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https://www.physicsforums.com/threads/a-square-matrix-a-with-ker-a-2-ker-a-3.532199/ | # A square matrix A with ker(A^2)= ker (A^3)
1. Sep 20, 2011
### yeland404
1. The problem statement, all variables and given/known data
a square matrix A with ker(A^2)= ker (A^3), is ker(A^3)= ker (A^4),verify...
2. Relevant equations
3. The attempt at a solution
2. Sep 20, 2011
### micromass
Staff Emeritus
3. Sep 20, 2011
### yeland404
it means that A^2*vector x= 0 and A*x=0 has same result,then I really confused how to do the next step
4. Sep 20, 2011
### micromass
Staff Emeritus
No, it means that
$$A^2x=0~\Leftrightarrow~A^3x=0$$
You need to prove that
$$A^3x=0~\Leftrightarrow~A^4x=0$$
5. Sep 20, 2011
### yeland404
emm...., to the difinition it says that ker(A) is T(x)=A(x)=0
6. Sep 20, 2011
### micromass
Staff Emeritus
Yes, but you're not working with ker(A) here, but with ker(A2).
7. Sep 20, 2011
### yeland404
should define a matrix A and write A^2 as dot product of A & A,and also to A^3...it seems to be so complex, or use the block to devide the matrix into some small matrix?
8. Sep 20, 2011
### micromass
Staff Emeritus
Do you understand my Post 4??
9. Sep 20, 2011
### yeland404
so times A on both side of the equation?
10. Sep 20, 2011
### micromass
Staff Emeritus
No, you need to prove two things:
If $A^3x=0$, then $A^4x=0$. This can indeed be accomplished by multiplying sides with A.
But you also need to prove that if $A^4x=0$, then $A^3x=0$.
11. Sep 26, 2011
### yeland404
so Ker (A^2)=0 can lead to Ker(A^4)=0,then?
12. Sep 26, 2011
### HallsofIvy
Staff Emeritus
NO ONE has said that Ker(A^2)= 0 so I do not understand why you are asking this question. You seem, frankly, to have no idea what the question is saying. ker(A^2)= ker(A^3) means, as micromass said, "A^2x= 0 if and only if A^3x= 0". You want to use that to prove "A^3x= 0 if and only if A^4x= 0". As micromass said, the first part is easy: if A^3x= 0 then, applying A to both sides, A^4x= A0= 0 which proves that ker(A^3) is a subset of ker(A^4). You still need to prove the other way: if A^4x= 0, then A^3= 0. You cannot just multiply by A^{-1} because you have no reason to think that A is invertible. But notice that ker(A^2)= ker(A^3) has not yet been used so it might help to note that A^4x= A^2(A^2x).
Similar Discussions: A square matrix A with ker(A^2)= ker (A^3) | {"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": 0.8831621408462524, "perplexity": 3217.1619880815574}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818691977.66/warc/CC-MAIN-20170925145232-20170925165232-00583.warc.gz"} |
https://www.physicsforums.com/threads/gravitational-field-question.271949/ | # Gravitational Field Question
1. Nov 14, 2008
### jessedevin
1. The problem statement, all variables and given/known data
Three objects -- two of mass m and one of mass M -- are located at three corners of a square of edge length l. Find the gravitational field g at the fourth corner due to these objects. (Express your answers in terms of the edge length l, the masses m and M, and the gravitational constant G).
2. Relevant equations
g=-GM/r2
3. The attempt at a solution
g= ga+gb+gc
g= Gm/l2 $$\hat{i}$$+ (GM/(l$$\sqrt{2}$$)2)(cos($$\pi/4$$)$$\hat{i}$$+sin($$\pi/4$$)$$\hat{j}$$)+Gm/l2 $$\hat{j}$$
I know you have to take the magnitude of this, but when I did that , I still get the wrong answer. Here's what I got:
||g||=$$\sqrt{2G^2/l^4(m^2+M^2)}$$
Did I start it right? Can someone help?
Last edited: Nov 14, 2008
2. Nov 14, 2008
### LowlyPion
Isn't the gravitational field given by GM/r ?
You have 3 vectors to add, but happily the 2 m's at right angles gives one lying in the direction of M
So ... √2Gm/L + GM/(√2*L) = √2*G*(m + M/2)/L ?
3. Nov 14, 2008
### jessedevin
So do you take the magnitude of that? Im still confused, because my book says otherwise. Can you go through your process?
4. Dec 2, 2008
### SonHa
I think what you did originally is correct, but it ask for the magnitude without the vector sign. So just put down the answer using c^2 = a^2 + b^2 and then I believe you have to indicate the degree according to the x-axis. I'm doing a similar problem. Wait, yeah you did that, never mind.
5. Dec 2, 2008
### SonHa
I got it!
Instead of converting M vectors into g forces of x and y, why don't you convert the other 2 m mass into direction of M which is Gm/l^2 * cos(45) * 2.
Then add it to the g force of M
My answer is (1.41Gm + 0.5GM)/l^2.
Hope it helps, the post was like half a month ago, lol. | {"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": 0.9554958939552307, "perplexity": 1246.4677800755096}, "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-2017-39/segments/1505818686077.22/warc/CC-MAIN-20170919235817-20170920015817-00560.warc.gz"} |
https://arxiv.org/abs/1902.04557 | Full-text links:
gr-qc
(what is this?)
# Title:Inferring neutron star properties from GW170817 with universal relations
Abstract: Because all neutron stars share a common equation of state, tidal deformability constraints from the compact binary coalescence GW170817 have implications for the properties of neutron stars in other systems. Using equation-of-state insensitive relations between macroscopic observables like moment of inertia ($I$), tidal deformability ($\Lambda$) and stellar compactness, we derive constraints on these properties as a function of neutron-star mass based on the LIGO-Virgo collaboration's canonical deformability measurement, $\Lambda_{1.4} = 190^{+390}_{-120}$. Specific estimates of $\Lambda$, $I$, dimensionless spin $\chi$, and stellar radius $R$ for a few systems targeted by radio or X-ray studies are extracted from the general constraints. We also infer the canonical neutron-star radius as $R_{1.4} = 10.9^{+1.9}_{-1.5}$ km at 90$\%$ confidence. We further demonstrate how a gravitational-wave measurement of $\Lambda_{1.4}$ can be combined with independent measurements of neutron-star radii to tighten constraints on the tidal deformability as a proxy for the equation of state. We find that GW170817 and existing observations of six thermonuclear bursters in low-mass X-ray binaries jointly imply $\Lambda_{1.4} = 196^{+92}_{-63}$ at the 90$\%$ confidence level.
Comments: 18 pages, 7 figures; corrected multimessenger tidal deformability constraint Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE); Nuclear Theory (nucl-th) Cite as: arXiv:1902.04557 [gr-qc] (or arXiv:1902.04557v4 [gr-qc] for this version)
## Submission history
From: Philippe Landry [view email]
[v1] Tue, 12 Feb 2019 18:58:46 UTC (403 KB)
[v2] Fri, 22 Feb 2019 22:19:00 UTC (354 KB)
[v3] Mon, 4 Mar 2019 10:13:34 UTC (368 KB)
[v4] Tue, 12 Mar 2019 07:21:48 UTC (372 KB) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8310767412185669, "perplexity": 4364.50224728289}, "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-2019-13/segments/1552912203378.92/warc/CC-MAIN-20190324063449-20190324085449-00369.warc.gz"} |
https://diw-econ.de/en/publications/the-economic-importance-of-onshore-wind-energy-in-schleswig-holstein/ | # The economic importance of onshore wind energy in Schleswig-Holstein
DIW Econ was commissioned by the Schleswig-Holstein Regional Association of the German Wind Energy Association to investigate the economic significance of onshore wind energy in Schleswig-Holstein.
This study analyses, on the one hand, the investments in new wind energy plants and on the other hand, the revenues and costs arising from the operation and maintenance of existing wind energy plants. It will thus determine the effects of the wind energy sector on regional value-added, employment and tax revenues in Schleswig-Holstein. The overall effect of the three indicators can be divided into direct, indirect and induced effects.
The study concludes that onshore wind energy in Schleswig-Holstein in 2018 will have triggered economic effects for a total of 11,900 employees and 1.3 billion euros in gross value added. Besides, the wind energy sector generates public revenues of at least 45.6 million euros. This makes it an essential driver of Schleswig-Holstein’s regional economy. | {"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": 0.8353236317634583, "perplexity": 2492.7947977485474}, "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/1634323588246.79/warc/CC-MAIN-20211028003812-20211028033812-00663.warc.gz"} |
https://www.esaral.com/q/given-that-the-standard-potentials-88394 | # Given that the standard potentials
Question:
Given that the standard potentials $\left(\mathrm{E}^{0}\right)$ of $\mathrm{Cu}^{2+} / \mathrm{Cu}$ and $\mathrm{Cu}^{+} /$ $\mathrm{Cu}$ are $0.34 \mathrm{~V}$ and $0.522 \mathrm{~V}$ respectively, the $\mathrm{E}^{0}$ of $\mathrm{Cu}^{2+} /$ $\mathrm{Cu}^{+}$is:
1. $+0.182 \mathrm{~V}$
2. $+0.158 \mathrm{~V}$
3. $-0.182 \mathrm{~V}$
4. $-0.158 \mathrm{~V}$
Correct Option: , 2
Solution:
$\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu}, \Delta \mathrm{G}_{1}^{0}=-2 \mathrm{~F}(0.34) \ldots$ (i)
$\mathrm{Cu}^{+}+e^{-} \longrightarrow \mathrm{Cu}, \Delta \mathrm{G}_{2}^{\circ}=-\mathrm{F}(0.522) \quad$...(ii)
Subtract (ii) from (i)
$\mathrm{Cu}^{2+}+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}^{+}, \quad \Delta \mathrm{G}_{3}^{\circ}=-\mathrm{F}\left(\mathrm{E}^{0}\right)$
$\therefore \Delta \mathrm{G}_{1}^{\circ}-\Delta \mathrm{G}_{2}^{\circ}=\mathrm{G}_{3}^{\circ}$
$\Rightarrow-\mathrm{FE}^{\circ}=-2 \mathrm{~F}(0.34)+\mathrm{F}(0.522)$
$\Rightarrow \mathrm{E}^{\circ}=0.68-0.522=0.158 \mathrm{~V}$ | {"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": 0.9848425984382629, "perplexity": 1746.3554780138281}, "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-2023-14/segments/1679296946637.95/warc/CC-MAIN-20230327025922-20230327055922-00637.warc.gz"} |
http://math.stackexchange.com/questions/55305/subset-relations-among-sobolev-spaces-and-their-duals | # subset relations among Sobolev spaces and their duals
This may be a rather dense question, but I would nevertheless be grateful for some guidance.
The question has to do with the Sobolev spaces $H^m (\Omega)$ on an open bounded domain $\Omega$ of $\mathbb{R}^n$, where $m \geq 0$ is integer. These are Hilbert spaces; thus the Riesz representation theorem tells us that there is a one-to-one and onto correspondence between elements of $H^m (\Omega)$ and elements of its dual $H^{-m} (\Omega)$. Yet, we also have the inclusion property $H^{m} (\Omega) \subset L_2 (\Omega) \subset H^{-m} (\Omega)$ (e.g. Oden and Reddy, Intro. to the Mathematical Theory of Finite Elements, p. 108). How can both of these hold? In other words, how can there be a one-to-one and onto correspondence between $H^m (\Omega)$ and $H^{-m} (\Omega)$, and yet the former is a strict subset of the latter?
-
That's a problem pretty much every one learning about Sobolev spaces seems to encounter sooner or later, see here. – lvb Aug 3 '11 at 11:45
@user14178: A bijection is not the same thing as equality. The set of all even numbers is in bijection with the set of all numbers, but is also a proper subset. (This is one of the possible definitions for an infinite set.) – Zhen Lin Aug 3 '11 at 11:58
The dual space is the space of continuous linear functionals, and for a statement like $H^m \subset (H^m)^*$ to make sense one has to define a way to interpret functions as functionals, i.e. a linear embedding $H^m \to (H^m)^*$. There are two seemingly natural candidates: $$i_R(u)(v):=\left < u,v \right >_{H^m}$$ and $$i_D(u)(v):=\left < u,v \right >_{L^2}$$ The strictness of the inclusion translates to the question whether the embedding is an isomorphism, and it turns out that $i_R$ is an isomorphism according to the representation theorem, but $i_D$ is not! However, in accordance with distribution theory, $i_D$ is universally used to identify functions with functionals.
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Thanks for the pointers and the clear explanation. The apparent paradox is resolved by realizing that the inclusions are effected with the L_2 duality pairing and not the H^1, as you said. – Mark Rashid Aug 4 '11 at 6:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9270322918891907, "perplexity": 140.50052640478364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500812662.69/warc/CC-MAIN-20140820021332-00050-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-equations/165071-solving-substituting-complex-function-2.html | That's the chain rule. If you want to simplify the notation, do a quick z = dy/dx substitution, and you'll see how it works out. | {"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": 0.89664226770401, "perplexity": 195.06257374378535}, "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/1526794863923.6/warc/CC-MAIN-20180521023747-20180521043747-00424.warc.gz"} |
https://danosproject.atlassian.net/wiki/spaces/DAN/pages/601489455/Access+Control+Management+ACM+and+Role-Based+Access+Control+RBAC | # Access Control Management (ACM) and Role-Based Access Control (RBAC)
Role-based Access Control (RBAC) is a method of restricting access to part of the configuration to authorized users. RBAC allows an administrator to define the rules for a group of users that restrict which commands users of that group are allowed to run.
RBAC is performed by first creating a group assigned to the Access Control Management (ACM) rule set, adding a user to the group, creating a rule set to match the group to the paths in the system, then configuring the system to allow or deny those paths that are applied to the group.
Users are allowed to be in one of three class of users with defined privilege levels:
• Operator—Allowed to execute commands that are defined in the DANOS CLI. Not allowed to into config mode.
• Administrator—Allowed to execute arbitrary Linux commands in addition to commands that are defined by the DANOS CLI and to enter configuration mode.
• Superuser—Allowed to execute commands with root privileges through the sudo command in addition to having administrator class privileges.
By default, all users that are defined to be in the superuser or the administrator class belong to a common group called vyattacfg. This group allows a rule set to be defined that pertains to both the superuser and administrator classes without defining two group matches. The operator class users belong to the vyattaop group.
DANOS allows a superuser to create new groups based on your requirements. We recommend creating a group with the highest level of privileges, called a security group. A superuser can set rules so that only members of the security group are allowed to modify the ACM and login information. This prevents administrators from inadvertently compromising the system image or the ACM list.
# Path matching
System configuration is modelled after a tree structure and enables the user to filter any path of that tree. The system supports only absolute addressing that begins with/as the root and uses the wildcard operator (*) as the path language.
Operational mode paths are absolute and do not match their children if a wildcard operator (*) is not included at the end of the path. Therefore, not using the wildcard operator restricts the user to specific commands.
In the following example, rule 1 restricts the use of the show command to only show interfaces and rule 2 denies all other show commands.
1 2 3 4 5 6 7 8 rule 1 { action allow path "/show/interfaces" } rule 2 { action deny path "/show/*" }
# Example of a rule set in operational mode
Operational mode has a rule set like the configuration mode that allows administrators to specify which operation mode commands a user is allowed to run. For example, as a protocol administrator, the user needs to execute only the show interfaces and show ip families of commands and, therefore, should not be allowed to run other administrative actions.
To define the operation mode rules for the protocol administrator group (protoadmin), perform the following steps in configuration mode.
Create a rule allowing all operations on /show/ip for the protoadmin group.
1 2 3 danos@R1# set system acm operational-ruleset rule 10 action 'allow' danos@R1# set system acm operational-ruleset rule 10 command '/show/ip/*' danos@R1# set system acm operational-ruleset rule 10 group 'protoadmin'
Create a rule allowing all operations on /show/interfaces for the protoadmin group.
1 2 3 danos@R1# set system acm operational-ruleset rule 20 action 'allow' danos@R1# set system acm operational-ruleset rule 20 command '/show/interfaces/*' danos@R1# set system acm operational-ruleset rule 20 group 'protoadmin'
Create a rule allowing all operations on /configure for the protoadmin group.
1 2 3 danos@R1# set system acm operational-ruleset rule 30 action 'allow' danos@R1# set system acm operational-ruleset rule 30 command '/configure' danos@R1# set system acm operational-ruleset rule 30 group 'protoadmin'
Deny all operations on all other paths for the protoadmin group.
1 2 3 danos@R1# set system acm operational-ruleset rule 40 action 'deny' danos@R1# set system acm operational-ruleset rule 40 command '*' danos@R1# set system acm operational-ruleset rule 40 group 'protoadmin'
The following example shows the operational mode rule set that is configured above.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 super@danos# show system acm operational-ruleset rule 10 { action allow command "/show/ip/*" group protoadmin } rule 20 { action allow command "/show/interfaces/*" group protoadmin } rule 30 { action allow command /configure group protoadmin } rule 40 { action deny command "*" group protoadmin }
The following example shows system login information regarding the protoadmin group with a user called john as a member of that group.
1 2 3 4 5 6 7 8 9 10 11 super@R1# show system login group protoadmin { } user john { authentication { encrypted-password ******* } group protoadmin level admin } super@R1# | {"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": 0.8379339575767517, "perplexity": 3913.089891116321}, "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-2021-25/segments/1623488550571.96/warc/CC-MAIN-20210624015641-20210624045641-00240.warc.gz"} |
https://math.stackexchange.com/questions/796438/bayesian-statistics-bivariate-prior-distribution | # Bayesian statistics, bivariate prior distribution
I've got a simple question buy I'm not sure how to solve it. It's a bit long.
Suppose you've got $n$ iid random variables $X_1$, $\dots$, $X_n$ from the normal distribution with unknown mean $M$ and unknown precision (inverse variance) $H$. Then we've got the likelihood function for data $X_1=x_1$, $\dots$, $X_n=x_n$ $$L_n(\mu,h)\propto h^{n/2}\exp\left(-\frac{1}{2}h\left(n(\bar{x}-\mu)^2+S\right)\right),$$ where $\bar{x}$ is the mean of $x_1$, $\dots$, $x_n$ and $S=\sum_i(x_i-\bar{x})^2$.
Now, a bivariate prior distribution for $(M,H)$ is specified, in terms of hyperparameters $(\alpha_0,\beta_0,m_0,\lambda_0)$, as follows. The marginal distribution of $H$ is $\Gamma(\alpha_0,\beta_0)$ with density $$\pi(h)\propto h^{\alpha_0-1}e^{-\beta_0h}$$ for $h>0$, and the conditional distribution of $M$ given $H=h$ is normal with mean $m_0$ and precision $\lambda_0h$.
Now I should find the posterior joint distribution of $(M,h)$ given data $X_1=x_1$, $\dots$, $X_n=x_n$ and give the updated hyperparameters $(\alpha_n,\beta_n,m_n,\lambda_n)$ in terms of the prior hyperparameters and the data.
Could somebody please tell me how to do this? Thank you very much.
Your prior is just a Normal-gamma distribution. The likelihood is a standard normal likelihood, but obviously taken as the product of the $n$ conditionally independent observations (with the terms in the exponent rewritten by completing the square). The prior is conjugate, so the posterior distribution is also a Normal-gamma distribution. I would advise you to work out & slog through the proportional form & posterior parameters through $$\text{Posterior} \propto \text{Prior} \times \text{Likelihood},$$ | {"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": 0.9848037362098694, "perplexity": 151.32603902430486}, "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-2019-43/segments/1570987750110.78/warc/CC-MAIN-20191020233245-20191021020745-00199.warc.gz"} |
http://clay6.com/qa/13877/if-the-angle-theta-between-the-vectors-overrightarrow-2x-2-overrightarrow-4 | Browse Questions
# If the angle $\theta$ between the vectors $\overrightarrow {a}=2x^2 \overrightarrow {i}+ 4x \overrightarrow {j}+ \overrightarrow {k}$ and $\overrightarrow {b}=7 \overrightarrow{i}-2 \overrightarrow {j}+x \overrightarrow {k}$ is such that $90^{\circ} < \theta <180^{\circ}$ then $x$ lies in the interval ::
$\begin {array} {1 1} (1)\;\bigg(0,\frac{1}{2}\bigg) & \quad (2)\;\bigg(\frac{1}{2},1\bigg) \\ (3)\;\bigg(1,\frac{3}{2}\bigg) & \quad (4)\;\bigg(\frac{1}{2},\frac{3}{2}\bigg) \end {array}$
$(1)\;\bigg(0,\frac{1}{2}\bigg)$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9109865427017212, "perplexity": 112.46320696386657}, "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-2017-09/segments/1487501172077.66/warc/CC-MAIN-20170219104612-00573-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.internal-interfaces.de/2020/09/14/momentum-resolved-charge-transfer-between-two-tmdc-layers-publication-by-b6-hofer-wallauer-and-a13-rohlfing/ | # Momentum-resolved charge transfer between two TMDC layers – Publication by B6 (Höfer/Wallauer) and A13 (Rohlfing)
### How fast is the charge transfer between two layers of transition metal dichalcogenides (TMDCs) and where does it take place in momentum space? Two-photon photoemission using high-harmonic probe pulses can answer these questions as Wallauer and coworkers demonstrate for the topmost layers of MoS2.
The experiment of Wallauer and coworkers exploits both the high surface sensititivity of photoelectron spectroscopy and the fact, that the bandgap of the topmost layer of TMDCs is enlarged due to reduced screening. By tuning pump pulses below the top-layer gap at K, it is thus possible to excite electrons in deeper layers and probe only the topmost layer. The experiment then images the population dynamics of initially unoccupied electronic states and the charge transfer directly in momentum space with femtosecond time resolution. The results show that the electron transfer between the topmost layers of a 2H-MoS2-crystal, takes place at Σ and proceeds on a timescale of less than 20 fs.
GW-based tight binding calculations by Marauhn and Rohlfing support the experimental findings and explain why the electron transfer takes place at Σ. The GW-based tight-binding calculations not only confirm that the band gap in the surface layer is indeed considerably larger than in deeper layers. They reveal that the coupling between surface and deeper layers is strongly momentum-dependent throughout the Brillouin zone. The coupling is found to be particularly strong at at the conduction-band minimum at Σ, which explains the ultrafast interlayer charge transfer observed in the experiment at this location.
The publication is an “Editor’s Suggestion” in the September 2020 issue of Physical Preview B.
Publication
R. Wallauer, P. Marauhn, J. Reimann, S. Zoerb, F. Kraus, J. Güdde, M. Rohlfing, and U. Höfer
Momentum-resolved observation of ultrafast interlayer charge transfer between the topmost layers of MoS2
Physical Review B 102, 125417 (2020)
Contact
Dr. Robert Wallauer
Philipps-Universität Marburg
SFB 1083 subproject B6
https://internal-interfaces.de/projects/B6
Phone: +49 6421 28-21406
EMAIL
Prof. Dr. Michael Rohlfing
Westfälische Wilhelms-Universität Münster
SFB 1083 subproject A13
https://internal-interfaces.de/projects/A13
Phone: +49 251 83-36340 | {"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": 0.9085094928741455, "perplexity": 3696.284990867426}, "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/1634323585450.39/warc/CC-MAIN-20211022021705-20211022051705-00320.warc.gz"} |
http://www.uppi.upd.edu.ph/acad/abstracts/2005/parcon | ABSTRACT OF THE THESIS
### The Social Network of the Filipino Older People
by Cristabel Rose F. Parcon, Master of Arts in Demography (October 2005)
The objectives of this study are to understand the dynamics of the social network of the Filipino older persons in terms of its structure and content, and to determine the influence of the socio-economic and demographic characteristics of the elderly on their network types. The study utilizes the 1996 Philippine Elderly Survey of the University of the Philippines Population Institute (UPPI). Due to data limitation, the social network of the elderly is limited to their spouse, children, parents, siblings and grandchildren.
The network structure is examined by size, composition and geographic dispersion of the network members, while the network content is analyzed by the frequency of interaction between the elderly and their network members and their support intensity. The study focuses on the frequency of the interaction and support exchanges that the quality of these interactions and exchanges are beyond the scope of the study. Two indices of social network, both considering the aspects of network structure and content, were created. These are: (1) Support Relations, defined by the support intensity and composition of the network; and (2) Family Embeddedness, characterized by the geographic dispersion and interaction between the elderly and network members.
Crosstabulations were done in order to determine the differences in the network features and network types by background characteristics of the elderly. Multinomial logistic regression was employed to establish the determinants of the social network of the older people, and then the odds were converted into proportions using the MCA Table. Results show that the young-old, male, high school educated and healthy elderly have better and more favorable network types compared to their respective counterparts. The place of residence of the elderly does not affect their support relations and family embeddedness. | {"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": 0.8499332666397095, "perplexity": 1409.0740348609847}, "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/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00125.warc.gz"} |
http://mathoverflow.net/questions/5479/milnors-cartography-problem | # Milnor's cartography problem
Let $\Omega$ be a round disc of radius $\alpha<\pi/2$ on the standard sphere. It is easy to construct a $(1,\tfrac{\alpha}{\sin\alpha})$-bi-Lipschitz map from $\Omega$ to the plane.
Is it true that any convex domain $\Omega'$ on $S^2$ with the same area as $\Omega$ also admits a $(1,\tfrac{\alpha}{\sin\alpha})$-bi-Lipschitz map to the plane? | {"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": 0.8239073753356934, "perplexity": 152.36742888758124}, "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/1430456360595.57/warc/CC-MAIN-20150501045920-00042-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Electrolysis | # 1911 Encyclopædia Britannica/Electrolysis
ELECTROLYSIS (formed from Gr. λύειν, to loosen). When the passage of an electric current through a substance is accompanied by definite chemical changes which are independent of the heating effects of the current, the process is known as electrolysis, and the substance is called an electrolyte. As an example we may take the case of a solution of a salt such as copper sulphate in water, through which an electric current is passed between copper plates. We shall then observe the following phenomena. (1) The bulk of the solution is unaltered, except that its temperature may be raised owing to the usual heating effect which is proportional to the square of the strength of the current. (2) The copper plate by which the current is said to enter the solution, i.e. the plate attached to the so-called positive terminal of the battery or other source of current, dissolves away, the copper going into solution as copper sulphate. (3) Copper is deposited on the surface of the other plate, being obtained from the solution. (4) Changes in concentration are produced in the neighbourhood of the two plates or electrodes. In the case we have chosen, the solution becomes stronger near the anode, or electrode at which the current enters, and weaker near the cathode, or electrode at which it leaves the solution. If, instead of using copper electrodes, we take plates of platinum, copper is still deposited on the cathode; but, instead of the anode dissolving, free sulphuric acid appears in the neighbouring solution, and oxygen gas is evolved at the surface of the platinum plate.
With other electrolytes similar phenomena appear, though the primary chemical changes may be masked by secondary actions, Thus, with a dilute solution of sulphuric acid and platinum electrodes, 'Ahydrogen gas is evolved at the cathode, while, as the result of a secondary action on the anode, sulphuric acid is there re-formed, and oxygen gas evolved. Again, with the solution of a salt such as sodium chloride, the sodium, which is primarily liberated at the cathode, decomposes the water and evolves hydrogen, while the chlorine may be evolved as such, may dissolve the anode, or may liberate oxygen from the water, according to the nature of the plate and the concentration of the solution.
Early History of Electrolysis.—Alessandro Volta of Pavia discovered the electric battery in the year 1800, and thus placed the means of maintaining a steady electric current in the hands of investigators, who, before that date, had been restricted to the study of the isolated electric charges given by frictional electric machines. Volta's cell consists essentially of two plates of different metals, such as zinc and copper, connected by an electrolyte such as a solution of salt or acid. Immediately on its discovery intense interest was aroused in the new invention, and the chemical effects of electric currents were speedily detected. W. Nicholson and Sir A. Carlisle found that hydrogen and oxygen were evolved at the surfaces of gold and platinum wires connected with the terminals of a battery and dipped in water. The volume of the hydrogen was about double that of the oxygen, .and, since this is the ratio in which these elements are combined in water, it was concluded that the process consisted essentially in the. decomposition of water. They also noticed that a similar kind of chemical action went on in the battery itself. Soon afterwards, William Cruickshank decomposed the magnesium, sodium and ammonium chlorides, and precipitated silver and copper from their solutions—an observation which led to the process of electroplating. He also found that the liquid round the anode became acid, and that round the cathode alkaline. In 1804 W. Hisinger and J. J. Berzelius stated that neutral salt solutions could be decomposed by electricity, the acid appearing at one pole and the metal at the other. This observation showed that nascent hydrogen was not, as had been supposed, the primary cause of the separation of metals from their solutions, but that the action consisted in a direct decomposition into metal and acid. During the earliest investigation of the subject it was thought that, since hydrogen and oxygen were usually evolved, the electrolysis of solutions of acids and alkalis was to be regarded as a direct decomposition of water. In 1806 Sir Humphry Davy proved that the formation of acid and alkali when water was electrolysed was due to saline impurities in the water. He had shown previously that decomposition of water could be effected although the two poles were placed in separate vessels connected by moistened threads. In 1807 he decomposed potash and soda, previously considered to be elements, by passing the current from a powerful battery through the moistened solids, and thus isolated the metals potassium and sodium.
The electromotive force of Volta's simple cell falls off rapidly when the cell is used, and this phenomenon was shown to be due to the accumulation at the metal plates of the products of chemical changes in the cell itself. This reverse electromotive force of polarization is produced in all electrolytes when the passage of the current changes the nature of the electrodes. In batteries which use acids as the electrolyte, a film of hydrogen tends to be deposited on the copper or platinum electrode; but, to obtain a constant electromotive force, several means were soon devised of preventing the formation of the film. Constant cells may be divided into two groups, according as their action is chemical (as in the bichromate cell, where the hydrogen is converted into water by an oxidizing agent placed in a, porous pot round the carbon plate) or electrochemical (as in Daniell's cell, where a copper plate is surrounded by a solution of copper sulphate, and the hydrogen, instead of being liberated, replaces copper, which is deposited on the plate from the solution).
Fig. 1
Faraday's Laws.—The first exact quantitative study of electrolytic phenomena was made about 1830 by Michael Faraday (Experimental Researches, 1833). When an electric current flows round a circuit, there is no accumulation of electricity anywhere in the circuit, hence the current strength is everywhere the same, and we may picture the current as analogous to the How of an incompressible fluid. Acting on this view, Faraday set himself to examine the relation between the flow of electricity round the circuit and the amount of chemical decomposition. He passed the current driven by a voltaic battery ZnPt (fig. 1) through two branches containing the two electrolytic cells A and B. The reunited current was then led through another cell C, in which the strength of the current must be the sum of those in the arms Aand B. Faraday found that the mass of substance liberated at the electrodes in the cell C was equal to the sum of the masses liberated in the cells A and B. He also found that, for the same current, the amount of chemical action was independent of the size of the electrodes and proportional to the time that the current flowed. Regarding the curre11t as the passage of a certain amount of electricity per second, it will be seen that the results of all these experiments may be summed up in the statement that the amount of chemical action is proportional to the quantity of electricity which passes through the cell.
Faraday's next step was to pass the same current through different electrolytes in series. He found that the amounts of the substances liberated in each cell were proportional to the chemical equivalent weights of those substances. Thus, if the current be passed through dilute sulphuric acid between hydrogen electrodes, and through a solution of copper sulphate, it will be found that the mass of hydrogen evolved in the first cell is to the mass of copper deposited in the second as 1 is to 31.8. Now this ratio is the same as that which gives the relative chemical equivalents of hydrogen and copper, for 1 gramme of hydrogen and 31.8 grammes of copper unite chemically with the same weight of any acid radicle such as chlorine or the sulphuric group, SO4. Faraday examined also the electrolysis of certain fused salts such as lead chloride and silver chloride. Similar relations were found to hold and the amounts of chemical change to be the same for the same electric transfer as in the case of solutions.
We may sum up the chief results of Faraday's work in the statements known as Faraday's laws: The mass of substance liberated from an electrolyte by the passage of a current is proportional (1) to the total quantity of electricity which passes through the electrolyte, and (2) to the chemical equivalent weight of the substance liberated.
Since Faraday's time his laws have been confirmed by modern research, and in favourable cases have been shown to hold good with an accuracy of at least one part in a thousand. The principal object of this more recent research has been the determination of the quantitative amount of chemical change associated with the passage for a given time of a current of strength known in electromagnetic units. It is found that the most accurate and convenient apparatus to use is a platinum bowl filled with a solution of silver nitrate containing about fifteen parts of the salt to one hundred of water. Into the solution dips a silver plate wrapped in filter paper, and the current is passed from the silver plate as anode to the bowl as cathode. The bowl is weighed before and after the passage of the current, and the increase gives the mass of silver deposited. The mean result of the best determinations shows that when a current of one ampere is passed for one second, a mass of silver is deposited equal to 0.001118 gramme. So accurate and convenient is this determination that it is now used conversely as a practical definition of the ampere, which (defined theoretically in terms of magnetic force) is defined practically as the current which in one second deposits 1.118 milligramme of silver.
Taking the chemical equivalent weight of silver, as determined by chemical experiments, to be 107.92, the result described gives as the electrochemical equivalent of an ion of unit chemical equivalent the value 1.036 × 10−5. If, as is now usual, we take the equivalent weight of oxygen as our standard and call it 16, the equivalent weight of hydrogen is 1.008, and its electrochemical equivalent is 1.044 × 105. The electrochemical equivalent of any other substance, whether element or compound, may be found by multiplying its chemical equivalent by 1.036 × 10−5. If, instead of the ampere, we take the C.G.S. electromagnetic unit of current, this number becomes 1.036 × 10−4.
Chemical Nature of the Ions.—A study of the products of decomposition does not necessarily lead directly to a knowledge of the ions actually employed in carrying the current through the electrolyte. Since the electric forces are active throughout the whole solution, all the ions must come under its influence and therefore move, but their separation from the electrodes is determined by the electromotive force needed to liberate them. Thus, as long as every ion of the solution is present in the layer of liquid next the electrode, the one which responds to the least electromotive force will alone be set free. When the amount of this ion in the surface layer becomes too small to carry all the current across the junction, other ions must also be used, and either they or their secondary products will appear also at the electrode. In aqueous solutions, for instance, a few hydrogen (H) and hydroxyl (OH) ions derived from the water are always present, and will be liberated if the other ions require a higher decomposition voltage and the current be kept so small that hydrogen and hydroxyl ions can be formed fast enough to carry all the current across the junction between solution and electrode.
The issue is also obscured in another way. When the ions are set free at the electrodes, they may unite with the substance of the electrode or with some constituent of the solution to form secondary products. Thus the hydroxyl mentioned above decomposes into water and oxygen, and the chlorine produced by the electrolysis of a chloride may attack the metal of the anode. This leads us to examine more closely the part played by water in the electrolysis of aqueous solutions. Distilled water is a very bad conductor, though, even when great care is taken to remove all dissolved bodies, there is evidence to show that some part of the trace of conductivity remaining is due to the water itself. By careful redistillation F. Kohlrausch has prepared water of which the conductivity compared with that of mercury was only 0.40 × 10−11 at 18° C. Even here some little impurity was present, and the conductivity of chemically pure water was estimated by thermodynamic reasoning as 0.36 × 10−11 at 18° C. As we shall see later, the conductivity of very dilute salt solutions is proportional to the concentration, so that it is probable that, in most cases, practically all the current. At the electrodes, however, the small quantity of hydrogen and hydroxyl ions from the water are liberated first in cases where the ions of the salt have a higher decomposition voltage. The water being present in excess, the hydrogen and hydroxyl are re-formed at once and therefore are set free continuously. If the current be so strong that new hydrogen and hydroxyl ions cannot be formed in time, other substances are liberated; in a solution of sulphuric acid a strong current will evolve sulphur dioxide, the more readily as the concentration of the solution is increased. Similar phenomena are seen in the case of a solution of hydrochloric acid. When the solution is weak, hydrogen and oxygen are evolved; but, as the concentration is increased, and the current raised, more and more chlorine is liberated.
An interesting example of secondary action is shown by the common technical process of electroplating with silver from a bath of potassium silver cyanide. Here the ions are potassium and the group Ag(CN)2.[1] Each potassium ion as it reaches the cathode precipitates silver by reacting with the solution in accordance with the chemical equation
K + KAg(CN)2 = 2KCN + Ag,
while the anion Ag(CN)2 dissolves an atom of silver from the anode, and re-forms the complex cyanide KAg(CN)2 by combining with the 2KCN produced in the reaction described in the equation. If the anode consist of platinum, cyanogen gas is evolved thereat from the anion Ag(CN)2, and the platinum becomes covered with the insoluble silver cyanide, AgCN, which soon stops the current. The coating of silver obtained by this process is coherent and homogeneous, while that deposited from a solution of silver nitrate, as the result of the primary action of the current, is crystalline and easily detached.
In the electrolysis of a concentrated solution of sodium acetate, hydrogen is evolved at the cathode and a mixture of ethane and carbon dioxide at the anode. According to H. Jahn,[2] the processes at the anode can be represented by the equations
2CH2 . COO + H2O = 2CH3 . COOH + O
2CH3 . COOH + O = C2H6 + 2CO2 + H2O.
The hydrogen at the cathode is developed by the secondary action
2Na + 2H2O = 2NaOH + H2.
Many organic compounds can be prepared by taking advantage of secondary actions at the electrodes, such as reduction by the cathodic hydrogen, or oxidation at the anode (see Electrochemistry).
It is possible to distinguish between double salts and salts of compound acids. Thus J. W. Hittorf showed that when a current was passed through a solution of sodium platino-chloride, the platinum appeared at the anode. The salt must therefore be derived from an acid, chloroplatinic acid, H2PtCl6, and have the formula Na2PtCl6, the ions being Na and PtCl6″, for if it were a double salt it would decompose as a mixture of sodium chloride and platinum chloride and both metals would go to the cathode.
Early Theories of Electrolysis.—The obvious phenomena to be explained by any theory of electrolysis are the liberation of the products of chemical decomposition at the two electrodes while the intervening liquid is unaltered. To explain these facts, Theodor Grotthus (1785–1822) in 1806 put forward an hypothesis which supposed that the opposite chemical constituents of an electrolyte interchanged partners all along the line between the electrodes when a current passed. Thus, if the molecule of a substance in solution is represented by AB, Grotthus considered a chain of AB molecules to exist from one electrode to the other. Under the influence of an applied electric force, he imagined that the B part of the first molecule was liberated at the anode, and that the A part thus isolated united with the B part of the second molecule, which, in its turn, passed on its A to the B of the third molecule. In this manner, the B part of the last molecule of the chain was seized by the A of the last molecule but one, and the A part of the last molecule liberated at the surface of the cathode.
Chemical phenomena throw further light on this question. If two solutions containing the salts AB and CD be mixed, double decomposition is found to occur, the salts AD and CB being formed till a certain part of the first pair of substances is transformed into an equivalent amount of the second pair. The proportions between the four salts AB, CD, AD and CB, which exist nnally in solution, are found to be the same whether we begin with the pair AB and CD or with the pair AD and CB. To explain this result, chemists suppose that both changes can occur simultaneously, and that equilibrium results when the rate at which AB and CD are transformed into AD and CB is the same as the rate at which the reverse change goes on. A freedom of interchange is thus indicated between the opposite parts of the molecules of salts in solution, and it follows reasonably that with the solution of a single salt, say sodium chloride, continual interchanges go on between the sodium and chlorine parts of the different molecules.
These views were applied to the theory of electrolysis by R. J. E. Clausius. He pointed out that it followed that the electric forces did not cause the interchanges between the opposite parts of the dissolved molecules but only controlled their direction. Interchanges must be supposed to go on whether a current passes or not, the function of the electric forces in electrolysis being merely to determine in what direction the parts of the molecules shall work their way through the liquid and to effect actual separation of these parts (or their secondary products) at the electrodes. This conclusion is supported also by the evidence supplied by the phenomena of electrolytic conduction (see Conduction, Electric, § II.). If we eliminate the reverse electromotive forces of polarization at the two electrodes, the conduction of electricity through electrolytes is found to conform to Ohm's law; that is, once the polarization is overcome, the current is proportional to the electromotive force applied to the bulk of the liquid. Hence there can be no reverse forces of polarization inside the liquid itself, such forces being confined to the surface of the electrodes. No work is done in separating the parts of the molecules from each other. This result again indicates that the parts of the molecules are effectively separate from each other, the function of the electric forces being merely directive.
Fig. 2
Migration of the Ions.—The opposite parts of an electrolyte, which work their way through the liquid under the action of the electric forces, were named by Faraday the ions—the travellers. The changes of concentration which occur in the solution near the two electrodes were referred by W. Hittorf (1853) to the unequal speeds with which he supposed the two opposite ions to travel. It is clear that, when two opposite streams of ions move past each other, equivalent quantities are liberated at the two ends of the system. If the ions move at equal rates, the salt which is decomposed to supply the ions liberated must be taken equally from the neighbourhood of the two electrodes. But if one ion, sav the anion, travels faster through the liquid than the other, the end of the solution from which it comes will be more exhausted of salt than the end towards which it goes. If we assume that no other cause is at work, it is easy to prove that, with non-dis solvable electrodes, the ratio of salt lost at the anode to the salt lost at the cathode must be equal to the ratio of the velocity of the cation to the velocity of the anion. This result may be illustrated by fig. 2. The black circles represent one ion and the white circles the other. If the black ions move twice as fast as the white ones, the state of things after the passage of a current will be represented by the lower part of the figure. Here the middle part of the solution is unaltered and the number of ions liberated is the same at either end, but the amount of salt left at one end is less than that at the other. On the right, towards which the faster ion travels, five molecules of salt are left, being a loss of two from the original seven. On the left, towards which the slower ion moves, only three molecules remain—a loss of four. Thus, the ratio of the losses at the two ends is two to one—the same as the ratio of the assumed ionic velocities. It should be noted, however, that another cause would be competent to explain the unequal dilution of the two solutions. If either ion carried with it some of the unaltered salt or some of the solvent, concentration or dilution of the liquid would be produced where the ion was liberated. There is reason to believe that in certain cases such complex ions do exist., and interfere with the results of the differing ionic velocities.
Hittorf and many other observers have made experiments to determine the unequal dilution of a solution round the two electrodes when a current passes. Various forms of apparatus have been used, the principle of them all being to secure efficient separation of the two volumes of solution in which the changes occur. In some cases porous diaphragms have been employed; but such diaphragms introduce a new complication, for the liquid as a whole is pushed through them by the action of the current, the phenomenon being known as electric endosmose. Hence experiments without separating diaphragms are to be preferred, and the apparatus may be considered effective when a considerable bulk of intervening solution is left unaltered in composition. It is usual to express the results in terms of what is called the migration constant of the anion, that is, the ratio of the amount of salt lost by the anode vessel to the whole amount lost by both vessels. Thus the statement that the migration constant or transport number for a decinormal solution of copper sulphate is 0.632 implies that of every gramme of copper sulphate lost by a solution containing originally one-tenth of a gramme equivalent per litre when a current is passed through it between platinum electrodes, 0.632 gramme is taken from the cathode vessel and 0.368 gramme from the anode vessel. For certain concentrated solutions the transport numberis found to be greater than unity; thus for a normal solution of cadmium iodide its value is 1.12. On the theory that the phenomena are wholly due to unequal ionic velocities this result would mean that the cation like the anion moved against the conventional direction of the current. That a body carrying a positive electric charge should move against the direction of the electric intensity is contrary to all our notions of electric forces, and we are compelled to seek some other explanation. An alternative hypothesis is given by the idea of complex ions. If some of the anions, instead of being simple iodine ions represented chemically by the symbol I, are complex structures formed by the union of iodine With unaltered cadmium iodide—structures represented by some such chemical formula as I(CdI2), the concentration of the solution round the anode would be increased by the passage of an electric current, and the phenomena observed would be explained. It is found that, in such cases as this, where it seems necessary to imagine the existence of complex ions, the transport number changes rapidly as the concentration of the original solution is changed. Thus, diminishing the concentration of the cadmium iodine solution from normal to one-twentieth normal changes the transport number from 1.12 to 0.64. Hence it is probable that in cases where the transport number keeps constant with changing concentration the hypothesis of complex ions is unnecessary, and we may suppose that the transport number is a true migration constant from which the relative velocities of the two ions may be calculated in the matter suggested by Hittorf and illustrated in ng. 2. This conclusion is confirmed by the results of the direct visual determination of ionic velocities (see Conduction, Electric, § II.), which, in cases where the transport number remains constant, agree with the values calculated from those numbers. Many solutions in which the transport numbers vary at high concentration often become simple at greater dilution. For instance, to take the two solutions to which we have already referred, we have—
Concentration 2.0 1.5 1.0 0.5 0.2 0.1 0.05 0.02 0.01 normal Copper sulphate transport numbers 0.72 0.714 0.696 0.668 0.643 0.632 0.626 0.62 .. Cadmium iodide 1.22 1.18 1.12 1.00 0.83 0.71 0.64 0.59 0.56
It is probable that in both these solutions complex ions exist at fairly high concentrations, but gradually gets less in number and finally disappear as the dilution is increased. In such salts as potassium chloride the ions seem to be simple throughout a wide range of concentration since the transport numbers for the same series of concentrations as those used above run—
Potassium chloride—
0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.506.
The next important step in the theory of the subject was made by F. Kohlrausch in 1879. Kohlrausch formulated a theory of electrolytic conduction based on the idea that, under the action of the electric forces, the oppositely charged ions moved in opposite directions through the liquid, carrying their charges with them. If we eliminate the polarization at the electrodes, it can be shown that an electrolyte possesses a definite electric resistance and therefore a definite conductivity. The conductivity gives us the amount of electricity conveyed per second under a dennite electromotive force. On the view of the process of conduction described above, the amount of electricity conveyed per second is measured by the product of the number of ions, known from the concentration of the solution, the charge carried by each of them, and the velocity with which, on the average, they move through the liquid. The concentration is known, and the conductivity can be measured experimentally; thus the average velocity with which the ions move past each other under the existent electromotive force can be estimated. The velocity with which the ions move past each other is equal to the sum of their individual velocities, which can therefore be calculated. Now Hittorf's transport number, in the case of simple salts in moderately dilute solution, gives us the ratio between the two ionic velocities. Hence the absolute velocities of the two ions can be determined, and we can calculate the actual speed with which a certain ion moves through a given liquid under the action of a given potential gradient or electromotive force. The details of the calculation are given in the article Conduction, Electric, § II., where also will be found an account of the methods which have been used to measure the velocities of many ions by direct visual observation. The results go to show that, where the existence of complex ions is not indicated by varying transport numbers, the observed velocities agree with those calculated on Kohlrausch's theory.
