MHD waves is addressed
18. Modeling of the propagation of low-frequency electromagnetic radiation in the Earth’s magnetosphere
International Nuclear Information System (INIS)
Lebedev, N. V.; Rudenko, V. V.
2015-01-01
A numerical algorithm for solving the set of differential equations describing the propagation of low-frequency electromagnetic radiation in the magnetospheric plasma, including in the presence of geomagnetic waveguides in the form of large-scale plasma density inhomogeneities stretched along the Earth’s magnetic field, has been developed. Calculations of three-dimensional ray trajectories in the magnetosphere and geomagnetic waveguide with allowance for radiation polarization have revealed characteristic tendencies in the behavior of electromagnetic parameters along the ray trajectory. The results of calculations can be used for magnetospheric plasma diagnostics
19. Stellar Streams Discovered in the Dark Energy Survey
Energy Technology Data Exchange (ETDEWEB)
Shipp, N.; et al.
2018-01-09
We perform a search for stellar streams around the Milky Way using the first three years of multi-band optical imaging data from the Dark Energy Survey (DES). We use DES data covering $\\sim 5000$ sq. deg. to a depth of $g > 23.5$ with a relative photometric calibration uncertainty of $< 1 \\%$. This data set yields unprecedented sensitivity to the stellar density field in the southern celestial hemisphere, enabling the detection of faint stellar streams to a heliocentric distance of $\\sim 50$ kpc. We search for stellar streams using a matched-filter in color-magnitude space derived from a synthetic isochrone of an old, metal-poor stellar population. Our detection technique recovers four previously known thin stellar streams: Phoenix, ATLAS, Tucana III, and a possible extension of Molonglo. In addition, we report the discovery of eleven new stellar streams. In general, the new streams detected by DES are fainter, more distant, and lower surface brightness than streams detected by similar techniques in previous photometric surveys. As a by-product of our stellar stream search, we find evidence for extra-tidal stellar structure associated with four globular clusters: NGC 288, NGC 1261, NGC 1851, and NGC 1904. The ever-growing sample of stellar streams will provide insight into the formation of the Galactic stellar halo, the Milky Way gravitational potential, as well as the large- and small-scale distribution of dark matter around the Milky Way.
20. Modular Stellarator Fusion Reactor (MSR) concept
International Nuclear Information System (INIS)
Miller, R.L.; Krakowski, R.A.
1981-01-01
A preliminary conceptual study has been made of the Modulator Stellarator Reactor (MSR) as a stedy-state, ignited, DT-fueled, magnetic fusion reactor. The MSR concept combines the physics of classic stellarator confinement with an innovative, modular-coil design. Parametric tradeoff calculations are described, leading to the selection of an interim design point for a 4.8-GWt plant based on Alcator transport scaling and an average beta value of 0.04 in an l = 2 system with a plasma aspect ratio of 11. Neither an economic analysis nor a detailed conceptual engineering design is presented here, as the primary intent of this scoping study is the elucidation of key physics tradeoffs, constraints, and uncertainties for the ultimate power-reactor embodiment
1. Time variations of stellar water masers
International Nuclear Information System (INIS)
Cox, G.G.; Parker, E.A.
1979-01-01
The 22-GHz H 2 O spectra of the stars RS Vir, RT Vir, R Aql, W Hya, U Her, S Cr B, Rx Boo, R Crt and VY CMa have been observed at intervals during the period 1974 September -1977 May. Optical and infrared measurements have also been made. New components have been observed in the H 2 O spectra of most of the stars, and the flux density of W Hya reached 2000 Jy near Jd 2442700. The intensities of the three main groups of components in VY CMa varied in phase consistent with a central pump source. In several stars the intensities were very different from those found by earlier observers, showing that stellar H 2 O masers are often not stable for more than a few cycles of the stellar luminosity. For part of the time the H 2 O and infrared intensities of R Aql and RS Vir were anticorrelated. (author)
2. A Compact Quasi-axisymmetric Stellarator Reactor
International Nuclear Information System (INIS)
Ku, L.P.
2003-01-01
We report the progress made in assessing the potential of compact, quasi-axisymmetric stellarators as power-producing reactors. Using an aspect ratio A=4.5 configuration derived from NCSX and optimized with respect to the quasi-axisymmetry and MHD stability in the linear regime as an example, we show that a reactor of 1 GW(e) maybe realizable with a major radius *8 m. This is significantly smaller than the designs of stellarator reactors attempted before. We further show the design of modular coils and discuss the optimization of coil aspect ratios in order to accommodate the blanket for tritium breeding and radiation shielding for coil protection. In addition, we discuss the effects of coil aspect ratio on the peak magnetic field in the coils
3. Excitation of solar and stellar oscillations
International Nuclear Information System (INIS)
Baudin, Frederic
2009-01-01
In this report for an Accreditation to Supervise Research (HDR), and after an introduction which outlines the potential of helio-seismology, the author addresses the problem of excitation and amplitude of stellar oscillations with respect to their most important aspects, i.e. the theoretical framework of the present understanding of excitation mechanisms, and instrumental influences on measurements which are used to assess excitation rates, the difficulty to perform these measurements, and their analysis in some various cases. Thus, the author addresses excitation mechanisms of stellar oscillation (stochastic excitation, opacity- related excitation, and other excitation mechanisms), the excitation of solar modes (observation and theoretical predictions, influence of magnetic phenomena, solar g modes), and the excitation of modes in other stars (solar-type pulsators, red giants, and not so conventional pulsators such as HD180642 and Be stars like HD49330)
4. Stellar evolution as seen by mixed modes
Directory of Open Access Journals (Sweden)
Mosser Benoît
2015-01-01
Full Text Available The detection of mixed modes in subgiants and red giants allows us to monitor stellar evolution from the main sequence to the asymptotic giant branch and draw seismic evolutionary tracks. Quantified asteroseismic definitions that characterize the change in the evolutionary stages have been defined. This seismic information can now be used for stellar modelling, especially for studying the energy transport in the helium burning core or for specifying the inner properties of stars all along their evolution. Modelling will also allow us to study stars identified in the helium subflash stage, high-mass stars either arriving or quitting the secondary clump, or stars that could be in the blue-loop stage.
5. Physics of stellar evolution and cosmology
International Nuclear Information System (INIS)
1981-01-01
Astrophysical phenomena are examined on a fundamental level, stressing basic physical laws, in a textbook suitable for a one-semester intermediate course. The ideal gas law, the meaning of temperature, black-body radiation, discrete spectra, and the Doppler effect are introduced and used to study such features of the interstellar medium as 21-cm radiation, nebulae and dust, and the galactic magnetic field. The phases of stellar evolution are discussed, including stellar collapse, quasi-hydrostatic equilibrium, the main sequence, red giants, white dwarves, neutron stars, supernovae, pulsars, and black holes. Among the cosmological topics covered are the implications of Hubble's constant, the red-shift curve, the steady-state universe, the evolution of the big bang (thermal equilibrium, hadron era, lepton era, primordial nucleosynthesis, hydrogen recombination, galaxy formation, and the cosmic fireball), and the future (cold end or big crunch). 72 references
6. Stellar physics with the ALHAMBRA photometric system
International Nuclear Information System (INIS)
Villegas, T Aparicio; Alfaro, E J; Moles, M; Benítez, N; Perea, J; Olmo, A del; Cristóbal-Hornillos, D; Cervio, M; Delgado, R M González; Márquez, I; Masegosa, J; Prada, F; Cabrera-Caño, J; Fernández-Soto, A; Aguerri, J A L; Cepa, J; Broadhurst, T; Castander, F J; Infante, L; Martínez, V J
2011-01-01
The ALHAMBRA photometric system was specifically designed to perform a tomography of the Universe in some selected areas. Although mainly designed for extragalactic purposes, its 20 contiguous, equal-width, medium-band photometric system in the optical wavelength range, shows a great capacity for stellar classification. In this contribution we propose a methodology for stellar classification and physical parameter estimation (T eff , log g, [Fe/H], and color excess E(B – V)) based on 18 independent reddening-free Q-values from the ALHAMBRA photometry. Based on the theoretical Spectral library BaSeL 2.2, and applied to 288 stars from the Next Generation spectral Library (NGSL), we discuss the reliability of the method and its dependence on the extinction law used.
7. Isotope ratio in stellar atmospheres and nucleosynthesis
International Nuclear Information System (INIS)
1987-01-01
The determination of isotopic ratios in stellar atmospheres is studied. The isotopic shift of atomic and molecular lines of different species of a certain element is examined. CH and MgH lines are observed in order to obtain the 12 C: 13 C and 24 Mg: 25 Mg: 26 Mg isotpic ratios. The formation of lines in stellar atmospheres is computed and the resulting synthetic spectra are employed to determine the isotopic abundances. The results obtained for the isotopic ratios are compared to predictions of nucleosynthesis theories. Finally, the concept of primary and secondary element is discussed, and these definitions are applied to the observed variations in the abundance of elements as a function of metallicity. (author) [pt
8. STELLTRANS: A Transport Analysis Suite for Stellarators
Science.gov (United States)
Mittelstaedt, Joseph; Lazerson, Samuel; Pablant, Novimir; Weir, Gavin; W7-X Team
2016-10-01
The stellarator transport code STELLTRANS allows us to better analyze the power balance in W7-X. Although profiles of temperature and density are measured experimentally, geometrical factors are needed in conjunction with these measurements to properly analyze heat flux densities in stellarators. The STELLTRANS code interfaces with VMEC to find an equilibrium flux surface configuration and with TRAVIS to determine the RF heating and current drive in the plasma. Stationary transport equations are then considered which are solved using a boundary value differential equation solver. The equations and quantities considered are averaged over flux surfaces to reduce the system to an essentially one dimensional problem. We have applied this code to data from W-7X and were able to calculate the heat flux coefficients. We will also present extensions of the code to a predictive capacity which would utilize DKES to find neoclassical transport coefficients to update the temperature and density profiles.
9. Energetic Particle Estimates for Stellar Flares
Science.gov (United States)
Youngblood, Allison; Chamberlin, Phil; Woods, Tom
2018-01-01
In the heliosphere, energetic particles are accelerated away from the Sun during solar flares and/or coronal mass ejections where they frequently impact the Earth and other solar system bodies. Solar (or stellar) energetic particles (SEPs) not only affect technological assets, but also influence mass loss and chemistry in planetary atmospheres (e.g., depletion of ozone). SEPs are increasingly recognized as an important factor in assessing exoplanet habitability, but we do not yet have constraints on SEP emission from any stars other than the Sun. Until indirect measurements are available, we must assume solar-like particle production and apply correlations between solar flares and SEPs detected near Earth to stellar flares. We present improved scaling relations between solar far-UV flare flux and >10 MeV proton flux near Earth. We apply these solar scaling relations to far-UV flares from exoplanet host stars and discuss the implications for modeling chemistry and mass loss in exoplanet atmospheres.
10. On Utmost Multiplicity of Hierarchical Stellar Systems
Directory of Open Access Journals (Sweden)
Gebrehiwot Y. M.
2016-12-01
Full Text Available According to theoretical considerations, multiplicity of hierarchical stellar systems can reach, depending on masses and orbital parameters, several hundred, while observational data confirm the existence of at most septuple (seven-component systems. In this study, we cross-match the stellar systems of very high multiplicity (six and more components in modern catalogues of visual double and multiple stars to find among them the candidates to hierarchical systems. After cross-matching the catalogues of closer binaries (eclipsing, spectroscopic, etc., some of their components were found to be binary/multiple themselves, what increases the system's degree of multiplicity. Optical pairs, known from literature or filtered by the authors, were flagged and excluded from the statistics. We compiled a list of hierarchical systems with potentially very high multiplicity that contains ten objects. Their multiplicity does not exceed 12, and we discuss a number of ways to explain the lack of extremely high multiplicity systems.
11. Stellar clusters in the Gaia era
Science.gov (United States)
Bragaglia, Angela
2018-04-01
Stellar clusters are important for astrophysics in many ways, for instance as optimal tracers of the Galactic populations to which they belong or as one of the best test bench for stellar evolutionary models. Gaia DR1, with TGAS, is just skimming the wealth of exquisite information we are expecting from the more advanced catalogues, but already offers good opportunities and indicates the vast potentialities. Gaia results can be efficiently complemented by ground-based data, in particular by large spectroscopic and photometric surveys. Examples of some scientific results of the Gaia-ESO survey are presented, as a teaser for what will be possible once advanced Gaia releases and ground-based data will be combined.
12. Clustering in the stellar abundance space
Science.gov (United States)
Boesso, R.; Rocha-Pinto, H. J.
2018-03-01
We have studied the chemical enrichment history of the interstellar medium through an analysis of the n-dimensional stellar abundance space. This work is a non-parametric analysis of the stellar chemical abundance space. The main goal is to study the stars from their organization within this abundance space. Within this space, we seek to find clusters (in a statistical sense), that is, stars likely to share similar chemo-evolutionary history, using two methods: the hierarchical clustering and the principal component analysis. We analysed some selected abundance surveys available in the literature. For each sample, we labelled the group of stars according to its average abundance curve. In all samples, we identify the existence of a main enrichment pattern of the stars, which we call chemical enrichment flow. This flow is set by the structured and well-defined mean rate at which the abundances of the interstellar medium increase, resulting from the mixture of the material ejected from the stars and stellar mass-loss and interstellar medium gas. One of the main results of our analysis is the identification of subgroups of stars with peculiar chemistry. These stars are situated in regions outside of the enrichment flow in the abundance space. These peculiar stars show a mismatch in the enrichment rate of a few elements, such as Mg, Si, Sc and V, when compared to the mean enrichment rate of the other elements of the same stars. We believe that the existence of these groups of stars with peculiar chemistry may be related to the accretion of planetary material on to stellar surfaces or may be due to production of the same chemical element by different nucleosynthetic sites.
13. Compact stellar object: the formation and structure
Energy Technology Data Exchange (ETDEWEB)
Duarte, S.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF/MCT), Rio de Janeiro, RJ (Brazil)
2012-07-01
Full text: The formation of compact objects is viewed at the final stages of stellar evolution. The supernova explosion events are then focalized to explain the formation of pulsars, hybrid neutron star and the limit case of the latter, the quark stars. We discuss the stability and structure of these objects in connection with the properties of the hadron and quark-gluon plasma equation of state. The hadron-quark phase transition in deep interior of these objects is discussed taking into account the implications on the density distribution of matter along the radial direction. The role of neutrinos confinement in the ultradense stellar medium in the early stages of pulsar formation is another interesting aspect to be mentioned in this presentation. Recent results for maximum mass of compact stellar objects for different forms of equations of state will be shown, presenting some theoretical predictions for maximum mass of neutron stars allowed by different equations of state assigned to dense stellar medium. Although a density greater than few times the nuclear equilibrium density appears in deep interior of the core, at the crust the density decreases by several orders of magnitude where a variety of hadronic states appears, the 'pasta'-states of hadrons. More externally, a lattice of nuclei can be formed permeated not only by electrons but also by a large amount of free neutrons and protons. These are possible structure of neutron star crust to have the density and pressures with null values at the neutron star surface. The ultimate goal of this talk is to give a short view of the compact star area for students and those who are introducing in this subject. (author)
14. Future prospects for stellar intensity interferometry
International Nuclear Information System (INIS)
Lake, R.J.W.
2002-01-01
Full text: The technique of Stellar Intensity lnterferometry (SII) was first successfully demonstrated by Hanbury-Brown in 1956 at Jodrell Bank. SII uses the correlation in intensity fluctuations of starlight as a function of observational baseline to determine angular diameters and other gross features of main sequence stars. In 1962 an observatory was established by Hanbury-Brown in Narrabri NSW. Between 1965 and 1972 the angular diameters of 32 stars covering the spectral range O to F were measured. Orbital parameters of several unresolved binary stars were also determined and attempts were made by the author to directly measure the limb darkening of Sirius and the rotational distortion of Altair. Following the success of the Narrabri SII the Australian Federal Government provided a grant to Sydney University to develop a Very Large SII capable of making observational measurements on about a thousand stars. The development of this VLSII was however shelved in preference to the development of a potentially more sensitive long baseline Michelson Stellar Interferometer. This latter instrument known as SUSI (Sydney University Stellar Interferometer) has been in operation at Narrabri since 1995. Encouraged by the early results of SUSI and their own efforts in the use of active optics to reduce the effects of atmospheric scintillation a number of international observatories are now active in the development of long baseline or large aperture Michelson Stellar Interferometers. However SII while sacrificing sensitivity has a number of technical advantages over MSI as SII is far less sensitive to atmospheric effects and can be readily developed to work over very long baselines. This paper through technical review and theoretical modeling examines how a modern VLSII could be constructed and operated and addresses the limitations to its sensitivity. In particular it examines how existing Australian industry could contribute to the development of a VLSII with sufficient
15. Detection of stellar oscillations in HWVir
Directory of Open Access Journals (Sweden)
Baran Andrzej S.
2016-08-01
Full Text Available We present our analysis of K2 observations of the binary system, HWVir. We processed the raw Kepler data and used Fourier analysis to search for periodic signals that could be associated with pulsations. We detect the binary frequency and its harmonic and discovered tens of peaks at both low and high frequencies. We interpreted those to be caused by stellar pulsations. Our discovery means we can apply the tools of asteroseismology to the HWVir system.
16. Stellarator approach to toroidal plasma confinement
International Nuclear Information System (INIS)
Johnson, J.L.
1981-12-01
An overview is presented of the development and current status of the stellarator approach to controlled thermonuclear confinement. Recent experimental, theoretical, and systems developments have made this concept a viable option for the evolution of the toroidal confinement program. Some experimental study of specific problems associated with departure from two-dimensional symmetry must be undertaken before the full advantages and opportunities of steady-state, net-current-free operation can be realized
17. SMASH: Survey of the MAgellanic Stellar History
Science.gov (United States)
Nidever, David L.; Olsen, Knut; Walker, Alistair R.; Vivas, A. Katherina; Blum, Robert D.; Kaleida, Catherine; Choi, Yumi; Conn, Blair C.; Gruendl, Robert A.; Bell, Eric F.; Besla, Gurtina; Muñoz, Ricardo R.; Gallart, Carme; Martin, Nicolas F.; Olszewski, Edward W.; Saha, Abhijit; Monachesi, Antonela; Monelli, Matteo; de Boer, Thomas J. L.; Johnson, L. Clifton; Zaritsky, Dennis; Stringfellow, Guy S.; van der Marel, Roeland P.; Cioni, Maria-Rosa L.; Jin, Shoko; Majewski, Steven R.; Martinez-Delgado, David; Monteagudo, Lara; Noël, Noelia E. D.; Bernard, Edouard J.; Kunder, Andrea; Chu, You-Hua; Bell, Cameron P. M.; Santana, Felipe; Frechem, Joshua; Medina, Gustavo E.; Parkash, Vaishali; Serón Navarrete, J. C.; Hayes, Christian
2017-11-01
The Large and Small Magellanic Clouds are unique local laboratories for studying the formation and evolution of small galaxies in exquisite detail. The Survey of the MAgellanic Stellar History (SMASH) is an NOAO community Dark Energy Camera (DECam) survey of the Clouds mapping 480 deg2 (distributed over ˜2400 square degrees at ˜20% filling factor) to ˜24th mag in ugriz. The primary goals of SMASH are to identify low surface brightness stellar populations associated with the stellar halos and tidal debris of the Clouds, and to derive spatially resolved star formation histories. Here, we present a summary of the survey, its data reduction, and a description of the first public Data Release (DR1). The SMASH DECam data have been reduced with a combination of the NOAO Community Pipeline, the PHOTRED automated point-spread-function photometry pipeline, and custom calibration software. The astrometric precision is ˜15 mas and the accuracy is ˜2 mas with respect to the Gaia reference frame. The photometric precision is ˜0.5%-0.7% in griz and ˜1% in u with a calibration accuracy of ˜1.3% in all bands. The median 5σ point source depths in ugriz are 23.9, 24.8, 24.5, 24.2, and 23.5 mag. The SMASH data have already been used to discover the Hydra II Milky Way satellite, the SMASH 1 old globular cluster likely associated with the LMC, and extended stellar populations around the LMC out to R ˜ 18.4 kpc. SMASH DR1 contains measurements of ˜100 million objects distributed in 61 fields. A prototype version of the NOAO Data Lab provides data access and exploration tools.
18. Rate of stellar collapses in the Galaxy
International Nuclear Information System (INIS)
Lande, K.; Stephens, W.E.
1977-01-01
From an analysis of pulsar spatial and luminosity distributions, the number density of observed pulsars in the local region is determined to be 1.1+-0.4x10 -7 pulsar pc -3 . Multiplication by the detection factor and by the ratio of Galaxy mass to local matter density and division by a mean lifetime of pulsars of 3x10 6 yr suggests a pulsar birth every 4 yr. A stellar collapse might occur even more often. (Auth.)
19. SMASH: Survey of the MAgellanic Stellar History
Energy Technology Data Exchange (ETDEWEB)
Nidever, David L.; Olsen, Knut; Blum, Robert D.; Saha, Abhijit [National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, AZ 85719 (United States); Walker, Alistair R.; Vivas, A. Katherina [Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, Casilla 603, La Serena (Chile); Kaleida, Catherine [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Choi, Yumi; Besla, Gurtina; Olszewski, Edward W. [Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson AZ, 85721 (United States); Conn, Blair C. [Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611 (Australia); Gruendl, Robert A. [National Center for Supercomputing Applications, 1205 West Clark Street, Urbana, IL 61801 (United States); Bell, Eric F. [Department of Astronomy, University of Michigan, 1085 S. University Avenue, Ann Arbor, MI 48109-1107 (United States); Muñoz, Ricardo R. [Departamento de Astronomía, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago (Chile); Gallart, Carme; Monelli, Matteo [Instituto de Astrofísica de Canarias, La Laguna, Tenerife (Spain); Martin, Nicolas F. [Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg (France); Monachesi, Antonela [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany); De Boer, Thomas J. L. [Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA (United Kingdom); Johnson, L. Clifton, E-mail: [email protected] [Center for Astrophysics and Space Sciences, UC San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0424 (United States); and others
2017-11-01
The Large and Small Magellanic Clouds are unique local laboratories for studying the formation and evolution of small galaxies in exquisite detail. The Survey of the MAgellanic Stellar History (SMASH) is an NOAO community Dark Energy Camera (DECam) survey of the Clouds mapping 480 deg{sup 2} (distributed over ∼2400 square degrees at ∼20% filling factor) to ∼24th mag in ugriz . The primary goals of SMASH are to identify low surface brightness stellar populations associated with the stellar halos and tidal debris of the Clouds, and to derive spatially resolved star formation histories. Here, we present a summary of the survey, its data reduction, and a description of the first public Data Release (DR1). The SMASH DECam data have been reduced with a combination of the NOAO Community Pipeline, the PHOTRED automated point-spread-function photometry pipeline, and custom calibration software. The astrometric precision is ∼15 mas and the accuracy is ∼2 mas with respect to the Gaia reference frame. The photometric precision is ∼0.5%–0.7% in griz and ∼1% in u with a calibration accuracy of ∼1.3% in all bands. The median 5 σ point source depths in ugriz are 23.9, 24.8, 24.5, 24.2, and 23.5 mag. The SMASH data have already been used to discover the Hydra II Milky Way satellite, the SMASH 1 old globular cluster likely associated with the LMC, and extended stellar populations around the LMC out to R ∼ 18.4 kpc. SMASH DR1 contains measurements of ∼100 million objects distributed in 61 fields. A prototype version of the NOAO Data Lab provides data access and exploration tools.
20. Stellar Atmospheric Modelling for the ACCESS Program
Science.gov (United States)
Morris, Matthew; Kaiser, Mary Elizabeth; Bohlin, Ralph; Kurucz, Robert; ACCESS Team
2018-01-01
A goal of the ACCESS program (Absolute Color Calibration Experiment for Standard Stars) is to enable greater discrimination between theoretical astrophysical models and observations, where the comparison is limited by systematic errors associated with the relative flux calibration of the targets. To achieve these goals, ACCESS has been designed as a sub-orbital rocket borne payload and ground calibration program, to establish absolute flux calibration of stellar targets at flight candidates, as well as a selection of A and G stars from the CALSPEC database. Stellar atmosphere models were generated using Atlas 9 and Atlas 12 Kurucz stellar atmosphere software. The effective temperature, log(g), metallicity, and redenning were varied and the chi-squared statistic was minimized to obtain a best-fit model. A comparison of these models and the results from interpolation between grids of existing models will be presented. The impact of the flexibility of the Atlas 12 input parameters (e.g. solar metallicity fraction, abundances, microturbulent velocity) is being explored.
1. The formation of stellar black holes
Science.gov (United States)
Mirabel, Félix
2017-08-01
It is believed that stellar black holes (BHs) can be formed in two different ways: Either a massive star collapses directly into a BH without a supernova (SN) explosion, or an explosion occurs in a proto-neutron star, but the energy is too low to completely unbind the stellar envelope, and a large fraction of it falls back onto the short-lived neutron star (NS), leading to the delayed formation of a BH. Theoretical models set progenitor masses for BH formation by implosion, namely, by complete or almost complete collapse, but observational evidences have been elusive. Here are reviewed the observational insights on BHs formed by implosion without large natal kicks from: (1) the kinematics in three dimensions of space of five Galactic BH X-ray binaries (BH-XRBs), (2) the diversity of optical and infrared observations of massive stars that collapse in the dark, with no luminous SN explosions, possibly leading to the formation of BHs, and (3) the sources of gravitational waves (GWs) produced by mergers of stellar BHs so far detected with LIGO. Multiple indications of BH formation without ejection of a significant amount of matter and with no natal kicks obtained from these different areas of observational astrophysics, and the recent observational confirmation of the expected dependence of BH formation on metallicity and redshift, are qualitatively consistent with the high merger rates of binary black holes (BBHs) inferred from the first detections with LIGO.
2. The Resolved Stellar Population of Leo A
Science.gov (United States)
Tolstoy, Eline
1996-05-01
New observations of the resolved stellar population of the extremely metal-poor Magellanic dwarf irregular galaxy Leo A in Thuan-Gunn r, g, i, and narrowband Hα filters are presented. Using the recent Cepheid variable star distance determination to Leo A by Hoessel et al., we are able to create an accurate color-magnitude diagram (CMD). We have used the Bavesian inference method described by Tolstoy & Saha to calculate the likelihood of a Monte Carlo simulation of the stellar population of Leo A being a good match to the data within the well understood errors in the data. The magnitude limits on our data are sensitive enough to look back at ~1 Gyr of star formation history at the distance of Leo A. To explain the observed ratio of red to blue stars in the observed CMD, it is necessary to invoke either a steadily decreasing star formation rate toward the present time or gaps in the star formation history. We also compare the properties of the observed stellar population with the known spatial distribution of the H I gas and H II regions to support the conclusions from CMD modeling. We consider the possibility that currently there is a period of diminished star formation in Leo A, as evidenced by the lack of very young stars in the CMD and the faint H II regions. How the chaotic H I distribution, with no observable rotation, fits into our picture of the evolution of Leo A is as yet unclear.
3. The doubling of stellar black hole nuclei
Science.gov (United States)
Kazandjian, Mher V.; Touma, J. R.
2013-04-01
It is strongly believed that Andromeda's double nucleus signals a disc of stars revolving around its central supermassive black hole on eccentric Keplerian orbits with nearly aligned apsides. A self-consistent stellar dynamical origin for such apparently long-lived alignment has so far been lacking, with indications that cluster self-gravity is capable of sustaining such lopsided configurations if and when stimulated by external perturbations. Here, we present results of N-body simulations which show unstable counter-rotating stellar clusters around supermassive black holes saturating into uniformly precessing lopsided nuclei. The double nucleus in our featured experiment decomposes naturally into a thick eccentric disc of apo-apse aligned stars which is embedded in a lighter triaxial cluster. The eccentric disc reproduces key features of Keplerian disc models of Andromeda's double nucleus; the triaxial cluster has a distinctive kinematic signature which is evident in Hubble Space Telescope observations of Andromeda's double nucleus, and has been difficult to reproduce with Keplerian discs alone. Our simulations demonstrate how the combination of an eccentric disc and a triaxial cluster arises naturally when a star cluster accreted over a preexisting and counter-rotating disc of stars drives disc and cluster into a mutually destabilizing dance. Such accretion events are inherent to standard galaxy formation scenarios. They are here shown to double stellar black hole nuclei as they feed them.
4. Intrinsic Turbulence Stabilization in a Stellarator
Directory of Open Access Journals (Sweden)
P. Xanthopoulos
2016-06-01
Full Text Available The magnetic surfaces of modern stellarators are characterized by complex, carefully optimized shaping and exhibit locally compressed regions of strong turbulence drive. Massively parallel computer simulations of plasma turbulence reveal, however, that stellarators also possess two intrinsic mechanisms to mitigate the effect of this drive. In the regime where the length scale of the turbulence is very small compared to the equilibrium scale set by the variation of the magnetic field, the strongest fluctuations form narrow bandlike structures on the magnetic surfaces. Thanks to this localization, the average transport through the surface is significantly smaller than that predicted at locations of peak turbulence. This feature results in a numerically observed upshift of the onset of turbulence on the surface towards higher ion temperature gradients as compared with the prediction from the most unstable regions. In a second regime lacking scale separation, the localization is lost and the fluctuations spread out on the magnetic surface. Nonetheless, stabilization persists through the suppression of the large eddies (relative to the equilibrium scale, leading to a reduced stiffness for the heat flux dependence on the ion temperature gradient. These fundamental differences with tokamak turbulence are exemplified for the QUASAR stellarator [G. H. Neilson et al., IEEE Trans. Plasma Sci. 42, 489 (2014].
5. Solar and Stellar X-ray Cycles
Science.gov (United States)
Martens, P. C. H.; SADE Team
2004-05-01
Stern et al. have shown that Yohkoh-SXT full disk X-ray irradiance shows an 11 year cycle with an max/min amplitude ratio of a factor 30. Similar cyclic X-ray variation in Sun-like stars observed by ROSAT and its predecessors is observed in only a few cases and limited to a factor two or three. We will show, by means of detailed bandpass comparisons, that this discrepancy cannot be ascribed to the differences in energy response between SXT and the stellar soft X-ray detectors. Is the Sun exceptional? After centuries of geocentric and heliocentric worldviews we find this a difficult proposition to entertain. But perhaps the Sun is a member of a small class of late-type stars with large amplitudes in their X-ray cycles. The stellar X-ray observations listed in the HEASARC catalog are too sparse to verify this hypothesis. To resolve these and related questions we have proposed a small low-cost stellar X-ray spectroscopic imager originally called SADE to obtain regular time series from late and early-type stars and accretion disks. This instrument is complimentary to the much more advanced Chandra and XMM-Newton observatories, and allows them to focus on those sources that require their full spatial and spectral resolution. We will describe the basic design and spectroscopic capability of SADE and show it meets the mission requirements.
6. STELLAR: fast and exact local alignments
Directory of Open Access Journals (Sweden)
Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
7. Plasma equilibrium and stability in stellarators
International Nuclear Information System (INIS)
Pustovitov, V.D.; Shafranov, V.D.
1987-01-01
A review of theoretical methods of investigating plasma equilibrium and stability in stellarators is given. Principles forming the basis of toroidal plasma equilibrium and its stabilization, and the main results of analytical theory and numerical calculations are presented. Configurations with spiral symmetry and usual stellarators with plane axis and spiral fields are considered in detail. Derivation of scalar two-dimensional equations, describing equilibrium in these systems is given. These equations were used to obtain one-dimensional equations for displacement and ellipticity of magnetic surfaces. The model of weak-elliptic displaced surfaces was used to consider the evolution of plasma equilibrium in stellarators after elevation of its pressure: change of profile of rotational transformation after change of plasma pressure, current generation during its fast heating and its successive damping due to finite plasma conductivity were described. The derivation of equations of small oscillations in the form, suitable for local disturbance investigation is presented. These equations were used to obtain Mercier criteria and ballon model equations. General sufficient conditions of plasma stability in systems with magnetic confinement were derived
8. Ripple transport in helical-axis advanced stellarators - a comparison with classical stellarator/torsatrons
International Nuclear Information System (INIS)
Beidler, C.D.; Hitchon, W.N.G.
1993-08-01
Calculations of the neoclassical transport rates due to particles trapped in the helical ripples of a stellarator's magnetic field are carried out, based on solutions of the bounce-averaged kinetic equation. These calculations employ a model for the magnetic field strength, B, which is an accurate approximation to the actual B for a wide variety of stellarator-type devices, among which are Helical-Axis Advanced Stellarators (Helias) as well as conventional stellarators and torsatrons. Comparisons are carried out in which it is shown that the Helias concept leads to significant reductions in neoclassical transport rates throughout the entire long-mean-free-path regime, with the reduction being particularly dramatic in the ν -1 regime. These findings are confirmed by numerical simulations. Further, it is shown that the behavior of deeply trapped particles in Helias can be fundamentally different from that in classical stellarator/torsatrons; as a consequence, the beneficial effects of a radial electric field on the transport make themselves felt at lower collision frequency than is usual. (orig.)
9. BOOK REVIEW: Stellarator and Heliotron Devices
Science.gov (United States)
Johnson, John L.
1999-02-01
Stellarators and tokamaks are the most advanced devices that have been developed for magnetic fusion applications. The two approaches have much in common; tokamaks have received the most attention because their axisymmetry justifies the use of simpler models and provides a more forgiving geometry. However, recent advances in treating more complicated three dimensional systems have made it possible to design stellarators that are not susceptible to disruptions and do not need plasma current control. This has excited interest recently. The two largest new magnetic experiments in the world are the LHD device, which commenced operation in Toki, Japan, in 1998 and W7-X, which should become operational in Greifswald, Germany, in 2004. Other recently commissioned stellarators, including H-1 in Canberra, Australia, TJ-II in Madrid, Spain, and IMS in Madison, Wisconsin, have joined these in rejuvenating the stellarator programme. Thus, it is most appropriate that the author has made the lecture material that he presents to his students in the Graduate School of Energy Science at Kyoto University available to everyone. Stellarator and Heliotron Devices provides an excellent treatment of stellarator theory. It is aimed at graduate students who have a good understanding of classical mechanics and mathematical techniques. It contains good descriptions and derivations of essentially every aspect of fusion theory. The author provides an excellent qualitative introduction to each subject, pointing out the strengths and weaknesses of the models that are being used and describing our present understanding. He judiciously uses simple models which illustrate the similarities and differences between stellarators and tokamaks. To some extent the treatment is uneven, rigorous derivations starting with basic principles being given in some cases and relations and equations taken from the original papers being used as a starting point in others. This technique provides an excellent training
10. Thermosphere as a sink of magnetospheric energy - a review of recent observations of dynamics
International Nuclear Information System (INIS)
Killeen, T.L.
1985-01-01
It is pointed out that the past few years have seen an unprecedented influx of new experimental information on the dynamics of the neutral upper atmosphere of the earth. Vector wind measurements provide new information for studies of the thermospheric response to magnetospheric forcing. This response occurs through the medium of convecting ionospheric ions set into motion by electric fields of magnetospheric origin. The ultimate sink for much of the energy and momentum coming from the magnetosphere is the neutral thermosphere whose dynamics have, in the past, received far less attention than their ionospheric counterpart because of basic experimental limitations. In this paper, a review is provided of the progress made in the last few years on the basis of the Dynamics Explorer neutral wind observations, taking into account the coupling between the magnetosphere and the thermosphere via the ionosphere. 26 references
11. Effects of construction and operation of a satellite power system upon the magnetosphere
International Nuclear Information System (INIS)
Chiu, Y.T.; Luhmann, J.G.; Schulz, M.; Cornwall, J.M.
1979-01-01
This is the final report of an initial assessment of magnetospheric effects of the construction and operation of a satellite power system. This assessment effort is based on application of present scientific knowledge rather than on original scientific research. As such, it appears that mass and energy injections of the system are sufficient to modify the magnetosphere substantially, to the extent of possibly requiring mitigation measures for space systems but not to the extent of causing major redirection of efforts and concepts. The scale of the SPS is so unprecedentedly large, however, that these impressions require verification (or rejection) by in-depth assessment based on scientific treatment of the principal issues. Indeed, it is perhaps appropriate to state that present ignorance far exceeds present knowledge in regard to SPS magnetospheric effects, even though we only seek to define the approximate limits of magnetospheric modifications here
12. Thick Escaping Magnetospheric Ion Layer in Magnetopause Reconnection with MMS Observations
Science.gov (United States)
Nagai, T.; Kitamura, N.; Hasagawa, H.; Shinohara, I.; Yokota, S.; Saito, Y.; Nakamura, R.; Giles, B. L.; Pollock, C.; Moore, T. E.;
2016-01-01
The structure of asymmetric magnetopause reconnection is explored with multiple point and high-time-resolution ion velocity distribution observations from the Magnetospheric Multiscale mission. On 9 September 2015, reconnection took place at the magnetopause, which separated the magnetosheath and the magnetosphere with a density ratio of 25:2. The magnetic field intensity was rather constant, even higher in the asymptotic magnetosheath. The reconnected field line region had a width of approximately 540 km. In this region, streaming and gyrating ions are discriminated. The large extension of the reconnected field line region toward the magnetosheath can be identified where a thick layer of escaping magnetospheric ions was formed. The scale of the magnetosheath side of the reconnected field line region relative to the scale of its magnetospheric side was 4.5:1.
13. Science.gov (United States)
Faganello, Matteo; Califano, Francesco
2017-12-01
The Kelvin-Helmholtz instability, proposed a long time ago for its role in and impact on the transport properties at magnetospheric flanks, has been widely investigated in the Earth's magnetosphere context. This review covers more than fifty years of theoretical and numerical efforts in investigating the evolution of Kelvin-Helmholtz vortices and how the rich nonlinear dynamics they drive allow solar wind plasma bubbles to enter into the magnetosphere. Special care is devoted to pointing out the main advantages and weak points of the different plasma models that can be adopted for describing the collisionless magnetospheric medium and in underlying the important role of the three-dimensional geometry of the system.
14. Low Energy Particle Oscillations and Correlations with Hydromagnetic Waves in the Jovian Magnetosphere: Ulysses Measurements
Science.gov (United States)
Krupp, N.; Tsurutani, B. T.; Lanzerotti, L. J.; Maclennan, C. G.
1996-01-01
We report on measurements of energetic particle modulations observed by the HI-SCALE instrument aboard the Ulysses Spacecraft that were associated with the only hydromagnetic wave event measured inside the Jovian magnetosphere by the Ulysses magnetometer investigation.
15. Recent progress in understanding of the ion composition in the magnetosphere and some major question mark
International Nuclear Information System (INIS)
Hultqvist, B.
1981-06-01
The observations of the energetic ion composition in the magnetosphere are reviewed with the emphasis on the recent measurements by means of GEOS-1 and -2, ISEE-1 and 2, PROGNOZ-7 and SCATHA. The observations are compared with the predictions of the open magnetosphere model. One of the major conclusions is that there are processes in the magnetosphere which play a much larger part than the model, as hitherto presented, predicts. Direct ejection of ionospheric ions, in combination with acceleration, along closed as well as open field lines may even be the dominating source process for the ring current/inner plasma sheet in magnetic storms. In very disturbed conditions this ejection mechanism must work over most of the hemispheres poleward of say 50degrees. Circulation of the ionospheric ions through the tail of the magnetosphere is not likely to be of primary importance for the energization of these ions in very disturbed conditions. (author)
16. Field line projections of 6300 AA auroral emissions into the outer magnetosphere
International Nuclear Information System (INIS)
Shepherd, M.M.
1979-07-01
An empirical magnetospheric model is employed to project auroral intensity boundaries into the magnetosphere. The auroral data are in the form of instantaneous maps of 6300AA emission, acquired with the ISIS-II spacecraft and correspond to fluxes of low energy electrons. These are specific to a particular universal time and date. The magnetospheric model used is a purely empirical one, designed by Mead and Fairfield (1975) from 44.76 x 10 6 magnetic measurements made by 4 IMP satellites. Their model includes the dipole tilt as a variable, and permits selection from four different disturbance levels, so is particularly suited to these data. In a general way, the auroral projections agree with what is expected, giving some confidence in this application of the model. But a number of features appear that were not predicted, and which should permit new insights into the relationship of specific auroral boundaries to the structure of the magnetosphere. (author)
17. Gamma-Ray Pulsar Light Curves as Probes of Magnetospheric Structure
Science.gov (United States)
Harding, A. K.
2016-01-01
The large number of gamma-ray pulsars discovered by the Fermi Gamma-Ray Space Telescope since its launch in 2008 dwarfs the handful that were previously known. The variety of observed light curves makes possible a tomography of both the ensemble-averaged field structure and the high-energy emission regions of a pulsar magnetosphere. Fitting the gamma-ray pulsar light curves with model magnetospheres and emission models has revealed that most of the high-energy emission, and the particles acceleration, takes place near or beyond the light cylinder, near the current sheet. As pulsar magnetosphere models become more sophisticated, it is possible to probe magnetic field structure and emission that are self-consistently determined. Light curve modeling will continue to be a powerful tool for constraining the pulsar magnetosphere physics.
18. Excitation of the Magnetospheric Cavity by Space-Based ELF/VLF Transmitters
National Research Council Canada - National Science Library
Bell, Timothy F; Inan, Umran; Kulkarni, P
2004-01-01
During the period of performance Stanford University: 1. Developed an analytical model describing the distribution of current along a dipole antenna radiating ELF/VLF waves in the magnetospheric cavity...
19. Modeling magnetospheric plasma; Proceedings of the First Huntsville Workshop on Magnetosphere/Ionosphere Plasma Models, Guntersville, AL, Oct. 14-16, 1987
International Nuclear Information System (INIS)
Moore, T.E.; Waite, J.H. Jr.