Dissociation Theory.—The verification of Kohlrausch's theory of ionic velocity verifies also the view of electrolysis which regards the electric current as due to streams of ions moving in opposite directions through the liquid and carrying their opposite electric charges with them. There remains the question how the necessary migratory freedom of the ions is secured. As we have seen, Grotthus imagined that it was the electric forces which sheared the ions past each other and loosened the chemical bonds holding the opposite parts of each dissolved molecule together. Clausius extended to electrolysis the chemical ideas which looked on the opposite parts of the molecule as always changing partners independently of any electric force, and regarded the function of the current as merely directive. Still, the necessary freedom was supposed to be secured by interchanges of ions between molecules at the instants of molecular collision only; during the rest of the life of the ions they were regarded as linked to each other to form electrically neutral molecules. In 1887 Svante Arrhenius, professor of physics at Stockholm, put forward a new theory which supposed that the freedom of the opposite ions from each other was not a mere momentary freedom at the instants of molecular collision, but a more or less permanent freedom, the ions moving independently of each other through the liquid. The evidence which led Arrhenius to this conclusion was based on van 't Hoff's work on the osmotic pressure of solutions (see Solution). If a solution, let us say of sugar, be confined in a closed vessel through the walls of which the solvent can pass but the solution cannot, the solvent will enter till a certain equilibrium pressure is reached. This equilibrium pressure is called the osmotic pressure of the solution, and thermodynamic theory shows that, in an ideal case of perfect separation between solvent and solute, it should have the same value as the pressure which a number of molecules equal to the number of solute molecules in the solution would exert if they could exist as agas inaspace equal to the volume of the solution, provided that the space was large enough (i.e. the solution dilute enough) for the intermolecular forces between the dissolved particles to be inappreciable. Van 't Hoff pointed out that measurements of osmotic pressure confirmed this value in the case of dilute solutions of cane sugar.
Thermodynamic theory also indicates a connexion between the osmotic pressure of a solution and the depression of its freezing point and its vapour pressure compared with those of the pure solvent. The freezing points and vapour pressures of solutions of sugar are also in conformity with the theoretical numbers. But when we pass to solutions of mineral salts and acids—to solutions of electrolytes in fact—we find that the observed values of the osmotic pressures and of the allied phenomena are greater than the normal values. Arrhenius pointed out that these exceptions would be brought into line if the ions of electrolytes were imagined to be separate entities each capable of producing its own pressure effects just as would an ordinary dissolved molecule.
Two relations are suggested by Arrhenius' theory. (1) In very dilute solutions of simple substances, where only one kind of dissociation is possible and the dissociation of the ions is complete, the number of pressure-producing particles necessary to produce the observed osmotic effects should be equal to the number of ions given by a molecule of the salt as shown by its electrical properties. Thus the osmotic pressure, or the depression of the freezing point of a solution of potassium chloride should, at extreme dilution, be twice the normal value, but of a solution of sulphuric acid three times that value, since the potassium salt contains two ions and the acid three. (2) As the concentration of the solutions increases, the ionization as measured electrically and the dissociation as measured osmotic ally might decrease more or less together, though, since the thermodynamic theory only holds when the solution is so dilute that the dissolved particles are beyond each other's sphere of action, there is much doubt whether this second relation is valid through any appreciable range of concentration.
At present, measurements of freezing point are more convenient and accurate than those of osmotic pressure, and we may test the validity of Arrhenius' relations by their means. The theoretical value for the depression of the freezing point of a dilute solution per gramme-equivalent of solute per litre is 1.857° C. Completely ionized solutions of salts with two ions should give double this number or 3.714°, while electrolytes with three ions should have a value of 5.57°.
The following results are given by H. B. Loomis for the concentration of 0.01 gramme-molecule of salt to one thousand grammes of water. The salts tabulated are those of which the equivalent conductivity reaches a limiting value indicating that complete ionization is reached as dilution is increased. With such salts alone is a valid comparison possible.
Electrolytes with two Ions. Potassium chloride 3.60 Nitric acid 3.73 Sodium chloride 3.67 Potassium nitrate 3.46 Potassium hydrate 3.71 Sodium nitrate 3.55 Hydrochloric acid 3.61 Ammonium nitrate 3.58 Electrolytes with three Ions. Sulphuric acid 4.49 Calcium chloride 5.04 Sodium sulphate 5.09 Magnesium chloride 5.08
At the concentration used by Loomis the electrical conductivity indicates that the ionization is not complete, particularly in the case of the salts with divalent ions in the second list. Allowing for incomplete ionization the general concordance of these numbers with the theoretical ones is very striking.
The measurements of freezing points of solutions at the extreme dilution necessary to secure complete ionization is a matter of great difficulty, and has been overcome only in a research initiated by E. H. Griffiths.[3] Results have been obtained for solutions of sugar, where the experimental number is 1.858, and for potassium chloride, which gives a depression of 3.720. These numbers agree with those indicated by theory, viz. 1.857 and 3.714, with astonishing exactitude. We may take Arrhenius' first relation as established for the case of potassium chloride.
The second relation, as we have seen, is not a strict consequence of theory, and experiments to examine it must be treated as an investigation of the limits within which solutions are dilute within the thermodynamic sense of the word, rather than as a test of the soundness of the theory. It is found that divergence has begun before the concentration has become great enough to enable freezing points to be measured with any ordinary apparatus. The freezing point curve usually lies below the electrical one, but approaches it as dilution is increased.[4]
Returning once more to the consideration of the first relation, which deals with the comparison between the number of ions and the number of pressure-producing particles in dilute solution, one caution is necessary. In simple substances like potassium chloride it seems evident that one kind of dissociation only is possible. The electrical phenomena show that there are two ions to the molecule, and that these ions are electrically charged. Corresponding with this result we find that the freezing point of dilute solutions indicates that two pressure-producing particles per molecule are present. But the converse relation does not necessarily follow. It would be possible for a body in solution to be dissociated into non-electrical parts, which would give osmotic pressure effects twice or three times the normal value, but, being uncharged, would not act as ions and impart electrical conductivity to the solution. L. Kahlenberg (Jour. Phys. Chem., 1901, v. 344, 1902, vi. 43) has found that solutions of diphenylamine in methyl cyanide possess an excess of pressure-producing particles and yet are non-conductors of electricity. It is possible that in complicated organic substances we might have two kinds of dissociation, electrical and non-electrical, occurring simultaneously, while the possibility of the association of molecules accompanied by the electrical dissociation of some of them into new parts should not be overlooked. It should be pointed out that no measurements on osmotic pressures or freezing points can do more than tell us that an excess of particles is present; such experiments can throw no light on the question whether or not those particles are electrically charged. That question can only be answered by examining whether or not the particles move in an electric field.
The dissociation theory was originally suggested by the osmotic pressure relations. But not only has it explained satisfactorily the electrical, properties of solutions, but it seems to be the only known hypothesis which is consistent with the experimental relation between the concentration of a solution and its electrical conductivity (see Conduction, Electric, § II., "Nature of Electrolytes"). It is probable that the electrical effects constitute the strongest arguments in favour of the theory. It is necessary to point out that the dissociated ions of such a body as potassium chloride are not in the same condition as potassium and chlorine in the free state. The ions are associated with very large electric charges, and, whatever their exact relations with those charges may be, it is certain that the energy of a system in such a state must be different from its energy when unelectrified. It is not unlikely, therefore, that even a compound as stable in the solid form as potassium chloride should be thus dissociated when dissolved. Again, water, the best electrolytic solvent known, is also the body of the highest specific inductive capacity (dielectric constant), and this property, to whatever cause it may be due, will reduce the forces between electric charges in the neighbourhood, and may therefore enable two ions to separate.
This view of the nature of electrolytic solutions at once explains many well-known phenomena. Other physical properties of these solutions, such as density, colour, optical rotatory power, &c., like the conductivities, are additive, i.e. can be calculated by adding together the corresponding properties of the parts. This again suggests that these parts are independent of each other. For instance, the colour of a salt solution is the colour obtained by the superposition of the colours of the ions and the colour of any undissociated salt that may be present. All copper salts in dilute solution are blue, which is therefore the colour of the copper ion. Solid copper chloride is brown or yellow, so that its concentrated solution, which contains both ions and undissociated molecules, is green, but changes to blue as water is added and the ionization becomes complete. A series of equivalent solutions all containing the same coloured ion have absorption spectra which, when photographed, show identical absorption bands of equal intensity.[5] The colour changes shown by many substances which are used as indicators (q.v.) of acids or alkalis can be explained in a similar way. Thus para-nitrophenol has colourless molecules, but an intensely yellow negative ion. In neutral, and still more in acid solutions, the dissociation of the indicator is practically nothing, and the liquid is colourless. If an alkali is added, however, a highly dissociated salt of para-nitrophenol is formed, and the yellow colour is at once evident. In other cases, such as that of litmus, both the ion and the undissociated molecule are coloured, but in different ways.
Electrolytes possess the power of coagulating solutions of colloids such as albumen and arsenious sulphide. The mean values of the relative coagulative powers of sulphates of monodi- and tri-valent metals have been shown experimentally to be approximately in the ratios 1:35:1023. The dissociation theory refers this to the action of electric charges carried by the free ions. If a certain minimum charge must be collected in order to start coagulation, it will need the conjunction of 6n monovalent, or 3n divalent, to equal the effect of 2n trivalent ions. The ratios of the coagulative powers can thus be calculated to be 1:x:x2, and putting x = 32 we get 1:32:1024, a satisfactory agreement with the numbers observed.[6]
The question of the application of the dissociation theory to the case of fused salts remains. While it seems clear that the conduction in this case is carried on by ions similar to those of solutions, since Faraday's laws apply equally to both, it does not follow necessarily that semi-permanent dissociation is the only way to explain the phenomena. The evidence in favour of dissociation in the case of solutions does not apply to fused salts, and it is possible that, in their case, a series of molecular interchanges, somewhat like Grotthus's chain, may represent the mechanism of conduction.
An interesting relation appears when the electrolytic conductivity of solutions is compared with their chemical activity. The readiness and speed with which electrolytes react are in sharp contrast with the difficulty experienced in the case of non-electrolytes. Moreover, a study of the chemical relations of electrolytes indicates that it is always the electrolytic ions that are concerned in their reactions. The tests for a salt, potassium nitrate, for example, are the tests not for KNO3, but for its ions K and NO3, and in cases of double decomposition it is always these ions that are exchanged for those of other substances. If an element be present in a compound otherwise than as an ion, it is not interchangeable, and cannot be recognized by the usual tests. Thus neither a chlorate, which contains the ion ClO3, nor monochloracetic acid, shows the reactions of chlorine, though it is, of course, present in both substances; again, the sulphates do not answer to the usual tests which indicate the presence of sulphur as sulphide. The chemical activity of a substance is a quantity which may be measured by different methods. For some substances it has been shown to be independent of the particular reaction used. It is then possible to assign to each body a specific coefficient of affinity. Arrhenius has pointed out that the coefficient of affinity of an acid is proportional to its electrolytic ionization.
The affinities of acids have been compared in several ways. W. Ostwald (Lehrbuch der allg. Chemie, vol. ii., Leipzig, 1893) investigated the relative affinities of acids for potash, soda and ammonia, and proved them to be independent of the base used. The method employed was to measure the changes in volume caused by the action. His results are given in column I. of the following table, the affinity of hydrochloric acid being taken as one hundred. Another method is to allow an acid to act on an insoluble salt, and to measure the quantity which goes into solution. Determinations have been made with calcium oxalate, CaC2O4 + H2O, which is easily decomposed by acids, oxalic acid and a soluble calcium salt being formed. The affinities of acids relative to that of oxalic acid are thus found, so that the acids can be compared among themselves (column II.). If an aqueous solution of methyl acetate be allowed to stand, a slow decomposition goes on. This is much quickened by the presence of a little dilute acid, though the acid itself remains unchanged. It is found that the influence of different acids on this action is proportional to their specific coefficients of affinity. The results of this method are given in column III. Finally, in column IV. the electrical conductivities of normal solutions of the acids have been tabulated. A better basis of comparison would be the ratio of the actual to the limiting conductivity, but since the conductivity of acids is chiefly due to the mobility of the hydrogen ions, its limiting value is nearly the same for all, and the general result of the comparison would be unchanged.
Acid. I. II. III. IV. Hydrochloric 100 100 100 100 Nitric 102 110 92 99.5 Sulphuric 68 67 74 65.1 Formic 4.0 2.5 1.3 1.7 Acetic 1.2 1.0 0.3 0.4 Propionic 1.1 .. 0.3 0.3 Monochloracetic 7.2 5.1 4.3 4.9 Dichloraeetic 34 18 23.0 25.3 Trichloracetic 82 63 68.2 62.3 Malic 3.0 5.0 1.2 1.3 Tartaric 5.3 6.3 2.3 2.3 Succinic 0.1 0.2 0.5 0.6
It must be remembered that, the solutions not being of quite the same strength, these numbers are not strictly comparable, and that the experimental difficulties involved in the chemical measurements are considerable. Nevertheless, the remarkable general agreement of the numbers in the four columns is quite enough to show the intimate connexion between chemical activity and electrical conductivity. We may take it, then, that only that portion of these bodies is chemically active which is electrolytically active—that ionization is necessary for such chemical activity as we are dealing with here, just as it is necessary for electrolytic conductivity.
The ordinary laws of chemical equilibrium have been applied to the case of the dissociation of a substance into its ions. Let ${\displaystyle x}$ be the number of molecules which dissociate per second when the number of undissociated molecules in unit volume is unity, then in a dilute solution where the molecules do not interfere with each other, ${\displaystyle xp}$ is the number when the concentration is ${\displaystyle p.}$ Recombination can only occur when two ions meet. and since the frequency with which this will happen is, in dilute solution, proportional to the square of the ionic concentration, we shall get for the number of molecules re-formed in one second ${\displaystyle yq^{2}}$ where ${\displaystyle q}$ is the number of dissociated molecules in one cubic centimetre; When there is equilibrium, ${\displaystyle xp{=}yq^{2}.}$ If ${\displaystyle \mu }$ be the molecular conductivity, and ${\displaystyle \mu _{\infty }}$ its value at infinite dilution, the fractional number of molecules dissociated is ${\displaystyle \mu /\mu _{\infty },}$ which we may write as ${\displaystyle \alpha }$ The number of undissociated molecules is then ${\displaystyle 1-\alpha ,}$ so that if ${\displaystyle {\text{V}}}$ be the volume of the solution containing 1 gramme-molecule of the dissolved substance, we get
${\displaystyle q{=}\alpha /{\text{V}}}$and${\displaystyle p{=}(1-\alpha )/{\text{V}},}$
hence${\displaystyle x(1-\alpha ){\text{ V}}{=}ya^{2}/{\text{V}}^{2},}$
and${\displaystyle {\frac {\alpha ^{2}}{{\text{V}}(1-\alpha )}}{=}{\frac {x}{y}}{=}{\text{constant}}{=}k.}$
This constant ${\displaystyle k}$ gives a numerical value for the chemical affinity, and the equation should represent the effect of dilution on the molecular conductivity of binary electrolytes.
In the case of substances like ammonia and acetic acid, where the dissociation is very small, ${\displaystyle 1-a}$ is nearly equal to unity, and only varies slowly with dilution. The equation then becomes ${\displaystyle a^{2}/{\text{V}}{=}k,}$ or ${\displaystyle \alpha {=}{\sqrt {{\text{V}}k}}}$ so that the molecular conductivity is proportional to the square root of the dilution. Ostwald has confirmed the equation by observation on an enormous number of weak acids (Zeits. pkysikal. Chemie, 1888, ii. p. 278; 1889, iii. pp. 170, 241, 369). Thus in the case of cyanacetic acid, while the volume ${\displaystyle {\text{V}}}$ changed by doubling from 16 to 1024 litres, the values of ${\displaystyle k}$ were 0.00 (376, 373, 374, 361, 362, 361, 368). The mean values of ${\displaystyle k}$ for other common acids were-formic, 0.0000214; acetic, 0.0000180; monochloracetic, 0.00155; dichloracetic, 0.051; trichloracetic, 1.21; propionic, 0.0000134. From these numbers we can, by help of the equation, calculate the conductivity of the acids for any dilution. The value of ${\displaystyle k,}$ however, does not keep constant so satisfactorily in the case of highly dissociated substances, and empirical formulae have been constructed to represent the effect of dilution on them. Thus the values of the expressions ${\displaystyle \alpha ^{2}/(1-\alpha {\sqrt {\text{V}}})}$ (Rudolphi, Zeits. physikal. Chemie, 1895, vol. xvii. p. 385) and ${\displaystyle \alpha ^{3}(1-\alpha )^{2}{\text{V}}}$ (van 't Hoff, ibid., 1895, vol. xviii. p. 300) are found to keep constant as ${\displaystyle {\text{V}}}$ changes. Van 't Hoff's formula is equivalent to taking the frequency of dissociation as proportional to the square of the concentration of the molecules, and the frequency of recombination as proportional to the cube of the concentration of the ions. An explanation of the failure of the usual dilution law in these cases may be given if we remember that, while the electric forces between bodies like undissociated molecules, each associated with equal and opposite charges, will vary inversely as the fourth power of the distance, the forces between dissociated ions, each carrying one charge only, will be inversely proportional to the square of the distance. The forces between the ions of a strongly dissociated solution will thus be considerable at a dilution which makes forces between undissociated molecules quite insensible, and at the concentrations necessary to test Ostwald's formula an electrolyte will be far from dilute in the thermodynamic sense of the term, which implies no appreciable intermolecular or inter ionic forces.
When the solutions of two substances are mixed, similar considerations to those given above enable us to calculate the resultant changes in dissociation. (See Arrhenius, loc. cit.) The simplest and most important case is that of two electrolytes having one ion in common, such as two acids. It is evident that the undissociated part of each acid must eventually be in equilibrium with the free hydrogen ions, and, if the concentrations are not such as to secure this condition, readjustment must occur. In order that there should be no change in the states of dissociation on mixing, it is necessary, therefore, that the concentration of the hydrogen ions should be the same in each separate solution. Such solutions were called by Arrhenius “isohydric.” The two solutions, then, will so act on each other when mixed that they become isohydric. Let us suppose that we have one very active acid like hydrochloric, in which dissociation is nearly complete, another like acetic, in which it is very small. In order that the solutions of these should be isohydric and the concentrations of the hydrogen ions the same, we must have a very large quantity of the feebly dissociated acetic acid, and a very small quantity of the strongly dissociated hydrochloric, and in such proportions alone will equilibrium be possible. This explains the action of a strong acid on the salt of a weak acid. Let us allow dilute sodium acetate to react with dilute hydrochloric acid. Some acetic acid is formed, and this process will go on till the solutions of the two acids are isohydric: that is, till the dissociated hydrogen ions are in equilibrium with both. In order that this should hold, we have seen that a considerable quantity of acetic acid must be present, so that a corresponding amount of the salt will be decomposed, the quantity being greater the less the acid is dissociated. This “replacement” of a “weak” acid by a “strong” one is a matter of common observation in the chemical laboratory. Similar investigations applied to the general case of chemical equilibrium lead to an expression of exactly the same form as that given by C. M. Guldberg and P. Waage, which is universally accepted as an accurate representation of the facts.
The temperature coefficient of conductivity has approximately the same value for most aqueous salt solutions. It decreases both as the temperature is raised and as the concentration is increased, ranging from about 3.5% per degree for extremely dilute solutions (i.e. practically pure water) at 0° to about 1.5 for concentrated solutions at 18°. For acids its value is usually rather less than for salts at equivalent concentrations. The influence of temperature on the conductivity of solutions depends on (1) the ionization, and (2) the frictional resistance of the liquid to the passage of the ions, the reciprocal of which is called the ionic fluidity. At extreme dilution, when the ionization is complete, a variation in temperature cannot change its amount. The rise of conductivity with temperature, therefore, shows that the fluidity becomes greater when the solution is heated. As the concentration is increased and un-ionized molecules are formed, a change in temperature begins to affect the ionization as well as the fluidity. But the temperature coefficient of conductivity is now generally less than before; thus the effect of temperature on ionization must be of opposite sign to its effect on fluidity. The ionization of a solution, then, is usually diminished by raising the temperature, the rise in conductivity being due to the greater increase in fluidity. Nevertheless, in certain cases, the temperature coefficient of conductivity becomes negative at high temperatures, a solution of phosphoric acid, for example, reaching maximum conductivity at 75° C.
The dissociation theory gives an immediate explanation of the fact that, in general, no heat-change occurs when two neutral salt solutions are mixed. Since the salts, both before and after mixture, exist mainly as dissociated ions, it is obvious that large thermal effects can only appear when the state of dissociation of the products is very different from that of the reagents. Let us consider the case of the neutralization of a base by an acid in the light of the dissociation theory. In dilute solution such substances as hydrochloric acid and potash are almost completely dissociated, so that, instead of representing the reaction as
HCl + KOH = KCl + H2O,
we must write
+ – + – + – H + Cl + K + OH = K + Ck + H2O
The ions K and Cl suffer no change, but the hydrogen of the acid and the hydroxyl (OH) of the potash unite to form water, which is only very slightly dissociated. The heat liberated, then, is almost exclusively that produced by the formation of water from its ions. An exactly similar process occurs when any strongly dissociated acid acts on any strongly dissociated base, so that in all such cases the heat evolution should be approximately the same. This is fully borne out by the experiments of Julius Thomsen, who found that the heat of neutralization of one gramme-molecule of a strong base by an equivalent quantity of a strong acid was nearly constant, and equal to 13,700 or 13,800 calories. In the case of weaker acids, the dissociation of which is less complete, divergences from this constant value will occur, for some of the molecules have to be separated into their ions. For instance, sulphuric acid, which in the fairly strong solutions used by Thomsen is only about half dissociated, gives a higher value for the heat of neutralization, so that heat must be evolved when it is ionized. The heat of formation of a substance from its ions is, of course, very different from that evolved when it is formed from its elements in the usual way, since the energy associated with an ion is different from that possessed by the atoms of the element in their normal state. We can calculate the heat of formation from its ions for any substance dissolved in a given liquid, from a knowledge of the temperature coefficient of ionization, by means of an application of the well-known thermodynamical process, which also gives the latent heat of evaporation of a liquid when the temperature coefficient of its vapour pressure is known. The heats of formation thus obtained may be either positive or negative, and by using them to supplement the heat of formation of water, Arrhenius calculated the total heats of neutralization of soda by different acids, some of them only slightly dissociated, and found values agreeing well with observation (Zeits. physikal. Chemie, 1889, 4, p. 96; and 1892, 9, p. 339)
Voltaic Cells.—When two metallic conductors are placed in an electrolyte, a current will flow through a wire connecting them provided that a difference of any kind exists between the two conductors in the nature either of the metals or of the portions of the electrolyte which surround them. A current can be obtained by the combination of two metals in the same electrolyte, of two metals in different electrolytes, of the same metal in different electrolytes, or of the same metal in solutions of the same electrolyte at different concentrations. In accordance with the principles of energetics (q.v.), any change which involves a decrease in the total available energy of the system will tend to occur, and thus the necessary and sufficient condition for the production of electromotive force is that the available energy of the system should decrease when the current flows.
In order that the current should be maintained, and the electromotive force of the cell remain constant during action, it is necessary to ensure that the changes in the cell, chemical or other, which produce the current, should neither destroy the difference between the electrodes, nor coat either electrode with a non-conducting layer through which the current cannot pass. As an example of a fairly constant cell we may take that of Daniell, which consists of the electrical arrangement—zinc | zinc sulphate solution | copper sulphate solution | copper,—the two solutions being usually separated by a pot of porous earthenware. When the zinc and copper plates are connected through a wire, a current flows, the conventionally positive electricity passing from copper to zinc in the wire and from zinc to copper in the cell. Zinc dissolves at the anode, an equal amount of zinc replaces an equivalent amount of copper on the other side of the porous partition, and the same amount of copper is deposited on the cathode. This process involves a decrease in the available energy of the system, for the dissolution of zinc gives out more energy than the separation of copper absorbs. But the internal rearrangements which accompany the production of a current do not cause any change in the original nature of the electrodes, fresh zinc being exposed at the anode, and copper being deposited on copper at the cathode. Thus as long as a moderate current flows, the only variation in the cell is the appearance of zinc sulphate in the liquid on the copper side of the porous wall. In spite of this appearance, however, while the supply of copper is maintained, copper, being more easily separated from the *solution than zinc, is deposited alone at the cathode, and the cell remains constant.
It is necessary to observe that the condition for change in a system is that the total available energy of the whole system should be decreased by the change. We must consider what change is allowed by the mechanism of the system, and deal with the sum of all the alterations in energy. Thus in the Daniell cell the dissolution of copper as well as of zinc would increase the loss in available energy. But when zinc dissolves, the zinc ions carry their electric charges with them, and the liquid tends to become positively electrified. The electric forces then soon stop further action unless an equivalent quantity of positive ions are removed from the solution. Hence zinc can only dissolve when some more easily separable substance is present in solution to be removed pari passu with the dissolution of zinc. The mechanism of such systems is well illustrated by an experiment devised by W. Ostwald. Plates of platinum and pure or amalgamated zinc are separated by a porous pot, and each surrounded by some of the same solution of a salt of a metal more oxidizable than zinc, such as potassium. When the plates are connected together by means of a wire, no current flows, and no appreciable amount of zinc dissolves, for the dissolution of zinc would involve the separation of potassium and a gain in available energy. If sulphuric acid be added to the vessel containing the zinc, these conditions are unaltered and still no zinc is dissolved. But, on the other hand, if a few drops of acid be placed in the vessel with the platinum, bubbles of hydrogen appear, and a current flows, zinc dissolving at the anode, and hydrogen being liberated at the cathode. In order that positively electrified ions may enter a solution, an equivalent amount of other positive ions must be removed or negative ions be added, and, for the process to occur spontaneously, the possible action at the two electrodes must involve a decrease in the total available energy of the system.
Considered thermodynamically, voltaic cells must be divided into reversible and non-reversible systems. If the slow processes of diffusion be ignored, the Daniell cell already described may be taken as a type of a reversible cell. Let an electromotive force exactly equal to that of the cell be applied to it in the reverse direction. When the applied electromotive force is diminished by an inhnitesimal amount, the cell produces a current in the usual direction, and the ordinary chemical changes occur. If the external electromotive force exceed that of the cell by ever so little, a current flows in the opposite direction, and all the former chemical changes are reversed, copper dissolving from the copper plate, while zinc is deposited on the zinc plate. The cell, together with this balancing electromotive force, is thus a reversible system in true equilibrium, and the thermodynamical reasoning applicable to such systems can be used to examine its properties.
Now a well-known relation connects the available energy of a reversible system with the corresponding change in its total internal energy.
The available energy ${\displaystyle {\text{A}}}$ is the amount of external work obtainable by an infinitesimal, reversible change in the system which occurs at a constant temperature ${\displaystyle {\text{T.}}}$ If ${\displaystyle {\text{I}}}$ be the change in the internal energy, the relation referred to gives us the equation
${\displaystyle {\text{A}}{=}{\text{I}}+{\text{T}}(d{\text{A}}/d{\text{T}}),}$
where ${\displaystyle d{\text{A}}/d{\text{T}}}$ denotes the rate of change of the available energy of the system per degree change in temperature. During a small electric transfer through the cell, the external work done is ${\displaystyle {\text{E}}e}$ where ${\displaystyle {\text{E}}}$ is the electromotive force. If the chemical changes which occur in the cell were allowed to take place in a closed vessel without the performance of electrical or other work, the change in energy would be measured by the heat evolved. Since the fina state of the system would be the same as in the actual processes of the cell, the same amount of heat must give a measure of the change in internal energy when the cell is in action. Thus, if ${\displaystyle {\text{L}}}$ denote the heat corresponding with the chemical changes associated with unit electric transfer, ${\displaystyle {\text{L}}e}$ will be the heat corresponding with an electric transfer ${\displaystyle e,}$ and will also be equal to the change in internal energy of the cell. Hence we get the equation
${\displaystyle {\text{E}}e{=}{\text{L}}e+{\text{T}}e(d{\text{E}}/d{\text{T}})}$or${\displaystyle {\text{E}}{=}{\text{L}}+{\text{T}}(d{\text{E}}/d{\text{T}}),}$
as a particular case of the general thermodynamic equation of available energy. This equation was obtained in different ways by J. Willard Gibbs and H. von Helmholtz.
It will be noticed that when ${\displaystyle d{\text{E}}/d{\text{T}}}$ is zero, that is, when the electromotive force of the cell does not change with temperature, the electromotive force is measured by the heat of reaction per unit of electrochemical change. The earliest formulation of the subject, due to Lord Kelvin, assumed that this relation was true in all cases, and, calculated in this way, the electromotive force of Daniell's cell, which happens to possess a very small temperature coefficient, was found to agree with observation.
When one gramme of zinc is dissolved in dilute sulphuric acid, 1670 thermal units or calories are evolved. Hence for the electrochemical unit of zinc or 0.003388 gramme, the thermal evolution is 5.66 calories. Similarly, the heat which accompanies the dissolution of one electrochemical unit of copper is 3.00 calories. Thus, the thermal equivalent of the unit of resultant electrochemical change in Daniell's cell is 5.66 – 3.00 = 2.66 calories. The dynamical equivalent of the calorie is 4.18 X 107 ergs or C.G.S. units of work, and therefore the electromotive force of the cell should be 1.112 X 108 C.G.S. units or 1.112 volts—a close agreement with the experimental result of about 1.08 volts. For cells in which the electromotive force varies with temperature, the full equation given by Gibbs and Helmholtz has also been confirmed experimentally.
As stated above, an electromotive force is set up whenever there is a difference of any kind at two electrodes immersed in electrolytes. In ordinary cells the difference is secured by using two dissimilar metals, but an electromotive force exists if two plates of the same metal are placed in solutions of different substances, or of the same substance at different concentrations. In the latter case, the tendency of the metal to dissolve in the more dilute solution is greater than its tendency to dissolve in the more concentrated solution, and thus there is a decrease in available energy when metal dissolves in the dilute solution and separates in equivalent quantity from the concentrated solution. An electromotive force is therefore set up in this direction, and, if we can calculate the change in available energy due to the processes of the cell, we can foretell the value of the electromotive force. Now the effective change produced by the action of the current is the concentration of the more dilute solution by the dissolution of metal in it, and the dilution of the originally stronger solution by the separation of metal from it. We may imagine these changes reversed in two ways. We may evaporate some of the solvent from the solution which has become weaker and thus re concentrate it, condensing the vapour on the solution which had become stronger. By this reasoning Helmholtz showed how to obtain an expression for the work done. On the other hand, we may imagine the processes due to the electrical transfer to be reversed by an osmotic operation. Solvent may be supposed to be squeezed out from the solution which has become more dilute through a semi-permeable wall, and through another such wall allowed to mix with the solution which in the electrical operation had become more concentrated. Again, we may calculate the osmotic work done, and, if the whole cycle of operations be supposed to occur at the same temperature, the osmotic work must be equal and opposite to the electrical work of the first operation.
The result of the investigation shows that the electrical work ${\displaystyle {\text{E}}e}$ is given by then equation
${\displaystyle {\text{E}}e{=}\int _{p1}^{p2}vdp,}$
where ${\displaystyle v}$ is the volume of the solution used and ${\displaystyle p}$ its osmotic pressure. When the solutions may be taken as effectively dilute, so that the gas laws apply to the osmotic pressure, this relation reduces to
${\displaystyle {\text{E}}{=}{\frac {nr{\text{RT}}}{ey}}\log _{e}{\frac {c_{1}}{c_{2}}}}$
where ${\displaystyle n}$ is the number of ions given by one molecule of the salt, ${\displaystyle r}$ the transport ratio of the anion, ${\displaystyle {\text{R}}}$ the gas constant, ${\displaystyle {\text{T}}}$ the absolute temperature, ${\displaystyle y}$ the total valency of the anions obtained from one molecule, and ${\displaystyle c_{1}}$ and ${\displaystyle c_{2}}$ the concentrations of the two solutions.
If we take as an example a concentration cell in which silver plates are placed in solutions of silver nitrate, one of which is ten times as strong as the other, this equation gives
{\displaystyle {\begin{aligned}{\text{E}}&{=}0.060\times 10^{3}{\text{ C.G.S. units}}\\&{=}0.060{\text{ volts}}\end{aligned}}}
Nernst, to whom this theory is due, determined the electromotive force of this cell experimentally, and found the value 0.055 volt.
The logarithmic formulae for these concentration cells indicate that theoretically their electromotive force can be increased to any extent by diminishing without limit the concentration of the more dilute solution, ${\displaystyle \log c_{1}/c_{2}}$ then becoming very great. This condition may be realized to some extent in a manner that throws light on the general theory of the voltaic cell. Let us consider the arrangement-silver | silver chloride with potassium chloride solution | potassium nitrate solution | silver nitrate solution | silver. Silver chloride is a very insoluble substance, and here the amount in solution is still further reduced by the presence of excess of chlorine ions of the potassium salt. Thus silver, at one end of the cell in contact with many silver ions of the silver nitrate solution, at the other end is in contact with a liquid in which the concentration of those ions is very small indeed. The result is that a high electromotive force is set up, which has been calculated as 0.52 volt, and observed as 0.51 volt. Again, Hittorf has shown that the effect of a cyanide round a copper electrode is to combine with the copper ions. The concentration of the simple copper ions is then so much diminished that the copper plate becomes an anode with regard to zinc. Thus the cell-copper | potassium cyanide solution | potassium sulphate solution-zinc sulphate solution | zinc-gives a current which carries copper into solution and deposits zinc. In a similar way silver could be made to act as anode with respect to cadmium.
It is now evident that the electromotive force of an ordinary chemical cell such as that of Daniell depends on the concentration of the solutions as well as on the nature of the metals. In ordinary cases possible changes in the concentrations only affect the electromotive force by a few parts in a hundred, but, by means such as those indicated above, it is possible to produce such immense differences in the concentrations that the electromotive force of the cell is not only changed appreciably but even reversed in direction. Once more we see that it is the total impending change in the available energy of the system which controls the electromotive force.
Any reversible cell can theoretically be employed as an accumulator, though, in practice, conditions of general convenience are more sought after than thermodynamic efficiency. The effective electromotive force of the common lead accumulator (q.v.) is less than that required to charge it. This drop in the electromotive force has led to the belief that the cell is not reversible. F. Dolezalek, however, has attributed the difference to mechanical hindrances, which prevent the equalization of acid concentration in the neighbourhood of the electrodes, rather than to any essentially irreversible chemical action. The fact that the Gibbs-Helmholtz equation is found to apply also indicates that the lead accumulator is approximately reversible in the thermodynamic sense of the term.
Polarization and Contact Diference of Potential.—If we connect together in series a single Daniell's cell, a galvanometer, and two platinum electrodes dipping into acidulated water, no visible chemical decomposition ensues. At first a considerable current is indicated by the galvanometer; the reflexion soon diminishes, however, and finally becomes very small. If, instead of using a single Daniell's cell, we employ some source of electromotive force which can be varied as we please, and gradually raise its intensity, we shall find that, when it exceeds a certain value, about 1.7 volt, a permanent current of considerable strength flows through the solution, and, after the initial period, shows no signs of decrease. This current is accompanied by chemical decomposition. Now let us disconnect the platinum plates from the battery and join them directly with the galvanometer. A current will flow for a while in the reverse direction; the system of plates and acidulated water through which a current has been passed, acts as an accumulator, and will itself yield a current in return. These phenomena are explained by the existence of a reverse electromotive force at the surface of the platinum plates. Only when the applied electromotive force exceeds this reverse force of polarization, will a permanent steady current pass through the liquid, and visible chemical decomposition proceed. It seems that this reverse electromotive force of polarization is due to the deposit on the electrodes of minute quantities of the products of chemical decomposition. Differences between the two electrodes are thus set up, and, as we have seen above, an electromotive force will therefore exist between them. To pass a steady current in the direction opposite to this electromotive force of polarization, the applied electromotive force ${\displaystyle {\text{E}}}$ must exceed that of polarization ${\displaystyle {\text{E}}',}$ and the excess ${\displaystyle {\text{E}}-{\text{E}}'}$ is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by ${\displaystyle ({\text{E}}-{\text{E}}')/{\text{R}},}$ where ${\displaystyle {\text{R}}}$ is a constant called the resistance of the circuit.
When we use platinum electrodes in acidulated water, hydrogen and oxygen are evolved. The opposing force of polarization is about 1.7 volt, but, when the plates are disconnected and used as a source of current, the electromotive force they give is only about 1.07 volt. This irreversibility is due to the work required to evolve bubbles of gas at the surface of bright platinum plates. If the plates be covered with a deposit of platinum black, in which the gases are absorbed as fast as they are produced, the minimum decomposition point is 1.07 volt, and the process is reversible. If secondary effects are eliminated, the deposition of metals also is a reversible process; the decomposition voltage is equal to the electromotive force which the metal itself gives when going into solution. The phenomena of polarization are thus seen to be due to the changes of surface produced, and are correlated with the differences of potential which exist at any surface of separation between a metal and an electrolyte.
Many experiments have been made with a View of separating the two potential-differences which must exist in any cell made of two metals and a liquid, and of determining each one individually. If we regard the thermal effect at each junction as a measure of the potential-difference there, as the total thermal effect in the cell undoubtedly is of the sum of its potential differences, in cases where the temperature coefficient is negligible, the heat evolved on solution of a metal should give the electrical potential-difference at its surface. Hence, if we assume that, in the Daniell's cell, the temperature coefficients are negligible at the individual contacts as well as in the cell as a whole, the sign of the potential-difference ought to be the same at the surface of the zinc as it is at the surface of the copper. Since zinc goes into solution and copper comes out, the electromotive force of the cell will be the difference between the two effects. On the other hand, it is commonly thought that the single potential differences at the surface of metals and electrolytes have been determined by methods based on the use of the capillary electrometer and on others depending on what is called a dropping electrode, that is, mercury dropping rapidly into an electrolyte and forming a cell with the mercury at rest in the bottom of the vessel. By both these methods the single potential-differences found at the surfaces of the zinc and copper have opposite signs, and the effective electromotive force of a Daniell's cell is the sum of the two effects. Which of these conflicting views represents the truth still remains uncertain.
Diffusion of Electrolytes and Contact Difference of Potential between Liquids.—An application of the theory of ionic velocity due to W. Nernst[7] and M. Planck[8] enables us to calculate the diffusion constant of dissolved electrolytes. According to the molecular theory, diffusion is due to the motion of the molecules of the dissolved substance through the liquid. When the dissolved molecules are uniformly distributed, the osmotic pressure will be the same everywhere throughout the solution, but, if the concentration vary from point to point, the pressure will vary also. There must, then, be a relation between the rate of change of the concentration and the osmotic pressure gradient, and thus we may consider the osmotic pressure gradient as a force driving the solute through a viscous medium. In the case of non electrolytes and of all non-ionized molecules this analogy completely represents the facts, and the phenomena of diffusion can be deduced from it alone. But the ions of an electrolytic solution can move independently through the liquid, even when no current flows, as the consequences of Ohm's law indicate. The ions will therefore diffuse independently, and the faster ion will travel quicker into pure water in contact with a solution. The ions carry their charges with them, and, as a matter of fact, it is found that water in contact with a solution takes with respect to it a positive or negative potential, according as the positive or negative ion travels the faster. This process will go on until the simultaneous separation of electric charges produces an electrostatic force strong enough to prevent further separation of ions. We can therefore calculate the rate at which the salt as a whole will difiuse by examining the conditions for a steady transfer, in which the ions diffuse at anlequal rate, the faster one being restrained and the slower one urged forward by the electric forces. In this manner the diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3 = 2.27, NaCl= 1.12), the unit of time being the day. By experiments on diffusion this constant has been found by Scheffer, and the numbers observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl = 1.11).
As we have seen above, when a solution is placed in contact with water the water will take a positive or negative potential with regard to the solution, according as the cation or anion has the greater specific velocity, and therefore the greater initial rate of diffusion. The difference of potential between two solutions of a substance at different concentrations can be calculated from the equations used to give the diffusion constants. The results give equations of the same logarithmic form as those obtained in a somewhat different manner in the theory of concentration cells described above, and have been verified by experiment.
The contact differences of potential at the interfaces of metals and electrolytes have been co-ordinated by Nernst with those at the surfaces of separation between different liquids. In contact with a solvent a metal is supposed to possess a definite solution pressure, analogous to the vapour pressure of a liquid. Metal goes into solution in the form of electrified ions. The liquid thus acquires a positive charge, and the metal a negative charge. The electric forces set up tend to prevent further separation, and finally a state of equilibrium is reached, when no more ions can go into solution unless an equivalent number are removed by voltaic action. On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to ${\displaystyle \log({\text{P}}_{1}/{\text{P}}_{2})}$ where ${\displaystyle {\text{P}}_{2}}$ is taken to mean the osmotic pressure of the cations in the solution, and ${\displaystyle {\text{P}}_{1}}$ the osmotic pressure of the cations in the substance of the metal itself. On these lines the equations of concentration cells, deduced above on less hypothetical grounds, may be regained.
Theory of Electrons.—Our views of the nature of the ions of electrolytes have been extended by the application of the ideas of the relations between matter and electricity obtained by the study of electric conduction through gases. The interpretation of the phenomena of gaseous conduction was rendered possible by the knowledge previously acquired of conduction through liquids; the newer subject is now reaching a position whence it can repay its debt to the older.
Sir J. J. Thomson has shown (see Conduction, Electric, § III.) that the negative ions in certain cases of gaseous conduction are much more mobile than the corresponding positive ions, and possess a mass of about the one-thousandth part of that of a hydrogen atom. These negative particles or corpuscles seem to be the ultimate units of negative electricity, and may be identified with the electrons required by the theories of H. A. Lorentz and Sir J. Larmor. A body containing an excess of these particles is negatively electrified, and is positively electrified if it has parted with some of its normal number. An electric current consists of a moving stream of electrons. In gases the electrons sometimes travel alone, but in liquids they are always attached to matter, and their motion involves the movement of chemical atoms or groups of atoms. An atom with an extra corpuscle is a univalent negative ion, an atom with one corpuscle detached is a univalent positive ion. In metals the electrons can slip from one atom to the next, since a current can pass without chemical action. When a current passes from an electrolyte to a metal, the electron must be detached from the atom it was accompanying and chemical action be manifested at the electrode.
Bibliography.—Michael Faraday, Experimental Researches in Electricity (London, 1844 and 1855; W. Ostwald, Lehrbuch der allgemeinen Chemie, 2te Aufl. (Leipzig, 1891); Elektrochemie (Leipzig, 1896); W Nernst, Theoretische Chemie, 3te Aufl: (Stuttgart, 1900; English translation, London, 1904); F. Kohlrausch and L. Holborn, Das Leitvermögen der Elektrolyte (Leipzig, 1898); C. D. Whetham, The Theory of Solution and Electrolysis (Cambridge, 1902); M. Le Blanc, Elements of Electrochemistry (Eng. trans., London, 1896); S. Arrhenius, Text-Book of Electrochemistry (Eng. trans., London, 1902); H. C. jones, The Theory of Electrolytic Dissociation (New York, 1900); N. Munroe Hopkins, Experimental Electrochemistry (London, 1905); Lüphe, Grundzüge der Elektrochemie (Berlin, 1896).
Some of the more important papers on the subject have been reprinted for Harper's Series of Scientific Memoirs in Electrolytic Conduction (1899) and the Modern Theory of Solution (1899). Several journals are published specially to deal with physical chemistry, of which electrochemistry forms an important part. Among them may be mentioned the Zeitschrift für physikalische Chemie (Leipzig); and the Journal of Physical Chemistry (Cornell University). In these periodicals will be found new work on the subject and abstracts of papers which appear in other physical and chemical publications.
1. See Hittorf, Pogg. Ann. cvi. 517 (1859).
2. Grundriss der Elektrochemie (1895), p. 292; see also F. Kaufler and C. Herzog, Ber., 1909, 42, p. 3858.
3. Brit. Ass. Rep., 1906, Section A, Presidential Address.
4. See Theory of Solution, by W. C. D. Whetham (1902), p. 328.
5. W. Ostwald, Zeits. physikal. Chemie, 1892, vol. ix. p. 579; T. Ewan, Phil. Mag. (5), 1892, vol. xxxiii. p. 317; G. D. Liveing, Cambridge Phil. Trans., 1900, vol. xviii. p. 298.
6. See W. B. Hardy, Journal of Physiology, 1899, vol. xxiv. p. 288; and W. C. D. Whetham Phil. Mag., November 1899.
7. Zeits. physikal. Chem. 2, p. 613.
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https://www.ias.ac.in/listing/articles/pram/079/02 | • Volume 79, Issue 2
August 2012, pages 173-335
• Complex dynamical invariants for two-dimensional complex potentials
Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}. y = x_{2} + ip_{4}, p_{x} = p_{1} + ix_{3}, p_{y} = p_{2} + ix_{4}$. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. THe obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.
• Solitons and cnoidal waves of the Klein–Gordon–Zakharov equation in plasmas
This paper studies the Klein–Gordon–Zakharov equation with power-law nonlinearity. This is a coupled nonlinear evolution equation. The solutions for this equation are obtained by the travelling wave hypothesis method, $(G'/G)$ method and the mapping method.
• Parallel decoherence in composite quantum systems
For the standard quantum Brownian motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard Brownian particle, we show that there is at least another system undergoing the dynamics described by the QBM model. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. The generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.
• Relativistic models of a class of compact objects
A class of general relativistic solutions in isotropic spherical polar coordinates which describe compact stars in hydrostatic equilibrium are discussed. The stellar models obtained here are characterized by four parameters, namely, 𝜆, 𝑘, 𝐴 and 𝑅 of geometrical significance related to the inhomogeneity of the matter content of the star. The stellar models obtained using the solutions are physically viable for a wide range of values of the parameters. The physical features of the compact objects taken up here are studied numerically for a number of admissible values of the parameters. Observational stellar mass data are used to construct suitable models of the compact stars.
• The final outcome of dissipative collapse in the presence of 𝛬
We investigate the role played by the cosmological constant during gravitational collapse of a radiating star with vanishing Weyl stresses in the interior. We highlight the role played by the cosmological constant during the latter stages of collapse. The evolution of the temperature of the collapsing body is studied by employing causal heat transport equation. We show that the inclusion of the cosmological constant enhances the temperature within the stellar core.
• Quantum Jarzynski equality with multiple measurement and feedback for isolated system
In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast with the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.
• Production parameters of the therapeutic 105Rh radionuclide using medium energy cyclotron
Production cross-sections of the therapeutic 105Rh radionuclide from proton-induced reactions on natural palladium target were measured using stacked-foil activation technique combined with high resolution 𝛾-ray spectrometry at the MC50 cyclotron of the Korea Institute of Radiological and Medical Sciences. Note that cyclotron production of the 105Rh radionuclide from natural palladium target was measured here for the first time. Results are compared with the theoretical values obtained using the model codes TALYS and ALICE-IPPE. Thick target integral yields for the investigated 105Rh radionuclide were deduced from the threshold energy to 40 MeV. Measured data of the 105Rh radionuclide are important because of its potential applications in nuclear medicine and/or therapeutic purposes. Optimal production circumstances for the therapeutic 105Rh radionuclide using a cyclotron are discussed elaborately.