1988-01-01
The conference presents papers on the global modeling of magnetospheric plasma processes, the modeling of the midlatitude ionosphere and plasmasphere, the modeling of the auroral zone and boundary layer, the modeling of the polar magnetosphere and ionosphere, and the modeling of the plasma sheet and ring current. Particular attention is given to the kinetic approach in magnetospheric plasma transport modeling, self-consistent neutral point current and fields from single particle dynamics, preliminary statistical survey of plasmaspheric ion properties from observations by DE 1/RIMS, and a model of auroral potential structures based on dynamics explorer plasma data. Other topics include internal shear layers in auroral dynamics, quantitative parameterization of energetic ionospheric ion outflow, and open flux merging in an expanding polarcap model
20. YOUNG STELLAR POPULATIONS IN MYStIX STAR-FORMING REGIONS: CANDIDATE PROTOSTARS
Energy Technology Data Exchange (ETDEWEB)
Romine, Gregory; Feigelson, Eric D.; Getman, Konstantin V. [Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802 (United States); Kuhn, Michael A. [Millennium Institute of Astrophysics, Camino El Observatorio 1515, Las Condes, Santiago (Chile); Povich, Matthew S., E-mail: [email protected] [Department of Physics and Astronomy, California State Polytechnic University, 3801 West Temple Ave., Pomona, CA 91768 (United States)
2016-12-20
The Massive Young Star-Forming Complex in Infrared and X-ray (MYStIX) project provides a new census on stellar members of massive star-forming regions within 4 kpc. Here the MYStIX Infrared Excess catalog and Chandra -based X-ray photometric catalogs are mined to obtain high-quality samples of Class I protostars using criteria designed to reduce extragalactic and Galactic field star contamination. A total of 1109 MYStIX Candidate Protostars (MCPs) are found in 14 star-forming regions. Most are selected from protoplanetary disk infrared excess emission, but 20% are found from their ultrahard X-ray spectra from heavily absorbed magnetospheric flare emission. Two-thirds of the MCP sample is newly reported here. The resulting samples are strongly spatially associated with molecular cores and filaments on Herschel far-infrared maps. This spatial agreement and other evidence indicate that the MCP sample has high reliability with relatively few “false positives” from contaminating populations. But the limited sensitivity and sparse overlap among the infrared and X-ray subsamples indicate that the sample is very incomplete with many “false negatives.” Maps, tables, and source descriptions are provided to guide further study of star formation in these regions. In particular, the nature of ultrahard X-ray protostellar candidates without known infrared counterparts needs to be elucidated. | {"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": 0.8878354430198669, "perplexity": 2685.5232013117243}, "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-2019-51/segments/1575540523790.58/warc/CC-MAIN-20191209201914-20191209225914-00396.warc.gz"} |
https://arxiv.org/abs/0811.3458 | hep-ph
(what is this?)
# Title: Mixed QCD-electroweak corrections to Higgs boson production in gluon fusion
Abstract: We compute the 3-loop O(\alpha \alpha_s) correction to the Higgs boson production cross section arising from light quarks using an effective theory approach. Our calculation probes the factorization of QCD and electroweak perturbative corrections to this process. We combine our results with the best current estimates for contributions from top and bottom quarks to derive an updated theoretical prediction for the Higgs boson production cross section in gluon fusion. With the use of the MSTW 2008 parton distribution functions that include the newest experimental data, our study results in cross sections approximately 4-6% lower for intermediate Higgs boson masses than those used in recent Tevatron analyses that imposed a 95% confidence level exclusion limit of a Standard Model Higgs boson with M_H=170 GeV.
Comments: 16 pgs., 5 figs. References and discussion added. Numerical results updated to use recent MSTW 2008 PDFs, which decrease the predicted Tevatron cross section Subjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Experiment (hep-ex) Journal reference: JHEP 0904:003,2009 DOI: 10.1088/1126-6708/2009/04/003 Cite as: arXiv:0811.3458 [hep-ph] (or arXiv:0811.3458v2 [hep-ph] for this version)
## Submission history
From: Frank J. Petriello [view email]
[v1] Fri, 21 Nov 2008 03:19:05 GMT (97kb)
[v2] Tue, 20 Jan 2009 19:07:04 GMT (86kb) | {"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": 0.8209426403045654, "perplexity": 4564.80364097672}, "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/1521257646875.28/warc/CC-MAIN-20180319101207-20180319121207-00696.warc.gz"} |
https://www.physicsforums.com/threads/infinite-acceleration-on-a-string.777421/ | # Infinite acceleration on a string?
1. Oct 21, 2014
### PhysicsKid0123
I'm trying to figure out what it says in my book. Here is the link of the picture. http://i941.photobucket.com/albums/...oads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg Could someone explain the part where it says "Otherwise, there would be a net tension force acting on the sections, and they would consequently suffer an infinite acceleration." Why does it necessarily have to be infinite? The only reason why I see it should be infinite is if the string is inextensible (unbreakable and maximally stretched) and if it so happened to not be straight it must have some infinite force so to not make it straight. Is my logic correct?http://[URL=http://s941.photobucket.com/user/markangela/media/Mobile%20Uploads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg.html][PLAIN]http://i941.photobucket.com/albums/ad259/markangela/Mobile%20Uploads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg [Broken]
Last edited by a moderator: May 7, 2017
2. Oct 21, 2014
### Staff: Mentor
The mass of the string is assumed to be negligible. If you put that into F=ma, a finite force leads to an extremely large ("infinite" in the limit) acceleration.
3. Oct 21, 2014
### PhysicsKid0123
What do you mean exactly by "put that into F=ma." You are saying that if there were to be some sort of force or tension then a approaches "infinity" as m approaches "zero" in some sense?
4. Oct 21, 2014
### Staff: Mentor
If tension would be different in different parts of the string, then there would be a force acting on a section of string.
A force acting on an object with a very small mass will lead to a very large acceleration (as F=m*a).
A force acting on an object with a very very small mass will lead to a very very large acceleration.
A force acting on an object with zero mass will lead to an "infinite" acceleration. (note the " ", because this does not exist in reality).
5. Oct 21, 2014
### PhysicsKid0123
Okay I think I see now. So the author's use of infinite accel. is ambiguous.
Similar Discussions: Infinite acceleration on a string? | {"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": 0.9257161021232605, "perplexity": 588.4788694707402}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109157.57/warc/CC-MAIN-20170821152953-20170821172953-00540.warc.gz"} |
https://www.physicsforums.com/threads/existence-and-mixed-derivatives.239323/ | # Existence and Mixed derivatives
1. Jun 8, 2008
### Physics_wiz
I remember before reading bits and pieces about how if we have a function of two variables, say f = f(x,y), then it must be true that d/dx(df/dy) = d/dy(df/dx), where the "d"'s are partials.
Can anyone guide me to what this theorem is called or to its implications? Also, does it work in reverse? i.e. if it is true that d/dx(df/dy) = d/dy(df/dx) for some function f, then does f necessarily exist?
2. Jun 8, 2008
### Crosson
This result is called Clairaut's theorem, and it merely requires that all the second partial derivatives are continuous. The reciprocal of this theorem is not true, since there is at least one function with a pair of 2nd partial derivatives equal at a point while at least one of the 2nd derivatives is not continuous at that point.
3. Jun 8, 2008
### HallsofIvy
Staff Emeritus
Provided the second partials are continuous.
If f does not exist then what in the world would you mean by "some function f"? Have you miswritten?
4. Jun 8, 2008
### Physics_wiz
Yes, I see now how I wrote doesn't make sense. I was trying to use this fact to solve the problem in my last post of the "Expressing multi-variable functions" Thread, but I guess I can't use this fact to check for whether a function exists or not.
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http://mathhelpforum.com/advanced-algebra/131164-what-eigen-values-eigen-vectors.html | # Math Help - what are eigen values and eigen vectors
1. ## what are eigen values and eigen vectors
I read in wikipedia
kindly explain me this.
Instead of writing f(x) we write M(v) where M is a matrix and v is a vector. Kindly explian this with example..
The rules for using a matrix to transform a vector are given in the article linear algebra.
If the action of a matrix on a (nonzero) vector changes its magnitude but not its direction, then the vector is called an eigenvector of that matrix.
2. Originally Posted by moonnightingale
I read in wikipedia
kindly explain me this.
Instead of writing f(x) we write M(v) where M is a matrix and v is a vector. Kindly explian this with example..
I don't see what you are asking. All that is said is that instead of calling the linear transformation "f", they are calling it "M". The second part of that sentence then says that we can always represent a linear transformation as multiplication by a matrix. Do you know what matrix multiplication is?
Presumably, it should be in this link:
The rules for using a matrix to transform a vector are given in the article linear algebra.
If the action of a matrix on a (nonzero) vector changes its magnitude but not its direction, then the vector is called an eigenvector of that matrix.
If two vectors have the same direction but possibly different lengths the each is a numerical multiple of the other. If M "changes the magniude but not the direction" of m, then Mv= av where a is a number, then applying the linear transformation to this v is just like multiplying by a number, which is much easier.
Of course, it is true that M0= 0= a0 but if Mv= av for v non-zero, then we say that "a" is an "eigenvalue" of M and v is a corresponding "eigenvector"
It's hard to say more without knowing what you do know and understand about vectors, matrices, linear transformations, and vector spaces. | {"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": 0.9712741374969482, "perplexity": 461.27432448820076}, "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-2015-14/segments/1427131302318.88/warc/CC-MAIN-20150323172142-00083-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/355854/how-should-i-understand-rotational-kinetic-energy | # How should I understand rotational kinetic energy?
I am looking at problem 26 of the physics 2001 GRE and am faced with the following problem:
A thin uniform rod of mass M and length L is positioned vertically above an anchored frictionless pivot point, as shown above, and then allowed to fall to the ground. With what speed does the free end of the rod strike the ground?
I understand that the total potential energy of the rod is $MgL/2$, and that this quantity must be conserved. I then think to myself, the sum of all of the energy in the rod right when it strikes the ground must be entirely translational, since the potential energy is 0 at the ground. This gives $$E_{translational} = \sum{}\frac{1}{2}m_iv_i^2 = \int{\frac{1}{2}dmv(r)^2} = \int{\frac{1}{2}dmr^2\omega^2} = \frac{1}{2}I\omega^2 = \frac{mL^2}{6}\omega^2$$ Where v(r) is the velocity of any mass dm a distance r from the pivot.
Solving for $\omega$ and using this to find $v(L)$ yields $v(L) = \sqrt{3gL}$ which is the correct answer. However, this derivation seems like a bad approach on the PGRE in that I haven't really used any center of mass ideas except for the fact that the potential energy of the rod can be treated as if the rod were a point mass at height $L/2$, that is, $U = U_{com}$. What other approaches are there to solving this problem?
• I think you have solved it in the most efficient way I can think of. – mwengler Sep 6 '17 at 20:28
• This looks like a list question... – DanielSank Sep 7 '17 at 1:26
Another approach: the moment of inertia of a rod of mass $m$ and length $\ell$, pivoted from one end, is $I=\frac13 m \ell^2$. The rotational kinetic energy is $E = \frac12 I \omega^2$, which must be equal to the potential energy at the start, which is $\frac12 m g \ell$.
Also, we know that the velocity at the tip of the rod $v=\omega \ell$
$$\frac12 \left(\frac13 m \ell^2 \right)\omega^2 = \frac12 m g \ell\\ v^2 = 3g\ell$$ | {"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": 0.9731454849243164, "perplexity": 124.7967529105356}, "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-2019-43/segments/1570986700435.69/warc/CC-MAIN-20191019214624-20191020002124-00129.warc.gz"} |
http://mathhelpforum.com/geometry/271486-stuck-2-column-proofs-congruency-triangles.html | # Thread: Stuck on 2 column proofs for congruency of triangles
1. ## Stuck on 2 column proofs for congruency of triangles
Ive gotten this done so far, but i'm pretty sure its wrong. Really frustrated with this. Anyone help?
Rectangle ABCD given ab=dc opposite sides ad=bc opposite sides bd=bd
2. ## Re: Stuck on 2 column proofs for congruency of triangles
both "proves" are written incorrectly; they should be written (a) Prove: $\Delta ABD \cong \Delta CDB$ and (b) Prove: $\Delta ABC \cong \Delta CDA$
note diagonals DB and AC equal themselves by the reflexive property of equality ... so you will have SSS for both proofs, correct? | {"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": 0.9383874535560608, "perplexity": 4103.42165605968}, "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-2017-09/segments/1487501170839.31/warc/CC-MAIN-20170219104610-00018-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.computer.org/csdl/trans/td/2010/06/ttd2010060857-abs.html | Issue No. 06 - June (2010 vol. 21)
ISSN: 1045-9219
pp: 857-871
Francesca Lo Piccolo , Universitá di Roma, Tor Vergata, Rome
Stefano Salsano , Universitá di Roma, Tor Vergata, Rome
Lorenzo Bracciale , Universitá di Roma, Tor Vergata, Rome
Nicola Blefari Melazzi , Universitá di Roma, Tor Vergata, Rome
Giuseppe Bianchi , Universitá di Roma, Tor Vergata, Rome
ABSTRACT
In this paper, we propose and evaluate an overlay distribution algorithm for P2P, chunk-based, streaming systems over forest-based topologies. In such systems, the stream is divided in chunks; chunks are delivered by each node in a store-and-forward way. A relaying node starts distributing a chunk only when it has completed its reception from another node. Peers are logically organized in a forest of trees, where each tree includes all peers. The source periodically distributes different chunks to each tree for their delivery. Our key idea consists in employing serial transmission: for each tree, and thus, for each chunk, the source node sends the chunk to its children in series; the same holds for each peer node of the tree, excluding the leaves. Besides this basic idea, the contributions of this paper are: 1) we demonstrate the feasibility of serial transmission over a forest of trees, which is not a trivial problem, unlike the case of parallel transmission; 2) we derive an analytical model to evaluate the system performance; 3) we derive a theoretical bound for the number of nodes reachable in a given time interval or equivalently for the time required to reach a given number of nodes; 4) we prove the optimality of our approach in terms of its capability to reach such bound; and 5) we develop a general simulation package for P2P streaming systems and use it to compare our solution to literature results. Finally, we stress that this paper is focused on the theoretical properties and performance understanding of the proposed distribution algorithm, rather than on its practical implementation in a real system. However, we also briefly describe a practical workable implementation of our algorithm.
INDEX TERMS
Distributed systems, distributed applications, performance of systems, performance attributes.
CITATION
Francesca Lo Piccolo, Stefano Salsano, Lorenzo Bracciale, Nicola Blefari Melazzi, Giuseppe Bianchi, "Streamline: An Optimal Distribution Algorithm for Peer-to-Peer Real-Time Streaming", IEEE Transactions on Parallel & Distributed Systems, vol. 21, no. , pp. 857-871, June 2010, doi:10.1109/TPDS.2009.114 | {"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": 0.8348640203475952, "perplexity": 1501.6971508005304}, "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-2017-22/segments/1495463612399.20/warc/CC-MAIN-20170529145935-20170529165935-00466.warc.gz"} |
http://www.computer.org/csdl/trans/ts/2002/09/e0904-abs.html | Subscribe
Issue No.09 - September (2002 vol.28)
pp: 904-912
ABSTRACT
<p><b>Abstract</b>—An enhanced technique for risk categorization is presented. This technique, PCA-ANN, provides an improved capability to discriminate high-risk software. The approach draws on the combined strengths of pattern recognition, multivariate statistics and neural networks. Principal component analysis is utilized to provide a means of normalizing and orthogonalizing the input data, thus eliminating the ill effects of multicollinearity. A neural network is used for risk determination/classification. A significant feature of this approach is a procedure, herein termed cross-normalization. This procedure provides the technique with capability to discriminate data sets that include disproportionately large numbers of high-risk software modules.</p>
INDEX TERMS
Software risk analysis and defect prediction, decision making, mathematical models, system process models.
CITATION
Donald E. Neumann, "An Enhanced Neural Network Technique for Software Risk Analysis", IEEE Transactions on Software Engineering, vol.28, no. 9, pp. 904-912, September 2002, doi:10.1109/TSE.2002.1033229 | {"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": 0.8623000979423523, "perplexity": 3678.0727486809506}, "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-2015-18/segments/1429246658061.59/warc/CC-MAIN-20150417045738-00009-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/tensor-transformations.396512/ | # Tensor transformations
1. Apr 19, 2010
### peterjaybee
Hi,
In component form the transformation for the following tensor can be written as
$$F^{\mu\nu}=\Lambda^{\mu}_{\alpha}\Lambda^{\nu}_{\beta}F^{\beta\alpha}$$
or in matrix notation, apparently as
$$F^{'}=LFL^{T}$$
Here L is the Lorentz transformation matrix
Im happy with the component form, but I dont understand where the transpose matrix bit comes from in the matrix equation, and why it is on the RHS of the F tensor.
2. Apr 19, 2010
### Fredrik
Staff Emeritus
It follows immediately from the definition of the product of two matrices.
$$(AB)_{ij}=A_{ik}B_{kj}$$
(What does this definition say is on row i, column j of $$LFL^T$$?)
3. Apr 20, 2010
### peterjaybee
Im sorry, I still can't see it.
4. Apr 20, 2010
### Fredrik
Staff Emeritus
No need to apologize. I know a lot of people are having difficulties with this. I'm genuinely interested in why that is, so when you do see it, I'd appreciate if you could tell me what it was that confused you.
If we write the component on row $\mu$, column $\nu$, of an arbitrary matrix X as $X_{\mu\nu}$, then
$$(LFL^T)_{\mu\nu}=(LF)_{\mu\rho}(L^T)_{\rho\nu}=L_{\mu\sigma}F_{\sigma\rho}L_{\nu\rho}=L_{\mu\sigma}L_{\nu\rho}F_{\sigma\rho}$$
5. Apr 20, 2010
### peterjaybee
I strugle with this concept (and alot of other index manipulations) because I find the index notation unfamiliar and a little alien. Because I dont understand it, my logic is flawed. For example when I initially saw
$$F^{\mu\nu}=\Lambda^{\mu}_{\alpha}\Lambda^{\nu}_{\beta}F^{\beta\alpha}$$,
I thought to get the transformed faraday components you just times two lorentz matricies together then right multiply by the untransformed faraday tensor. Even though I know this is wrong (having tried it) I do not understand why it is wrong. It is very difficult to describe.
Thanks to you, I now understand how to do the manipulation which is a relief . The manipulation itself makes sense, I just dont understand where my logic in the above fails if you see what I mean.
Ill try expressing it in another way if someone asked me...
"Can you get the transformed faraday components by just multiplying two lorentz matricies together then right multiply by the untransformed faraday tensor?"...
I would say no, but if they then asked me why not, I would be stuck.
6. Apr 20, 2010
### dx
Maybe it will be help a little if we say it in coordinate free language. In spacetime, the distinction between a vector and a covector is only conceptually useful, but computationally, we can convert a vector into a covector or a covector into a vector using the metric tensor g(_,_). So if we have a vector v, then the covector corresponding to that is defined as g(v,_), i.e. the vector vμ corresponds to the covector vα through vα = gαμvμ
Similarly, if we have a contravariant tensor Fαβ, then we use this by contracting it with covectors v and w thus: Fαβvαwβ. But, as we have seen above, vα = gαμvμ and wβ = gβνvν. So Fαβvαwβ = Fαβgαμvμgβνvν = gβνgαμFαβvμvν.
So the contravariant tensor, which acts on pairs of covectors, can be made to act on their corresponding vectors by replacing it with the covariant tensor gβνgαμFαβ = Fμν.
7. Apr 20, 2010
### dx
Just noticed the question was not about raising and lowering indices. Ignore my previous post.
8. Apr 20, 2010
### Fredrik
Staff Emeritus
Look at the definition of matrix multiplication again, in #2. Note that the sum is always over an index that's a column index for the matrix on the left and a row index for the matrix on the right. Since $\Lambda^\nu{}_{\beta}$ is row $\nu$, column $\beta$ of a $\Lambda$, and $F^{\beta\alpha}$ is row $\beta$, column $\alpha$ of a $F$, the result
$$\Lambda^\nu{}_\beta F^{\beta\alpha}=(\Lambda F)^{\nu\alpha}$$
follows immediately from the definition of matrix multiplication. But now look at
$$\Lambda^\mu{}_\alpha F^{\beta\alpha}$$
Note that the sum is over the column index of F. If you have another look at the definition of matrix multiplication, you'll see that this means that if the above is a component of the product of two matrices, one of which is F, then F must be the matrix on the left. When you understand that, the rest should be easy.
Also note that you should LaTeX $\Lambda^\mu{}_\nu$ as \Lambda^\mu{}_\nu, so that the column index appears diagonally to the right below the row index. And check out the comment about the inverse here to see why the horizontal position of the indices matters.
9. Apr 20, 2010
### peterjaybee
I finally get it! Its a miracle.
Similar Discussions: Tensor transformations | {"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": 0.9668834209442139, "perplexity": 557.7335235841211}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106779.68/warc/CC-MAIN-20170820150632-20170820170632-00561.warc.gz"} |
http://mathonline.wikidot.com/hoelder-s-inequality-for-l1-e-and-lp-e | Hölder's Inequality for L1(E) and Lp(E)
# Hölder's Inequality for L1(E) and Lp(E)
Recall from the Young's Inequality page that if $1 < p < \infty$ and $q$ is the conjugate index of $p$ and if $a, b \geq 0$ then:
(1)
\begin{align} \quad ab \leq \frac{a^p}{p} + \frac{b^q}{q} \end{align}
We will use Young's inequality to prove the significant Hölder's inequality for $L^1(E)$ and for $L^p(E)$ where $1 < p < \infty$.
Theorem 1 (Hölder's Inequality for $L^1(E)$ and $L^p(E)$): Let $E$ be a measurable set and let $1 \leq p < \infty$ with $q$ the conjugate index of $p$. If $f \in L^p(E)$ and $g \in L^q(E)$ then $fg \in L^1(E)$ and $\| fg \|_1 \leq \| f \|_p \| g \|_q$.
• Proof: Observe that if $f = 0$ a.e. on $E$ or $g = 0$ a.e. on $E$ then Young's inequality holds trivially. So assume that $f \neq 0$ and $g \neq 0$ a.e. on $E$. We break the proof up into a few cases.
• Case 1: Suppose that $p = 1$. Then $q = \infty$. Since $g \in L^q(E)$ we have that $|g(x)| \leq \| g \|_{\infty}$ a.e. on $E$. Then:
(2)
\begin{align} \quad \| fg \|_1 = \int_E |fg| = \int_E |f||g| \leq \int_E |f| \| g \|_{\infty} = \| g \|_{\infty}\int_E |f| = \| f \|_1 \| g \|_{\infty} \end{align}
• Case 2: Suppose that $1 < p < \infty$. Let $f \in L^p(E)$], $g \in L^q(E)$ be such that $\| f \|_p = 1$ and $\| g \|_q = 1$. Since $|f(x)|, |g(x)| \geq 0$ for each $x \in E$, we have by Young's inequality that:
(3)
\begin{align} |f(x)g(x)| \leq \frac{|f(x)|^p}{p} + \frac{|g(x)|^q}{q} \end{align}
• Taking the integral of both sides gives us that:
(4)
\begin{align} \quad \| fg \|_1 = \int_E |fg| \leq \int_E \left [ \frac{|f|^p}{p} + \frac{|g|^q}{q} \right ] = \frac{1}{p} \int_E |f|^p + \frac{1}{q} \int_E |g|^q = \frac{\| f \|_p}{p} + \frac{\| g \|_q}{q} = \frac{1}{p} + \frac{1}{q} = 1 = 1 \cdot 1 = \| f \|_p \| g \|_q \end{align}
• So Young's Inequality holds if $\| f \|_p = 1$ and $\| g \|_q = 1$.
• Let $f \in L^p(E)$ and let $g \in L^q(E)$. Define $F \in L^p(E)$ and $G \in L^q(E)$ by:
(5)
• Then $\| F \|_p = 1$ and $\| G \|_q = 1$, and so: | {"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": 7, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998624324798584, "perplexity": 511.78700261272047}, "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/1555578765115.93/warc/CC-MAIN-20190426093516-20190426115516-00345.warc.gz"} |
https://byjus.com/ncert-exemplar-solutions-class-6-maths/ | # NCERT Exemplar Solutions for Class 6 Maths
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NCERT Exemplar Solutions for Class 6 Maths Chapter 1 – Number System
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Chapter 1 involves the study of the Number System. A system for representing or expressing numbers of a certain type is known as the number system. A number system can also be defined as a writing system to express a number. In this Chapter, we will study about large numbers upto one crore, reading and writing of large numbers, comparing large numbers, Indian system of numeration, International system of numeration, natural numbers. This Chapter also contains predecessor and successor of a natural numbers, whole numbers, representation of whole numbers on the number line and properties of whole numbers.
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This Chapter is about Fractions and Decimals. A fraction is a number representing a part of a whole. This whole may be a single object or a group of objects. Fractions with denominators 10, 100, etc. can be written in a form, using a decimal point, called decimal numbers or decimals. A fraction whose numerator is less than the denominator is called a proper fraction, otherwise it is called an improper fraction. This lesson includes multiplication and division of fractions, along with some other concepts, like types of fractions, method of changing unlike fractions to like fractions, method of comparing more than two fractions. Method of converting a decimal into a fraction, converting fraction into a decimal, addition and subtraction of decimals, multiplication of decimal by 10,100, 1000, etc., multiplication of decimal by whole number, multiplication of decimal by a decimal.
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• Solving the NCERT Exemplar helps the students to develop problem-solving abilities and helps them to tackle any type of question in the exams. | {"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": 0.9022040963172913, "perplexity": 956.9780453913919}, "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/1669446711121.31/warc/CC-MAIN-20221206225143-20221207015143-00018.warc.gz"} |
https://www.vrcbuzz.com/tutorials/statistics/page/2/ | # Statistics
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Five number summary for ungrouped data A five number summary is a quick and easy way to determine the the... | {"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": 0.9617183804512024, "perplexity": 1279.950847812695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154126.73/warc/CC-MAIN-20210731203400-20210731233400-00468.warc.gz"} |
https://en.wikipedia.org/wiki/Frame_dragging | # Frame-dragging
(Redirected from Frame dragging)
Frame-dragging is an effect on spacetime, predicted by Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static, rotating for instance. The first frame-dragging effect was derived in 1918, in the framework of general relativity, by the Austrian physicists Josef Lense and Hans Thirring, and is also known as the Lense–Thirring effect.[1][2][3] They predicted that the rotation of a massive object would distort the spacetime metric, making the orbit of a nearby test particle precess. This does not happen in Newtonian mechanics for which the gravitational field of a body depends only on its mass, not on its rotation. The Lense–Thirring effect is very small—about one part in a few trillion. To detect it, it is necessary to examine a very massive object, or build an instrument that is very sensitive. More generally, the subject of effects caused by mass–energy currents is known as gravitomagnetism, in analogy with classical electromagnetism.
## Frame dragging effects
Rotational frame-dragging (the Lense–Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects. Under the Lense–Thirring effect, the frame of reference in which a clock ticks the fastest is one which is revolving around the object as viewed by a distant observer. This also means that light traveling in the direction of rotation of the object will move past the massive object faster than light moving against the rotation, as seen by a distant observer. It is now the best known frame-dragging effect, partly thanks to the Gravity Probe B experiment. Qualitatively, frame-dragging can be viewed as the gravitational analog of electromagnetic induction.
Also, an inner region is dragged more than an outer region. This produces interesting locally rotating frames. For example, imagine that a north-south–oriented ice skater, in orbit over the equator of a black hole and rotationally at rest with respect to the stars, extends her arms. The arm extended toward the black hole will be "torqued" spinward due to gravitomagnetic induction ("torqued" is in quotes because gravitational effects are not considered "forces" under GR). Likewise the arm extended away from the black hole will be torqued anti-spinward. She will therefore be rotationally sped up, in a counter-rotating sense to the black hole. This is the opposite of what happens in everyday experience. There exists a particular rotation rate that, should she be initially rotating at that rate when she extends her arms, inertial effects and frame-dragging effects will balance and her rate of rotation will not change. Due to the Principle of Equivalence gravitational effects are locally indistinguishable from inertial effects, so this rotation rate, at which when she extends her arms nothing happens, is her local reference for non-rotation. This frame is rotating with respect to the fixed stars and counter-rotating with respect to the black hole. This effect is analogous to the hyperfine structure in atomic spectra due to nuclear spin. A useful metaphor is a planetary gear system with the black hole being the sun gear, the ice skater being a planetary gear and the outside universe being the ring gear. See Mach's principle.
Another interesting consequence is that, for an object constrained in an equatorial orbit, but not in freefall, it weighs more if orbiting anti-spinward, and less if orbiting spinward. For example, in a suspended equatorial bowling alley, a bowling ball rolled anti-spinward would weigh more than the same ball rolled in a spinward direction. Note, frame dragging will neither accelerate or slow down the bowling ball in either direction. It is not a "viscosity". Similarly, a stationary plumb-bob suspended over the rotating object will not list. It will hang vertically. If it starts to fall, induction will push it in the spinward direction.
Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging (but see Einstein, 1921).[4]
Static mass increase is a third effect noted by Einstein in the same paper.[5] The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging is not used by Einstein), it is demonstrated by Einstein that it derives from the same equation of general relativity. It is also a tiny effect that is difficult to confirm experimentally.
## Experimental tests of frame-dragging
In 1976 Van Patten and Everitt[6][7] proposed to implement a dedicated mission aimed to measure the Lense–Thirring node precession of a pair of counter-orbiting spacecraft to be placed in terrestrial polar orbits with drag-free apparatus. A somewhat equivalent, cheaper version of such an idea was put forth in 1986 by Ciufolini[8] who proposed to launch a passive, geodetic satellite in an orbit identical to that of the LAGEOS satellite, launched in 1976, apart from the orbital planes which should have been displaced by 180 deg apart: the so-called butterfly configuration. The measurable quantity was, in this case, the sum of the nodes of LAGEOS and of the new spacecraft, later named LAGEOS III, LARES, WEBER-SAT.
Limiting the scope to the scenarios involving existing orbiting bodies, the first proposal to use the LAGEOS satellite and the Satellite Laser Ranging (SLR) technique to measure the Lense–Thirring effect dates back to 1977–1978.[9][10] Tests have started to be effectively performed by using the LAGEOS and LAGEOS II satellites in 1996,[11] according to a strategy[12] involving the use of a suitable combination of the nodes of both satellites and the perigee of LAGEOS II. The latest tests with the LAGEOS satellites have been performed in 2004-2006[13][14] by discarding the perigee of LAGEOS II and using a linear combination.[15] Recently, a comprehensive overview of the attempts to measure the Lense-Thirring effect with artificial satellites was published in the literature.[16] The overall accuracy reached in the tests with the LAGEOS satellites is subject to some controversy.[17][18][19]
The Gravity Probe B experiment[20][21] was a satellite-based mission by a Stanford group and NASA, used to experimentally measure another gravitomagnetic effect, the Schiff precession of a gyroscope,[22][23] to an expected 1% accuracy or better. Unfortunately such accuracy was not achieved. The first preliminary results released in April 2007 pointed towards an accuracy of[24] 256–128%, with the hope of reaching about 13% in December 2007.[25] In 2008 the Senior Review Report of the NASA Astrophysics Division Operating Missions stated that it was unlikely that Gravity Probe B team will be able to reduce the errors to the level necessary to produce a convincing test of currently untested aspects of General Relativity (including frame-dragging).[26][27] On May 4, 2011, the Stanford-based analysis group and NASA announced the final report,[28] and in it the data from GP-B demonstrated the frame-dragging effect with an error of about 19 percent, and Einstein's predicted value was at the center of the confidence interval.[29][30]
In the case of stars orbiting close to a spinning, supermassive black hole, frame dragging should cause the star's orbital plane to precess about the black hole spin axis. This effect should be detectable within the next few years via astrometric monitoring of stars at the center of the Milky Way galaxy.[31] By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the no-hair theorems of general relativity, in addition to measuring the spin of the black hole.[32]
## Astronomical evidence
Relativistic Jet. The environment around the AGN where the relativistic plasma is collimated into jets which escape along the pole of the supermassive black hole
Relativistic jets may provide evidence for the reality of frame-dragging. Gravitomagnetic forces produced by the Lense–Thirring effect (frame dragging) within the ergosphere of rotating black holes[33][34] combined with the energy extraction mechanism by Penrose[35] have been used to explain the observed properties of relativistic jets. The gravitomagnetic model developed by Reva Kay Williams predicts the observed high energy particles (~GeV) emitted by quasars and active galactic nuclei; the extraction of X-rays, γ-rays, and relativistic e–e+ pairs; the collimated jets about the polar axis; and the asymmetrical formation of jets (relative to the orbital plane).
## Mathematical derivation of frame-dragging
Frame-dragging may be illustrated most readily using the Kerr metric,[36][37] which describes the geometry of spacetime in the vicinity of a mass M rotating with angular momentum J
{\displaystyle {\begin{aligned}c^{2}d\tau ^{2}=&\left(1-{\frac {r_{s}r}{\rho ^{2}}}\right)c^{2}dt^{2}-{\frac {\rho ^{2}}{\Lambda ^{2}}}dr^{2}-\rho ^{2}d\theta ^{2}\\&{}-\left(r^{2}+\alpha ^{2}+{\frac {r_{s}r\alpha ^{2}}{\rho ^{2}}}\sin ^{2}\theta \right)\sin ^{2}\theta \ d\phi ^{2}+{\frac {2r_{s}r\alpha c\sin ^{2}\theta }{\rho ^{2}}}d\phi dt\end{aligned}}}
where rs is the Schwarzschild radius
${\displaystyle r_{s}={\frac {2GM}{c^{2}}}}$
and where the following shorthand variables have been introduced for brevity
${\displaystyle \alpha ={\frac {J}{Mc}}}$
${\displaystyle \rho ^{2}=r^{2}+\alpha ^{2}\cos ^{2}\theta \,\!}$
${\displaystyle \Lambda ^{2}=r^{2}-r_{s}r+\alpha ^{2}\,\!}$
In the non-relativistic limit where M (or, equivalently, rs) goes to zero, the Kerr metric becomes the orthogonal metric for the oblate spheroidal coordinates
${\displaystyle c^{2}d\tau ^{2}=c^{2}dt^{2}-{\frac {\rho ^{2}}{r^{2}+\alpha ^{2}}}dr^{2}-\rho ^{2}d\theta ^{2}-\left(r^{2}+\alpha ^{2}\right)\sin ^{2}\theta d\phi ^{2}}$
We may rewrite the Kerr metric in the following form
${\displaystyle c^{2}d\tau ^{2}=\left(g_{tt}-{\frac {g_{t\phi }^{2}}{g_{\phi \phi }}}\right)dt^{2}+g_{rr}dr^{2}+g_{\theta \theta }d\theta ^{2}+g_{\phi \phi }\left(d\phi +{\frac {g_{t\phi }}{g_{\phi \phi }}}dt\right)^{2}}$
This metric is equivalent to a co-rotating reference frame that is rotating with angular speed Ω that depends on both the radius r and the colatitude θ
${\displaystyle \Omega =-{\frac {g_{t\phi }}{g_{\phi \phi }}}={\frac {r_{s}\alpha rc}{\rho ^{2}\left(r^{2}+\alpha ^{2}\right)+r_{s}\alpha ^{2}r\sin ^{2}\theta }}}$
In the plane of the equator this simplifies to:[38]
${\displaystyle \Omega ={\frac {r_{s}\alpha c}{r^{3}+\alpha ^{2}r+r_{s}\alpha ^{2}}}}$
Thus, an inertial reference frame is entrained by the rotating central mass to participate in the latter's rotation; this is frame-dragging.
The two surfaces on which the Kerr metric appears to have singularities; the inner surface is the spherical event horizon, whereas the outer surface is an oblate spheroid. The ergosphere lies between these two surfaces; within this volume, the purely temporal component gtt is negative, i.e., acts like a purely spatial metric component. Consequently, particles within this ergosphere must co-rotate with the inner mass, if they are to retain their time-like character.
An extreme version of frame dragging occurs within the ergosphere of a rotating black hole. The Kerr metric has two surfaces on which it appears to be singular. The inner surface corresponds to a spherical event horizon similar to that observed in the Schwarzschild metric; this occurs at
${\displaystyle r_{\text{inner}}={\frac {r_{s}+{\sqrt {r_{s}^{2}-4\alpha ^{2}}}}{2}}}$
where the purely radial component grr of the metric goes to infinity. The outer surface is not a sphere, but an oblate spheroid that touches the inner surface at the poles of the rotation axis, where the colatitude θ equals 0 or π; its radius is defined by the formula
${\displaystyle r_{\text{outer}}={\frac {r_{s}+{\sqrt {r_{s}^{2}-4\alpha ^{2}\cos ^{2}\theta }}}{2}}}$
where the purely temporal component gtt of the metric changes sign from positive to negative. The space between these two surfaces is called the ergosphere. A moving particle experiences a positive proper time along its worldline, its path through spacetime. However, this is impossible within the ergosphere, where gtt is negative, unless the particle is co-rotating with the interior mass M with an angular speed at least of Ω. However, as seen above, frame-dragging occurs about every rotating mass and at every radius r and colatitude θ, not only within the ergosphere.
### Lense–Thirring effect inside a rotating shell
The Lense–Thirring effect inside a rotating shell was taken by Albert Einstein as not just support for, but a vindication of Mach's principle, in a letter he wrote to Ernst Mach in 1913 (five years before Lense and Thirring's work, and two years before he had attained the final form of general relativity). A reproduction of the letter can be found in Misner, Thorne, Wheeler.[39] The general effect scaled up to cosmological distances, is still used as a support for Mach's principle.[39]
Inside a rotating spherical shell the acceleration due to the Lense–Thirring effect would be[40]
${\displaystyle {\bar {a}}=-2d_{1}\left({\bar {\omega }}\times {\bar {v}}\right)-d_{2}\left[{\bar {\omega }}\times \left({\bar {\omega }}\times {\bar {r}}\right)+2\left({\bar {\omega }}{\bar {r}}\right){\bar {\omega }}\right]}$
where the coefficients are
{\displaystyle {\begin{aligned}d_{1}&={\frac {4MG}{3Rc^{2}}}\\d_{2}&={\frac {4MG}{15Rc^{2}}}\end{aligned}}}
for MGRc2 or more precisely,
${\displaystyle d_{1}={\frac {4\alpha (2-\alpha )}{(1+\alpha )(3-\alpha )}},\qquad \alpha ={\frac {MG}{2Rc^{2}}}}$
The spacetime inside the rotating spherical shell will not be flat. A flat spacetime inside a rotating mass shell is possible if the shell is allowed to deviate from a precisely spherical shape and the mass density inside the shell is allowed to vary.[41]
## References
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2. ^ Thirring, H. (1921). "Berichtigung zu meiner Arbeit: 'Über die Wirkung rotierender Massen in der Einsteinschen Gravitationstheorie'". Physikalische Zeitschrift. 22: 29. Bibcode:1921PhyZ...22...29T. [Correction to my paper "On the Effect of Rotating Distant Masses in Einstein's Theory of Gravitation"]
3. ^ Lense, J.; Thirring, H. (1918). "Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie". Physikalische Zeitschrift. 19: 156–163. Bibcode:1918PhyZ...19..156L. [On the Influence of the Proper Rotation of Central Bodies on the Motions of Planets and Moons According to Einstein's Theory of Gravitation]
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8. ^ Ciufolini, I. (1986). "Measurement of Lense–Thirring Drag on High-Altitude Laser-Ranged Artificial Satellites". Phys. Rev. Lett. 56 (4): 278–281. Bibcode:1986PhRvL..56..278C. doi:10.1103/PhysRevLett.56.278. PMID 10033146.
9. ^ Cugusi, L., Proverbio E. Relativistic effects on the Motion of the Earth's. Satellites, paper presented at the International Symposium on Satellite Geodesy in Budapest from June 28 to July 1, 1977, J. of Geodesy, 51, 249–252, 1977.
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12. ^ Ciufolini, I., On a new method to measure the gravitomagnetic field using two orbiting satellites., Il Nuovo Cimento A, 109, 1709–1720, 1996.
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14. ^ Ciufolini, I., Pavlis, E.C., and Peron, R., Determination of frame-dragging using Earth gravity models from CHAMP and GRACE, New Astron., 11, 527–550, 2006.
15. ^ Iorio, L.; Morea, A. (2004). "The Impact of the New Earth Gravity Models on the Measurement of the Lense-Thirring Effect". General Relativity and Gravitation. 36 (6): 1321–1333. arXiv:gr-qc/0304011. Bibcode:2004GReGr..36.1321I. doi:10.1023/B:GERG.0000022390.05674.99.
16. ^ Renzetti, G. (2013). "History of the attempts to measure orbital frame-dragging with artificial satellites". Central European Journal of Physics. 11 (5): 531–544. Bibcode:2013CEJPh..11..531R. doi:10.2478/s11534-013-0189-1.
17. ^ Renzetti, G. (2014). "Some reflections on the Lageos frame-dragging experiment in view of recent data analyses". New Astronomy. 29: 25–27. Bibcode:2014NewA...29...25R. doi:10.1016/j.newast.2013.10.008.
18. ^ Iorio, L.; Lichtenegger, H.I.M.; Ruggiero, M.L.; Corda, C. (2011). "Phenomenology of the Lense-Thirring effect in the solar system". Astrophysics and Space Science. 331 (2): 351–395. arXiv:1009.3225. Bibcode:2011Ap&SS.331..351I. doi:10.1007/s10509-010-0489-5.