• Measurement of 232Th$(n, \gamma)$ and 232Th$(n, 2n)$ cross-sections at neutron energies of 13.5, 15.5 and 17.28 MeV using neutron activation techniques
The 232Th$(n, \gamma)$ reaction cross-section at average neutron energies of 13.5, 15.5 and 17.28 MeV from the 7Li$(p, n)$ reaction has been determined for the first time using activation and off-line 𝛾-ray spectrometric technique. The 232Th$(n, 2n)$ cross-section at 17.28 MeV neutron energy has also been determined using the same technique. The experimentally determined 232Th$(n, \gamma)$ and 232Th$(n, 2n)$ reaction cross-sections from the present work were compared with the evaluated data of ENDF/BVII and JENDL-4.0 and were found to be in good agreement. The present data, along with literature data in a wide range of neutron energies, were interpreted in terms of competition between 232Th$(n, \gamma)$, $(n, f)$, $(n, nf)$ and $(n, xn)$ reaction channels. The 232Th$(n, \gamma)$ and 232Th$(n, 2n)$ reaction cross-sections were also calculated theoretically using the TALYS 1.2 computer code and were found to be in good agreement with the experimental data from the present work but were slightly higher than the literature data at lower neutron energies.
• Design of a 10 MeV, 352.2 MHz drift tube Linac
A conventional 10 MeV drift tube Linac is designed as a part of the $H^-$ front end accelerator system for the future Indian Spallation Neutron Source. The front end Linac consists of a 50 keV H- ion source, low energy beam transport (LEBT), a 3 MeV radio frequency quadrupole (RFQ), and a 10 MeV drift tube Linac (DTL), which will be operated at 1.25% duty factor. Cell geometry of the DTL is optimized to house quadrupole magnets and to get maximum effective shunt impedance. Transmission efficiency and various other output parameters depend on the input design parameters. Beam dynamic studies are done to maximize the transmission efficiency with minimum emittance growth. Errors in the alignment of the quadrupoles inside the drift tubes or the DTL tank alignment with respect to transport line will degrade the beam quality and may reduce the transmission efficiency. Error study is performed to assess the acceptable tolerances on various parameters. This paper describes the 2D and 3D electromagnetic and beam dynamics simulations of the 352.2 MHz, 10 MeV drift tube Linac. Details of the DTL design are reported in this paper.
• On wave characteristics of piezoelectromagnetics
This report gives a discussion of a new wave characteristic as a material parameter for a composite with the magnetoelectric effect. The new parameter depends on the material constants of a piezoelectromagnetic composite. It can be implemented on : (A) mechanically free, electrically and magnetically open surface and (B) mechanically free, electrically and magnetically closed surface. These theoretical investigations are useful for researches in the firlds of acousto-optics, photonics and opto-acousto-electronics. Some sample calculations are carried out for BaTiO3 - CoFe2O4 and PZT-5H-Terfenol-D composites of class $6 mm$. Also, the first and second derivatives of the new parameter with respect to the electromagnetic constant 𝛼 are graphically shown.
• Analytical model of transient temperature and thermal stress in continuous wave double-end-pumped laser rod: Thermal stress minimization study
A time-dependent analytical thermal model of the temperature and the corresponding induced thermal stresses in continuous wave double-end-pumped laser rod are derived from the first principle using the integral transform method. The aim of the paper is to study the effect of increasing the pumping powers while the laser crystals are still in the safe zone (i.e. far away from failure stress) and to suitably choose a crystal that achieves this task. The result of this work is compared with a well-verified finite element solution and a good agreement has been found. Some conclusions are obtained: Tm:YAP crystal, which has high thermal conductivity, low expansion coefficient, low absorption coefficient, low thermal factor and low product of $\gamma E/(1−\nu)$, is the best choice to reduce induced stress although it is responded and brought to thermal equilibrium faster than the other types of crystal usually used in the end-pumped solid-state laser.
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The application of calibration-free laser-induced breakdown spectroscopy (CF-LIBS) for quantitative analysis of materials, illustrated by CF-LIBS applied to a brass sample of known composition, is presented in this paper. The LIBS plasma is produced by a 355 nm pulsed Nd:YAG laser with a pulse duration of 6 ns focussed onto a brass sample in air at atmospheric pressure. The time-resolved atomic and ionic emission lines of Cu and Zn from the LIBS spectra recorded by an Echelle spectrograph coupled with a gated intensified charge coupled detector are used for the plasma characterization and the quantitative analysis of the sample. The time delay where the plasma is optically thin and is also in local thermodynamic equilibrium (LTE), necessary for the elemental analysis of samples from the LIBS spectra, is deduced. An algorithm relating the experimentally measured spectral intensity values with the basic physics of the plasma is developed. Using the algorithm, the Zn and Cu concentratioins in the brass sample are determined. The analytical result obtained from the CF-LIBS technique agree well with the certified valued of the elements in the sample, with an accuracy error < 1%
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We have analytically explored the temperature dependence of critical number of particales for the collapse of a harmonically trapped attractively interacting Bose gas below the condensation point by introducing a kinetic approach within the Hartee-Fock approximation. The temperature dependence obtained by this easy approach is consistant with that obtained from the scaling theory.
• Electronic structure and equilibrium properties of hcp titanium and zirconium
The electronic structures of hexagonal-close-packed divalent titanium (3-d) and zirconium (4-d) transition metals are studied by using a non-local model potential method. From the present calculation of energy bands, Fermi energy, density of states and the electronic heat capacity of these two metals are determined and compared with the existing results in the literature.
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https://www.arxiv-vanity.com/papers/1005.5317/ | # The effect of activity-related meridional flow modulation on the strength of the solar polar magnetic field
J. Jiang1 , E. Işık2 , R.H. Cameron1 , D. Schmitt1 & M. Schüssler1
1affiliation: Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany
2affiliation: Department of Physics, Faculty of Science & Letters, İstanbul Kültür University, Ataköy Campus, Bakırköy 34156, İstanbul, Turkey
###### Abstract
We studied the effect of the perturbation of the meridional flow in the activity belts detected by local helioseismology on the development and strength of the surface magnetic field at the polar caps. We carried out simulations of synthetic solar cycles with a flux transport model, which follows the cyclic evolution of the surface field determined by flux emergence and advective transport by near-surface flows. In each hemisphere, an axisymmetric band of latitudinal flows converging towards the central latitude of the activity belt was superposed onto the background poleward meridional flow. The overall effect of the flow perturbation is to reduce the latitude separation of the magnetic polarities of a bipolar magnetic region and thus diminish its contribution to the polar field. As a result, the polar field maximum reached around cycle activity minimum is weakened by the presence of the meridional flow perturbation. For a flow perturbation consistent with helioseismic observations, the polar field is reduced by about 18% compared to the case without inflows. If the amplitude of the flow perturbation depends on the cycle strength, its effect on the polar field provides a nonlinearity that could contribute to limiting the amplitude of a Babcock-Leighton type dynamo.
Sun: activity, Sun: magnetic fields, Sun: meridional circulation
## 1 Introduction
Surface flux transport models treat the evolution of the large-scale magnetic field on the surface of the Sun (e.g., Wang et al., 1989; Schrijver, 2001; Mackay et al., 2002; Baumann et al., 2004). In such models, the evolution of the radial magnetic field at the solar surface is governed by the emergence of new flux in the form of bipolar magnetic regions and by advective transport through large-scale flows (differential rotation, meridional circulation) and supergranular turbulent diffusion. The well-known cyclic variations of differential rotation in the form of zonal flows (e.g., Howard & Labonte, 1980; Howe et al., 2006) so far have not been considered in flux transport simulations. On the other hand, variations in the large-scale meridional flow (Komm et al., 1993; Basu & Antia, 2003; Hathaway & Rightmire, 2010) have been considered in flux-transport simulations by assuming cycle-to-cycle changes in the overall amplitude of the flow (Wang et al., 2002a; Dikpati et al., 2004; Wang et al., 2009).
Another cycle-related modulation of the surface flow field is the modulation of the axisymmetric component of the meridional flow in the form of bands of latitudinal velocity centered on the dominant latitudes of magnetic activity, first detected at depths greater than 20 Mm (Chou & Dai, 2001; Beck et al., 2002). In the case of near-surface flows, the residual meridional flow velocities (after subtraction of the mean flow) during cycle 23 were of the order of 35 ms and converge toward the dominant latitudes of magnetic activity while migrating towards the equator in parallel to the activity belts (Gizon & Rempel, 2008; González Hernández et al., 2008, 2010). These flows are probably related to the meridional motions of sunspots and pores (Ribes & Bonnefond, 1990, and references therein) and other magnetic features (Komm, 1994; Meunier, 1999). The cumulative effect of the near-surface horizontal flows converging towards active regions (e.g., Haber et al., 2004; Hindman et al., 2004) appear to contribute to the axisymmetric meridional flow perturbation (Gizon, 2004; González Hernández et al., 2008), but there is evidence that at least part of this perturbation is unrelated to surface activity (González Hernández et al., 2010).
The effect of the near-surface inflows on the evolution of single active regions was recently studied by De Rosa & Schrijver (2006). Considering results obtained with a surface flux transport model (cf. Schrijver, 2001), these authors find that inflows of the order of ms significantly affect the dispersal of magnetic flux from an isolated active region. These results indicate that the axisymmetric meridional flow perturbations associated with the activity belts could also affect the evolution of the solar surface field on a global scale. Particularly interesting in this connection is the effect on the polar field strength, which is an important source of the heliospheric field and also plays a significant role in Babcock-Leighton-type dynamo models. Here we present results of solar-cycle simulations using the flux transport code of Baumann et al. (2004), including axisymmetric bands of converging latitudinal flows centered on the migrating activity belts. The aim of this work is to study the general effect of these flows on the evolution of the solar surface field, and particularly on the strength of the polar field. This is an exploratory study focussing on understanding the physical mechanisms; we do not intend to reproduce any actual solar data. We need not consider the zonal flows in this study because the buildup of magnetic field to the Sun’s poles is dominated by the latitude separation of the polarities of a bipolar magnetic region and thus essentially is an axisymmetric problem (Cameron & Schüssler, 2007); zonal flows (and differential rotation in general, see Leighton:1964) have no effect on the amount of signed flux reaching the poles.
This paper is organized as follows. The flux transport model is described in Section 2. The relevant effects of the latitudinal flow bands on the surface flux evolution are illustrated with simulations of single bipolar regions in Section 3. The results of full solar-cycle simulations are presented in Section 4, which includes a study of the dependence of the polar field on various model parameters. The implication of our results are discussed in Section 5.
## 2 Flux-transport model
The induction equation considered in our flux transport model is given by (for details see Baumann et al., 2004; Jiang et al., 2009, 2010)
∂B∂t= −Ω(λ,t)∂B∂ϕ−1R⊙cosλ∂∂λ[v(λ,t)Bcosλ] (1) +ηH[1R2⊙cosλ∂∂λ(cosλ∂B∂λ)+1R2⊙cos2λ∂2B∂ϕ2] +S(λ,ϕ,t)+D(ηr),
where and are longitude and latitude, respectively, is the radial component of the magnetic field, is the rotational velocity, is the meridional flow velocity, is the turbulent surface diffusivity due to the random granular and supergranular velocity field, is a source term which describes the emergence of new flux, and the term models the radial diffusion of the field (Baumann et al., 2006) with the diffusivity parameter set to kms. We use the synodic rotation rate (in degrees per day) determined by Snodgrass (1983) and take kms.
The meridional flow velocity consists of a background flow plus a perturbation, , representing axisymmetric bands of converging latitudinal flow (one per hemisphere), viz.
v(λ,t)={vmsin(2.4λ)+Δv(λ,t)% for\ |λ|≤75∘0otherwise, (2)
where ms and
Δv(λ,t)=⎧⎪⎨⎪⎩v0sin[(λ−λc(t))/Δλυ]for\ −180∘≤(λ−λc(t))/Δλυ<180∘0otherwise. (3)
The bands of perturbed meridional flow are characterized by their velocity amplitude, , their width, , and their central latitude, . The equatorward migration of the bands in the course of the solar cycle is represented by the time dependence of (see Section 4.1). Note that Equation (3) describes one band, its counterpart on the other hemisphere is obtained by changing . For sufficiently small central latitudes, the two bands can overlap and the corresponding velocities are added.
## 3 Evolution of single bipolar magnetic regions
In order to illustrate the effect of the meridional flow perturbation on the latitudinal flux transport as the source of the polar field, we first study a single bipolar magnetic region (BMR). The temporal evolution of the corresponding surface flux depends on the relative position of the bands of latitudinal flow perturbation and the emergence latitude. We consider the evolution of a BMR that emerges at at a latitude of on the northern hemisphere under the influence of four different meridional flow patterns (see Figure 1) described by Eqs. (2) and (3). The initial flux distribution of the BMR is chosen following the approach of Baumann et al. (2004).
Snapshots of the surface distribution of the magnetic field are shown in Figure 2. The four cases shown correspond to no flow perturbation (top row) and to converging flow bands centered on different latitudes . The corresponding time evolution of the polar fields is shown in Figure 3. When the flow perturbation is centered equatorward of the BMR emergence latitude (, second row in Figure 2), the overlap of the flow perturbations from both hemispheres (see blue curve in Figure 1) has the consequence that preceding and following polarities of the BMR experience an increased latitude separation: the leading polarity is advected toward the equator while the following polarity is less affected. As a consequence, the latitudinal separation between preceding and following polarity increases, so that the polar field becomes stronger in comparison to the case without flow perturbation. The opposite effect results in the case (third row in Figure 2, red curves in Figs. 1 and 3): now the latitudinal gradient of the meridional flow at the emergence location is such that the two polarities are now advected towards each other, thus reducing the azimuthally averaged field and, consequently, the flux reaching the pole. In the third case (, fourth row in Figure 2, green curves in Figs. 1 and 3), there are two opposing effects: the meridional flow gradient near the emergence location tends to separate the polarities while the following polarity experiences an overall decrease of its poleward advection, thus tending to reduce the azimuthally averaged field. The net effect is a slight reduction of the contribution to the polar field.
These results show that the emergence location of a BMR relative to the position of the bands of flow perturbation is important for its effect on the development of the polar field. Note that the (axisymmetric) meridional flow perturbation considered here results from the cumulative effect of the individual inflows. A given active region (which can appear anywhere in the activity belt) therefore experiences the superposition of these inflows, which needs not necessarily be centered on this active region.
## 4 Simulation of activity cycles
### 4.1 Cycle parameters
As next step, we consider sequences of simulated activity cycles by periodically varying the number of BMRs that appear on the surface. The emerging BMRs have a tilt angle of half their emergence latitude, follow Hale’s polarity rules, and are introduced in activity belts that migrate toward the equator. The BMR area, , follows the distribution derived from observations (Schrijver & Harvey, 1994). The number of BMRs emerging during the cycle is taken to vary proportional to a Gaussian time profile, viz.
ni(t) ∝ {exp{−[(t−ti+6.5)/3.25]2}0≤(t−ti)≤130otherwise (4)
where is the starting time of the cycle and all times are in years. With new cycles starting every 11 years and having a duration of 13 years we thus take into account the overlap of solar activity cycles. The emergence of new BMRs occurs randomly with a Gaussian distribution of half-width about the central latitudes of the activity belts, , which migrate equatorward according to
λ±(t) = ±[λ0−(λ0−8∘)(t−ti)/13], (5)
so that the belts progress from their starting latitudes, , to in the course of 13 years. The resulting emergence pattern of new BMRs (butterfly diagram) for and is shown in Figure 4.
The latitudinal bands of the meridional flow perturbation move in parallel to the active region belts, their central latitudes (on both hemispheres), , coinciding with the centers of the corresponding activity belts, . We do not assume an overlap of the meridional flow perturbations from consecutive cycles; therefore, we include the flow perturbation only for 11 years, starting from the third year of each 13-year cycle. Since the early flux emergence at mid latitudes affects the polar field only little, this assumption does not influence the results in a significant way (see also Section 4.4).
### 4.2 Dependence on the flow perturbation parameters
Figure 5 shows the cyclic variation of the polar fields for three values of the flow perturbation amplitude: ms. The latitudinal width of the bands was kept fixed at and the activity belt parameters were and . As already suggested by the results of the study of single BMRs shown in Section 3, we find that the net effect of the flow perturbation on BMRs emerging in an extended activity belt is a reduction of the polar field amplitudes. The effect becomes more pronounced with increasing flow perturbation amplitude.
On a more quantitative level, the dependence of the mean polar field amplitude (averages over three consecutive cycles)111We omit the first two simulated cycles from the analysis as these could be affected by the arbitrary initial magnetic field. With kms, the -folding time of the magnetic field in the absence of sources (and thus the ‘memory’ of the system) is of about 5 years. on the width, , and the amplitude, , of the flow perturbation is given in Table 1. The numbers in parentheses give the percentage change of the polar field with respect to the case with unperturbed meridional flow. In all cases we find a reduction of the polar field. For parameters roughly corresponding to the helioseismic results ms, , the flow perturbation leads to a reduction of the polar field amplitude by about 18% with respect to the same case but without flow perturbation. Apart from the reduction becoming more pronounced with increasing perturbation amplitude, it also is stronger for bigger , i.e., for wider bands of perturbed flow. This is plausible because wider flow bands affect a larger proportion of the BMRs emerging in the activity belts and, at the same time, influence latitudinal flux advection for a longer time. In all cases, the evolution of the total unsigned surface flux is almost unaffected by the presence of the flow perturbation.
### 4.3 Dependence on the activity belt parameters
Keeping the parameters of the meridional flow perturbation fixed at values of ms and , we also considered the dependence of the polar field amplitude on the starting latitude, , and the width, , of the activity belt. The results are summarized in Table 2. As already suggested by the results of Section 3, the biggest effect on the polar field occurs when BMRs always emerge near the center (latitude of convergence) of the bands of perturbed flow, i.e., for . The flow perturbation then always tends to decrease the latitude extent of the BMR and thus reduces its azimuthally averaged field. The broader the activity belt (relative to the band of perturbed flow), the smaller is the effect on the polar field. On the other hand, for a given activity belt width, the variation of the starting latitude, , of the activity belt in a cycle does not significantly change the effect of the flow perturbation. In most cases, there is a tendency for the polar field amplitude to decrease with increasing . This result may have implications for the nonlinear limitation of a Babcock-Leighton dynamo as further discussed in Section 5.
### 4.4 Time-dependent flow perturbation amplitude
The observations based on helioseismology indicate that the amplitude of the axisymmetric flow perturbation peaks around the maximum of magnetic activity (González Hernández et al., 2010). We therefore also considered the effect of a temporal variation of the flow perturbation in parallel to the activity level. To this end, we modulated the perturbation amplitude, , with the same time profile as that assumed for the number of emerging BMRs given by Equation (4), so that the maximum speed is reached at activity maximum. With the previously used parameters for the flow perturbation (, ) and for the width of the activity belt (), this results in a polar field with an amplitude (three-cycle average) of 5.66 G, about 2.5% higher than the value of 5.52 G found for constant flow perturbation amplitude. The effect of the time variation is somewhat stronger if we assume zero spread of the activity belt (); in this case we obtain a polar field of 5.22 G, which is about 6% higher than the corresponding value of 4.92 G for constant flow perturbation amplitude. This is to be expected since the polar field is dominated by the trans-equatorial transport (or cancellation) of leading-polarity flux; therefore, in the case of very narrow activity belts, the late phase of a cycle with flux emergence near the equator contributes more strongly to the strength of the polar field (Cameron & Schüssler, 2007).
Altogether, the effect of a temporal variation of the inflow amplitude is found to be rather small. Since the temporal modulation strongly reduces the flow perturbation during the rise and decay phases of a cycle, this result implies that the influence of the meridional flow perturbation on the polar field is dominated by the period around activity maximum.
## 5 Discussion and conclusion
The results presented here show that the observed cycle-related meridional flow perturbations in the form of bands migrating with the activity belts decrease the strength of the polar fields resulting from the latitudinal transport of surface flux. For a flow perturbation corresponding to the helioseismic observations, this reduction amounts to about 18% with respect to the case without flow perturbation. This indicates that these effects should be taken into account in surface flux transport simulations aiming at a quantitative pre- or postdiction of the polar field strength.
It is doubtful whether this kind of flow perturbation could have significantly contributed to the low polar polar field strength during the activity minimum between solar cycles 23 and 24 (e.g., Schrijver & Liu, 2008) as compared to previous minima: the perturbation is probably present during every cycle, so that only an increase of the perturbation in cycle 23 compared to its amplitude in previous cycles would contribute to a comparatively weaker polar field during the recent minimum. In any case, other effects must have been affecting the polar field in addition since the observed reduction by nearly a factor of 2 exceeds the decrease that could be caused by the flow perturbation considered here.
The observed variation of the flow perturbation amplitude during the activity cycle (González Hernández et al., 2010) and the probable contribution of the near-surface inflows toward active regions to the driving of the perturbations (Gizon & Rempel, 2008) suggest that the amplitude of the flow perturbation should increase with cycle strength. According to our results, this would lead to a stronger reduction of the polar field built up during cycles of higher activity. Since, in the framework of a Babcock-Leighton dynamo, the polar field is a measure of the poloidal field providing the basis for the toroidal field in the subsequent cycle, the meridional flow perturbation is potentially important for the nonlinear modulation and limitation of the cycle amplitude. Furthermore, we have also seen that the polar field decreases for increasing starting latitude, , of the activity belt at the beginning of a cycle. Since stronger cycles typically have higher values of (Solanki et al., 2008), this relationship would strengthen the nonlinear effect of the flow perturbation in the subsequent cycle amplitude.
We conclude that, in addition to global variations of the meridional flow speed (Wang et al., 2002a, b), the cyclic perturbation of the meridional flow by converging bands migrating with activity belts has an appreciable effect on the build-up of the magnetic field at the polar caps. Its relation to the strength of a cycle means that the flow perturbation could be an important factor in determining the amplitude of Babcock-Leighton-type flux transport dynamos.
## References
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Let $G = \mathbb Z ^ \mathbb N$ (with pointwise addition as the product). Then let $f:G \times G \longrightarrow G$ be $$f(g,h)(n) = \begin{cases} g(k), &n = 2k \\ h(k), &n = 2k+1 \end{cases}$$ You can verify $f$ is an isomorphism.
2
For $n\in\mathbb Z$ and group $G$ denote $r_n(G)=\{g\in G:g^n=1\}$. Obviously, if $G$ abelian group, then $r_n(G)\leq G$. Group of invertible elements of the ring $R$ denote $R^*$. We can say, that we are looking for $|r_{m-1}(\mathbb{Z}_m^*)|$. Denote $n=m-1$. By the chinese remainder theorem, $$\mathbb{Z}_m^* \simeq ... 2 Given any matrix M\in \mathbb R^{m\times n} define a function T:\mathbb R^n\to \mathbb R^m as T(v)=Mv for all v\in \mathbb R^n. It is your exercise to show that T is well-defined (hence a function) and a linear transformation. 2 Yes, the elements of$$R := \Bbb Z [x] / \langle (x - 1) (x - 2) \rangle$$"look like" a + bx, a, b \in \Bbb Z. Put more precisely, each element of R has a unique representative in \Bbb Z of degree \leq 1, like you say exactly because of the division algorithm. This identification alone, however, does not determine the ring structure. The additive ... 2 They are not isomorphic. In (\mathbb Q\setminus \{0\},\cdot) you have an element that is its own inverse (-1). This does not happen in (\mathbb Z,+) 2 No. (\Bbb Z, +) is generated by \{1,-1\} and (\Bbb Q^\times, \cdot) is not finitely generated. 2 The Grothendieck group \mathcal{G}(M) of a commutative monoid M is the unique commutative group satisfying the following universal property: there is a monoid morphism i\colon M \to \mathcal{G}(M) such that for every monoid morphism f \colon M \to G, where G is a commutative group, there is a unique group morphism \mathcal{G}(f) \colon ... 2 Suppose that your regular polygon has a vertice on the x-axis. Then the first vertice counted counter clock wise has coordinates (\cos(\frac{2\pi}{n}),\sin(\frac{2\pi}{n})). Hence if you know the construction of the polygon, by projecting the first vertice on the x axis, which can be done with a ruler and a compass, you can get \cos(\frac{2\pi}{n}). ... 1 The proposition can be reformulated as if \mathfrak{a}+\mathfrak{b}=(1), then \mathfrak{a}\cap\mathfrak{b}=\mathfrak{a}\mathfrak{b} The word “provided” is used in the sense of “when it is given that”. In your case \mathfrak{a}+\mathfrak{b}=(2)+(2)=(2)\ne(1). 1 If a=b, then a^2+ab+b^2=3a^2=a^2=0 and a=0=b, we are done. Suppose that a\neq b. Observe that 0=(a-b)(a^2+ab+b^2)=a^3-b^3. Thus, a^3=b^3. We claim that a=0 and b=0. If a\neq 0, then (a^{-1}b)^3=1 and the multiplicative order of a^{-1}b in the multiplicative group F-\{0\} is 1 because 3\not\mid |F-\{0\}|=2^n-1. Hence, ... 1 aL=0 and bN=0 implies (ab)x=0 for all x\in M: 1 Let G=p_1^{a_1}p_2^{a_2}\cdots p_n^{a_n}, where p_1<p_2<\cdots<p_n are distinct primes and a_i\geq 1 for all i. Let N_p denote the number of Sylow p-subgroups and let N denote the total number of Sylow subgroups, i.e. the sum of all N_{p_i}. By the fact that N_p\equiv 1\pmod{p} and N_p||G| we must have that$$N_{p_i}\leq ...
1
I guess (from the comment discussion mostly) your question is not really about free objects but rather: given an adjunction $F \dashv U$, how can I explicitly write the bijection $\hom(FA, B) \to \hom(A, UB)$ so that the special case $\mathsf{Set} \leftrightarrows \mathsf{Grp}$ gives me the restriction $\varphi \mapsto \varphi\restriction A$? Given $F ... 1 From a computational point of view it amounts to saying that, each time you meet$x^2$, you can replace it with$3x-2$,$x^3$will be replaced with$\,3x^2-2x=7x-6$, &c. 1 I like the rest above, so I just wanted to suggest an argument for b). Suppose there is an$\overline{x} \in G/P$with order$p$, then$(x+P)^p=P$. But this means$x^p \in P$, so$(x^p)^{p^k}=e$for some$k$. But this means$x\in P$and thus$\overline{x}$is actually the identity in$G/P$. But the identity cannot have order$p$, so this is not possible. ... 1 Showing a subgroup isn't too bad. Note$P$is nonempty as$e\in P$. Also,$a_1,a_2\in P$with$p^k,p^m$such that$a^{p^k}=e=a^{p^m}$and$(a_1a_2^{-1})^{p^{m+k}}=e$since$G$is abelian. If some element$\bar{x}$was of order$p$in$G/P$, then$x\in P$so$\bar{x}=e\in G/P$. If$|P|\neq p^n$, then$G/P$has an element of order$p^k$for some$k$by ... 1 You found an$a\in\mathbb Z$such that$p\mid a^2+1$. If$p$is prime in$\mathbb Z[i]$then, from$p\mid a^2+1$you get$p\mid a+i$or$p\mid a-i$, and both cases lead to a contradiction. This shows that$p$isn't prime in$\mathbb Z[i]$. Then$p=(m+ni)(m-ni)$, so$p=m^2+n^2$. Now just take the ideal generated by$m+ni$. 1 $$\dfrac{|x+3|+x}{x+2} >1$$ Assume$x\le -3$$$\dfrac{|x+3|+x}{x+2} >1\iff\dfrac{-(x+3)+x}{x+2} >1\iff -(x+3)+x<x+2\iff-5<x$$ So the first interval is indeed$(-5,-3]$Now let$-3\le x < -2$$$\dfrac{|x+3|+x}{x+2} >1\iff\dfrac{+(x+3)+x}{x+2} >1\iff +(x+3)+x<x+2\iff x<-1$$ So the second interval is$[-3,-2)$Now$x>-2$... 1 Let$G$be the trivial group, for the only finite example. 1 Put in very simple terms, as polynomials two polynomials are equal if and only if all their coefficients are the same. So in$\Bbb Z_3[x]$, we have:$x^8 + 1 \neq x^3 + 1$, because the coefficient of$x^8$in the first is$1$, but the coefficient of$x^8$is$0$in the second (it has no$x^8$term). However, in$\Bbb Z_3$, we do have an$a \in \Bbb Z_3$... 1$\mathbb{Z_6}[X]/(2x+4)\simeq\mathbb{Z_2}[X]/(2x+4)\times\mathbb{Z_3}[X]/(2x+4)\simeq\mathbb{Z_2}[X]\times\mathbb{Z_3}\$
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https://aimsciences.org/article/doi/10.3934/krm.2014.7.755 | # American Institute of Mathematical Sciences
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December 2014, 7(4): 755-778. doi: 10.3934/krm.2014.7.755
## Microscopic and soliton-like solutions of the Boltzmann--Enskog and generalized Enskog equations for elastic and inelastic hard spheres
1 Steklov Mathematical Institute of the Russian Academy of Sciences, Gubkina str. 8, 119991 Moscow, Russian Federation
Received March 2014 Revised July 2014 Published November 2014
N. N. Bogolyubov discovered that the Boltzmann--Enskog kinetic equation has microscopic solutions. They have the form of sums of delta-functions and correspond to trajectories of individual hard spheres. But the rigorous sense of the product of the delta-functions in the collision integral was not discussed. Here we give a rigorous sense to these solutions by introduction of a special regularization of the delta-functions. The crucial observation is that the collision integral of the Boltzmann--Enskog equation coincides with that of the first equation of the BBGKY hierarchy for hard spheres if the special regularization to the delta-functions is applied. This allows to reduce the nonlinear Boltzmann--Enskog equation to the BBGKY hierarchy of linear equations in this particular case.
Also we show that similar functions are exact smooth solutions for the recently proposed generalized Enskog equation. They can be referred to as particle-like'' or soliton-like'' solutions and are analogues of multisoliton solutions of the Korteweg--de Vries equation.
Citation: Anton Trushechkin. Microscopic and soliton-like solutions of the Boltzmann--Enskog and generalized Enskog equations for elastic and inelastic hard spheres. Kinetic & Related Models, 2014, 7 (4) : 755-778. doi: 10.3934/krm.2014.7.755
##### References:
[1] L. Arkeryd and C. Cercignani, On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation,, Comm. PDE, 14 (1989), 1071. doi: 10.1080/03605308908820644. Google Scholar [2] L. Arkeryd and C. Cercignani, Global existence in $L_1$ for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation,, J. Stat. Phys., 59 (1990), 845. doi: 10.1007/BF01025854. Google Scholar [3] N. Bellomo and M. Lachowicz, On the asymptotic theory of the Boltzmann and Enskog equations: A rigorous $H$-theorem for the Enskog equation,, Springer Lecture Notes in Mathematics: Mathematical Aspects of Fluid and Plasma Dynamics, 1460 (1991), 15. doi: 10.1007/BFb0091358. Google Scholar [4] A. V. Bobylev, Tochnye resheniya uravneniya Boltsmana,, (Russian) [Exact solutions of the Boltzmann equation], 225 (1975), 1296. Google Scholar [5] L. Boltzmann, Vorlesungen Über Gastheorie,, (German) [Lectures on gas theory], (1896). Google Scholar [6] N. V. Brilliantov and T. Pöschel, Kinetic theory of granular gases,, Oxford University Press, (2004). doi: 10.1093/acprof:oso/9780198530381.001.0001. Google Scholar [7] N. N. Bogolyubov, Microscopic solutions of the Boltzmann-Enskog equation in kinetic theory for elastic balls,, Theor. Math. Phys., 24 (1975), 242. Google Scholar [8] N. N. Bogolubov and N. N. Bogolubov, Jr., Introduction to Quantum Statistical Mechanics,, Gordon and Breach, (2010). doi: 10.1142/7623. Google Scholar [9] M. S. Borovchenkova and V. I. Gerasimenko, On the non-Markovian Enskog equation for granular gases,, J. Phys. A: Math. Theor., 47 (2014). doi: 10.1088/1751-8113/47/3/035001. Google Scholar [10] C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina, Many-Particle Dynamics and Kinetic Equations,, Kluwer Academic Publishing, (1997). doi: 10.1007/978-94-011-5558-8. Google Scholar [11] C. Cercignani, On the Boltzmann equation for rigid spheres,, Transport Theory and Statistical Physics, 2 (1972), 211. doi: 10.1080/00411457208232538. Google Scholar [12] C. Cercignani, Theory and Application of the Boltzmann Equation,, Elsevier, (1975). Google Scholar [13] V. I. Gerasimenko and I. V. Gapyak, Hard sphere dynamics and the Enskog equation,, Kinet. Relat. Models, 5 (2012), 459. doi: 10.3934/krm.2012.5.459. Google Scholar [14] S.-Y. Ha and S. E. Noh, Global weak solutions and uniform $L^p$-stability of the Boltzmann-Enskog equation,, J. Differential Equations, 251 (2011), 1. doi: 10.1016/j.jde.2011.03.021. Google Scholar [15] R. Illner and M. Pulvirenti, A derivation of the BBGKY hierarchy for hard sphere particle systems,, Trans. Theory Stat. Phys., 16 (1987), 997. doi: 10.1080/00411458708204603. Google Scholar [16] V. V. Kozlov, Teplovoye Ravnovesie Po Gibbsu i Puankare,, (Russian) [Thermal Equilibrium in the sense of Gibbs and Poincaré], (2002). Google Scholar [17] V. V. Kozlov, Thermal Equilibrium in the sense of Gibbs and Poincar'e,, Dokl. Akad. Nauk, 382 (2002), 602. Google Scholar [18] V. V. Kozlov and D. V. Treshchev, Weak convergence of solutions of the Liouville equation for nonlinear Hamiltonian systems,, Theor. Math. Phys., 134 (2003), 339. doi: 10.1023/A:1022697321418. Google Scholar [19] V. V. Kozlov and D. V. Treshchev, Evolution of measures in the phase space of nonlinear Hamiltonian systems,, Theor. Math. Phys., 136 (2003), 1325. doi: 10.1023/A:1025607517444. Google Scholar [20] M.-Y. Lee, T.-P. Liu and S.-H. Yu, Large-time behavior of solutions for the Boltzmann equation with hard potentials,, Comm. Math. Phys., 269 (2007), 17. doi: 10.1007/s00220-006-0108-z. Google Scholar [21] T.-P. Liu and S.-H. Yu, The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation,, Comm. Pure Appl. Math., 57 (2004), 1543. doi: 10.1002/cpa.20011. Google Scholar [22] T.-P. Liu and S.-H. Yu, Green's function of Boltzmann equation, 3-D waves,, Bulletin of Institute of Mathematics, 1 (2006), 1. Google Scholar [23] A. I. Mikhailov, Functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem,, $p$-Adic Numbers, 3 (2011), 205. doi: 10.1134/S2070046611030046. Google Scholar [24] D. Ya. Petrina and V. I. Gerasimenko, Mathematical problems of statistical mechanics of a system of elastic balls,, Russian Mathematical Surveys, 45 (1990), 153. doi: 10.1070/RM1990v045n03ABEH002360. Google Scholar [25] D. Ya. Petrina and G. L. Garaffini, Analog of the Liouville equation and BBGKY hierarchy for a system of hard spheres with inelastic collisions,, Ukrainian Mathematical Journal, 57 (2005), 967. doi: 10.1007/s11253-005-0242-3. Google Scholar [26] D. Ya. Petrina and G. L. Garaffini, Solutions of the BBGKY hierarchy for a system of hard spheres with inelastic collisions,, Ukrainian Mathematical Journal, 58 (2006), 371. doi: 10.1007/s11253-006-0075-8. Google Scholar [27] E. V. Piskovskiy, On functional approach to classical mechanics,, $p$-Adic Numbers, 3 (2011), 243. doi: 10.1134/S2070046611030095. Google Scholar [28] E. V. Piskovskiy and I. V. Volovich, On the correspondence between Newtonian and functional mechanics,, in Quantum Bio-Informatics IV. From Quantum Infarmation to Bio-Informatics, (2011), 363. doi: 10.1142/9789814343763_0028. Google Scholar [29] P. Resibois, $H$-theorem for the (modified) nonlinear Enskog equation,, Phys. Rev. Lett., 40 (1978), 1409. doi: 10.1103/PhysRevLett.40.1409. Google Scholar [30] S. Simonella, Evolution of correlation functions in the hard sphere dynamics,, J. Stat. Phys., 155 (2014), 1191. doi: 10.1007/s10955-013-0905-7. Google Scholar [31] H. Spohn, On the integrated form of the BBGKY hierarchy for hard spheres, preprint,, , (1985). Google Scholar [32] A. S. Trushechkin, Microscopic solutions of the Boltzmann-Enskog equation and the irreversibility problem,, Proc. Steklov Inst. Math., 285 (2014), 251. Google Scholar [33] A. S. Trushechkin, Irreversibility and the role of an instrument in the functional formulation of classical mechanics,, Theoret. and Math. Phys., 164 (2010), 1198. doi: 10.1007/s11232-010-0100-9. Google Scholar [34] A. S. Trushechkin and I. V. Volovich, Functional classical mechanics and rational numbers,, p-Adic Numbers Ultrametric Anal. Appl., 1 (2009), 361. doi: 10.1134/S2070046609040086. Google Scholar [35] A. A. Vlasov, Many-Particle Theory and Its Application to Plasma,, Gordon and Breach, (1961). Google Scholar [36] I. V. Volovich, The irreversibilty problem and functional formulation of classical mechanics, preprint,, , (). Google Scholar [37] I. V. Volovich, Randomness in classical mechanics and quantum mechanics,, Found. Phys., 41 (2011), 516. doi: 10.1007/s10701-010-9450-2. Google Scholar [38] I. V. Volovich, Bogolyubov equations and functional mechanics,, Theoret. and Math. Phys., 164 (2010), 1128. doi: 10.1007/s11232-010-0090-7. Google Scholar
show all references
##### References:
[1] L. Arkeryd and C. Cercignani, On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation,, Comm. PDE, 14 (1989), 1071. doi: 10.1080/03605308908820644. Google Scholar [2] L. Arkeryd and C. Cercignani, Global existence in $L_1$ for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation,, J. Stat. Phys., 59 (1990), 845. doi: 10.1007/BF01025854. Google Scholar [3] N. Bellomo and M. Lachowicz, On the asymptotic theory of the Boltzmann and Enskog equations: A rigorous $H$-theorem for the Enskog equation,, Springer Lecture Notes in Mathematics: Mathematical Aspects of Fluid and Plasma Dynamics, 1460 (1991), 15. doi: 10.1007/BFb0091358. Google Scholar [4] A. V. Bobylev, Tochnye resheniya uravneniya Boltsmana,, (Russian) [Exact solutions of the Boltzmann equation], 225 (1975), 1296. Google Scholar [5] L. Boltzmann, Vorlesungen Über Gastheorie,, (German) [Lectures on gas theory], (1896). Google Scholar [6] N. V. Brilliantov and T. Pöschel, Kinetic theory of granular gases,, Oxford University Press, (2004). doi: 10.1093/acprof:oso/9780198530381.001.0001. Google Scholar [7] N. N. Bogolyubov, Microscopic solutions of the Boltzmann-Enskog equation in kinetic theory for elastic balls,, Theor. Math. Phys., 24 (1975), 242. Google Scholar [8] N. N. Bogolubov and N. N. Bogolubov, Jr., Introduction to Quantum Statistical Mechanics,, Gordon and Breach, (2010). doi: 10.1142/7623. Google Scholar [9] M. S. Borovchenkova and V. I. Gerasimenko, On the non-Markovian Enskog equation for granular gases,, J. Phys. A: Math. Theor., 47 (2014). doi: 10.1088/1751-8113/47/3/035001. Google Scholar [10] C. Cercignani, V. I. Gerasimenko and D. Ya. Petrina, Many-Particle Dynamics and Kinetic Equations,, Kluwer Academic Publishing, (1997). doi: 10.1007/978-94-011-5558-8. Google Scholar [11] C. Cercignani, On the Boltzmann equation for rigid spheres,, Transport Theory and Statistical Physics, 2 (1972), 211. doi: 10.1080/00411457208232538. Google Scholar [12] C. Cercignani, Theory and Application of the Boltzmann Equation,, Elsevier, (1975). Google Scholar [13] V. I. Gerasimenko and I. V. Gapyak, Hard sphere dynamics and the Enskog equation,, Kinet. Relat. Models, 5 (2012), 459. doi: 10.3934/krm.2012.5.459. Google Scholar [14] S.-Y. Ha and S. E. Noh, Global weak solutions and uniform $L^p$-stability of the Boltzmann-Enskog equation,, J. Differential Equations, 251 (2011), 1. doi: 10.1016/j.jde.2011.03.021. Google Scholar [15] R. Illner and M. Pulvirenti, A derivation of the BBGKY hierarchy for hard sphere particle systems,, Trans. Theory Stat. Phys., 16 (1987), 997. doi: 10.1080/00411458708204603. Google Scholar [16] V. V. Kozlov, Teplovoye Ravnovesie Po Gibbsu i Puankare,, (Russian) [Thermal Equilibrium in the sense of Gibbs and Poincaré], (2002). Google Scholar [17] V. V. Kozlov, Thermal Equilibrium in the sense of Gibbs and Poincar'e,, Dokl. Akad. Nauk, 382 (2002), 602. Google Scholar [18] V. V. Kozlov and D. V. Treshchev, Weak convergence of solutions of the Liouville equation for nonlinear Hamiltonian systems,, Theor. Math. Phys., 134 (2003), 339. doi: 10.1023/A:1022697321418. Google Scholar [19] V. V. Kozlov and D. V. Treshchev, Evolution of measures in the phase space of nonlinear Hamiltonian systems,, Theor. Math. Phys., 136 (2003), 1325. doi: 10.1023/A:1025607517444. Google Scholar [20] M.-Y. Lee, T.-P. Liu and S.-H. Yu, Large-time behavior of solutions for the Boltzmann equation with hard potentials,, Comm. Math. Phys., 269 (2007), 17. doi: 10.1007/s00220-006-0108-z. Google Scholar [21] T.-P. Liu and S.-H. Yu, The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation,, Comm. Pure Appl. Math., 57 (2004), 1543. doi: 10.1002/cpa.20011. Google Scholar [22] T.-P. Liu and S.-H. Yu, Green's function of Boltzmann equation, 3-D waves,, Bulletin of Institute of Mathematics, 1 (2006), 1. Google Scholar [23] A. I. Mikhailov, Functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem,, $p$-Adic Numbers, 3 (2011), 205. doi: 10.1134/S2070046611030046. Google Scholar [24] D. Ya. Petrina and V. I. Gerasimenko, Mathematical problems of statistical mechanics of a system of elastic balls,, Russian Mathematical Surveys, 45 (1990), 153. doi: 10.1070/RM1990v045n03ABEH002360. Google Scholar [25] D. Ya. Petrina and G. L. Garaffini, Analog of the Liouville equation and BBGKY hierarchy for a system of hard spheres with inelastic collisions,, Ukrainian Mathematical Journal, 57 (2005), 967. doi: 10.1007/s11253-005-0242-3. Google Scholar [26] D. Ya. Petrina and G. L. Garaffini, Solutions of the BBGKY hierarchy for a system of hard spheres with inelastic collisions,, Ukrainian Mathematical Journal, 58 (2006), 371. doi: 10.1007/s11253-006-0075-8. Google Scholar [27] E. V. Piskovskiy, On functional approach to classical mechanics,, $p$-Adic Numbers, 3 (2011), 243. doi: 10.1134/S2070046611030095. Google Scholar [28] E. V. Piskovskiy and I. V. Volovich, On the correspondence between Newtonian and functional mechanics,, in Quantum Bio-Informatics IV. From Quantum Infarmation to Bio-Informatics, (2011), 363. doi: 10.1142/9789814343763_0028. Google Scholar [29] P. Resibois, $H$-theorem for the (modified) nonlinear Enskog equation,, Phys. Rev. Lett., 40 (1978), 1409. doi: 10.1103/PhysRevLett.40.1409. Google Scholar [30] S. Simonella, Evolution of correlation functions in the hard sphere dynamics,, J. Stat. Phys., 155 (2014), 1191. doi: 10.1007/s10955-013-0905-7. Google Scholar [31] H. Spohn, On the integrated form of the BBGKY hierarchy for hard spheres, preprint,, , (1985). Google Scholar [32] A. S. Trushechkin, Microscopic solutions of the Boltzmann-Enskog equation and the irreversibility problem,, Proc. Steklov Inst. Math., 285 (2014), 251. Google Scholar [33] A. S. Trushechkin, Irreversibility and the role of an instrument in the functional formulation of classical mechanics,, Theoret. and Math. Phys., 164 (2010), 1198. doi: 10.1007/s11232-010-0100-9. Google Scholar [34] A. S. Trushechkin and I. V. Volovich, Functional classical mechanics and rational numbers,, p-Adic Numbers Ultrametric Anal. Appl., 1 (2009), 361. doi: 10.1134/S2070046609040086. Google Scholar [35] A. A. Vlasov, Many-Particle Theory and Its Application to Plasma,, Gordon and Breach, (1961). Google Scholar [36] I. V. Volovich, The irreversibilty problem and functional formulation of classical mechanics, preprint,, , (). Google Scholar [37] I. V. Volovich, Randomness in classical mechanics and quantum mechanics,, Found. Phys., 41 (2011), 516. doi: 10.1007/s10701-010-9450-2. Google Scholar [38] I. V. Volovich, Bogolyubov equations and functional mechanics,, Theoret. and Math. Phys., 164 (2010), 1128. doi: 10.1007/s11232-010-0090-7. Google Scholar
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2018 Impact Factor: 1.38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8273357152938843, "perplexity": 4840.249290322152}, "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-2019-35/segments/1566027330750.45/warc/CC-MAIN-20190825151521-20190825173521-00531.warc.gz"} |
http://physicsformom.blogspot.com/2010_02_01_archive.html | ## Friday, February 26, 2010
### Fourier analysis - Sines and integrals
In case anyone is still reading this, now that it is being updated so sporadically, I'm finally managing another post on Fourier analysis. In this post, I'll try to set up a little bit of the math behind the theory. To do so, I'm going to first remind everyone about the sine function, which I wrote about when talking about the Double Slit Experiment. In that post, I said that the sine function was a mathematical representation of a wave. Here is a plot of y = sin(θ):
Now, that looks an awful lot like the sound waves I was looking at with my guitar back in November. Because they are the same. In fact, when I wanted to depict the sound waves graphically, I used the sine and its partner, the cosine to do it. Going back to the post on the double slit experiment, I believed I compared these functions to a part of speech; by using them, I can now describe a whole host of different phenomena that were previously inaccessible. Including sound waves.
Next, I want to talk about integrals. My mother never took calculus and says she has no idea what an integral is, which means I'm going to try to give a brief introduction (without going into details, alas). The first thing I was taught about integrals is that they represent the "area under the curve," and I think that's really all we need to know about them. If I draw a curve on a coordinate system, for example, like the sine curve above, then the integral is the area between the curve and the x-axis. Therefore, we need to know one other thing to define it, and that is the range of the integral. For example, I am going to zoom in slightly on that sine curve, and then I'll take the integral from x = 0.5 to x = 2.5, which is just the area below the curve between those limits, or the region shaded green.
Now, things can get a bit trickier conceptually when the curve crosses the x-axis and becomes negative-valued. In this case, the integral is still the area under the curve, except that it is now negative. This is represented by the yellow shading.
Finally, if you look carefully, you'll notice that the sine function appears to be symmetric. This will be really important for Fourier analysis. If you integrate the sign function over an entire period, the positive part and the negative part cancel each other out, and we're left with a total integral of 0.