19. ^ Ciufolini, I.; Paolozzi, A.; Pavlis, E.C..; Ries, J.; Koenig, R.; Matzner, R.; Sindoni, G.; Neumeyer, H. (2011). "Testing gravitational physics with satellite laser ranging". The European Physical Journal Plus. 126 (8): 72. Bibcode:2011EPJP..126...72C. doi:10.1140/epjp/i2011-11072-2.
20. ^ Everitt, C.W.F, The Gyroscope Experiment I. General Description and Analysis of Gyroscope Performance. In: Bertotti, B. (Ed.), Proc. Int. School Phys. "Enrico Fermi" Course LVI. New Academic Press, New York, pp. 331–360, 1974. Reprinted in: Ruffini, R.J., Sigismondi, C. (Eds.), Nonlinear Gravitodynamics. The Lense–Thirring Effect. World Scientific, Singapore, pp. 439–468, 2003.
21. ^ Everitt, C.W.F., et al., Gravity Probe B: Countdown to Launch. In: Laemmerzahl, C., Everitt, C.W.F., Hehl, F.W. (Eds.), Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space. Springer, Berlin, pp. 52–82, 2001.
22. ^ Pugh, G.E., Proposal for a Satellite Test of the Coriolis Prediction of General Relativity, WSEG, Research Memorandum No. 11, 1959. Reprinted in: Ruffini, R.J., Sigismondi, C. (Eds.), Nonlinear Gravitodynamics. The Lense–Thirring Effect. World Scientific, Singapore, pp. 414–426, 2003.
23. ^ Schiff, L., On Experimental Tests of the General Theory of Relativity, Am. J. of Phys., 28, 340–343, 1960.
24. ^ Muhlfelder, B., Mac Keiser, G., and Turneaure, J., Gravity Probe B Experiment Error, poster L1.00027 presented at the American Physical Society (APS) meeting in Jacksonville, Florida, on 14–17 April 2007, 2007.
26. ^ [1] Report of the 2008 Senior Review of the Astrophysics Division Operating Missions, NASA
27. ^ Gravity Probe B scores 'F' in NASA review, Jeff Hecht, New Scientist – Space, May 20, 2008
28. ^ http://einstein.stanford.edu/highlights/status1.html
29. ^
30. ^ "Gravity Probe B: Final results of a space experiment to test general relativity". Physical Review Letters. 2011-05-01. Retrieved 2011-05-06.
31. ^ Merritt, D.; Alexander, T.; Mikkola, S.; Will, C. (2010). "Testing Properties of the Galactic Center Black Hole Using Stellar Orbits". Physical Review D. 81 (6): 062002. arXiv:0911.4718. Bibcode:2010PhRvD..81f2002M. doi:10.1103/PhysRevD.81.062002.
32. ^ Will, C. (2008). "Testing the General Relativistic "No-Hair" Theorems Using the Galactic Center Black Hole Sagittarius A*". Astrophysical Journal Letters. 674 (1): L25–L28. arXiv:0711.1677. Bibcode:2008ApJ...674L..25W. doi:10.1086/528847.
33. ^ Williams, R. K. (1995). "Extracting X rays, Ύ rays, and relativistic e–e+ pairs from supermassive Kerr black holes using the Penrose mechanism". Physical Review D. 51 (10): 5387–5427. Bibcode:1995PhRvD..51.5387W. doi:10.1103/PhysRevD.51.5387.
34. ^ Williams, R. K. (2004). "Collimated escaping vortical polar e–e+ jets intrinsically produced by rotating black holes and Penrose processes". The Astrophysical Journal. 611 (2): 952–963. arXiv:astro-ph/0404135. Bibcode:2004ApJ...611..952W. doi:10.1086/422304.
35. ^ Penrose, R. (1969). "Gravitational collapse: The role of general relativity". Nuovo Cimento Rivista. 1 (Numero Speciale): 252–276. Bibcode:1969NCimR...1..252P.
36. ^ Kerr, R. P. (1963). "Gravitational field of a spinning mass as an example of algebraically special metrics". Physical Review Letters. 11 (5): 237–238. Bibcode:1963PhRvL..11..237K. doi:10.1103/PhysRevLett.11.237.
37. ^ Landau, LD; Lifshitz, EM (1975). The Classical Theory of Fields (Course of Theoretical Physics, Vol. 2) (revised 4th English ed.). New York: Pergamon Press. pp. 321–330. ISBN 978-0-08-018176-9.
38. ^ Tartaglia, A. (2008). "Detection of the gravitometric clock effect". arXiv:gr-qc/9909006v2. Bibcode:2000CQGra..17..783T. doi:10.1088/0264-9381/17/4/304.
39. ^ a b Misner, Thorne, Wheeler, Graviation, Figure 21.5, page 544
40. ^ Pfister, Herbert (2005). "On the history of the so-called Lense–Thirring effect". General Relativity and Gravitation. 39 (11): 1735–1748. Bibcode:2007GReGr..39.1735P. doi:10.1007/s10714-007-0521-4.
41. ^ Pfister, H.; et al. (1985). "Induction of correct centrifugal force in a rotating mass shell". Class. Quantum Grav. 2 (6): 909–918. Bibcode:1985CQGra...2..909P. doi:10.1088/0264-9381/2/6/015. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 15, "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": 0.8659546971321106, "perplexity": 2515.534988468123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721278.88/warc/CC-MAIN-20161020183841-00561-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3045843/prime-gaps-sort-of | # prime gaps, sort of!
Consider the odd numbers: 1, 3, 5, ...
If we delete every multiple of 3, the largest gap between the remaining odd numbers is 4.
If we delete all multiples of 3 and 5, we get {1, 7, 11, 13, 17, 19, 23, 29...} The largest gap is 6.
If we delete multiples of all primes up to the nth prime starting from 3, can we tell what the largest gap (lg) will be between the remaining odd numbers? My hunch is that $$2p_{n-1}$$ <= lg < $$2p_n$$ where $$p_n$$ is the nth prime.
Can this be solved in a simple way? Is this a known result?
Thanks,
mmk.
• Your conjecture can be restated as follows: If $p$ is prime, then for every $k$, the set $\{k,k+1,k+2,\ldots,k+2p\}$ contains a number relatively prime to $p!$. (You can actually drop the assumption that $p$ is prime when stating it this way. I.e., For every $n$ and $k$, the set $\{k,k+1,k+2,\ldots,k+2n\}$ contains a number relatively prime to $n!$.) – Barry Cipra Dec 19 '18 at 15:58
• My previous comment was posted before the OP added $2p_{n-1}\le$ lg to the conjecture. – Barry Cipra Dec 19 '18 at 16:59
• I believe youtu.be/pp06oGD4m00 this video is relevant. – Zachary Hunter Dec 31 '18 at 7:05
Let $$p_{n}$$ be the $$n$$-th prime. If you delete all odd numbers which have a factor in $$\{3,5,\ldots,p_{n}\}$$ then the least number remaining will be the $$(n+1)$$-th prime $$p_{n+1}$$. Hence the gap will be $$p_{n+1}-1$$.
When you remove multiples of 3 the first number remaining is 5 and the gap is $$5-1=4$$. Similarly when you also remove multiples of $$5$$ the first number remaining is $$7$$ and the gap is $$7-1=6$$. | {"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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8543530702590942, "perplexity": 126.57810837689357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655908294.32/warc/CC-MAIN-20200710113143-20200710143143-00203.warc.gz"} |
https://ohhaskme.com/7361/houses-of-three-colours-on-a-road | Houses of three colours on a road
It's not really an equation to be solved. You can set up some inequalities that describe the situation, e.g.:
b > r + y
y > r
3r > b
Then you can substitute and simplify, e.g. 3r > r + y or 2r > y
There would be a lot of possible solutions here.
r=3, y=4, b=8 is one using small integers.
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https://www.physicsforums.com/threads/solution-for-this-integral.4105/ | # Solution for this integral!
• #1
AndersHermansson
61
0
Is it possible to find an exact solution for this integral?
Is it possible to differentiate a root expression?
I found that:
pi = 4 * ∫√(1-x*x)dx from 0 to 1
• #2
Suicidal
22
1
the equation is for a semicircle of radius 1 from 0 to 1 you get a quarter circle and 1/4 pi *r^2=1/4pi
you could also evaluate the integral using a trig subsitution
you already found the answer if you divide both sides of the equation by 4 in your solution you also get the answer
Last edited:
• #3
Suicidal
22
1
for the trig sub
x=sin(θ)
dx=cos(θ)dθ
substitute into original integral simpligy trig expresion and switch limits of integration (evaluate interms of theta) and you will get &pi/4
if you haven't learned trig subs check it out in your calc book it not a very hard topic.
• #4
lethe
653
0
what is x*? is x a complex variable? i don t quite understand your integral
• #5
AndersHermansson
61
0
Probably because it's a lot easier than you're used to. :)
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https://dsp.stackexchange.com/questions/30362/image-averaging-for-impulse-noise | # Image averaging for impulse noise
I understand the mathematics behind the use of image averaging for gaussian noise. Why can't it be used for impulse noise ? Would it be because there is no way to prove that impulse noise is additive ? And that it has no mean ?
Also, am I right to say that impulse noise does not affect every pixel in an image, as opposed to gaussian noise ?
Thanks !
• Anyone any comments ? Apr 26, 2016 at 13:06
I'm not in the image processing filed, but I would say:
Yes, Gaussian noise means that each of your pixel is assumed to be produced by a stochastic process. Hence you can for instance think of it as a "real" intensity corrupted by an additive normally distributed white noise. Normally distributed means also that if you take $n$ observations of the same pixel you most likely will end up with $n$ wrong measurements. I think this is actually the worst kind of noise since given any pixel, then any other pixel inside a given neighbourhood will be corrupted, hence telling which observation is to trust more is difficult. The way I would go is probably (low pass) filtering.
You can think to the impulsive noise again as an additive noise potentially present in all the pixels, but potentially also localized in only a subset of pixels or observations (either it is or it is not). I personally would not go for averaging or low pass filtering since it will never erase completely the noise.
Assume indeed to have $n$ images of the same scene. Assume that for a given pixel $p$ whose "actual" value is $p=0$ you measure it as $255$ in one image and as $0$ in $n$ images. If you take the mean then you will chose $p = 255/n$ as the actual value. Infact a low pass filter is a process with infinite impulse response and it tends to zero only asymptotically.
In such case for me it looks more effective to take the median, over the $n$ samples. With the median you obtain that you estimate of the actual values of $p$ is exactly $0$.
You can also take the most-frequent value (the mode) and it will perform better than the mean. In general you can also use a median or a mode inside the same image by taking them in a neighbourhood of a given pixel. Infact for example, take a $10\times 10$ sub-image and assume it corresponds to a white background. Assume that 30 over the 100 pixels are black due to the impulsive noise, then you can substitute to each pixel the median over the entire sub-image obtaining a completely white patch. A mean will lead to a 30% grey (76 / 255)
• Hi thanks ! But wouldn't it work if I have many images ? 1000 for example. I am just curious since I can't seem to find anything online that talks about the use of image averaging for impulse noise. Apr 26, 2016 at 15:04
• well if you take 1000 images in which the same pixel $p$ is white (255) in 200 and black (0) in 700 you will end up with an estimate of $p$ of $\hat{p} = (255*200 + 0*700)/1000 = 51$ therefore you will have a 80% gray pixel instead of a black pixel. In general it depends on the probability of the impulse to be there. Apr 26, 2016 at 15:08
• Ah i get it now. The 'mathematical proof' would be to use probability. Thanks so much ! Apr 26, 2016 at 15:12
• well, It depends on what you want to prove. What do you want to prove? Apr 26, 2016 at 15:13
• For image with gaussian noise, we can treat it as an addition of the original image with the noise i.e. f(x) + n(x). Image averaging then reduces the noise variance and if I have infinity images then theoretically the noise is eliminated. Can I show the same with impulse noise ? i.e. f(x) + impulse(x). If I can, then theoretically, wouldn't averaging over infinity images eliminate the impulse noise ? Apr 26, 2016 at 15:22 | {"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": 0.8885518312454224, "perplexity": 440.2882269052826}, "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/1659882571232.43/warc/CC-MAIN-20220811012302-20220811042302-00076.warc.gz"} |
http://mathoverflow.net/users/1540/otis-chodosh?tab=recent | # Otis Chodosh
less info
reputation
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bio website math.stanford.edu/~ochodosh location Stanford, CA age 25 member for 4 years, 1 month seen 6 mins ago profile views 1,649
Stanford PhD student, interested in differential geometry and analysis.
9 Dimension of eigenspaces of Laplacian on a compact Riemannian manifold 8 Intuition for mean curvature. 7 Are there some other notions of “curvature” which measure how space curves? 7 the left hand side of the Ricci flow equation at the initial value 7 Geometric picture of scalar curvature
# 1,546 Reputation
+5 Planar sets where any line through the center of mass divides the set into two regions of equal area. +35 On the Geroch's argument +55 Minor technical question in diff geometry +10 Are there some other notions of “curvature” which measure how space curves?
# 13 Questions
23 What are “good” examples of spin manifolds? 10 Planar sets where any line through the center of mass divides the set into two regions of equal area. 9 Applications of the notion of of Gromov-Hausdorff distance 9 Converse to Bishop-Gromov Inequality 8 Physical Interpretation of Robin Boundary Conditions
# 47 Tags
59 dg.differential-geometry × 20 10 geometric-measure-theory × 4 23 reference-request × 7 9 fa.functional-analysis × 3 18 ricci-flow × 4 9 complex-geometry 16 riemannian-geometry × 10 8 measure-theory × 4 14 ap.analysis-of-pdes × 6 7 gt.geometric-topology
# 9 Accounts
MathOverflow 1,546 rep 1621 Mathematics 234 rep 15 TeX - LaTeX 234 rep 3510 Area 51 151 rep 1 Bicycles 101 rep | {"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": 0.9037596583366394, "perplexity": 2368.49633495978}, "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-2013-48/segments/1386164645800/warc/CC-MAIN-20131204134405-00059-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://demo.formulasearchengine.com/wiki/Topological_group | # Topological group
The real numbers form a topological group under addition
In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.[1] A topological group is a mathematical object with both an algebraic structure and a topological structure. Thus, one may perform algebraic operations, because of the group structure, and one may talk about continuous functions, because of the topology.
Topological groups, along with continuous group actions, are used to study continuous symmetries, which have many applications, for example in physics.
## Formal definition
A topological group G is a topological space and group such that the group operations of product:
${\displaystyle G\times G\to G:(x,y)\mapsto xy}$
and taking inverses:
${\displaystyle G\to G:x\mapsto x^{-1}}$
are continuous functions. Here, G × G is viewed as a topological space by using the product topology.
Although not part of this definition, many authors[2] require that the topology on G be Hausdorff; this corresponds to the identity map ${\displaystyle *\to G}$ being a closed inclusion (hence also a cofibration). The reasons, and some equivalent conditions, are discussed below. In the end, this is not a serious restriction—any topological group can be made Hausdorff in a canonical fashion.[3]
In the language of category theory, topological groups can be defined concisely as group objects in the category of topological spaces, in the same way that ordinary groups are group objects in the category of sets. Note that the axioms are given in terms of the maps (binary product, unary inverse, and nullary identity), hence are categorical definitions. Adding the further requirement of Hausdorff (and cofibration) corresponds to refining to a model category.
### Homomorphisms
A homomorphism between two topological groups G and H is just a continuous group homomorphism G ${\displaystyle \to }$ H. An isomorphism of topological groups is a group isomorphism which is also a homeomorphism of the underlying topological spaces. This is stronger than simply requiring a continuous group isomorphism—the inverse must also be continuous. There are examples of topological groups which are isomorphic as ordinary groups but not as topological groups. Indeed, any nondiscrete topological group is also a topological group when considered with the discrete topology. The underlying groups are the same, but as topological groups there is not an isomorphism.
Topological groups, together with their homomorphisms, form a category.
## Examples
Every group can be trivially made into a topological group by considering it with the discrete topology; such groups are called discrete groups. In this sense, the theory of topological groups subsumes that of ordinary groups.
The real numbers R, together with addition as operation and its usual topology, form a topological group. More generally, Euclidean n-space Rn with addition and standard topology is a topological group. More generally yet, the additive groups of all topological vector spaces, such as Banach spaces or Hilbert spaces, are topological groups.
The above examples are all abelian. Examples of non-abelian topological groups are given by the classical groups. For instance, the general linear group GL(n,R) of all invertible n-by-n matrices with real entries can be viewed as a topological group with the topology defined by viewing GL(n,R) as a subset of Euclidean space Rn×n.
An example of a topological group which is not a Lie group is given by the rational numbers Q with the topology inherited from R. This is a countable space and it does not have the discrete topology. For a nonabelian example, consider the subgroup of rotations of R3 generated by two rotations by irrational multiples of 2π about different axes.
In every Banach algebra with multiplicative identity, the set of invertible elements forms a topological group under multiplication.
## Properties
The algebraic and topological structures of a topological group interact in non-trivial ways. For example, in any topological group the identity component (i.e. the connected component containing the identity element) is a closed normal subgroup. This is because if C is the identity component, a*C is the component of G (the group) containing a. In fact, the collection of all left cosets (or right cosets) of C in G is equal to the collection of all components of G. Therefore, the quotient topology induced by the quotient map from G to G/C is totally disconnected.[4]
The inversion operation on a topological group G is a homeomorphism from G to itself. Likewise, if a is any element of G, then left or right multiplication by a yields a homeomorphism GG.
Every topological group can be viewed as a uniform space in two ways; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps. If G is not abelian, then these two need not coincide. The uniform structures allow one to talk about notions such as completeness, uniform continuity and uniform convergence on topological groups.
As a uniform space, every topological group is completely regular. It follows that if a topological group is T0 (Kolmogorov) then it is already T2 (Hausdorff), even T (Tychonoff).
Every subgroup of a topological group is itself a topological group when given the subspace topology. If H is a subgroup of G, the set of left or right cosets G/H is a topological space when given the quotient topology (the finest topology on G/H which makes the natural projection q : GG/H continuous). One can show that the quotient map q : GG/H is always open.
Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G \ H.
If H is a normal subgroup of G, then the factor group, G/H becomes a topological group when given the quotient topology. However, if H is not closed in the topology of G, then G/H will not be T0 even if G is. It is therefore natural to restrict oneself to the category of T0 topological groups, and restrict the definition of normal to normal and closed.
The isomorphism theorems known from ordinary group theory are not always true in the topological setting. This is because a bijective homomorphism need not be an isomorphism of topological groups. The theorems are valid if one places certain restrictions on the maps involved. For example, the first isomorphism theorem states that if f : GH is a homomorphism then G/ker(f) is isomorphic to im(f) if and only if the map f is open onto its image.
If H is a subgroup of G then the closure of H is also a subgroup. Likewise, if H is a normal subgroup, the closure of H is normal.
A topological group G is Hausdorff if and only if the trivial one-element subgroup is closed in G. If G is not Hausdorff then one can obtain a Hausdorff group by passing to the quotient space G/K where K is the closure of the identity. This is equivalent to taking the Kolmogorov quotient of G.
The fundamental group of a topological group is always abelian. This is a special case of the fact that the fundamental group of an H-space is abelian, since topological groups are H-spaces.
## Relationship to other areas of mathematics
A compact group is a topological group whose topology is compact. Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory.
Of particular importance in harmonic analysis are the locally compact groups, because they admit a natural notion of measure and integral, given by the Haar measure. The theory of group representations is almost identical for finite groups and for compact topological groups. In general, σ-compact Baire topological groups are locally compact.
In topology, the homeomorphism group of a topological space is the group consisting of all homeomorphisms from the space to itself with function composition as the group operation. The homeomorphism group can be given a topology, such as the compact-open topology (in the case of regular, locally compact spaces), making it into a topological group.
## Generalizations
Various generalizations of topological groups can be obtained by weakening the continuity conditions:[5]
## Notes
1. {{#invoke:citation/CS1|citation |CitationClass=book }}
2. Armstrong, p. 73; Bredon, p. 51; Willard, p. 91.
3. D. Ramakrishnan and R. Valenza (1999). "Fourier Analysis on Number Fields". Springer-Verlag, Graduate Texts in Mathematics. Pp. 6–7.
4. {{#invoke:citation/CS1|citation |CitationClass=citation }}
5. Arhangel'skii & Tkachenko, p12
## References
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• Bourbaki, Nicolas (1966). General Topology, Part 1, chapter 3: "Topological Groups", Hermann, Paris.
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• {{#invoke:citation/CS1|citation
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|CitationClass=book }} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "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": 0.8755195736885071, "perplexity": 282.6527005511408}, "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-2021-39/segments/1631780057274.97/warc/CC-MAIN-20210921221605-20210922011605-00343.warc.gz"} |
https://flatearth.ws/false-analogy | # False Analogy
A false analogy is a fallacy in which similarity in one respect of two concepts, objects, or events is taken as sufficient to establish that they are similar in another respect in which they are actually are not similar.
Almost all of what flat-Earthers happily claim as “experiments” are actually false analogies. They would take everyday objects and use them as analogies for actual objects. In reality, a shared similarity in both the analogy and the real thing is not sufficient to ‘prove’ both are similar in some other respect.
For example, a ball is round, so is the Earth. Therefore, both must be similar in some other respect. The ball does not attract water, but the Earth does, then they would wrongly conclude that the Earth is not round.
The fault in reasoning is easy to demonstrate. Both a basketball and a volleyball are also round. A basketball is red. Can we conclude from that fact that a volleyball is also red?
Analogies can be valid inductive arguments. It can be used to infer further similarity that has yet to be observed. However, like all inductive arguments, it can be strong or weak, and it requires more information than just the similarities to reach a conclusion. Using it deductively —or taking the conclusion as a certainty from the analogy alone— is the fallacy of false analogy.
Analogies are also useful to explain things to people. The usual classroom model of an eclipse is also an analogy. However, it is used for explaining an eclipse, and never intended to prove an eclipse. The mechanism of an eclipse is determined from observation of the actual eclipses themselves.
Observation of the actual object or phenomenon is always stronger evidence than any argument from analogy. We cannot devise a contraption that can seemingly simulate the appearance of a natural phenomenon, and then use it to “prove” that our conclusion from real-world observation of such phenomenon is somehow wrong. | {"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": 0.8118014931678772, "perplexity": 688.9001946214377}, "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/1656104205534.63/warc/CC-MAIN-20220702222819-20220703012819-00313.warc.gz"} |
https://www.hackmath.net/en/math-problem/6495 | # Circular pool
The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
Result
V = 9161 l
#### Solution:
$D=3.6 \ m=3.6 \cdot \ 10 \ dm=36 \ dm \ \\ h=90 \ cm=90 / 10 \ dm=9 \ dm \ \\ \ \\ r=D/2=36/2=18 \ \text{dm} \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 18^2 \doteq 1017.876 \ \text{dm}^2 \ \\ 1l=dm^3 \ \\ V=S \cdot \ h=1017.876 \cdot \ 9 \doteq 9160.8842 \doteq 9161 \ \text{l}$
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Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm. | {"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": 0.8407341241836548, "perplexity": 1334.3410787092432}, "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-2020-16/segments/1585370518767.60/warc/CC-MAIN-20200403220847-20200404010847-00345.warc.gz"} |
http://math.stackexchange.com/questions/166289/time-series-question | # Time Series Question
Consider the time series defined by $$Y_t = \phi Y_{t-1}+ \epsilon_t + \theta \epsilon_{t-1}$$
Why is $E(\epsilon_{t} Y_{t}) = \sigma_{\epsilon}^{2}$?
-
You might get better results at stats.stackexchange.com. I'm not sure what the variables here are and therefore can't try to help. – Cocopuffs Jul 3 '12 at 21:11
This is indeed more appropiate for stats.stackexchange.com or dsp.stackexchange.com Actually, this is a ARMA(1,1) process – leonbloy Jul 3 '12 at 23:00
Simply work it out. By assumption, the white noise term $\varepsilon_t$ satisfies the following:
1. $E[\varepsilon_t]=0$
2. $E[\varepsilon^2_t]=\sigma_\varepsilon^2$
3. $E[\varepsilon_t\varepsilon_s]=0$, for $t\neq s$
Now multiply $Y_t$ by $\varepsilon_t$ and use linearity of expectation. The white noise terms are all uncorrelated for different times, so their expectations vanish. Explictely, write out $Y_t$ as a geometric series by recursively using the equation for $Y_t$. Otherwise apply induction. The point is that $\varepsilon_t$ and $Y_{s}$ for $s<t$ are uncorrelated.
-
Use what sam mentioned but it is not necessary to write Yt out as a geometric series. Substitute ϕY$_t$$_−$$_1$+ϵ$_t$+θϵ$_t$$_−$$_1$ for Y$_t$ multiply by e$_t$ to get ϕϵ$_t$Y$_t$$_−$$_1$+ϵ$^2$$_t+θ(ϵ_t$$_−$$_1 ϵ_t) take expectations. You get ϕ E(ϵ_tY_t$$_−$$_1) + E(ϵ^2$$_t$) + θ E(ϵ$_t$$_−$$_1$ ϵ$_t$).
Now from condition 3 given by Sam E(ϵ$_t$$_−$$_1$ ϵ$_t$)=0 and since ϵ$_t$ is independent of Y$_t$$_-$$_1$,
E(ϵ$_t$Y$_t$$_−$$_1$)=0. So you are only left with E(ϵ$^2$$_t) which you know is σ^2$$_ϵ$.
- | {"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": 0.8659525513648987, "perplexity": 1391.5474249601027}, "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/1432207928780.77/warc/CC-MAIN-20150521113208-00299-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://face2ai.com/Math-Probability-3-4-Bivariate-Distribution/ | # 二维分布
## 联合分布 Joint Distribution
$$\text{Bivariate}= \begin{cases} Discrete & \text{Discrete,Discrete}\\ Continuous & \text{Continuous,Continuous}\\ Hybrid & \text{Discrete,Continuous} \end{cases}$$
Definition Joint/Bivariate Distribution:Let $X$ and $Y$ be random varibales.The joint distribution or bivariate distribution of $X$ and $Y$ is the collection of all probabilities of the form $Pr[(X,Y)\in C]$ for all sets $C$ of pairs of real numbers such that ${(X,Y)\in C}$ is an event
## 离散联合分布 Discrete Joint Distribution
Definition Joint Distribution:Let X and Y be random variables,and consider the ordered pair(X,Y).If there are only finitely or at most countably many different possible values (x,y) for the pair (X,Y),then we say that x and Y have a discrete joint distribution
1 $\frac{1}{12}$ $\frac{1}{12}$
2 $\frac{1}{12}$ $\frac{1}{12}$
3 $\frac{1}{12}$ $\frac{1}{12}$
4 $\frac{1}{12}$ $\frac{1}{12}$
5 $\frac{1}{12}$ $\frac{1}{12}$
6 $\frac{1}{12}$ $\frac{1}{12}$
Theorem: Suppose that two random variable X and Y each have a discrete distribution.Then X and Y have a discrete joint distribution
1. 如果两个样本空间有限，那么其笛卡尔积有限，这个是集合论中已经明确的结论了
2. 如果两个样本空间可数无限，那么气笛卡尔积也是可数无限的，这个相关证明也在集合论中，这里不再证明
Definition Joint Probability Function,p.f. The joint probability function,or the joint p.f. of X and Y is defined as the function f such that for every point (x,y) in xy-plane:
$$f(x,y)=Pr(X=x\text{ and } Y=y)$$
Theorem Let $X$ and $Y$ have a discrete joint distribution.If $(x,y)$ is not one of the possible values of the pair $(X,Y)$ the $f(x,y)=0$ .Also,
$$\sum_{\text{All }(x,y)}f(x,y)$$
Finally,for each set $C$ of ordered pairs
$$Pr[(X,Y)\in C]=\sum_{(x,y)\in C}f(x,y)$$
$$Pr[(X,Y)\in C]=\frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{1}{4}$$
## 连续联合分布 Continuous Joint Distribution
$$Pr[(X,Y)\in C]=\int_C\int \frac{1}{100000}dx dy$$
Definition Continuous Joint Distribution/Joint p.d.f./Support:Two random varibales X and Y have a continuous joint distribution if there exists a nonnegative function f defined over the entire xy-plane such that for every subset C of the plane,
$$Pr[(X,Y)\in C]=\int_C\int f(x,y)dx dy$$
if the integral exists.The function $f$ is called the joint probability density function(abbreviated joint p.d.f)of $X$ and $Y$.The closure of the set ${(x,y):f(x,y)>0}$ is called the support of (the distribution of) $(X,Y)$
A joint p.d.f. must satisfy the following two conditions:
$$f(x,y)\geq 0 \text{ for } -\infty <x<\infty \text{ and } -\infty <y<\infty$$
and
$$\int^{\infty}_{-\infty}\int^{\infty}_{-\infty}f(x,y)dxdy=1$$
Theorem For every contimuous joint distribution on the xy-plane,the following two statements hold:
1. Every individual point,and every infinite sequence of points,in the xy-plane has pribability 0.
2. Let $f$ be a continuous function of one real variable defined on a(possibly unbounded) interval(a,b).The sets ${(x,y):y=f(x),a<x<b}$ and ${(x,y):x=f(y),a<y<b}$ have probability 0
## 混合二维分布 Mixed Bivariate Distribution
Definition Joint p.f/p.d.f: Let $X$ and $Y$ be random variables such that $X$ is discrete and $Y$ is continuous.Suppose that there is a function $f(x,y)$ define on the xy-plane such that,for every pair A and B of subsets of the real numbers
$$Pr(X\in A \text{ and } Y \in B)=\int_B\sum_{x\in A}f(x,y)dy$$
if the integral exists.Then the function $f$ is called the joint p.f./p.d.f of $X$ and $Y$
$$\int^{\infty}_{-\infty}\sum^{\infty}_{i=1}f(x_i,y)dy=1$$
$$(X,Y)\in C\\ \text{we set } C_x={y:(x,y)\in C}\\ \text{then } Pr((X,Y)\in C)=\sum_{\text{All } x}\int_{C_x}f(x,y)dy$$
$$f(x,p)=p^x(1-p)^{1-x}\text{ for } x=0,1 \text{ and } 0<p<1$$
$$Pr(X\leq 0 \text{ and } P\leq \frac{1}{2})=\int_0^{\frac{1}{2}}(1-p)dp\\ =-\frac{1}{2}[(1-\frac{1}{2})^2-(1-0)^2]=\frac{3}{8}$$
## 二维累积分布函数 Bivariate Cumulative Distribution Functions
Definition: Joint(Cumulative) Distribution Function/c.d.f. The joint distribution function or joint cumulative distribution function (joint c.d.f) of two random variables X and Y is defined as the function F such that for all values of x and y( $-\infty<x<\infty$ and $-\infty<y<\infty$)
$$F(x,y)=Pr(X\leq x \text{ and } Y\leq y )$$
$$Pr(a<x\leq b \text{ and } c<Y\leq d)\\ =Pr(a<X\leq b \text{ and } y\leq d) -Pr(a<x\leq b \text{ and } y\leq c)\\ =[Pr(X\leq b \text{ and } Y \leq d)-Pr(X\leq a \text{ and } Y \leq d)]-\\ [Pr(X\leq b \text{ and } Y \leq c)-Pr(X\leq a \text{ and } Y \leq c)]\\ =F(b,d)-F(a,d)-F(b,c)+F(a,c)$$
Theorem Let $X$ and $Y$ have a joint c.d.f. $F$.The c.d.f. $F_1$ of just the single random variable $X$ can be derived from the joint c.d.f. $F$ as $F_1(x)=lim_{y\to \infty}F(x,y)$.Similarly,the c.d.f. $F_2$ of $Y$ equals $F_2(y)=lim_{x\to \infty}F(x,y)$ ,for $0<y\leq \infty$
1. 离散情况下：
$$\text{Let }\\ B_0={X\leq x \text{ and } Y\leq 0} \\ B_1={X\leq x \text{ and }n-1<y\leq n}\text{ ,for } n=1,2\dots\\ A_m=\bigcup^{m}_{n=0}B_n\text{ ,for }m=1,2,\dots\\$$
我们可以确定:${X\leq x}=\bigcup^{\infty}_{n=-0}B_n$ ，并且 $A_m={X\leq x \text{ and } Y\leq m} \text{ for } m=1,2,\dots$ 这样我们有 $Pr(A_m)=F(x,m) \text{ for each } m$
$$F_1(x)=Pr(X\leq x)=Pr(\bigcup^{\infty}_{n=1}B_n)\\ =\sum^{\infty}_{n=0}Pr(B_n)=lim_{m\to \infty} Pr(A_m)\\ =lim_{m\to \infty}F(x,m)=lim_{y\to \infty}Pr(A_m)$$
2. 连续情况下：
$$F(x,y)=\int^y_{-\infty}\int^x_{-\infty}f(r,s)drds\\ f(x,y)=\frac{\partial^2F(x,y)}{\partial x\partial y}$$
Subscribe | {"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": 0.977737307548523, "perplexity": 568.1323641769984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347389309.17/warc/CC-MAIN-20200525161346-20200525191346-00183.warc.gz"} |
http://www.cesm.ucar.edu/models/atm-cam/docs/description/node39.html | Next: 6.8 Snow-Ice Conversion Up: 6. Sea Ice Thermodynamics Previous: 6.6 Brine Pockets and Contents
# 6.7 Open-Water Growth and Ice Concentration Evolution
When coupled to a mixed layer ocean, the ice model must account for new ice growth over open water and other processes that alter the lateral sea ice coverage. New ice growth occurs whenever the surface layer in the ocean is at the freezing temperature and the fluxes would draw additional heat out of the ocean (see Eq. 5.1). In this case the additional heat comes from freezing sea water, as the ocean cannot supercool in this model. Hence
(6.48)
where is the energy of melting for new ice growth (assuming the salinity is 4psu and the new ice temperature is -1.8C), is the thickness of the new ice, and is the additional heat lost by slab ocean once it reaching the freezing point (see section 5.1). When new ice grows over open water, it is recombined with the rest of the ice in the grid cell by first reshaping the new ice volume so its thickness is at least 15 cm - this recreates ice-free ocean if the thickness was below 15 cm. Then the new ice is added to the old ice in the grid cell and a new thickness and concentration are computed by conserving ice volume.
In motionless sea ice model, such as this one, open water is not created by deformation as in nature, and hence the ice concentration would tend to 0 or 100% unless open water production is parameterized somehow. A typical method is to assume the ice thickness on a subgrid-scale is linearly distributed between 0 and , so that when ice melts vertically, it also reduces the concentration:
(6.49)
The ice concentration is also reduced by a lateral heat flux from the ocean (see Eq. 6.36):
(6.50)
although it is typically only a small contribution to the concentration tendency.
It is not possible to combine Eqs. 6.48-6.50 to make a single analytic expression for in Eq. 6.6. Instead the model using time splitting to solve the three equations independently.
Next: 6.8 Snow-Ice Conversion Up: 6. Sea Ice Thermodynamics Previous: 6.6 Brine Pockets and Contents
Jim McCaa 2004-06-22 | {"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": 0.9196406006813049, "perplexity": 1815.4248316084108}, "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-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00196-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/576/ | ## Results (1-50 of 390 matches)
Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.1.b.a $2$ $0.287$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+q^{25}+iq^{31}-3q^{49}-q^{73}+\cdots$$
576.1.e.a $2$ $0.287$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{5}-\beta q^{17}-q^{25}+\beta q^{29}+2q^{37}+\cdots$$
576.1.g.a $1$ $0.287$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{13}-q^{25}-2q^{37}+q^{49}-2q^{61}+\cdots$$
576.1.n.a $4$ $0.287$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{11}+\cdots$$
576.1.o.a $4$ $0.287$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-q^{9}+\cdots$$
576.2.a.a $1$ $4.599$ $$\Q$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $-$ $$q-4q^{5}+6q^{13}+8q^{17}+11q^{25}+\cdots$$
576.2.a.b $1$ $4.599$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $+$ $$q-2q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots$$
576.2.a.c $1$ $4.599$ $$\Q$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $+$ $$q-2q^{5}-6q^{13}-2q^{17}-q^{25}-10q^{29}+\cdots$$
576.2.a.d $1$ $4.599$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $-$ $$q-2q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots$$
576.2.a.e $1$ $4.599$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $+$ $$q-4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots$$
576.2.a.f $1$ $4.599$ $$\Q$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $-$ $$q+4q^{7}-2q^{13}+8q^{19}-5q^{25}+4q^{31}+\cdots$$
576.2.a.g $1$ $4.599$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$-4$$ $-$ $$q+2q^{5}-4q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots$$
576.2.a.h $1$ $4.599$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$4$$ $-$ $$q+2q^{5}+4q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots$$
576.2.a.i $1$ $4.599$ $$\Q$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $-$ $$q+4q^{5}+6q^{13}-8q^{17}+11q^{25}+\cdots$$
576.2.c.a $2$ $4.599$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}-4q^{13}+\beta q^{17}-13q^{25}+\cdots$$
576.2.c.b $2$ $4.599$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}+4q^{13}+5\beta q^{17}+3q^{25}+\cdots$$
576.2.c.c $4$ $4.599$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}-4q^{13}+\cdots$$
576.2.d.a $2$ $4.599$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{11}+6q^{17}+iq^{19}+5q^{25}+\cdots$$
576.2.d.b $4$ $4.599$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-6q^{17}-\zeta_{12}^{3}q^{19}+\cdots$$
576.2.d.c $4$ $4.599$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots$$
576.2.f.a $8$ $4.599$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{2}q^{5}-\zeta_{24}q^{7}-\zeta_{24}^{6}q^{11}+\cdots$$
576.2.i.a $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$0$$ $$2$$ $$q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
576.2.i.b $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$4$$ $$2$$ $$q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$$
576.2.i.c $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$-3$$ $$q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$$
576.2.i.d $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$3$$ $$q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$$
576.2.i.e $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$$
576.2.i.f $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$3$$ $$1$$ $$q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$$
576.2.i.g $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$0$$ $$-2$$ $$q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
576.2.i.h $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$4$$ $$-2$$ $$q+(1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$$
576.2.i.i $4$ $4.599$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$-4$$ $$-2$$ $$-2$$ $$q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$$
576.2.i.j $4$ $4.599$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$-1$$ $$-1$$ $$-3$$ $$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$$
576.2.i.k $4$ $4.599$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots$$
576.2.i.l $4$ $4.599$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None None $$0$$ $$1$$ $$-1$$ $$3$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$$
576.2.i.m $4$ $4.599$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$4$$ $$-2$$ $$2$$ $$q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
576.2.i.n $8$ $4.599$ 8.0.170772624.1 None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}-\beta _{7})q^{5}+\cdots$$
576.2.k.a $2$ $4.599$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}+2iq^{7}+(1+i)q^{11}+(-1+\cdots)q^{13}+\cdots$$
576.2.k.b $8$ $4.599$ 8.0.18939904.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$$
576.2.k.c $8$ $4.599$ 8.0.629407744.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$$
576.2.l.a $16$ $4.599$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots$$
576.2.p.a $16$ $4.599$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{12}q^{3}+(\beta _{3}-\beta _{4}-\beta _{7})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$$
576.2.p.b $16$ $4.599$ 16.0.$$\cdots$$.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{14}-\beta _{15})q^{7}+\cdots$$
576.2.p.c $16$ $4.599$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{12}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{7})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$$
576.2.r.a $4$ $4.599$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$-12$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
576.2.r.b $4$ $4.599$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$12$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
576.2.r.c $8$ $4.599$ $$\Q(\zeta_{24})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}^{4}+\zeta_{24}^{6})q^{3}+(-1+\zeta_{24}+\cdots)q^{9}+\cdots$$
576.2.r.d $8$ $4.599$ 8.0.12960000.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$$
576.2.r.e $12$ $4.599$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$-18$$ $$0$$ $$q+(-\beta _{4}+\beta _{5})q^{3}+(-2-\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
576.2.r.f $12$ $4.599$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$18$$ $$0$$ $$q+(-\beta _{4}+\beta _{5})q^{3}+(2+\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
576.2.s.a $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-3$$ $$6$$ $$6$$ $$q+(-1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots$$
576.2.s.b $2$ $4.599$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-3$$ $$-3$$ $$q+(-1+2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$ | {"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": 0.9499295353889465, "perplexity": 820.3423245814034}, "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/1652663048462.97/warc/CC-MAIN-20220529072915-20220529102915-00464.warc.gz"} |
https://www.physicsforums.com/threads/what-different-between-covariant-metric-tensor-and-contravariant-metric-tensor.127897/ | # What different between covariant metric tensor and contravariant metric tensor
1. Aug 3, 2006
### HeilPhysicsPhysics
I read some books and see that the definition of covariant tensor and contravariant tensor.
Covariant tensor(rank 2)
A'_ab=(&x_u/&x'_a)(&x_v/&x'_b)A_uv
Where A_uv=(&x_u/&x_p)(&x_u/&x_p)
Where p is a scalar
Contravariant tensor(rank 2)
A'^uv=(&x'^u/&x^a)(&x'^v/&x^b)A^ab
Where A^ab=dx_a dx_b
Metric tensor sometimes g^uv,sometimes g_uv
ds^2=g_uv dx^u dx^v=g^uv dx_u dx_v
What different between them?
2. Aug 21, 2006
### coalquay404
Essentially, there is no difference between the covariant and contravariant forms of the metric in the sense that they both "measure" things. However, consider the following. If you have a metric $$g$$ on a manifold then it is usually regarded as being a map which takes two vectors into a real number. For example, you can calculate the squared length of a vector $$X$$ as being
$$g(X,X) = g_{ab}X^aX^b$$.
However, vectors aren't the only things which you may want to measure the length of. Another interesting class of objects are "one-forms." If you want to measure the "squared length" of a one-form $$\alpha$$ then you can do it thusly:
$$g(\alpha,\alpha) = g^{ab}\alpha_a\alpha_b$$
where $$g^{ab}$$ is the covariant form of the metric. The covariant form of a metric can always be obtained from the contravariant form by virtue of something called a "musical isomorphism" (it's a technical point that you really don't need to worry about). The only restriction on the relationship between the covariant and contravariant forms of the metric are that they should satisfy the following:
$$g_{ab}g^{bc} = \delta^{a}_{c}.$$
Last edited: Aug 21, 2006
3. Aug 23, 2011
### victorneto
Friend,
I offer a simple explanation that clarifies in definitive the essential difference enters the meanings of covariante and contravariant. It considers a vector V in the space. It represents this vector in a system of oblique ortogonais axles.
1) It now calculates the components of vector V according to oblique axles (that is, it decomposes vector V throughout the oblique axles);
2) In the origin of the system of oblique axles it considers another system of ortogonais axles. Now, it decomposes vector V throughout the axles of this ortogonal system the same.
Then you have the same vector V represented in oblique components (system S) and in ortogonais components. (The vector the same continues being. But the ways to represent it are different).
Now:
1) The components of vector V in the ortogonal system are called covariantes components; 2) The components of the vector in the oblique system are called contravariant components!
An so on.
VictorNeto
4. Aug 17, 2012
Huh? | {"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": 0.9645684957504272, "perplexity": 981.2032446911637}, "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-2018-17/segments/1524125946011.29/warc/CC-MAIN-20180423125457-20180423145457-00571.warc.gz"} |
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onegirl Group Title Check the hypotheses of Rolle’s Theorem and the Mean Value Theorem and find a value of c that makes the appropriate conclusion true. Illustrate the conclusion with a graph. f(x) = x^2 + 1, [2,-2] one year ago one year ago Edit Question Delete Cancel Submit
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1. abb0t
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Well, to satisfy rolle's theorem, you must satisfy the 3 conditions (you can find them in your book - if not, I can write them down for you if you don't have access to a book). Now to find the value of "c" using mean value theorem, you must start by finding the derivative of the function I'll leave you to find it's derivative as it is quite simple for this function. Basically, it must follow the first two conditions of rolle's theorem to apply the formula Then, plug it in to the formula: $f'(c) = \frac{ f(b)-f(a) }{ b-a }$ on the given interval, which for your case it's -2<x<2 Now, set your derivative equal to that. and solve for "c" pick the value which matches the solution in the given interval. if the value falls outside of the given interval then the solution is excluded.
• one year ago
2. onegirl
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so find the derivative of x^2 + 1?
• one year ago
3. abb0t
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Yes. Find the derivative. Use the formula f'(c) = to solve for "c".
• one year ago
4. onegirl
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okay got you thanks
• one year ago
5. abb0t
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You don't need to check first two conditions since you know that your functions IS in fact continuous on the given interval and differentiable. So with that being said, best of luck.
• one year ago
6. onegirl
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@zepdrix can u help?
• one year ago
7. onegirl
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i did it but i think i got it wrong
• one year ago
8. onegirl
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f'(c) = f(-2) - f(2)/ -2 - 2 so f(-2) -2^2 + 1 = -3, f(2) 2^2 + 1 = 5. So the slope will be 2 because -3 - 5/-2-2 = -8/-4 which is 2. So To c : f'(x) = 2x, f'(c) = 2c = 2 2c = 2 so c will equal one (1) but when i checked (a< c <b ) (2, 1 , -2) it doesn't make sense because 1 is not less than -2 :/
• one year ago
9. onegirl
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@abb0t @zepdrix @experimentX ?
• one year ago
10. experimentX
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• one year ago
11. experimentX
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pick any two points ... on two sides of 0, you see that it satisfies the Rolle's theorem.
• one year ago
12. onegirl
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Did i go wrong when i found f'x? and find the f prime of c?
• one year ago
13. experimentX
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equate it to zero ... and you get x=0
• one year ago
14. experimentX
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your graph is symmetric f(-2) - f(2) should be zero ... probably you made mistake somewhere.
• one year ago
15. onegirl
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okay so c = to 0 right? i made a mistake in putting -2 and 2 ?
• one year ago
16. onegirl
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@zepdrix are u there?
• one year ago
17. onegirl
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@wio can u help
• one year ago
18. onegirl
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okay so its 0?
• one year ago
19. experimentX
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yes yes it is ..
• one year ago
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"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": 0.9955079555511475, "perplexity": 3048.550600920801}, "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-2014-42/segments/1413507442420.22/warc/CC-MAIN-20141017005722-00025-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/satelite-questions.87312/ | # Satelite Questions
1. Sep 2, 2005
### ngkamsengpeter
I want to know that what provide the tangetial speed of satelite.
Is it the satelites have a engine that provide its tangetial speed or the gravitational field strength that provide the tangetial speed ?
2. Sep 3, 2005
### Dr.Brain
Satellite orbiting around earth free falls under gravity . Earth's Gravitational Force tries to pull satellite towards itself , and thus the satellite keeps falling from the straightline path that it otherwise would have taken in absence of earth's Gravitational Pull.When a satellite is launched , its gravitational potential energy is changed into K.E , and the initial velocity given to satellite is given in accordance with the height at which it is to be placed , so that a particular height it starts orbiting.Now the tangential velocity it once acquires is maintained by the circular motion it possesses .Wor done by earth's gravitational force is zero in this case and thus the change in K.E in circular orbit is also zero.So the satellite comes to an orbit with a particular velocity which is then maintained in circular motion.
BJ
3. Sep 3, 2005
### ngkamsengpeter
Can you explain clearly
4. Sep 3, 2005
### HallsofIvy
Staff Emeritus
It is the speed orginally given to the satellite in putting into orbit. Once the satellite is in orbit there is only the force of gravity acting on it (ignoring slight resistance from a few atoms at that height) and that is perpendicular to the orbit (assuming an near circular orbit) and so does not affect the speed. | {"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": 0.9785580635070801, "perplexity": 1122.768063128744}, "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-2017-09/segments/1487501170651.78/warc/CC-MAIN-20170219104610-00239-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/107728-partial-fraction.html | # Math Help - Partial Fraction
1. ## Partial Fraction
so I have
x^2 / (x-1)(x-2)
The answer is 1 - 1/(x-1) + 4/(x-2).
Where did the 1 come from. I did the whole solving for A and B thing and got the same answer without the 1.
Thanks.
2. $\frac {x^2}{(x-1)(x-2)}=\frac {x^2}{x^2-3x+2}= 1+\frac{3x-2}{x^2-3x+2}=1+\frac{3x-2}{(x-1)(x-2)}$
now resolve $\frac{3x-2}{(x-1)(x-2)}$ into partial fraction
$\frac{3x-2}{(x-1)(x-2)}=\frac{- 1}{(x-1)} + \frac{4}{(x-2)}$
$therefore\quad \frac {x^2}{(x-1)(x-2)}=1-\frac{ 1}{(x-1)} + \frac{4}{(x-2)}$ | {"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": 0.9675261974334717, "perplexity": 2385.6382086384483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737911339.44/warc/CC-MAIN-20151001221831-00045-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://etna.mcs.kent.edu/volumes/2011-2020/vol44/abstract.php?vol=44&pages=1-24 | ## Structure preserving deflation of infinite eigenvalues in structured pencils
Volker Mehrmann and Hongguo Xu
### Abstract
The long standing problem is discussed of how to deflate the part associated with the eigenvalue infinity in a structured matrix pencil using structure preserving unitary transformations. We derive such a deflation procedure and apply this new technique to symmetric, Hermitian or alternating pencils and in a modified form to (anti)-palindromic pencils. We present a detailed error and perturbation analysis of this and other deflation procedures and demonstrate the properties of the new algorithm with several numerical examples.
Full Text (PDF) [375 KB]
### Key words
structured staircase form, structured Kronecker canonical form, symmetric pencil, Hermitian pencil, alternating pencil, palindromic pencil, linear quadratic control, $H_\infty$ control
### AMS subject classifications
65F15, 15A21, 93B40
### Links to the cited ETNA articles
[5] Vol. 26 (2007), pp. 1-33 Ralph Byers, Volker Mehrmann, and Hongguo Xu: A structured staircase algorithm for skew-symmetric/symmetric pencils
< Back | {"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": 0.8376985788345337, "perplexity": 4874.739521079583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863277.18/warc/CC-MAIN-20180520092830-20180520112830-00593.warc.gz"} |
http://link.springer.com/chapter/10.1007%2F978-3-642-12535-5_77 | Chapter
Large-Scale Scientific Computing
Volume 5910 of the series Lecture Notes in Computer Science pp 645-652
# Additive Operator Decomposition and Optimization–Based Reconnection with Applications
• Pavel BochevAffiliated withApplied Mathematics and Applications
• , Denis RidzalAffiliated withSandia National Laboratories, Optimization and Uncertainty Quantification
* Final gross prices may vary according to local VAT.
## Abstract
We develop an optimization-based approach for additive decomposition and reconnection of algebraic problems arising from discretizations of partial differential equations (PDEs). Application to a scalar convection–diffusion PDE illustrates the new approach. In particular, we derive a robust iterative solver for convection–dominated problems using standard multilevel solvers for the Poisson equation. | {"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": 0.8480548858642578, "perplexity": 2367.5527758420817}, "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-2017-09/segments/1487501172775.56/warc/CC-MAIN-20170219104612-00360-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.math.princeton.edu/events/normal-smoothings-smooth-cube-manifolds-2013-05-02t190005 | # Normal Smoothings for Smooth Cube Manifolds
-
Pedro Ontaneda , SUNY Binghamton
Fine Hall 214
A smooth cube manifold M is a smooth n-manifold M together with a smooth cubification on M. The cube structure provides rays that are normal to the open k-subcubes. Using these rays we can construct "normal charts" in an obvious and natural way. A complete set of normal charts gives a (topological) "normal atlas" on M. If this atlas is smooth it is called a "normal smooth atlas" on M and induces a "normal smooth structure" on M (normal with respect to the cube structure). We prove that every smooth cube manifold has a normal smooth structure, which is diffeomorphic to the original one. This result also holds for smooth all-right-spherical manifolds. | {"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": 0.97803795337677, "perplexity": 1575.004751183765}, "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/1521257647244.44/warc/CC-MAIN-20180319234034-20180320014034-00127.warc.gz"} |
https://math.stackexchange.com/questions/2928923/map-from-schemes-to-stacks | # Map from schemes to stacks
I have just started studying stacks. Trying to understand the theory I was thinking about a (very interesting) toy example: $$BG$$ the classifying stack of a smooth (over a base scheme $$S$$) group G. It is well known that a (smooth) cover is given by its canonical point $$s_0: S \rightarrow BG$$ (the trivial torsor over $$S$$ seen through Yoneda). Is it true that a map from a scheme $$X$$ to $$BG$$ factor through $$s_0$$?
In particular I had in mind the concrete example where $$S=\mathrm{Spec}(\mathbb C)$$ and where $$G=GL_n$$ (so it is true that every torsor is locally trivial in the étale topology).
• When $S=\operatorname{Spec}(\mathbb{C})$ and If $X\rightarrow BG$ factors through $s_0$, then I think the corresponding family is necessarily trivial – loch Sep 24 '18 at 14:39
• @loch: If you take $X \rightarrow \mathrm{Spec}(\mathbb C)$ as the structure morphism then you're certainly right. But I was thinking about something like an endomorphism of $X$ composed with the structure morphism $x:X \rightarrow \mathrm{Spec}(\mathbb C)$ and then $s_0$. But I am not comfortable with stacks yet, so maybe I am making huge mistakes. – user192820 Sep 24 '18 at 15:47
• @loch: as stated by Sasha you were right, thank you both. – user192820 Sep 24 '18 at 15:59
No, a map $$X \to BG$$ is determined by a map $$f:X \to S$$ and a $$f^*G$$-torsor over $$X$$, while those map that factor through $$s_0$$ correspond to trivial torsors. So, as soon as there are nontrivial torsors over $$X$$, there are maps that do not factor through $$s_0$$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8826731443405151, "perplexity": 243.51679441913578}, "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-2019-30/segments/1563195525009.36/warc/CC-MAIN-20190717021428-20190717043428-00039.warc.gz"} |
http://mathhelpforum.com/calculus/165672-triple-integral-volterra-equation-problem.html | # Math Help - Triple Integral - Volterra equation problem
1. ## Triple Integral - Volterra equation problem
Here's the problem:
y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.
Perform three integrations to show that a solution may be written
y(x) = $\int_{0}^{2}L(x,t)f(t)dt$
Determine L(x,t).
My attempt:
After triple integration I get
y(x) = $Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt$
where A and B are constants which I've determined but won't write here.
Anyway, I don't see how this can be converted to find the desired L(x,t)
(I'm assuming my triple integration is correct- I think it is)
2. Originally Posted by ark600
Here's the problem:
y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.
Perform three integrations to show that a solution may be written
y(x) = $\int_{0}^{2}L(x,t)f(t)dt$
Determine L(x,t).
My attempt:
After triple integration I get
y(x) = $Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt$
where A and B are constants which I've determined but won't write here.
Anyway, I don't see how this can be converted to find the desired L(x,t)
(I'm assuming my triple integration is correct- I think it is)
The form of your solution is correct, and if you have solve for A and B you are done!
3. I couldn't see the wood for the trees: the question just asked for a solution.
I just stick x=2 in.
LOL
Cheers | {"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": 0.8932383060455322, "perplexity": 1091.5359105642096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430459915807.89/warc/CC-MAIN-20150501055835-00097-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://stacks.math.columbia.edu/tag/0411 | ## 66.7 Submersive morphisms
For a representable morphism of algebraic spaces we have already defined (in Section 66.3) what it means to be universally submersive. Hence before we give the natural definition we check that it agrees with this in the representable case.
Lemma 66.7.1. Let $S$ be a scheme. Let $f : X \to Y$ be a representable morphism of algebraic spaces over $S$. The following are equivalent
1. $f$ is universally submersive (in the sense of Section 66.3), and
2. for every morphism of algebraic spaces $Z \to Y$ the morphism of topological spaces $|Z \times _ Y X| \to |Z|$ is submersive.
Proof. Assume (1), and let $Z \to Y$ be as in (2). Choose a scheme $V$ and a surjective étale morphism $V \to Y$. By assumption the morphism of schemes $V \times _ Y X \to V$ is universally submersive. By Properties of Spaces, Section 65.4 in the commutative diagram
$\xymatrix{ |V \times _ Y X| \ar[r] \ar[d] & |Z \times _ Y X| \ar[d] \\ |V| \ar[r] & |Z| }$
the horizontal arrows are open and surjective, and moreover
$|V \times _ Y X| \longrightarrow |V| \times _{|Z|} |Z \times _ Y X|$
is surjective. Hence as the left vertical arrow is submersive it follows that the right vertical arrow is submersive. This proves (2). The implication (2) $\Rightarrow$ (1) is immediate from the definitions. $\square$
Thus we may use the following natural definition.
Definition 66.7.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.
1. We say $f$ is submersive1 if the continuous map $|X| \to |Y|$ is submersive, see Topology, Definition 5.6.3.
2. We say $f$ is universally submersive if for every morphism of algebraic spaces $Y' \to Y$ the base change $Y' \times _ Y X \to Y'$ is submersive.
We note that a submersive morphism is in particular surjective.
Lemma 66.7.3. The base change of a universally submersive morphism of algebraic spaces by any morphism of algebraic spaces is universally submersive.
Proof. This is immediate from the definition. $\square$
Lemma 66.7.4. The composition of a pair of (universally) submersive morphisms of algebraic spaces is (universally) submersive.
Proof. Omitted. $\square$
[1] This is very different from the notion of a submersion of differential manifolds.
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https://www.physicsforums.com/threads/elastic-collisions-proof.683993/ | # Elastic collisions proof
1. Apr 8, 2013
### Bipolarity
Suppose that a mass M1 is moving with speed V1 and collides with mass M2 which is initially at rest. After the elastic collision they make, both momentum and kinetic energy are conserved.
$$m_{1}v_{1f} + m_{2}v_{2f} = m_{1}v_{1i}$$
$$\frac{1}{2}m_{1}||v_{1i}||^{2}= \frac{1}{2}m_{1}||v_{1f}||^{2} + \frac{1}{2}m_{2}||v_{2f}||^{2}$$
Derive the following equations:
$$v_{1f} = \frac{m_{1}-m_{2}}{m_{1}+m_{2}}v_{1i}$$
$$v_{2f} = \frac{2m_{1}}{m_{1}+m_{2}}v_{1i}$$
Resnick & Halliday give a fairly staightfoward proof. But in the proof it fails to recognize the fact that the v values in the momentum conservation are vectors, whereas those in the energy conservation are scalars. So the proof is not rigorous. I was curious how one would prove this rigorously, (preferably without casework), given this remark.
Thanks!
BiP
2. Apr 8, 2013
### Staff: Mentor
Those equations are true in the 1-dimensional case only, where you can treat the velocity as scalar.
For two dimensions, you get an additional degree of freedom in the collision, and there are no equivalent fixed equations for the velocity.
3. Apr 8, 2013
### Staff: Mentor
Some 2D collisions can be solved, but you need more information than just the masses and initial (vector) velocities. For example, consider two spheres (or rather, circular pucks sliding on a frictionless surface), with one at rest initially. In addition to the initial velocity of the other puck, you need to specify the impact parameter: the transverse distance between the path of the moving puck's center, and the the center of the stationary puck. This specifies whether the collision is head-on, slightly off center, lightly glancing, etc.
Halliday/Resnick don't discuss this, but you can probably find it in a higher-level classical mechanics book, or maybe with a suitable Google search.
4. Apr 8, 2013
### AlephZero
You didn't say exactly what part of the proof you think is not rigorous, but I suppose one objection to it is this: if two particles moving north-south collide with each other, it is an assumption (with no justification) that there they have no velocity components in the east-west direction after collision.
It would be possible to justify that by a symmetry argument. Suppose after the collision particle 1 moves east and particle 2 moves west. In that case there would be another solution where particle 1 moves west and particle 2 moves east. Since Newtonian mechanics is assumed to be deterministic, there is no reason to choose one of these solutions rather than the other one, therefore the east-west velocity components must be zero.
Note that as the previous answers said or implied, this result is only true for point particles, not for finite sized objects which can have rotational kinetic energy and angular momentum.
5. Apr 8, 2013
### Staff: Mentor
I just remembered that it also makes a difference whether the pucks collide with or without friction against each other. If there is (sliding) friction between them when they come in contact, that generally causes each of the pucks to rotate around their centers of mass after the collision. This gives them rotational kinetic energy which has to be accounted for when applying conservation of energy.
I've done this derivation only for the frictionless case.
6. Apr 8, 2013
### Staff: Mentor
If you want to go into detail, you can also consider the shape and orientation of the objects - if they are not round disks, the shapes are relevant, too.
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https://physics.stackexchange.com/questions/517292/is-ds-frac-delta-q-irevt-true-for-non-reversible-processes | Is $dS=\frac{\delta Q_{irev}}{T}$ true for non-reversible processes?
Das Differential $$\mathrm {d} S$$ ist nach Clausius bei reversiblen Vorgängen zwischen Zuständen im Gleichgewicht das Verhältnis von übertragener Wärme $$\delta Q_{\mathrm {rev} }$$ und absoluter Temperatur $$T$$: $$dS=\frac{Q_{\mathrm {rev} }}{T}$$
Which translates to
According to Clausius the differential $$\mathrm {d} S$$ for reversible processes between equilibirum states is the ratio between transmitted heat $$\delta Q_{\mathrm {rev} }$$ and absolute temperature $$T$$: $$dS=\frac{Q_{\mathrm {rev} }}{T}$$
This formulation seems confusing to me. Why do we need reversibility? I do not see why this shouldn't be true for quasi-static irreversible processes. We start at a state of entropy $$S_1$$ and by some process we reach $$S_2$$. As the entropy by axiom is path-independent it shouldn't matter weather the path is reversible or not.
Addendum: Many people stated in the comments that one can use a reversible process starting and resulting in the same equilibrium state, as the irreversible one. While this is true and an important concept, my question was aimed at the actual heat $$\delta Q_{irev}$$ that is transferred to the system during a irreversible process.
• I think its because they are using the reversible heat Qrev not the heat to actually heat the non-reversible process – ChemEng Dec 2 '19 at 16:43
• In addition to entropy transferred from the surroundings to the system during a process (which is described by dq/T), in an irreversible process, entropy is generated within the system, which is not accounted for by dq/T. Therefore, using dq/T for an irreversible process will give the wrong answer for the change in entropy. – Chet Miller Dec 2 '19 at 17:21
• The title of your post should have the subscript $rev$ with $\delta Q$. – Bob D Dec 2 '19 at 18:06
• @ChetMiller How do we account for that entropy? I always took the formula in the title as the defintion of entropy and now I'm confused on how it is really defined. It seems like theres some sort of inner degrees of freedom that are triggered during a irreversible process? – TheoreticalMinimum Dec 3 '19 at 6:43
• @BobD I changed the title to make more clear what I was asking and added an explanation. – TheoreticalMinimum Dec 3 '19 at 6:44
One counterexample is a quasi static irreversible adiabatic free expansion. Here d$$S>0$$ and d$$Q=0$$, so the equality is not valid for this irreversible process.
• How would you realize a quasi-static free expansion? By definition of q.s. the gas has to expand in a sequence of equilibria, which is not given in the case of, let's say, spontaneously removing a partition. – Nephente Dec 2 '19 at 16:04
• You can still use assume a reversible transfer of heat process to get the entropy change for the irreversible adiabatic free expansion. In that case you can assume a reversible isothermal compression to return the system to its original state before the free expansion. The magnitude of the entropy change for the reversible isothermal compression will equal the entropy change that occurred in the free expansion. $\Delta S$ for the system will be zero when returned to its original state, but the isothermal compression will increase the entropy of the surroundings so that $\Delta S_{TOT}$ >0. – Bob D Dec 2 '19 at 16:26
• @Nephente I imagine it as removing a series of partitions very close to each other, so the new volume is incremented in steps – Wolphram jonny Dec 2 '19 at 16:35
• @BobD I agree with you, and perhaps I misinterpreted the question. It was not if you can find a reversible process to calculate the change in entropy, but if the equation was valid for an irreversible process, which is different to me, that is, use the change in entropy and heat transferred during that specific irreversible process.. – Wolphram jonny Dec 2 '19 at 16:38
• @Wolphramjonny I see your point, it could be viewed that way as well. The equation is, of course, defines entropy change in terms of a reversible transfer of heat. There are many irreversible work processes between two equilibrium states not of which involves any heat transfer. But to determine what the entropy generated is we can assume a process between the states involving a reversible transfer of heat and we will obtain the entropy generated for the irreversible work process. – Bob D Dec 2 '19 at 16:50
Why do we need reversibility? I do not see why this shouldn't be true for quasi-static irreversible processes.
Although the definition is in terms of a reversible transfer of heat, you are correct that it is not limited to a reversible process, i.e., it applies to an irreversible process as well. Entropy is a state function or property, like internal energy. That means the difference in entropy between two equilibrium states is independent of the path or process between the states.
So if you have an irreversible process taking you between two states you can determine the entropy change of the system by assuming any convenient reversible process between the states. That will give you the entropy change for the system for the irreversible process as well since entropy is a state function.
However, if the process is irreversible, entropy is generated by the system. In order to return the system to its original state (perform a cycle) the entropy generated will need to be transferred to the surroundings making the total entropy change (system + surroundings) >0 for a complete cycle. For a reversible cycle the overall entropy change = 0.
Hope this helps.
• "So if you have an irreversible process taking you between two states you can determine the entropy change of the system by assuming any convenient reversible process between the states." I think it is worth stressing here, for clarity, that, since heat is a path dependant property, the heat transfer on this conveinient reversible path will in general not be the same as the amount of heat transfered on the real physical irriversible process. This means we can't simply plug the measured $\delta Q$ in in place of $dQ_\mathrm{rev}$ and expect to get the right answer – By Symmetry Dec 2 '19 at 17:36
• @BySymmetry "While heat is a path dependent property". First of all, heat is not a property. While heat is path dependent a reversible transfer of heat divided by temperature is not path dependent. If it were, it would be tantamount to saying entropy between equilibrium states is path dependent since $dS=\frac{\delta Q_{rev}}{T}$. Second of all, I never said you can simply plug in $\delta q$ for $\delta q_{rev}$. I was responding to the text of the OP's question where the subscript $rev$ is always used and not the title which incorrectly left out the $rev$ subscript. – Bob D Dec 2 '19 at 18:02
• I don't think we disagree on anything here. When I say "Heat is a path dependant property" I mean it is a property of a path and not of the system. My comment was trying to emphasise a point rather than imply that anything you said was wrong – By Symmetry Dec 2 '19 at 18:14
• @BySymmetry Got it, no problem. Sorry but when I hear the word property in a thermodynamics discussion it has a specific meaning to me- $U$, $P$. $V$, $T$ etc. that goes beyond the dictionary definition, which I now see is the way you were using it. – Bob D Dec 2 '19 at 18:22 | {"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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8381600379943848, "perplexity": 336.50366351195515}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143963.79/warc/CC-MAIN-20200219000604-20200219030604-00453.warc.gz"} |
http://www.reference.com/browse/Space+Balls | Definitions
# Hausdorff dimension
In mathematics, the Hausdorff dimension (also known as the Hausdorff–Besicovitch dimension) is an extended non-negative real number associated to any metric space. The Hausdoff dimension generalizes the notion of the dimension of a real vector space. In particular, the Hausdorff dimension of a single point is zero, the Hausdoff dimension of a line is one, the Hausdoff dimension of the plane is two, etc. There are however many irregular sets that have noninteger Hausdorff dimension. The concept was introduced in 1918 by the mathematician Felix Hausdorff. Many of the technical developments used to compute the Hausdorff dimension for highly irregular sets were obtained by Abram Samoilovitch Besicovitch.
## Informal discussion
Intuitively, the dimension of a set (for example, a subset of Euclidean space) is the number of independent parameters needed to describe a point in the set. One mathematical concept which closely models this naive idea is that of topological dimension of a set. For example a point in the plane is described by two independent parameters (the Cartesian coordinates of the point), so in this sense, the plane is two-dimensional. As one would expect, the topological dimension is always a natural number.
However, topological dimension behaves in quite unexpected ways on certain highly irregular sets such as fractals. For example, the Cantor set has topological dimension zero, but in some sense it behaves as a higher dimensional space. Hausdorff dimension gives another way to define dimension, which takes the metric into account.
To define the Hausdorff dimension for X as non-negative real number (that is a number in the half-closed infinite interval [0, ∞)), we first consider the number N(r) of balls of radius at most r required to cover X completely. Clearly, as r gets smaller N(r) gets larger. Very roughly, if N(r) grows in the same way as 1/rd as r is squeezed down towards zero, then we say X has dimension d. In fact the rigorous definition of Hausdorff dimension is somewhat roundabout, as it allows the covering of $X$ by balls of different sizes.
For many shapes that are often considered in mathematics, physics and other disciplines, the Hausdorff dimension is an integer. However, sets with non-integer Hausdorff dimension are important and prevalent. Benoît Mandelbrot, a popularizer of fractals, advocates that most shapes found in nature are fractals with non-integer dimension, explaining that "[c]louds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."
There are various closely related notions of possibly fractional dimension. For example box-counting dimension, generalizes the idea of counting the squares of graph paper in which a point of X can be found, as the size of the squares is made smaller and smaller. (The box-counting dimension is also called the Minkowski-Bouligand dimension). The packing dimension is yet another notion of dimension admitting fractional values. These notions (packing dimension, Hausdorff dimension, Minkowski-Bouligand dimension) all give the same value for many shapes, but there are well documented exceptions.
## Formal definition
Let $X$ be a metric space. If $Ssubset X$ and $din\left[0,infty\right)$, the $d$-dimensonal Hausdorff content of $S$ is defined by
$C_H^d\left(S\right):=infBigl\left\{sum_i r_i^d:text\left\{ there is a cover of \right\} Stext\left\{ by balls with radii \right\}r_i>0Bigr\right\}.$
In other words, $C_H^d\left(S\right)$ is the infimum of the set of numbers $deltage 0$ such that there is some (indexed) collection of balls $\left\{B\left(x_i,r_i\right):iin I\right\}$ with $r_i>0$ for each $iin I$ which satisfies Hausdorff dimension of $X$ is defined by
$operatorname\left\{dim\right\}_\left\{operatorname\left\{H\right\}\right\}\left(X\right):=inf\left\{dge 0: C_H^d\left(X\right)=0\right\}.$
Equivalently, $operatorname\left\{dim\right\}_\left\{operatorname\left\{H\right\}\right\}\left(X\right)$ may be defined as the infimum of the set of $din\left[0,infty\right)$ such that the $d$-dimensional Hausdorff measure of $X$ is zero. This is the same as the supremum of the set of $din\left[0,infty\right)$ such that the $d$-dimensional Hausdorff measure of $X$ is infinite (except that when this latter set of numbers $d$ is empty the Hausdorff dimension is zero).
## Examples
• The Euclidean space Rn has Hausdorff dimension n.
• The circle S1 has Hausdorff dimension 1.
• Countable sets have Hausdorff dimension 0.
• Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension. For example, the Cantor set (a zero-dimensional topological space) is a union of two copies of itself, each copy shrunk by a factor 1/3; this fact can be used to prove that its Hausdorff dimension is $ln 2/ln 3,$ which is approximately $0\left\{.\right\}63$ (see natural logarithm). The Sierpinski triangle is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of $ln 3/ ln 2$, which is approximately $1\left\{.\right\}58$.
• Space-filling curves like the Peano and the Sierpiński curve have the same Hausdorff dimension as the space they fill.
• The trajectory of Brownian motion in dimension 2 and above has Hausdorff dimension 2 almost surely.
• An early paper by Benoit Mandelbrot entitled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension and subsequent work by other authors have claimed that the Hausdorff dimension of many coastlines can be estimated. Their results have varied from 1.02 for the coastline of South Africa to 1.25 for the west coast of Great Britain. However, 'fractal dimensions' of coastlines and many other natural phenomena are largely heuristic and cannot be regarded rigorously as a Hausdorff dimension. It is based on scaling properties of coastlines at a large range of scales, but which does not however include all arbitrarily small scales, where measurements would depend on atomic and sub-atomic structures, and are not well defined.
## Properties of Hausdorff dimension
### Hausdorff dimension and inductive dimension
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dimind(X).
Theorem. Suppose X is non-empty. Then
$operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(X\right) geq operatorname\left\{dim\right\}_\left\{mathrm\left\{ind\right\}\right\}\left(X\right)$
Moreover
$inf_Y operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(Y\right) =operatorname\left\{dim\right\}_\left\{mathrm\left\{ind\right\}\right\}\left(X\right)$
where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric dY of Y is topologically equivalent to dX.
These results were originally established by Edward Szpilrajn (1907-1976). The treatment in Chapter VIII of the Hurewicz and Wallman reference is particularly recommended.
### Hausdorff dimension and Minkowski dimension
The Minkowski dimension is similar to the Hausdorff dimension, except that it is not associated with a measure. The Minkowski dimension of a set is at least as large as the Hausdorff dimension. In many situations, they are equal. However, the set of rational points in $\left[0,1\right]$ has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.
### Hausdorff dimensions and Frostman measures
If there is a measure $mu$ defined on Borel subsets of a metric space $X$ such that $mu\left(X\right)>0$ and $mu\left(B\left(x,r\right)\right)le r^s$ holds for some constant $s>0$ and for every ball $B\left(x,r\right)$ in $X$, then $operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(X\right) geq s$. A partial converse is provided by Frostman's lemma. That article also discusses another useful characterization of the Hausdorff dimension.
### Behaviour under unions and products
If $X=bigcup_\left\{iin I\right\}X_i$ is a finite or countable union, then
$operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(X\right) =sup_\left\{iin I\right\} operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(X_i\right).$
This can be verified directly from the definition.
If $X$ and $Y$ are metric spaces, then the Hausdorff dimension of their product satisfies
$operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(Xtimes Y\right)ge operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(X\right)+ operatorname\left\{dim\right\}_\left\{mathrm\left\{Haus\right\}\right\}\left(Y\right).$
An example in which the inequality is strict has been constructed by J. M. Marstrand. It is known that when $X$ and $Y$ are Borel subsets of $R^n$, the Hausdorff dimension of $Xtimes Y$ is bounded from above by the Hausdorff dimension of $X$ plus the upper packing dimension of $Y$. These facts are discussed in Mattila (1995).
## Self-similar sets
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.
Theorem. Suppose
$psi_i: mathbb\left\{R\right\}^n rightarrow mathbb\left\{R\right\}^n, quad i=1, ldots , m$
are contractive mappings on Rn with contraction constant rj < 1. Then there is a unique non-empty compact set A such that
$A = bigcup_\left\{i=1\right\}^m psi_i \left(A\right).$
The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of Rn with the Hausdorff distance.
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition on the sequence of contractions ψi which is stated as follows: There is a relatively compact open set V such that
$bigcup_\left\{i=1\right\}^mpsi_i \left(V\right) subseteq V$
where the sets in union on the left are pairwise disjoint.
Theorem. Suppose the open set condition holds and each ψi is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of
$sum_\left\{i=1\right\}^m r_i^s = 1.$
Note that the contraction coefficient of a similitude is the magnitude of the dilation.
We can use this theorem to compute the Hausdorff dimension of the Sierpinski triangle (or sometimes called Sierpinski gasket). Consider three non-collinear points a1, a2, a3 in the plane R² and let ψi be the dilation of ratio 1/2 around ai. The unique non-empty fixed point of the corresponding mapping ψ is a Sierpinski gasket and the dimension s is the unique solution of
$left\left(frac\left\{1\right\}\left\{2\right\}right\right)^s+left\left(frac\left\{1\right\}\left\{2\right\}right\right)^s+left\left(frac\left\{1\right\}\left\{2\right\}right\right)^s = 3 left\left(frac\left\{1\right\}\left\{2\right\}right\right)^s =1.$
Taking natural logarithms of both sides of the above equation, we can solve for s, that is:
$s = frac\left\{ln 3\right\}\left\{ln 2\right\}.$
The Sierpinski gasket is self-similar. In general a set E which is a fixed point of a mapping
$A mapsto psi\left(A\right) = bigcup_\left\{i=1\right\}^m psi_i\left(A\right)$
is self-similar if and only if the intersections
$H^sleft\left(psi_i\left(E\right) cap psi_j\left(E\right)right\right) =0$
where s is the Hausdorff dimension of E and $H^s$ denotes Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:
Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.
## Historical references
• A. S. Besicovitch, On Linear Sets of Points of Fractional Dimensions, Mathematische Annalen 101 (1929).
• A. S. Besicovitch and H. D. Ursell, Sets of Fractional Dimensions, Journal of the London Mathematical Society, v12 (1937). Several selections from this volume are reprinted in Classics on Fractals,ed. Gerald A. Edgar, Addison-Wesley (1993) ISBN 0-201-58701-7 See chapters 9,10,11.
• F. Hausdorff, Dimension und äußeres Maß, Mathematische Annalen 79(1–2) (March 1919) pp. 157–179.
## References
Search another word or see Space Ballson Dictionary | Thesaurus |Spanish | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 59, "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": 0.9748363494873047, "perplexity": 314.0445237732751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657129229.10/warc/CC-MAIN-20140914011209-00177-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://puzzling.stackexchange.com/questions/98736/complete-this-cross-sequence | # Complete this cross sequence
What is the next element of this sequence and why?
Possible choices:
Hint 1
There are more than one answers, but only one of the listed options is correct.
Hint 2
Consider each cross as two Cartesian axes with the same scale.
Hint 3
(Apparently this puzzle is really, really hard) Consider the lines that are not crosses as the graph of a function $$y=f(x)$$. Draw a grid (or the ticks in the axes). Any scale will be fine but some scales are more convenient than the others.
Hint 4
There is a progressive pattern in the sequence. That means that the answer does not have something in common with all the elements in the sequence: it really continues the sequence in some sense. Also, $$[-3;3]$$ is a good scale for the two axes.
Hint 5
Using $$[-3; 3]$$ as scale write the value of $$f(x)$$ for each diagram and for each $$x \in [-3; 3]$$. Now it should be clear what is the pattern
C
Reasoning
Following the hints, if we consider the axes to have the same scale with displayed range as $$[-3,3]$$ for both axes, then the four functions in order seem to be $$f(x) = x-2 \,\,\,,\,\,\, f(x) = 3-x \,\,\,,\,\,\, f(x) = x \,\,\,,\,\,\, f(x) = 3$$ Now consider the value of $$f(2)$$. Reading in order we have $$f(2) = 0,1,2,3$$
This suggests that the next graph in the sequence will have $$f(2) = 4$$. As we can see, graph C is the only such candidate and, indeed, the graph appears to be $$f(x) = 2x$$ so this is the next in the sequence.
The answer might be this: Considering that the picture can be of any scale in all diagrams i.e. : each cross (axes) may have different scales as scales or markings are not mentioned.
First diagram : $$\fbox{1}x - 1y = \text{ (some constant say } \fbox{2})$$ i.e. $$\fbox{1}x - 1y = \fbox{2}$$ Second $$\fbox{1}x + 1y = \fbox{1}$$ Third: $$\fbox{1}x-1y=\fbox{0}$$ [Note: the right hand side constant and the coefficient of $$x$$ form a base 3 number system. i.e first : $$12$$, second: $$11$$, third: $$10$$, fourth: $$02$$. The plus and minus alternate]. Fourth: $$\fbox{0}x + 1y = \fbox{2}$$, Fifth: $$\fbox{0}x-1y = \fbox{1}$$ Thus option E.
• considering the pictures as diagrams is a ggod starting point. The issue is that this solution works only if the diagrams have different scales – melfnt Jun 1 at 6:35
Given the recent hints about Cartesian coordinates here's a new attempt:
E
Since
Suppose the range is [3,3] for each diagram (per hint 3), we could make a chart regarding the slope, y-intercept, and integral of each one. There is no obvious pattern, still. However, there is a clear link between the signs of y-intercept and integral. Per hint 1 which states that there could be more than 1 possibilities compatible with the existing sequence, E is the only option that combines negativity and the relation between y-intercept and integral
Ι say it is
figure B.
The reason is:
the top set has 4 figures with an even number of angles, namely 12,6,6,6. The bottom set has four figures with an even number of angles and one figure with an odd number of angles. Figure B has 9 angles.
• I really don't get the point of this answer. If your reasoning is correct the answer should have an even number of angles too – melfnt May 31 at 17:28
• @melfnt. When you draw geometric figures with straight lines you should have in mind two fundamental aspects: a) the number of straight lines b) the number of angles. – Vassilis Parassidis May 31 at 18:02
• Sure, maybe your reasoning about the number of angles is corrected. The issue is: since you are finding the next element of a sequence you should add an item with the same parity of the pre-existing elements, not with the opposite parity. – melfnt May 31 at 20:53
• The reason I put 9 is all numbers on the first group have a common factor. In addition to that the second group has one odd number and I thought you did that intentionally. These are the reasons why I chose B.. – Vassilis Parassidis May 31 at 23:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8051401376724243, "perplexity": 491.5687625182566}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401632671.79/warc/CC-MAIN-20200929060555-20200929090555-00147.warc.gz"} |
https://brilliant.org/problems/mixing-of-concepts/ | # Mixing of concepts!
Calculus Level 5
A function is defined as $$f(x)=ax^4+bx^3+cx^2+dx+\lambda$$. This function has a special property: $$\dfrac{f(1)}{1}=\dfrac{f(2)}{2}=\dfrac{f(3)}{3}$$. If $$\displaystyle \lim _{ x\to \infty }{ \dfrac { f( x ) }{ { x }^{ 4 } } } =1$$, then find $$f(i)+f(-i)$$ where $$i=\sqrt{-1}$$.
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http://math.stackexchange.com/questions/22310/help-solving-an-integral-int-left-frac-x-13-x-right-frac12-dx/22319 | # help solving an integral $\int\left(\frac {x-1}{3-x}\right)^\frac{1}{2} dx$
$\displaystyle\int \left(\frac {x-1}{3-x}\right)^\frac{1}{2}\,\rm dx$
I am stuck on this part:
Let $u=\dfrac{x-1}{3-x}~\longrightarrow$ $~~\rm du=\dfrac {2}{(x-3)^2}\,\rm dx,$ which can be represented as
$\rm du=\dfrac{1}{3-x} - \dfrac{1-x}{(3-x)^2}\,\rm dx$
I cannot "see" how to get to this $2$ $\displaystyle\int \: \frac{(u)^\frac{1}{2}}{(u+1)^2} \:\rm dx$
after this part I know how to solve it; I just wish someone would show me "step by step" this part It seems it involves some sort of "leap" of thought; or is there a systematic way doing this using basic algebra?
Thanks.
-
First note $$du=\frac{2}{(x-3)^2}dx$$ which implies $$\frac{(x-3)^2}{2}du=dx.$$ Also, $$u+1=\frac{x-1}{3-x}+\frac{3-x}{3-x}=\frac{2}{3-x}$$ which implies $$(u+1)^2=\left(\frac{2}{3-x}\right)^2=\frac{4}{(x-3)^2}.$$
Putting it together you have $$\int \left(\frac {x-1}{3-x}\right)^\frac{1}{2} dx = \int u^{1/2}\cdot\frac{(x-3)^2}{2}du = 2\int u^{1/2}\cdot\frac{(x-3)^2}{4}du = 2\int \frac{u^{1/2}}{(u+1)^2}du.$$
-
You probably reached this point after inserting u:
$\int u^\frac{1}{2} \frac{(x-3)^2}{2}du$
The leap of thought you would need here is to realize that the remaining x must be substituted by u and so what you want to find is a function which in terms of u can replace x, in this case we can go for $(x-3)$.