I want to make two final comments about integrals. The key to calculus is finding out that you can generally solve for these areas if you know the functional form of the curve (in this case, for example, we know the curve is a sine curve, so I could write down the function representing the area from calculus). And because I know this is the kind of thing that might interest my mom, in math, we represent an integral with a symbol that looks a little bit like an "S". For example, the integral of sin(x) is written like this:
$\int sin\left(x\right)dx$
The "dx" is there partly to let the reader know that the integral is being performed over the x variable. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9413956999778748, "perplexity": 159.51413928986665}, "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/1508187827662.87/warc/CC-MAIN-20171023235958-20171024015958-00148.warc.gz"} |
https://www.themathcitadel.com/articles/red-head-step-dist.html | ## The Red-Headed Step-Distributions
#### R. Traylor
Almost every textbook in probability or statistics will speak of classifying distributions into two different camps: discrete (singular in some older textbooks) and continuous. Discrete distributions have either a finite or a countable sample space (also known as a set of Lebesgue measure 0), such as the Poisson or binomial distribution, or simply rolling a die. The probability of each point in the sample space is nonzero. Continuous distributions have a continuous sample space, such as the normal distribution. A distribution in either of these classes is either characterized by a probability mass function (pmf) or probability distribution function (pdf) derived from the distribution function via taking a derivative. There is, however, a third kind.
This class is one rarely talked about, or mentioned quickly and then discarded. This class of distributions is defined on a set of Lebesgue measure 0, yet the probability of any point in the set is 0, unlike discrete distributions. The distribution function is continuous, even uniformly continuous, but not absolutely continuous, meaning it's not a continuous distribution. The pdf doesn't exist, but one can still find moments of the distribution (e.g. mean, variance). They are almost never encountered in practice, and the only real example I've been able to find thus far is based on the Cantor set. This class is the set of red-headed step-distributions-- the singular continuous distributions.
## What is Lebesgue measure?
Measure theory itself can get extremely complicated and abstract. The idea of measures is to give the "size" of subsets of a space. Lebesgue measure is one type of measure, and is actually something most people are familiar with: the "size" of subsets of Euclidean space in $n$ dimensions. For example, when $n=1$, we live in 1D space. Intervals. The Lebesgue measure of an interval $[a,b]$ on the real line is just the length of that interval: $b-a$. When we move to two dimensions, $\mathbb{R}\times \mathbb{R}$, the Cartesian product of 1D space with itself, our intervals combine to make rectangles. The Lebesgue measure in 2D space is area; so a rectangle built from $[a,b]\times [c,d]$ has Lebesgue measure $(b-a)(d-c)$. Lebesgue measure in 3D space is volume. And so forth.
Now, points are 0-dimensional in Euclidean space. They have no size, no mass. They have Lebesgue measure 0. The proof for why this is true gets a bit abstract, dealing with first defining Lebesgue outer measure, and showing a point is covered by a sequence of closed intervals with measure as small as you want, with the smallest possible having outer measure 0. Intuitively, we can simply see that Lebesgue measure helps us see how much "space" something takes up in the Euclidean world, and points take up no space, and hence should have measure 0.
In fact, any countable set of points has Lebesgue measure 0. Even an infinite but countable set. The union of disjoint Lebesgue measurable sets has a measure equal to the sum of the individual sets. Points are certainly disjoint, and they each have measure 0, and summing 0 forever still yields 0. This isn't a formal proof; it is merely a way to establish the intuition. The set $\{0,1,2\}$ has Lebesgue measure 0. But so do the natural numbers $\mathbb{N}$,and the rational numbers$\mathbb{Q}$, even though the rational numbers contain the set of natural numbers.
It is actually possible to construct an uncountable infinite set that has Lebesgue measure 0, and we will need that in constructing our example of a singular continuous distribution. For now, we'll examine discrete and continuous distributions briefly.
## Discrete (Singular) Distributions
These are the ones most probability textbooks begin with, and most of the examples that are familiar.
### Roll a fair die.
The sample space for a roll of a fair die $X$ is $S =\{1,2,3,4,5,6\}$. The PMF is $P(X = x) = 1/6$, where $x \in S$. The CDF is given by the function $P(X\leq x) = \sum_{j\leq x}P(X=j)$ Example: $$P(X \leq 4) = \sum_{j\leq 4}\frac{1}{6} = \frac{2}{3}$$
### Binomial Distribution
A binomial random variable $X$ counts the number of "successes" or 1s in a binary sequence of $n$ Bernoulli random variables. Think a sequence of coin tosses, and counting the number of heads. In this case, the sample space is infinite, but countable: $S = \{0,1,2,\ldots\}$. If the probability of a 1, or "success" is $p$, then the PMF of $X$ is given by $$P(X=x) = {n \choose x}p^{x}(1-p)^{n-x}$$ Note here again that the sample space is of Lebesgue measure 0, but the probability of any point in that space is a positive number.
## Continuous Distributions
Continuous distributions operate on a continuous sample space, usually an interval or Cartesian product of intervals or even a union of intervals. Continuous distribution functions $F$ areabsolutely continuous, meaning that (in one equivalent definition), the distribution function has a derivative $f=F'$ almost everywhere that is Lebesgue integrable, and obeys the Fundamental Theorem of Calculus: $$F(b)-F(a) = \int_{a}^{b}f(x)dx$$ for $a< b$. This $f$ is the probability distribution function (PDF), derived by differentiating the distribution function. Let's mention some examples of these:
### The Continuous Uniform Distribution
Suppose we have a continuous interval $[a,b]$, and the probability mass is spread equally along this interval, meaning that the probability that our random variable $X$ lies in any subinterval of size $s$ has the same probability, regardless of location. Suppose we do not allow the random variable to take any values outside the interval. The sample space is continuous but over a finite interval. The distribution function for this $X$ is given by $$F(x) = \left\{\begin{array}{lr}0&x< a\\\frac{x-a}{b-a}&a\leq x \leq b\\1&x > b\end{array}\right.$$ This is an absolutely continuous function. Then we may easily derive the PDF by differentiating $F$: $$f(x) = \mathbb{1}_{x \in [a,b]}\frac{1}{b-a}$$ where $\mathbb{1}_{x \in [a,b]}$ is theindicator function that takes value 1 if $x$ is in the interval, and 0 otherwise.
This distribution is the continuous version of a die roll. The die roll is the discrete uniform distribution, and here we just allow for a die with uncountably many sides with values in $[a,b]$. The probability of any particular point is 0, however, even though it is possible to draw a random number from this interval. To see this, note that the probability that the random variable $X$ lies between two points in the interval, say $x_{1}$ and $x_{2}$ is given by multiplying the height of the PDF by the length (Lebesgue measure) of the subinterval. The Lebesgue measure of a point is 0, so even though a value for the PDF exists at that point, the probability is 0.
We don't run into issues here mathematically because we are on a continuous interval.
### The Normal Distribution
Likely the most famous continuous distribution, the normal distribution is given by the famous "bell curve." In this case, the sample space is the entire real line. The probability that a normally distributed random variable $X$ lies between any two points $a$ and $b$ is given by $$P(a\leq X \leq b) = \int_{a}^{b}\frac{1}{\sqrt{2\pi\sigma^{2}}}\exp\left(-\frac{(x-\mu)^{2}}{2\sigma^{2}}\right)dx$$ where $\mu$ is the mean and $\sigma^{2}$ is the variance.
## Singular Continuous Distributions
We're going to begin this section by discussing everyone's favorite counterexample in mathematics: the Cantor set.
### The Cantor set
The Cantor set is given by the limit of the following construction:
1. Take the interval $[0,1]$.
2. Remove the middle third: $(1/3, 2/3)$, so you're left with $[0,1/3]\cup[2/3,1]$
3. Remove the middle third of each of the remaining intervals. So you remove $(1/9,2/9)$ from $[0,1/3]$ and $(7/9,8/9)$ from $[2/3,1]$, leaving you with the set $[0,1/9]\cup[2/9,1/3]\cup[2/3,7/9]\cup[8/9,1]$
Continue this process infinitely.
This is an example of a set that is uncountable, yet has Lebesgue measure 0. Earlier, when we discussed Lebesgue measure, we noted that all countable sets had measure 0. Thus we may conclude that only uncountable sets (like intervals) have nonzero Lebesgue measure. However, the Cantor set illustrates that not all uncountable sets have positive Lebesgue measure. To see why the Cantor set has Lebesgue measure 0, we will look at the measure of the sets that are removed (the complement of the Cantor set):
At the first step, we have removed one interval of size 1/3. At the second step, we remove two intervals of size 1/9. At the third step, we remove four intervals of size 1/27. Let's call $S_{n}$ the subset removed from the interval [0,1] by the $n$th step. By the end of the third step, we have removed a set of size $$m(S_{3}) = \frac{1}{3} + \frac{2}{3^{2}} + \frac{4}{3^{3}}$$ By the $n$th step, $$m(S_{n}) = \sum_{j=0}^{n}\frac{2^{j}}{3^{j+1}}$$ This is the partial sum of a geometric series, so $$m(S_{n}) = 1-\left(\frac{2}{3}\right)^{n}$$ Now, the Cantor set is formed when $n \to \infty$. The measure of the complement of the Cantor set, which we called $S_{\infty}$ then has measure $$m(S_{\infty}) = \lim_{n \to \infty}m(S_{n}) = \lim_{n \to \infty}1-\left(\frac{2}{3}\right)^{n} = 1$$ But the original interval we started with had Lebesgue measure 1, and the union of the Cantor set with its complement $S_{\infty}$ is the interval [0,1]. That means that the measure of the Cantor set plus the measure of its complement must add to 1, which implies that the Cantor set is of measure 0. However, since we removed open intervals during the construction, there must be something left; in fact, there are uncountably many points left.
Now we have an uncountable set of Lebesgue measure 0. We're going to use this set to construct the only example I could find of a singular continuous distribution. It is very important that the Cantor set is an uncountable set of Lebesgue measure 0.
### Building the Cantor distribution
Update: Following a correction from an earlier version, I'm going to show how to construct this distribution directly and via the complement of the Cantor set. The latter was used in a textbook I found, and is a bit convoluted in its construction, but I'm going to leave it.
The direct construction is to look at the intervals left behind at each stage $n$ of constructing the Cantor set. Assign a probability mass of $\frac{1}{2^{n}}$ to each of the $2^{n}$ intervals left behind, and this is your distribution function. It's basically a continuous uniform distribution, but on stages of the Cantor set construction. Sending $n \to \infty$ yields the Cantor set, but the probability distribution moves to 0 on a set of measure 0. Thus, unlike the continuous uniform distribution, where the probability of any single point was 0, but the support has positive measure, we essentially have the continuous uniform distribution occurring on a set of measure 0, which means we have a continuous distribution function on a singular support of measure 0 that is uncountable and thus not discrete. This distribution is therefore neither continuous nor discrete.
Another way to construct this is by complement,via Kai Lai Chung's A Course in Probability Theory. (Note: after a second glance at this, I found this to be a relatively convoluted way of constructing this distribution, since it can be fairly easily constructed directly. However, I imagine the author's purpose was to be very rigid and formal to cover all his bases, so I present a review of it here:) Let's go back to the construction of the Cantor set. At each step $n$ we have removed in total $2^{n}-1$ disjoint intervals. Let's number those intervals, going from left to right as $J_{n,k}$, where $k = 1,2,\ldots, 2^{n}-1$. For example, at $n=2$ we have that $J_{2,1} = (1/9,2/9)$,$J_{2,2} = (1/3,2/3)$, and $J_{2,3} = (7/9,8/9)$. Now let the quantity $c_{n,k} = \frac{k}{2^{n}}$. This will be the probability mass assigned to interval $J_{n,k}$. So we define the distribution function as $$F(x) = c_{n,k}, x \in J_{n,k}$$
Let $U_{n} = \cup_{k=1}^{2^{n}-1}J_{n,k}$, and $U = \lim_{n\to\infty}U_{n}$ The function $F$ is indeed a distribution function and can be shown to be uniformly continuous on the set $D = (-\infty,0)\cup U \cup (1,\infty)$. However, none of the points in $D$ is in the support of $F$, so the support of $F$ is contained in the Cantor set (and in fact is the Cantor set). The support (the Cantor set) has measure 0, so it is singular, but the distribution function is continuous, so it cannot be a discrete distribution. This distribution fits nowhere in our previous two classes, so we must now create a third class -- the singular continuous distribution.
(By the way, even though the PDF doesn't exist, the Cantor distribution still has mean of 1/2 and a variance of 1/8, but no mode. It does have a moment generating function.)
## Any other examples?
With some help, I spent some time poring through quite a few probability books to seek further study and other treatment of singular continuous distributions. Most said absolutely nothing at all, as if the class didn't exist.
One book,Modern Probability Theory and Its Applications has a rather grumpy approach:
There also exists another kind of continuous distribution function, called singular continuous, whose derivative vanishes at almost all points. This is a somewhat difficult notion to picture, and examples have been constructed only by means of fairly involved analytic operations. From a practical point of view, one may act as if singular continuous distribution functions do not exist, since examples of these functions are rarely, if ever, encountered in practice. | {"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": 0.9761698246002197, "perplexity": 155.1647712325605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104215790.65/warc/CC-MAIN-20220703043548-20220703073548-00711.warc.gz"} |
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Pick the right output capacitors for LED drivers
Posted: 01 Apr 2008 ?? ?Print Version ?
Keywords:LED? LED array? output capacitor? white LED?
By John Betten
Texas Instruments
Driving an LED or LED array is not without its challenges. The LEDs require a well-designed constant-current source for controlled brightness. More specifically, the output capacitor in the traditional buck converter that serves to drive the LEDs can have a significant effect on control-loop characteristics, and the capacitor type as well as the output circuit configuration is often critical.
Placing the capacitor in parallel with the LEDs, vs. from output to ground, for example, can make the difference between using the simpler type-two compensation circuit and a type-three circuit for reduced parts count, a more linear and stable loop transfer function, and ease in design.
Ultimately, output capacitor sizing and type is determined by what is best for the intended application and there are several options. The output capacitor can be ceramic or aluminum; sometimes the designer may choose to omit the output capacitor entirely. SPICE circuit modeling provides a good way to validate and confirm the design.
LED design
The use of LEDs in automotive and outdoor lighting applications and the like has grown substantially, largely due to the availability of more efficient, white high-power devices. Luminous efficacies of greater than 175 lumens/W in white LEDs are now commercially available. Operational lifetimes of greater than 50,000hrs and compact size are driving their increased usage.
An LED has a forward V-I characteristic curve that is similar to a diode. Below the LED turn-on threshold, which for a white LED is approximately 3.5V, very little current will flow through it. Above that threshold, current flow increases rapidly for incremental increases in forward voltage. The rise in current is exponential. Thus, the LED can be accurately modeled in SPICE, for a given operating current, as a voltage source in series with a resistor. That is, for accurate modeling the resistor's value depends on the amount of current flowing through the LED. Figure 1 shows the measured impedance of a 1W white LED. The slope of the LED's V-I curve essentially represents the LED's dynamic impedance as a function of the load current.
A 1W LED illuminates at currents as low as 1mA, although not very brightly. At large forward currents, the LED operates at a high power level, which in turn begins to heat the die. As a result, the LED's forward drop increases, as does its dynamic impedance. It is critical to consider the thermal environment when the LED's impedance is determined.
Modeling the converter
The LED's driving source must be designed very carefully. Consider, for example, the voltage-mode buck converter in Figure 2 using the TPS40200 controller, with the converter designed to drive three series LEDs at a constant current of 1A. It regulates the voltage across the current sense resistor (R8) at a constant 0.7V. In essence, R8 programs the current regulated in the LED string.
The output from the converter is equal to the voltage across the LED string, plus the reference voltage (0.7V). For three white LEDs, the output is approximately (3.5)(3) + 0.7 = 11.2V. In a typical buck converter, the output capacitor (C8) is connected from the output-to-ground. However, in this circuit the output capacitor is connected across the LEDs. Although this may seem like a minor difference, it greatly simplifies stabilizing the control loop.
Figure 3: SPICE model for LED buck converter.
Figure 3 shows the SPICE model of the AC control loop. The modulator "gain" block is internally set to a fixed gain of 8V/V (minimum), as programmed by the TPS40200 controller. This gain is constant over input voltage due to the voltage feed-forward feature of the controller, which changes the oscillator ramp amplitude in proportion to any input voltage variations. From Figure 1, the dynamic impedance of a single LED driven with 1A is 0.5?. Three LEDs are modeled as a lump sum of three series 0.5? resistors and three series 3.5V sources. Note that the resultant 10.5V DC source has no effect on the AC control loop model (SPICE shorts out all DC voltage sources in AC loop analyses). To measure the closed loop gain and phase margin, we break the feedback path and insert an AC voltage source (Vac) at the current regulation point (R8).
Simulation with ceramic capacitor across LEDs
Figure 4 shows the results of the AC simulation in terms of total loop gain, phase response, and the power stage's voltage gain (defined as the sum of the modulator's fixed "gain" block of eight (i.e., 18dB) and the output filter response. This control-to-output gain is a measure of the full loop gain minus the error amplifier gain and is equal to Vo/Vea out.
The power stage gain starts out flat at 7.5dB and rolls off with a slope of -1 (i.e., -20dB/decade) at 3.7kHz. At frequencies below the single-order pole at 3.7kHz, the gain is equal to R8/ (R8 + RLED + RL1) multiplied by the "gain" block. The inductor resistance (RL1) is small relative to the other terms, and does not affect the overall transfer function much. The frequency of the pole in the power stage gain is
The actual measured gain and phase plots for the circuit modeled in Figure 2 is shown in Figure 5.
Figure 5: Measured transfer functions, ceramic output capacitor across LED.
With a loop gain of 26KHz and 77 phase margin, the measured response correlates well with the simulated response.
So why isn't the output capacitor a factor in the above equation? At frequencies above the pole, the impedance of C8 is large relative to the lower impedances of RLED and R8, allowing those two terms to dominate. At these higher frequencies, the impedance of L1 is large and forms a voltage divider with RLED and R8. A zero occurs at
The frequency of the zero is where the impedance of capacitor C8 is equal to the sum of the LED's impedance and the capacitor's ESR. Normally this would cause the power stage gain to flatten out from its slope of -1. This does not happen because C8 is "shorting out" only a portion of the impedance at the output and the increasing impedance of L1 dominates the filter response. C8 essentially has no impact on the filter's response when the value of C8 is small (where the boundary condition for C8 is met). For large values of C8, the zero it introduces becomes noticeable at a frequency lower than the pole of the power stage gain. If the value of C8 is equal to the boundary condition in the first equation, the zero frequency of the first equation and the pole frequency in the second equation are equal.
Simulation with a large aluminum capacitor
Now we replace the output capacitor in the simulation circuit with a large aluminum electrolytic capacitor (Figure 6).
Figure 6: SPICE model, large aluminum capacitor across LED.
The ESR is significantly larger than that of a ceramic capacitor. The capacitance value is selected to demonstrate the change in the loop transfer functions when the zero from the second equation is placed at a frequency lower than the pole frequency in the first equation.
As seen in Figure 7, a low-frequency zero causes an increase in gain, but ultimately the gain is limited to 18dB by the "gain" block in Figure 3. Above this zero frequency, a low-frequency pole begins to decrease the gain at a frequency determined by
Thus, the pole is shifted slightly lower in frequency than indicated by the first equation. The above equation is an approximation based on a large capacitance, where the ESR dominates C8's capacitive reactance at the pole frequency. Essentially, the ESR is in parallel with the LED impedance. At higher frequencies, the gain rolls off at a slope of -1, similar to the response shown previously for the smaller value of C8.
To compensate the loop gain for this given power stage gain, the zero of the type-two compensation circuit should be located near the pole frequency in the equation above. Once the loop is properly compensated, the size of C8 has little difference in the overall loop gain and phase margin. The choice of capacitor value and type is up to the designer, and the choice impacts the ripple current in the LED.
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https://infoscience.epfl.ch/record/135642 | Infoscience
Thesis
# Ground state properties of large atoms and quantum dots
We investigate the ground state properties of large atoms and quantum dots described by a d-dimensional N-body Hamiltonian of confinement ZV. In atoms, d = 3 and V is the Coulomb interaction; in dots, d = 2 and V is phenomenologically determined. We express the grand-canonical partition function in a path integral approach, and evaluate its expansion in Z-1. The problem can be seen as that of field theory possessing a saddle point. This saddle point results in a mean-field contribution to the energy, while the fluctuations result in the correlation energy. The mean-field contribution to the energy is self-consistently determined by the Hartree potential and contains an exchange term. Its smooth contribution is evaluated by a semiclassical method, with ε = Z-1/d in the role of ℏ, while its oscillating contribution can be related to the periodic orbits in the corresponding classical Hamiltonian. In the case of atoms, the leading order in ε of the correlation energy contains a term in Z ln Z1/3, which is essential in reproducing the behaviour shown by reference values, and a term in Z. While we have evaluated the contribution to the Z-term provided by the leading fluctuation order, the numerical evaluation of the contributions provided by higher order fluctuations remains an open problem. The self-consistent contribution to the energy corresponds to the statistical atom, composed of Thomas-Fermi and its corrections, comprehensively analysed, including oscillations, by Schwinger and Englert. In the case of dots, the leading order in ε of the correlation energy is a universal contribution of order Z, which we obtain in closed form. We then determine the expansion in ε of the smooth contributions down to this correlation order. We apply the approach to dots of quadratic and quartic confinement, including the oscillating contribution in the case of a chaotic quartic confinement.
Thèse École polytechnique fédérale de Lausanne EPFL, n° 4406 (2009)
Programme doctoral Physique
Faculté des sciences de base
Institut de théories des phénomènes physiques
Groupe de chaos et désordre
#### Reference
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https://www.physicsforums.com/threads/whats-the-meaning-of-the-cartesian-coordinates-of-the-atom.106327/ | # Homework Help: What's the meaning of the Cartesian coordinates of the atom?
1. Jan 10, 2006
### zsglly
How to get the Cartesian coordinates of an atom?
Dear friends,
Such a question confused me when reading!
"xi,yi and zi are the Cartesian coordinates of the ith atom"
How to get the coordinate of an atom? For example: carbon, oxygen?
I think the atom is only a dot! What's the way to indicate it with Cartesian coordinate?
Thank you!!
Sincerely,
zsglly
Last edited: Jan 10, 2006
2. Jan 10, 2006
### lightgrav
They're telling you the coordinate of the atom's center-of-mass
(we always describe the location of an object by its c.o.m. location!).
The C atom is at ( x_c , y_c , z_c ) ; the O atom is at ( x_o , y_o , z_o ) .
3. Jan 10, 2006
### zsglly
But I need the specific numerical value for calculating.
How to get it?
4. Jan 10, 2006
### lightgrav
Well, if they're not given in the problem, choose:
a) the text might list some inter-atom spacings in the chapter
b) you're supposed to keep them as variables (x,y,z)
What are you supposed to be calculating / computing ?
5. Jan 10, 2006
### zsglly
Until now, I didn't find any text about inter-atom spacings
To calculate moments of inertia.
I only want to get the value of several atoms.
Last edited: Jan 10, 2006
6. Jan 11, 2006
### zsglly
Actually, I'm not sure whether I need calculate the Cartesian coordinates or not. But I hope not. Because my only intention is to get the value of carbon, oxygen and so on.
7. Jan 11, 2006
### Gokul43201
Staff Emeritus
Of what ??? ( For instance, a carbon dioxide molecule about an axis perpendicular to the molecular axis ?) Please write down the given question completely. You have not provided enough information.
8. Jan 11, 2006
### algebra_chem
are you trying to say something like:
how many atoms does a carbon or oxygen have????
9. Jan 28, 2006
### zsglly
To calulate the moment of inertia using J.O. Hirshfelder's method
Do you know? | {"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": 0.81623375415802, "perplexity": 3134.1951885211815}, "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-2018-43/segments/1539583514005.65/warc/CC-MAIN-20181021115035-20181021140535-00468.warc.gz"} |
https://zbmath.org/?q=an:0924.41001 | ×
# zbMATH — the first resource for mathematics
Korovkin-type approximation theory and its applications. (English) Zbl 0924.41001
de Gruyter Studies in Mathematics. 17. Berlin: Walter de Gruyter. xi, 627 p. (1994).
In 1953 P. P. Korovkin discovered a criterion in order to decide whether a given sequence $$(L_n)$$ of positive linear operators on the space $$C[0,1]$$ is an approximation process, i.e., $$L_nf\to f$$ uniformly on [0,1] for every $$f\in C[0,1]$$: in fact, it is sufficient to verify that $$L_nf\to f$$ only for $$f\in \{1,x,x^2\}$$.
This result has been extended to other function spaces and to abstract spaces. Now the Korovkin approximation theory (KAT) has fruitful connections with functional analysis (notably with Choquet’s theory and Banach algebras theory), harmonic analysis, measure and probability theory, partial differential equations; an important feature of this monograph is the systematic presentation of all these connections.
The book is addressed to specialists in the above mentioned fields; a large part of it can also serve as a textbook for a graduate-level course. The authors have contributed significantly to the development of this theory. They give a survey on classical as well as recent developments in the field. Most of the results appear in book form for the first time.
In order to make the exposition self-contained, the prerequisites (from topology and analysis, measure and probability theory, locally convex spaces and Choquet’s integral representation theory, semigroups of operators) are collected in Chapter 1. Chapters 2, 3 and 4 are devoted to the main aspects of KAT in $$C_0(X)$$ $$(X$$ locally compact) and $$C(X)$$ $$(X$$ compact). The fundamental problem consists in studying, for a given positive linear operator $$T:C_0(X)\to C_0(Y)$$, those subspaces $$H$$ of $$C_0(X)$$ (if any) which have the property that every equicontinuous net of positive linear operators (or positive contractions) from $$C_0(X)$$ into $$C_0(Y)$$ converges strongly to $$T$$ whenever it converges to $$T$$ on $$H$$. (Such subspaces are called Korovkin subspaces for $$T$$). The classical case when $$T$$ is the identity operator is discussed in Chapter 4, where the authors present also the strong interplay between KAT and Choquet’s integral representation theory, as well as Stone-Weierstrass-type theorems. Furthermore, the existence of finite dimensional Korovkin subspaces is carefully analysed. The Korovkin subspaces for arbitrary positive linear operators, positive projections and finitely defined operators are characterized in Chapter 3. Here we find also applications to potential theory, Bauer simplices and Chebyshev systems. The results contained in Chapters 3 and 4 are based on the general Korovkin-type theorems for “bounded positive Radon measures, presented in Chapter 2 in connection with the theory of Choquet boundaries. Chapter 5 contains applications to the approximation of continuous functions defined on real intervals, by means of various kinds of operators. The rates of convergence are described by using classical moduli of continuity.
Chapter 6 contains a detailed analysis of some sequences $$(B_n)$$ of positive linear operators that have been studied recently; they connect the theory of $$C_0$$-semigroups of operators, partial differential equations and Markov processes. The operators $$B_n$$ are constructed by means of a positive projection $$T$$ acting on the space of continuous functions on a convex compact set $$K$$. This general construction has been proposed by F. Altomare [Ann. Sc. Norm. Sup. Pisa, Cl. Sci., IV. Ser. 16, No. 2, 259-279 (1989; Zbl 0706.47022]. By specializing $$K$$ and $$T$$ some well-known approximation processes can be obtained; new approximation processes (e.g., in the context of the infinite-dimensional Bauer simplices) are described and investigated.
The approximation properties of the operators $$B_n$$, their monotonicity properties and the preservation of some global smoothness properties are carefully analysed. Then a Feller semigroup is constructed in terms of powers of $$B_n$$. The infinitesimal generator of this semigroup is explicitly determined in a core of its domain; in the finite dimensional case it is an elliptic second-order differential operator which degenerates on the Choquet boundary of the range of $$T$$.
This theory is used to derive a representation and some qualitative properties of the solutions of the Cauchy problems which correspond to the involved diffusion equations. The transition function and the asymptotic behavior of the Markov processes governed by these diffusion equations are also described.
After the publication of the book, the theory presented in Chapter 6 has been further developed; see , e.g., [M. Campiti, G. Metafune, J. Approximation Theory 87, No. 3, 243-269 (1996; Zbl 0865.41027) and ibid., 270-290 (1996; Zbl 0874.41010)], [F. Altomare, I. Carbone, J. Math. Anal. Appl. 213, No. 1, 308-333 (1997; Zbl 0894.35044)], [F. Altomare, A. Attalienti, Math. Z. 225, No. 2, 211-229 (1997; Zbl 0871.41016)], [A. Favini, J. A. Goldstein, S. Romanelli, in: Stochastic processes and functional analysis, J. A. Goldstein, Marcel Dekker, New York, 1997, 85-100 (1997; Zbl 0889.35039)], [M. Romito, Mh. Math. (to appear)], [F. Altomare and the reviewer, Atti Semin. Mat. Fis. Univ. Modena 46, Suppl. 13-38 (1998; Zbl 0917.35042)].
In two appendices, written by M. Pannenberg and F. Beckhoff respectively, the main developments of KAT in the setting of Banach algebras are outlined.
The book contains also a subject classification, a symbol index and a subject index, all of them very useful. The historical notes and the references are very detailed. Well written and well produced, this comprehensive research monograph is a timely and welcome addition to the mathematical literature.
##### MSC:
41-02 Research exposition (monographs, survey articles) pertaining to approximations and expansions 41A36 Approximation by positive operators 41A25 Rate of convergence, degree of approximation 41A35 Approximation by operators (in particular, by integral operators) 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
##### Keywords:
Korovkin approximation theory | {"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": 0.8982203006744385, "perplexity": 576.4859862960278}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703529080.43/warc/CC-MAIN-20210122020254-20210122050254-00716.warc.gz"} |
https://physics.stackexchange.com/questions/709069/what-does-it-mean-if-the-fermi-level-crosses-into-the-valence-band-how-about-in | # What does it mean if the Fermi level crosses into the valence band? How about into the conduction band?
I've been working on this material to get more accustomed to Quantum Espresso, and I've gone on and performed calculations to get their band structures. Here are the band structures that I got for two of the variations of my material:
Used EV-GGA to get these band structures, I could have used others, but I'm just curious as to what these particular band structures imply. As you can see, for the first one, the Fermi level has crossed into the valence band while for the second one the Fermi level is in the conduction band. Do these both imply metallic nature? These are undoped materials, can doping possibly cause the Fermi levels to move accordingly and make these materials semiconductors? Thank you everyone for your help.
The terms "conduction band" and "valence band" sort of lose their usefulness if you are not talking about a standard band insulator where you have a filled valence band and the chemical potential lies in the gap.
In your two cases, both materials will be metallic because there is finite density of states at the Fermi level.
Yes with doping you can move the Fermi level. Electron doping will move the Fermi level up and hole doping will move it down. But in the actual real(physical) material it may not be possible to dope it sufficiently to put the Fermi level within the gap.
• Thank you so much for your answer. The doping thing may be a good avenue for further study because I'm also curious about how the location of the Fermi level changes with doping. I'd like to ask about what you what you said about the finite density of states. Would much denser bands around the Fermi level imply some other characteristic for the material? May 17 at 7:43
• It depends on what you mean by "denser bands". If you mean more bands, then that will affect what your Fermi surface looks like. For example, In both of your cases multiple bands cross the Fermi level, so you will have fairly complicated Fermi surfaces with multiple hole and electron pockets. This will certainly affect the material properties, such as the conductivity tensor. If you mean tuning the density of states itself, that is related to the curvature of the bands and that will also affect the material in many ways, some simple like it will change the conductivity,
– pmal
May 17 at 7:54
• but also potentially in more complex ways because if you have a high density of states then the system will be more susceptible to collective instabilities like magnetism or superconductivity.
– pmal
May 17 at 7:54
• Thank you so much! You've given me a good place to start with how to rationalize these band structures. Do you have any good references that I could use to read more about this? May 17 at 8:07
• That is a bit hard to answer without knowing your background knowledge. If you are doing DFT calculations, I would think you have already read some standard solid state physics books? If not, Ashcroft and Mermin is a standard, and also Kittel. My favorite more modern condensed matter book is Girvin and Yang.
– pmal
May 17 at 8:11
In the book by Naeman, Semiconductor Physics, the equation $$E_F -E_{Fi}=kT\ln{\frac{n_0}{n_i}}$$ is derived and relates the change in the Fermi level due to doping. $$E_F$$ is the Fermi level after doping and $$E_{Fi}$$ is the intrinsic Fermi level, where $$n_0$$ and $$n_i$$ are the initial and final electron number densities before and after doping.
So the Fermi level clearly changes due to doping.
• Thank you for this! I will be looking into Naeman's book as well, thanks for giving me a reference. May 17 at 7:45
• That's ok. good luck with your studies. May 17 at 7:46 | {"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8208430409431458, "perplexity": 353.96655609239053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104244535.68/warc/CC-MAIN-20220703134535-20220703164535-00703.warc.gz"} |
https://physics.stackexchange.com/questions/453890/why-is-the-mainstream-theory-of-cosmological-redshift-inconsistent-with-the-main | # Why is the mainstream theory of cosmological redshift inconsistent with the mainstream theory of gravitational redshift
Gravitational redshift
Cause : A reduction in the decompression of space* over distance (due to the presence of mass).
Mainstream theory: Photons are emitted in a region of higher gravity with Energy A, and received in a region of lower gravity with Energy A, where Energy A is lower than the Energy B that would have been emitted by a similar event in a region of lower gravity.
Evidence: There is plenty of experimental evidence to support this theory.
Cosmological redshift
Cause: A reduction in the decompression of space* over time (due to universal expansion).
Mainstream Theory: Photons were emitted in the distant past with Energy B and received in the present with lower Energy A, where B is the energy that would be emitted from a similar event in the present.
Evidence: No hard evidence that I am aware of. Some may argue that CMB was emitted as ultraviolet radiation and we now see it as microwave radiation. I agree, but if we are being consistent with the hard evidence we have about gravitational redshift, then we should expect that time is moving much more quickly today than it was when the CMB was emitted, just as it moves more quicky in regions of lower gravity. So yesterday's ultraviolet wave is today's microwave - with the same energy.
*I use the word space for brevity, but really mean the universal metric through which light travels.
As far as I can see, apart from their causes, the only difference between cosmological redshift and gravitational redshift is that one happens over space and the other happens over time. So why is the mainstream view on cosmological redshift inconsistent with the mainstream view on gravitational redshift, for which there is ample supporting evidence?
• Both of these effects can be computed in the same way from the same equation. It is true that, in the usual coordinate systems, one of them involves a change in $g_{tt}$ (temporal component) while the other involves a change in $g_{ii}$ (spatial component). – knzhou Jan 13 at 11:49
• Of course, you can change your coordinates so that both are due to $g_{tt}$, I suppose, or both due to $g_{ii}$, or really anything else. But it really doesn't matter. You can solve a problem in more than one coordinate system. So it is unclear what "inconsistency" you're referring to. – knzhou Jan 13 at 11:51
• @knzhou I'm referring to the difference I highlighted in bold. In the one case we say that the energy of the photon remained constant, in the other case we say it reduced. – Alan Gee Jan 13 at 15:44
• what you describe as redshift is not a shift, if the energy does not change. Do you have a link for the statement? – anna v Jan 13 at 15:53
• @anna v a shift in frequency is not necessarily an energy change if time is running faster, So my question can also be phrased as 'why do we think time dilation occurs due to gravity but not due to (opposite of)expansion?' – Alan Gee Jan 13 at 16:02
Consider a garden pond with evenly spaced pebbles across it.
A frog and a fish start out at one end and cross it. The frog with a constant hop rate across the pebbles, the fish at a constant swim speed. They reach the other side at the same time. In this static situation there is little to choose between the two creatures because they both get the same job done in the same time.
Now the owner of the pond decides to extend it a little, and after doing so, adjusts the spacing of the existing pebbles to make it look pretty again. The frog and the fish repeat their journey, and this time the frog gets to the other side first. That's because the frog had the same number of pebbles to hop, at a constant hop rate, while the fish had further to swim.
When Physicists analyse light from distant galaxies, they assume that it travelled through space and time like the fish through an expanding pond. Gravitational time dilation, on the other hand, indicates that it travels more like the frog.
I know that when light travels through space that has been warped by the presence of mass its speed varies accordingly. Yet I am expected to believe that when light passes through space that has been warped by universal expansion, its speed remains constant. Correct me if I'm wrong, but for me that smacks of inconsistency.
• If you would like to verify that the current paradigm is self-consistent, you're free to get any textbook on general relativity and verify the equations yourself. We're not hiding anything -- the book will even help you evaluate it. The problem, as I stated in the comments above, is that the math-free intuition one uses can be quite unreliable, changing depending on the reference frame. In practice, in GR physicists often calculate things rigorously first, and only afterward drape some intuitive words around the final result. – knzhou Feb 27 at 2:40
• @knzhou I am not basing anything on intuition. I am basing it on what I know about light, and I know a lot about light. I refuse to blindly accept things just because most people do. You are welcome to GR with all of its abstractions, I will focus on simple truths. – Alan Gee Feb 27 at 8:04
• And from where did you get that information about light? Light is quite unintuitive. Electrical engineers can spend a lifetime studying its subtleties. And you're sure you know everything about it without even knowing any of the math? – knzhou Feb 27 at 11:23
• What I do know is, that by stubbornly insisting that the speed of light can never vary, you are hiding the majority of the meaning of $$E = mc^2$$ which as far as I am concerned is like self inflicted harm. It will probably take someone with far more clout than me to convince people of this, but it will happen. – Alan Gee Feb 27 at 18:20
• What are you actually proposing? If you're proposing an alternative theory that makes alternative predictions, go find out what they are, and make sure they're not already observed to be false. If you're proposing a different way of looking at the same theory, nobody really cares unless you can explain why your way is more useful. Right now you are saying that you really really really like one particular classical fact, and will take any interpretation that preserves it at the cost of ruining everything else. You can choose to do that but you can't choose to make others do it. – knzhou Feb 27 at 18:44 | {"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": 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": 0.8068775534629822, "perplexity": 444.690025074371}, "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/1563195525312.3/warc/CC-MAIN-20190717141631-20190717163631-00485.warc.gz"} |
http://link.springer.com/article/10.1007%2Fs00396-012-2850-4 | , Volume 291, Issue 5, pp 1201-1210
Date: 17 Nov 2012
# Colloidal crystallization of cationic gel spheres of lightly cross-linked poly(2-vinylpyridine) in the deionized aqueous suspension
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## Abstract
Colloidal crystallization of deionized suspensions of the cationic gel spheres of lightly cross-linked poly(2-vinylpyridine) (PEGMA-P2VP) has been studied from the microscopic observation, morphology, phase diagram, and elastic property. Critical concentrations of melting coexisted with ion-exchange resins were low compared with those without resins and increased but slightly as the degree of cross-linking decreased. The densities of the gel spheres, i.e., weight percent of the gel spheres divided by the corresponding volume percent, were between 0.7 and 0.9 and rather insensitive to the degree of cross-linking of the spheres examined from 0.1 to 1 mol%. This means that the gel spheres are rather dense. The closest inter-sphere distances of the crystals were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. Fluctuation parameters evaluated from the rigidities of the crystals of PEGMA-P2VP were similar to those of colloidal crystals of typical hard spheres. Mono-layered adsorption of cationic gel spheres at the nearest-neighbored layer from a cover glass of the cell was observed microscopically. The stable ordered layers, however, formed beyond the monolayer in the suspension phase. These experimental findings support the important role of the extended electrical double layers around the cationic gel spheres in addition to the excluded volume effect of the sphere themselves on the crystallization. | {"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": 0.918904721736908, "perplexity": 4636.2607253913375}, "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-2014-35/segments/1408500830746.39/warc/CC-MAIN-20140820021350-00034-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.computer.org/csdl/trans/tp/2007/07/i1165-abs.html | Issue No. 07 - July (2007 vol. 29)
ISSN: 0162-8828
pp: 1165-1179
Tom? Werner , IEEE Computer Society
ABSTRACT
The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.
INDEX TERMS
Markov random fields, undirected graphical models, constraint satisfaction, belief propagation, linear programming relaxation, max-sum, max-plus, max-product, supermodular optimization.
CITATION
T. Werner, "A Linear Programming Approach to Max-Sum Problem: A Review," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 29, no. , pp. 1165-1179, 2007.
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https://www.physicsforums.com/threads/physics-speed-mph-question.56502/ | # Physics speed mph question
1. Dec 12, 2004
I thought the answer was 90mph, but my friend says it's wrong. I just can't figure out any other answer.
----
You drive to the store which is a 2 mile trip. In the first mile you average 30 mph, how fast must you drive the second mile in order to average 60mph for the entire 2 mile trip?
----
thnx
Jennifer
2. Dec 12, 2004
### Zurtex
I would have thought it would have been an average 90mph in the 2nd mile as well
3. Dec 12, 2004
Nobody?
4. Dec 12, 2004
### master_coda
If your average speed for the trip were 60 mph, it would take you 2 minutes to complete the entire trip. Thus you have to drive fast enough on the second leg to complete the trip in 2 minutes.
However if you only drive at 30 mph for the first mile then it you will already have taken 2 minutes; no matter how fast you drive for the second mile, you'll take longer than 2 minutes so you can't actually average 60 mph for the whole trip.
Note that this is because "average speed = distance travelled / travel time" and not the average of all the speeds over each segment.
5. Dec 12, 2004
thnx! That makes sense! :) | {"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": 0.8985326290130615, "perplexity": 849.0694727529109}, "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/1476988719027.25/warc/CC-MAIN-20161020183839-00196-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/help-with-poisson-equation.315876/ | # Help with Poisson equation
1. May 23, 2009
### zebra
1. The problem statement, all variables and given/known data
Hi, I am looking for a hint, how to solve the following Dirichlet problem. All the standard textbooks have only examples for Dirichlet problems in rectangular or polar coordinate systems, but this problem is defined for a parabolic region.
2. Relevant equations
uxx+uyy=2, x>y2
u(x,y)=0, x=y2
3. The attempt at a solution
Transformation into parabolic coordinates and using separation of variables? I am having a problem even with that. The parabolic coordinates with the parabolic Laplacian are here http://eom.springer.de/P/p071170.htm. I don´t even know, how to transform the boundaries. The parabolic coordinates are so unusual. Is this a right method or would you solve it differently? (with Green functions, or Laplace transform etc)
Can you offer guidance or do you also need help?
Draft saved Draft deleted
Similar Discussions: Help with 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": 0.8791823387145996, "perplexity": 844.074348904217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948588294.67/warc/CC-MAIN-20171216162441-20171216184441-00604.warc.gz"} |
http://mathhelpforum.com/differential-geometry/168060-transformation-matrices-tetrahedra.html | # Math Help - Transformation Matrices - Tetrahedra
1. ## Transformation Matrices - Tetrahedra
Hello everyone!
I was wondering if anyone out there could help me with some 3d geometry transformations.
What I've got:
I have a tetrahedron (A) in Cartesian space, centred at the origin, with vertices at:
(1,1,1) , (-1,-1,1) , (-1,1-1) & (1,-1,-1).
What I would like:
A tetrahedron (B) with vertices at:
(-1,-1,-1), (0,-1,0), (-1,0,0), (0,0,-1)
The question:
How does one find the transformation matrix to transform tetrahedron A into tetrahedron B?
Any help will be greatly appreciated
2. This can't be expressed as a linear transformation A.
Your original vectors v1+v2+v3+v4 = 0
However, your new vectors v1'+v2'+v3'+v4' = (-2,-2,-2)
If this was a linear transformation:
Av1 + Av2 + Av3 + Av4 = A(v1+v2+v3+v4) = 0
If you wanted this transformation, you will at least have to use affine transformations.
Trying to solve the matrices I just realised (as you say) it is unsolvable as a linear transform. So how would one find the affine transformation?
4. For affine transformations, you just add in a scale factor (which is normally the unit).
For example, (1,1,1) would be represented as (1,1,1,1).
Then you can do a linear transformation in 4 dimensions.
In general, an affine vector (a,b,c,d) is the same thing as the 3d vector (a/d, b/d, c/d).
However, I'm not sure this is the best way for you to go.
What are you trying to do?
5. I'm using structure synth to create a fractal. So I want to put map tetrahedrons onto the 4 face's of a larger tetrahedron. In sturcture synth you only have option of using a 3x3 transformation matrix though...
6. Actually, most 3d drawing software allow affine transformations. They are needed for translations and also perspective projections.
My suggestion is for a fractal, the tetrahedron should at least be similar (which is not the case for your example).
If they are similar, you can easily draw it with a scaling, rotation, and translation (which is an affine transformation).
Also, perhaps it is easier to use the scaling rotation and translation primitive instead of constructing the matrix yourself (essentially let the computer do it for you).
7. The tetrahedrons are self similar, I can post a screen shot if you'd like... The second one is a smaller version of the larger, but all lengths are scaled linearly and then rotated and translated...
Attached Thumbnails
8. So to clarify the larger tetrahedron (red) has edges all of length 2sqrt(2) and smaller has edges sqrt(2). All faces are equilateral -> so they must be self similar...
9. Originally Posted by perrelet
The tetrahedrons are self similar, I can post a screen shot if you'd like... The second one is a smaller version of the larger, but all lengths are scaled linearly and then rotated and translated...
Yes, they are definitely similar
I didn't do a thorough calculation.
Some kind of 3D Koch curve I see.
So you must have been able to describe the transformations to draw that picture.
10. Hey snowtea
I drew that picture by explicitly stating the coordinates of both tetrahedra to the program. However I want the program to build the second by reiterating the first and applying a transformation, as this method will allow me to add levels of tetrahedra arbitrarily deep into the figure...
I've tried to solve the system of equations by transforming each vertex on one tetrahedron into the vertex on another, as (for example) follows:
(1,1,1) => (0,-1,0)
(-1,-1,1) => (-1,-1,-1)
(1,-1,-1) => (0,0,-1)
(-1,1,-1) => (-1,0,0)
But when I solve the system for the transformation matrix as it is done in 2D in this thread: https://nrich.maths.org/discus/messa...tml?1140864401. My system of equations is not solvable...
Not sure why?
11. Like a said, it is not a linear transformation (in 3 dimensions), so of course you won't be able to solve it.
Express it as a composition of simple transformations (on your coordinate axes) in this order:
Scaling then Rotation then Translation.
Then you can use the exact same drawing routine since your new coordinate axes are transformed.
Note: You will have to use quite a bit of trig. | {"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": 0.8034534454345703, "perplexity": 879.9222434679867}, "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/1393999642134/warc/CC-MAIN-20140305060722-00032-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/182725/how-to-recover-three-successive-rotations-of-a-vector | # How to recover three successive rotations of a vector
I have a vector, which I rotated with respect to $x$, $y$ and $z$ axes, respectively.
Now I want to recover this operation, that means I want to bring it to the previous position by rotating it with $-\theta$, $-\alpha$ and $-\beta$, where $\theta$, $\alpha$ and $\beta$ are the amounts of initial rotation, in radians/degrees.
I tried to do it by computing the dot product of this vector with axis vectors ($(1,0,0)$ for $x$-axis, $(0,1,0)$ for $y$-axis and $(0,0,1)$ for $z$-axis).
However, this did not produce the right result possibly because It was rotated in 3d, thus the dot product was resulting in a different value that it should be.
What I should do in order to perform this operation? Thanks.