$x-3 = f(u)$
A trial and error approach would be to inspect $u$ and see that (as you realized) $u$ can be written as: $u = -1 + \frac{2}{3-x}$, here we already see the term $3-x$ so we just need to manipulate the equation to let $x-3$ be on one side. step by step:
$u+1 = \frac{2}{3-x}$
$\frac{2}{u+1} = 3-x$
$-\frac{2}{u+1} = x-3$
I.e. $f(u) = -\frac{2}{u+1}$
Now we can substitute $(x-3)$ with $-\frac{2}{u+1}$ in the integral to get $2$ $\int \frac{(u)^\frac{1}{2}}{(u+1)^2}dx$
-
why the downvote? – j-a Jan 24 '12 at 17:46
Notice the $u+1$ in the denominator. What is $u+1$ in terms of $x$? In particular, what is $\frac{1}{(u+1)^2}$?
-
You can write the fraction as $\frac{(x-1)^{1/2}}{(3-x)^{1/2}}$. Then put $3-x =t$. So you have $dt= -dx$ and $x-1 =3-t-1=2-t$. So you have to now evaluate the integral $$\int \sqrt{ \frac{2-t}{t}}\ -\rm{dt}$$ which can be evaluated by sing the subsitution $t = 2 \cos^{2}{v}$.
-
You only came unstuck at the point where you needed to set $\text{d}x$ equal to $\frac{(3-x)^2}{2} \text{d}u,$ an equality you already had. So your problem reduces to expressing $3-x$ in terms of $u.$
From your expression for $u$ you have $u(3-x)=x-1,$ and adding $3-x$ to both sides gives $(3-x)(u+1)=2$ and hence $3-x=2/(1+u).$
The sure, but slightly longer approach, is to solve $u(3-x)=x-1$ for $x$ and subtract from $3.$
-
The integrand is so seductively pointing to the use of complex variables which reduces it to a trivial problem. Beware we have a pole within a branch cut!
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https://www.physicsforums.com/threads/newtons-third-law-help-pls.187378/ | # Newton's Third Law. Help Pls!
1. Sep 27, 2007
### jessemarquez
1. The problem statement, all variables and given/known data
Three blocks are stacked on top of each other inside an elevator as shown in the figure.
Answer the following questions with reference to the eight forces defined as follows.
the force of the 3kg block on the 2kg block, F of 3 on 2,
the force of the 2kg block on the 3kg block, F of 2 on 3,
the force of the 3kg block on the 1kg block, F of 3 on 1,
the force of the 1kg block on the 3kg block, F of 1 on 3,
the force of the 2kg block on the 1kg block, F of 2 on 1,
the force of the 1kg block on the 2kg block, F of 1 on 2,
the force of the 1kg block on the floor, F of 1 on floor, and
the force of the floor on the 1kg block, F of floor on 1.
Assume the elevator is at rest. Rank the magnitude of the forces.
Rank from largest to smallest.
__________
| |
| |
| 3 kg |
|________|
| |
| 2 Kg |
|______ |
| |
| 1 kg |
|______|______
3. The attempt at a solution
F of floor on 1 and F 1 on floor, F of 3 on 2 and F of 2 on 3, F of 2 on 1 and F of 1 on 2, F of 3 on 1 and F of 1 on 3.
Last edited: Sep 27, 2007
2. Sep 27, 2007
### jessemarquez
can anyone offer any insight if the order stated is correct.
Similar Discussions: Newton's Third Law. Help Pls! | {"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": 0.8072776794433594, "perplexity": 1203.711668334415}, "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-2017-13/segments/1490218186780.20/warc/CC-MAIN-20170322212946-00041-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://pos.sissa.it/256/233/ | # PoS(LATTICE2016)233
Asymptotic safety of gauge theories beyond marginal interactions
T. Buyukbese, D. Litim
Contribution: pdf
Abstract
Following up on the recent disovery of asymptotic safety and exact interacting UV fixed points in four-dimensional gauge theories coupled to matter, we investigate the impact of higher dimensional operators using the method of functional renormalisation. In the Veneziano limit, we establish that classically irrelevant couplings take well-defined interacting fixed point values of their own, despite of their non-renormalisability within standard perturbation theory. We also establish vacuum stability in the presence of higher dimensional scalar operators. Universal scaling exponents are found as well, showing that the higher order couplings remain parametrically irrelevant with near-Gaussian values. Our results provide a crucial consistency check for exact asymptotic safety of weakly coupled gauge theories. Similarities with fixed points in other theories including $4d$ quantum gravity are indicated. | {"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": 0.8384647369384766, "perplexity": 1425.3785378667317}, "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-2017-47/segments/1510934806317.75/warc/CC-MAIN-20171121055145-20171121075145-00560.warc.gz"} |
https://link.springer.com/article/10.1007/s10958-018-4133-1?error=cookies_not_supported&code=72f9b1f2-b2d2-428f-9047-70cea27a7543 | # Turán-Type Results for Distance Graphs in an Infinitesimal Plane Layer
In this paper, we obtain a lower bound on the number of edges in a unit distance graph Γ in an infinitesimal plane layer 2 × [0, ε]d, which relates the number of edges e(Γ), the number of vertices ν(Γ), and the independence number α(Γ). Our bound $$e\left(\varGamma \right)\ge \frac{19\nu \left(\varGamma \right)-50\alpha \left(\varGamma \right)}{3}$$ is a generalization of a previous bound for distance graphs in the plane and a strong improvement of Turán’s bound in the case where $$\frac{1}{5}\le \frac{\alpha \left(\varGamma \right)}{v\left(\varGamma \right)}\le \frac{2}{7}$$.
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## References
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E. I. Ponomarenko and A. M. Raigorodskii, “New upper bounds for the independence numbers of graphs with vertices in {−1, 0, 1}n and their applications to problems of the chromatic numbers of distance graphs,” Mat. Zametki, 96, No. 1, 138–147 (2014).
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A. M. Raigorodskii, “The Erdős–Hadwiger problem and the chromatic numbers of finite geometric graphs,” Mat. Sb., 196, No. 1, 123–156 (2005).
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## Author information
Authors
### Corresponding author
Correspondence to L. E. Shabanov.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 464, 2017, pp. 132–168.
## Rights and permissions
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https://optimization-online.org/2009/03/2246/ | # Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems
We consider a quadratic optimal control problem governed by a nonautonomous affine differential equation subject to nonnegativity control constraints. For a general class of interior penalty functions, we show how to compute the principal term of the pointwise expansion of the state and the adjoint state. Our main argument relies on the following fact: If the control of the initial problem satisfies strict complementarity conditions for its Hamiltonian except for a finite number of times, the estimates for the penalized optimal control problem can be derived from the estimations of a related stationary problem. Our results provide several types of efficiency measures of the penalization technique: error estimations of the control for $L^s$ norms ($s$ in $[1,+\infty]$), error estimations of the state and the adjoint state in Sobolev spaces $W^{1,s}$ ($s$ in $[1,+\infty)$) and also error estimates for the value function. For the $L^1$ norm and the logarithmic penalty, the optimal results are given. In this case we indeed establish that the penalized control and the value function errors are of order $O(\eps|\log\eps|)$.
## Citation
Published as Rapport de Recherche INRIA RR 6863, March 2009. | {"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": 0.9387781023979187, "perplexity": 297.05724024667506}, "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/1659882571222.74/warc/CC-MAIN-20220810222056-20220811012056-00115.warc.gz"} |
http://www.nag.com/numeric/MB/manual64_24_1/html/E02/e02caf.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_fit_2dcheb_lines (e02ca)
Purpose
nag_fit_2dcheb_lines (e02ca) forms an approximation to the weighted, least squares Chebyshev series surface fit to data arbitrarily distributed on lines parallel to one independent coordinate axis.
Syntax
[a, ifail] = e02ca(m, k, l, x, y, f, w, xmin, xmax, nux, nuy, 'n', n, 'inuxp1', inuxp1, 'inuyp1', inuyp1)
[a, ifail] = nag_fit_2dcheb_lines(m, k, l, x, y, f, w, xmin, xmax, nux, nuy, 'n', n, 'inuxp1', inuxp1, 'inuyp1', inuyp1)
Description
nag_fit_2dcheb_lines (e02ca) determines a bivariate polynomial approximation of degree k$k$ in x$x$ and l$l$ in y$y$ to the set of data points (xr,s,ys,fr,s)$\left({x}_{\mathit{r},\mathit{s}},{y}_{\mathit{s}},{f}_{\mathit{r},\mathit{s}}\right)$, with weights wr,s${w}_{\mathit{r},\mathit{s}}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$ and r = 1,2,,ms$\mathit{r}=1,2,\dots ,{m}_{\mathit{s}}$. That is, the data points are on lines y = ys$y={y}_{s}$, but the x$x$ values may be different on each line. The values of k$k$ and l$l$ are prescribed by you (for guidance on their choice, see Section [Further Comments]). The function is based on the method described in Sections 5 and 6 of Clenshaw and Hayes (1965).
The polynomial is represented in double Chebyshev series form with arguments x$\stackrel{-}{x}$ and y$\stackrel{-}{y}$. The arguments lie in the range 1$-1$ to + 1$+1$ and are related to the original variables x$x$ and y$y$ by the transformations
x = (2x − (xmax + xmin))/((xmax − xmin)) and y = (2y − (ymax + ymin))/((ymax − ymin)). $x-=2x-(xmax+xmin) (xmax-xmin) and y-=2y-(ymax+ymin) (ymax-ymin) .$
Here ymax${y}_{\mathrm{max}}$ and ymin${y}_{\mathrm{min}}$ are set by the function to, respectively, the largest and smallest value of ys${y}_{s}$, but xmax${x}_{\mathrm{max}}$ and xmin${x}_{\mathrm{min}}$ are functions of y$y$ prescribed by you (see Section [Further Comments]). For this function, only their values xmax(s) ${x}_{\mathrm{max}}^{\left(s\right)}$ and xmin(s) ${x}_{\mathrm{min}}^{\left(s\right)}$ at each y = ys$y={y}_{s}$ are required. For each s = 1,2,,n$s=1,2,\dots ,n$, xmax(s) ${x}_{\mathrm{max}}^{\left(s\right)}$ must not be less than the largest xr,s${x}_{r,s}$ on the line y = ys$y={y}_{s}$, and, similarly, xmin(s) ${x}_{\mathrm{min}}^{\left(s\right)}$ must not be greater than the smallest xr,s${x}_{r,s}$.
The double Chebyshev series can be written as
k l ∑ ∑ aijTi(x)Tj(y) i = 0 j = 0
$∑i=0k∑j=0laijTi(x-)Tj(y-)$
where Ti(x)${T}_{i}\left(\stackrel{-}{x}\right)$ is the Chebyshev polynomial of the first kind of degree i$i$ with argument x$\stackrel{-}{x}$, and Tj(y)${T}_{j}\left(y\right)$ is similarly defined. However, the standard convention, followed in this function, is that coefficients in the above expression which have either i$i$ or j$j$ zero are written as (1/2)aij$\frac{1}{2}{a}_{ij}$, instead of simply aij${a}_{ij}$, and the coefficient with both i$i$ and j$j$ equal to zero is written as (1/4)a0,0$\frac{1}{4}{a}_{0,0}$. The series with coefficients output by the function should be summed using this convention. nag_fit_2dcheb_eval (e02cb) is available to compute values of the fitted function from these coefficients.
The function first obtains Chebyshev series coefficients cs,i${c}_{s,\mathit{i}}$, for i = 0,1,,k$\mathit{i}=0,1,\dots ,k$, of the weighted least squares polynomial curve fit of degree k$k$ in x$\stackrel{-}{x}$ to the data on each line y = ys$y={y}_{\mathit{s}}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$, in turn, using an auxiliary function. The same function is then called k + 1$k+1$ times to fit cs,i${c}_{\mathit{s},i}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$, by a polynomial of degree l$l$ in y$\stackrel{-}{y}$, for each i = 0,1,,k$i=0,1,\dots ,k$. The resulting coefficients are the required aij${a}_{ij}$.
You can force the fit to contain a given polynomial factor. This allows for the surface fit to be constrained to have specified values and derivatives along the boundaries x = xmin$x={x}_{\mathrm{min}}$, x = xmax$x={x}_{\mathrm{max}}$, y = ymin$y={y}_{\mathrm{min}}$ and y = ymax$y={y}_{\mathrm{max}}$ or indeed along any lines x = $\stackrel{-}{x}=\text{}$ constant or y = $\stackrel{-}{y}=\text{}$ constant (see Section 8 of Clenshaw and Hayes (1965)).
References
Clenshaw C W and Hayes J G (1965) Curve and surface fitting J. Inst. Math. Appl. 1 164–183
Hayes J G (ed.) (1970) Numerical Approximation to Functions and Data Athlone Press, London
Parameters
Compulsory Input Parameters
1: m(n) – int64int32nag_int array
n, the dimension of the array, must satisfy the constraint n > 0${\mathbf{n}}>0$.
m(s)${\mathbf{m}}\left(\mathit{s}\right)$ must be set to ms${m}_{\mathit{s}}$, the number of data x$x$ values on the line y = ys$y={y}_{\mathit{s}}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$.
Constraint: m(s) > 0${\mathbf{m}}\left(\mathit{s}\right)>0$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,{\mathbf{n}}$.
2: k – int64int32nag_int scalar
k$k$, the required degree of x$x$ in the fit.
Constraint: for s = 1,2,,n$s=1,2,\dots ,n$, inuxp11k < mdist(s) + inuxp11${\mathbf{inuxp1}}-1\le {\mathbf{k}}<\mathit{mdist}\left(s\right)+{\mathbf{inuxp1}}-1$, where mdist(s)$\mathit{mdist}\left(s\right)$ is the number of distinct x$x$ values with nonzero weight on the line y = ys$y={y}_{s}$. See Section [Further Comments].
3: l – int64int32nag_int scalar
l$l$, the required degree of y$y$ in the fit.
Constraints:
• l0${\mathbf{l}}\ge 0$;
• inuyp11l < n + inuyp11${\mathbf{inuyp1}}-1\le {\mathbf{l}}<{\mathbf{n}}+{\mathbf{inuyp1}}-1$.
4: x(mtot) – double array
mtot, the dimension of the array, must satisfy the constraint mtot s = 1n m(s) $\mathit{mtot}\ge \sum _{\mathit{s}=1}^{{\mathbf{n}}}{\mathbf{m}}\left(\mathit{s}\right)$.
The x$x$ values of the data points. The sequence must be
• all points on y = y1$y={y}_{1}$, followed by
• all points on y = y2$y={y}_{2}$, followed by
• $⋮$
• all points on y = yn$y={y}_{n}$.
Constraint: for each ys${y}_{s}$, the x$x$ values must be in nondecreasing order.
5: y(n) – double array
n, the dimension of the array, must satisfy the constraint n > 0${\mathbf{n}}>0$.
y(s)${\mathbf{y}}\left(\mathit{s}\right)$ must contain the y$y$ value of line y = ys$y={y}_{\mathit{s}}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$, on which data is given.
Constraint: the ys${y}_{s}$ values must be in strictly increasing order.
6: f(mtot) – double array
mtot, the dimension of the array, must satisfy the constraint mtot s = 1n m(s) $\mathit{mtot}\ge \sum _{\mathit{s}=1}^{{\mathbf{n}}}{\mathbf{m}}\left(\mathit{s}\right)$.
f$f$, the data values of the dependent variable in the same sequence as the x$x$ values.
7: w(mtot) – double array
mtot, the dimension of the array, must satisfy the constraint mtot s = 1n m(s) $\mathit{mtot}\ge \sum _{\mathit{s}=1}^{{\mathbf{n}}}{\mathbf{m}}\left(\mathit{s}\right)$.
The weights to be assigned to the data points, in the same sequence as the x$x$ values. These weights should be calculated from estimates of the absolute accuracies of the fr${f}_{r}$, expressed as standard deviations, probable errors or some other measure which is of the same dimensions as fr${f}_{r}$. Specifically, each wr${w}_{r}$ should be inversely proportional to the accuracy estimate of fr${f}_{r}$. Often weights all equal to unity will be satisfactory. If a particular weight is zero, the corresponding data point is omitted from the fit.
8: xmin(n) – double array
n, the dimension of the array, must satisfy the constraint n > 0${\mathbf{n}}>0$.
xmin(s)${\mathbf{xmin}}\left(\mathit{s}\right)$ must contain xmin(s)${x}_{\mathrm{min}}^{\left(\mathit{s}\right)}$, the lower end of the range of x$x$ on the line y = ys$y={y}_{\mathit{s}}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$. It must not be greater than the lowest data value of x$x$ on the line. Each xmin(s)${x}_{\mathrm{min}}^{\left(s\right)}$ is scaled to 1.0$-1.0$ in the fit. (See also Section [Further Comments].)
9: xmax(n) – double array
n, the dimension of the array, must satisfy the constraint n > 0${\mathbf{n}}>0$.
xmax(s)${\mathbf{xmax}}\left(\mathit{s}\right)$ must contain xmax(s) ${x}_{\mathrm{max}}^{\left(\mathit{s}\right)}$, the upper end of the range of x$x$ on the line y = ys$y={y}_{\mathit{s}}$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$. It must not be less than the highest data value of x$x$ on the line. Each xmax(s)${x}_{\mathrm{max}}^{\left(s\right)}$ is scaled to + 1.0$+1.0$ in the fit. (See also Section [Further Comments].)
Constraint: xmax(s) > xmin(s)${\mathbf{xmax}}\left(s\right)>{\mathbf{xmin}}\left(s\right)$.
10: nux(inuxp1) – double array
inuxp1, the dimension of the array, must satisfy the constraint 1inuxp1k + 1$1\le {\mathbf{inuxp1}}\le {\mathbf{k}}+1$.
nux(i)${\mathbf{nux}}\left(\mathit{i}\right)$ must contain the coefficient of the Chebyshev polynomial of degree (i1)$\left(\mathit{i}-1\right)$ in x$\stackrel{-}{x}$, in the Chebyshev series representation of the polynomial factor in x$\stackrel{-}{x}$ which you require the fit to contain, for i = 1,2,,inuxp1$\mathit{i}=1,2,\dots ,{\mathbf{inuxp1}}$. These coefficients are defined according to the standard convention of Section [Description].
Constraint: ${\mathbf{nux}}\left({\mathbf{inuxp1}}\right)$ must be nonzero, unless inuxp1 = 1${\mathbf{inuxp1}}=1$, in which case nux is ignored.
11: nuy(inuyp1) – double array
nuy(i)${\mathbf{nuy}}\left(\mathit{i}\right)$ must contain the coefficient of the Chebyshev polynomial of degree (i1)$\left(\mathit{i}-1\right)$ in y$\stackrel{-}{y}$, in the Chebyshev series representation of the polynomial factor which you require the fit to contain, for i = 1,2,,inuyp1$\mathit{i}=1,2,\dots ,{\mathbf{inuyp1}}$. These coefficients are defined according to the standard convention of Section [Description].
Constraint: ${\mathbf{nuy}}\left({\mathbf{inuyp1}}\right)$ must be nonzero, unless inuyp1 = 1${\mathbf{inuyp1}}=1$, in which case nuy is ignored.
Optional Input Parameters
1: n – int64int32nag_int scalar
Default: The dimension of the arrays m, y, xmin, xmax. (An error is raised if these dimensions are not equal.)
The number of lines y = $y=\text{}$ constant on which data points are given.
Constraint: n > 0${\mathbf{n}}>0$.
2: inuxp1 – int64int32nag_int scalar
Default: The dimension of the array nux.
inux + 1$\mathit{inux}+1$, where inux$\mathit{inux}$ is the degree of a polynomial factor in x$\stackrel{-}{x}$ which you require the fit to contain. (See Section [Description], last paragraph.)
If this option is not required, inuxp1 should be set equal to 1$1$.
Constraint: 1inuxp1k + 1$1\le {\mathbf{inuxp1}}\le {\mathbf{k}}+1$.
3: inuyp1 – int64int32nag_int scalar
Default: The dimension of the array nuy.
inuy + 1$\mathit{inuy}+1$, where inuy$\mathit{inuy}$ is the degree of a polynomial factor in y$\stackrel{-}{y}$ which you require the fit to contain. (See Section [Description], last paragraph.) If this option is not required, inuyp1 should be set equal to 1$1$.
Input Parameters Omitted from the MATLAB Interface
mtot na work nwork
Output Parameters
1: a(na) – double array
na(k + 1) × (l + 1)$\mathit{na}\ge \left({\mathbf{k}}+1\right)×\left({\mathbf{l}}+1\right)$, the total number of coefficients in the fit.
Contains the Chebyshev coefficients of the fit. a(i × (l + 1) + j)${\mathbf{a}}\left(i×\left({\mathbf{l}}+1\right)+j\right)$ is the coefficient aij${a}_{ij}$ of Section [Description] defined according to the standard convention. These coefficients are used by nag_fit_2dcheb_eval (e02cb) to calculate values of the fitted function.
2: 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:
ifail = 1${\mathbf{ifail}}=1$
On entry, k or l < 0${\mathbf{l}}<0$, or inuxp1 or inuyp1 < 1${\mathbf{inuyp1}}<1$, or inuxp1 > k + 1${\mathbf{inuxp1}}>{\mathbf{k}}+1$, or inuyp1 > l + 1${\mathbf{inuyp1}}>{\mathbf{l}}+1$, or m(i) < k − inuxp1 + 2${\mathbf{m}}\left(i\right)<{\mathbf{k}}-{\mathbf{inuxp1}}+2$ for some i = 1,2, … ,n$i=1,2,\dots ,{\mathbf{n}}$, or n < l − inuyp1 + 2${\mathbf{n}}<{\mathbf{l}}-{\mathbf{inuyp1}}+2$, or na is too small, or nwork is too small, or mtot is too small.
ifail = 2${\mathbf{ifail}}=2$
xmin(i)${\mathbf{xmin}}\left(i\right)$ and xmax(i)${\mathbf{xmax}}\left(i\right)$ do not span the data x values on y = y(i)${\mathbf{y}}={\mathbf{y}}\left(i\right)$ for some i = 1,2,,n$i=1,2,\dots ,{\mathbf{n}}$, possibly because xmin(i)xmax(i)${\mathbf{xmin}}\left(i\right)\ge {\mathbf{xmax}}\left(i\right)$.
ifail = 3${\mathbf{ifail}}=3$
The data x values on y = y(i)${\mathbf{y}}={\mathbf{y}}\left(i\right)$ are not nondecreasing for some i = 1,2,,n$i=1,2,\dots ,{\mathbf{n}}$, or the y(i)${\mathbf{y}}\left(i\right)$ themselves are not strictly increasing.
ifail = 4${\mathbf{ifail}}=4$
The number of distinct x values with nonzero weight on y = y(i)${\mathbf{y}}={\mathbf{y}}\left(i\right)$ is less than kinuxp1 + 2${\mathbf{k}}-{\mathbf{inuxp1}}+2$ for some i = 1,2,,n$i=1,2,\dots ,{\mathbf{n}}$.
ifail = 5${\mathbf{ifail}}=5$
On entry, = 0.0${\mathbf{nux}}\left({\mathbf{inuxp1}}\right)=0.0$ and inuxp1 ≠ 1${\mathbf{inuxp1}}\ne 1$, or = 0.0${\mathbf{nuy}}\left({\mathbf{inuyp1}}\right)=0.0$ and inuyp1 ≠ 1${\mathbf{inuyp1}}\ne 1$.
Accuracy
No error analysis for this method has been published. Practical experience with the method, however, is generally extremely satisfactory.
The time taken is approximately proportional to k × (k × mtot + n × l2)$k×\left(k×\mathit{mtot}+n×{l}^{2}\right)$.
The reason for allowing xmax${x}_{\mathrm{max}}$ and xmin${x}_{\mathrm{min}}$ (which are used to normalize the range of x$x$) to vary with y$y$ is that unsatisfactory fits can result if the highest (or lowest) data values of the normalized x$x$ on each line y = ys$y={y}_{s}$ are not approximately the same. (For an explanation of this phenomenon, see page 176 of Clenshaw and Hayes (1965).) Commonly in practice, the lowest (for example) data values x1,s${x}_{1,s}$, while not being approximately constant, do lie close to some smooth curve in the (x,y)$\left(x,y\right)$ plane. Using values from this curve as the values of xmin${x}_{\mathrm{min}}$, different in general on each line, causes the lowest transformed data values x1,s${\stackrel{-}{x}}_{1,s}$ to be approximately constant. Sometimes, appropriate curves for xmax${x}_{\mathrm{max}}$ and xmin${x}_{\mathrm{min}}$ will be clear from the context of the problem (they need not be polynomials). If this is not the case, suitable curves can often be obtained by fitting to the lowest data values x1,s${x}_{1,s}$ and to the corresponding highest data values of x$x$, low degree polynomials in y$y$, using function nag_fit_1dcheb_arb (e02ad), and then shifting the two curves outwards by a small amount so that they just contain all the data between them. The complete curves are not in fact supplied to the present function, only their values at each ys${y}_{s}$; and the values simply need to lie on smooth curves. More values on the complete curves will be required subsequently, when computing values of the fitted surface at arbitrary y$y$ values.
Naturally, a satisfactory approximation to the surface underlying the data cannot be expected if the character of the surface is not adequately represented by the data. Also, as always with polynomials, the approximating function may exhibit unwanted oscillations (particularly near the ends of the ranges) if the degrees k$k$ and l$l$ are taken greater than certain values, generally unknown but depending on the total number of coefficients (k + 1) × (l + 1)$\left(k+1\right)×\left(l+1\right)$ should be significantly smaller than, say not more than half, the total number of data points. Similarly, k + 1$k+1$ should be significantly smaller than most (preferably all) the ms${m}_{s}$, and l + 1$l+1$ significantly smaller than n$n$. Closer spacing of the data near the ends of the x$x$ and y$y$ ranges is an advantage. In particular, if ys = cos(π(s1) / (n1)) ${\stackrel{-}{y}}_{\mathit{s}}=-\mathrm{cos}\left(\pi \left(\mathit{s}-1\right)/\left(n-1\right)\right)$, for s = 1,2,,n$\mathit{s}=1,2,\dots ,n$ and xr,s = cos(π(r1) / (m1)) ${\stackrel{-}{x}}_{\mathit{r},s}=-\mathrm{cos}\left(\pi \left(\mathit{r}-1\right)/\left(m-1\right)\right)$, for r = 1,2,,m$\mathit{r}=1,2,\dots ,m$, (thus ms = m${m}_{s}=m$ for all s$s$), then the values k = m1$k=m-1$ and l = n1$l=n-1$ (so that the polynomial passes exactly through all the data points) should not give unwanted oscillations. Other datasets should be similarly satisfactory if they are everywhere at least as closely spaced as the above cosine values with m$m$ replaced by k + 1$k+1$ and n$n$ by l + 1$l+1$ (more precisely, if for every s$s$ the largest interval between consecutive values of arccosxr,s$\mathrm{arccos}{\stackrel{-}{x}}_{\mathit{r},s}$, for r = 1,2,,m$\mathit{r}=1,2,\dots ,m$, is not greater than π / k$\pi /k$, and similarly for the ys${\stackrel{-}{y}}_{s}$). The polynomial obtained should always be examined graphically before acceptance. Note that, for this purpose it is not sufficient to plot the polynomial only at the data values of x$x$ and y$y$: intermediate values should also be plotted, preferably via a graphics facility.
Provided the data are adequate, and the surface underlying the data is of a form that can be represented by a polynomial of the chosen degrees, the function should produce a good approximation to this surface. It is not, however, the true least squares surface fit nor even a polynomial in x$x$ and y$y$, the original variables (see Section 6 of Clenshaw and Hayes (1965), ), except in certain special cases. The most important of these is where the data values of x$x$ are the same on each line y = ys$y={y}_{s}$, (i.e., the data points lie on a rectangular mesh in the (x,y)$\left(x,y\right)$ plane), the weights of the data points are all equal, and xmax${x}_{\mathrm{max}}$ and xmin${x}_{\mathrm{min}}$ are both constants (in this case they should be set to the largest and smallest data values of x$x$, respectively).
If the dataset is such that it can be satisfactorily approximated by a polynomial of degrees k${k}^{\prime }$ and l${l}^{\prime }$, say, then if higher values are used for k$k$ and l$l$ in the function, all the coefficients aij${a}_{ij}$ for i > k$i>{k}^{\prime }$ or j > l$j>{l}^{\prime }$ will take apparently random values within a range bounded by the size of the data errors, or rather less. (This behaviour of the Chebyshev coefficients, most readily observed if they are set out in a rectangular array, closely parallels that in curve-fitting, examples of which are given in Section 8 of Hayes (1970).) In practice, therefore, to establish suitable values of k${k}^{\prime }$ and l${l}^{\prime }$, you should first be seeking (within the limitations discussed above) values for k$k$ and l$l$ which are large enough to exhibit the behaviour described. Values for k${k}^{\prime }$ and l${l}^{\prime }$ should then be chosen as the smallest which do not exclude any coefficients significantly larger than the random ones. A polynomial of degrees k${k}^{\prime }$ and l${l}^{\prime }$ should then be fitted to the data.
If the option to force the fit to contain a given polynomial factor in x$x$ is used and if zeros of the chosen factor coincide with data x$x$ values on any line, then the effective number of data points on that line is reduced by the number of such coincidences. A similar consideration applies when forcing the y$y$-direction. No account is taken of this by the function when testing that the degrees k$k$ and l$l$ have not been chosen too large.
Example
```function nag_fit_2dcheb_lines_example
m = [int64(8);7;7;6];
k = int64(3);
l = int64(2);
x = [0.1;
1;
1.6;
2.1;
3.3;
3.9;
4.2;
4.9;
0.1;
1.1;
1.9;
2.7;
3.2;
4.1;
4.5;
0.5;
1.1;
1.3;
2.2;
2.9;
3.5;
3.9;
1.7;
2;
2.4;
2.7;
3.1;
3.5 ];
y = [0;
1;
2;
4];
f = [1.01005;
1.10517;
1.17351;
1.23368;
1.39097;
1.47698;
1.52196;
1.63232;
2.0201;
2.23256;
2.4185;
2.61993;
2.75426;
3.01364;
3.13662;
3.15381;
3.34883;
3.41649;
3.73823;
4.00928;
4.2572;
4.43094;
5.92652;
6.10701;
6.35625;
6.54982;
6.81713;
7.09534 ];
w = ones(28, 1);
xmin = [0;
0.1;
0.4;
1.6];
xmax = [5;
4.5;
4;
3.5];
nux = [0];
nuy = [0];
[a, ifail] = nag_fit_2dcheb_lines(m, k, l, x, y, f, w, xmin, xmax, nux, nuy)
```
```
a =
15.3482
5.1507
0.1014
1.1472
0.1442
-0.1046
0.0490
-0.0031
-0.0070
0.0015
-0.0003
-0.0002
ifail =
0
```
```function e02ca_example
m = [int64(8);7;7;6];
k = int64(3);
l = int64(2);
x = [0.1;
1;
1.6;
2.1;
3.3;
3.9;
4.2;
4.9;
0.1;
1.1;
1.9;
2.7;
3.2;
4.1;
4.5;
0.5;
1.1;
1.3;
2.2;
2.9;
3.5;
3.9;
1.7;
2;
2.4;
2.7;
3.1;
3.5 ];
y = [0;
1;
2;
4];
f = [1.01005;
1.10517;
1.17351;
1.23368;
1.39097;
1.47698;
1.52196;
1.63232;
2.0201;
2.23256;
2.4185;
2.61993;
2.75426;
3.01364;
3.13662;
3.15381;
3.34883;
3.41649;
3.73823;
4.00928;
4.2572;
4.43094;
5.92652;
6.10701;
6.35625;
6.54982;
6.81713;
7.09534 ];
w = ones(28, 1);
xmin = [0;
0.1;
0.4;
1.6];
xmax = [5;
4.5;
4;
3.5];
nux = [0];
nuy = [0];
[a, ifail] = e02ca(m, k, l, x, y, f, w, xmin, xmax, nux, nuy)
```
```
a =
15.3482
5.1507
0.1014
1.1472
0.1442
-0.1046
0.0490
-0.0031
-0.0070
0.0015
-0.0003
-0.0002
ifail =
0
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https://math.cornell.edu/first-year-calculus | # First-Year Calculus
## Overview
Prospective math, science, computer science, economics, and engineering majors will all need some calculus and are advised to get an early start on this requirement. Students with one semester of advanced placement or transfer credit for calculus are advised to take a second semester of calculus immediately rather than postponing it. The material is fresher in the mind, and the instructor will give more review in the fall than in the spring.
## Precalculus
The standard prerequisite for freshman-level calculus is three years of high school mathematics, including trigonometry and logarithms. Students who need to take calculus but are lacking the necessary prerequisites should start with a precalculus course. MATH 1101: Calculus Preparation (fall only) is a 1-credit course that introduces a variety of topics of algebra to prepare students for MATH 1106 or 1110.
## Calculus I: Derivatives
Students who need to take calculus and do not have (or wish to forfeit) AP credit, should start with Calculus I. Options for Calculus I include:
• MATH 1106 - Modeling with Calculus for the Life Sciences (spring only)
• MATH 1110 - Calculus I
These courses have different emphases, and each takes a different perspective on the material than AP calculus classes.
MATH 1106 is an option for students whose major requires only one semester of calculus. Some topics are covered in less depth than in MATH 1110, while more advanced topics are introduced. MATH 1106 focuses on modeling using examples from the life sciences. It introduces some fundamental concepts of calculus and provides a brief introduction to differential equations.
MATH 1110 is the best choice for students who plan to take more calculus and is recommended for students who aren't sure about their plans but want to keep their options open. It goes in depth on the fundamental concepts of calculus, such as limits, derivatives, and integrals. It also uses more computations and algebraic manipulations by hand. Students who do very well in MATH 1106 may continue with MATH 1120, but some extra study will be necessary between semesters.
## Calculus II: Integrals and Series
After taking Calculus I or earning a 4 or 5 on the AP Calculus AB exam (or equivalent), students typically continue with Calculus II. Options for Calculus II include:
• MATH 1120 - Calculus II
• MATH 1910 - Calculus for Engineers
MATH 1120 is a good choice for students who need a standard second-semester calculus course and may or may not continue with more advanced mathematics courses.
MATH 1910 is the first course in a sequence designed for engineers that assumes familiarity with differential calculus as taught in MATH 1110. Students not in an engineering program or physical sciences major who take MATH 1910 may decide to continue with MATH 2130 or 2210 rather than 1920, but MATH 1910 is the best preparation for MATH 1920. | {"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": 0.8227787613868713, "perplexity": 1077.7771154461777}, "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/1679296945381.91/warc/CC-MAIN-20230326013652-20230326043652-00669.warc.gz"} |
http://www.springerplus.com/content/3/1/135 | # A new inversion method of estimation of simultaneous near surface bulk density variations and terrain correction across the Bandar Charak (Hormozgan-Iran)
Reza Toushmalani* and Azizalah Rahmati
Author Affiliations
Department of Computer, Faculty of engineering, Kangavar Branch, Islamic Azad University, Kangavar, Iran
For all author emails, please log on.
SpringerPlus 2014, 3:135 doi:10.1186/2193-1801-3-135
The electronic version of this article is the complete one and can be found online at: http://www.springerplus.com/content/3/1/135
Received: 16 January 2014 Accepted: 27 February 2014 Published: 10 March 2014
© 2014 Toushmalani and Rahmati; 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 credited.
### Abstract
A gravity inversion method based on the Nettleton-Parasnis technique is used to estimate near surface density in an area without exposed outcrop or where outcrop occurrences do not adequately represent the subsurface rock densities. Its accuracy, however, strongly depends on how efficiently the regional trends and very local (terrain) effects are removed from the gravity anomalies processed. Nettleton’s method implemented in a usual inversion scheme and combined with the simultaneous determination of terrain corrections. This method may lead to realistic density estimations of the topographical masses. The author applied this technique in the Bandar Charak (Hormozgan-Iran) with various geological/geophysical properties. These inversion results are comparable to both values obtained from density logs in the mentioned area and other methods like Fractal methods. The calculated densities are 2.4005 gr/cm3. The slightly higher differences between calculated densities and densities of the hand rock samples may be caused by the effect of sediment-filled valleys.
##### Keywords:
Inversion method; Estimation near surface bulk density variations; Terrain correction
### Introduction
Bulk density serves as an important parameter and it is needed to interpret gravity data and determine subsurface structures. Density can be estimated from hand samples when outcrop rocks are exposed. Samples collected in the field tend to have a bias toward lower values of density because they are more weathered, less fluid-saturated, or otherwise unrepresentative of the overall density. In regions that have no exposed outcrop borehole density, logs are useful for determining subsurface densities.
The researcher determined the estimate of subsurface densities by using an inversion technique based on Nettleton (1939), and Parasnis’s (1952) which has been described in Niti (Mankhemthong et al. 2012). The author applied these techniques to analyze the gravity data. The data has been collected in the Bandar Charak area in Hormozgan- Iran. In this case, Free Air anomaly data corrected from raw observed gravity and station coordinates were considered as observed data. The obtained density estimates from the inversion method were compared to existing density data from well logs’ density and rock outcrop sample measurements. Algorithms of the proposed method were implemented via using MATLAB from Math Works, Inc.
#### Geology of Bandar Charak area
Charak area is between latitudes 27_10, 27_140, and longitudes 53_350 and 53_590. The under study area is surrounded by Ashkenan, Ahal, Boochir, Hamiran, Hashniz and Kemeshck cities. Tabnack gas structure is located in the west of this district. The area can be accessed through Asalouie (Bandar Lengeh, Lamard, and Ashkenan-Gavbandy roads). The area has a very harsh topography with mountains and valleys. The climate of the area is very hot and wet in the summer and an average climate condition in the winter. From geological point of view, Dehnow area is a part of the Fars sedimentary basin in south-east of Iran. The evidences of the salt outcrops can be recognized at two points from Dehnow anticline. Khamy formation and Bangestan group are the oldest geological structures in the area that have outcrops. Younger structures consist of Aghajary, Mokhtari, Mishan, Gachsaran and Asmary. Dominant structural trend in the area is northwest- southeast. Dehnow anticline is located between Hendurabi and Razak faults. These faults are almost perpendicular to the Dehnow anticline. Taking the combined geological-residual gravity contour map into account a northwest-southeast trend can be considered for the Dehnow anticline. A low gravity anomaly fits well the salt outcrop in the southeast of the anticline. A basic study of the geology of the area, a detail investigation of structural features such as faults associated with the Dehnow anticline, and application of the geophysical techniques, and other exploration methods is necessary to investigate the subsurface extension of the this anticline and to identify salt plug intrusion into the anticline. Gravity anomalies are the result of the interference among geological sources with different shape, densities, and depths. Of particular interest to the geologist are the linear anomalies in geophysical maps which may correspond to buried faults, contacts, and other tectonic and geological features. Most short-wavelength anomalies are caused by near-surface contacts of rocks that have different density contrasts. (Esmaeil Zadeh, et al, 2010). Table 1 show Density determination by Sampling and System Measurement in Charak region and Figure 1show Geological map of Charak area.
Table 1. Density determination by sampling and system measurement in Charak region (Source: national oil company of Iran, Farmani (2003))
Figure 1. Geological map of Charak area (National Oil Company of Iran, 2003)
#### Formulations of Nettleton and parasnis density determination methods
Nettleton’s method is based on the observation that over an area of constant density no gravity anomalies should remain after applying the Bouguer correction (Papp, 2009), and that any residual Bouguer anomaly should represent the gravitational attraction of the body of interest. In the Bouguer correction formula, density value that provide the best fit of the Bouguer gravity represents the best estimate of the near surface density. Nettleton developed these methods as follow:
The relative Bouguer gravity anomaly (∆BA) between the reference station and any station is
(1)
Where,
BA = Gravity Bouguer anomaly
Gob = Absolute gravity
Gl = latitude correction
Gfc = Free air correction (0.3086 m Gal/m)
Gbc = Bouguer slab correction (0.418ρ m Gal/m) where ρ is a rock density in g/cm3
If the correction (∆Gbc) is ignored, Equation (1) is equivalent to the Free Air anomaly formula.
(2)
Where,
∆FA = Relative gravity Free Air anomaly.
(3)
According to Nettleton (1939), the relative Bouguer anomaly (∆BA) should go to zero if the correct subsurface density is applied during the Bouguer slab correction.
(4)
Where,
∆h = relative elevation change with respect to the reference station (R).
Parasnis’s method is based on the fact that the Bouguer anomaly can be expressed as an equation of the form of “y = mx + b” (Mankhemthong et al. 2012). If the region between the two stations is assumed to be homogeneous in topographic relief and density (ρ), equation (2) represents a straight line with classic form of y = mx, where the ∆FA are the y-values and 0.418∆h are the x-values. The calculated slope (m) corresponds to the average density (ρ) of the surface density rocks or sediments. The Nettleton and Parasnis methods can be used to determine near surface density if a small enough distance between gravity stations is considered. Therefore, deeper regional gravity effects do not dominate.