-
do you mean you rotated using Euler angles? or did you rotate around the fixed axes? – nbubis Aug 15 '12 at 7:03
I'm not really sure what you're asking. Do you mean that you know the position $x$ of your point before rotating, the position $x'$ of the point after rotating, and then you want to find the angles $\theta,\alpha,\beta$ such that $x'$ gets send back to $x$? Or do you already know $\theta, \alpha,\beta$ and you just want to know how to use these to create a rotation that sends $x'$ back to $x$? – Lieven Aug 15 '12 at 7:12
@Lieven The latter one. I know $\theta$,$\alpha$ and $\beta$, and I want to find the rotation that sends $x'$ back to $x$. – user13791 Aug 15 '12 at 8:00
@nbubis using Euler angles. – user13791 Aug 15 '12 at 8:31
As @nbubis mentioned, Euler angles is what you are looking for. – Sait Aug 15 '12 at 8:34
If you used Euler angles, simply multiply your vector by the rotation matrices in reverse order. If you used $\alpha$ around $\hat{x}$, then $\beta$ around $\hat{y}$, and finally $\gamma$ around $\hat{z}$ to get at a vector $v$, then the original vector $v_0$ is given by: $$v_0 = Z(-\gamma)Y(-\beta)X(-\alpha)v$$ Where $X,Y,Z$ are the rotation matrices. | {"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": 0.8448513746261597, "perplexity": 250.98178804246984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988305.14/warc/CC-MAIN-20150728002308-00305-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/4175914/why-1n-1-fracn3n-1-is-divergent/4175919 | # Why $(-1)^{n-1} \frac{n}{3n + 1}$ is divergent?
I am wondering the reason $$(-1)^{n-1} \frac{n}{3n + 1}$$ is divergent although the limit of $$\frac{n}{3n + 1}$$ is $$1/3.$$
Any explanation will be greatly appreciated!
• @DonThousand: The sequence can't converge since the limit is not $0$ and it does not have an ultimately constant sign. Jun 17, 2021 at 20:48
• A sequence is divergent if it doesn't converge. Since $n/(3n+1)$ converges to $1/3$, your sequence looks like $1/3,-1/3,1/3,-1/3,...$, which is osscilating.
– pax
Jun 17, 2021 at 20:49
Let $$a_n = (-1)^{n-1} \frac{n}{3n+1}$$. Then $$a_{2n} = -\frac{2n}{6n+1}$$ and $$a_{2n+1} = \frac{2n+1}{6n+4}$$. Observe that $$\lim_{n\to \infty}a_{2n} = -\frac{1}{3} \qquad \lim_{n\to \infty}a_{2n+1} = \frac{1}{3}$$
Since the limits along two subsequences differ, then $$a_n$$ diverges.
• Hi, what is the criterium that have you used? At this moment I have forgotten it. +1 Jun 17, 2021 at 21:00
• @Sebastiano If $x_n \to a$ , then any subsequence satisfies $x_{n_k} \to a$. If the conclusion does not hold for a sequence, by contrapositive it must be that the parent sequence does not converge. Jun 17, 2021 at 21:01
• Thank you very much for your collaboration....thank you again. Jun 17, 2021 at 21:04
Consider two subsequences of the given sequence, viz. the even subsequence, and the odd subsequence.
• For even $$n$$, we may write $$n=2k$$ for $$k\in\mathbb{N}$$. Then we have : $$\lim_{n\to\infty}(-1)^{n-1} \frac{n}{3n + 1} = \lim_{k\to\infty}(-1)^{2k-1} \frac{2k}{6k + 1} = -\lim_{k\to\infty} \frac{1}{3 + \frac{1}{2k}} = -\frac{1}{3}$$
• For odd $$n$$, we may write $$n=2k+1$$ for $$k\in\mathbb{N}$$. Then we have : $$\lim_{n\to\infty}(-1)^{n-1} \frac{n}{3n + 1} = \lim_{k\to\infty}(-1)^{2k+1-1} \frac{2k+1}{6k + 3 + 1} = \lim_{k\to\infty} \frac{1}{3 + \frac{1}{2k+1}} = \frac{1}{3}$$
So, the odd and the even subsequences of the original sequence converge to two different limit points. Thus, the sequence is not convergent.
Convergence implies that there exists a singular limit to the sequence, which itself requires that for all $$\epsilon > 0$$, there exists an $$N \in \mathbb{N}$$ such that $$|a_n - a| < \epsilon, \quad \forall n \geq N.$$ This convergence condition does not hold true for the sequence $$a_n = \frac{(-1)^{n-1}n}{3n+1}$$ purely due to its oscillatory nature and the fact that its limit when the $$(-1)^n$$ is removed, is nonzero.
Since the sequence $$\frac{n}{3n+1}$$ converges to a nonzero value, convergence of $$(-1)^n\frac{n}{3n+1}$$ would imply convergence of $$(-1)^n.$$ However, this sequence is known to be divergent.
Suppose a limit $$L$$ exists.
Case $$1$$: $$L\ge 0$$. Then for all $$\epsilon > 0$$, there is some $$N\in\mathbb N$$ such that for all $$n\ge N$$
$$|a_n-L|<\epsilon.$$
Choose $$\epsilon = 1/5$$, and find such an $$N$$ as above. Then as $$n=2N > N$$ we must have $$|a_{2N}-L|<1/5$$ or
$$-1/5 < L-1/5 < -\dfrac{N}{3N+1}=a_{2N} < L+1/5$$
but $$a_{2N}=-\dfrac{N}{3N+1} <-\dfrac{N}{3N+N} = -\dfrac{N}{4N} = -\dfrac{1}{4} \not > -\dfrac{1}{5}$$.
Case $$2$$: $$L<0$$. Apply similar thinking. | {"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": 39, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9875104427337646, "perplexity": 194.33527501449393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104585887.84/warc/CC-MAIN-20220705144321-20220705174321-00660.warc.gz"} |
http://www.maplesoft.com/support/help/Maple/view.aspx?path=Ore_algebra/Ore_to_diff | Ore_algebra - Maple Programming Help
Home : Support : Online Help : Mathematics : Algebra : Skew Polynomials : Ore Algebra : Ore_algebra/Ore_to_diff
Ore_algebra
Ore_to_diff
convert a differential operator to a differential equation
Ore_to_shift
convert a shift operator to a recurrence equation
Ore_to_DESol
convert a differential operator to a DESol structure
Ore_to_RESol
convert a shift operator to an RESol structure
Calling Sequence Ore_to_diff(G, f, A) Ore_to_diff(G, f, A, 'D') Ore_to_shift(G, u, A) Ore_to_shift(G, u, A, 'indexed') Ore_to_DESol(P, f, A) Ore_to_RESol(P, u, A)
Parameters
G - list of operators of the Ore algebra A P - operator of the Ore algebra A f - expression denoting a mathematical function A - Ore algebra table
Description
• The Ore_to_diff command converts a differential operator or a list of differential operators of the skew algebra A into a differential equation or a list of differential equations in the function f. The output is expressed in terms of the diff function by default, or in terms of the D function when the optional parameter is set.
• The Ore_to_DESol command converts a single differential operator of the skew algebra A into a DESol structure in the function f.
• The Ore_to_shift command converts a shift operator or a list of shift operators of the skew algebra A into a recurrence equation or a list of recurrence equations in the sequence u. The output is expressed in functional notation ( $u\left(n\right),...$ ) by default, or in the indexed notation ( ${u}_{n},...$ ) when the optional argument is set.
• The Ore_to_RESol command converts a single recurrence operator of the skew algebra A into an RESol structure in the sequence u.
Examples
> $\mathrm{with}\left(\mathrm{Ore_algebra}\right):$
Differential case.
> $A≔\mathrm{diff_algebra}\left(\left[\mathrm{Dx},x\right],\left[\mathrm{comm},\mathrm{μ}\right]\right):$
> $P≔{x}^{2}{\mathrm{Dx}}^{2}+x\mathrm{Dx}+{x}^{2}-{\mathrm{μ}}^{2}:$
> $\mathrm{Ore_to_diff}\left(P,f,A\right)$
${{x}}^{{2}}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right)\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{f}{}\left({x}\right)\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)$ (1)
> $\mathrm{Ore_to_diff}\left(P,f,A,\mathrm{D}\right)$
${{x}}^{{2}}{}{{\mathrm{D}}}^{\left({2}\right)}{}\left({f}\right){}\left({x}\right){+}{x}{}{\mathrm{D}}{}\left({f}\right){}\left({x}\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)$ (2)
> $\mathrm{Ore_to_DESol}\left(P,f,A\right)$
${\mathrm{DESol}}{}\left(\left\{{{x}}^{{2}}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right)\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{f}{}\left({x}\right)\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)\right\}{,}\left\{{f}{}\left({x}\right)\right\}\right)$ (3)
> $\mathrm{normal}\left(\mathrm{applyopr}\left(P,,A\right)\right)$
${0}$ (4)
Euler case.
> $A≔\mathrm{skew_algebra}\left(\mathrm{euler}=\left[\mathrm{Tx},x\right],\mathrm{comm}=\mathrm{μ}\right):$
> $P≔{\mathrm{Tx}}^{2}+{x}^{2}-{\mathrm{μ}}^{2}:$
> $\mathrm{Ore_to_diff}\left(P,f,A\right)$
${x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{f}{}\left({x}\right){+}{x}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right)\right)\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)$ (5)
Recurrence case.
> $A≔\mathrm{shift_algebra}\left(\left[\mathrm{Sn},n\right],\left[\mathrm{comm},\mathrm{α}\right]\right):$
> $P≔{\mathrm{Sn}}^{2}+\mathrm{α}\mathrm{Sn}+1:$
> $\mathrm{Ore_to_shift}\left(P,u,A\right)$
${u}{}\left({n}{+}{2}\right){+}{\mathrm{α}}{}{u}{}\left({n}{+}{1}\right){+}{u}{}\left({n}\right)$ (6)
> $\mathrm{Ore_to_shift}\left(P,u,A,\mathrm{indexed}\right)$
${\mathrm{α}}{}{{u}}_{{n}{+}{1}}{+}{{u}}_{{n}}{+}{{u}}_{{n}{+}{2}}$ (7)
> $\mathrm{Ore_to_RESol}\left(P,u,A\right)$
${\mathrm{RESol}}{}\left(\left\{{u}{}\left({n}{+}{2}\right){+}{\mathrm{α}}{}{u}{}\left({n}{+}{1}\right){+}{u}{}\left({n}\right){=}{0}\right\}{,}\left\{{u}{}\left({n}\right)\right\}{,}\left\{{u}{}\left({0}\right){=}{u}{}\left({0}\right){,}{u}{}\left({1}\right){=}{u}{}\left({1}\right)\right\}{,}{\mathrm{INFO}}\right)$ (8)
Multivariate differential case.
> $A≔\mathrm{diff_algebra}\left(\left[\mathrm{Dx},x\right],\left[\mathrm{Dy},y\right],\left[\mathrm{comm},\mathrm{μ}\right]\right):$
> $G≔\left[-2\mathrm{Dx}x+\mathrm{Dy}y,-4\left(\mathrm{μ}-x{y}^{2}\right)\left(\mathrm{μ}+x{y}^{2}\right)+2\mathrm{Dx}x+{y}^{2}{\mathrm{Dy}}^{2},-2\left(\mathrm{μ}-x{y}^{2}\right)\left(\mathrm{μ}+x{y}^{2}\right)+\mathrm{Dy}\mathrm{Dx}yx,-\left(\mathrm{μ}-x{y}^{2}\right)\left(\mathrm{μ}+x{y}^{2}\right)+\mathrm{Dx}x+{\mathrm{Dx}}^{2}{x}^{2}\right]:$
These are operators for BesselJ(mu,x*y^2).
> $\mathrm{Ore_to_diff}\left(G,f,A\right)$
$\left[{-}{2}{}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){+}{y}{}\left(\frac{{\partial }}{{\partial }{y}}{}{f}{}\left({x}{,}{y}\right)\right){,}{-}{4}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{{y}}^{{2}}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{f}{}\left({x}{,}{y}\right)\right){+}{2}{}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){,}{-}{2}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{y}{}{x}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{y}{}{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){,}{-}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){+}{{x}}^{{2}}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{f}{}\left({x}{,}{y}\right)\right)\right]$ (9)
> $\mathrm{Ore_to_diff}\left(G,f,A,\mathrm{D}\right)$
$\left[{-}{2}{}{x}{}{\mathrm{D}}{[}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right){+}{y}{}{\mathrm{D}}{[}{2}{]}{}\left({f}\right){}\left({x}{,}{y}\right){,}{-}{4}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{{y}}^{{2}}{}{\mathrm{D}}{[}{2}{,}{2}{]}{}\left({f}\right){}\left({x}{,}{y}\right){+}{2}{}{x}{}{\mathrm{D}}{[}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right){,}{-}{2}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{y}{}{x}{}{\mathrm{D}}{[}{1}{,}{2}{]}{}\left({f}\right){}\left({x}{,}{y}\right){,}{-}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{x}{}{\mathrm{D}}{[}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right){+}{{x}}^{{2}}{}{\mathrm{D}}{[}{1}{,}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right)\right]$ (10)
No conversion is available to a multivariate DESol.
> $\mathrm{Ore_to_DESol}\left(G,f,A\right)$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 32, "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": 0.9362044930458069, "perplexity": 2166.516285659589}, "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-2017-17/segments/1492917125881.93/warc/CC-MAIN-20170423031205-00118-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://en.m.wikipedia.org/wiki/One-repetition_maximum | # One-repetition maximum
One-repetition maximum (one rep maximum or 1RM) in weight training is the maximum amount of weight that a person can possibly lift for one repetition. It may also be considered as the maximum amount of force that can be generated in one maximal contraction.[1] One repetition maximum can be used for determining an individual's maximum strength and is the method for determining the winner in events such as powerlifting and weightlifting competitions. One repetition maximum can also be used as an upper limit, in order to determine the desired "load" for an exercise (as a percentage of the 1RM).
## Calculating 1RM
This chart compares the different formulas
The 1RM can either be calculated directly using maximal testing or indirectly using submaximal estimation. The submaximal estimation method is preferred as it is safer, quicker, and less unnerving for inexperienced exercisers;[2] however, it may underestimate the actual 1RM.[3] One rep maximum calculators are used to predict a one rep maximum lift. The degree of accuracy can vary largely depending on the weight training experience and muscular composition of the athlete. Also, most one rep maximum calculators are designed for seasoned strength trainers, and those with little experience may find their actual one rep maximum is much lower because their nervous system cannot handle the stress of a high weight. This test should be performed with a spotter for reasons of safety.
Weight training protocols often use 1RM when programming to ensure the exerciser reaches resistance overload, especially when the exercise objective is muscular strength, endurance or hypertrophy. By understanding the maximal potential of the muscle, it is possible to reach resistance overload by increasing the number of repetitions for an exercise.
Determining the 1 rep max can be done directly through trial and error and simply requires the exerciser to complete one full repetition with the maximum weight. There are several common formulas used to estimate 1RM using the submaximal method, the Epley and the Brzycki being the most common.[4] In the formulas below, ${\displaystyle r}$ is the number of repetitions performed and ${\displaystyle w}$ is the amount of weight used (note that ${\displaystyle w}$ is a factor of each formula, so the unit of measurement doesn't matter).
### Epley formula
${\displaystyle 1{\text{ RM}}=w\left(1+{\frac {r}{30}}\right),}$ assuming ${\displaystyle r>1.}$ [5]
### Brzycki
This version of the one rep maximum calculation is often referred to as the Brzycki Formula after its creator, Matt Brzycki,[6] and can be written either in terms
${\displaystyle 1{\text{ RM}}=w\cdot {\frac {36}{37-r}}={\frac {w}{{\frac {37}{36}}-{\frac {1}{36}}r}}\approx {\frac {w}{1.0278-0.0278r}}}$
Formula 1 (Epley) and formula 2 (Brzycki) return identical results for 10 repetitions. However, for fewer than 10 reps, formula 1 returns a slightly higher estimated maximum. For example, if a person can lift 100 pounds on a given exercise for 10 reps, the estimated one rep max would be 133 pounds for both formulae. However, if the person were to complete only 6 reps, then formula 1 would estimate a one rep maximum of approximately 120 pounds, while formula 2 would return an estimate of approximately 116 pounds.
These types of calculations may not always produce accurate results, but can be used as starting points. The weight can then be changed as needed to perform the number of reps called for by the training protocol.
Several more complex formulae have been proposed which use different coefficients for different rep numbers and sometimes even for different exercises.[7]
### McGlothin
${\displaystyle 1{\text{ RM}}={\frac {100w}{101.3-2.67123r}}}$
### Lombardi
${\displaystyle 1{\text{ RM}}=wr^{0.10}}$
### Mayhew et al.
${\displaystyle 1{\text{ RM}}={\frac {100w}{52.2+41.9e^{-0.055r}}}}$
### O'Conner et al.
${\displaystyle 1{\text{ RM}}=w\left(1+{\frac {r}{40}}\right)}$
### Wathen
${\displaystyle 1{\text{ RM}}={\frac {100w}{48.80+53.8e^{-0.075r}}}}$
## References
1. ^ Marchese, Rosemary; Hill, Andrew (2011). The essential guide to fitness: for the fitness instructor. Sydney, NSW: Pearson Australia. p. 135. ISBN 9781442510203.
2. ^ Marchese, Rosemary; Hill, Andrew (2011). The essential guide to fitness: for the fitness instructor. Sydney, NSW: Pearson Australia. pp. 158–159. ISBN 9781442510203.
3. ^ Knutzen, Kathleen; Brilla, Lorraine; Caine, Dennis (August 1999). "Validity of 1RM Prediction Equations for Older Adults". The Journal of Strength & Conditioning Research. p. Vol 13, Issue 3, Page 242–246. Retrieved 11 July 2014.
4. ^ Calculate your One Rep Max (1RM).
5. ^ Epley, Boyd (1985). "Poundage Chart". Boyd Epley Workout. Lincoln, NE: Body Enterprises. p. 86.
6. ^ Brzycki, Matt (1998). A Practical Approach To Strength Training. McGraw-Hill. ISBN 978-1-57028-018-4.
7. ^ LeSuer, Dale A.; McCormick, James H.; Mayhew, Jerry L.; Wasserstein, Ronald L.; Arnold, Michael D. (November 1997). "The Accuracy of Prediction Equations for Estimating 1-RM Performance in the Bench Press, Squat, and Deadlift". Journal of Strength and Conditioning Research. 11 (4): 211–213. doi:10.1519/00124278-199711000-00001. S2CID 144001941.
• Lesuer, DA, Mccormick, JH, Mayhew, JL; et al. (1997). "The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift". J Strength Cond Res. 11: 211–213.{{cite journal}}: CS1 maint: multiple names: authors list (link) | {"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": 0.8509405255317688, "perplexity": 4026.9046091636237}, "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/1669446710765.76/warc/CC-MAIN-20221130160457-20221130190457-00448.warc.gz"} |
https://www.physicsforums.com/threads/logic-gate-xor-and-xnor.263261/ | # Logic gate XOR and XNOR
1. Oct 10, 2008
### speck
I want to simplfy M'(A'B'C+ABC')+M(AB'C'+A'BC) to as simple a circuit as possible.
I don't know the boolean algebra to simplfy the ABC terms. Help please, Speck
2. Oct 10, 2008
### rootX
Tried K-maps?
From quick Venn inspection of (A'B'C+ABC') and (AB'C'+A'BC), I don't think you can simplify them further using AND, OR, NOT only
3. Oct 10, 2008
### speck
K-map is how I initial got the Eq. , right, it won't simplify with AND, OR, NOT. I want to use XOR with XNOR gates. I would really like it to simplify to something like (AB Oplus C) using XOR, but it does not. Thks, Speck
4. Oct 12, 2008
### speck
Does anyone think that the (A'B'C+ABC') part of the Eq. will reduce to (A Oplus B Oplus C)?
5. Oct 12, 2008
### Phrak
By simple, do you mean the least number of packages? It's trivial with a single PLA, but you'd need a burner...
Last edited: Oct 12, 2008
6. Oct 13, 2008
### rootX
I tried to put it into XOR/XNOR but I really couldn't find any way.
P.S. (I learned this stuff few weeks ago, so all I know is that there should be checkboard pattern)
Now that I said that I realized that there is infact a pattern and it is easier to isolate it when you look at it. You gotta approach it differently.
See K-Map When A = 0 and C = 1
A = 1 C = 0
I get something like
A!C!(B XOR M) + A!C (M XOR B)
So far, I look at K-Map and try to isolate 2 literal K-Maps that look like XOR and "and" it with conditions like A = 1 and C = 0 .. It works so far
Last edited: Oct 13, 2008
7. Nov 15, 2008
### Enthalpy
Another PLA-type cheater's answer: use a multiplexer. Input ABCM as the addresses, hardwire the 16 inputs to 1 or 0 to synthetise the desired logic function. The 4067 is such a 16-to-1 mux-demux and seems to be still relatively common (hey, I just feel younger!). One single package, no programming needed.
For a non-cheater answer, you'll have to wait a bit more. M and B have similar roles, as do A and C, so combining these pairs first could bring something.
Last edited: Nov 15, 2008
8. Nov 15, 2008
### Enthalpy
(A xnor C) nor (B xor M) | {"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": 0.8139030337333679, "perplexity": 3019.4049383594356}, "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/1521257649508.48/warc/CC-MAIN-20180323235620-20180324015620-00135.warc.gz"} |
http://mathhelpforum.com/number-theory/43856-modulo-proof.html | Math Help - Modulo proof
1. Modulo proof
Let n E Z. and supposed that 5 does not divide n. Prove that n^4 is congruent to 1 mod 5.
2. Originally Posted by kel1487
Let n E Z. and supposed that 5 does not divide n. Prove that n^4 is congruent to 1 mod 5.
Nothing fancy here. For example,
$n \equiv 1~\text{ (mod 5)}$
so
$n^4 \equiv (1)^4 \equiv 1~\text{ (mod 5)}$
Similarly for $n \equiv 2~\text{ (mod 5)}$
$n^4 \equiv (2)^4 \equiv 16 \equiv 1~\text{ (mod 5)}$
etc.
-Dan
3. Thanks!! I was thinking too much into it!!
4. If n is not divisible by 5, then one of $n+1$, $n-1$, $n+2$, $n-2$ must be divisible by 5.
Hence the product $(n+1)(n-1)(n+2)(n-2)=(n^2-1)(n^2-4)$ must be divisible by 5.
Note however that $n^2-4\equiv n^2+1\pmod{5}$.
Hence $(n^2-1)(n^2+1)=n^4-1$ is divisible by 5; in other words $n^4\equiv1\pmod{5}$.
In general, Fermat's little theorem states that if p is prime and p does not divide n, then $n^{p-1}\equiv1\pmod{p}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8502430319786072, "perplexity": 279.6842631178617}, "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-2014-35/segments/1409535917463.1/warc/CC-MAIN-20140901014517-00034-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.preprints.org/manuscript/201804.0137/v1 | Preprint Article Version 1 This version is not peer-reviewed
# The ECL Optimization and Experiment of HSPMSM with Improved Method
Version 1 : Received: 9 April 2018 / Approved: 11 April 2018 / Online: 11 April 2018 (05:45:35 CEST)
How to cite: Liu, X. The ECL Optimization and Experiment of HSPMSM with Improved Method. Preprints 2018, 2018040137 (doi: 10.20944/preprints201804.0137.v1). Liu, X. The ECL Optimization and Experiment of HSPMSM with Improved Method. Preprints 2018, 2018040137 (doi: 10.20944/preprints201804.0137.v1).
## Abstract
The eddy current loss should be optimized to be as less as possible for the stability of permanent magnet in high speed permanent magnet synchronous motor (HSPMSM) rotor and ensure the high efficiency and low temperature of the motor. This paper analyzes the eddy current distribution in rotor, with consideration of the conflict of the thickness of sleeve and diameter of the rotor, calculating the eddy current loss (ECL) and the thermal distribution via Separation of variables method for solving Maxwell's equations with analytical hieratical model of ECL constructed. The optimization result of ECL of the HSPMSM whose power and rated speed is 30kw 48000r/min can be got by multi-objective optimization method, combined weighting coefficient method and traversal algorithm based on chaotic local search particle swarm optimization (CLSPSO), utilizing ECL analytical model and other analytical constraints. Related experiment and measurement has been implemented with new approach of loss separation.
## Subject Areas
eddy current loss; multi-objective optimization (MOO); electromagnetic analysis; equivalent hierarchical method | {"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": 0.8050485849380493, "perplexity": 4230.028516000328}, "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-2020-05/segments/1579251705142.94/warc/CC-MAIN-20200127174507-20200127204507-00354.warc.gz"} |
https://www.electricalclassroom.com/conductance-what-is-conductance/ | # Conductance | What is conductance?
Every material in the universe is believed to be made up of atoms. In an atom, electrons are bound to its nucleus by a strong force of attraction by the protons in the nuclei. In some materials few free electrons are available. These electrons can move freely along the material. Such materials with free electrons can conduct electricity.
When a charge (i.e., an excess or deficit of electrons) is applied to one side of such a conducting material, the electrons throughout will realign themselves, spreading out by virtue of their mutual repulsion, and thus conduct the charge to the other side.
Most of the conducting materials are metals. In metals, some electrons are always free for available for conduction. But the conductivity of these metals also depends on the amount of energy the electrons can transfer without colliding on the neighbouring atoms.
## Conductivity
Conductivity is the reciprocal of resistance. When resistance is the opposition to the current flow, conductance is the amount of current that a material can conduct. Therefore, conductance can be defined as the ability of a material to conduct electric current. For example, a material with low resistance is highly conductive and vice Versa. Conductivity is denoted by the letter G.
## Unit of conductance
As conductance is the reciprocal of resistance it is mentioned in “mho” or “ Ω−1 ” or “℧”. Sometimes it is mentioned in “siemens” which is the derived unit of ℧ .
where Ω is the ohm, A is the ampere, and V is the volt.
## Superconductors
Superconductivity is a property of a material to conduct without any resistance. Some material can conduct electricity at zero resistance when they are supercooled. For example, some ceramic metals can turn to superconductors when they are cooled to -319 deg. F. At this stage, the free electrons can move more easily losing their energy by collisions. Scientists are working on superconducting material and are finding ways how they can be used for electric power transmission. | {"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": 0.8845406174659729, "perplexity": 646.9840098363352}, "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-2022-21/segments/1652662578939.73/warc/CC-MAIN-20220525023952-20220525053952-00776.warc.gz"} |
https://chemistry.stackexchange.com/questions/96545/why-dont-i-get-the-same-value-of-percentage-ionic-character-of-a-particular-mol | # Why don't I get the same value of percentage ionic character of a particular molecule from different equations?
About the ionic character of a polar covalent compound Pauling gave two equations as
1. [1-$e^{.25(x_a - x_b)}]$%
1. [18$(x_a-x_b)^{1.4}$]%
Hanary and Smith gave the equation
1. [$16(x_a-x_b)+3.5(x_a-x_b)^2$]%
Where $x_a$ and $x_b$ stands for the electronegativity of $a$ and $b$ atom in bond $a-b$.
Now if I put $x_a-x_b = 2,$ The 1st, 2nd & 3rd equations respectively give the value as -.648%, 47.5% & 46%. What is the reason behind these different values of percentage ionic character of the same molecule? At where am I wrong?
• You are wrong in thinking that percentage of ionic character is a real observable thing, like mass or energy. It isn't. (Neither is electronegativity, BTW.) – Ivan Neretin May 8 '18 at 5:29
• @IvanNeretin then how Pauling gave the equations and how do we have an electronegativity table? – user187604 May 8 '18 at 11:01
• When Pauling gave the equations, he knew their limitations. As for the electronegativity table, we surely have not one, but many such tables, all subtly different. – Ivan Neretin May 8 '18 at 11:16 | {"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": 0.8051592111587524, "perplexity": 1983.6685032377288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986660323.32/warc/CC-MAIN-20191015205352-20191015232852-00176.warc.gz"} |
https://c21.phas.ubc.ca/article/stretching-rubber-bands/ | # Stretching Rubber Bands
We can use common household objects to measure properties that match physical laws. This experiment takes a very common household item, the rubber band, and applies physical laws (Hooke’s Law and the Young’s Modulus) to them in a hands-on way.
Purpose:
To describe the stretching action of rubber bands, and explore the connection between Hooke’s Law and Young’s modulus.
Introduction:
Rubber bands stretch when we pull on them, but pulling as hard as you can on a 2-by-4 will probably have no visible effect. The stretchability of solid materials is expressed as their Young’s Modulus (a.k.a. “Elastic Constant”), $Y$. Here is the formula for Young’s modulus (Eqn.1):
$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\ \Delta L\ }{L_0}} \tag{1}$
• $F$ = Force applied to solid [N]
• $A$ = Cross-sectional area of solid [m$^2$]
• $L$ = stretched length of solid [m]
• $L_0$ = original length of solid [m]
A simple way to understand this formula is $Y = \frac{\text{stress}}{\text{strain}}$. The stress is the amount of force applied to the object, per unit area ($F/A$). The strain is the relative change in the length of the solid ($\Delta L/L_0$). Therefore, a solid with a greater value of $Y$ will stretch less than a solid with a smaller $Y$, when the same force is applied.
Let’s return to rubber bands. Rubber bands are elastic solids and can be described with Hooke’s Law (Eqn.2). We can think of Hooke’s Law as a simplified version of Young’s Modulus, and it is classically applied to spring systems. However, it can also, to some extent, describe the stretch patterns observed for rubber bands.
$F=k \Delta L \tag{2}$
• $F$ = Force applied to elastic material [N]
• $k$ = spring constant [N/m]
• $ΔL$ = change in length of the elastic material [m]
If you compare the two equations, you will find (try this as an exercise) that the spring constant $k$ contains Young’s modulus $Y$ (which describes the material), the length $L_0$, and the cross-sectional area $A$ of the material, can be related as in Eqn.3.
$k=Y\dfrac{A}{L_0} \tag{3}$
This allows us now to make predictions before we do an experiment. For example, a thicker rubber band should have a larger spring constant due to its larger cross-sectional area. In this experiment you can check this prediction and investigate the way in which Hooke’s Law applies to rubber bands. You can also think about what happens if you use two rubber bands at the same time, either to hang an object from both bands in parallel or to create a longer band by knotting one band to the end of the other band. Write down your hypothesis and test it with an experiment.
The Challenge:
Design an experiment to measure the constant $k$ for rubber bands. Use items of known mass to provide the applied force. Measure the change in length and the original length for each rubber band; also record the physical properties of each band.
Key Concepts:
• Young’s modulus is a measure of stress over strain.
• Hooke’s Law takes only applied force and change in length into account.
• Different rubber bands will have different constants for both laws.
Skills:
• Applying Hooke’s Law
• Relating graphs of experimental data to given equations
• Understanding relationship between Hooke’s Law and Young’s modulus
• Simple graphical analysis
• Assigning errors and understanding error calculations
Materials/Equipment:
• Three rubber bands of different sizes and thicknesses
• Objects of given weight (granola bars, packaged foods, etc.)
• Small metal hanger
• Pushpin
• Ruler (30cm) or flexible tape measure
Suggested assigned time: 2 weeks
• Why does Hooke’s law not apply for greater forces?
• Why is Young’s modulus a more general descriptor of rubber band action than Hooke’s law?
Variations:
• Try the experiment with something other than a rubber band.
• Compare rubber band action with spring action. How do the graphs for Hooke’s law compare?
• Combine multiple rubbers bands and analyze stretching action. | {"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": 0.8188735246658325, "perplexity": 950.0951798596244}, "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-2023-06/segments/1674764500154.33/warc/CC-MAIN-20230204205328-20230204235328-00408.warc.gz"} |
http://link.springer.com/article/10.1007%2FBF02480328 | , Volume 32, Issue 1, pp 241-245
# Nonparametric estimation of Matusita's measure of affinity between absolutely continuous distributions
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## Abstract
LetF andG be two distribution functions defined on the same probability space which are absolutely continuous with respect to the Lebesgue measure with probability densitiesf andg, respectively. Matusita [3] defines a measure of the closeness, affinity, betweenF andG as: $\rho = \rho (F,G) = \int {[f(x)g(x)]^{1/2} } dx$ . Based on two independent samples fromF andG we propose to estimate ρ by $\hat \rho = \int {[\hat f(x)\hat g(x)]^{1/2} } dx$ , where $\hat f(x)$ and $\hat g(x)$ are taken to be the kernel estimates off(x) andg(x), respectively, as given by Parzen [5].
In this note sufficient conditions are given such that (i) $E(\hat \rho - \rho )^2 \to 0$ asx→∞ and (ii) $\hat \rho - \rho$ with probability one, asn→∞.
Research supported in part by the National Research Council of Canada and by McMaster University Science and Engineering Research Board.
The author is presently with the Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152. | {"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": 0.9303005337715149, "perplexity": 1037.7758350129377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997888972.38/warc/CC-MAIN-20140722025808-00155-ip-10-33-131-23.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/708373/for-every-rational-number-does-there-exist-a-sequence-of-irrationals-which-conv | # For every rational number, does there exist a sequence of irrationals which converges to it?
I can think of of examples where a sequence of irrationals converges to $0$. But if we pick any rational will there always exist a sequence of irrationals which converges to it?
I cannot find a straight answer to this question.
-
Let $r$ be our rational. Look at $r+\frac{\sqrt{2}}{n}$. This may be the example you had in mind, "shifted" by $r$. – André Nicolas Mar 11 '14 at 18:47
Assume your number is $\frac{p}{q}$. Then the sequence $$a_n=\frac{\pi}{n}+\frac{p}{q}$$ converges to the given number and is irrational (any irrational number in the place of $\pi$ would do).
-
this is assuming $\lim_{n\to\inf}$, right? – Cole Johnson Mar 11 '14 at 23:47
@ColeJohnson Yes, right! – Stef Mar 11 '14 at 23:49
Yes, take a sequence consisting of your sequence of irrationals converging to $0$ plus your desired rational limit.
-
Yes: If $r\in\Bbb Q$, then $\forall n\in\Bbb N$: ${rn\over n+\sqrt2}\in{\Bbb Q}^c$ and $$\lim_{n\to\infty}{rn\over n+\sqrt2}=r.$$
-
For any rational number $x=\frac{p}{q}$ with $\gcd(p,q)=1$, just consider: $$x_n = \frac{p}{q}\cdot\frac{n}{\sqrt{n^2+1}}.$$ Clearly any $x_n$ belong to $\mathbb{R}\setminus\mathbb{Q}$ and we have $\lim_{n\to +\infty} x_n = x$.
-
Yes. Consider
$\frac{p}{q} - \frac{\sqrt{2}}{n}$
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9719931483268738, "perplexity": 388.5646166588615}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644065488.33/warc/CC-MAIN-20150827025425-00217-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://astronomy.stackexchange.com/questions/35142/is-there-a-distinction-between-neos-and-near-earth-asteroids-is-there-a-differe | # Is there a distinction between NEOs and near-Earth asteroids? Is there a difference?
My "real question" is in Space Exploration Meta (neo (near-earth-object) and near-earth-asteroid tags, do we need both?), but I think that astronomers will be able to help understand the situation and terminology.
Question: Is there a distinction between NEOs and near-Earth asteroids? Is there a difference? Or is it a distinction without a difference?
I noticed for example that here in Astronomy SE there is just . | {"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": 0.8825864195823669, "perplexity": 1932.4112455172499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991650.73/warc/CC-MAIN-20210518002309-20210518032309-00423.warc.gz"} |
http://www.tug.org/twg/mfg/mail-html/1993-08/msg00115.html | # Re: technical question
• To: [email protected]
• Subject: Re: technical question
• From: Michael Downes <[email protected]>
• Date: 11 Aug 1993 11:53:33 -0400 (EDT)
> Would it be possible, using the existant macro in plain to produce an
> estensible integral sign ?
>
> on a font and charlist point of view, there is no problem !
> But i'm wondering if the \left\int bit would work.
> how should \int be defined ?
Is it possible, that in a paper where \left\int is used, it will be
desired to have \int always act as a delimiter, and never in the plain
TeX way? If so, changing the definition and syntax of \int might
be the best approach, so that the \left is built-in. For example:
\def\int#1#2{\left\intdelim #1\right.#2}
with usage:
\int{f(x)}{dx}
(I don't recall from previous mail, is the differential placed after
the \right. or before?)
Of course there are complications with subscripts and superscripts
that would have to be dealt with.
As a syntax of this sort could also handle non-delimiter integrals,
the obvious next thought is a question: whether the old integral
syntax should be retired in favor of a new syntax. The old
backward-compatibility viper rears its ugly head. Using a new name
e.g. \integral would help, but at the cost of taking longer to type.
As for backward compatibility in general: Of course it is very | {"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": 0.9161642789840698, "perplexity": 4084.1179447457725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864019.29/warc/CC-MAIN-20180621020632-20180621040632-00020.warc.gz"} |
http://www.maths.lu.se/english/research/seminars/oresundseminar-2018/ | lunduniversity.lu.se
# Öresund seminar 2018
## Thursday 15 November
Hörmander auditorium, Centre for Mathematical Sciences, Sölvegatan 18A
## Registration
Please register here by Wednesday, November 7.
## 13.15–14.05 Jan-Fredrik Olsen, Lund University
Balian-Low type theorems for finite sequences
This talk is based on a joint work with Shahaf Nitzan, where we formulate and prove finite dimensional analogues for the classical Balian-Low theorem as well as for a quantitative version previously obtained by Nitzan and Olsen. In particular, this answers the Finite Balian-Low conjecture'' posed in 2015 by Lammers and Stampe.
## 14.15–15.05 Magnus Goffeng, Chalmers/University of Gothenburg
The magnitude of geometry
Around a decade ago, Leinster introduced the notion of magnitude as a generalization of the Euler characteristic of a finite category. It has since been extended to an invariant of compact metric spaces. Taking these ideas one step further, one often considers the magnitude function: the magnitude of the space rescaled by a variable R>0, which captures several of the space's geometric features. I will recall this invariant and, focusing on the case of Riemannian manifolds with boundaries, describe the structure of the magnitude function. There are surprisingly few computations of magnitude that have been done. It was nevertheless conjectured by Leinster-Willerton that for convex domains, the magnitude function is a polynomial in R where the coefficients are the intrinsic volumes of the convex body (e.g.\ volume, surface volume, total mean curvature, ..., Euler characteristic). We prove an asymptotic version of this conjecture and show that the magnitude function extends meromorphically to the complex plane. For surfaces, we prove that the magnitude function recovers the Euler characteristic.
Based on joint work with Heiko Gimperlein.
## 15.45–16.35 Gerd Grubb, University of Copenhagen
Heat problems for operators of fractional order
When $P$ is a strongly elliptic pseudodifferential operator of order $2a>0$ for noninteger $a$, $P$ is nonlocal, but one can define a realization of the homogeneous Dirichlet problem on an open subset $\Omega$ of $\mathbb R^n$ by a variational construction. This includes the example $(-\Delta)^a$, which has been much studied in recent years because of its interest in finance and probability as well as mathematical physics. When $P$ moreover has even symbol, the regularity properties of solutions are well understood, always involving a power $d^a$, where $d(x)$ is the distance to the boundary (assumed $C^\infty$). In particular, a solution $u$ with data in $C^\infty$ has $u/d^a$ in $C^\infty$.
After recalling these results, we shall discuss the associated heat equation $Pu(x,t) + \partial_t u(x,t) = f(x,t)$, $t>0$. Here regularity of solutions can be obtained in relatively low-order function spaces, but one meets the surprising fact that the smoothness in $x$ at the boundary cannot in general be lifted beyond a certain point, even when $f(x,t)$ is $C^\infty$ up to the boundary. This is contrary to the properties of standard differential operator heat equations.
## 16.45–17.35 John Wheater, University of Oxford
Sums of Random Matrices and the Potts Model on Random Planar Maps
I will start by briefly reviewing the random matrix method for understanding spin systems on quantum geometry represented by random planar maps. Then I will describe some improved techniques and new results for the case of the q-state Potts Model which enable the calculation of an extended set of correlation functions. These reveal some unexpected features.
## CONTACT
Erik Wahlén
Associate Professor
[email protected]
+46 46 222 81 43 | {"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": 0.8925475478172302, "perplexity": 567.9666836449305}, "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-2018-47/segments/1542039743294.62/warc/CC-MAIN-20181117061450-20181117083450-00367.warc.gz"} |
https://qanda.ai/en/search/%5Cleft(%20%202x%20%5E%7B%204%20%20%7D%20%20%2B25x%20%5E%7B%203%20%20%7D%20%20%2B4x%2B10%20%5Cright)%20%20%20%5Cdiv%20%20%20%5Cleft(%20%202x%2B1%20%5Cright)?search_mode=expression | # Calculator search results
Formula
Calculate the value
Use the synthetic division to find the quotient and the remainder
$\left( 2x ^{ 4 } +25x ^{ 3 } +4x+10 \right) \div \left( 2x+1 \right)$
$\dfrac { 2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10 } { 2 x + 1 }$
Arrange the rational expression
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
Calculate the multiplication expression
$\color{#FF6800}{ \dfrac { 2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10 } { 2 x + 1 } }$
Quotient $: x ^ { 3 } + 12 x ^ { 2 } - 6 x + 5 \\$ Remainder $: 5$
Use the synthetic division to find the quotient and the remainder
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
Divide $2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10$ by $2 x + 1$ using the synthetic division
Quotient $: x ^ { 3 } + 12 x ^ { 2 } - 6 x + 5 \\$ Remainder $: 5$
Solution search results | {"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": 0.8020371794700623, "perplexity": 1332.719769148557}, "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-20220529072915-20220529102915-00339.warc.gz"} |
https://morethingsjapanese.com/what-is-nomological-thinking/ | # What is nomological thinking?
## What is nomological thinking?
The nomology of mind is the branch of science and philosophy concerned with the laws or principles governing the thought processes and operation of the mind, especially as defined by custom or culture.
## What is a Nomological net in psychology?
A nomological network (or nomological net) is a representation of the concepts (constructs) of interest in a study, their observable manifestations, and the interrelationships between these.
What is deductive Nomological?
Deductive-Nomological Explanation The deductive-nomological model used to be the standard conception of explanation: one explains a phenomenon by deducing the description of the phenomenon from a law and a description of the particular circumstances in which the phenomenon in question occurs.
### What is nomological network analysis?
A nomological network (or nomological net) is a representation of the concepts (constructs) of interest in a study, their observable manifestations, and the interrelationships between these. The term “nomological” derives from the Greek, meaning “lawful”, or in philosophy of science terms, “law-like”.
### What is a Nonology?
Nonology is one of several nonce words created by analogy with trilogy (along with duology, heptalogy and other [Greek number prefix]+logy constructions).
Is Behaviourism idiographic or nomothetic?
Idiographic vs Nomothetic It is a nomothetic approach as it views all behavior governed by the same laws of conditioning. However, it does account for individual differences and explain them in terms of difference of history of conditioning.
## How do you describe a Nomological network?
A nomological network (or nomological net) is a representation of the concepts (constructs) of interest in a study, their observable manifestations, and the interrelationships between these. Correspondence rules, allowing each construct to be measured empirically.
## Which is the best definition of the word nomological?
Definition of nomological. : relating to or expressing basic physical laws or rules of reasoning. nomological universals.
What’s the difference between a merely universal and a nomological statement?
The difference between a nomological and a merely universal statement is that from the universal all As are Bs one cannot, but from the nomological all As must be Bs one can, infer the counterfactual if this were an A it would (have to) be a B
### What are the principles of the nomological network?
The nomological network is founded on a number of principles that guide the researcher when trying to establish construct validity. They are: Scientifically, to make clear what something is or means, so that laws can be set forth in which that something occurs.
### Why did Cronbach and Meehl create the nomological network?
The nomological network was Cronbach and Meehl’s view of construct validity. That is, in order to provide evidence that your measure has construct validity, Cronbach and Meehl argued that you had to develop a nomological network for your measure. | {"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": 0.8125994801521301, "perplexity": 3432.7729349548717}, "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/1669446710734.75/warc/CC-MAIN-20221130092453-20221130122453-00813.warc.gz"} |
https://socratic.org/questions/can-you-help-me-with-this-20-g-of-glucose-is-dissolved-in-150-g-of-water-calcula | Chemistry
Questions Topics
# Can you help me with this? 20 g of glucose is dissolved in 150 g of water. Calculate the molarity, molality & mole fraction of glucose in solution.
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
16
Jul 8, 2015
Here's how you can go about solving this one.
#### Explanation:
The problem gives you all the information you need in order to solve for the molality and mole fraction of the solution. In order to determine its molarity, you're going to need the solution's volume.
To get the volume, you have to know what the density of the solution is. Determine the percent concentration by mass of the solution first
$\text{%w/w" = m_"solute"/m_"solution} \cdot 100$
In your case, the mass of the solution will be
${m}_{\text{solution" = m_"glucose" + m_"water}}$
${m}_{\text{solution" = 20 + 150 = "170 g}}$
This means that you get
$\text{%w/w" = (20cancel("g"))/(170cancel("g")) * 100 = "11.8%}$
The density of this solution will thus be
http://us.mt.com/us/en/home/supportive_content/application_editorials/D_Glucose_de_e.html
$\rho = \text{1.045 g/mL}$
Use glucose's molar mass to determine how many moles you have
20cancel("g") * "1 mole glucose"/(180.16cancel("g")) = "0.111 moles glucose"
The solution's volume will be
170cancel("g") * "1 mL"/(1.045cancel("g")) = "162.7 mL"
This means that its molarity is - do not forget to convert the volume to liters!
C = n/V = "0.111 moles"/(162.7 * 10^(-3)"L") = color(green)("0.68 M")
A solution's molality is defined as the number of moles of solute divided by the mass of the solvent - in kilograms! This means that you have
b = n/m_"water" = "0.111 moles"/(150 * 10^(-3)"kg") = color(green)("0.74 molal")
To get the mole fraction of sucrose, you need to know how many moles of water you have present. Once again, use water's molar mass
150cancel("g") * "1 mole water"/(18.02cancel("g")) = "8.24 moles water"
The total number of moles the solution contains is
${n}_{\text{total" = n_"glucose" + n_"water}}$
${n}_{\text{total" = 0.111 + 8.24 = "8.351 moles}}$
This means that the mole fraction of sucrose, which is defined as the number of moles of sucrose divided by the total number of moles in the solution, will be
chi_"sucrose" = n_"sucrose"/n_"total" = (0.111cancel("moles"))/(8.351cancel("moles")) = color(green)("0.013")
SIDE NOTE I've left the values rounded to two sig figs, despite the fact that you only gave one sig fig for the mass of glucose.
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##### Impact of this question
19979 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "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": 0.8566948175430298, "perplexity": 3051.0919839376147}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814124.25/warc/CC-MAIN-20180222140814-20180222160814-00490.warc.gz"} |
http://tex.stackexchange.com/questions/72983/alias-for-verbatim-environment?answertab=votes | # Alias for verbatim environment
I'm trying to create an alias for the verbatim environment like this:
\newcommand{\vb}[1]{\begin{verbatim} #1 \end{verbatim}}
So I can use it like this:
\vb{
word.
}
But when using it, I get this error:
! Missing $inserted. <inserted text>$
l.93 \end{verbatim}
Where line 93 is the end of a verbatim environment I used after later down the file after closing the \vb. If I replace all verbatim environments with the \vb syntax, then I get this error:
Runaway argument?
zip([],B) = case ([],B) of ([],_) => [] | (_,[]) => [] | (x::L,y::R\ETC.
! File ended while scanning use of \@xverbatim.
<inserted text>
\par
So it seems like the \vb is not closing the environment correctly? How do I get this to work ? The end goal is to get a \vb command that I can use like I described above, and bonus points if I could indent the stuff in the \vb command by a few mm.
-
As far as I know, there’s no way in replacing the environment with a command. Nonetheless you should take a deep look into the fancyvrbdocumentation. – Speravir Sep 18 '12 at 2:29
If you just want oneline verbatim text, you could use a \Verb variant in Fancyvrb. – Speravir Sep 18 '12 at 2:32
Your statement "So it seems like the \vb is not closing the environment correctly" is absolutely correct. Tokens are scanned in search of \end{verbatim} and is never found. – Werner Sep 18 '12 at 5:26
Werner forgot to provide the following link (I found it in another answer of him) from the UK TeX FAQ: Why doesn’t verbatim work within …?. – Speravir Sep 18 '12 at 22:41
A general rule is that you can't have \begin{verbatim} or the \verb command in the argument to another command, including an argument to \newcommand.
If you really want to use that syntax, you of course can't have braces in the argument and hope that they will be printed as themselves: either they delimit the argument or they must be printed.
If this limitation satisfies you, then
\makeatletter
\newcommand{\vb}{%
\begingroup
\@verbatim
\catcode{=1 \catcode}=2 \catcode =10
\frenchspacing
\@vb}
\def\@vb#1{#1\endtrivlist\endgroup}
\makeatother
will allow you to write
\vb{
word.
}
I don't think this is a great improvement than saying
\begin{verbatim}
word.
\end{verbatim}
If you want a margin indent of the verbatim, look at the option xleftmargin in to the Verbatim environment provided by the package fancyvrb`.
- | {"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": 0.9716785550117493, "perplexity": 2453.629408426012}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776437410.51/warc/CC-MAIN-20140707234037-00098-ip-10-180-212-248.ec2.internal.warc.gz"} |
http://export.arxiv.org/abs/1103.0038 | cs.IT
(what is this?)
# Title: On the Sum-Capacity with Successive Decoding in Interference Channels
Abstract: In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We provide two algorithms (a simple one and a finer one) to translate the optimal schemes in the deterministic channel model to the Gaussian channel model. We also derive two upper bounds on the sum-capacity of the Gaussian Han-Kobayashi schemes, which automatically upper bound the sum-capacity using successive decoding of Gaussian codewords. Numerical evaluations show that, similar to the deterministic channel results, the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Han-Kobayashi schemes and that with single message schemes.
Comments: 32 pages, 21 figures Subjects: Information Theory (cs.IT) Cite as: arXiv:1103.0038 [cs.IT] (or arXiv:1103.0038v2 [cs.IT] for this version)
## Submission history
From: Yue Zhao [view email]
[v1] Mon, 28 Feb 2011 22:04:06 GMT (1827kb)
[v2] Tue, 29 Mar 2011 01:22:20 GMT (1940kb)
Link back to: arXiv, form interface, contact. | {"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": 0.8436934947967529, "perplexity": 1140.445555220054}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986673538.21/warc/CC-MAIN-20191017095726-20191017123226-00293.warc.gz"} |
https://mathoverflow.net/questions/28157/breaking-the-circularity-in-the-definition-of-n | # Breaking the circularity in the definition of N
Some days ago, I posted a question about models of arithmetic and incompleteness. I then made a mixture of too many scattered ideas. Thinking again about such matters, I realize that what really annoyed me was the assertion by Ken Kunen that the circularity in the informal definition of natural number (what one gets starting from 0 by iterating the successor operation a finite number of times) is broken “by formalizing the properties of the order relation on ω” ( page 23 of his “The Foundations of Mathematics”). What does actually “breaking the circularity” mean? Is there a precise model theoretic statement that expresses this meaning? And what about proving that statement? Is that possible?
-
If possible, could you please quote a couple of sentences to give us the context? This is a relatively new book and therefore many readers will not have access to it. Since "breaking the circularity" doesn't sound like a technical mathematical term, some more information is necessary to determine what Kunen means by it. – Timothy Chow Jun 15 '10 at 1:04
– Halfdan Faber Jun 15 '10 at 4:52
Looking at the draft that was linked above, it's more clear what Kunen means. He is just saying that the informal "definition" of the natural numbers that you might think of in school is circular when examined closely. And it is, in the sense that you have to start with some undefined concept, be it "natural number", "finite set", "proof", etc., to capture finiteness.
However, Kunen does not dwell on that sort of philosohical point. He is simply saying that there is a formal and non-circular definition of ω in set theory, as the smallest infinite ordinal. This does give a rigorous definition, but it doesn't ensure that "finite" in an aribitrary model corresponds to our actual notion of finite. That is something that cannot be ensured in first-order logic.
-
As Tim mentioned in his answer to my other post, sometimes model theorists studying nonstandad models of arithmetic refer to N as the standard model, and to Th(N) as "true arithmetic", i. e. the set of sentences in the language of PA true in that model. Then they prove things like that if M is a nonstandard model of PA then M contains an isomorphic copy of N (in fact an initial segment of M). When one thinks informally about the natural numbers one has in mind N, not omega, which as Harald says is but a formal definition not capable of capturing what N really is. Hence the confusion. – Marc Alcobé García Jun 15 '10 at 13:18
In other words, we avoid circularity at the expenses of precisely stating what we'd like to mean. – Marc Alcobé García Jun 15 '10 at 13:24
On notation: one convention in computability theory is to use ω to refer to the standard natural numbers and blackboard bold N to refer to an arbitrary model of (some fragment of) arithmetic. This is related to the use of the term "ω-model". But this convention is not universal; Kaye's book uses blackboard bold N for the standard model, and Kossak/Schmerl use both b.b. N and ω for the standard model. I have never seen a book that uses ω to refer to a nonstandard model, though. – Carl Mummert Jun 15 '10 at 13:31
@Carl, my impression was that $\omega$ is used when the emphasis is on the set or at most an ordered set and $\mathbb{N}$ is used when one wants to put emphasis on the structure of natural numbers usually including at least addition and multiplication and $N$ is used for possibly nonstandard objects in models satisfying those properties of $\mathbb{N}$ that are expressible in the language. – Kaveh Jul 15 '13 at 9:37
@Kaveh: in most of the reverse mathematics literature, $\mathbb{N}$ is used for an arbitrary, possibly nonstandard model and $\omega$ is used for the standard model. But although this is common in that field, it is not universal. – Carl Mummert Jul 15 '13 at 11:53
I don't have that book, but as far as I can understand, the “circularity” must mean this: in the phrase “iterating the successor operation a finite number of times”, we should mean a number of times corresponding to a natural number. But since the natural numbers are what we are defining, this is circular. So one has to define the natural numbers without reference to the concept of “finite”. Where the circularity is broken is if you rewrite your definition as follows:
1. 0 is a natural number,
2. the successor of any natural number is a natural number, and
3. nothing is a natural number unless it must be, by 1 and 2.
(All this stated in more technical language, of course.)
There is no reference to the notion of “finite” here. Instead, number 3 above gives us, by definition, the principle of induction. For example, how do you show that some object X is not a natural number? Well, if for some property P, you can show P(0) and you can also show that ∀n: P(n)⇒P(n') where the prime denotes the successor function, but X fails property P, then you can know for sure that X is not a natural number.
Edit: I see I did not answer all your questions. I am not a logician, so take this with a grain of salt. But basically, in first order logic (in which ZFC is expressed) it is impossible to make circular definitions, and if you can't make one, you can't repair it. The circularity, as I see it, all exists on the meta-level, before you have even gotten around to formalizing the theory. So “breaking the circularity” must in essence happen in the transition between the informal and the formal.
Strictly speaking, first order theories don't even allow definitions at all! What you have to do is to notice that there is a complicated formula NN(x) that we interpret as “x is the set of natural numbers”, and a theorem ∃!x NN(x) in ZFC (where ∃! is short for “there exists a unique …”); then we create a new theory by adding the symbol ω and adding the axiom NN(ω). Now, any formula A(ω) in the new theory can be rewritten in the old theory as ∃x:NN(x)∧A(x), so nothing new has really happened, except for a great amount of simplification.
-
Yes, that is the circularity. But the inductive definition doesn't really help, in first-order logic: there are still nonstandard models that satisfy all the same first-order induction axioms as the standard model. These nonstandard models think that all their nonstandard numbers "must be" obtained by rule 3. Maybe what Kunen means is that, once we have axiomatized enough of the true properties of the natural numbers, we can use those axioms to prove interesting theorems, and we don't have to worry too much about nonstandard models at that point. But I also don't have the book. – Carl Mummert Jun 14 '10 at 22:48
@Harald: I would guess that "circularity" refers to the fact that the following three concepts are all mutually dependent: "natural number", "string of symbols", "proof". All three of these rely on the same notion of "finiteness", so in the end if you are doubtful about whether "finite" is well defined you cannot use any of the three concepts to clarify the other two. But this assumes that you are doubtful about what "finite" means. If we simply accept "finite" as an undefined term, and axiomatize the properties that "finite" things have, this starts to sound more like Kunen's proposal. – Carl Mummert Jun 14 '10 at 22:53
@Carl: Yes, the existence of nonstandard models are indeed a fact of life and there is no way out of that. I think you're right on in your first comment. Re your second comment, now you are talking about the meta level and the formalization of things like well-formed formulas and proof, right? Lacking Kunen's book I cannot be sure, but I did not get the impression that this sort of question is at issue here. – Harald Hanche-Olsen Jun 14 '10 at 23:04
## protected by François G. Dorais♦Jul 15 '13 at 15:12
Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.
Would you like to answer one of these unanswered questions instead? | {"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": 0.8638436198234558, "perplexity": 354.11371560572337}, "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-2015-35/segments/1440645390745.87/warc/CC-MAIN-20150827031630-00301-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://mathzsolution.com/surprise-exam-paradox/ | I just remembered about a problem/paradox I read years ago in the fun section of the newspaper, which has had me wondering often times. The problem is as follows:
A maths teacher says to the class that during the year he’ll give a surprise exam, so the students need be prepared the entire year. One student starts thinking though:
1. The teacher can’t wait until the last day of school, because then the exam won’t be unexpected. So it can’t be the last day.
2. Since we’ve removed the last day from the list of possible days, the same logic applies to the day before the last day.
3. By applying 1) and 2) we remove all the days from the list of possible days.
4. So, it turns out that the teacher can’t give a surprise exam at all.
Following this logic, our student doesn’t prepare for this test and is promptly flunked when the teacher does give it somewhere during the middle of the year (but that’s my own creative addition to the problem).
This problem reminds me about the prisoner’s dilemma for finite number of turns – you have to betray at the last turn because tit-for-tat retaliation is no longer relevant (no next turn), but then that means that you have to betray at the turn before that, and so on, until you reach the conclusion that you can’t cooperate at all.
So is the student’s reasoning correct or not? Mathematically it looks like it should be, but that would imply that surprise exams are not possible (and they are).
There is a model of knowledge, essentially due to Robert Aumann, in which knowledge is represented by a partition $$Π\Pi$$ of a set of states of the world $$Ω\Omega$$. If the true state of the world is $$ω\omega$$, the agent with partition $$Π\Pi$$ only knows that some state in the cell $$π(ω)\pi(\omega)$$ (the value of the projection at $$ω\omega$$) obtained. An event is simply a subset of $$Ω\Omega$$. We say that an agent knows that the event $$EE$$ obtains at $$ω\omega$$ if $$π(ω)⊆E\pi(\omega)\subseteq E$$. Now let the state space be $$Ω={1,2,…,T}\Omega=\{1,2,\ldots,T\}$$, where we interpret $$tt$$ as “there is an exam at $$tt$$“. Now there is no partition $$Π\Pi$$ such that the following holds:
2. If there was no exam at $${1,…,t−1}\{1,\ldots,t-1\}$$, then the student knows this at $$tt$$.
Proof: Let $$tt$$ be an element in $$Ω\Omega$$ such that $$π(t)\pi(t)$$ is not a singleton. Such an element must exist by 1. Let $$t′t'$$ be the largest element in $$π(t)\pi(t)$$. By assumption $$t′>tt'>t$$ and so by 2., $${1,…,t′−1}\{1,\ldots,t'-1\}$$ is a union of cells in $$Π\Pi$$ that contains $$tt$$. Since $$Π\Pi$$ is a partition, $$π(t)⊆{1,…,t′−1}\pi(t)\subseteq\{1,\ldots,t'-1\}$$, contradicting $$t′∈π(t)t'\in\pi(t)$$. | {"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": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8072791695594788, "perplexity": 139.4945653262435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494986.94/warc/CC-MAIN-20230127132641-20230127162641-00221.warc.gz"} |
https://geekyisawesome.blogspot.com/2015/07/probabilities-are-average-proportions.html | ## Wednesday, July 8, 2015
### Probabilities are average proportions (expected value)
Intuitively, if a coin flip has a probability of 1/2 of turning out heads, and we flipped the coin 100 times, we expect that 1/2 of those 100 flips will be heads. What is meant by "expect" is that if we do this 100 coin flip experiment for many times, count the number of times it turns out heads for each 100 flip trial, and take the average of these counts, the average will be close to 1/2 of 100. Furthermore, the more 100 flip trials we include in our average, the closer the average will be 1/2 of 100.
If this were the case, then a probability can be treated as an average proportion, because if a probability of something happening is, say, 1/100, then after 1000 attempts we should find that, on average, 1/100 of those 1000 attempts would be the thing happening. In general, if the probability of an outcome is "p", and "n" attempts are made, then we should have "pn" positive outcomes. That probability is acting as a proportion of the average number of attempts made which will result in a positive outcome out of the attempts made. In fact, semantically speaking, the phrase "This outcome occurs with probability 1/100" and the phrase "This outcome occurs once every 100 times" are identical.
A simple proof of this is in the way we estimate the probability of an outcome. We attempt to produce the outcome (such as a coin flip resulting in heads) for a number of times "n", count the number of times "x" the outcome is positive (heads), and then just find x/n. But in order for this probability to be reliable, the quotient must remain constant for different values of "n" (the value "x" will change according to "n" to keep x/n equal). Given this statement, if we know a reliable probability x/n, and have performed the experiment "m" times, then the number of positive outcomes "y" can be predicted as follows:
For x/n to be reliable, x/n = y/m
Therefore, y = m(y/m) = m(x/n)
That is, since x/n is known and "m" is known, "y" can be found using those two values only.
Of course this is not a rigorous proof. To get a rigorous proof we need to turn to a field of probability called expected value. The expected value of a random variable (such as a coin flip) is the average of the values (assumed to be numerical) of the outcomes after a large number of trials. It is defined as the sum of each outcome multiplied by its probability. For example, the expected value of the value on a die is
1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6
because for each outcome from 1 to 6, the probability is 1/6.
In general, if the probability of outcome "o_i" is "p_i", then the expected outcome is
sum(o_i*p_i for all i)
But this isn't useful for proving the statement in the title. The proof is in this Math Exchange answer which explains that the expected number of positive outcomes out of "n" attempts, given that the probability of each outcome each time is "p", is "pn". It goes like this:
Let the random variable "U_i" be the outcome of the "i"th attempt (heads or tails). If the outcome is positive (heads), "U_i" is 1, otherwise it is 0. Given "n" attempts, the number of positive outcomes is
U_1 + U_2 + U_3 + ... + U_n
Call this actual number of positive outcomes "X", that is
X = U_1 + U_2 + U_3 + ... + U_n
The expected value of "X", written as E(X) is
E(X) = E(U_1 + U_2 + U_3 + ... + U_n)
Since the expected value is a linear operator,
E(X) = E(U_1) + E(U_2) + E(U_3) + ... + E(U_n)
Now, given the above definition of what an expected value is,
E(U_i) = 1*(probability of U_i = 1) + 0*(probability of U_i = 0)
If the probability of "U_i" being 1 is "p_i", then
E(U_i) = p_i
But for all "i", the probability of "U_i" is the same. That is
E(U_i) = p
So that means that
E(X) = p + p + p + ... + p
E(X) = pn
And there we have it, the expected number of positive outcomes out of "n" attempts, each of which has a probability of "p", is "pn", which means that the probability "p" can be treated exactly as if it was the proportion of positive outcomes out of a number of trials. | {"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": 0.9637914299964905, "perplexity": 538.6036363356237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251669967.70/warc/CC-MAIN-20200125041318-20200125070318-00268.warc.gz"} |
https://alice-publications.web.cern.ch/node/3881 | # Two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
The first measurement of two-pion Bose--Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC. | {"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": 0.9957699179649353, "perplexity": 2155.761280483599}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337631.84/warc/CC-MAIN-20221005140739-20221005170739-00301.warc.gz"} |
https://www.computer.org/csdl/trans/td/2012/11/ttd2012112024-abs.html | The Community for Technology Leaders
Issue No. 11 - Nov. (2012 vol. 23)
ISSN: 1045-9219
pp: 2024-2032
Gregory D. Peterson , University of Tennessee, Knoxville
Junqing Sun , Marvell Semiconductor, Santa Clara
ABSTRACT
In performance modeling of parallel synchronous iterative applications, the longest individual execution time among parallel processors determines the iteration time and often must be estimated for performance analysis. This involves the mean maximum calculation which has been a challenge in computer modeling for a long time. For large systems, numerical methods are not suitable because of heavy computation requirements and inaccuracy caused by rounding. On the other hand, previous approximation methods face challenges of accuracy and generality, especially for heterogeneous computing environments. This paper presents an interesting property of extreme values to enable Effective Mean Maximum Approximation (EMMA). Compared to previous mean maximum execution time approximation methods, this method is more accurate and general to different computational environments.
INDEX TERMS
Program processors, Random variables, Approximation methods, Computational modeling, Mathematical model, Distribution functions, Shape, heterogeneous computing, Performance modeling, extreme value, mean maximum, execution time
CITATION
Gregory D. Peterson, Junqing Sun, "An Effective Execution Time Approximation Method for Parallel Computing", IEEE Transactions on Parallel & Distributed Systems, vol. 23, no. , pp. 2024-2032, Nov. 2012, doi:10.1109/TPDS.2012.21
FULL ARTICLE
CITATIONS
SHARE
153 ms
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https://manualzz.com/doc/48852668/citrix%C2%AE-xenconvert%E2%84%A2-guide | # Citrix® XenConvert™ Guide
```Citrix® XenConvert™ Guide
XenConvert 1.1
Revision 6
December 15, 2008
Use of the product documented in this guide is subject to your prior acceptance of the End User License Agreement.
Information in this document is subject to change without notice. Companies, names, and data used in examples herein are
fictitious unless otherwise noted. No part of this document may be reproduced or transmitted in any form or by any means,
electronic or mechanical, for any purpose, without the express written permission of Citrix Systems, Inc.
Xen and Citrix are registered trademarks, and Citrix Provisioning Server, XenConvert and XenServer are trademarks of Citrix
Systems, Inc. in the United States and other countries.
Microsoft, Windows, Windows Server are either registered trademarks or trademarks of Microsoft Corporation in the United
States and/or other countries.
All other trademarks and registered trademarks are the property of their respective owners.
Document Code: December 15, 2008 (MS)
C ONTENTS
Contents
Chapter 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Intended Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Related Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Contact Us. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Chapter 2
What’s New in This Release. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Converting from Microsoft Virtual Server 2005 . . . . . . . . . . . . . . . . . . . . . . . . .5
Additional Physical Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Upgrading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Consolidation of XenConvert Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Known Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Converting a VHD Containing a Windows OS That is Newer Than the Host OS
6
Windows Boot and System Drives Must be on the Same Volume . . . . . . . . . . .6
Source Disk Limited to Basic Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Running From a Terminal Services Session. . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Known Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Converting a Workload with Files in Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Mapped Network Drive Can Interfere with Conversion. . . . . . . . . . . . . . . . .7
Autorun Can Interfere with Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Safe to Remove Messages During Physical to XVA Conversion . . . . . . . . . . . .8
XenConvert Fails When Automount is Disabled . . . . . . . . . . . . . . . . . . . . . . . . .8
Problem Ejecting Citrix Virtual Hard Disk Messages . . . . . . . . . . . . . . . . . . . . .8
Service or Device Specific to the Source Machine May Fail to Start in a Virtual
Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
VHD Appears to be Mounted After Cancelling XenConvert . . . . . . . . . . . . . . .9
Exception Message Appears on First Boot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Virtual Display Adapter Driver is Not Installed Automatically. . . . . . . . . . . . .10
Unknown Device on Windows 2000 SP4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2
Citrix XenConvert Guide
Chapter 3
Installing XenConvert
Obtaining the Installation File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
XenConvert System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
Installing XenConvert Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Upgrading XenConvert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Remove XenConvert Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Chapter 4
Using XenConvert
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Converting From Physical Machines to Virtual Machines . . . . . . . . . . . . . . . .15
Converting From Microsoft Virtual Server . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Starting the XenConvert Wizard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Conversion Summary Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Controlling XenConvert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Converting from a Physical Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Before Converting From a Physical Machine. . . . . . . . . . . . . . . . . . . . . . . . . . .18
Enable Automount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Stop Security Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Working with Provisioning Server . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Physical to VHD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Physical to XVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Physical to XenServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
Converting from Microsoft Virtual Server. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Before Converting From Microsoft Virtual Server . . . . . . . . . . . . . . . . . . . . . .21
After Converting From Microsoft Virtual Server. . . . . . . . . . . . . . . . . . . . . . . .21
VMC to XVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
VMC to XenServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
VHD to XVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
VHD to XenServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
XenServer Account Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
C HAPTER 1
This document provides instructions on installing and using Citrix XenConvert
software. This document is organized as follows:
•
“About XenConvert” provides information such as new features and known
issues.
•
“Installing XenConvert” describes how to install the XenConvert software.
•
“Using XenConvert” describes how to use XenConvert.
Introduction
Citrix® XenConvert™ converts a server or desktop workload from either a
physical machine or from another type of virtual machine, to a XenServer virtual
machine.
•
Converting to a XenServer VM produces an intermediate XVA containing a
bootable XenServer VM and automatically imports it into a XenServer.
•
Converting to an XVA produces an offline package of a bootable
XenServer VM ready to manually import into a XenServer.
•
Converting to a VHD produces a VHD compatible with Provisioning
Server 5.0 if the target device software included with Provisioning Server
5.0 was installed beforehand.
XenConvert includes a wizard, to use interactively, and a command line interface,
to use from a script.
Intended Audience
This document is intended for XenServer system administrators and software
installers. It is assumed that readers are familiar with basic installation and system
management tasks for Microsoft Windows systems.
4
Citrix XenConvert Guide
Related Information
Information on XenConvert is provided with the software in the form of an online
help file, which is available from the product, and as a PDF document.
may also be required during installation and use of this product. This information
can be found at the following locations:
•
XenServer: http://support.citrix.com/product/xens/
•
Provisioning Server: http://support.citrix.com/product/provsvr/
Your feedback on Citrix XenConvert documentation is important to us. Use the
http://support.citrix.com/docfeedback/
C HAPTER 2
This chapter contains information relevant to this release of XenConvert
software. This information includes:
•
“What’s New in This Release”
•
“Known Limitations”
What’s New in This Release
This section describes enhancements and other changes made to XenConvert in
this release.
Converting from Microsoft Virtual Server 2005
Convert a single VHD or an entire virtual machine to a XVA or XenServer:
•
“VHD to XVA”
Convert a single Virtual Hard Disk (VHD) to a XVA.
•
“VHD to XenServer”
Convert from a single VHD to a XenServer.
•
“VMC to XVA”
Convert an entire virtual machine to a XVA.
•
“VMC to XenServer”
Convert an entire virtual machine to a XenServer.
A source VHD can be of the fixed or dynamic type.
Physical conversion enhancements include converting a physical source machine
without any ATA devices (pure SCSI machine, such as a blade system).
6
Citrix XenConvert Guide
Run the XenConvert installer to upgrade XenConvert. It is no longer necessary to
remove the previous version.
Consolidation of XenConvert Documentation
The Release Notes, Installation Guide, and Help documents were consolidated
into a single document to create this guide. This consolidation increases usability
by making it easier to locate and search for XenConvert information.
Known Limitations
This section describes known limitations for the XenConvert software. Wherever
possible, a workaround for the problem is included.
Converting a VHD Containing a Windows OS That
is Newer Than the Host OS
If the Windows OS version of a VHD is newer than the host’s OS, XenConvert
cannot convert the VHD. For example, if the VHD contains Windows XP and the
host contains Windows 2000.
Issue # 7875
Windows Boot and System Drives Must be on the
Same Volume
XenConvert can only convert a workload from a source machine on which the
system drive is the same as the boot drive. For example, boot.ini and the
\Windows must both reside on C:.
Source Disk Limited to Basic Disk
The source disk is limited to a physical disk initialized as a basic disk. Converting
a physical disk initialized as a dynamic disk type is not yet supported.
Running From a Terminal Services Session
XenConvert cannot run from a Terminal Services session when the Terminal
Server is a Window 2000 operating system. Mounting a VHD either fails after
several minutes or does not appear to complete. This issue does not occur with
VNC.
To workaround this issue, run XenConvert from the Console.
Chapter 2
7
To change the amount of time that XenConvert waits to mount the VHD, change
the registry key value VhdPluginTimeoutAsMs described in “Controlling
XenConvert” section.
Known Problems
This section describes known problems for the XenConvert software. Wherever
possible, a workaround for the problem is included.
Converting a Workload with Files in Use
XenConvert cannot copy a file in use by another application or service. To ensure
that the file is included in the conversion, stop the respective service before
starting the conversion.
It is not recommended to convert a workload executing a critical service that
keeps critical files open that cannot be stopped (such as a Domain Controller with
Active Directory service).
Mapped Network Drive Can Interfere with
Conversion
If a network drive was mapped to the next available drive letter (e.g. F: when last
local drive was E), then XenConvert is unable to get the drive letter for the new
VHD that it just created, mounted, and formatted because Windows assigned it to
the same drive letter as the network drive. See http://support.microsoft.com/kb/
297694/ for a description of the same problem affecting other removable disks.
Although that KB pertains to Windows XP, the problem also affects Windows
Server 2003 when automount is enabled.
The workaround is to remap the network drive to a drive letter other than the
lowest available one before running XenConvert.
Autorun Can Interfere with Conversion
If enabled, Autorun can interfere when converting from a VHD. After a VHD
containing at least one file system is mounted, Autorun scans the file system and
leaves a dialog box open, causing the conversion to stall because the VHD cannot
be automatically dismounted.
To work around this issue, disable Autorun for fixed drives by setting the
following DWORD to 0x8:
HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Policie
s\Explorer \NoDriveTypeAutoRun
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Citrix XenConvert Guide
For details, refer to http://www.microsoft.com/technet/
prodtechnol/windows2000serv/reskit/regentry/
91525.mspx?mfr=true.
Issue # 7911
Safe to Remove Messages During Physical to XVA
Conversion
You may see a “safe to remove” balloon message on Windows XP and dialog box
on Windows 2000 after the file copy stage. The message occurs when the VHD
that was created is dismounted before creation of the XVA file. This is a normal
message and can be ignored.
Issue # 7307
XenConvert Fails When Automount is Disabled
The following message appears in the log file when XenConvert is run with
automount disabled:
Windows Automount may be disabled
Windows Server 2003 Enterprise and Datacenter editions disable automount by
default. This prevents programmatically formatting a volume without assigning a
drive letter or mount point.
You can work around this issue by enabling automount before running
XenConvert. Use the Windows diskpart program to enable automount:
C:\> DiskPart
DISKPART> automount enable
DISKPART> exit
Automount can be disabled after XenConvert completes. Note that automount
will be enabled in the VM you create and can be disabled from within the VM.
Issue # 7282
Problem Ejecting Citrix Virtual Hard Disk
Messages
The following messages may appear with a Problem Ejecting Citrix Virtual Hard
Disk during the VHD to XVA stage of a conversion.
•
The device 'Generic volume' cannot be stopped right now. Try stopping the
device again later.'
•
The device 'Citrix Virtual Hard Disk' cannot be stopped because of an
unknown error. Since the device is still being used, do not remove it.
Chapter 2
9
These messages may display if applications or services (for example, a virus scan
or the Windows Autorun feature) open a file on the mounted VHD. The open file
prevents a dismount, causing the messages to appear. Increasing the amount of
time that XenConvert waits to automatically dismount a VHD dismount time out
may resolve the issue. Refer to “Controlling XenConvert” for details on how to
change this value. Disabling Autorun may also resolve the issue.
Issue # 7308
Service or Device Specific to the Source Machine
May Fail to Start in a Virtual Machine
Messages similar to the following may be displayed when booting a virtual
machine:
"The Parallel port driver service failed to start due to the
following error: The service cannot be started, either because it is
disabled or because it has not enabled devices associated with it.”
This problem occurs when a service or a device on the physical machine fails to
start on the virtual machine. The failure may be caused by the fact that the
particular device or service is not available or supported on the machine that is
running the virtual machine.
Issue # 7337
VHD Appears to be Mounted After Cancelling
XenConvert
If you cancel a conversion while the VHD is being mounted, the VHD does not
appear to get unmounted after the cancel.
The VHD isn't actually mounted. Windows Explorer displays a stale view of the
drives, showing a red question mark over the device that was the VHD.
You can update the view by choosing “Refresh” from the “View” menu in
Windows Explorer.
Issue # 7394
Exception Message Appears on First Boot
After converting from a physical machine to a XenServer, the following message
may appear once after the virtual machine boots for the first time.
"An exception occurred while trying to run "newdev.dll,ClientSideInstall
\\.\pip\PNP_Device_Install_Pipe_0..."
You can ignore this message.
Issue # 7389
10
Citrix XenConvert Guide
Virtual Display Adapter Driver is Not Installed
Automatically
After converting a physical machine equipped with the Intel 82945G chipset or
Intel Q33 Express chipset, the virtual display adapter device may appear as an
unknown device in Device Manager in Windows Server 2003 R2 Standard
Edition.
A standard VGA mode driver is installed.
Issue # 7340
Unknown Device on Windows 2000 SP4
After a conversion to XVA on Windows 2000 SP4 systems, an unknown device
may be present. This device has no negative impact on the operation of the VM.
Issue # 7280
C HAPTER 1
Installing XenConvert
Obtaining the Installation File
Citrix XenConvert software is distributed electronically. Consult with your sales
representative for information on obtaining the software.
The product distribution contains this guide and the product installation wizard:
•
XenConvert_Install.exe
•
XenConvert_Install_x64.exe
XenConvert System Requirements
The system requirements for systems running the XenConvert software are listed
in the following table.
Requirements
XenConvert supports Microsoft Windows 64-bit:
the following
Windows Server 2003 Standard, Enterprise SP2
Operating Systems
Microsoft Windows 32-bit:
Windows Server 2003, Standard, Enterprise SP1/SP2/R2
Windows Small Business Server 2003 R2 SP2
Windows XP SP2/SP3
Windows 2000 SP4
CPU
Same as the requirements specified for the installed
operating system.
Memory
Same as the requirements specified for the installed
operating system.
12
XenConvert Installation Guide
Requirements
Disk space
requirements
When converting to VHD, the required amount of free space
is 101% of the used space on the source physical disk.
When converting to XVA or XenServer, the required amount
of free space is typically 115% of the used space on the
source disks. Note that these conversions involve
compression that depends on the disk contents. Therefore,
the required free space could be greater. The absolute worst
case would be 200% of the used space on the source
physical disk.
XenServer
XenServer Versions 4.0, 4.1, and 5.0 support import of VMs
created with XenConvert.
requirements
Microsoft .NET Framework version 2.0, which installs
automatically if necessary.
Installing XenConvert Programs
1.
On the target system, close all Windows applications.
2.
In My Computer or Windows Explorer, navigate to the directory where the
installer file: XenConvert_install.exe
3.
The XenConvert Welcome screen is displayed. Click Next to begin the
installation.
4.
The License Agreement screen appears. Click I accept..... and Next to
continue the installation. Click I do not accept to terminate the installation.
Click Print to print a copy of the License Agreement.
5.
The Destination Folder screen appears. Click Next to install XenConvert in
the default directory. Click Change to select a directory other than the
default. Click Next after the directory is selected.
6.
The Ready to Install the Program screen appears. Click Install to begin the
installation. The Installing XenConvert screen displays, showing the
installation progress.
7.
When the installation is complete, the InstallShield Wizard Complete
screen appears. Click Finish to exit the installer.
For details on using the XenConvert Wizard, refer to the chapter titled “Using
XenConvert”.
Chapter 1
Installing XenConvert
13
installer.
Remove XenConvert Programs
Use the Windows Control Panel to remove XenConvert programs.
1.
To remove XenConvert programs, access Control Panel > Add or
Remove Programs and select XenConvert.
2.
Click Remove to begin removing XenConvert programs.
3.
The ‘Are you sure you want to remove XenConvert from your computer?’
dialog box appears. Click Yes to uninstall the software from your system,
then wait for the uninstall to finish.
14
XenConvert Installation Guide
C HAPTER 2
Using XenConvert
This chapter provides the information necessary to use the XenConvert wizard
and command line interface.
Introduction
Citrix XenConvert converts a server or desktop workload from either a physical
machine, or from another type of virtual machine, to a XenServer virtual
machine.
Converting From Physical Machines to Virtual
Machines
XenConvert supports the following physical-to-virtual conversions:
•
“Physical to VHD”
•
“Physical to XVA”
•
“Physical to XenServer”
Converting From Microsoft Virtual Server
XenConvert supports the following virtual-to-virtual machine conversions:
•
“VMC to XVA”
•
“VMC to XenServer”
•
“VHD to XVA”
•
“VHD to XenServer”
Starting the XenConvert Wizard
Supported conversion methods are selected and performed using the XenConvert
Wizard.
16
Citrix XenConvert Guide
To start the wizard, click XenConvert.exe in directory that was selected
during the installation process. The default location is:
C:\Program Files\Citrix\XenConvert
The Citrix XenConvert Welcome screen appears. The information that the wizard
displays next will depend on the conversion method selected on this screen. Refer
to the appropriate conversion method for conversion specific details.
Conversion Summary Screen
After a conversion method is selected and the conversion information is entered
using the wizard, the conversion summary screen appears. This screen
summarizes and provides the conversion information and options that follow.
Conversion summary information includes:
Conversion method
The selected conversion method displays at the top of the screen.
The name given to this workload.
Source
The source directory where this unconverted workload currently resides.
Destination Folder
The destination folder where this converted workload will reside.
Status
The current step, user instructions, and status messages that are associated
with this conversion process.
Progress
The progress for this step of the conversion.
After reviewing conversion information on this screen, select one of the
following conversion options:
Back
Use the Back button to return to the previous window to make changes, or
to enter new parameters.
Convert
Click Convert to begin the conversion process.
Cancel
Chapter 2
Using XenConvert
17
Click Cancel to cancel a conversion that is in process. When you cancel a
conversion, a message displays in the status field and is written to the log
file. Files that were created during the conversion remain on the source
system.
Finish
Click Finish to exit XenConvert. This button displays after the conversion
completes or after cancelling the conversion process.
Log
Click Log to display the conversion log file in Notepad. For each
conversion run, detailed status information is stored in the log file. The log
file, XenConvert.txt, is created in the installation directory and
provides the following information:
•
Start and stop time stamps
•
Error and informational messages,
The Log button appears after you click the Convert button.
Controlling XenConvert
XenConvert reads the following parameters from the registry to manage some
functionality. These parameters may be changed to correct problems encountered
with VHDs and are located in:
HKEY_LOCAL_MACHINE\SOFTWARE\Citrix\XenConvert\Paramete
rs\.
Name
Type
Description
AutoDismountTimeoutAsMs DWORD
Number of milliseconds to wait before retrying to
automatically dismount a VHD. Default is 60
seconds.
VhdPluginTimeoutAsMs
Number of milliseconds to wait for a VHD to mount.
Default is 10 minutes.
DWORD
18
Citrix XenConvert Guide
Converting from a Physical Machine
This section describes the following physical-to-virtual conversion methods
supported by XenConvert:
•
“Physical to VHD”
•
“Physical to XVA”
•
“Physical to XenServer”
Before Converting From a Physical Machine
•
“Enable Automount”
•
“Stop Security Services”
•
“Working with Provisioning Server”
Enable Automount
On Windows Server 2003, enable the Windows Automount feature.
•
Enter the following command at a command shell prompt:
DISKPART
•
Enter the following command at the DISKPART prompt:
•
automount enable
Automount will be enabled in the VM you create and can be disabled from within
the VM.
Stop Security Services
Some security services such as anti-virus and end-point protection services can
interfere with a conversion. Stop these types of security services before
converting.
Working with Provisioning Server
XenConvert produces a virtualized instance of a workload usable with
XenServer. To produce a virtualized instance of a workload that is also usable
with Citrix Provisioning Server, install Provisioning Server Target Device
software on the physical source machine before using XenConvert. After a
conversion completes, use the Provisioning Server Console to add the new VHD
and configure a compatible target device to boot from it. Refer to the
Provisioning Server product documentation set for details.
Chapter 2
Using XenConvert
19
Physical to VHD
Select this method to convert a single partition of a physical disk to a partition
within a VHD.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
Name to use.
Source
Choose the physical disk to convert from the drop-down menu.
Destination Folder
Type or browse to the folder to contain the VHD related files. These files
are excluded from the conversion. The folder is created if it does not
After providing conversion information, select from the following options:
Empty Recycle Bin
Check this box to automatically empty the recycle bin before the
conversion process begins. The option is enabled by default. Emptying the
recycle bin reduces the disk space required by the conversion.
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
Physical to XVA
Select this method to convert a single partition of a physical disk to a XVA.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
Name to use for the Xen virtual machine.
Source
Select the disk to convert from the drop-down menu.
Destination Folder
20
Citrix XenConvert Guide
Type or browse to the folder to contain the XVA related files. These files
are excluded from the conversion. The folder is created if it does not
After providing conversion information, select from the following options:
Empty Recycle Bin
Check this box to automatically empty the recycle bin before the
conversion process begins. The option is enabled by default. Emptying the
recycle bin reduces the disk space required by the conversion.
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
Physical to XenServer
Select this method to convert a single partition of a physical disk to XenServer.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
Name to use for the Xen virtual machine.
Source
Choose the physical disk to convert from the drop-down menu.
Destination Folder
Specify or browse to the folder to contain the intermediate files. These files
are excluded from the conversion. The folder is created if it does not
After providing conversion information, select from the following options:
Empty Recycle Bin
Check this box to automatically empty the recycle bin before the
conversion process begins. The option is enabled by default. Emptying the
recycle bin reduces the disk space required by the conversion.
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
Chapter 2
Using XenConvert
21
Converting from Microsoft Virtual Server
This section describes the methods available when converting from Microsoft
Virtual Server.
•
“VMC to XVA”
•
“VMC to XenServer”
•
“VHD to XVA”
•
“VHD to XenServer”
Before Converting From Microsoft Virtual Server
•
Disable Autorun
Consider disabling the Windows Autorun feature because it can interfere
with a conversion. One method of disabling this feature is to set the value of
the following registry value to 0x8 for fixed drives including VHD, or
0xFF for all drives.
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curr
entVersion\policies\Explorer\NoDriveTypeAutoRun
•
Shutdown VM
After Converting From Microsoft Virtual Server
1.
Boot the new XenServer VM.
2.
3.
Use Add/Remove Programs feature of Windows to remove the program
VMC to XVA
Select this method to convert a Microsoft Virtual Server 2005 VM to a XVA.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VMC
Type or browse to the path of the VMC file.
Destination Folder
22
Citrix XenConvert Guide
Type or browse to the folder to contain the XVA. The folder is created if it
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
VMC to XenServer
Select this method to convert a Microsoft Virtual Server 2005 VM to a XenServer
VM. This conversion requires a XenServer accessible on the network and a valid
account on that XenServer. The conversion creates an intermediate XVA that
remains on the host.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VMC
Type or browse to the path of the VMC file.
Destination Folder
Type or browse to the folder to contain the intermediate files. The folder is
created if it does not already exist.
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “XenServer Account Screen”.
VHD to XVA
Select this method to convert a single VHD to a XVA.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VHD
Type or browse to the path of the VHD file.
Destination Folder
Chapter 2
Using XenConvert
23
Type or browse to the folder to contain the XVA. The folder is created if it
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
VHD to XenServer
Convert a single VHD to a XenServer. This conversion requires a XenServer
accessible on the network and a valid account on that XenServer. The conversion
creates an intermediate XVA that remains on the host.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VHD
Type or browse to the path of the VHD file.
Destination Folder
Type or browse to the folder to contain the intermediate files. The folder is
created if it does not already exist.
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “XenServer Account Screen”.
XenServer Account Screen
Enter the following information to identify the XenServer that will be used to
Hostname
Simple host name, fully qualified domain name, or IP address of the
XenServer.
User name
Name of the account with import privileges. Consult the XenServer product
documentation for information on account requirements.
24
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https://artofproblemsolving.com/wiki/index.php/2004_AMC_12A_Problems/Problem_25 | # 2004 AMC 12A Problems/Problem 25
## Problem
For each integer , let denote the base- number . The product can be expressed as , where and are positive integers and is as small as possible. What is ?
## Solution
This is an infinite geometric series with common ratio and initial term , so .
Alternatively, we could have used the algebraic manipulation for repeating decimals,
Some factors cancel, (after all, isn't one of the answer choices)
Since the only factor in the numerator that goes into is , is minimized. Therefore the answer is .
## Solution 2
Note thatby geometric series. Thus, we're aiming to find the value ofExpanding the product out, this is equivalent to Note that the numerator of the th fraction and the denominator of the th fraction for cancel out to be sinceby the binomial theorem on the the denominator of the aforementioned. Since this forms a telescoping series, our product is now equivalent towhich, after simplification gives giving an answer of
-fidgetboss_4000 | {"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": 0.9945226907730103, "perplexity": 732.1575892915317}, "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/1679296949958.54/warc/CC-MAIN-20230401094611-20230401124611-00055.warc.gz"} |
https://mathzsolution.com/graph-theoretic-proof-for-six-irrational-numbers-there-are-three-among-them-such-that-the-sum-of-any-two-of-them-is-irrational/ | # Graph theoretic proof: For six irrational numbers, there are three among them such that the sum of any two of them is irrational.
Problem. Let there be six irrational numbers. Prove that there exists three irrational numbers among them such that the sum of any two of those irrational numbers is also irrational.
I have tried to prove it in the following way, but I am not sure whether it is watertight or not as I have just started learning graph theory.
Let there be a graph with $$66$$ vertices. We assign a weight equal to those six irrational numbers to each of the vertices. We join all the vertices with edges and color the edges in the following way:
• Edge is colored red if the sum of the weights of its end points is irrational.
• Edge is colored blue if the sum of the weights of its end points is rational.
We know that when we color a $$66$$-vertex graph with $$22$$ colors then there must be a monochromatic triangle.
• If the triangle is red then we are done.
• If it is blue, then let the irrational numbers be $$aa$$, $$bb$$ and $$cc$$. Therefore $$a+ba+b$$, $$b+cb+c$$ and $$c+ac+a$$ are all rational. Which implies $$2(a+b+c)2(a+b+c)$$ and $$a+b+ca+b+c$$ is rational. As $$a+ba+b$$ is rational and hence $$cc$$ is also rational. But this is a contradiction.
Hence, our original statement is proved.
## Answer
Your proof is OK.
But more easily we can prove more strong and general claim. Assume we have a collection of $n$ irrational numbers. We shall call numbers $a$ and $b$ equivalent if the difference $a-b$ is rational. So we can partition our collection into equivalence classes. We shall call classes $C$ and $C’$ complementary if $c+c’$ is rational for any $c\in C$ and $c’\in C’$. From our partition we can choose such classes which contain in total at least $n/2$ elements and no two complementary classes are chosen. It remains to remark that a sum of any two chosen elements is irrational. In particular, among $5$ irrational numbers we can choose $3$ with all mutual sums are irrational. From the other hand, a collection consisting of $n/2$ numbers $\sqrt{2}$ and $n/2$ numbers $2-\sqrt{2}$ witnesses that the bound $n/2$ is strict.
Attribution
Source : Link , Question Author : Arpon Basu , Answer Author : Alex Ravsky | {"extraction_info": {"found_math": true, "script_math_tex": 17, "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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9007171392440796, "perplexity": 121.20124294005706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337480.10/warc/CC-MAIN-20221004054641-20221004084641-00332.warc.gz"} |
https://mathhelpboards.com/threads/arundevs-question-at-yahoo-answers-a-triangle-inscribed-in-a-semicircle-is-a-right-triangle.8154/ | # Arundev's question at Yahoo! Answers: a triangle inscribed in a semicircle is a right triangle
• #1
#### MarkFL
Staff member
Feb 24, 2012
13,775
Here is the question:
Using coordinate geometry prove that angle in a semicircle is a right angle?
I have posted a link there to this thread so the OP can view my work.
• #2
#### MarkFL
Staff member
Feb 24, 2012
13,775
Hello Arundev,
Consider the following diagram:
Without loss of generality, I have chosen a unit semicircle whose center is at the origin.
Point $P$ is $$\displaystyle (x,y)=\left(x,\sqrt{1-x^2} \right)$$.
The slope of line segment $A$ is:
$$\displaystyle m_A=\frac{\sqrt{1-x^2}-0}{x-(-1)}=\frac{\sqrt{1-x^2}}{1+x}=\sqrt{\frac{1-x}{1+x}}$$
The slope of line segment $B$ is:
$$\displaystyle m_B=\frac{\sqrt{1-x^2}-0}{x-1}=-\frac{\sqrt{1-x^2}}{1-x}=-\sqrt{\frac{1+x}{1-x}}$$
As proven >>>here<<<, two lines are perpendicular if the prodict of their slopes is $-1$.
$$\displaystyle m_Am_B=\left(\sqrt{\frac{1-x}{1+x}} \right)\left(-\sqrt{\frac{1+x}{1-x}} \right)=-1$$
Thus, we know line segments $A$ and $B$ are perpendicular, and so the triangle is a right triangle. | {"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": 0.959025502204895, "perplexity": 842.22945146351}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141182776.11/warc/CC-MAIN-20201125100409-20201125130409-00454.warc.gz"} |
http://www.math.stonybrook.edu/~oleg/Rokhlin/RokhlinInErgodic.html | Leningrad Math. J. Vol. 2 (1991), No. 2
On the work of V. A. Rokhlin in ergodic theory
by A. M. Vershik
The scientific heritage of Vladimir Abramovich Rokhlin consists of about sixty publications and several unfinished manuscripts from the 1950's and 60's, and can be conditionally split into four parts: topology - mainly four-dimensional topology and the algebraic apparatus of topology; real algebraic geometry (the last years); ergodic theory; and, finally, work on the history, teaching methods, and methodology of mathematics. The last group, unfortunately, was not reflected sufficiently in his publications, though it occupied Rokhlin constantly, and his ideas, presented often in reports and public lectures, are widely enough known and have had an influence on those around him.