Rao and Murty (1973) noted that the Parasnis’s method ignored the existence of any regional gravity field. They considered the existence of uniform regional gradients in the x and y directions, with a new model where α∆x and β∆y are added to Equation (4). Here ∆x and ∆y are the distances between the gravity stations and the reference station in the x and y directions, respectively, α and β are prospered terms for unknown regional gradients that are uniform along the profiles of the two points in m Gal/km unit (Papp, 2009). After reducing the regional gravity with respect to near surface masses, it becomes:
(5)
∆x, ∆y, ∆h, and ∆FA are known parameters and a, b, and ρ are unknown parameters, while ρ representing the density of the subsurface. Note that Equation (5) is still a linear function of the form of “d = a1x1 + a2x2 + a3x3” Thus, a least squares inversion technique can be used to determine the unknown quantities.
#### Development of inversion scheme
In preset study, the researcher determined estimates of subsurface densities by using an inversion technique based on Nettleton (1939) and Parasnis (1952). The last method has been described in Niti (Mankhemthong). As described in the previous section, the unknowns in Equation (5) can be determined by using a least squares inversion method. We begin by formulating the problem as
(6)
Where Y is the vector of reduced ∆FA, A is a matrix of perfectly known parameters containing ∆x, ∆y, and ∆h, and x represents a vector of the unknowns (α, β, and ρ).
Following the technique of Jackson (1979), Equation (6) is weighted by the diagonal matrix of the estimated covariance uncertainties (Ca-1) of given free air anomalies, which are approximately 0.1-0.5 mGal.
(7)
Then, we multiply both side by AT to begin to formulate the least squares solution.
(8)
Following the method of Tarantola and Valette (1982), let Cp-1 be the expected covariance of the unknowns. It is assumed the covariance of the near surface density equal to the covariance of given densities from rock sample and density log measurements (~0.05 g/cm3). <x > is an expected unknown vector of a priori information. In an ideal situation, <x> should be equal to x.
Thus
(9)
And adding (10) to (11) gives;
(10)
Rearranging terms the below formula is obtained
(11)
Now x can be solved as:
(12)
Once the estimated unknown (x) is determined, the free air anomaly can be estimated as
(13)
#### Inversion results
Based on the obtained results, the calculated densities were around 2.4005 g/cm3, while the lab measurements resulted in an average value of 2.3 g/cm3. Because of Application of Fractal methods to determine the Bouguer density in Charak region, an averaged density value equal to 2.4 g/cm3 was calculated Mehrnia et al. (2013). The result is in a good agreement with lab measurement and Fractal estimations. Moreover, from the obtained data, it is possible to mention these values:
### Conclusions
Near surface density determinations based on the Nettleton-Parasnis inversion method can be utilized for estimating representative surface densities where no outcrop or log data may exist. Densities were determined by using two methods with consistent results: (1) Nettleton’s inversion, (2) rock sampling. Based on the results, the calculated densities are around 2.4005 g/cm3. The greater densities from the inversion method (compared to hand samples) over the mountain loops are probably caused by the effects of un modeled topographic relief or valley fill. The calculated density uncertainties reflected the complexities of near surface lithology and structural geology beneath selected gravity stations and provided valuable information on the range of acceptable densities that can be used in further 2.5-D and 3-D forward or inverse modeling in a region.
### Competing interests
The author declares that they have no competing interests.
### Authors’ contributions
Both authors read and approved the final manuscript.
### References
• Esmaeil Zadeh A, Doulati AF, Ziaii M, Mohammado Khorasani M (2010) Investigation of salt plugs intrusion into Dehnow anticline using image processing and geophysical magnetotelluric methods. Russ J Earth Sci 11:
ES3008, doi:10.2205/2009ES000375
• Farmani F (2003) Gravity explorations report in Namakin-Charak region. Persian: NIOC press. p 129
• Jackson DD (1979) The use of a priori data to resolve non-uniqueness in linear inversion. Geophys J R Astron Soc 57:137-157 Publisher Full Text
• Mankhemthong N, Doser DI, Baker MR (2012) Practical Estimation of Near-surface Bulk Density Variations Across the Border Ranges Fault System, Central Kenai Peninsula, Alaska. J Environ Eng Geophys 17(3):51-158
• Mehrnia R, Ebrahimzadeh Ardestani V, Teymoorian A (2013) Application of fractal methods to determine the Bouguer density in Charak Region (South of Iran). Geophysical J Iran 7(1):34-50
• Nettleton LL (1939) Determination of density for reduction of gravitimeter observations. Geophysics 4:8176-8183
• Papp G (2009) Simultaneous determination of terrain correction and local average topographic density. Acta Geodaetica et Geophysica Hungarica 44:191-202 Publisher Full Text
• Parasnis DS (1952) A study of rock densities in English Midlands. Geophys J Int 6:252-271
• Rao VB, Murty BVS (1973) Note on Parasnis’ method for surface density. Pure Appl Geophys 110:1927-1931 Publisher Full Text
• Tarantola A, Valette B (1982) Generalized non-linear inverse problems solved using least squares Criterion. Rev Geophys Space Phys 20:219-232 Publisher 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": 0.8738207817077637, "perplexity": 3805.6580836202907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398445679.7/warc/CC-MAIN-20151124205405-00122-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/conservation-law-using-killing-vector.244024/ | # Conservation law using Killing vector
1. Jul 8, 2008
### stephenmitten
In Hartle's GR book (p. 177), there is a derivation of $$\xi \cdot u = constant$$, where $$\xi$$ is a Killing vector, $$u$$ is four-velocity along a geodesic in an arbitrary metric, and
$$L = (-g_{\alpha\beta}\frac{dx^\alpha}{d\sigma}\frac{dx^\beta}{d\sigma})^\frac{1}{2}$$
The derivation goes:
$$\frac{\partial}{\partial \sigma}\frac{\partial L}{\partial \frac{dx^1}{d\sigma}}} = 0 \\ \Rightarrow \frac{\partial L}{\partial \frac{dx^1}{d\sigma}} = -g_{1\beta}\frac{1}{L}\frac{dx^\beta}{d\sigma} = ... = -\xi \cdot u$$
is conserved along the geodesic. (Here the symmetry associated with $$\xi$$ is in $$x^1$$.) It seems to be saying that
$$\frac{\partial L}{\partial \frac{dx^1}{d\sigma}} = \frac{1}{2L}({-g_{\alpha 1}\frac{1}{L}\frac{dx^\alpha}{d\sigma}-g_{1\beta}\frac{1}{L}\frac{dx^\beta}{d\sigma}) = {-g_{1\beta}\frac{1}{L}\frac{dx^\beta}{d\sigma}$$
but it appears to me that $$\frac{\partial L}{\partial \frac{dx^1}{d\sigma}}$$ has only seven terms, not eight, since $$-g_{11}\frac{dx^1}{d\sigma}}\frac{dx^1}{d\sigma}}$$ appears only once. I'd appreciate it if someone could point out where I went wrong.
Thanks.
Last edited: Jul 8, 2008
Can you help with the solution or looking for help too?
Draft saved Draft deleted
Similar Discussions: Conservation law using Killing vector | {"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": 0.9006714820861816, "perplexity": 690.3699990638781}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718840.18/warc/CC-MAIN-20161020183838-00067-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://planetmath.org/pathintegral | # path integral
The path integral is a generalization of the integral that is very useful in theoretical and applied physics. Consider a vector field $\vec{F}\!:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}$ and a path (http://planetmath.org/PathConnected) $\gamma\subset\mathbb{R}^{n}$. The path integral of $\vec{F}$ along the path $\gamma$ is defined as a definite integral. It can be constructed to be the Riemann sum of the values of $\vec{F}$ along the curve $\gamma$. Thusly, it is defined in terms of the parametrization of $\gamma$, mapped into the domain $\mathbb{R}^{n}$ of $\vec{F}$. Analytically,
$\int_{\gamma}\vec{F}\cdot d\vec{x}=\int_{a}^{b}\vec{F}(\vec{\gamma}(t))\cdot d% \vec{x}$
where $\vec{\gamma}(a),\vec{\gamma}(b)$ are elements of $\mathbb{R}^{n}$, and $d\vec{x}=\langle\frac{dx_{1}}{dt},\cdots,\frac{dx_{n}}{dt}\rangle dt$ where each $x_{i}$ is parametrized into a function of $t$.
Proof and existence of path integral:
Assume we have a parametrized curve $\vec{\gamma}(t)$ with $t\in[a,b]$. We want to construct a sum of $\vec{F}$ over this interval on the curve $\gamma$. Split the interval $[a,\,b]$ into $n$ subintervals of size $\Delta t=(b-a)/n$. Note that the arc lengths need not be of equal length, though the intervals are of equal size. Let $t_{i}$ be an element of the $i$th subinterval. The quantity $|\vec{\gamma}^{\prime}(t_{i})|$ gives the average magnitude of the vector tangent to the curve at a point in the interval $\Delta t$. $|\vec{\gamma}^{\prime}(t_{i})|\Delta t$ is then the approximate arc length of the curve segment produced by the subinterval $\Delta t$. Since we want to sum $\vec{F}$ over our curve $\vec{\gamma}$, we let the range of our curve equal the domain of $\vec{F}$. We can then dot this vector with our tangent vector to get the approximation to $\vec{F}$ at the point $\vec{\gamma}(t_{i})$. Thus, to get the sum we want, we can take the limit as $\Delta t$ approaches 0.
$\lim_{\Delta t\rightarrow 0}\sum_{a}^{b}\vec{F}(\vec{\gamma}(t_{i}))\cdot\vec{% \gamma}^{\prime}(t_{i})\Delta t$
This is a Riemann sum, and thus we can write it in integral form. This integral is known as a path or line integral (the older name).
$\int_{\gamma}\vec{F}\cdot d\vec{x}=\int_{a}^{b}\vec{F}(\vec{\gamma}(t))\cdot% \vec{\gamma}^{\prime}(t)dt$
Note that the path integral only exists if the definite integral exists on the interval $[a,\,b]$.
A path integral that begins and ends at the same point is called a closed path integral, and is denoted with the summa symbol with a centered circle: $\oint$. These types of path integrals can also be evaluated using Green’s theorem.
Another property of path integrals is that the directed path integral on a path $\Gamma$ in a vector field is equal to the negative of the path integral in the opposite direction along the same path. A directed path integral on a closed path is denoted by summa and a circle with an arrow denoting direction.
Visualization Aids:
This is an image of a path $\gamma$ superimposed on a vector field $\vec{F}$.
This is a visualization of what we are doing when we take the integral under the curve $S:P\rightarrow\vec{F}$.
Title path integral PathIntegral 2013-03-22 12:16:14 2013-03-22 12:16:14 slider142 (78) slider142 (78) 19 slider142 (78) Definition msc 81S40 msc 46T12 line integral ComplexIntegral ContourIntegral RealAndImaginaryPartsOfContourIntegral | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 42, "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": 0.9995967745780945, "perplexity": 143.62772598803681}, "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-2019-13/segments/1552912203547.62/warc/CC-MAIN-20190325010547-20190325032547-00538.warc.gz"} |
https://research.aston.ac.uk/en/publications/nonlinear-fourier-transform-for-analysis-of-coherent-structures-i | # Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems
I. S. Chekhovskoy, O. V. Shtyrina, M. P. Fedoruk, S. B. Medvedev, S. K. Turitsyn
Research output: Contribution to journalArticle
### Abstract
Using the cubic Ginzburg-Landau equation as an example, we demonstrate how the inverse scattering transform can be applied to characterize coherent structures in dissipative nonlinear systems. Using this approach one can reduce the number of the effective degrees of freedom in the system when the dynamic is dominated by the coherent structures, even if they are embedded in the dispersive waves and demonstrate unstable behavior.
Original language English 153901 Physical Review Letters 122 15 https://doi.org/10.1103/PhysRevLett.122.153901 Published - 15 Apr 2019
### Bibliographical note
© 2019 American Physical Society. Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems. I. S. Chekhovskoy, O. V. Shtyrina, M. P. Fedoruk, S. B. Medvedev, and S. K. Turitsyn. Phys. Rev. Lett. 122, 153901 – Published 15 April 2019 | {"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": 0.8899751901626587, "perplexity": 1838.0712206795272}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400249545.55/warc/CC-MAIN-20200926231818-20200927021818-00006.warc.gz"} |
http://physics.stackexchange.com/questions/22862/finding-electric-power-generated-using-heat-transfer/22866 | # Finding electric power generated using heat transfer
I'm working through an example I have been given to study. Suppose I have a 2m X 4m photovoltaic panel on my roof that is irradiated with a solar flux of $G_s = 700W/m^2$.
Given:
$\alpha_s = 0.83$
$\eta = P/\alpha_sG_sA = 0.553-0.001T_p/K$
$\epsilon = 0.90$ $T_{sur} = T_\infty = 35^oC$
$h = 10W/m^2K$
I want to find how much electric power is generated. I start by using the energy balance equation.
$E_{in} - E_{out} + E_{generated} = E_{stored}$
$E_{in} = \alpha_sG_sA$
$E_{out} = \epsilon\sigma(T_s^4 - T_{sur}^4)A + h(T_s - T_\infty)$
$E_{generated} = -P_{elec}$
$E_{stored} = 0$
Okay, so here is my first question - why is $E_{generated} = -P_{elec}$ and not $E_{generated} = +P_{elec}$? Where did the negative come from?
After plugging it all into the energy balance equation, I get: $\alpha_sG_sA -[\epsilon\sigma(T_s^4 - T_{sur}^4)A + h(T_s - T_\infty)]-P_{elec} = 0$
$(0.83)(700)(2)(4) -[(0.90)(5.67X10^{-8})((T_p)^4 - (35+273)^4)(2)(4) + (10)(T_p - (35+273))]- (0.553-0.001T_p)(0.83)(700)(2)(4) = 0$
Plugging this into my TI-89 calculator, I get $T_p = -666.633$ or $T_p = 335.051$
Obviously, I take $T_p = 335$ since it probably shouldn't go below absolute zero :-) but since I am asking questions - what does the negative value represent? Does it mean anything at all?
Now that I have $T_p$, I plug that into $\eta = P/\alpha_sG_sA = 0.553-0.001T_p/K$ to solve for the power generated. If I do it this way, I get $P = 1010W$. Here's a funny problem, though - if I plug $T_p$ into $\alpha_sG_sA -[\epsilon\sigma(T_p^4 - T_{sur}^4)A + h(T_p - T_\infty)]-P_{elec} = 0$, I get $P = 1032W$. Why the difference? Does it have something to do with the way the calculator solves the problem? Or is there a mistake somewhere?
Thanks so much for looking at this and leading me in the right direction.
-
You wrote effectively the following:
$$E_{in} - E_{out} - P_{elec} = 0$$
We just need to look at the balances. All of the variables in the above equation are positive. The $E_{in}$ term is energy coming in from the sun. You have energy entering the system and energy leaving the system. The electric power production is energy leaving the system that would have otherwise went to heat (and then radiating or convecting). It didn't, it left in the form of electrons crossing an electric potential. This same accounting goes on for all power producing technology. Electrical power is energy leaving the system.
I don't understand the use of $T_{sur}$ by the way. Looking at a balance of radiative heat transfer, you've accounted for radiative absorption from the sun in another term. So what's the use of this one? It seems like the other transfer would be from the sky to the panel, and I don't think it would be handled in this way.
There could be some transfer from the Earth's surface to the panel, but it wouldn't be the full angle. The panel points to the sky.
- | {"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": 0.8931936025619507, "perplexity": 232.9084533036567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049276131.97/warc/CC-MAIN-20160524002116-00063-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.springerprofessional.de/fluids-under-pressure/17945340 | main-content
## Über dieses Buch
This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include:Oceanic and atmospheric dynamicsIncompressible flowsViscous compressible flowsWell-posedness of the Navier-Stokes equationsWeak solutions to the Navier-Stokes equationsFluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.
## Inhaltsverzeichnis
### Chapter 1. An Approach to the Primitive Equations for Oceanic and Atmospheric Dynamics by Evolution Equations
Abstract
The primitive equations for oceanic and atmospheric dynamics are a fundamental model for many geophysical flows. In this chapter we present a summary of an approach to these equations based on the theory of evolution equations. In particular, we discuss the hydrostatic Stokes operator, well-posedness results in critical spaces within the L p(L q)-scale, within the scaling invariant space L (L 1) for Neumann boundary conditions, and within the L (L p) space for mixed boundary conditions and p > 3. In addition, we investigate real analyticity of solutions, convergence of the scaled Navier-Stokes equations to the primitive equations, and the existence of periodic solutions for large forces.
Matthias Hieber, Amru Hussein
### Chapter 2. Viscous Compressible Flows Under Pressure
Abstract
This chapter deals with the role of pressure in the theory of viscous compressible flows. The pressure state laws and viscosities are described. Special attention is devoted to non-monotone pressure laws and pressure dependent viscosities. The global existence proofs are discussed for approximate systems. Some relevant physical applications are described, including among others the anelastic Euler equations, shallow water model, granular media, or mixture problems.
Didier Bresch, Pierre-Emmanuel Jabin
### Chapter 3. Global Well-Posedness for Incompressible–Incompressible Two-Phase Problem
Abstract
This chapter is devoted to some mathematical analysis of the two-phase problem for the viscous incompressible–incompressible capillary flows separated by sharp interface, this problem being called two-phase problem for short, and the Stokes equations with transmission conditions on the sharp interface which is arised from the two-phase problem.
The maximal regularity is a character of the system of equations of parabolic type, and it is a very powerful tool in solving quasilinear equations of parabolic type. The authors of this lecture note have developed a systematic method to derive the maximal regularity theorem for the initial-boundary value problem for the Stokes equations with non-homogeneous boundary conditions, which is based on the $$\mathcal {R}$$ bounded solution operators theory and L. Weis’ operator valued Fourier multiplier theorem. The notion of $$\mathcal {R}$$ boundedness plays an essential role in the Weis’ theory, which takes the place of boundedness in the standard Fourier multiplier theorem of Marcinkiewicz-Mikhilin-Hölmander type.
In this lecture note, we explain how to use the $$\mathcal {R}$$-bounded solution operators to derive the maximal regularity theorem for the Stokes equations with transmission conditions, and as an application of our maximal regularity theorem, we prove the local well-posedness of the two-phase problem, where the solutions are obtained in the L p in time and L q in space maximal regularity class. So far, this framework gives us the best possible regularity class of parabolic quasilinear equations.
Moreover, we prove the global well-posedness for the two-phase problem both in the bounded domain case and the unbounded domain case. A key tool is the decay property of the C 0 analytic semigroup associated with the Stokes equations with transmission conditions. In the bounded domain case, the decay properties are obtained essentially from the analysis of zero eigenvalue. As a result we prove the exponential stability of our C 0 analytic semigroup in some quotient space, which, together with the conservation of momentum and angular momentum and the maximal regularity theorem, yields the global well-posedness in the case of small initial data and the ball-like reference domain.
On the other hand, in the unbounded domain case, the zero is a continuous spectrum for the Stokes equations with transmission conditions, and so we can prove the polynomial decay properties for the C 0 analytic semigroup only, which, combined with L p-L q maximal regularity theorem with suitable choices of p and q, yields the L p time summability of the L q space norm of solutions to the nonlinear problem. From this we prove the global well-posedness for the small initial data in the unbounded domain case. Notice that the L p summability yields L 1 summability in view of the Hölder inequality, which is enough to handle the kinetic equations.
What we want to emphasize here is that our method is based on the construction of $$\mathcal {R}$$ bounded solution operators and spectral analysis of the zero eigenvalue or generalized eigenvalue of the generalized resolvent problem for the Stokes equations with transmission conditions. The spectral analysis here can be used widely to study the other parabolic linear and quasilinear equations arising from the mathematical study of viscous fluid flows as well as other models in mathematical physics like MHD, multicomponent flows, namatic crystal flows, and so on.
Yoshihiro Shibata, Hirokazu Saito
### Chapter 4. The Role of Pressure in the Theory of Weak Solutions to the Navier-Stokes Equations
Abstract
Sections 4.1 and 4.2 contain an introduction, notation and definitions and basic properties of used function spaces and operators. A pressure, associated with a weak solution to the Navier-Stokes equations for incompressible fluid, is constructed in Sect. 4.3. The interior regularity of the pressure in regions, where the velocity satisfies Serrin’s integrability conditions, is studied in Sect. 4.4. Finally, Sect. 4.5 is devoted to criteria of regularity for weak solutions to the Navier-Stokes equations, formulated in terms of the pressure.
Jiří Neustupa
### Chapter 5. Flows of Fluids with Pressure Dependent Material Coefficients
Abstract
It has been well documented in many studies that the material parameters of a fluid may essentially depend on the pressure and that they can vary by several orders of magnitude. The material parameters, for which this dependence is observed, are mainly the viscosity (due to the internal forces in the fluid) and the friction (due to fluid–(rigid) solid interaction). In addition, these large variations with respect to the pressure in the material parameters occur although the variations of the density are almost negligible (in comparison with other parameters). Therefore it is still reasonable to describe the above mentioned phenomena in many fluids by incompressible models. Likewise, the viscosity and the drag of many fluids vary with the shear rate and such shear (rate)-dependent viscosity and friction are extensively used, ranging from geophysics, chemical engineering, and bio-material science up to the food industry, enhanced oil recovery, carbon dioxide sequestration, or extraction of unconventional oil deposits, etc.
The aim of this study is to present an overview of available results for models with very complicated rheological laws used in engineering praxes. As particular examples that fit into the class of models studied here, we refer to the Darcy model, to the Brinkman models, and to the Bingham models. Nevertheless, the aim of this study is much more ambitious and we go much beyond these standard models and present a kind of unifying theory, which is based on the use of the so-called maximal monotone graphs, which seems to be very appropriate from the point of view of mathematical analysis of the problem.
Miroslav Bulíček
### Chapter 6. Finite Element Pressure Stabilizations for Incompressible Flow Problems
Abstract
The simulation of incompressible flow problems with pairs of velocity-pressure finite element spaces that do not satisfy the discrete inf-sup condition requires a so-called pressure stabilization. This chapter provides a survey of available methods which are presented for the Stokes problem to concentrate on the main ideas and to avoid additional difficulties originating from more complicated models. The methods can be divided into residual-based stabilizations and stabilizations that utilize only the pressure. For the first class, a comprehensive numerical analysis is presented, whereas for the second class, the presentation is more concise except for a detailed analysis of a local projection stabilization method. Connections of various pressure stabilizations to inf-sup stable discretizations with velocity spaces enriched by bubble functions are also discussed. Numerical studies compare several of the available pressure stabilizations.
Volker John, Petr Knobloch, Ulrich Wilbrandt
### Chapter 7. Finite-Volume Methods for Navier-Stokes Equations
Abstract
Flows of engineering interest can only be predicted by using numerical solution methods, because the governing equations cannot be solved analytically. Among many possible approaches, finite-volume methods have become popular in this field and are the basis for most commercial and public computer codes used to simulate fluid flow. One of the most widely used methods, which is applicable to complex geometries and arbitrary polyhedral computational grids, is described in this chapter. The solution method was originally developed for incompressible flows and later extended to compressible flows at any speed. It is also described how to deal with moving grids which follow the motion of solid bodies. The applicability of the method to various flow types is demonstrated by simulating flow around sphere at various Reynolds numbers, ranging from a creeping flow at Re = 5 to a supersonic flow at Re = 5,000,000. The final example involves a sphere oscillating in water at 6000 Hz with a very small amplitude, which requires that compressibility of water is taken into account. The fact that the same method can be applied to such a wide class of flows, including a wide range of turbulence-modeling approaches, is the main reason why it is used in general-purpose commercial codes.
Milovan Perić
Weitere Informationen | {"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": 0.8698096871376038, "perplexity": 445.9784709439256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348519531.94/warc/CC-MAIN-20200606190934-20200606220934-00292.warc.gz"} |
https://arxiv.org/abs/gr-qc/0305029 | gr-qc
(what is this?)
# Title: On the dynamics of Gowdy space times
Abstract: We study the behavior near the singularity t=0 of Gowdy metrics. We prove existence of an open dense set of boundary points near which the solution is smoothly "asymptotically velocity term dominated" (AVTD). We show that the set of AVTD solutions satisfying a uniformity condition is open in the set of all solutions. We analyse in detail the asymptotic behavior of "power law" solutions at the (hitherto unchartered) points at which the asymptotic velocity equals zero or one. Several other related results are established.
Comments: latex 2e, a few figures, several style files, 69 pages Subjects: General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:gr-qc/0305029 (or arXiv:gr-qc/0305029v1 for this version)
## Submission history
From: Piotr Chrusciel [view email]
[v1] Thu, 8 May 2003 08:54:26 GMT (92kb) | {"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": 0.8342658877372742, "perplexity": 2865.3741113155525}, "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-2017-22/segments/1495463605188.47/warc/CC-MAIN-20170522151715-20170522171715-00032.warc.gz"} |
http://mathhelpforum.com/differential-geometry/25496-pursuit-curve-differential-geom.html | # Thread: PURSUIT CURVE (differential geom)
1. ## PURSUIT CURVE (differential geom)
I have here a problem in my Diff. Geom class.
----> Suppose an enemy plane begins at (0,0) and travels up the y-axis at constant speed $v_{p}.$ A missile is fired at (a,0) with speed $v_{m}$ and the missile has a heat sensor which always directs it toward the plane.
1.] Show that the pusuit curve which the missile follows is given implicitly by the differential-integral equation
$y=xy^{'}+ \frac{v_{p}}{v_{m}} \int \sqrt{1+y^{' 2}}dx$
2.] Differentiate this expression to get a separable diff. eq. Integate to get the closed form expression fo the pusuit cuve
$y= \frac{a^{\frac{v_{p}}{v_{m}}}}{2(1-\frac{v_{p}}{v_{m}})} [x^{1-\frac{v_{p}}{v_{m}}}-\frac{v_{p}}{v_{m}} a^{1-\frac{v_{p}}{v_{m}}}] - \frac{a^{-\frac{v_{p}}{v_{m}}}}{2(1+\frac{v_{p}}{v_{m}})} [x^{1+\frac{v_{p}}{v_{m}}}+\frac{v_{p}}{v_{m}} a^{1+\frac{v_{p}}{v_{m}}}]$
I already finished no.1. I did no.2 but I got a slightly different answer from the right hand side of the eq. there. Can someone help me out?
2. I cannot answer this question, as it goes against my pacifist beliefs. | {"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": 0.9509300589561462, "perplexity": 1337.860614413946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549425737.60/warc/CC-MAIN-20170726002333-20170726022333-00539.warc.gz"} |
http://hal.in2p3.fr/in2p3-01410271 | Can tetraneutron be a narrow resonance?
Abstract : The search for a resonant four-neutron system has been revived thanks to the recent experimental hints reported in Phys. Rev. Lett. 116, 052501 (2016). The existence of such a system would deeply impact our understanding of nuclear matter and requires a critical investigation. In this work, we study the existence of a four-neutron resonance in the quasi-stationary formalism using ab initio techniques with various two-body chiral interactions. We employ the No-Core Gamow Shell Model and the Density Matrix Renormalization Group method, both supplemented by the use of natural orbitals and a new identification technique for broad resonances. We demonstrate that while the energy of the four-neutron system may be compatible with the experimental value, its width must be larger than the reported upper limit, supporting the interpretation of the experimental observation as a reaction process too short to form a nucleus.
Document type :
Journal articles
http://hal.in2p3.fr/in2p3-01410271
Contributor : Michel Lion <>
Submitted on : Tuesday, December 6, 2016 - 3:30:23 PM
Last modification on : Wednesday, August 7, 2019 - 2:32:05 PM
Citation
K. Fossez, J. Rotureau, N. Michel, M. Ploszajczak. Can tetraneutron be a narrow resonance?. Physical Review Letters, American Physical Society, 2017, 119, pp.032501. ⟨10.1103/PhysRevLett.119.032501⟩. ⟨in2p3-01410271⟩
Record views | {"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": 0.843484103679657, "perplexity": 1865.0202727424435}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986684425.36/warc/CC-MAIN-20191018181458-20191018204958-00336.warc.gz"} |
https://byjus.com/chemistry/henrys-law/ | # Henry's Law
## What is Henry’s Law?
Henry’s law is a gas law which states that at the amount of gas that is dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid when the temperature is kept constant. The constant of proportionality for this relationship is called Henry’s law constant (usually denoted by ‘kH‘). The mathematical formula of Henry’s law is given by:
P ∝ C (or) P = kH.C
Where,
• ‘P’ denotes the partial pressure of the gas in the atmosphere above the liquid.
• ‘C’ denotes the concentration of the dissolved gas.
• ‘kH’ is the Henry’s law constant of the gas.
## Introduction
This law was formulated in the early 19th century by the English chemist William Henry. It can be noted that the Henry’s law constant can be expressed in two different ways. If the constant is defined in terms of solubility/pressure, it is referred to as the Henry’s law solubility constant (denoted by ‘H’). On the other hand, if the proportionality constant is defined in terms of pressure/solubility, it is called the Henry’s law volatility constant (denoted by ‘kH’).
An illustration detailing the relationship between the solubility of a gas in a liquid and the partial pressure of that gas in the atmosphere above the liquid (as dictated by Henry’s law) is provided above. Note that the greater the partial pressure of the gas, the greater its solubility in the liquid.
## Examples of Henry’s Law
### Pepsi and other Carbonated Drinks
Henry’s law comes into play every time a bottle of Pepsi (or any other carbonated drink) is opened. The gas above the unopened carbonated drink is usually pure carbon dioxide, kept at a pressure which is slightly above the standard atmospheric pressure. As a consequence of Henry’s law, the solubility of carbon dioxide in the unopened drink is also high.
When the bottle is opened, the pressurized CO2 escapes into the atmosphere (which is usually accompanied by a hissing sound). As the partial pressure of CO2 in the atmosphere above the drink rapidly decreases, the solubility of the carbon dioxide in the drink also decreases (due to Henry’s law). This causes the dissolved CO2 to come to the surface of the drink in the form of tiny bubbles and escape into the atmosphere.
If the carbonated drink is left open long enough, the concentration of carbon dioxide in the drink will reach an equilibrium with the concentration of carbon dioxide in the atmosphere (~0.05%), causing it to go flat (the drink loses its ‘fizzy’ taste).
### Respiration and the Oxygenation of Blood
In the process of respiration, inhalation is accompanied by an increase in the partial pressure of oxygen in the alveoli. When deoxygenated blood interacts with the oxygen-rich air in the alveoli, the following gas-exchanges take place as a consequence of Henry’s law:
• Since the partial pressure of oxygen in the alveoli is high and the amount of dissolved oxygen in the deoxygenated blood is low, oxygen flows from the alveoli into the deoxygenated blood.
• The partial pressure of carbon dioxide in the alveoli is very low (CO2 constitutes approximately 0.05% of the atmosphere). Since the concentration of dissolved CO2 in the deoxygenated blood is very high, the gas moves from the blood into the alveoli. This carbon dioxide is expelled from the body via exhalation.
Thus, Henry’s law plays an integral role in the respiration of many organisms.
## Factors Affecting the Henry’s Law Constant
The value of the Henry’s law constant of a gas is dependent on the following factors:
• The nature of the gas
• The nature of the solvent
• Temperature & pressure
Therefore, different gases have different Henry’s laws constant in different solvents, as illustrated graphically below.
## Limitations of Henry’s Law
• This law is only applicable when the molecules of the system are in a state of equilibrium.
• Henry’s law does not hold true when gases are placed under extremely high pressure.
• The law is not applicable when the gas and the solution participate in chemical reactions with each other.
## Solved Examples
### Example 1
Calculate the solubility of gaseous oxygen in water at a temperature of 293 K when the partial pressure exerted by O2 is 1 bar. (Given: kH for O2 34840 bar.L.mol-1)
As per Henry’s law, P = kH*C
Substituting, kH = 34840 bar.L.mol-1 and P = 1 bar, the equation becomes
C = 1/34840 mol.L-1 = 2.87*10-5 mol/L
Therefore, the solubility of oxygen in water under the given conditions is 2.87*10-5 M.
### Example 2
The value of kH for carbon dioxide at a temperature of 293 K is 1.6*103 atm.L.mol-1. At what partial pressure would the gas have a solubility (in water) of 2*10-5 M?
Substituting the given values kH = 1.6*103 atm.L.mol-1 and C = 2*10-5 M into the Henry’s law formula:
P = kH*C = (1.6*103 atm.L.mol-1) * (2*10-5 mol.L-1) = 0.032 atm.
## Frequently Asked Questions on Henry’s Law
### Henry’s Law does not apply to which gas? Why?
• Gases such as NH3 and CO2 do not obey Henry’s law.
• This is due to the fact that these gases react with water.
NH3 +H2O → NH4+ + OH
CO2 + H2O → H2CO3
• They have higher solubilities than expected by Henry’s law due to reactions of gases such as NH3, and CO2(g).
### What are the conditions for using Henry’s Law?
Henry’s law is only applicable when the molecules are in equilibrium. Henry’s law does not apply to gases at high pressures (for example, N2(g) at high pressure becomes very soluble and dangerous when introduced into the blood supply).
### What does Henry’s law constant depend on?
It’s important to remember that Henry’s law constants are highly temperature-dependent because vapour pressure and solubility are both temperature-dependent.
### What is the unit for Henry’s law constant?
Henry’s law constant is expressed in mol L–1 bar–1.
### What are the Limitations of Henry’s Law?
The limitations of Henry’s law are as follows:
• The law is only valid when the molecules in the system are in equilibrium.
• When the gases are under extremely high pressure, Henry’s Law does not apply.
• This law also does not apply when the solution and gas are involved in a chemical reaction with each other. | {"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": 0.8705193996429443, "perplexity": 1105.5149466339817}, "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/1669446710890.97/warc/CC-MAIN-20221202014312-20221202044312-00281.warc.gz"} |
https://math.stackexchange.com/questions/2629212/questions-on-how-to-prove-that-a-set-of-connectives-is-not-functionally-complete | # Questions on how to prove that a set of connectives is NOT functionally complete
In my textbook I am introduced to two ways to prove that a set of connectives is functionally incomplete. The first one is to prove that it has a property that not all truth functions do.
I am stuck at finding one such property for $\{\lnot\}$ (and I can't believe I am so dumb to be stuck...). I have two ideas: first one is to prove that $\lnot$ always returns a $F$ for any true argument (thus rendering a truth function that returns $T$ from a true arugment impossible).
Prove that if $\phi$ is built up using the variable $P$ with $\lnot$, and $v$ is the truth assignment s.t. $v(p)=T$, then $v(\phi)=F$.
Induction on the number $n$ of connectives in $\phi$.
Base case $n=0$: $\phi=P$ - there isn't any $\lnot$ to talk about, so it is vacuously true.
Assume that it holds true for $\le n$, prove that it holds true for $n+1$.
$\phi=\lnot \psi$: Number of connectives within $\psi=n$, thus it holds true for $\psi$. Therefore $v(p)=T\to v(\psi)=F$.
As you can see, if $v(\psi)=F$, then $v(\phi)=v(\lnot \psi)=T$, which is not what we want. This seems to be an instance of double negation; it can flip whatever truth value to the opposite, so it seems futile to try and show that there is a truth function $\{\lnot\}$ cannot show, because with double negation you can always show a $T/F$.
The second idea to show that a negation can only show a truth function with one argument, but not one with more than one. But this seems only to be a syntactical problem: yes, you can't show a formula of $>1$ variables with only negation, but you can still draw a truth table for it nonetheless.
So my first question is,
1) what went wrong with my proof, and how to prove $\{\lnot\}$ is functionally incomplete by showing a property that only this set has?
The second way is to show how many truth functions of $n$ arguments can be represented; if this number is $<2^{2^n}$, then it is not complete; vice versa.
The book showed how to use this approach to prove that $\{\land\}$ is incomplete. The number for this set is $2^n -1$. My question is,
2) how do we know the number for $\{\lnot,\land,\lor\}=2^{2^n}$?
It must be so since it is complete, but I just don't know how to prove it.
(The book equivalated formulas $\phi$ built up using variables in the set $\{p_1, p_2, . . . , p_n\}$ to a normal form where no parenthesis remains and only variables are left, and explained that the number of non-empty subsets of this set of variables used to build the normal form $=2^n -1$. e.g. $\phi=(p_3\land p_1)\land (p_2\land(p_1\land p_4))$, normal form=$p_1\land p_2 \land p_3 \land p_4$)
Really appreciate any help offered!
• Using $\lnot$ you can only create two functions. Jan 31, 2018 at 5:56
• If you assign $F$ to all variables, any formula composed with the connective $\land$ has the value $F$. Jan 31, 2018 at 6:02
• Use the Boole expansion and induction to show that a formula can be created for any given truth table. Jan 31, 2018 at 6:05
• which textbook are you using may I ask? Oct 17, 2018 at 17:57
• Thank you! @DanielMak Oct 18, 2018 at 6:49
Daniil wrote an excellent post, but just to add to that a little bit:
As Daniil pointed out, you can't capture any truth-functions that non-trivially depend on more than $1$ variable, such as $P \land Q$, with only a $\neg$. So, let's restrict ourselves to functions defined over one variable, $P$, and see if maybe we can capture all those using a $\neg$?
Unfortunately, the answer is still no. Again, as Daniil already pointed out, we can't capture any tautology or contradiction. That is, we can't capture the truth-function that always returns true (i.e. the function $f$ such that $f(T)=f(F)=T$), nor can we capture the truth-function that always returns false (i.e. the function $f'$ such that $f'(T)=f'(F)=F$)
So in this post I just wanted to show you how you can prove that result using induction. In particular, let's prove the following:
Claim
For any expression $\phi$ built up from $P$ and $\neg$ alone, it will be true that if $v$ is the valuation that sets $P$ to true (i.e. $v(P)=T$), and $v'$ is the valuation that sets $P$ to false (i.e. $v'(P)=F$), then either $v(\phi)=T$ and $v'(\phi)=F$, or $v'(\phi)=T$ and $v(\phi)=F$ (in other words, $v(\phi)$ and $v'(\phi)$ will always opposite values, meaning that $\phi$ can not be a tautology or contradiction, for that would require that $\phi$ has the same value for any valuation)
Proof
We'll prove the claim by structural induction on the formation of $\phi$:
*Base: *
$\phi=P$. Then $v(\phi)=v(P)=T$, while $v'(\phi)=v'(P)=F$. Check!
Step:
If $\phi$ is not an atomic proposition, then there is only one possibility: $\phi$ is the negation of some other statement $\psi$, i.e. $\phi = \neg \psi$.
Now, by inductive hypothesis we can assume that $v(\psi)=T$ and $v'(\psi)=F$, or $v'(\psi)=T$ and $v(\psi)=F$
Well, if $v(\psi)=T$ and $v'(\psi)=F$, then $v(\phi)=v(\neg \psi)=F$ and $v'(\phi)=v'(\neg \psi) =T$. On the other hand, if $v(\psi)=F$ and $v'(\psi)=T$, then $v(\phi)=v(\neg \psi)=T$ and $v'(\phi)=v'(\neg \psi) =F$. So, we can conclude that $v(\phi)=T$ and $v'(\phi)=F$, or $v'(\phi)=T$ and $v(\phi)=F$, as desired.
• Thank you for your help time and again! The whole approach is crystal clear to me; just wanna follow up: so trying to show that for any formula constructed from $\{\lnot\}$, $v(p)=T\to v(\phi)=F$ would never work because the double negation can always flip it back to $T$, correct? And to prove that $\{¬\}$ cannot show any truth function with 2 or more arguments, would we need to use induction or just an argument? Because this seems to be a counter-argument example type of work, so an induction doesn't seem to work, but I am just not sure. Feb 2, 2018 at 0:35
• @DanielMak well, the only kind of statement you can get with only a $\neg$ is of the form $\neg \neg \neg .... P$ with $P$ some atomic propsition; I don't think that would need any further elaboration. Feb 2, 2018 at 1:33
Let's begin with a definition.
A set of classical logical connectives is called “functionally complete” w.r.t. class of Boolean functions iff any Boolean function with a finite number of arguments can be expressed using only the connectives from that set.
In your first question you want to find such a property for negation that there are some other functions lacking it. Well, it is simple: if you have only negation, you cannot do any of the following.
1. Construct tautologies and contradictory formulas. You can make tautologies, e.g. if you have only implication and XOR is enough for contradictiory formulas.
2. You cannot construct formulas with more than one variable. This can be done using any function with at least two arguments.
I am sure, there are some other properties.
Now, to your second question.
We can prove an equivalent result: that $\{\wedge,\vee,\neg\}$ is functionally complete as defined above. But first let us recall, that there are exactly $2^{2^n}$ Boolean functions with $n$ arguments. Hence, if $\{\wedge,\vee,\neg\}$ is functionally complete, then there will be $2^{2^n}$ Boolean functions with $n$ arguments for any $n$.
$\{\neg,\vee,\wedge\}$ is functionally complete with respect to the class of all $n$-ary Boolean functions.
Assume now, we have arbitrary $n$-ary Boolean function $\eta$ defined as follows.
$$\begin{matrix} p_1&\ldots&p_n&\eta(p_1,\ldots,p_n)\\ \alpha_{1_1}&\ldots&\alpha_{1_n}&\beta_1\\ \vdots&\ddots&\vdots&\vdots\\ \alpha_{k_1}&\ldots&\alpha_{k_n}&\beta_k\\ \end{matrix}$$
Here $\alpha_{i_j},\beta_{i}\in\{\mathbf{T},\mathbf{F}\}$ and $k=2^n$ with $i\in\{1,\ldots,k\}$ and $j\in\{1,\ldots,n\}$. We construct the conjunction $\bigwedge\limits^{n}_{m=1}p^*_m$ for every truth value assignment with number $i$ of propositional variables $p_1,\ldots,p_n$.
$$p^*_m=\left\{\begin{matrix}p_m&\Leftrightarrow&\alpha_{i_j}=\mathbf{T}\\\neg p_m&\Leftrightarrow&\alpha_{i_j}=\mathbf{F}\end{matrix}\right.$$ We will call these conjunctions truth constituents.