Here we touch briefly on his work in ergodic theory; a detailed analysis of his work in topology and real algebraic geometry is contained in the paper of Viro and Kharlamov. Twenty-four publications were devoted to ergodic theory, along with several unpublished manuscripts which were not finished, unfortunately, and are among his unrealized plans. He returned more than once to the idea of writing a book on the metric theory of dynamical systems, including a large section on general measure theory in his own spirit; as far back as the 1940s he wrote several chapters and proposed continuing the work later with young coauthors, but after ceasing to study ergodic theory, he cooled somewhat to the idea. It should be remarked that some traces of his plans were realized in surveys and books that came out later.
In ergodic theory Vladimir Abramovich introduced a geometric and algebraic culture that it lacked by origin, which was rather analytic in the spirit of the traditions of the theory of dynamical systems of Poincare and, on the other hand, Boltzmann. In this he was continuing the tradition of von Neumann. In Rokhlin's work the geometric side of things (partitions, dynamics, etc.) pre-dominated over the analytic aspects. He proposed that systems of algebraic, analytic, probabilistic, number-theoretic, and other origins should be considered simultaneously. This tradition became established and yielded excellent results in his work and later in the work of his students. On the other hand, he strictly followed axiomatic constructions of measure theory, also affected by the influence of Kolmogorov and von Neumann.
Lebesgue spaces, introduced by Rokhlin in his undergraduate work and thoroughly investigated in the subsequent dissertation and paper 0n the fundamental concepts of measure theory'', have turned out to be a very successful concept, and his axiomatics an exceptionally convenient refinement of the axiomatizations used previously. It can be said without doubt that, after the axiomatics of Kolmogorov and von Neumann, Rokhlin made the most important step for distinguishing the proper category of measure spaces. Unfortunately, the convenience and importance of the theory of Lebesgue spaces were not realized for some time. It was perhaps for this reason that investigators resorted for a long time to topological concepts for constructions that are in essence purely metric. At present there is no doubt that the category of Lebesgue spaces is a fundamental construction in ergodic theory, measure theory, and other theories. In passing it should be mentioned that Rokhlin also made the important observation that a system of conditional measures, or, as he said, a canonical system of measures, exists only for measurable partitions of Lebesgue spaces, and attempts to introduce them in other categories were incorrect.
If one now asks any specialist in ergodic theory what the two most fundamental results at the basis of the theory are, the answer will be:
1. the Birkhoff-von Neumann ergodic theorem;
2. the Rokhlin-Halmos lemma.
This lemma, which is the starting point of all approximation constructions, was proved by Rokhlin at the end of the 1940s, and independently by Halmos in a weaker formulation. It states that, for every aperiodic transformation $T$ of a Lebesgue space $X$ with a finite invariant measure $\mu$, every integer $n$, and every positive number $\varepsilon$, there exists a periodic transformation $T_n$ with period $n$ such that $$\mu\{x\in X\mid T_nx\ne Tx\}<\frac1n+\varepsilon.$$ This lemma on periodic approximation has been generalized many times; it is the basis for category theorems, approximation theorems, entropy theorems, and so on.
Further, in early work on decomposition of automorphisms into ergodic components, Rokhlin actually proved a variant of a measurable selection theorem now called the Rokhlin-Kuratowski-Ryll-Nardzewski theorem. Influenced by the Gel'fand-Naimark-Raikov-Shilov theory of normed rings, Rokhlin made an (incomplete) attempt to construct a theory of so-called unitary rings. This theory is dual to the theory of Lebesgue spaces, which is a function-analytic version of it.
The first period of development of ergodic theory (the 1930's and 40's) concerned, for the most part, spectral theory. Here Vladimir Abramovich was the author of a number of the results included in his surveys of 1949 and 1958. Widely known are his categorical mixing estimates, the first investigations of automorphisms of compact Abelian groups as dynamical systems, and work on measurable flows.
Many papers, ideas, and initiatives of Vladimir Abramovich were completed or developed in investigations of his students and subsequent authors. These include, for example, the proposal to develop a trajectory theory (R. E. Belinskaya, A. M. Vershik), realization theorems and systems over systems'' (we would now say quantization dynamical systems), Gaussian systems (Vershik), the mixed spectrum, fiber bundles (L. M. Abramov), mixing (Ya. G. Sinai), and others.
We should dwell especially on his favorite topic of study in later years (and most important in the 1960's and 7O's) - entropy theory. Kolmogorov's discovery of entropy made a strong impression on Rokhlin. The language of this theory was the language of measurable partitions worked out earlier by Rokhlin and used by Kolmogorov in his work on entropy.
The precise analysis of the concept of the entropy of dynamical systems carried out in a cycle of papers by Kolmogorov and Sinai and then by Rokhlin, Abramov, Pinsker, and others, was simply not possible without the theory of measurable partitions, especially the part of it relating to decreasing sequences. A small and insignificant error in Kolmogorov's first paper, which was discovered by Vladimir Abramovich and made it necessary to give a somewhat different definition of the entropy in the Sinai sense, involved certain subtleties of the theory (see the remark in Kolmogorov's second paper). The unity of the two definitions was finally reestablished considerably later after Rokhlin proved a theorem on generators for aperiodic automorphisms. The concluding results on generators are due here to Krieger.
Vladimir Abramovich's two survey papers in Uspekhi Matematicheskikh Nauk (1960 and 1967) played an enormous role in the development of entropy theory in our country and abroad. The second paper summarizes the development of the concept of entropy and its applications to the theory of transformations with invariant measure.
The theory of invariant partitions for automorphisms especially interested Rokhlin, and he returned to it in later years, in the period when he finished his work on ergodic theory (this was the topic of several unpublished sketches). The start of this theory was the classical joint work of Rokhlin and Sinai in which it was proved, in particular, that the class of $K$-automorphisms coincides with the class of automorphisms with completely positive entropy (this was proved earlier in one direction by M. S. Pinsker). The very first formulas in entropy theory were the Abramov formulas for the derived automorphism and flow; formulas for the entropy of automorphisms of compact groups (Sinai, Arov, Yuzvinskii, and others) were a development of ideas and suggestions of Vladimir Abramovich. Also, the metric properties of automorphisms of compact Abelian groups were investigated (Rokhlin, Sinai, Yuzvinskii) on his initiative.
Rokhlin's interest in ergodic theory gradually began to fall, after the appearance of new post-entropy ideas - approximation and, especially, the fireworks of Ornstein's contributions and that of his successors. Vladimir Abramovich was undoubtedly interested in the course of events, but he did not take part, all the more so because his algebro-topological interests had prevailed by this time.
We mention two more circumstances. For a long time Rokhlin has been interested in number theory and the possibility of applying ergodic theory to it. Although he had only one paper on this topic, and that devoted mainly to the theory of exact endomorphisms (namely, the paper on continued fractions and the Gauss endomorphism), he thought (and this opinion had an indirect confirmation, for example, in the work of Linnik on the ergodic method in number theory) that the possibilities of metric theory in number theory were far from exhausted. Incidentally, Vladimir Abramovich always had an intense interest in the theory of endomorphisms (or semigroups of endomorphisms), and the paper mentioned is a vault of metric concepts and theorems relating precisely to this case. Especially important is the concept of a natural extension; this concept provides an invariant formulation of the immersion of a one-sided process in a two-sided process (metric dilatation). The other circumstance had to do with the interrelations with smooth and classical dynamics. It may seem strange that he, an outstanding specialist in the area of smooth manifolds who had a good knowledge of classical dynamics and physics, did not try to connect ergodic theory with smooth dynamics, all the more so because many of his students, and those who were close to him or felt his influence, studied this topic actively (Sinai, Arnol'd, Anosov, and others). Moreover, communications about the work of Smale, Anosov, and others were heard repeatedly in the seminar. Vladimir Abramovich himself said that here he was an advocate of purely'' posed problems not involving a mixture of categories completely unlike each other. In other words, he regarded smooth and metric dynamics as immiscible areas. This point of view was perhaps affected by an echo of axiomatic rigorism, which is now certainly not popular, but one cannot say that it is inconsistent.
At the sources of ergodic theory as a mathematical discipline stand the names of von Neumann and Kolmogorov; after them can be named a few others who shaped this theory from the 1930's to the 1950's and gave it its modern form - G. Birkhoff, S. Ya. Khinchin, E. Hopf, S. Kakutani, P. Halmos, and Vladimir Abramovich Rokhlin.
Work of Vladimir Abramovich Rokhlin on measure theory and ergodic theory
1. 0n classification of measurable partitions, Dokl. Akad. Nauk SSSR 58 (1947), 29 - 32. (Russian)
2. 0n the problem of classification of automorphisms of Lebesgue spaces, Dokl. Akad. Nauk SSSR 58:2 (1947), 189 - 191. (Russian)
3. Unitary rings, Dokl. Akad. Nauk SSSR 59 (1948), 643 - 646. (Russian)
4. A general transformation with invariant measure is not mixing, Dokl. Akad. Nauk SSSR 60 (1948), 349 - 351. (Russian)
5. 0n the fundamental concepts of measure theory, Mat. Sb. 25 (67) (1949), 107 - 150; English transl., Amer. Math. Soc. Transl. (1) 10 (1962).
6. 0n decomposition of a dynamical system into transitive components, Mat. Sb. 25 (67) (1949), 235 - 249. (Russian)
7. On dynamical systems whose irreducible components have purely point spectrum, Dokl. Akad. Nauk SSSR 64 (1949), 167 - 169. (Russian)
8. with A. A. Gurevich, 0n approximation of nonperiodic flows by periodic flows, Dokl. Akad. Nauk SSSR 64 (1949), 619-620. (Russian)
9. 0n endomorphisms of compact Abelian groups, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 329-340. (Russian)
10. Selected topics in the metric theory of dynamical systems, Uspekhi Mat. Nauk 4 (1949), no. 2 (30), 57 - 123. (Russian)
11. with A. A. Gurevich, Approximation theorems for measurable flows, Izv. Akad. Nauk SSSR, Ser. Mat. 14 (1950), no. 6 (40), 537 - 548. (Russian)
12. Metric classification of measurable functions, Uspekhi Mat. Nauk 12 (1957), no. 2 (74), 169 - 174. (Russian)
13. with S. V. Fomin, Spectral theory of dynamical systems, Proc. Third All-Union Math. Congress (1956), Vol. 3, 1958, p. 284. (Russian)
14. On the entropy of a metric automorphism, Dokl. Akad. Nauk SSSR 124 (1959), 980 - 982. (Russian)
15. New progress in the theory of transformations with invariant measure, Uspekhi Mat. Nauk 15 (1960), no. 4 (94), 3 - 26; English transl. in Russian Math. Surveys 15 (1960).
16. Structure and properties of invariant measurable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038-1041; English transl. in Soviet Math. Dokl. 2 (1961).
17. with Ya. G. Sinai, 0n the entropy of an automorphism of a compact Abelian group, Teor. Veroyatnost. i Primenen. 6 (1961), 351 - 352; English transl. in Theory Probab. Appl. 6 (1961).
18. Exact endomorphisms ofa Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499-5 30; English transl. in Amer. Math. Soc. Transl. (2) 39 (1964).
19. with L. M. Abramov, The entropy of a fiber bundle of transformations with invariant measure, Vestnik Leningrad. Univ. 1962, no. 7 (Ser. Mat. Mekh. Astr. vyp. 2), 5 - 13. (Russian)
20. An axiomatic definition of the entropy of transformations with invariant measure, Dokl. Akad. Nauk SSSR 148 (1963), 779 - 781; English transl. in Soviet Math. Dokl. 4 (1963).
21. Generators in ergodic theory, Vestnik Leningrad. Univ. 1963, no. 1 (Ser. Mat. Mekh. Astr. vyp. 1), 26 - 32. (Russian)
22. Metric properties of endomorphisms of compact Abelian groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 867 - 874; English transl. in Amer. Math. Soc. Transl. (2) 64 (1967).
23. Generators in ergodic theory. II, Vestnik Leningrad. Univ. 1965, no. 13 (Ser. Mat. Mekh. Astr. vyp. 3), 68 - 72. (Russian)
24. Lectures on entropy theory of transformations with invariant measure, Uspekhi Mat. Nauk 22 (1967), no. 5 (137), 4 - 56; English transl. in Russian Math. Surveys 22 (1967)
List of manuscript material of Vladimir Abramovich Rokhlin on ergodic theory
1. Notebook of small format in black binding without heading, about 80 pages, materials for a book (apparently from the 1940's), Table of contents: Part I. Lebesgue spaces, Chapters 1 - 13.
2. Sketch: Foreword''. Organization of the book. History of the theory of transformations with invariant measure, its connections and applications. Measure theory as an independent science, and the true place of the theory of transformations with invariant measure. What is usually understood by measure theory; purpose of the first chapter, what is assumed known. Main goal of the book - new things. Begin with this. Characteristics of the old parts. Selection of materials. Degree of generality - Lebesgue spaces.
3. Manuscript, Transformations with invariant measure''. Written parenthetically: book'', 69 pages + 29 (apparently later) - probably relates to the 1960's.
4. Manuscript, Unitary rings'', 18 pages (apparently from the 1950s).
5. Ergodic theory 1966 - 1967. Lectures (plans), 4 pages.
6. Invariant partitions, June 1967, 2 pages; additions - July 1967, September 1967.
7. Closed partitions. Report October 1, 1968'', 1 page; additions - October 11 and 21, 1968.
8. Saturated partitions. December 1969'', 2 pages, 24 items. | {"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": 0.8771312832832336, "perplexity": 1011.4475460636345}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865809.59/warc/CC-MAIN-20180523200115-20180523220115-00443.warc.gz"} |
http://mathhelpforum.com/pre-calculus/22560-solved-conic-section-what-each-equation-represents.html | # Math Help - [SOLVED] Conic section what each equation represents
1. ## [SOLVED] Conic section what each equation represents
I am suppose to state which type of conic section is represented by each equation step by step if its possible
1. x^2-6x+y=8
2. 3x^2+5y^2+6x-10y=16
3. 2x^2+8x=2y^2-y+10
4. 3x^2+x-y^2+y=12
5. x^2+4y^2=8
2. Originally Posted by xterminal01
I am suppose to state which type of conic section is represented by each equation step by step if its possible
1. x^2-6x+y=8
2. 3x^2+5y^2+6x-10y=16
3. 2x^2+8x=2y^2-y+10
4. 3x^2+x-y^2+y=12
5. x^2+4y^2=8
Hello,
rearrange your equations until you can determine the type of conic. All of them have their axes parallel to the coordinate axes so completing the square will do:
to #1:
$x^2-6x+y = 8~\iff~(x^2-6x+9)+y=8+9~\iff~ y = -(x-3)^2+17$
That's a parabola opening down.
to #2:
$
3x^2+5y^2+6x-10y=16~\iff~3(x^2+2x+1) + 5(y^2-2y+1)=16+3+5~\iff~$
$3(x+1)^2+5(y-1)^2=24$ . Now divide by 24 and you'll get:
$\frac{(x+1)^2}{8}+\frac{(y-1)^2}{\frac{24}{5}}=1$ That's the equation of an ellipse.
The ##3 to 5 should be done similary.(H, H, E)
3. Thanks alot for the help can you please state the step by step for number 3,4,5
4. Originally Posted by xterminal01
Thanks alot for the help can you please state the step by step for number 3,4,5
Hi,
I was quite sure that you could do the last problems using the way I demonstrated to you, but .... I'll start the problems and I'll leave the final brush up to you:
to #3:
$2x^2+8x=2y^2-y+10~\iff~2x^2+8x-2y^2+y=10~\iff~$ $2(x^2+4x+4)-2(y^2+\frac12 y+\frac{1}{16})= 10+8-\frac{2}{16}$ . Simplify and you should come out with a hyperbola
to #4:
$3x^2+x-y^2+y=12~\iff~3(x^2+\frac13 x+\frac{1}{36})-(y^2-y+\frac14)=12 + \frac{3}{36} - \frac14$ Simplify. It's a hyperbola too.
to #5:
$x^2+4y^2=8$ Divide by 8. Then you get the equation of an ellipse.
5. Okey so i tried to finish number 3 and this is what i came up with please check if its right
3 i got stuck with this...
$2(x+2)^2 -2(x+1/4)^2 = 143/8$
4 i dont know how to finish
5 should be $x^2/8+y^2/2=1$
6. Hello, xterminal01!
State which type of conic section is represented by each equation.
$1)\;\;x^2-6x+y\:=\:8$
$2)\;\;3x^2+5y^2+6x-10y\:=\:16$
$3)\;\;2x^2+8x\:=\:2y^2-y+10\quad\Rightarrow\quad 2x^2+8x-2y^2+y\:=\:10$
$4)\;\;3x^2+x-y^2+y\:=\:12$
$5)\;\;x^2+4y^2\:=\:8$
If we are to identity the type of conic only , there is an "eyeball" method.
First, get all the variables on one side of the equation.
. . (As we did in #3.)
If it has either $x^2$ or $y^2$, but not both, it is a parabola. .(#1)
If $x^2$ and $y^2$ have the same coefficient, it is a circle. .(None listed)
If $x^2$ and $y^2$ have the same sign, it is an ellipse. .(#2 and 5)
If $x^2$ and $y^2$ have opposite signs, it is a hyperbola. .(#3 and 4)
7. Originally Posted by xterminal01
3 i got stuck with this...
$2(x+2)^2 -2(x+1/4)^2 = 143/8$
4 i dont know how to finish
5 should be $x^2/8+y^2/2=1$
Hello,
you've done #5 correctly. I would have written:
$\frac{x^2}{(2\sqrt{2})^2}+\frac{y^2}{(\sqrt{2})^2} =1$
#4: I'll continue:
$3(x^2+\frac13 x+\frac{1}{36})-(y^2-y+\frac14)= \frac{71}{6}~\iff~ 3\left(x+\frac16\right)^2-\left(y-\frac12\right)^2=\frac{71}{6}$ and now divide by $\frac{71}{6}$. That's all.
#3: Divide by $\frac{143}{8}$ to get a 1 at the RHS.
8. Yea but i cant solve the equation to the end ...
9. Originally Posted by xterminal01
Yea but i cant solve the equation to the end ...
You have all the steps and all but the last one, the division, is given to you. What more do you need?
-Dan | {"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": 29, "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": 0.8479231595993042, "perplexity": 891.5092025519921}, "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/1461860111313.83/warc/CC-MAIN-20160428161511-00035-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://www.marinebiotech.eu/c/index.php?title=Wave_run-up&oldid=76391 | # Wave run-up
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Definition of Wave run-up: Landward incursion of a wave. Wave run-up is usually expressed as the maximum onshore elevation reached by a wave, relative to the wave-averaged shoreline position. This is the common definition for Wave run-up, other definitions can be discussed in the article
Wave run-up is an important parameter for assessing the safety of sea dikes or coastal settlements. Wave run-up is the sum of wave set-up and swash uprush (see Swash zone dynamics) and must be added to the water level reached as a result of tides and storm setup.
By waves is meant: waves generated by wind (locally or on the ocean) or waves generated by incidental disturbances of the sea surface such as tsunamis, seiches or ship waves. Wave run-up is often indicated with the sympol $R$.
For waves collapsing on the beach, the wave run-up can be estimated in first approach with the formula of Hunt (1959) [1],
$R = H \xi ,$
where $H$ is the offshore wave height and $\xi$ is the wave similarity parameter,
$\xi = \Large\frac{S}{\sqrt{H/L}}\normalsize = S \, T \Large\sqrt{\frac{g}{4\pi H}}\normalsize ,$
where $L = g T^2/(2 \pi)$ is the offshore wave length, $S$ is the beach slope and $T$ is the wave period. The horizontal wave incursion is approximately given by $R / S$.
For more precise estimates of wave run-up see:
Swash zone dynamics
Tsunami
## References
1. Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152 | {"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": 0.9747862219810486, "perplexity": 4594.663775183026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389798.91/warc/CC-MAIN-20210309092230-20210309122230-00501.warc.gz"} |
https://www.physicsforums.com/threads/statistic-problems-with-quartiles-and-standard-deviations.196301/ | # Statistic Problems With Quartiles and Standard Deviations
1. Nov 5, 2007
### Rawr
There are two different problems that I am confused with:
1) The taste of mature cheese is related to the concentration of lactic acid in cheese. Use the concentrations of lactic acid in 30 samples of cheddar cheese on page 15.
Well, what's important is that using all the numbers it gave me, the mean is 1.44, the median is 1.45 and the standard deviation is .3035.
Then it asks, "Calculate the percent of data that lie within one, two and three standard deviations. I attempted to work with one standard deviation, but I can't seem to get the right answer, which is 66% (or something close).
What I did was... one standard deviation is 1.45 +/- .3035, which gets 1.15 and 1.75. Then you need to calculate the percentage of numbers that fall within that range.
So, I take the z-score of each number: (1.15 - 1.45)/1.44 = -0.21 and it's the same for the other, except it comes out a positive 0.21 using 1.75 instead of 1.15. Using the A chart.. I get numbers of .4168 and .5832 respectively. Subtracting them gives me something like.. 12%. What am I doing wrong? Am I even in the right direction?
The second question..is "How many standard deviations away from the mean do the quartiles lie in any normal distribution? What are the quartile for the lengths of human pregnancies? (which says that... for human pregnancies, the mean is 266 days and the Standard deviation is 16 days)
Frankly, I have no idea how to start and I was hoping I would get a little push in the right direction.
2. Nov 5, 2007
### EnumaElish
z_ = 0 - 1 = -1 is the standard z score for "one std below" and z+ = 0 + 1 = +1 is for "one std above."
Similar Discussions: Statistic Problems With Quartiles and Standard Deviations | {"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": 0.8747324347496033, "perplexity": 626.0016519003749}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806615.74/warc/CC-MAIN-20171122160645-20171122180645-00527.warc.gz"} |
http://mathhelpforum.com/discrete-math/169973-compactness-theorem-partial-orderings-print.html | # Compactness Theorem and partial orderings
• Feb 1st 2011, 07:44 PM
Compactness Theorem and partial orderings
Hello folks,
I've been asked 'If P is a partial ordering, how do I use the compactness theorem to show that P is the union of k chains iff each finite subset on P is the union of k chains?'
But, I have absolutely no idea what this question is even driving at. Set theory and logic is easily my weakest area of maths and any help would be much appreciated (I will attempt to reciprocate in differenctial equations or algebra - things I can actually do!)
• Feb 2nd 2011, 12:35 PM
emakarov
A chain is a totally ordered subset.
There is a question what a subset of P is. Let's say P is an order on a set A, i.e., $P\subseteq A\times A$. Then a subset of P could mean a subrelation on the same set A. However, if A is infinite, the premise of the statement is trivially false and so the statement is trivially true. Indeed, each finite subrelation has infinitely many isolated points, and each of them is a degenerate chain. So I think the problem is talking about finite subsets of A and restrictions of P on these subsets.
I have not worked out all details, but the idea may be as follows. Let C be a formula saying that for any k + 1 elements, some pair of them are comparable. We can prove that C holds for P.
Let A_n be a subset of A with n elements and let P_n be the restriction of P to A_n. By [P_n] I will denote a single formula that records the structure of P_n. It has constants c_1, ..., c_n and is a big conjunction of inequalities between these constants. If constants' names are chosen consistently, then [P_n] implies [P_k] for k < n. The problem statement implies that for each n, the set {[P_1], ..., [P_n], C} is consistent since P_n is its model. Therefore, the union of these sets is consistent by compactness theorem. A model of this union must include P as a substructure and so C is true on P. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9631028771400452, "perplexity": 435.9117816926251}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118740.31/warc/CC-MAIN-20170423031158-00525-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://worldwidescience.org/topicpages/v/vlasov+ions+cold.html | #### Sample records for vlasov ions cold
1. Hybrid (Vlasov-Fluid) simulation of ion-acoustic soliton chain formation and validity of Korteweg de-Vries model
Science.gov (United States)
Aminmansoor, F.; Abbasi, H.
2015-08-01
The present paper is devoted to simulation of nonlinear disintegration of a localized perturbation into ion-acoustic solitons train in a plasma with hot electrons and cold ions. A Gaussian initial perturbation is used to model the localized perturbation. For this purpose, first, we reduce fluid system of equations to a Korteweg de-Vries equation by the following well-known assumptions. (i) On the ion-acoustic evolution time-scale, the electron velocity distribution function (EVDF) is assumed to be stationary. (ii) The calculation is restricted to small amplitude cases. Next, in order to generalize the model to finite amplitudes cases, the evolution of EVDF is included. To this end, a hybrid code is designed to simulate the case, in which electrons dynamics is governed by Vlasov equation, while cold ions dynamics is, like before, studied by the fluid equations. A comparison between the two models shows that although the fluid model is capable of demonstrating the general features of the process, to have a better insight into the relevant physics resulting from the evolution of EVDF, the use of kinetic treatment is of great importance.
2. Vlasov simulations of multi-ion plasma turbulence in the solar wind
CERN Document Server
Perrone, Denise; Servidio, Sergio; Dalena, Serena; Veltri, Pierluigi
2012-01-01
Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according with solar wind observations. Anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy, and also depends on the local differential flo...
3. Vlasov Simulations of Electron-Ion Collision Effects on Damping of Electron Plasma Waves
CERN Document Server
Banks, J W; Berger, R L; Tran, T M
2016-01-01
Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wave damping is about a factor of two smaller than is obtained from linearized fluid theory. To our knowledge, this simple result has not been published before. Simulations have been carried out using a grid-based (Vlasov) approach, based on a high-order conservative finite difference method for discretizing the Fokker-Planck equation describing the evolution of the electron distribution function. Details of the implementat...
4. Vlasov simulations of electron-ion collision effects on damping of electron plasma waves
Energy Technology Data Exchange (ETDEWEB)
Banks, J. W., E-mail: [email protected] [Rensselaer Polytechnic Institute, Department of Mathematical Sciences, Troy, New York 12180 (United States); Brunner, S.; Tran, T. M. [Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne (Switzerland); Berger, R. L. [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94551 (United States)
2016-03-15
Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wave damping significantly reduced from that obtained through linearized fluid theory. To our knowledge, this simple result has not been published before. Simulations have been carried out using a grid-based (Vlasov) approach, based on a high-order conservative finite difference method for discretizing the Fokker-Planck equation describing the evolution of the electron distribution function. Details of the implementation of the collision operator within this framework are presented. Such a grid-based approach, which is not subject to numerical noise, is of particular interest for the accurate measurements of the wave damping rates.
5. Nanofriction in cold ion traps.
Science.gov (United States)
Benassi, A; Vanossi, A; Tosatti, E
2011-01-01
Sliding friction between crystal lattices and the physics of cold ion traps are so far non-overlapping fields. Two sliding lattices may either stick and show static friction or slip with dynamic friction; cold ions are known to form static chains, helices or clusters, depending on the trapping conditions. Here we show, based on simulations, that much could be learnt about friction by sliding, through, for example, an electric field, the trapped ion chains over a corrugated potential. Unlike infinite chains, in which the theoretically predicted Aubry transition to free sliding may take place, trapped chains are always pinned. Yet, a properly defined static friction still vanishes Aubry-like at a symmetric-asymmetric structural transition, found for decreasing corrugation in both straight and zig-zag trapped chains. Dynamic friction is also accessible in ringdown oscillations of the ion trap. Long theorized static and dynamic one-dimensional friction phenomena could thus become accessible in future cold ion tribology.
6. Cold Ion Escape from Mars
Science.gov (United States)
Fränz, M.; Dubinin, E.; Wei, Y.; Morgan, D.; Andrews, D.; Barabash, S.; Lundin, R.; Fedorov, A.
2013-09-01
It has always been challenging to observe the flux of ions with energies of less than 10eV escaping from the planetary ionospheres. We here report on new measurements of the ionospheric ion flows at Mars by the ASPERA-3 experiment on board Mars Express in combination with the MARSIS radar experiment. We first compare calculations of the mean ion flux observed by ASPERA-3 alone with previously published results. We then combine observations of the cold ion velocity by ASPERA-3 with observations of the cold plasma density by MARSIS since ASPERA-3 misses the cold core of the ion distribution. We show that the mean density of the nightside plasma observed by MARSIS is about two orders higher than observed by ASPERA-3 (Fig.1). Combining both datasets we show that the main escape channel is along the shadow boundary on the tailside of Mars (Fig. 2). At a distance of about 0.5 R_M the flux settles at a constant value (Fig. 3) which indicates that about half of the transterminator ionospheric flow escapes from the planet. Possible mechanism to generate this flux can be the ionospheric pressure gradient between dayside and nightside or momentum transfer from the solar wind via the induced magnetic field since the flow velocity is in the Alfvénic regime.
7. Cold Strontium Ion Source for Ion Interferometry
Science.gov (United States)
Jackson, Jarom; Durfee, Dallin
2015-05-01
We are working on a cold source of Sr Ions to be used in an ion interferometer. The beam will be generated from a magneto-optical trap (MOT) of Sr atoms by optically ionizing atoms leaking out a carefully prepared hole in the MOT. A single laser cooling on the resonant transition (461 nm) in Sr should be sufficient for trapping, as we've calculated that losses to the atom beam will outweigh losses to dark states. Another laser (405 nm), together with light from the trapping laser, will drive a two photon transition in the atom beam to an autoionizing state. Supported by NSF Award No. 1205736.
8. Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory
CERN Document Server
Colombi, Stephane
2014-01-01
We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central "S" shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay between the central S and the halo. Our theoretical predictions are checked against measurements in entropy conserving numerical simulations based on the waterbag method. While our post-collapse Lagrangian approach does not allow us to compute rigorously the long term behavior of the system, i.e. after many crossing times, it explains the close to power-law behavior of the projected density observed in numerical simulations. ...
9. 3D Maxwell-Vlasov boundary value problem solution in stellarator geometry in ion cyclotron frequency range. Final report
Energy Technology Data Exchange (ETDEWEB)
Vdovin, V.; Watari, T.; Fukuyama, A.
1996-12-01
We develop the theory for the wave excitation, propagation and absorption in 3-dimensional (3D) stellarator equilibrium high beta plasma in ion cyclotron frequency range (ICRF). This theory forms a basis for a 3D code creation, urgently needed for the ICRF heating scenarios development for the constructed LHD and projected W7-X stellarators and for the stellarators being at operation (like CHS, W7-AS, etc.). The theory solves the 3D Maxwell-Vlasov antenna-plasma-conducting shell boundary value problem in the non - orthogonal flux coordinates ({psi}, {theta}, {phi}), {psi} being magnetic flux function, {theta} and {phi} being the poloidal and toroidal angles, respectively. All basic physics, like wave refraction, reflection and diffraction are firstly self consistently included, along with the fundamental ion and ion minority cyclotron resonances, two ion hybrid resonance, electron Landau and TTMP absorption. Antenna reactive impedance and loading resistance are also calculated and urgently needed for an antenna -generator matching. This is accomplished in a real confining magnetic field being varying in a plasma major radius direction, in toroidal and poloidal directions, through making use of the hot dense plasma dielectric kinetic tensor. The theory is developed in a manner that includes tokamaks and magnetic mirrors as the particular cases through general metric tensor (provided by an equilibrium solver) treatment of the wave equations. We describe the structure of newly developed stellarator ICRF 3D full wave code STELION, based on theory described in this report. (J.P.N.)
10. Study of the heavy ions (Au+Au at 150 AMeV) collisions with the FOPI detector. Comparison with the Landau-Vlasov model; Etude des collisions dions lourds AU+AU a 150 A.MeV avec le detecteur FOPI. Comparaison avec le modele de Landau-Vlasov
Energy Technology Data Exchange (ETDEWEB)
Boussange, S.
1995-09-15
In this thesis, heavy ions (Au+Au) collisions experiments are made at 150 AMeV.In the first part, a general study of the nuclear matter equation is presented. Then the used Landau-Vlasov theoretical model is describe. The third part presents the FOPI experience and the details of how to obtain this theoretical predictions (filter, cuts, corrections, possible centrality selections).At the end, experimental results and comparisons with the Landau-Vlasov model are presented. (TEC). 105 refs., 96 figs., 14 tabs.
11. Cold molecular ions on a chip
CERN Document Server
Mokhberi, A
2014-01-01
We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. N$_2^+$ and CaH$^+$ ions were confined in a surface-electrode radiofrequency ion trap and cooled by the interaction with laser-cooled Ca$^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to Coulomb-crystallized molecular ions with potential applications in mass spectrometry, cold chemistry, quantum information science and spectroscopy.
12. Cold heteronuclear atom-ion collisions
CERN Document Server
Zipkes, Christoph; Ratschbacher, Lothar; Sias, Carlo; Köhl, Michael
2010-01-01
We study cold heteronuclear atom ion collisions by immersing a trapped single ion into an ultracold atomic cloud. Using ultracold atoms as reaction targets, our measurement is sensitive to elastic collisions with extremely small energy transfer. The observed energy-dependent elastic atom-ion scattering rate deviates significantly from the prediction of Langevin but is in full agreement with the quantum mechanical cross section. Additionally, we characterize inelastic collisions leading to chemical reactions at the single particle level and measure the energy-dependent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes.
13. Cold Trapped Ions as Quantum Information Processors
CERN Document Server
Sasura, M; Sasura, Marek; Buzek, Vladimir
2002-01-01
In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on...
14. Cold fission as heavy ion emission
Energy Technology Data Exchange (ETDEWEB)
Poenaru, D.N.; Maruhn, J.A.; Greiner, W.; Ivascu, M.; Mazilu, D.; Gherghescu, R.
1987-11-01
The last version of the analytical superasymmetric fission model is applied to study cold fission processes. Strong shell effects are present either in one or both fission fragments. A smooth behaviour is observed when the proton or the neutron numbers are changed by four units. Increasing Z and N, in the transuranium region, a sharp transition from asymmetry with a large peak-to-valley ratio to symmetry at Z=100 and/or N=164 is obtained. The transition toward asymmetry at higher Z and N is much smoother. The most probable cold fission light fragments from /sup 234/U, /sup 236/U, /sup 239/Np and /sup 240/Pu are /sup 100/Zr, /sup 104/Mo, /sup 106/Mo and /sup 106/Mo, respectively, in good agreement with experimental data. The unified treatment of alpha decay, heavy ion radioactivities and cold fission is illustrated for /sup 234/U - the first nucleus in which all three groups have been already observed.
15. Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance; Resolution numerique des equations de Maxwell-Vlasov en regime periodique. Application a l'etude de la separation isotopique par resonance cyclotron ionique
Energy Technology Data Exchange (ETDEWEB)
Omnes, P
1999-01-25
This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear,whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)
16. The whistler mode in a Vlasov plasma
Science.gov (United States)
Tokar, R. L.; Gary, S. P.
1985-01-01
In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.
17. Tokamak-like Vlasov equilibria
CERN Document Server
Tasso, H
2014-01-01
Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.
18. Quasineutral limit of the Vlasov-Poisson system with massless electrons
CERN Document Server
Han-Kwan, Daniel
2010-01-01
In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behaviour of ions in a plasma. We consider massless electrons, with a charge density following a Maxwell-Boltzmann law. For cold ions, using the relative entropy method, we derive the classical Isothermal Euler or the (inviscid) Shallow Water systems from fluid mechanics. In a second time, we study the combined quasineutral and strong magnetic field regime for such plasmas.
19. Solving the Vlasov equation in complex geometries
Directory of Open Access Journals (Sweden)
Sonnendrücker E.
2011-11-01
Full Text Available This paper introduces an isoparametric analysis to solve the Vlasov equation with a semi-Lagrangian scheme. A Vlasov-Poisson problem modeling a heavy ion beam in an axisymmetric configuration is considered. Numerical experiments are conducted on computational meshes targeting different geometries. The impact of the computational grid on the accuracy and the computational cost are shown. The use of analytical mapping or Bézier patches does not induce a too large computational overhead and is quite accurate. This approach successfully couples an isoparametric analysis with a semi-Lagrangian scheme, and we expect to apply it to a gyrokinetic Vlasov solver. Nous présentons ici une analyse isoparamétrique pour résoudre l’équation de Vlasov à l’aide d’un schéma Semi-Lagrangien. Le cas test d’un faisceau axisymétrique d’ions lourds est étudié dans le cadre du système Vlasov-Poisson. Des tests numériques sont effectués sur différents maillages a fin d’étudier diverses géométries. L’impact du choix de maillage sur la précision numérique et le coût de calcul est quantifié. L’utilisation de mapping analytique ou de patches de Bézier ne semble pas trop coûteux et permet une précision numérique suffisante. Le couplage de l’analyse isoparamétrique au schéma Semi-Lagrangien est donc réeussi, nous espérons pouvoir appliquer cette méthode à des solveurs de l’équation de Vlasov gyrocinétique.
20. Verification of high efficient broad beam cold cathode ion source
Science.gov (United States)
Abdel Reheem, A. M.; Ahmed, M. M.; Abdelhamid, M. M.; Ashour, A. H.
2016-08-01
An improved form of cold cathode ion source has been designed and constructed. It consists of stainless steel hollow cylinder anode and stainless steel cathode disc, which are separated by a Teflon flange. The electrical discharge and output characteristics have been measured at different pressures using argon, nitrogen, and oxygen gases. The ion exit aperture shape and optimum distance between ion collector plate and cathode disc are studied. The stable discharge current and maximum output ion beam current have been obtained using grid exit aperture. It was found that the optimum distance between ion collector plate and ion exit aperture is equal to 6.25 cm. The cold cathode ion source is used to deposit aluminum coating layer on AZ31 magnesium alloy using argon ion beam current which equals 600 μA. Scanning electron microscope and X-ray diffraction techniques used for characterizing samples before and after aluminum deposition.
1. Cold atom-ion experiments in hybrid traps
CERN Document Server
Härter, Arne
2013-01-01
In the last 5 years, a novel field of physics and chemistry has developed in which cold trapped ions and ultracold atomic gases are brought into contact with each other. Combining ion traps with traps for neutral atoms yields a variety of new possibilities for research and experiments. These range from studies of cold atom-ion collisions and atom-ion chemistry to applications in quantum information science and condensed matter related research. In this article we give a brief introduction into this new field and describe some of the perspectives for its future development.
2. a Continuous Supersonic Expansion Discharge Nozzle for Rotationally Cold Ions
Science.gov (United States)
Kauffman, Carrie A.; Crabtree, Kyle N.; McCall, Benjamin J.
2009-06-01
Molecular ions play an important role in chemistry and astronomy. In particular, molecular ions are key reaction intermediates, and in the interstellar medium, where temperatures and densities are low, they dominate the chemistry. Studying these ions spectroscopically in the laboratory poses a difficult challenge due to their reactivity. In our effort to study molecular ions, our research group is building SCRIBES (Sensitive Cooled Resolved Ion BEam Spectroscopy), which combines a cold ion source, mass spectrometry, and cavity ring-down spectroscopy. With this apparatus, we will be able to record rotationally-resolved gas-phase spectra, enabling interstellar searches for these species. The SCRIBES instrument requires a source of rotationally cold ions, and this has been accomplished by coupling a supersonic expansion with an electric discharge. Other groups (e.g. Thaddeus and McCarthy at Harvard, Salama et. al at NASA-Ames) have produced cold ions in a similar fashion, but always with a pulsed discharge source. Due to our need for a continuous ion source for SCRIBES, we have designed a continuous supersonic expansion discharge nozzle. We will discuss the various design factors considered during the construction of our continuous self-aligning cold ion source.
3. Production of translationally cold barium monohalide ions
CERN Document Server
DePalatis, M V
2013-01-01
We have produced sympathetically cooled barium monohalide ions BaX$^+$ (X = F, Cl, Br) by reacting trapped, laser cooled Ba$^+$ ions with room temperature gas phase neutral halogen-containing molecules. Reaction rates for two of these (SF$_6$ and CH$_3$Cl) have been measured and are in agreement with classical models. BaX$^+$ ions are promising candidates for cooling to the rovibrational ground state, and our method presents a straightforward way to produce these polar molecular ions.
4. Rotational Laser Cooling of Vibrationally and Translationally Cold Molecular Ions
DEFF Research Database (Denmark)
Drewsen, Michael
2011-01-01
[7,8,9]. Furthermore, in order to learn more about the chemistry in interstellar clouds, astrochemists can benefit greatly from direct measurements on cold reactions in laboratories [9]. Working with MgH+ molecular ions in a linear Paul trap, we routinely cool their translational degree of freedom...... of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid...
5. Reduced Vlasov-Maxwell simulations
Science.gov (United States)
Helluy, Philippe; Navoret, Laurent; Pham, Nhung; Crestetto, Anaïs
2014-10-01
In this paper we review two different numerical methods for Vlasov-Maxwell simulations. The first method is based on a coupling between a Discontinuous Galerkin (DG) Maxwell solver and a Particle-In-Cell (PIC) Vlasov solver. The second method only uses a DG approach for the Vlasov and Maxwell equations. The Vlasov equation is first reduced to a space-only hyperbolic system thanks to the finite-element method. The two numerical methods are implemented using OpenCL in order to achieve high performance on recent Graphic Processing Units (GPU).
6. Controlling fast transport of cold trapped ions
CERN Document Server
Walther, Andreas; Ruster, Thomas; Dawkins, Sam T; Ott, Konstantin; Hettrich, Max; Singer, Kilian; Schmidt-Kaler, Ferdinand; Poschinger, Ulrich
2012-01-01
We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10^4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 micro meter in 3.6 micro seconds). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10 $\\pm$ 0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.
7. Exact Quantum Logic Gates with a Single Trapped Cold Ion
Institute of Scientific and Technical Information of China (English)
韦联福; 刘世勇; 雷啸霖
2001-01-01
We present an alternative scheme to exactly implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a travelling laser field. The internal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the external vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the internal and external degrees of freedom of the ion is considered.
8. A proposal for sympathetically cooling neutral molecules using cold ions
CERN Document Server
Robicheaux, F
2014-01-01
We describe a method for cooling neutral molecules that have magnetic and electric dipole moments using collisions with cold ions. An external magnetic field is used to split the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kinetic energy with no change in internal energy. We present results for the specific case of OH molecules cooled by Be$^+$, Mg$^+$, or Ca$^+$ ions.
9. DESIREE: Physics with cold stored ion beams
Directory of Open Access Journals (Sweden)
Thomas R.D.
2015-01-01
Full Text Available Here we will briefly describe the commissioning of the Double ElectroStatic Ion Ring ExpEriment (DESIREE facility at Stockholm University, Sweden. This device uses purely electrostatic focussing and deflection elements and allows ion beams of opposite charge to be confined under extreme high vacuum and cryogenic conditions in separate “rings” and then merged over a common straight section. This apparatus allows for studies of interactions between cations and anions at very low and well-defined centre-of-mass energies (down to a few meV and at very low internal temperatures (down to a few K.
10. Cryogenic linear Paul trap for cold highly charged ion experiments.
Science.gov (United States)
Schwarz, M; Versolato, O O; Windberger, A; Brunner, F R; Ballance, T; Eberle, S N; Ullrich, J; Schmidt, P O; Hansen, A K; Gingell, A D; Drewsen, M; López-Urrutia, J R Crespo
2012-08-01
Storage and cooling of highly charged ions require ultra-high vacuum levels obtainable by means of cryogenic methods. We have developed a linear Paul trap operating at 4 K capable of very long ion storage times of about 30 h. A conservative upper bound of the H(2) partial pressure of about 10(-15) mbar (at 4 K) is obtained from this. External ion injection is possible and optimized optical access for lasers is provided, while exposure to black body radiation is minimized. First results of its operation with atomic and molecular ions are presented. An all-solid state laser system at 313 nm has been set up to provide cold Be(+) ions for sympathetic cooling of highly charged ions.
11. Cryogenic linear Paul trap for cold highly charged ion experiments
DEFF Research Database (Denmark)
Schwarz, Maria; Versolato, Oscar; Windberger, Alexander
2012-01-01
Storage and cooling of highly charged ions require ultra-high vacuum levels obtainable by means of cryogenic methods. We have developed a linear Paul trap operating at 4 K capable of very long ion storage times of about 30 h. A conservative upper bound of the H2 partial pressure of about 10−15 mbar...... (at 4 K) is obtained from this. External ion injection is possible and optimized optical access for lasers is provided, while exposure to black body radiation is minimized. First results of its operation with atomic and molecular ions are presented. An all-solid state laser system at 313 nm has been...... set up to provide cold Be+ ions for sympathetic cooling of highly charged ions....
12. Disordered complex systems using cold gases and trapped ions
CERN Document Server
De, A S; Lewenstein, M; Ahufinger, V; Pons, M L; Sanpera, A; De, Aditi Sen; Sen, Ujjwal; Lewenstein, Maciej; Ahufinger, Veronica; Pons, Marisa Ll.; Sanpera, Anna
2005-01-01
We report our research on disordered complex systems using cold gases and trapped ions, and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are revisited here. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses), which can be implemented with a Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian, characteristic of neural networks (Hopfield model), which can be implemented in a chain of trapped ions with appropriately designed interactions.
13. Rotational Laser Cooling of Vibrationally and Translationally Cold Molecular Ions
DEFF Research Database (Denmark)
Drewsen, Michael
2011-01-01
by sympathetic cooling with Doppler laser cooled Mg+ ions. Giving the time for the molecules to equilibrate internally to the room temperature blackbody radiation, the vibrational degree of freedom will freeze out, leaving only the rotational degree of freedom to be cooled. We report here on the implementation...... of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid......-infrared laser sources such as a quantum cascade laser are available. In recent experiments, a nearly 15-fold increase in the rotational ground-state population was obtained, with the resulting ground-state population of 36,7±1,2 %, equivalent to that of a thermal distribution at about 20 K. The obtained cooling...
14. A cloudy Vlasov solution
CERN Document Server
Alard, C
2004-01-01
We propose to integrate the Vlasov-Poisson equations giving the evolution of a dynamical system in phase-space using a continuous set of local basis functions. In practice, the method decomposes the density in phase-space into small smooth units having compact support. We call these small units clouds'' and choose them to be Gaussians of elliptical support. Fortunately, the evolution of these clouds in the local potential has an analytical solution, that can be used to evolve the whole system during a significant fraction of dynamical time. In the process, the clouds, initially round, change shape and get elongated. At some point, the system needs to be remapped on round clouds once again. This remapping can be performed optimally using a small number of Lucy iterations. The remapped solution can be evolved again with the cloud method, and the process can be iterated a large number of times without showing significant diffusion. Our numerical experiments show that it is possible to follow the 2 dimensional ...
15. Small amplitude ion-acoustic double layers with cold electron beam and q-nonextensive electrons
Energy Technology Data Exchange (ETDEWEB)
Ali Shan, S., E-mail: [email protected] [Theoretical Plasma Physics Division, PINSTECH, Nilore, 44000 Islamabad (Pakistan); National Centre for Physics (NCP), Shahdra Valley Road, 44000 Islamabad (Pakistan); Department of Mathematics and Applied Physics (DPAM), PIEAS, Islamabad (Pakistan); Saleem, H., E-mail: [email protected] [National Centre for Physics (NCP), Shahdra Valley Road, 44000 Islamabad (Pakistan); Department of Mathematics and Applied Physics (DPAM), PIEAS, Islamabad (Pakistan)
2014-02-01
Small amplitude ion-acoustic double layers in an unmagnetized and collisionless plasma consisting of cold positive ions, q-nonextensive electrons, and a cold electron beam are investigated. Small amplitude double layer solution is obtained by expanding the Sagdeev potential truncated method. The effects of entropic index q, speed and density of cold electron beam on double layer structures are discussed.