The proof splits into three parts depending on under how many (none, one, some) assignments $\eta(p_1,\ldots,p_n)=\mathbf{T}$.
One
Assume $\eta$ returns $\mathbf{T}$ on exactly one assignment, say, $\alpha_{i_1},\ldots,\alpha_{i_n}$. We construct a truth constituent for this assignment which contains only negation and conjuction and is true under this assignment. It is quite easy to see that this truth constituent is true only under $\alpha_{i_1},\ldots,\alpha_{i_n}$. The case is proven.
Some
Assume there are $r$ such different assignments that $\eta$ is true. We construct a truth constituent $\mathbf{C}_i$ for every such assignment and then join them together into $\bigvee\limits^{r}_{i=1}\mathbf{C}_i$. It is easy to see that our formula is true under the same assignments as $\eta$.
None
In this case $\eta$ is represented as $\bigvee\limits^{n}_{i=1}(p_i\wedge\neg p_i)$. Obviously, this is a contradictory formula.
Now, since we have shown that $\{\wedge,\vee,\neg\}$ is indeed functionally complete, we know that for any $n$ it can express any Boolean function with $n$ arguments. Since we know that there are $2^{2^n}$ of them, we proved what we needed.
• Thank you so much for your help! I don't quite understand the diagram you drew to illustrate the Boolean function, but I am guessing you constructed a conjunctive normal form that can represent any truth function? The whole approach is understandable to me, but is there a way to count the number of truth functions any given normal form can represent? Feb 2, 2018 at 0:22
• We know that this number for a CNF/DNF is $2^{2^n}$ because we know there are in total that many truth functions given $n$ arguments, but what if we are given a normal form (eg. like the one I talked about above where a string of conjunction is being rearranged into an orderly one by equivalence) that cannot represent every possible truth function? Feb 2, 2018 at 0:24
• And to prove that {¬} cannot show any truth function with 2 or more arguments, would we need to use induction or just an argument along the lines of what you wrote above would do? I think whether to use induction or not is where I am getting stuck with that one. Спасибо! Feb 2, 2018 at 0:37 | {"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": 0.8946276903152466, "perplexity": 196.0199922111557}, "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-2022-21/segments/1652663006341.98/warc/CC-MAIN-20220527205437-20220527235437-00514.warc.gz"} |
https://www.physicsforums.com/threads/page13-on-griffiths-quantum-mechanics.568202/ | # Page13 on Griffiths quantum mechanics
• Start date
4
0
## Main Question or Discussion Point
In the prove of the Schrodinger equation preserves the normalization I don't understand the step
from
∂ψ/∂t=ih/2m ∂2ψ/∂x2- i/h Vψ
to
∂ψ*/∂t=-ih/2m ∂2ψ/∂x2+ i/h Vψ* (h represents h bar)
the book says "taking complex conjugate equation" but I don't see how.
Related Quantum Physics News on Phys.org
207
0
In the prove of the Schrodinger equation preserves the normalization I don't understand the step
from
∂ψ/∂t=ih/2m ∂2ψ/∂x2- i/h Vψ
to
∂ψ*/∂t=-ih/2m ∂2ψ/∂x2+ i/h Vψ* (h represents h bar)
the book says "taking complex conjugate equation" but I don't see how.
Welcome Frank, it says it's your first post~
Alright so we literally just change any aspect of the equation which contains an imaginary component to minus said component.
For example...
$e^{-iHt/ \hbar}$
goes to
$e^{iHt/ \hbar}$
We make the assumption that V is real and that ψ is complex.
Given the above should help, I'm sure you're familiar but, just in case ψ* refers to the complex conjugate of ψ.
Let me know if I missed what you were asking some how, though I'm sure someone can answer a little more cleanly.
http://en.wikipedia.org/wiki/Complex_conjugate
The wiki page provides the general information on conjugating as well.
1,006
104
If you have some equation a = b then you can take the complex conjugate of both sides and get a* = b*. Then you just have to know that the complex conjugate of a product is the product of the complex conjugate; the complex conjugate of a derivative is the derivative of the complex conjugate; the complex conjugate of i is -i; etc.
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4K | {"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": 0.8709736466407776, "perplexity": 1757.7793697013283}, "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/1575540547165.98/warc/CC-MAIN-20191212205036-20191212233036-00310.warc.gz"} |
https://www.nag.com/numeric/nl/nagdoc_28.3/flhtml/f01/f01dgf.html | # NAG FL Interfacef01dgf (real_tri_matmul_inplace)
## ▸▿ Contents
Settings help
FL Name Style:
FL Specification Language:
## 1Purpose
f01dgf performs one of the matrix-matrix operations
$B←αAB, B←αATB, B←αBA or B←αBAT,$
where $A$ and $B$ are real triangular matrices, and $\alpha$ is a real scalar.
## 2Specification
Fortran Interface
Subroutine f01dgf ( side, uplo, n, a, lda, b, ldb,
Integer, Intent (In) :: n, lda, ldb Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: alpha, a(lda,*) Real (Kind=nag_wp), Intent (Inout) :: b(ldb,*) Character (1), Intent (In) :: side, uplo, transa
#include <nag.h>
void f01dgf_ (const char *side, const char *uplo, const char *transa, const Integer *n, const double *alpha, const double a[], const Integer *lda, double b[], const Integer *ldb, Integer *ifail, const Charlen length_side, const Charlen length_uplo, const Charlen length_transa)
The routine may be called by the names f01dgf or nagf_matop_real_tri_matmul_inplace.
## 3Description
f01dgf computes the matrix product $B=\alpha AB$ or $B=\alpha BA$ for two upper triangular or two lower triangular matrices. The storage method for matrices $A$ and $B$ must match (e.g., $A$ and $B$ must both be upper triangular or lower triangular matrices). When the transpose of the input matrix $A$ is used during computation, the solution matrix $B$ is a general matrix. Otherwise, the solution matrix $B$ is a triangular matrix with the storage method identified by the input argument uplo.
None.
## 5Arguments
1: $\mathbf{side}$Character(1) Input
On entry: specifies whether $B$ is operated on from the left or the right.
${\mathbf{side}}=\text{'L'}$
$B$ is pre-multiplied from the left.
${\mathbf{side}}=\text{'R'}$
$B$ is post-multiplied from the right.
Constraint: ${\mathbf{side}}=\text{'L'}$ or $\text{'R'}$.
2: $\mathbf{uplo}$Character(1) Input
On entry: specifies whether $A$ and $B$ are upper or lower triangular.
${\mathbf{uplo}}=\text{'U'}$
$A$ and $B$ are upper triangular.
${\mathbf{uplo}}=\text{'L'}$
$A$ and $B$ are lower triangular.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
3: $\mathbf{transa}$Character(1) Input
On entry: specifies whether the operation involves $A$ or ${A}^{\mathrm{T}}$.
${\mathbf{transa}}=\text{'N'}$
The operation involves $A$.
${\mathbf{transa}}=\text{'T'}$ or $\text{'C'}$
The operation involves ${A}^{\mathrm{T}}$.
Constraint: ${\mathbf{transa}}=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.
4: $\mathbf{n}$Integer Input
On entry: $n$, the order of the triangular matrices $A$ and $B$.
Constraint: ${\mathbf{n}}\ge 0$.
5: $\mathbf{alpha}$Real (Kind=nag_wp) Input
On entry: the scalar $\alpha$.
6: $\mathbf{a}\left({\mathbf{lda}},*\right)$Real (Kind=nag_wp) array Input
Note: the second dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the $n×n$ triangular matrix $A$.
• If ${\mathbf{uplo}}=\text{'U'}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{uplo}}=\text{'L'}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
7: $\mathbf{lda}$Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f01dgf is called.
Constraint: ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
8: $\mathbf{b}\left({\mathbf{ldb}},*\right)$Real (Kind=nag_wp) array Input/Output
Note: the second dimension of the array b must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the $n×n$ triangular matrix $B$.
• If ${\mathbf{uplo}}=\text{'U'}$, $B$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{uplo}}=\text{'L'}$, $B$ is lower triangularand the elements of the array above the diagonal are not referenced.
If ${\mathbf{alpha}}=0$, b need not be set.
On exit: $B$ is overwritten.
• If ${\mathbf{transa}}=\text{'N'}$,
• if ${\mathbf{uplo}}=\text{'U'}$, $B$ is upper triangular and the elements of the array below the diagonal are not set.
• if ${\mathbf{uplo}}=\text{'L'}$, $B$ is lower triangular and the elements of the array above the diagonal are not set.
• If ${\mathbf{transa}}=\text{'T'}$ or $\text{'C'}$, $B$ is a general matrix.
9: $\mathbf{ldb}$Integer Input
On entry: the first dimension of the array b as declared in the (sub)program from which f01dgf is called.
Constraint: ${\mathbf{ldb}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
10: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).
## 6Error Indicators and Warnings
If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{side}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{side}}=\text{'L'}$ or $\text{'R'}$.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{uplo}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{transa}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{transa}}=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.
${\mathbf{ifail}}=4$
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=5$
On entry, ${\mathbf{lda}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
${\mathbf{ifail}}=6$
On entry, ${\mathbf{ldb}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldb}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
Not applicable.
## 8Parallelism and Performance
f01dgf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
None.
## 10Example
This example reads in two upper triangular matrices $A$ and $B$. It then calls f01dgf to compute the triangular matrix product $B=\alpha {A}^{\mathrm{T}}B$.
### 10.1Program Text
Program Text (f01dgfe.f90)
### 10.2Program Data
Program Data (f01dgfe.d)
### 10.3Program Results
Program Results (f01dgfe.r) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 126, "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": 0.9426679015159607, "perplexity": 3189.346295515975}, "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/1679296945248.28/warc/CC-MAIN-20230324051147-20230324081147-00224.warc.gz"} |
https://scite.ai/reports/certain-integral-and-differential-formulas-n69380p6 | 2022
DOI: 10.3390/fractalfract6020093
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Abstract:Many authors have established various integral and differential formulas involving different special functions in recent years. In continuation, we explore some image formulas associated with the product of Srivastava’s polynomials and extended Wright function by using Marichev–Saigo–Maeda fractional integral and differential operators, Lavoie–Trottier and Oberhettinger integral operators. The obtained outcomes are in the form of the Fox–Wright function. It is worth mentioning that some interesting special cas… Show more
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“…The extensions of Mittag-Leffler function is an interesting topic for researchers in which the classical notions linked with predefined Mittag-Leffler functions are investigated in more general prospect, see [9][10][11]. The Wright function is the generalization of hypergeometric function and several other special functions based on the gamma function, see [12][13][14][15]. The extensions of Mittag-Leffler function which are due to the gamma function can be obtained from the Wright function.…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…The extensions of Mittag-Leffler function is an interesting topic for researchers in which the classical notions linked with predefined Mittag-Leffler functions are investigated in more general prospect, see [9][10][11]. The Wright function is the generalization of hypergeometric function and several other special functions based on the gamma function, see [12][13][14][15]. The extensions of Mittag-Leffler function which are due to the gamma function can be obtained from the Wright function.…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
“…Proof. In (13) writing the Wright generalized function in terms of Mellin-Barnes integral by using (11), one can have (15).…”
Section: Relationship Of Mmentioning
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https://math.libretexts.org/Courses/Mount_Royal_University/MATH_1200%3A_Calculus_for_Scientists_I/2%3A_Derivatives/2.1%3A_Derivative_as_a_Function/2.1_E_Exercises | $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
# 2.1 E Exercises
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
###### Exercise $$\PageIndex{1}$$
For the following functions, use the definition of a derivative to find $$f′(x)$$. You may use derivative rules (will be learned in the next section to check if your answer is correct.
1) $$f(x)=6$$
2) $$f(x)=2−3x$$
3) $$f(x)=\frac{2x}{7}+1$$
4) $$f(x)=4x^2$$
5) $$f(x)=5x−x^2$$
6) $$f(x)=\sqrt{2x}$$
7) $$f(x)=\sqrt{x−6}$$
8) $$f(x)=\frac{9}{x}$$
9) $$f(x)=x+\frac{1}{x}$$
10) $$f(x)=\frac{1}{\sqrt{x}}$$
Under Construction
###### Exercise $$\PageIndex{2}$$
For the following exercises, use the graph of $$y=f(x)$$ to sketch the graph of its derivative $$f′(x).$$.
1)
2)
3)
4)
2.
4.
###### Exercise $$\PageIndex{3}$$
For the following exercises, the given limit represents the derivative of a function $$y=f(x)$$ at $$x=a$$. Find $$f(x)$$ and $$a$$.
1) $$lim_{h→0}\frac{(1+h)^{2/3}−1}{h}$$
2) $$lim_{h→0}\frac{[3(2+h)^2+2]−14}{h} 3) \(lim_{h→0}\frac{cos(π+h)+1}{h}$$
4) $$lim_{h→0}\frac{(2+h)^4−16}{h}$$
5) $$lim_{h→0}\frac{[2(3+h)^2−(3+h)]−15}{h}$$
6) $$lim_{h→0}\frac{e^h−1}{h}$$
2. $$f(x)=3x^2+2, a=2$$
4. $$f(x)=x^4, a=2$$
6. $$f(x)=e^x, a=0$$
###### Exercise $$\PageIndex{4}$$
For the following functions,
a. sketch the graph and
b. use the definition of a derivative to show that the function is not differentiable at $$x=1$$
1) $$f(x)=\begin{cases}2\sqrt{x} & 0≤x≤1\\3x−1 & x>1\end{cases}\ 2) \(f(x)=\begin{cases}3 & x<1\\3x & x≥1\end{cases}$$
3) $$f(x)=\begin{cases}−x^2+2 & x≤1\\x & x>1\end{cases}$$
4) $$f(x)=\begin{cases}2x, & x≤1\\\frac{2}{x} & x>1\end{cases}$$
2a.
b. $$lim_{h→1^−}\frac{3−3}{h}≠lim_{h→1^+}\frac{3h}{h}$$
4a.
b. $$lim_{h→1^−}\frac{2h}{h}≠lim_{h→1^+}\frac{\frac{2}{x+h}−2x}{h}.$$
###### Exercise $$\PageIndex{5}$$
For the following graphs,
a. determine for which values of $$x=a$$ the $$lim_{x→a}f(x)$$ exists but $$f$$ is not continuous at $$x=a$$, and
b. determine for which values of $$x=a$$ the function is continuous but not differentiable at $$x=a$$.
1)
2)
2. $$a. x=1, b. x=2$$
###### Exercise $$\PageIndex{6}$$
Use the graph to evaluate $$a. f′(−0.5), b. f′(0), c. f′(1), d. f′(2),$$ and e. $$f′(3),$$ if it exists.
Under Construction
###### Exercise $$\PageIndex{7}$$
For the following exercises, describe what the two expressions represent in terms of each of the given situations. Be sure to include units.
a. $$\frac{f(x+h)−f(x)}{h}$$
b. $$f′(x)=lim_{h→0}\frac{f(x+h)−f(x)}{h}$$
1) $$P(x)$$ denotes the population of a city at time $$x$$ in years.
2) $$C(x)$$ denotes the total amount of money (in thousands of dollars) spent on concessions by $$x$$ customers at an amusement park.
3) $$R(x)$$ denotes the total cost (in thousands of dollars) of manufacturing $$x$$ clock radios
4) $$g(x)$$ denotes the grade (in percentage points) received on a test, given $$x$$ hours of studying.
5) $$B(x)$$denotes the cost (in dollars) of a sociology textbook at university bookstores in the United States in $$x$$ years since $$1990$$.
6) $$p(x)$$ denotes atmospheric pressure at an altitude of $$x$$ feet.
2a. Average rate at which customers spent on concessions in thousands per customer.
b. Rate (in thousands per customer) at which $$x$$ customers spent money on concessions in thousands per customer.
4a. Average grade received on the test with an average study time between two values.
b. Rate (in percentage points per hour) at which the grade on the test increased or decreased for a given average study time of $$x$$ hours.
6a. Average change of atmospheric pressure between two different altitudes.
b. Rate (torr per foot) at which atmospheric pressure is increasing or decreasing at $$x$$ feet.
###### Exercise $$\PageIndex{8}$$
Sketch the graph of a function $$y=f(x)$$ with all of the following properties:
a. $$f′(x)>0$$ for $$−2≤x<1$$
b. $$f′(2)=0$$
c. $$f′(x)>0$$ for $$x>2$$
d. $$f(2)=2$$ and $$f(0)=1$$
e. $$lim_{x→−∞}f(x)=0$$ and $$lim_{x→∞}f(x)=∞$$
f. $$f′(1)$$ does not exist.
Under Construction
###### Exercise $$\PageIndex{9}$$
Suppose temperature T in degrees Fahrenheit at a height $$x$$ in feet above the ground is given by $$y=T(x).$$
a. Give a physical interpretation, with units, of $$T′(x).$$
b. If we know that $$T′(1000)=−0.1,$$ explain the physical meaning.
a. The rate (in degrees per foot) at which temperature is increasing or decreasing for a given height $$x.$$
b. The rate of change of temperature as altitude changes at $$1000$$ feet is $$−0.1$$ degrees per foot.
###### Exercise $$\PageIndex{10}$$
Suppose the total profit of a company is $$y=P(x)$$ thousand dollars when $$x$$ units of an item are sold.
a. What does $$\frac{P(b)−P(a)}{b−a}$$ for $$0<a<b$$ measure, and what are the units?
b. What does $$P′(x)$$ measure, and what are the units?
c. Suppose that $$P′(30)=5$$, what is the approximate change in profit if the number of items sold increases from $$30$$ to $$31$$?
Under Construction
###### Exercise $$\PageIndex{11}$$
The graph in the following figure models the number of people $$N(t)$$ who have come down with the flu t weeks after its initial outbreak in a town with a population of 50,000 citizens.
a. Describe what $$N′(t)$$ represents and how it behaves as $$t$$ increases.
b. What does the derivative tell us about how this town is affected by the flu outbreak?
a. The rate at which the number of people who have come down with the flu is changing t weeks after the initial outbreak.
b. The rate is increasing sharply up to the third week, at which point it slows down and then becomes constant.
###### Exercise $$\PageIndex{12}$$
For the following exercises, use the following table, which shows the height $$h$$ of the Saturn $$V$$ rocket for the Apollo $$11$$ mission $$t$$ seconds after launch.
$$Time(seconds)$$ $$Height(meters)$$ 0 0 1 2 2 4 3 13 4 25 5 32
1) What is the physical meaning of $$h′(t)$$? What are the units?
2) Construct a table of values for $$h′(t)$$ and graph both $$h(t)$$ and $$h′(t)$$ on the same graph. (Hint: for interior points, estimate both the left limit and right limit and average them.)
3) The best linear fit to the data is given by $$H(t)=7.229t−4.905$$, where $$H$$ is the height of the rocket (in meters) and t is the time elapsed since takeoff. From this equation, determine $$H′(t)$$. Graph $$H(t$$ with the given data and, on a separate coordinate plane, graph $$H′(t).$$
4) The best quadratic fit to the data is given by $$G(t)=1.429t^2+0.0857t−0.1429,$$ where $$G$$ is the height of the rocket (in meters) and $$t$$ is the time elapsed since takeoff. From this equation, determine $$G′(t)$$. Graph $$G(t)$$ with the given data and, on a separate coordinate plane, graph $$G′(t).$$
5) The best cubic fit to the data is given by $$F(t)=0.2037t^3+2.956t^2−2.705t+0.4683$$, where $$F$$ is the height of the rocket (in m) and $$t$$ is the time elapsed since take off. From this equation, determine $$F′(t)$$. Graph $$F(t)$$ with the given data and, on a separate coordinate plane, graph $$F′(t)$$. Does the linear, quadratic, or cubic function fit the data best?
6) Using the best linear, quadratic, and cubic fits to the data, determine what $$H''(t),G''(t) and F''(t)$$ are. What are the physical meanings of $$H''(t),G''(t )and F''(t),$$ and what are their units?
$$Time(seconds)$$ $$h′(t)(m/s)$$ 0 2 1 2 2 5.5 3 10.5 4 9.5 5 7
4. $$G′(t)=2.858t+0.0857$$
6. $$H''(t)=0,G''(t)=2.858 and f''(t)=1.222t+5.912$$ represent the acceleration of the rocket, with units of meters per second squared $$(m/s2).$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9152199029922485, "perplexity": 350.73853062043105}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583730728.68/warc/CC-MAIN-20190120184253-20190120210253-00159.warc.gz"} |
https://www.physicsforums.com/threads/kinematics-solve-for-time.113313/ | # Kinematics: Solve for Time
1. Mar 6, 2006
### Firestrider
Ok well I'm making a program to solve all my physics formulas quick and easy. But for the equation D = ViT + .5AT^2 I can't solve for T. I forgot some of my algebra 2 skills, which would come in handy here . This is what I have so far:
Since this is somewhat similar to deriving the quadratic equation I wrote that down to try to mirror it.
$$d = v_{i}t + \frac{1}{2}at^{2}$$
$$0 = v_{i}t + \frac{1}{2}at^{2} - d$$
$$\frac{1}{2}at^{2} + v_{i}t - d = 0$$
$$\frac{1}{2}at^{2} + v_{i}t = d$$
$$t^{2} + \frac{2v_{i}t}{a} = \frac{2d}{a}$$
$$t^{2} + \frac{2v_{i}t}{a} + \frac{v_{i}^{2}}{a^{2}} = \frac{2d}{a} + \frac{v_{i}^{2}}{a^{2}}$$
$$(t + \frac{v_{i}}{a})^{2} = \frac{2d}{a} + \frac{v_{i}^{2}}{a^{2}}$$
$$t + \frac{v_{i}}{a} = \sqrt{\frac{2d}{a} + \frac{v_{i}}{a^{2}}}$$
$$t = - \frac{v_{i}}{a}\pm\sqrt{\frac{2d}{a} + \frac{v_{i}}{a^{2}}}$$
$$t = - \frac{v_{i}}{a}\pm\sqrt{\frac{2da}{a^{2}} + \frac{v_{i}}{a^{2}}}$$
$$t = - \frac{v_{i}}{a}\frac{\pm\sqrt{v_{i} + 2ad}}{a}$$
$$t = \frac{-v_{i}\pm\sqrt{v_{i} + 2ad}}{a}$$
Is there any way of simlifing this more? Any help is appreciated. Well I can't seem to get my LaTeX image to show up, can anyone edit it so it will?
Last edited: Mar 6, 2006
2. Mar 6, 2006
### xman
are you referring the the kinematic eq.
$$x=x_{0}+v_{0} t+\frac{a}{2}t^{2}$$
if so why do you not just use the quadratic formula if you're trying to solve for t.
$$t = \frac{-v_{0} \pm \sqrt{v_{0}^{2}-2ax_{0}}}{a}$$
if you want to derive the quad. equation then, start with the first formula, complete the square in terms of t, and solve remember in completing the square you have to make it such that the coefficient in front of the squared term is 1, otherwise it's a little messier.
Last edited: Mar 6, 2006
3. Mar 6, 2006
### Firestrider
Ya thats what I did... if only the latex from the first post would show up :grumpy:
This is the first equation:
$$d = v_{i}t + \frac{1}{2}at^2$$
And this is the final equation I got:
$$t = \frac{-v_{i} \pm \sqrt{v_{i} + 2ad}}{a}$$
Last edited: Mar 6, 2006
4. Mar 7, 2006
### Firestrider
Is the final equation right? I don't think it is.
5. Mar 7, 2006
### robphy
The usual response to this is: "plug your solution back into your initial equation!"
However, before carrying that out, it's a good idea to check that the units of your expression are consistent.
6. Mar 7, 2006
### Firestrider
Tried that, didn't work! Plugged in 5's and got a 3m as displacement.
7. Mar 7, 2006
### xman
You should get with your equation
$$t = \frac{-v_{i} \pm \sqrt{v_{i}^{2}-2a (\pm d)}}{a}$$
remember
$$d=d_{f}-d_{i}$$
so if
$$d_{f}<d_{i}$$
Last edited: Mar 7, 2006
Similar Discussions: Kinematics: Solve for Time | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.927838921546936, "perplexity": 1544.0917396533555}, "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-2017-17/segments/1492917125074.20/warc/CC-MAIN-20170423031205-00273-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/101015-3-questions.html | # Math Help - 3 questions
1. ## 3 questions
Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .
Find the quotient and remainder using long division for
Simplify the expression
2. Originally Posted by wannous
Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .
Find the quotient and remainder using long division for
Simplify the expression
For Q.3 note that
$7x^3 - 8x^2 - 12x = x(x-2)(7x+3)$
and
$6x^2 - 16x + 8 = 2(x - 2)(3x - 2)$.
So $\frac{7x^3 - 8x^2 - 12x}{6x^2 - 16x + 8} = \frac{x(x-2)(7x+3)}{2(x - 2)(3x - 2)}$
$= \frac{x(7x + 3)}{2(3x - 2)}$.
Therefore $f(x) = x(7x + 3)$ and $g(x) = 2(3x - 2)$.
3. Hello wannous
Originally Posted by wannous
Solve the following inequality. Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter as infinity and as -infinity .
To solve this type of inequality, find the values of $x$ that make each factor zero, and then look at their signs as $x$ moves along the number line from left to right, through each of these 'zero values' in turn.
Now the 'zeros' occurs when $x =4$ and $x=5$. So we look at what happens when:
• $x<4$
• $4
• $5
First, if $x<4,\, (x-5)$ is negative and $(x-4)$ is also negative; and $-^{ve}\times -^{ve} = +^{ve}$. So $(x-5)(x-4)>0$ in this range.
Next, if $4 is $-^{ve}$ and $(x-4)$ is $+^{ve}$; $-^{ve}\times+^{ve} = -^{ve}$. So $(x-5)(x-4) < 0$ in this range.
Finally, if $x>5$, we get $+^{ve}\times+^{ve}=+^{ve}$. So $(x-5)(x-4)>0$ in this range.
So the values we want are $4\le x \le 5$, or in interval notation $[4,5]$.
Find the quotient and remainder using long division for
See the attached image.
So the quotient is
$x^2-4x+1$ and the remainder is $-5$. | {"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": 0.9373084306716919, "perplexity": 1392.5209399145838}, "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/1416931011477.80/warc/CC-MAIN-20141125155651-00013-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3262582/what-does-paul-halmos-mean-here | # What does Paul Halmos mean here?
In Naive Set Theory, in Section 1.3 "Unordered Pairs", Paul Halmos mentions the following:
If, temporarily, we refer to the sentence $$”x=a \text{ or } x=b”$$ as $$S(x)$$, we may express the axiom of pairing by saying that there exists a set $$B$$ such that $$x\in B\text{ if and only if } S(x).\tag{*}$$ The axiom of specification applied to a set $$A$$ [such that $$a\in A\text{ and } b\in A$$, whose existence is guaranteed by axiom of pairing], asserts the existence of a set $$B$$ such that $$x\in B\text{ if and only if } (x\in A\text{ and } S(x)).\tag{**}$$ The relation between $$(*)$$ and $$(**)$$ typifies something that occurs quite frequently. All the remaining principles of set construction are pseudo-special cases of the axiom of specification in the sense in which $$(*)$$ is a pseudo-special case of $$(**)$$.
Question: What does Halmos mean by stating that remaining principles of set construction and $$(*)$$ are pseudo-special cases of axiom of specification and $$(**)$$, respectively?
In fact, $$(**)$$ seems a special case of $$(*)$$.
I think the general principle here is that if you want to show that there exists a set containing precisely those elements $$x$$ satisfying some first-order formula $$S(x)$$, it is sufficient to show there exists a set containing at least those elements, and then invoke the axiom of specification. This is what's done when we use (**) to establish (*) - the original axiom of pairing, as stated by Halmos, asserts there exists a set containing $$a$$ and $$b$$, but allows for the possibility that all such sets contain additional unwanted elements. You need specification to rule out the latter.
So whenever one writes something like "let $$A$$ be the set of all $$x$$ such that $$S(x)$$", there may be a hidden use of the axiom of specification.
Without Pairing, we cannot use Specification (a.k.a. Comprehension) to obtain any set with exactly 1 or 2 members. Because without Pairing, we cannot show that for any $$x,y$$ there exists $$A$$ with $$x\in A$$ and $$y\in A.$$
I have no comment on what "pseudo-special case" means.
The issue is with the so-called (unrestricted) Principle of comprehension :
$$\exists B \ [x \in B \leftrightarrow S(x)]$$.
As we know, this principle leads to Russell's Paradox.
If we have the said principle available, we can prove that, for $$a,b$$ whatever, the pair $$\{ a, b \}$$ exists, using it (as Halmos says) with $$x=a \lor x=b$$ as the formula $$S(x)$$.
But in axiomatic set theory, the above principle is replaced by Specification : $$x \in B \text { iff } (x \in A \text { and } S(x))$$.
Thus, in order to prove that the pair $$\{ a, b \}$$ exists, we have to find a previous existing set $$A$$ to which $$a$$ and $$b$$ belongs.
Pair axiom allows us to avoid this detour, licensing the existence of the pair without further conditions.
In this sense, it is a sort of "limited comprehension" principle : we can sey that it is a special case of Comprehension.
In this sense, IMO, Halmos calls Pair a "pseudo-special" case of Specification. | {"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": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 37, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9803408980369568, "perplexity": 278.4324568296448}, "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-2021-39/segments/1631780057973.90/warc/CC-MAIN-20210926205414-20210926235414-00127.warc.gz"} |
https://help.algebrakit.com/exercises/use-within-text-or-formulae/ | # Tutorial
## Inline interactions
The interaction types Algebra, Math Entry, and Multiple Choice can be used as block elements or ‘inline’ within a text or formula.
The image below shows an instruction with two interactions. One is added inline and one is added as a block element.
This is shown as follows to the student:
The three options to include an interaction in your question are listed below. Click on each item for more details.
Block
0 / 0
Inline in text
0 / 0
Inline in formula
Use the $f(x)$ button to create a mathematical expression. Click the bucket symbol () in the formula editor to choose the interaction you want to add to the expression.
Click the name of the interaction you want to insert.
In the example below, the question has two mathematical expressions with inline interactions:
The interactions are defined as follows:
I1a – Algebra – Task Simplify$\sqrt{9}$
I1b – Math Entry – Same expression, literal$16$
This yields the following interactive AlgebraKiT exercise:
Refer to the overview of all possible interaction usages 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": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 3, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8615375757217407, "perplexity": 2255.712215460595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358786.67/warc/CC-MAIN-20211129164711-20211129194711-00527.warc.gz"} |
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/760 | ## A set with finite curvature and projections of zero length
• A compact subset E of the complex plane is called removable if all bounded analytic functions on its complement are constant or, equivalently, i f its analytic capacity vanishes. The problem of finding a geometric characterization of the removable sets is more than a hundred years old and still not comp letely solved.
$Rev: 13581$ | {"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": 0.8507604002952576, "perplexity": 426.84199714207796}, "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/1461860113553.63/warc/CC-MAIN-20160428161513-00184-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-concepts-through-functions-a-unit-circle-approach-to-trigonometry-3rd-edition/chapter-4-exponential-and-logarithmic-functions-section-4-7-financial-models-4-7-assess-your-understanding-page-346/37 | ## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
$6.823 \%$
Effective Rate of Interest Formula $$r_e = \left(1+\dfrac{r}{n} \right)^n - 1$$ $r_e:$ Effective Rate of Interest $r:$ Annual Interest Rate $n:$ Number of compoundings per year $r_e = 0.07$ $\text{Compounded quarterly} \to n = 4$ $0.07 = \left(1+\dfrac{r}{4} \right)^4 -1$ $0.07+1 = \left(1+\dfrac{r}{4} \right)^4$ $1.07 = \left(1+\dfrac{r}{4} \right)^4$ $\left(1+\dfrac{r}{4} \right) = \sqrt[4]{1.07}$ $\dfrac{r}{4} = \sqrt[4]{1.07}-1$ $r = 4(\sqrt[4]{1.07}-1)$ $r \approx 0.06823$ $r = \boxed{6.823 \%}$ | {"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": 0.851736843585968, "perplexity": 426.9272572051858}, "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/1634323585281.35/warc/CC-MAIN-20211019202148-20211019232148-00336.warc.gz"} |
https://mail.python.org/pipermail/pypy-commit/2012-August/064779.html | Mon Aug 6 10:57:57 CEST 2012
Author: Carl Friedrich Bolz <cfbolz at gmx.de>
Changeset: r4419:5b6cc23a781f
Date: 2012-08-06 09:20 +0200
Log: clarify
diff --git a/talk/dls2012/paper.tex b/talk/dls2012/paper.tex
--- a/talk/dls2012/paper.tex
+++ b/talk/dls2012/paper.tex
@@ -1030,21 +1030,10 @@
\section{Related Work}
\label{sec:related}
-\reva{
-First sentence of the related work section is kind of
-unfortunate. It is unclear what the reference at the end of the
-sentence is good for. To support the meaning of the entire sentence?
-Or is it just a reference to the standard loop invariant code motion
-techniques? The contribution of your paper seems much smaller than
-in the former case compared to the latter one. While I have not
-checked the content of the book, I believe the latter is the correct
-interpretation. You should remove this opportunity for
-misinterpretation.}
-
-The effect of combining a one pass optimization with loop peeling gives
-completely standard loop invariant code motion optimizations
-\cite{muchnick_advanced_1997}. We do not claim any novelty in the effect, but
-think that our implementation scheme is a very simple one.
+Loop invariant code motion optimizations are completely
+standard~\cite{muchnick_advanced_1997}. Therefore, the effects that our
+optimization achieves is not in any way new. However, we think that achieving
+it as described in this paper is simpler than explicit algorithms.
\revc{
The discussion of LuaJIT is unsatisfying. It's not clear to me from that one | {"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": 0.8755728602409363, "perplexity": 2731.7285157914107}, "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-2017-30/segments/1500549427749.61/warc/CC-MAIN-20170727062229-20170727082229-00201.warc.gz"} |
https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Natural_Resources_Biometrics_(Kiernan)/02%3A_Sampling_Distributions_and_Confidence_Intervals/2.02%3A_Confidence_Intervals | # 2.2: Confidence Intervals
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In the preceding chapter we learned that populations are characterized by descriptive measures called parameters. Inferences about parameters are based on sample statistics. We now want to estimate population parameters and assess the reliability of our estimates based on our knowledge of the sampling distributions of these statistics.
### Point Estimates
We start with a point estimate. This is a single value computed from the sample data that is used to estimate the population parameter of interest.
• The sample mean ($$\bar {x}$$) is a point estimate of the population mean ($$\mu$$).
• The sample proportion ($$\hat {p}$$) is the point estimate of the population proportion (p).
We use point estimates to construct confidence intervals for unknown parameters.
• A confidence interval is an interval of values instead of a single point estimate.
• The level of confidence corresponds to the expected proportion of intervals that will contain the parameter if many confidence intervals are constructed of the same sample size from the same population.
• Our uncertainty is about whether our particular confidence interval is one of those that truly contains the true value of the parameter.
Example $$\PageIndex{1}$$: bear weight
We are 95% confident that our interval contains the population mean bear weight.
If we created 100 confidence intervals of the same size from the same population, we would expect 95 of them to contain the true parameter (the population mean weight). We also expect five of the intervals would not contain the parameter.
Figure $$\PageIndex{1}$$: Confidence intervals from twenty-five different samples.
In this example, twenty-five samples from the same population gave these 95% confidence intervals. In the long term, 95% of all samples give an interval that contains µ, the true (but unknown) population mean.
Level of confidence is expressed as a percent.
• The compliment to the level of confidence is α (alpha), the level of significance.
• The level of confidence is described as $$(1- \alpha) \times 100%$$.
What does this really mean?
• We use a point estimate (e.g., sample mean) to estimate the population mean.
• We attach a level of confidence to this interval to describe how certain we are that this interval actually contains the unknown population parameter.
• We want to estimate the population parameter, such as the mean (μ) or proportion (p).
$\bar {x}-E < \mu < \bar {x}+E$
or
$\hat {p}-E < p <\hat {p}+E$
where $$E$$ is the margin of error.
The confidence is based on area under a normal curve. So the assumption of normality must be met (Chapter 1).
### Confidence Intervals about the Mean (μ) when the Population Standard Deviation (σ) is Known
A confidence interval takes the form of: point estimate $$\pm$$ margin of error.
##### The point estimate
• The point estimate comes from the sample data.
• To estimate the population mean ($$μ$$), use the sample mean ($$\bar{x}$$) as the point estimate.
##### The margin of error
• Depends on the level of confidence, the sample size and the population standard deviation.
• It is computed as $$E=Z_{\frac {\alpha}{2}}\times \frac {\sigma}{\sqrt {n}}$$where $$Z_{\frac {\alpha}{2}}$$ is the critical value from the standard normal table associated with α (the level of significance).
##### The critical value $$Z_{\frac {\alpha}{2}}$$
• This is a Z-score that bounds the level of confidence.
• Confidence intervals are ALWAYS two-sided and the Z-scores are the limits of the area associated with the level of confidence.
Figure $$\PageIndex{1}$$: The middle 95% area under a standard normal curve.
• The level of significance (α) is divided into halves because we are looking at the middle 95% of the area under the curve.
• Go to your standard normal table and find the area of 0.025 in the body of values.
• What is the Z-score for that area?
• The Z-scores of ± 1.96 are the critical Z-scores for a 95% confidence interval.
Table $$\PageIndex{1}$$: Common critical values (Z-scores).
Steps
Construction of a confidence interval about $$μ$$ when $$σ$$ is known:
1. $$Z_{\frac {\alpha}{2}}$$ (critical value)
2. $$E=Z_{\frac {\alpha}{2}}\times \frac {\sigma}{\sqrt {n}}$$ (margin of error)
3. $$\bar {x} \pm E$$ (point estimate ± margin of error)
Example $$\PageIndex{3}$$: Construct a confidence interval about the population mean
Researchers have been studying p-loading in Jones Lake for many years. It is known that mean water clarity (using a Secchi disk) is normally distributed with a population standard deviation of σ = 15.4 in. A random sample of 22 measurements was taken at various points on the lake with a sample mean of = 57.8 in. The researchers want you to construct a 95% confidence interval for μ, the mean water clarity.
A secchi disk to measure turbidly of water. (CC SA; publiclab.org)
Solution
1) $$Z_{\frac {\alpha}{2}}$$ = 1.96
2) $$E=Z_{\frac {\alpha}{2}}\times \frac {\sigma}{\sqrt {n}}$$ = $$1.96 \times \frac {15.4}{\sqrt {22}}$$ = 6.435
3) $$\bar {x} \pm E$$ = 57.8 ± 6.435
95% confidence interval for the mean water clarity is (51.36, 64.24).
We can be 95% confident that this interval contains the population mean water clarity for Jones Lake.
Now construct a 99% confidence interval for μ, the mean water clarity, and interpret.
1) $$Z_{\frac {\alpha}{2}}$$= 2.575
2) $$E=Z_{\frac {\alpha}{2}}\times \frac {\sigma}{\sqrt {n}}$$ = $$2.575 \times \frac {15.4}{\sqrt {22}}$$ = 8.454
3) $$\bar {x} \pm E$$= 57.8± 8.454
99% confidence interval for the mean water clarity is (49.35, 66.25).
We can be 99% confident that this interval contains the population mean water clarity for Jones Lake.
As the level of confidence increased from 95% to 99%, the width of the interval increased. As the probability (area under the normal curve) increased, the critical value increased resulting in a wider interval.
## Software Solutions
### Minitab
You can use Minitab to construct this 95% confidence interval (Excel does not construct confidence intervals about the mean when the population standard deviation is known). Select Basic Statistics>1-sample Z. Enter the known population standard deviation and select the required level of confidence.
Figure 3. Minitab screen shots for constructing a confidence interval.
#### One-Sample Z: depth
Variable N Mean StDev SE Mean 95% CI depth 22 57.80 11.60 3.28 (51.36, 64.24)
### Confidence Intervals about the Mean (μ) when the Population Standard Deviation (σ) is Unknown
Typically, in real life we often don’t know the population standard deviation (σ). We can use the sample standard deviation (s) in place of σ. However, because of this change, we can’t use the standard normal distribution to find the critical values necessary for constructing a confidence interval.
The Student’s t-distribution was created for situations when σ was unknown. Gosset worked as a quality control engineer for Guinness Brewery in Dublin. He found errors in his testing and he knew it was due to the use of s instead of σ. He created this distribution to deal with the problem of an unknown population standard deviation and small sample sizes. A portion of the t-table is shown below.
Table $$\PageIndex{2}$$: Portion of the student’s t-table.
Example $$\PageIndex{4}$$
Find the critical value $$t_{\frac {\alpha}{2}}$$ for a 95% confidence interval with a sample size of n=13.
Solution
• Degrees of freedom (down the left-hand column) is equal to n-1 = 12
• α = 0.05 and α/2 = 0.025
• Go down the 0.025 column to 12 df
• $$t_{\frac {\alpha}{2}}$$= 2.179
The critical values from the students’ t-distribution approach the critical values from the standard normal distribution as the sample size (n) increases.
Table 3. Critical values from the student’s t-table.
Using the standard normal curve, the critical value for a 95% confidence interval is 1.96. You can see how different samples sizes will change the critical value and thus the confidence interval, especially when the sample size is small.
Construction of a Confidence Interval
When σ is Unknown
1. $$t_{\frac {\alpha}{2}}$$ critical value with n-1 df
2. $$E = t_{\frac {\alpha}{2}} \times \frac{s}{\sqrt {n}}$$
3. $$\bar {x} \pm E$$
Example $$\PageIndex{5}$$:
Researchers studying the effects of acid rain in the Adirondack Mountains collected water samples from 22 lakes. They measured the pH (acidity) of the water and want to construct a 99% confidence interval about the mean lake pH for this region. The sample mean is 6.4438 with a sample standard deviation of 0.7120. They do not know anything about the distribution of the pH of this population, and the sample is small (n<30), so they look at a normal probability plot.
Figure 4. Normal probability plot.
Solution
The data is normally distributed. Now construct the 99% confidence interval about the mean pH.
1) $$t_{\frac {\alpha}{2}}$$ = 2.831
2) $$E = t_{\frac {\alpha}{2}} \times \frac{s}{\sqrt {n}}$$ = $$2.831 \times \frac {0.7120}{\sqrt {22}}$$= 0.4297
3) $$\bar {x} \pm E$$ = 6.443 ± 0.4297
The 99% confidence interval about the mean pH is (6.013, 6.863).
We are 99% confident that this interval contains the mean lake pH for this lake population.
Now construct a 90% confidence interval about the mean pH for these lakes.
1) $$t_{\frac {\alpha}{2}}$$ = 1.721
2) $$E = t_{\frac {\alpha}{2}} \times \frac{s}{\sqrt {n}}$$ = $$1.71221 \times \frac {0.7120}{\sqrt {22}}$$0.2612
3) $$\bar {x} \pm E$$ = 6.443 ± 0.2612
The 90% confidence interval about the mean pH is (6.182, 6.704).
We are 90% confident that this interval contains the mean lake pH for this lake population.
Notice how the width of the interval decreased as the level of confidence decreased from 99 to 90%.
Construct a 90% confidence interval about the mean lake pH using Excel and Minitab.
## Software Solutions
### Minitab
For Minitab, enter the data in the spreadsheet and select Basic statistics and 1-sample t-test.
#### One-Sample T: pH
Variable N Mean StDev SE Mean 90% CI pH 22 6.443 0.712 0.152 (6.182, 6.704)
### Excel
For Excel, enter the data in the spreadsheet and select descriptive statistics. Check Summary Statistics and select the level and confidence.
Mean 6.442909 Standard Error 0.151801 Median 6.4925 Mode #N/A Standard Deviation 0.712008 Sample Variance 0.506956 Kurtosis -0.5007 Skewness -0.60591 Range 2.338 Minimum 5.113 Maximum 7.451 Sum 141.744 Count 22 Confidence Level(90.0%) 0.26121
Excel gives you the sample mean in the first line (6.442909) and the margin of error in the last line (0.26121). You must complete the computation yourself to obtain the interval (6.442909±0.26121).
### Confidence Intervals about the Population Proportion (p)
Frequently, we are interested in estimating the population proportion (p), instead of the population mean (µ). For example, you may need to estimate the proportion of trees infected with beech bark disease, or the proportion of people who support “green” products. The parameter p can be estimated in the same ways as we estimated µ, the population mean.
#### The Sample Proportion
• The sample proportion is the best point estimate for the true population proportion.
• Sample proportion $$\hat {p} = \frac {x}{n}$$where x is the number of elements in the sample with the characteristic you are interested in, and n is the sample size.
#### The Assumption of Normality when Estimating Proportions
• The assumption of a normally distributed population is still important, even though the parameter has changed.
• Normality can be verified if:$$n \times \hat {p} \times (1- \hat {p}) \ge 10$$
#### Constructing a Confidence Interval about the Population Proportion
Constructing a confidence interval about the proportion follows the same three steps we have used in previous examples.
1. $$Z_{\frac {\alpha}{2}}$$(critical value from the standard normal table)
2. $$E = Z_{\frac {\alpha}{2}} \times \sqrt {\frac{\hat {p}(1-\hat {p})}{n}}$$ (margin of error)
3. $$\hat {p} \pm E$$(point estimate ± margin of error)
Example $$\PageIndex{6}$$:
A botanist has produced a new variety of hybrid soybean that is better able to withstand drought. She wants to construct a 95% confidence interval about the germination rate (percent germination). She randomly selected 500 seeds and found that 421 have germinated.
Solution
First, compute the point estimate
$\hat {p} = \frac {x}{n} =\frac {421}{500}=0.842$
Check normality:
n \times \hat {p} \times (1-\hat {p}) \ge 10 = 500 \times 0.842 \times (1-0.842) =66.5\]
You can assume a normal distribution.
Now construct the confidence interval:
1) $$Z_{\frac {\alpha}{2}}$$ = 1.96
2) $$E = Z_{\frac {\alpha}{2}} \times \sqrt {\frac{\hat {p}(1-\hat {p})}{n}}$$ =$$1.96 \times \sqrt {\frac {0.842(1-0.842)}{500}}$$ = 0.032
3) $$\hat {p} \pm E =0.842 \pm 0.0032$$
The 95% confidence interval for the germination rate is (81.0%, 87.4%).
We can be 95% confident that this interval contains the true germination rate for this population.
## Software Solutions
### Minitab
You can use Minitab to compute the confidence interval. Select STAT>Basic stats>1-proportion. Select summarized data and enter the number of events (421) and the number of trials (500). Click Options and select the correct confidence level. Check “test and interval based on normal distribution” if the assumption of normality has been verified.
#### Test and CI for One Proportion
Sample X N Sample p 95% CI 1 421 500 0.842000 (0.810030, 0.873970)
Using the normal approximation.
### Excel
Excel does not compute confidence intervals for estimating the population proportion.
### Confidence Interval Summary
Which method do I use?
The first question to ask yourself is: Which parameter are you trying to estimate? If it is the mean (µ), then ask yourself: Is the population standard deviation (σ) known? If yes, then follow the next 3 steps:
#### Confidence Interval about the Population Mean (µ) when σ is Known
1. $$Z_{\frac {\alpha}{2}}$$ critical value (from the standard normal table)
2. $$E=Z_{\frac {\alpha}{2}} \times \frac {\sigma}{\sqrt {n}}$$
3. $$\bar {x} \pm E$$
If no, follow these 3 steps:
#### Confidence Interval about the Population Mean (µ) when σ is Unknown
1. $$t_{\frac {\alpha}{2}}$$ critical value with n-1 df from the student t-distribution
2. $$E=t_{\frac {\alpha}{2}} \times \frac {s}{\sqrt {n}}$$
3. $$\bar {x} \pm E$$
If you want to construct a confidence interval about the population proportion, follow these 3 steps:
#### Confidence Interval about the Proportion
1. $$Z_{\frac {\alpha}{2}}$$ critical value from the standard normal table
2. $$E = Z_{\frac {\alpha}{2}} \times \sqrt {\frac{\hat {p}(1-\hat {p})}{n}}$$
3. $$\hat {p} \pm E$$
Remember that the assumption of normality must be verified.
This page titled 2.2: Confidence Intervals is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Diane Kiernan (OpenSUNY) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9466829299926758, "perplexity": 957.9763430713248}, "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/1664030337504.21/warc/CC-MAIN-20221004121345-20221004151345-00246.warc.gz"} |
https://arxiv.org/abs/1305.4961 | math-ph
(what is this?)
# Title:Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks
Abstract: We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.
Comments: 14 pages, 1 figure Subjects: Mathematical Physics (math-ph) MSC classes: 74B05, 35R02 Journal reference: Networks and Heterogeneous Media, 9 (2014), no. 2, pp 299-314 DOI: 10.3934/nhm.2014.9.299 Cite as: arXiv:1305.4961 [math-ph] (or arXiv:1305.4961v1 [math-ph] for this version)
## Submission history
From: Fernando Guevara Vasquez [view email]
[v1] Tue, 21 May 2013 20:47:31 UTC (28 KB) | {"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": 0.941297173500061, "perplexity": 1923.1389641426913}, "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-2019-18/segments/1555578732961.78/warc/CC-MAIN-20190425173951-20190425195951-00021.warc.gz"} |
https://www.physicsforums.com/threads/in-my-experiment-on-transformers-the-data-showed.868677/ | # In my experiment on transformers, the data showed
1. Apr 24, 2016
### Chezz42
So I did an experiment a this week on the relationship between two tightly wrapped coils with same length and number of coils in a transformer. This was in a compete circuit using AC currents. I measured the Voltage, keeping the currents the same. One experiment had an iron core between the two coils and I varied the distance between the two coils and got a linear relationship. When I used an air core, the relationship between distance and voltage became and inverse function. I don't understand why.
2. Apr 24, 2016
### BvU
Hello Chezz, and
Aren't your notes or textbook supposed to help you in this ? No background amterial anywherer in sight ? This experiment does have a context, though, I suppose ?
3. Apr 24, 2016
### Chezz42
Well, I did this experiment on my own and was wondering about how wireless charging works. I think i figured out myself, but thanks for dropping by to help.
4. Apr 24, 2016
### BvU
Kudos for this initiative to find out ! I think you're on the right track. Closeness of sender and receiver and high frequencies are key in wireless charging I think, but I'm no expert. Let's ask @CWatters !
Draft saved Draft deleted
Similar Discussions: In my experiment on transformers, the data showed | {"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": 0.8461906313896179, "perplexity": 1412.4574152798912}, "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/1508187824325.29/warc/CC-MAIN-20171020192317-20171020212317-00348.warc.gz"} |
http://technotantor.blogspot.com/2005/10/tomcat-5-as-nt-service.html | ## Wednesday, October 05, 2005
### Tomcat 5 as an NT Service
This really should be much easier than it is, if you fail to update the VM options the thing fails, after a day of work the following example is the only one that worked for me.
install.bat
`set JAVA_HOME=C:\j2sdk1.4.2_06set CATALINA_HOME=c:\tomcat5set CATALINA_BASE=c:\tomcat5set EXECUTABLE=tomcat5.exeset SERVICE_NAME=tomcat5serverset PR_STDOUTPUT=%CATALINA_HOME%\logs\stdout.logset PR_STDERROR=%CATALINA_HOME%\logs\stderr.log"%EXECUTABLE%" //IS//%SERVICE_NAME% --DisplayName=cipc --Install="%CATALINA_HOME%\bin\tomcat5.exe" --Jvm=auto --JvmMs=128 --JvmMx=512 --StartMode=jvm --Classpath="%CATALINA_HOME%\bin\bootstrap.jar;%CATALINA_HOME%\bin\servlet.jar;%JAVA_HOME%\lib\tools.jar" --StopMode=jvm --StartClass=org.apache.catalina.startup.Bootstrap --StartParams=start --StopClass=org.apache.catalina.startup.Bootstrap --StopParams=stop"%EXECUTABLE%" //US//"%SERVICE_NAME%" --JvmOptions "-Xms128M;-Xmx512M;-Dcatalina.base=%CATALINA_BASE%;-Dcatalina.home=%CATALINA_HOME%;-Djava.endorsed.dirs=%CATALINA_HOME%\common\endorsed" --StartMode jvm --StopMode jvm"%EXECUTABLE%" //US//"%SERVICE_NAME%" ++JvmOptions "-Djava.io.tmpdir=%CATALINA_BASE%\temp" --JvmMs 128 --JvmMx 512` | {"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": 0.9352443814277649, "perplexity": 1166.0666309899077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657155816.86/warc/CC-MAIN-20200715035109-20200715065109-00397.warc.gz"} |
https://stats.stackexchange.com/questions/406091/consistency-of-the-maximum-likelihood-estimator-for-the-variance-of-a-normal-ran/406099 | # Consistency of the maximum likelihood estimator for the variance of a normal random variable when the parameter is perturbed with white noise
Let $$X_1, X_2, \dots , X_n$$ be normally distributed independent observations with known variance $$\sigma^2$$ and mean respectively given by $$\mu_i = \mu + \epsilon_i$$ where $$\epsilon_i$$ is white noise, i. e., $$E[\epsilon_i] = 0$$, $$E[\epsilon_i^2] = \sigma_{\epsilon}$$ and the $$\epsilon_i$$ are all symmetrically identically distributed and independent from one another.
We can see that the maximum likelihood estimator for $$\mu$$ remains consistent by maximizing the log-likelihood function
$$\sum_{i=1}^n \log \frac{1}{\sqrt{2 \pi \sigma^2}} - \frac{(X_i - \mu - \epsilon_i)^2}{2 \sigma^2}$$
taking the derivative wrt $$\mu$$ and setting the result equal to zero one obtains that
$$+2 \hat{\mu} = \frac{2}{n} \left( \sum_{i=1}^n X_i + \sum_{i=1}^n \epsilon_i \right)$$
by the strong law of large numbers $$\sum_{i=1}^n X_i \rightarrow \mu$$ and $$\sum_{i=1}^n \epsilon_i \rightarrow 0$$ almost surely. So from the linearity of the limit we obtain the consistency.
Is this true even for the variance? that is; if we had $$X_1, X_2, \dots , X_n$$ be normally distributed independent observations with known mean $$\mu$$ and variance respectively given by $$\sigma_i^2 = \sigma^2 + \epsilon_i$$ would the maximum likelihood estimator for $$\sigma^2$$ still be consistent ?
• Based on your description of $\epsilon_i$, it is possible that $-\epsilon_i > \sigma^2$. Then what happens? – user158565 May 1 at 19:54
• @user158565 Right, One would need to adjust the distribution of the noise to adapt to that. You are correct, it is badly specified as written. – Monolite May 1 at 20:03
No, if we look at the model implied covariance matrix for $$X_1,\ldots,X_n$$ for the example case of $$n=3$$ $$\begin{bmatrix} \sigma^2+\sigma_\epsilon^2 & 0 & 0 \\\\ 0 & \sigma^2+\sigma_\epsilon^2 & 0 \\\\ 0 & 0 &\sigma^2+\sigma_\epsilon^2 \end{bmatrix}$$
We see that your model is not identified. Model Identification is defined here: https://en.wikipedia.org/wiki/Maximum_likelihood_estimation#Consistency. Essentially, if two different parameter values imply the same distribution your model is not identified. In your case, there is an infinite amount of parameters that imply the same distribution. All parameters for which $$\sigma^2+\sigma_\epsilon^2=c$$ for some constant $$c$$ describe the same distribution; namely the one where all variances are $$c$$. So, as an example $$\sigma^2=1,\sigma_\epsilon^2=1$$, describes the same distribution as $$\sigma^2=0,\sigma_\epsilon^2=2$$.
If we now turn to how this influences maximum likelihood estimation. The likelihood of any parameter combination is only influenced by which $$c$$ it implies. Let's assume that $$\hat{c}$$ is the maximum likelihood estimate of $$c$$. You can get at this $$\hat{c}$$ with all parameters that satisfy $$\sigma^2+\sigma_\epsilon^2=\hat{c}$$, which are infinitely many. Thus, a maximum likelihood point estimate does not exist and can also not converge to the true value. Thus, it is not consistent. | {"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": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9888448119163513, "perplexity": 154.51122899322212}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313936.42/warc/CC-MAIN-20190818145013-20190818171013-00247.warc.gz"} |
https://mathoverflow.net/questions/143270/is-small-dependence-enough-for-central-limit-theorem | # Is “small” dependence enough for central limit theorem?
Writing down a paper about some estimation of some combinatorial quantities, i realized that i would have much more precise results if these two questions have positive answer:
1) Suppose you have a sequence of random variables $X_n$(boolean random variable with $Pr(X_i=1)=1/2$), such that $Cov(X_n,X_{n+1})=c$(in my case $c=-1/12$) and $X_i,X_j$ are independent whenever $|i-j|>1$. What can be said of $X_1+...+X_n$? Does the central limit theorem hold, altough there is no complete indipendence but "almost"?
2) Consider the well known relation ${2n} \choose {n}$$\sim\frac{4^n}{\sqrt \pi n}$. Is there a purely probabilistic way(using the central limit theorem or something near there) to prove this? The setting i've in mind is of course Bernoulli of parameter 1/2 $X_1,...,X_{2n}$ independent each other. And i can see that it would suffice to prove the convergence in 0 of the discrete densities to the gaussian in 0. Moreover if the answer in 1) is positive, does it allows, also there, the same asymptotics for the central term of $X_1+...+X_n$?
Thanks for any explanation!
For point 1, search for CLT for mixing sequences'' you will be drowned by the number of hits. Also, there are CLT's for stationary sequences in many textbooks - Hall and Heyde's book has a section on that.
For point 2, search for local CLT for lattice variables'' | {"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": 0.9625173807144165, "perplexity": 365.5666840037165}, "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/1618038071212.27/warc/CC-MAIN-20210413000853-20210413030853-00394.warc.gz"} |
http://tex.stackexchange.com/questions/74110/where-to-put-floats-definitions | # Where to put floats definitions?
I always use floats for figures, tables, graphs, and any other object that is not part of the text. LaTeX do a really good job. Normally I put the definition when i use a withe line (after the paragraph that contains the reference to the float). It is correct? Where we have to put float definition (after the reference with input, at the end of the sentence, ...) to have the best positioning of float (decided by LaTeX, without options like h, b, ... that i never use)?
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If the question is unclear, please tell me. I will try to improve it! ;) – R. M. Sep 25 '12 at 20:46
This is most likely based on user preference and where you want the floats to end up. Related, if not duplicate: Keeping tables/figures close to where they are mentioned and How to influence the position of float environments like figure and table in LaTeX? – Werner Sep 25 '12 at 20:54
@Werner I don't want to keep floats close to to where we defined it or influence positioning of floats. I want LaTeX to do it completly automatically. I just want to know if there is a "rule" over definition position to obtain the best typographical result. – R. M. Sep 25 '12 at 21:10
If I understand you correctly you are placing the float definition after the paragraph containing the first reference. That has the advantage of making the source text a bit more readable as the paragraph text is not broken by the \begin{figure}... markup, but that is less of a problem if your figure environment is in a separate file as the markup is then just
... text text text \ref{zzz}{\input{file-with-figure-zzz} text text ....
The disadvantage of always putting the float definition at the end of a paragraph is that LaTeX never moves floats forward more than the top of the page that contains the point of definition, so if you have a long paragraph with \ref{zzz} near the start, then if the \begin{figure} is included at the end of the paragraph that is on the next page, there is no way that LaTeX can put the figure on the page with the reference, even if it would fit. | {"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": 0.9368875026702881, "perplexity": 730.5938458896404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645330816.69/warc/CC-MAIN-20150827031530-00013-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://gradestack.com/GMAT-Complete-Course/Inequalities/Positive-Negative/18883-3742-34328-study-wtw | # Positive & Negative Numbers
A number greater than 0 is positive. On the number line, positive numbers are to the right of 0. A number less than 0 is negative. On the number line, negative numbers are to the left of 0. Zero is the only number that is neither positive nor negative; it divides the two sets of numbers. On the number line, numbers increase to the right and decrease to the left.
The expression x > y means that x is greater than y. In other words, x is to the right of y on the number line:
​
We usually have no trouble determining which of two numbers is larger when both are positive or one is positive and the other negative (e.g., 5 > 2 and 3.1 > –2). However, we sometimes hesitate when both numbers are negative (e.g., –2 > –4.5). When in doubt, think of the number line: if one number is to the right of the number, then it is larger. As the number line below illustrates, –2 is to the right of –4.5. Hence, –2 is larger than –4.5.
​ | {"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": 0.8560724258422852, "perplexity": 290.1041466483763}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549425082.56/warc/CC-MAIN-20170725062346-20170725082346-00182.warc.gz"} |
http://mathoverflow.net/questions/104141/maximal-ideals-of-the-rings-of-baire-one-functions | # Maximal ideals of the rings of Baire-One Functions
A real function $f:X\rightarrow \mathbb{R}$ is called Baire-one function, if there is a sequence $(f_n)_{n=1} ^\infty$ of continuous functions $f_n:X\rightarrow \mathbb{R}$ on $X$ so that for all $x\in X$ $$\lim_{n\rightarrow \infty}f_n(x)=f(x).$$
When $X$ is a Banach space, we have the following theorem referred to as Baire factorization theorem.
Theorem: The real function $f:X\rightarrow \mathbb{R}$ is in the class of Baire-one if and only if for all closed subset $K\subset X$, the restricted function $f|_K$ has a point of continuity with respect to $K$.
Definition: We denote the set of all Baire-one real functions on the space $X$ by $Ba_1(X)$.
As you could easily see, $Ba_1(X)$ forms a ring with pointwise addition and multiplication. For simplicity let me consider $X=[0 , 1]$.
Suppose $C[0 , 1]$ denotes the ring of all continuous real valued functions on the interval $[0 , 1]$. By the theorem of Gelfond and Kolmogrov we know that the set of all maximal ideals of the ring $C[0 , 1]$ is of the form $\{M_x: x\in X\}$, where $M_x=\{f\in C[0, 1]: f(x)=0\}$.
Compared with the ring $C[0 , 1]$ we could easily find that the sets of the form $M_x^1=\{f\in Ba_1[0 , 1]: f(x)=0\}$ are maximal ideals of the ring $Ba_1[0 , 1]$. From this property some questions came in my mind as follows:
Question 1: Does there exist a maximal ideal in $Ba_1[0 , 1]$ other than maximal ideals of the form $M_x^1$ for $x\in X$?
Question 2: Is the ring $Ba_1[0 , 1]$ a $\mathbf{PM}$-ring? $($i.e. a ring in which each prime ideal is contained in a unique maximal ideal.$)$
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It looks to me like the collection of functions with finite support (that is, those which are zero on a cofinite set) forms an ideal not contained in any of the maximal ideals you've listed. If I understand your question correctly, that means the answer to question 1 is "yes." – Clinton Conley Aug 6 '12 at 23:00
Yes Dear Clinton. Very Good. Also we could consider the ideal generated by all $\chi_{(a,1]}$ for $a \in (0,1]$, where $\chi_{(a,1]}$ is the characteristic function of the interval $(a , 1]$. then we could find a maximal ideal which contains all of these functions.I think this over ring of $C[0,1]$ has a complex behavior, because as you consider, it is full of idempotents. – Ali Reza Aug 6 '12 at 23:20
Isn't $Ba_1(X)$ a commutative C*-algebra (in which case it is certainly a PM-ring)? – Douglas Somerset Mar 22 '13 at 22:43
D. Somerset: Perhaps $Ba_1(X)$ is a commutative C*-algebra, and thus a PM-ring. | {"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": 0.9533716440200806, "perplexity": 116.7502686544323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398454553.89/warc/CC-MAIN-20151124205414-00120-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://www.hongliangjie.com/2011/03/09/reviews-on-user-modeling-in-topic-models/ | # Reviews on User Modeling in Topic Models
In this post, I would like to review several papers that wish to extend standard topic models with incorporating user information. The first paradigm or group of papers is introduced by M. Rosen-Zvi et al.
These three papers define a “Author-Topic” model, a simple extension of LDA. The generation process is as follows:
1. For each document $latex d$:
1. For each word position:
1. Sample an author $latex x$ uniformly sampled from the group of authors for this document.
2. Sample an topic assignment $latex z$ from per-author multinomial distribution over topics $latex \theta_{x}$.
3. Sample a word $latex w$ from topic $latex z$, a multinomial distribution over words.
The inference of the model is done by Gibbs Sampling. The biggest drawback of the model is that it loses the distribution over topics for documents. In “Learning Author-Topic Models from Text Corpora“, the authors proposed a heuristic solution to this problem: adding a fictitious author for each document. The second group of papers is from UMass.
They proposed several models. The first one is “Author-Recipient-Topic” model, which is suitable for message data, like emails. The generation process is as follows:
1. For each document $latex d$, we observe its author $latex a_{d}$ and a set of recipients $latex \mathbf{r}_{d}$:
1. For each word position:
1. Sample a recipient $latex x$ uniformly sampled from $latex \mathbf{r}_{d}$.
2. Sample an topic assignment $latex z$ from author-recipient multinomial distribution over topics $latex \theta_{a_{d},x}$.
3. Sample a word $latex w$ from topic $latex z$, a multinomial distribution over words.
This model is further extended into “Role-Author-Recipient-Topic” model. The idea is that each author or recipient may play different roles in the exchange of messages. Therefore, it is better to explicitly model them. Three possible variants are introduced. The first variant is that for each word position, we first sample a role for author and for the sampled recipient as well. Once the roles are sampled, the topic assignments are sampled from role-role pair-determined multinomial distribution over topics. The second variant is that only one role is generated for the author of the message. However, for recipients, each one has a role. For each word position, a recipient with his corresponding role is firstly sampled and a topic assignment is sampled from author-role author-role pair multinomial distribution over topics. The third variant is that all recipients share a single role. The third model is “Author-Persona-Topic” model. The generation process is as follows:
1. For each author $latex a$:
1. Sample a multinomial distribution over persona $latex \eta_{a}$.
2. For each persona $latex g$, sample a multinomial distribution over topics $latex \theta_{g}$.
2. For each document $latex d$ with author $latex a_{d}$:
1. Sample a persona $latex g_{d}$ from $latex \eta_{a_{d}}$.
2. For each word position:
1. Sample an topic assignment $latex z$ from $latex \theta_{g_{d}}$.
2. Sample a word $latex w$ from topic $latex z$, a multinomial distribution over words.
All these models do not have a per-document distribution for topics.
The third group of papers is from Noriaki Kawamae. Both models introduced in these papers extended the ideas of “Author-Topic” model and “Author-Persona-Topic” model in particular.
The first model is “Author-Interest-Topic” model. It introduced a notion of “document-class”. The authors have a distribution over document-classes and for each document class, it has a distribution over topics. Here, we can think of document-class as “persona” in previous models. For each document, it firstly samples a document-class from per-author distibution over document classes. Then, by using this document-class, we can draw topics from this particular class. The difference between “Author-Interest-Topic” model and “Author-Persona-Topic” model is that the distribution over topics for each persona is under author level in “Author-Persona-Topic” but they are global variables in “Author-Interest Topic” model. The “Latent-Interest-Topic” model is much complicated than all previous models. It adds another layer of abstraction, author-classes. For each author, it has variable to indicate his author-class, which is drawn from a multinomial distribution. For each author-class, there is a multinomial distribution over topics. For each document, we first draw a document-class from its author’s per author-class distribution over document-classes. Then, the later generation process is same as “Author-Interest-Topic“. The key for “Author-Interest-Topic” and “Latent-Interest-Topic” models is that they are clustering models, in the sense that authors or documents are forced clustered into either author classes or document classes.
The last group of papers is from Jie Tang et al. All the proposed models are based on “Author-Topic” model.
They firstly proposed three variants of “Author-Conference-Topic” model. For each author, there is a multinomial distribution over topics. For each token in the document, an author is uniformly sampled and the topic assignment is sampled from per-author multinomial distribution over topics. The differences between three variants are how the conference stamp is generated. We omit the discussion 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": 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": 0.8814207315444946, "perplexity": 1687.3484916898028}, "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-2018-05/segments/1516084890771.63/warc/CC-MAIN-20180121135825-20180121155825-00045.warc.gz"} |
https://infoscience.epfl.ch/record/153444 | Infoscience
Journal article
# Electric and magnetic interaction of dyonic D-branes and odd spin structure
We present a general description of electromagnetic RR interactions between pairs of magnetically dual D-branes, focusing on the interaction of a magnetically charged brane with an electrically charged one. In the boundary state formalism, it turns out that while the electric-electric and/or magnetic-magnetic interaction corresponds to the usual RR even spin structure, the magnetic-electric interaction is described by the RR odd spin structure. As representative of the generic case of a dual pair of p and 6-p-branes, we discuss in detail the case of the self-dual 3-brane wrapped on a T-6/Z(3), which looks like an extremal dyonic black hole in four dimensions. (C) 1998 Elsevier Science B.V. | {"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": 0.9257063269615173, "perplexity": 1072.199225311995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687484.46/warc/CC-MAIN-20170920213425-20170920233425-00686.warc.gz"} |
https://quant.stackexchange.com/questions/15356/how-do-i-price-pt-pt-t-n-sum-i-1npt-t-i-1-pt-t-i | # How do I price $P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$?
Derive the pricing formula $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$$directly, by constructing a self-financing portfolio which replicates the cash flow of the floating rate bond.
$P(t,T_{i-1})$ means Buy, at time $t$, one $T_{i−1}$-bond. This will cost $P(t, T_{i−1})$
$P(t)$ means price at $t$ time
This question is related to the Arbitrage Theory in Continuous Time book by Tomas Bjork.
• You should go more into detail. What the difference between $P$ and $p$? $p$ does not appear in the formula. I assume $P$ are the prices of zero-coupon bonds? – Ric Nov 7 '14 at 12:44
• @Richardour. your right all the $P$ are same. I took mistake. – pual ambagher Nov 7 '14 at 13:22
In another solution, the answer is based on replication approach. Here, we provide some other approaches for the valuation of the LIBOR rate, \begin{align} L(T_{i-1}; T_{i-1}, T_i) = \frac{1}{\Delta T_i}\left(\frac{1}{P(T_{i-1}, T_i)}-1\right), \end{align} set a $T_{i-1}$ and paid at $T_i$, where $\Delta T_i =T_i-T_{i-1}$.
Let $E$ be the expectation operator under the risk-neutral measure $P$, which has the money market account value process $B_t$ as the numeraire. Then the value at time $t$ of the float payment $L(T_{i-1}; T_{i-1}, T_i)\Delta T_i$ made at $T_i$ is given by \begin{align*} B_t E\left(\frac{L(T_{i-1}; T_{i-1}, T_i)\Delta T_i}{B_{T_i}}\mid\mathcal{F}_t \right) &= B_t E\left(\frac{L(T_{i-1}; T_{i-1}, T_i)\Delta T_i}{B_{T_{i-1}}} E\left(\frac{B_{T_{i-1}}}{B_{T_i}} \mid \mathcal{F}_{T_{i-1}}\right)\mid\mathcal{F}_t \right)\\ &=B_t E\left(\frac{L(T_{i-1}; T_{i-1}, T_i)\Delta T_i}{B_{T_{i-1}}} P(T_{i-1}, T_i)\mid\mathcal{F}_t \right)\\ &=B_t E\left(\frac{1}{B_{T_{i-1}}} \Big[1 - P(T_{i-1}, T_i)\Big]\mid\mathcal{F}_t \right)\\ &= B_t E\left(\frac{1}{B_{T_{i-1}}}\mid\mathcal{F}_t \right) - B_t E\left(\frac{P(T_{i-1}, T_i)}{B_{T_{i-1}}}\mid\mathcal{F}_t \right)\\ &=P(t, T_{i-1}) - B_t \times \frac{P(t, T_i)}{B_t}\\ &= P(t, T_{i-1}) - P(t, T_i). \end{align*}
Alternatively, let $E_{T_i}$ be the expectation operator under the $T_i$-forward measure $P_{T_i}$, which has the bond price process $\{P(t, T_i)\mid t \geq 0\}$ as the numeraire. Then the LIBOR rate process $\{L(t; T_{i-1}, T_i) \mid 0\leq t \leq T_{i-1} \}$ is a martingale under $P_{T_i}$. Moreover, for $0 \leq t \leq T_{i-1}$, let \begin{align} \eta_t &\triangleq \frac{dP}{dP_{T_{i}}}\big|_t\\ &=\frac{B_t P(0, T_{i})}{P(t, T_i)}. \end{align} By Bayes formula, for $0 \leq t \leq T_{i-1}$, the value at time $t$ of the float payment $L(T_{i-1}; T_{i-1}, T_i)\Delta T_i$ made at $T_i$ is given by \begin{align*} B_t E\left(\frac{L(T_{i-1}; T_{i-1}, T_i)\Delta T_i}{B_{T_i}}\mid\mathcal{F}_t \right) &= B_t E_{T_i}\left(\frac{\eta_{T_i}}{\eta_t}\frac{L(T_{i-1}; T_{i-1}, T_i)\Delta T_i}{B_{T_i}}\mid\mathcal{F}_t \right)\\ &=P(t, T_i)E_{T_i}\left(L(T_{i-1}; T_{i-1}, T_i)\Delta T_i\mid\mathcal{F}_t \right)\\ &=P(t, T_i)L(t; T_{i-1}, T_i) \Delta T_i\\ &=P(t, T_{i-1}) - P(t, T_i), \end{align*} from the martingale property of $L$ under the $T_i$-forward measure $P_{T_i}$.
Edit for Gordon. First, fix point in time $T_0,...,T_n$ whereas $T_1,...,T_n$ are the coupon dates and $T_0$ is interpreted as the emission date of the bond. At time $T_i$, $i = 1,...,n$ the owner of the bond receives $c_i$.At time $T_n$ the owner receives the face value K.We now go on to compute the price of this bond, and it is obvious that the coupon bond can be replicated by holding a portfolio of zero coupon bonds with maturities $T_i$, $i = 1,...,n$.So the price,$P(t)$, at a time $t < T_1$, of the coupon bond is given by $$P(t)=KP(t,T_{n})+\sum_{i=1}^{n}c_i P(t,T_{i})$$
If the coupon rate $r_i$ is set to the spot LIBOR rate $L(T_{i−1}, T_i)$ ,then \begin{align} c_i=(T_i-T_{i−1})L(T_{i−1}, T_i)K \end{align} We now go on to compute the value of this bond at some time $t < T_0$, in the case when the coupon dates are equally spaced, with $T_i−T_{i−1}=\delta$, and to this end we study the individual coupon $c_i$. Without loss of generality we may assume that $K = 1$, and inserting the definition of the LIBOR rate \begin{align} c_i=\frac{1}{P(T_{i−1}, T_i)}-1 \end{align} The value at $t$, of the term $−1$ , is of course equal to $-P(t, T_i)$ and it remains to compute the value of the term$\frac{1}{P(T_{i−1}, T_i)}$ which is paid out at $T_i$.This is, however, easily done through the following argument.
1. Buy, at time $t$, one $T_{i−1}$-bond. This will cost $P(t, T_{i−1})$.
2. At time $T_{i−1}$ you will receive the amount $1$.
3. Invest this unit amount in $T_{i−1}$-bond. This will give you exactly $\frac{1}{P(T_{i−1}, T_i)}$ bonds.
4. At $\,T_i$ the bonds will mature, each at the face value $1$. Thus, at time $T_i$, you will obtain the amount $\frac{1}{P(T_{i−1}, T_i)}$
Thus the value at $t$, of obtaining $\frac{1}{P(T_{i−1}, T_i)}$ at $T_i$, is given by $P(t, T_{i-1})$, and the value at t of the coupon $c_i$ is $P(t, T_{i−1}) − P(t, T_i)$. then, by summing up all values of $c_i$ and the value of the notional amount (i.e. 1) at $T_n$, we have $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}P(t,T_{i-1})-P(t,T_{i})=p(t,T_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": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9935563206672668, "perplexity": 1201.2360929931167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00390.warc.gz"} |
https://stacks.math.columbia.edu/tag/04LW | Lemma 59.40.3. Let $X$, $Y$ be schemes. Any two morphisms $a, b : X \to Y$ of schemes for which there exists a $2$-isomorphism $(a_{small}, a_{small}^\sharp ) \cong (b_{small}, b_{small}^\sharp )$ in the $2$-category of ringed topoi are equal.
Proof. Let us argue this carefuly since it is a bit confusing. Let $t : a_{small}^{-1} \to b_{small}^{-1}$ be the $2$-isomorphism. Consider any open $V \subset Y$. Note that $h_ V$ is a subsheaf of the final sheaf $*$. Thus both $a_{small}^{-1}h_ V = h_{a^{-1}(V)}$ and $b_{small}^{-1}h_ V = h_{b^{-1}(V)}$ are subsheaves of the final sheaf. Thus the isomorphism
$t : a_{small}^{-1}h_ V = h_{a^{-1}(V)} \to b_{small}^{-1}h_ V = h_{b^{-1}(V)}$
has to be the identity, and $a^{-1}(V) = b^{-1}(V)$. It follows that $a$ and $b$ are equal on underlying topological spaces. Next, take a section $f \in \mathcal{O}_ Y(V)$. This determines and is determined by a map of sheaves of sets $f : h_ V \to \mathcal{O}_ Y$. Pull this back and apply $t$ to get a commutative diagram
$\xymatrix{ h_{b^{-1}(V)} \ar@{=}[r] & b_{small}^{-1}h_ V \ar[d]^{b_{small}^{-1}(f)} & & a_{small}^{-1}h_ V \ar[d]^{a_{small}^{-1}(f)} \ar[ll]^ t & h_{a^{-1}(V)} \ar@{=}[l] \\ & b_{small}^{-1}\mathcal{O}_ Y \ar[rd]_{b^\sharp } & & a_{small}^{-1}\mathcal{O}_ Y \ar[ll]^ t \ar[ld]^{a^\sharp } \\ & & \mathcal{O}_ X }$
where the triangle is commutative by definition of a $2$-isomorphism in Modules on Sites, Section 18.8. Above we have seen that the composition of the top horizontal arrows comes from the identity $a^{-1}(V) = b^{-1}(V)$. Thus the commutativity of the diagram tells us that $a_{small}^\sharp (f) = b_{small}^\sharp (f)$ in $\mathcal{O}_ X(a^{-1}(V)) = \mathcal{O}_ X(b^{-1}(V))$. Since this holds for every open $V$ and every $f \in \mathcal{O}_ Y(V)$ we conclude that $a = b$ as morphisms of schemes. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9971814751625061, "perplexity": 133.28198941230607}, "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/1659882570651.49/warc/CC-MAIN-20220807150925-20220807180925-00438.warc.gz"} |
http://www.ipam.ucla.edu/abstract/?tid=16654&pcode=CTF2021 | ## Can convective heat transport be more efficient than the so-called 'ultimate' regime?
#### Basile GalletCommissariat à l'Énergie Atomique (CEA)Condensed matter physics
Decades of investigation of the Rayleigh-Bénard (RB) thermal convection setup indicate that the heat transport is strongly restricted by boundary layers near the hot and cold solid plates. This prevents the observation of the 'ultimate' scaling-regime of thermal convection, where bulk turbulence controls the convective heat flux independently of molecular diffusivities. In contrast to the RB setup, many geophysical and astrophysical convective flows are driven radiatively: absorption of incoming light by a body of fluid induces local internal heating. We have developed a laboratory experiment that reproduces such radiative heating: heat is input radiatively, directly inside the bulk turbulent flow and away from the boundary layers.
After providing experimental and numerical evidence that this setup naturally leads to the ultimate regime of thermal convection, I will discuss the maximum theoretical Nusselt number that can be achieved by such internally heated and cooled convection. I will show that there exist steady laminar solutions that transport heat more efficiently than the ultimate regime, with a scaling behavior Nu~Ra. These solutions can be stable in 2D, but they are unstable in 3D and quickly evolve into a turbulent state. I will show that a maximization of the heat transport over turbulent flows only (i.e., over flows that satisfy the zeroth law of turbulence) leads to an upper bound on the Nusselt number that is proportional to the square root of the Nusselt number, in line with the experimental and numerical data.
Back to Transport and Mixing in Complex and Turbulent Flows | {"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": 0.8368076086044312, "perplexity": 1046.9975045971494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585507.26/warc/CC-MAIN-20211022114748-20211022144748-00123.warc.gz"} |
https://forum.allaboutcircuits.com/threads/trapezoidal-method.61419/ | # Trapezoidal Method
Discussion in 'Homework Help' started by Kayne, Nov 1, 2011.
1. ### Kayne Thread Starter Active Member
Mar 19, 2009
105
0
Hi All,
I would like an answer checked that I have found for the following problem.
$y = 5 \int^1_0 \frac{1}{1+x^2} dx$
using
$\int^1_0 f(x) dx = (b-a)[\frac{f(a)+f(b)}{2}]$
$5*((1-0)*[\frac{{\frac{1}{1+0^2}+\frac{1}{1+1^2}}}{2}])$
$5*0.75 = 3.75$
Have I solved this correctly?
I have tried to chack this in matlab with the code below but I am not getting this answer which now I am not sure which is incorrect.
X = 0:0.5:1;
Y = 5*(1./X.^2)
Z = trapz(X,Y)
2. ### Papabravo Expert
Feb 24, 2006
12,164
2,673
I think you are supposed to use more than a single trapezoid to approximate the integral. Did you really think one would do the trick?
3. ### t_n_k AAC Fanatic!
Mar 6, 2009
5,448
790
Plus your matlab code isn't correct.
For three terms it would be something like .... [I don't use Matlab]
X=0:0.5:1
Z=trapz(X,Y)
So to compare values for three terms, your pencil & paper method should have the sum of two trapezoidal approximations with limits from [0 to 0.5] and [0.5 to 1]
As Papbravo implies you should probably use several terms to come up with a good approximation to the 'exact' integral.
$ans=\frac{5\pi}{4}$
With 11 terms X=[0 0.1 0.2 .... 1.0] I get a value of Z=3.9249075
Last edited: Nov 2, 2011
4. ### Papabravo Expert
Feb 24, 2006
12,164
2,673
A graduate degree in Mathematics comes in handy on an occasional basis.
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2,074 | {"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": 0, "mimetex.cgi": 5, "/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": 0.8062214851379395, "perplexity": 3975.29693056408}, "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-2019-30/segments/1563195527474.85/warc/CC-MAIN-20190722030952-20190722052952-00354.warc.gz"} |
https://www.zbmath.org/?q=ai%3Ailic-stepic.angelina+se%3A00006948 | ×
# zbMATH — the first resource for mathematics
$$p$$-adic probability logics. (English) Zbl 1353.03013
Summary: This paper represents an comprehensive overview of the results from three papers where we developed several propositional logics for reasoning about $$p$$-adic valued probability. Each of these logics is a sound, complete and decidable extension of classical propositional logic.
##### MSC:
03B48 Probability and inductive logic 03B25 Decidability of theories and sets of sentences 03B42 Logics of knowledge and belief (including belief change)
Full Text: | {"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": 0.9133339524269104, "perplexity": 3149.5874534222426}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703517159.7/warc/CC-MAIN-20210118220236-20210119010236-00434.warc.gz"} |
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