16. Spectra of Cold Molecular Ions from Hot Helium Nanodroplets
Science.gov (United States)
Drabbels, Marcel
2012-06-01
The function of a molecule is intimately related to its structure. Accordingly, in the quest for a better understanding of molecular function, the development of spectroscopic methods to elucidate molecular structures increasingly takes central stage. The amount of detail that can be derived from spectra depends on the experimental conditions, most notably on the temperature of the sample and the intermolecular interactions a molecule experiences. Helium nanodroplets provide in this respect an almost ideal matrix [1, 2]. For neutral molecules, helium nanodroplet spectroscopy thus has led to important discoveries related to the structure of key molecular systems and has provided insight into the mechanisms underlying chemical reactions. Compared to the level of sophistication that has been reached for neutrals, the spectroscopic exploration of ions is still in its infancy. The use of helium droplets as a cryogenic matrix could potentially solve many of the technical challenges associated with recording high-resolution spectra of cold molecular ions. Here, we will present a method to record spectra of ion containing helium nanodroplets that finds its roots in the nonthermal cooling dynamics of excited molecular ions. In addition, spectra of several molecular ions will be present and the influence of the helium environment on these spectra will be discussed. [1] G. Scoles, and K. K. Lehmann, Science 287, 2429 (2000). [2] J. P. Toennies, and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622 (2004).
17. Precision Spectroscopy on Single Cold Trapped Molecular Nitrogen Ions
Science.gov (United States)
Hegi, Gregor; Najafian, Kaveh; Germann, Matthias; Sergachev, Ilia; Willitsch, Stefan
2016-06-01
The ability to precisely control and manipulate single cold trapped particles has enabled spectroscopic studies on narrow transitions of ions at unprecedented levels of precision. This has opened up a wide range of applications, from tests of fundamental physical concepts, e.g., possible time-variations of fundamental constants, to new and improved frequency standards. So far most of these experiments have concentrated on atomic ions. Recently, however, attention has also been focused on molecular species, and molecular nitrogen ions have been identified as promising candidates for testing a possible time-variation of the proton/electron mass ratio. Here, we report progress towards precision-spectroscopic studies on dipole-forbidden vibrational transitions in single trapped N2+ ions. Our approach relies on the state-selective generation of single N2+ ions, subsequent infrared excitation using high intensity, narrow-band quantum-cascade lasers and a quantum-logic scheme for non-destructive state readout. We also characterize processes limiting the state lifetimes in our experiment, which impair the measurement fidelity. P. O. Schmidt et. al., Science 309 (2005), 749. M. Kajita et. al., Phys. Rev. A 89 (2014), 032509 M. Germann , X. Tong, S. Willitsch, Nature Physics 10 (2014), 820. X. Tong, A. Winney, S. Willitsch, Phys. Rev. Lett. 105 (2010), 143001
18. Wave dispersion in the hybrid-Vlasov model: Verification of Vlasiator
OpenAIRE
Kempf, Yann; Pokhotelov, Dimitry; von Alfthan, Sebastian; Vaivads, Andris; Palmroth, Minna; Koskinen, Hannu E. J.
2013-01-01
Vlasiator is a new hybrid-Vlasov plasma simulation code aimed at simulating the entire magnetosphere of the Earth. The code treats ions (protons) kinetically through Vlasov's equation in the six-dimensional phase space while electrons are a massless charge-neutralizing fluid [M. Palmroth et al., Journal of Atmospheric and Solar-Terrestrial Physics 99, 41 (2013); A. Sandroos et al., Parallel Computing 39, 306 (2013)]. For first global simulations of the magnetosphere, it is critical to verify ...
19. Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
OpenAIRE
H ABBASI; R Shokoohi; Moridi, M.
2012-01-01
In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons ...
20. Spectroscopic studies of cold, gas-phase biomolecular ions
Science.gov (United States)
Rizzo, Thomas R.; Stearns, Jaime A.; Boyarkin, Oleg V.
While the marriage of mass spectrometry and laser spectroscopy is not new, developments over the last few years in this relationship have opened up new horizons for the spectroscopic study of biological molecules. The combination of electrospray ionisation for producing large biological molecules in the gas phase together with cooled ion traps and multiple-resonance laser schemes are allowing spectroscopic investigation of individual conformations of peptides with more than a dozen amino acids. Highly resolved infrared spectra of single conformations of such species provide important benchmarks for testing the accuracy of theoretical calculations. This review presents a number of techniques employed in our laboratory and in others for measuring the spectroscopy of cold, gas-phase protonated peptides. We show examples that demonstrate the power of these techniques and evaluate their extension to still larger biological molecules.
1. Rotational laser cooling of vibrationally and translationally cold molecular ions
DEFF Research Database (Denmark)
Staanum, Peter; Højbjerre, Klaus; Skyt, Peter Sandegaard
2010-01-01
-molecular reactions with coherent light fields 8, 9 , for quantum-state-selected bi-molecular reactions 10, 11, 12 and for astrochemistry 12 . Here, we demonstrate rotational ground-state cooling of vibrationally and translationally cold MgH+ ions, using a laser-cooling scheme based on excitation of a single...... rovibrational transition 13, 14 . A nearly 15-fold increase in the rotational ground-state population of the X 1Σ+ electronic ground-state potential has been obtained. The resulting ground-state population of 36.7±1.2% is equivalent to that of a thermal distribution at about 20 K. The obtained cooling results...
2. Formation of molecular ions by radiative association of cold trapped atoms and ions
CERN Document Server
Silva, Humberto Da; Aymar, Mireille; Dulieu, Olivier
2015-01-01
Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca + , Sr + , Ba +) and Yb + are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to available experiments. Narrow shape resonances are expected, which could be detectable at low temperature with an experimental resolution at the limit of the present standards. Vibrational distributions are also calculated, showing that the final molecular ions are not created in their ground state level.
3. Stick-slip nanofriction in cold-ion traps
Science.gov (United States)
Mandelli, Davide; Vanossi, Andrea; Tosatti, Erio
2013-03-01
Trapped cold ions are known to form linear or planar zigzag chains, helices or clusters depending on trapping conditions. They may be forced to slide over a laser induced corrugated potential, a mimick of sliding friction. We present MD simulations of an incommensurate 101 ions chain sliding subject to an external electric field. As expected with increasing corrugation, we observe the transition from a smooth-sliding, highly lubric regime to a strongly dissipative stick-slip regime. Owing to inhomogeneity the dynamics shows features reminiscent of macroscopic frictional behaviors. While the chain extremities are pinned, the incommensurate central part is initially free to slide. The onset of global sliding is preceded by precursor events consisting of partial slips of chain portions further from the center. We also look for frictional anomalies expected for the chain sliding across the linear-zigzag structural phase transition. Although the chain is too short for a proper critical behavior, the sliding friction displays a frank rise near the transition, due to opening of a new dissipative channel via excitations of transverse modes. Research partly sponsored by Sinergia Project CRSII2 136287/1.
4. Vlasov Analysis of Microbunching Gain for Magnetized Beams
Energy Technology Data Exchange (ETDEWEB)
Tsai, Cheng Ying [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Derbenev, Yaroslav [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Douglas, David R. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Li, Rui [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Tennant, Christopher D. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-10-01
For a high-brightness electron beam with low energy and high bunch charge traversing a recirculation beamline, coherent synchrotron radiation and space charge effect may result in the microbunching instability (MBI). Both tracking simulation and Vlasov analysis for an early design of Circulator Cooler Ring for the Jefferson Lab Electron Ion Collider reveal significant MBI. It is envisioned these could be substantially suppressed by using a magnetized beam. In this work, we extend the existing Vlasov analysis, originally developed for a non-magnetized beam, to the description of transport of a magnetized beam including relevant collective effects. The new formulation will be further employed to confirm prediction of microbunching suppression for a magnetized beam transport in a recirculating machine design.
5. Vlasov simulations of parallel potential drops
Directory of Open Access Journals (Sweden)
H. Gunell
2013-07-01
Full Text Available An auroral flux tube is modelled from the magnetospheric equator to the ionosphere using Vlasov simulations. Starting from an initial state, the evolution of the plasma on the flux tube is followed in time. It is found that when applying a voltage between the ends of the flux tube, about two thirds of the potential drop is concentrated in a thin double layer at approximately one Earth radius altitude. The remaining part is situated in an extended region 1–2 Earth radii above the double layer. Waves on the ion timescale develop above the double layer, and they move toward higher altitude at approximately the ion acoustic speed. These waves are seen both in the electric field and as perturbations of the ion and electron distributions, indicative of an instability. Electrons of magnetospheric origin become trapped between the magnetic mirror and the double layer during its formation. At low altitude, waves on electron timescales appear and are seen to be non-uniformly distributed in space. The temporal evolution of the potential profile and the total voltage affect the double layer altitude, which decreases with an increasing field aligned potential drop. A current–voltage relationship is found by running several simulations with different voltages over the system, and it agrees with the Knight relation reasonably well.
6. Lagrangian formulation of the one-dimensional Vlasov equation. [in plasma physics
Science.gov (United States)
Lewak, G. J.
1974-01-01
A new formulation of the one-dimensional Vlasov equation is derived which is analogous to the Kalman-transformed cold-plasma equations. The equations are shown to yield nonsecular, nonlinear approximations to a source or boundary-value problem. It is suggested that the formulation may have other applications in nonlinear plasma theory.
7. Vlasov on GPU (VOG Project)
CERN Document Server
Mehrenberger, M; Marradi, L; Crouseilles, N; Sonnendrucker, E; Afeyan, B
2013-01-01
This work concerns the numerical simulation of the Vlasov-Poisson set of equations using semi- Lagrangian methods on Graphical Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented. First and foremost, a reformulation of semi-Lagrangian methods is performed, which enables us to rewrite the governing equations as a circulant matrix operating on the vector of unknowns. This product calculation can be performed efficiently using FFT routines. Second, to overcome the limitation of single precision inherent in GPU, a {\\delta}f type method is adopted which only needs refinement in specialized areas of phase space but not throughout. Thus, a GPU Vlasov-Poisson solver can indeed perform high precision simulations (since it uses very high order reconstruction methods and a large number of grid points in phase space). We show results for rather academic test cases on Landau damping and also for physically relevant phenomena such as the bump on tail instability and t...
8. Vlasov-Poisson in 1D: waterbags
CERN Document Server
Colombi, Stéphane
2014-01-01
We revisit in one dimension the waterbag method to solve numerically Vlasov-Poisson equations. In this approach, the phase-space distribution function $f(x,v)$ is initially sampled by an ensemble of patches, the waterbags, where $f$ is assumed to be constant. As a consequence of Liouville theorem it is only needed to follow the evolution of the border of these waterbags, which can be done by employing an orientated, self-adaptive polygon tracing isocontours of $f$. This method, which is entropy conserving in essence, is very accurate and can trace very well non linear instabilities as illustrated by specific examples. As an application of the method, we generate an ensemble of single waterbag simulations with decreasing thickness, to perform a convergence study to the cold case. Our measurements show that the system relaxes to a steady state where the gravitational potential profile is a power-law of slowly varying index $\\beta$, with $\\beta$ close to $3/2$ as found in the literature. However, detailed analys...
9. Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
Directory of Open Access Journals (Sweden)
H Abbasi
2012-12-01
Full Text Available In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.
10. Range of plasma ions in cold cluster gases near the critical point
Energy Technology Data Exchange (ETDEWEB)
Zhang, G. [Cyclotron Institute, Texas A& M University, 77843 College Station, TX (United States); Quevedo, H.J. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States); Bonasera, A., E-mail: [email protected] [Cyclotron Institute, Texas A& M University, 77843 College Station, TX (United States); Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Donovan, M.; Dyer, G.; Gaul, E. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States); Guardo, G.L. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Gulino, M. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Libera Universita' Kore, 94100 Enna (Italy); La Cognata, M.; Lattuada, D. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Palmerini, S. [Department of Physics and Geology, University of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Istituto Nazionale di Fisica Nucleare, Section of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Pizzone, R.G.; Romano, S. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Smith, H. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States); Trippella, O. [Department of Physics and Geology, University of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Istituto Nazionale di Fisica Nucleare, Section of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Anzalone, A.; Spitaleri, C. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Ditmire, T. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States)
2017-05-18
We measure the range of plasma ions in cold cluster gases by using the Petawatt laser at the University of Texas-Austin. The produced plasma propagated in all directions some hitting the cold cluster gas not illuminated by the laser. From the ratio of the measured ion distributions at different angles we can estimate the range of the ions in the cold cluster gas. It is much smaller than estimated using popular models, which take only into account the slowing down of charged particles in uniform matter. We discuss the ion range in systems prepared near a liquid–gas phase transition. - Highlights: • We present experimental results obtained at the UT Petawatt laser facility, Austin, TX. • The ion range is strongly modified for cluster gases as compared to its value in a homogeneous system. • Large fluctuations are found if the cluster gas is prepared near the liquid–gas phase transition region.
11. Stability analysis of cylindrical Vlasov equilibria
Energy Technology Data Exchange (ETDEWEB)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by cylindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma.
12. Superstatistical velocity distributions of cold trapped ions in molecular dynamics simulations
CERN Document Server
Rouse, I
2015-01-01
We present a realistic molecular-dynamics treatment of laser-cooled ions in radiofrequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.
13. Vlasov moments, integrable systems and singular solutions
Energy Technology Data Exchange (ETDEWEB)
Gibbons, John [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: [email protected]; Tronci, Cesare [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); TERA Foundation for Oncological Hadrontherapy, 11 V. Puccini, Novara 28100 (Italy)
2008-02-11
The Vlasov equation governs the evolution of the single-particle probability distribution function (PDF) for a system of particles interacting without dissipation. Its singular solutions correspond to the individual particle motions. The operation of taking the moments of the Vlasov equation is a Poisson map. The resulting Lie-Poisson Hamiltonian dynamics of the Vlasov moments is found to be integrable is several cases. For example, the dynamics for coasting beams in particle accelerators is associated by a hodograph transformation to the known integrable Benney shallow-water equation. After setting the context, the Letter focuses on geodesic Vlasov moment equations. Continuum closures of these equations at two different orders are found to be integrable systems whose singular solutions characterize the geodesic motion of the individual particles.
14. Deterministic delivery of externally cold and precisely positioned single molecular ions
CERN Document Server
Leschhorn, G; Schaetz, T
2011-01-01
We present the preparation and deterministic delivery of a selectable number of externally cold molecular ions. A laser cooled ensemble of Mg^+ ions subsequently confined in several linear Paul traps inter-connected via a quadrupole guide serves as a cold bath for a single or up to a few hundred molecular ions. Sympathetic cooling embeds the molecular ions in the crystalline structure. MgH^+ ions, that serve as a model system for a large variety of other possible molecular ions, are cooled down close to the Doppler limit and are positioned with an accuracy of one micrometer. After the production process, severely compromising the vacuum conditions, the molecular ion is efficiently transfered into nearly background-free environment. The transfer of a molecular ion between different traps as well as the control of the molecular ions in the traps is demonstrated. Schemes, optimized for the transfer of a specific number of ions, are realized and their efficiencies are evaluated. This versatile source applicable f...
15. Decoherence bounds on the capabilities of cold trapped ion quantum computers
Energy Technology Data Exchange (ETDEWEB)
James, D.F.V.; Hughes, R.J.; Knill, E.H. [and others
1997-05-01
Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions of the type recently proposed by Cirac and Zoller. From the limitations imposed on such a device by decoherence due to spontaneous decay, laser phase coherence times, ion heating and other possible sources of error, we derive bounds on the number of laser interactions and on the number of ions that may be used. As a quantitative measure of the possible performance of these devices, the largest number which may be factored using Shors quantum factoring algorithm is determined for a variety of species of ion.
16. Rotational state-changing cold collisions of hydroxyl ions with helium
CERN Document Server
Hauser, Daniel; Carelli, Fabio; Spieler, Steffen; Lakhmanskaya, Olga; Endres, Eric S; Kumar, Sunil S; Gianturco, Franco; Wester, Roland
2015-01-01
Cold molecules are important for many applications, from fundamental precision measurements, quantum information processing, quantum-controlled chemistry, to understanding the cold interstellar medium. Molecular ions are known to be cooled efficiently in sympathetic collisions with cold atoms or ions. However, little knowledge is available on the elementary cooling steps, because the determination of quantum state-to-state collision rates at low temperature is prohibitively challenging for both experiment and theory. Here we present a method to manipulate molecular quantum states by non-resonant photodetachment. Based on this we provide absolute quantum scattering rate coefficients under full quantum state control for the rotationally inelastic collision of hydroxyl anions with helium. Experiment and quantum scattering theory show excellent agreement without adjustable parameters. Very similar rate coefficients are obtained for two different isotopes, which is linked to several quantum scattering resonances a...
17. Kinetic Boltzmann, Vlasov and Related Equations
CERN Document Server
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
18. Achieving translational symmetry in trapped cold ion rings
CERN Document Server
Li, Hao-Kun; Noel, Crystal; Chuang, Alexander; Xia, Yang; Ransford, Anthony; Hemmerling, Boerge; Wang, Yuan; Li, Tongcang; Haeffner, Hartmut; Zhang, Xiang
2016-01-01
Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of crystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual constituents. Periodic boundary conditions, on the other hand, could allow for translational symmetry in small systems where single particle control is achievable. Here, we crystallize up to fifteen 40Ca+ ions in a microscopic ring with inherent periodic boundary conditions. We show the ring's translational symmetry is preserved at millikelvin temperatures by delocalizing the Doppler laser cooled ions. This establishes ...
19. Cold highly charged ions in a cryogenic Paul trap
DEFF Research Database (Denmark)
Versolato, O.O.; Schwarz, M.; Windberger, A.
2013-01-01
17 + . However, lasers pectroscopy of HCIs is hindered by the large (∼ 106 K) temperatures at which they are produced and trapped. An unprecedented improvement in such laser spectroscopy can be obtained when HCIs are cooled down to the mK range in a linear Paul trap. We have developed a cryogenic...... linear Paul trap in which HCIs will be sympathetically cooled by 9Be + ions. Optimized optical access for laser light is provided while maintaining excellent UHV conditions. The Paul trap will be connected to an electron beam ion trap (EBIT) which is able to produce a wide range of HCIs. This EBIT...... will also provide the first experimental input needed for the determination of the transition energies inIr 17+ , enabling further laser-spectroscopic investigations of this promising HCI....
20. Low-energy, high-current, ion source with cold electron emitter
Energy Technology Data Exchange (ETDEWEB)
Vizir, A. V.; Oks, E. M. [High Current Electronics Institute, Russian Academy of Sciences, Tomsk 634055 (Russian Federation); State University of Control Systems and Radioelectronics, Tomsk 634050 (Russian Federation); Shandrikov, M. V.; Yushkov, G. Yu. [High Current Electronics Institute, Russian Academy of Sciences, Tomsk 634055 (Russian Federation)
2012-02-15
An ion source based on a two-stage discharge with electron injection from a cold emitter is presented. The first stage is the emitter itself, and the second stage provides acceleration of injected electrons for gas ionization and formation of ion flow (<20 eV, 5 A dc). The ion accelerating system is gridless; acceleration is accomplished by an electric field in the discharge plasma within an axially symmetric, diverging, magnetic field. The hollow cathode electron emitter utilizes an arc discharge with cathode spots hidden inside the cathode cavity. Selection of the appropriate emitter material provides a very low erosion rate and long lifetime.
1. Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
CERN Document Server
Kuiroukidis, Ap; Tasso, H
2015-01-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
2. Rotational state resolved photodissociation spectroscopy of translationally and vibrationally cold MgH+ ions: toward rotational cooling of molecular ions
DEFF Research Database (Denmark)
Højbjerre, Klaus; Hansen, Anders Kragh; Skyt, Peter Sandegaard
2009-01-01
and vibrationally cold MgH+ ions are presented, with and without the optical pumping laser being present. While rotational cooling is as yet not evident, first results showed evidence of a change in the rotational distribution in the presence of the optical pumping laser.......The first steps toward the implementation of a simple scheme for rotational cooling of MgH+ ions based on rotational state optical pumping is considered. The various aspects of such an experiment are described in detail, and the rotational state-selective dissociation spectra of translationally...
3. Solar Illumination of the Polar Ionosphere and Its Effects on Cold Ion Outflow.
Science.gov (United States)
Maes, L.; Maggiolo, R.; Haaland, S.; Li, K.; Andre, M.; Eriksson, A. I.
2015-12-01
Solar illumination is the most important form of energy driving the outflow of cold ionospheric ions in the polar regions, called the polar wind. Due to the offset of the magnetic poles from the rotation axis and Earth's rotational and orbital motion, the part of the magnetic polar cap being illuminated and the part being in the dark, will vary throughout the day and the seasons. Therefore the outflowing ion flux from the whole polar cap will vary accordingly. Moreover, the offset in the Northern hemisphere is different from the one in the Southern hemisphere. Thus the flux from both polar caps will also be different. With a very simple model we will explore the effects of this on the outflowing flux, which will affect the atmospheric erosion as well as the supply of ionospheric ions to the plasma sheet. In recent observations with the Cluster satellites, the heavier O⁺ ions have been shown to be affected more strongly by solar illumination than H⁺ ions. So this may lead to an alteration of the mass density in the plasma sheet on a periodic basis. This study will also look for signatures of the effects predicted by this model in data of cold ion outflow. The Cluster extensive data set from André et al. [2015] seems best suited for this. It uses the technique detecting the wake formed behind a charged spacecraft in a low density and low energy plasma environment. This technique will generally only observe ions with an energy too low to overcome the spacecraft potential (i.e. ~< 40 eV). The measurements are made in the magnetospheric lobes, up to altitudes of 20 RE, between 2001 and 2010. This long period of observations creates the possibility to study the seasonal variation of cold ion outflow from the polar ionosphere and look for possible differences between both hemispheres.
4. Vlasov analysis of microbunching instability for magnetized beams
Directory of Open Access Journals (Sweden)
C.-Y. Tsai
2017-05-01
Full Text Available For a high-brightness electron beam with high bunch charge traversing a recirculation beam line, coherent synchrotron radiation and space charge effects may result in microbunching instability (MBI. Both tracking simulation and Vlasov analysis for an early design of a circulator cooler ring (CCR for the Jefferson Lab Electron Ion Collider (JLEIC reveal significant MBI [Ya. Derbenev and Y. Zhang, Proceedings of the Workshop on Beam Cooling and Related Topics, COOL’09, Lanzhou, China, 2009 (2009, FRM2MCCO01]. It is envisioned that the MBI could be substantially suppressed by using a magnetized beam. In this paper we have generalized the existing Vlasov analysis, originally developed for a nonmagnetized beam (or transversely uncoupled beam, to the description of transport of a magnetized beam including relevant collective effects. The new formulation is then employed to confirm prediction of microbunching suppression for a magnetized beam transport in the recirculation arc of a recent JLEIC energy recovery linac (ERL based cooler design for electron cooling. It is found that the smearing effect in the longitudinal beam phase space originates from the large transverse beam size as a nature of the magnetized beams and becomes effective through the x-z correlation when the correlated distance is larger than the microbunched scale. As a comparison, MBI analysis of the early design of JLEIC CCR is also presented in this paper.
5. Hydrodynamic limits of the Vlasov equation
Energy Technology Data Exchange (ETDEWEB)
Caprino, S. (Universita' de L' Aquila Coppito (Italy)); Esposito, R.; Marra, R. (Universita' di Roma tor Vergata, Roma (Italy)); Pulvirenti, M. (Universita' di Roma la Sapienza, Roma (Italy))
1993-01-01
In the present work, the authors study the Vlasov equation for repulsive forces in the hydrodynamic regime. For initial distributions at zero temperature the limit equations turn out to be the compressible and incompressible Euler equations under suitable space-time scalings. 17 refs.
6. Irreversible energy flow in forced Vlasov dynamics
KAUST Repository
Plunk, Gabriel G.
2014-10-01
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag. The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.
7. Dynamics of a ground-state cooled ion colliding with ultra-cold atoms
CERN Document Server
Meir, Ziv; Ben-shlomi, Ruti; Akerman, Nitzan; Dallal, Yehonatan; Ozeri, Roee
2016-01-01
Ultra-cold atom-ion mixtures are gaining increasing interest due to their potential applications in quantum chemistry, quantum computing and many-body physics. The polarization potential between atoms and ions scales as 1/r^4 and extends to 100's of nm. This long length-scale interaction can form macroscopic objects while exhibiting quantum features such as Feshbach and shape resonances at sufficiently low temperatures. So far, reaching the quantum regime of atom-ion interaction has been impeded by the ion's excess micromotion (EMM) which sets a scale for the steady-state energy. In this work, we studied the dynamics of a ground-state cooled ion with negligible EMM during few, to many, Langevin (spiraling) collisions with ultra-cold atoms. We measured the energy distribution of the ion using both coherent (Rabi) and non-coherent (photon scattering) spectroscopy. We observed a clear deviation from a Maxwell-Boltzmann thermal distribution to a Tsallis energy distribution characterized by a power-law tail of hig...
8. Cold ion UV photofragmentation spectroscopy and dynamics (Invited)
Energy Technology Data Exchange (ETDEWEB)
Feraud, Geraldine; Dedonder, Claude; Jouvet, Christophe [CNRS, Aix Marseille Université, laboratoire de Physique des Interactions Ioniques et Moléculaires (PIIM) UMR 7345, 13397 Marseille cedex 20 (France); Broquier, Michel [Université Paris Sud, CLUPS (Centre Laser de l' Université Paris Sud) LUMAT FR 2764, 91405 Orsay Cedex, France and CNRS, Université Paris Sud, Institut des Sciences Moléculaires d' Orsay (ISMO) UMR 8624, 91405 Orsay Cedex (France); Gregoire, Gilles [CNRS, Université Paris 13, Sorbonne Paris Cité, Laboratoire de Physique des Lasers, UMR 7538, 93430 Villetaneuse (France); Soorkia, Satchin [CNRS, Université Paris Sud, Institut des Sciences Moléculaires d' Orsay (ISMO) UMR 8624, 91405 Orsay Cedex (France)
2014-12-09
Up to ten years ago, very little was known about the excited states of protonated amino acids isolated in the gas phase. From the experimental point of view, the study was hampered by the lack of ease of production of such species in sufficient density to apply photon-based techniques. With the development and widespread use of electrospray ionization sources coupled with modified or homebuilt mass spectrometers, there has been significant research into the spectroscopy of biomimetic and biologically relevant molecules. Besides, these species are floppy such that an efficient cooling is required to record clear spectroscopy. Warm protonated species display congested spectra. To extract precise spectroscopic information and avoid spectral congestion, the species need to be cooled down to less than 50 K. We present our latest results on the electronic spectroscopy of protonated phenylalanine and tyrosine on a large spectral domain (225-290 nm). These species are studied in a new simplified apparatus combining an electrospray ionization source, a cryogenically cooled quadrupole ion trap (∼10 K) and time-of-flight mass spectrometry. The role of proton transfer from the NH{sub 3}{sup +} moiety to the p-ring or to CO of the carboxylic acid group is evidenced by UV photofragment spectroscopy. This first step controls the fragmentation pathways, which strongly depend on the nature of the electronic excited states, i.e. ππ*, ππ*{sub CO} and πσ{sub NH3}.
9. Cold ion UV photofragmentation spectroscopy and dynamics (Invited)
Science.gov (United States)
Feraud, Geraldine; Broquier, Michel; Dedonder, Claude; Jouvet, Christophe; Gregoire, Gilles; Soorkia, Satchin
2014-12-01
Up to ten years ago, very little was known about the excited states of protonated amino acids isolated in the gas phase. From the experimental point of view, the study was hampered by the lack of ease of production of such species in sufficient density to apply photon-based techniques. With the development and widespread use of electrospray ionization sources coupled with modified or homebuilt mass spectrometers, there has been significant research into the spectroscopy of biomimetic and biologically relevant molecules. Besides, these species are floppy such that an efficient cooling is required to record clear spectroscopy. Warm protonated species display congested spectra. To extract precise spectroscopic information and avoid spectral congestion, the species need to be cooled down to less than 50 K. We present our latest results on the electronic spectroscopy of protonated phenylalanine and tyrosine on a large spectral domain (225-290 nm). These species are studied in a new simplified apparatus combining an electrospray ionization source, a cryogenically cooled quadrupole ion trap (˜10 K) and time-of-flight mass spectrometry. The role of proton transfer from the NH3+ moiety to the p-ring or to CO of the carboxylic acid group is evidenced by UV photofragment spectroscopy. This first step controls the fragmentation pathways, which strongly depend on the nature of the electronic excited states, i.e. ππ*, ππ*CO and πσNH 3.
10. Noxious cold ion channel TRPA1 is activated by pungent compounds and bradykinin.
Science.gov (United States)
Bandell, Michael; Story, Gina M; Hwang, Sun Wook; Viswanath, Veena; Eid, Samer R; Petrus, Matt J; Earley, Taryn J; Patapoutian, Ardem
2004-03-25
Six members of the mammalian transient receptor potential (TRP) ion channels respond to varied temperature thresholds. The natural compounds capsaicin and menthol activate noxious heat-sensitive TRPV1 and cold-sensitive TRPM8, respectively. The burning and cooling perception of capsaicin and menthol demonstrate that these ion channels mediate thermosensation. We show that, in addition to noxious cold, pungent natural compounds present in cinnamon oil, wintergreen oil, clove oil, mustard oil, and ginger all activate TRPA1 (ANKTM1). Bradykinin, an inflammatory peptide acting through its G protein-coupled receptor, also activates TRPA1. We further show that phospholipase C is an important signaling component for TRPA1 activation. Cinnamaldehyde, the most specific TRPA1 activator, excites a subset of sensory neurons highly enriched in cold-sensitive neurons and elicits nociceptive behavior in mice. Collectively, these data demonstrate that TRPA1 activation elicits a painful sensation and provide a potential molecular model for why noxious cold can paradoxically be perceived as burning pain.
11. Stimulated Raman Adiabatic Passage for Improved Performance of a Cold Atom Electron and Ion Source
CERN Document Server
Sparkes, B M; Taylor, R J; Spiers, R W; McCulloch, A J; Scholten, R E
2016-01-01
We experimentally implement high-efficiency coherent excitation to a Rydberg state using stimulated Raman adiabatic passage in a cold atom electron and ion source, leading to a peak efficiency of 85%, a 1.7 times improvement in excitation probability relative to incoherent pulsed-laser excitation. Using streak measurements and pulsed electric field ionization of the Rydberg atoms we demonstrate electron bunches with duration of 250 ps. High-efficiency excitation will increase source brightness, crucial for ultrafast electron diffraction experiments, while using coherent excitation to high-lying Rydberg states could allow for the reduction of internal bunch heating and the creation of a high-speed single ion source.
12. Vlasov simulation in multiple spatial dimensions
CERN Document Server
Rose, Harvey A
2011-01-01
A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010, http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown promising results, in this paper we present an alternative, the Vlasov Multi Dimensional (VMD) model, that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone, as may be the case for stimulated Raman scatter in large optic f# laser beams. Perpendicular grid spacing large compared to a Debye length is then possible without instability, enabling an order 10 decrease in required computational resources compared to standard particle in cell (PIC) methods in 2D, with another reduction of that order in 3D. Fur...
13. Commissioning of the DESIREE storage rings - a new facility for cold ion-ion collisions
Science.gov (United States)
Gatchell, M.; Schmidt, H. T.; Thomas, R. D.; Rosén, S.; Reinhed, P.; Löfgren, P.; Brännholm, L.; Blom, M.; Björkhage, M.; Bäckström, E.; Alexander, J. D.; Leontein, S.; Hanstorp, D.; Zettergren, H.; Liljeby, L.; Källberg, A.; Simonsson, A.; Hellberg, F.; Mannervik, S.; Larsson, M.; Geppert, W. D.; Rensfelt, K. G.; Danared, H.; Paál, A.; Masuda, M.; Halldén, P.; Andler, G.; Stockett, M. H.; Chen, T.; Källersjö, G.; Weimer, J.; Hansen, K.; Hartman, H.; Cederquist, H.
2014-04-01
We report on the ongoing commissioning of the Double ElectroStatic Ion Ring ExpEriment, DESIREE, at Stockholm University. Beams of atomic carbon anions (C-) and smaller carbon anion molecules (C-2, C-3, C-4 etc.) have been produced in a sputter ion source, accelerated to 10 keV or 20 keV, and stored successfully in the two electrostatic rings. The rings are enclosed in a common vacuum chamber cooled to below 13 Kelvin. The DESIREE facility allows for studies of internally relaxed single isolated atomic, molecular and cluster ions and for collision experiments between cat- and anions down to very low center-of-mass collision energies (meV scale). The total thermal load of the vacuum chamber at this temperature is measured to be 32 W. The decay rates of stored ion beams have two components: a non-exponential component caused by the space charge of the beam itself which dominates at early times and an exponential term from the neutralization of the beam in collisions with residual gas at later times. The residual gas limited storage lifetime of carbon anions in the symmetric ring is over seven minutes while the 1/e lifetime in the asymmetric ring is measured to be about 30 seconds. Although we aim to improve the storage in the second ring, the number of stored ions are now sufficient for many merged beams experiments with positive and negative ions requiring milliseconds to seconds ion storage.
14. Mechanosensitive ion channel MscL controls ionic fluxes during cold and heat stress in Synechocystis.
Science.gov (United States)
Bachin, Dmitry; Nazarenko, Lyudmila V; Mironov, Kirill S; Pisareva, Tatiana; Allakhverdiev, Suleyman I; Los, Dmitry A
2015-06-01
Calcium plays an essential role in a variety of stress responses of eukaryotic cells; however, its function in prokaryotes is obscure. Bacterial ion channels that transport Ca(2+) are barely known. We investigated temperature-induced changes in intracellular concentration of Ca(2+), Na(+) and K(+) in the cyanobacterium Synechocystis sp. strain PCC 6803 and its mutant that is defective in mechanosensitive ion channel MscL. Concentration of cations rapidly and transiently increased in wild-type cells in response to cold and heat treatments. These changes in ionic concentrations correlated with the changes in cytoplasmic volume that transiently decreased in response to temperature treatments. However, no increase in ionic concentrations was observed in the MscL-mutant cells. It implies that MscL functions as a non-specific ion channel, and it participates in regulation of cell volume under temperature-stress conditions.
15. Energy and charge dependence of the rate of electron-ion recombination in cold magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Gao, H.; Schuch, R.; Zong, W.; Justiniano, E.; DeWitt, D.R.; Lebius, H.; Spies, W. [Stockholm Univ., Atomic Physics Dept., Stockholm (Sweden)
1997-07-28
We have measured electron-ion recombination rates for bare ions of D{sup +}, He{sup 2+}, N{sup 7+}, Ne{sup 10+} and Si{sup 14+} in a storage ring. For the multi-charged ions an unexpected energy dependence was found, showing a strong increase of the measured rates over the calculated radiative recombination rate for electron beam detuning energies below the electron beam transverse temperature. The measured enhanced rates increase approximately as Z{sup 2.8} with the charge state Z. A comparison of these rates with theoretical predictions for collisional-radiative recombination in the cold magnetized electron plasma, in particular three-body recombination including radiative de-excitation of electrons in Rydberg levels, is made. (author).
16. Rotationally Cold OH^{-} Ions in the Cryogenic Electrostatic Ion-Beam Storage Ring DESIREE.
Science.gov (United States)
Schmidt, H T; Eklund, G; Chartkunchand, K C; Anderson, E K; Kamińska, M; de Ruette, N; Thomas, R D; Kristiansson, M K; Gatchell, M; Reinhed, P; Rosén, S; Simonsson, A; Källberg, A; Löfgren, P; Mannervik, S; Zettergren, H; Cederquist, H
2017-08-18
We apply near-threshold laser photodetachment to characterize the rotational quantum level distribution of OH^{-} ions stored in the cryogenic ion-beam storage ring DESIREE at Stockholm University. We find that the stored ions relax to a rotational temperature of 13.4±0.2 K with 94.9±0.3% of the ions in the rotational ground state. This is consistent with the storage ring temperature of 13.5±0.5 K as measured with eight silicon diodes but in contrast to all earlier studies in cryogenic traps and rings where the rotational temperatures were always much higher than those of the storage devices at their lowest temperatures. Furthermore, we actively modify the rotational distribution through selective photodetachment to produce an OH^{-} beam where 99.1±0.1% of approximately one million stored ions are in the J=0 rotational ground state. We measure the intrinsic lifetime of the J=1 rotational level to be 145±28 s.
17. Rotationally Cold OH- Ions in the Cryogenic Electrostatic Ion-Beam Storage Ring DESIREE
Science.gov (United States)
Schmidt, H. T.; Eklund, G.; Chartkunchand, K. C.; Anderson, E. K.; Kamińska, M.; de Ruette, N.; Thomas, R. D.; Kristiansson, M. K.; Gatchell, M.; Reinhed, P.; Rosén, S.; Simonsson, A.; Källberg, A.; Löfgren, P.; Mannervik, S.; Zettergren, H.; Cederquist, H.
2017-08-01
We apply near-threshold laser photodetachment to characterize the rotational quantum level distribution of OH- ions stored in the cryogenic ion-beam storage ring DESIREE at Stockholm University. We find that the stored ions relax to a rotational temperature of 13.4 ±0.2 K with 94.9 ±0.3 % of the ions in the rotational ground state. This is consistent with the storage ring temperature of 13.5 ±0.5 K as measured with eight silicon diodes but in contrast to all earlier studies in cryogenic traps and rings where the rotational temperatures were always much higher than those of the storage devices at their lowest temperatures. Furthermore, we actively modify the rotational distribution through selective photodetachment to produce an OH- beam where 99.1 ±0.1 % of approximately one million stored ions are in the J =0 rotational ground state. We measure the intrinsic lifetime of the J =1 rotational level to be 145 ±28 s .
18. Preparation of cold Mg{sup +}ion clouds for sympathetic cooling of highly charged ions at SPECTRAP
Energy Technology Data Exchange (ETDEWEB)
2012-02-15
The bound electrons in hydrogen-like or lithium-like heavy ions experience extremely strong electric and magnetic fields in the surrounding of the nucleus. Laser spectroscopy of the ground-state hyperfine splitting in the lead region provides a sensitive tool to test strong-field quantum electro dynamics (QED), especially in the magnetic sector. Previous measurements on hydrogen-like systems performed in an electron-beam ion trap (EBIT) or at the experimental storage ring (ESR) were experimentally limited in accuracy due to statistics, the large Doppler broadening and the ion energy. The full potential of the QED test can only be exploited if measurements for hydrogen- and lithium-like ions are performed with accuracy improved by 2-3 orders of magnitude. Therefore, the new Penning trap setup SPECTRAP - dedicated for laser spectroscopy on trapped and cooled highly charged ions - is currently commissioned at GSI Darmstadt. Heavy highly charged ions will be delivered to this trap by the HITRAP facility in the future. SPECTRAP is a cylindrical Penning trap with axial access for external ion injection and radial optical access mounted inside a cold-bore superconducting Helmholtz-type split-coil magnet. To reach the targeted accuracy in laser spectroscopy, an efficient and fast cooling process for the highly charged ions must be employed. This can be realized by sympathetic cooling with a cloud of laser-cooled light ions. Within this thesis work, a laser system and an ion source for the production of such a {sup 24}Mg{sup +} ion cloud was developed and commissioned at SPECTRAP. An all-solid-state laser system for the generation of 279.6 nm light was designed and built. It consists of a fiber laser at 1118.5 nm followed by frequency quadrupling using two successive second-harmonic generation stages with actively stabilized ring resonators and nonlinear crystals. The laser system can deliver more than 15 mW of UV laser power under optimal conditions and requires little
19. Ionization and fragmentation of cold clusters of PAH molecules - collisions with keV ions
Science.gov (United States)
Holm, A. I. S.; Zettergren, H.; Gatchell, M.; Johansson, H. A. B.; Seitz, F.; Schmidt, H. T.; Rousseau, P.; Ławicki, A.; Capron, M.; Domaracka, A.; Lattouf, E.; Maclot, S.; Maisonny, R.; Chesnel, J.-Y.; Manil, B.; Adoui, L.; Huber, B. A.; Cederquist, H.
2012-11-01
We discuss the ionization and fragmentation of isolated monomers and cold clusters of polycyclic aromatic hydrocarbon (PAH) molecules in collisions with keV ions in low or high charge states. With low charge state projectile ions, PAH cluster or monomer targets are thermally excited through electronic stopping processes directly in close peripheral or penetrating collisions while only single or few electrons are removed. With high charge state projectiles, electrons are very effectively removed from both the cluster and the monomer target already at very large distances with very little direct target heating. Singly charged and internally very hot PAH monomers are dominant fragmentation products following collisions between Xe20+ ions and PAH clusters. We suggest that this due to an unusually strong dominance of multiple-ionization over single ionization for PAH clusters interacting with highly charged ions. Here, charge and excitation energy is very rapidly redistributed within the clusters before they Coulomb explode and we suggest that these Coulomb explosions induce strong internal heating in the individual PAH molecules. We thus conclude that PAH cluster fragmentation always dominates strongly for all ionization processes regardless if these are due to interactions with ions in high or low charge states. These findings are discussed in view of simple models for cluster evaporation or single and multiple ionizations of PAH clusters.
20. Investigation of cold cathodes of plasma sources generating of hydrogen ion beams
CERN Document Server
Veresov, L P; Dzkuya, M I; Zhukov, Y N; Kuznetsov, G V; Tsekvava, I A
2001-01-01
Designs of a hollow cellular cathode (HCC) and of an inverse cylindrical multichamber magnetronic cathode (ICMMC), used as cold cathodes in duoplasmatron for hydrogen ion beam generation, are described. Their service characteristics are compared. It is ascertained that emission ability of both HCC and ICMMC is approximately the same. However, duoplasmatron with ICMMC features a three times higher gas effectiveness compared with HCC. Service life of duoplasmatron with both types of cathodes amounts to several thousand hours. On the basis of test results the choice is made in favour of ICMMC
1. Wave dispersion in the hybrid-Vlasov model: verification of Vlasiator
CERN Document Server
Kempf, Yann; von Alfthan, Sebastian; Vaivads, Andris; Palmroth, Minna; Koskinen, Hannu E J
2013-01-01
Vlasiator is a new hybrid-Vlasov plasma simulation code aimed at simulating the entire magnetosphere of the Earth. The code treats ions (protons) kinetically through Vlasov's equation in the six-dimensional phase space while electrons are a massless charge-neutralizing fluid [M. Palmroth et al., Journal of Atmospheric and Solar-Terrestrial Physics 99, 41 (2013); A. Sandroos et al., Parallel Computing 39, 306 (2013)]. For first global simulations of the magnetosphere, it is critical to verify and validate the model by established methods. Here, as part of the verification of Vlasiator, we characterize the low-\\beta\\ plasma wave modes described by this model and compare with the solution computed by the Waves in Homogeneous, Anisotropic Multicomponent Plasmas (WHAMP) code [K. R\\"onnmark, Kiruna Geophysical Institute Reports 179 (1982)], using dispersion curves and surfaces produced with both programs. The match between the two fundamentally different approaches is excellent in the low-frequency, long wavelength...
2. Comparison of free-streaming ELM formulae to a Vlasov simulation
Energy Technology Data Exchange (ETDEWEB)
Moulton, D., E-mail: [email protected] [CEA, IRFM, F-13108 Saint-Paul Lez Durance (France); Fundamenski, W. [Imperial College of Science, Technology and Medicine, London (United Kingdom); Manfredi, G. [Institut de Physique et Chimie des Matériaux, CNRS and Université de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S. [INRIA Nancy Grand-Est and Institut de Recherche en Mathématiques Avancées, 7 rue René Descartes, F-67084 Strasbourg (France); Tskhakaya, D. [Association EURATOM-ÖAW, University of Innsbruck, A-6020 Innsbruck (Austria)
2013-07-15
The main drawbacks of the original free-streaming equations for edge localised mode transport in the scrape-off layer [W. Fundamenski, R.A. Pitts, Plasma Phys. Control Fusion 48 (2006) 109] are that the plasma potential is not accounted for and that only solutions for ion quantities are considered. In this work, the equations are modified and augmented in order to address these two issues. The new equations are benchmarked against (and justified by) a numerical simulation which solves the Vlasov equation in 1d1v. When the source function due to an edge localised mode is instantaneous, the modified free-streaming ‘impulse response’ equations agree closely with the Vlasov simulation results. When the source has a finite duration in time, the agreement worsens. However, in all cases the match is encouragingly good, thus justifying the applicability of the free-streaming approach.
3. Canonical derivation of the Vlasov-Coulomb noncanonical Poisson structure
Energy Technology Data Exchange (ETDEWEB)
Kaufman, A.N.; Dewar, R.L.
1983-09-01
Starting from a Lagrangian formulation of the Vlasov-Coulomb system, canonical methods are used to define a Poisson structure for this system. Successive changes of representation then lead systematically to the noncanonical Lie-Poisson structure for functionals of the Vlasov distribution.
4. Preparation of Schr\\"odinger cat states with cold ions in a cavity beyond the Lamb-Dicke limit
CERN Document Server
Freitas, Dagoberto S
2010-01-01
We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity. We have used an approach for preparing the SC states of motion of ion. This approach, based on unitary transformating the Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke aproximation. We show that is possible to generate a SC states having rather simple initial state preparation, e.g., the vacuum sate for both cavity field and the ion motion.
5. Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas
OpenAIRE
S. D. Bergeson; Lyon, M
2016-01-01
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, ...
6. Stimulated Raman adiabatic passage for improved performance of a cold-atom electron and ion source
Science.gov (United States)
Sparkes, B. M.; Murphy, D.; Taylor, R. J.; Speirs, R. W.; McCulloch, A. J.; Scholten, R. E.
2016-08-01
We implement high-efficiency coherent excitation to a Rydberg state using stimulated Raman adiabatic passage in a cold-atom electron and ion source. We achieve an efficiency of 60% averaged over the laser excitation volume with a peak efficiency of 82%, a 1.6 times improvement relative to incoherent pulsed-laser excitation. Using pulsed electric field ionization of the Rydberg atoms we create electron bunches with durations of 250 ps. High-efficiency excitation will increase source brightness, crucial for ultrafast electron diffraction experiments, and coherent excitation to high-lying Rydberg states could allow for the reduction of internal bunch heating and the creation of a high-speed single-ion source.
7. Diamond-Like Carbon Film Deposition Using DC Ion Source with Cold Hollow Cathode
Directory of Open Access Journals (Sweden)
E. F. Shevchenko
2014-01-01
Full Text Available Carbon diamond-like thin films on a silicon substrate were deposited by direct reactive ion beam method with an ion source based on Penning direct-current discharge system with cold hollow cathode. Deposition was performed under various conditions. The pressure (12–200 mPa and the plasma-forming gas composition consisting of different organic compounds and hydrogen (C3H8, CH4, Si(CH32Cl2, H2, the voltage of accelerating gap in the range 0.5–5 kV, and the substrate temperature in the range 20–850°C were varied. Synthesized films were researched using nanoindentation, Raman, and FTIR spectroscopy methods. Analysis of the experimental results was made in accordance with a developed model describing processes of growth of the amorphous and crystalline carbon materials.
8. Spin-orbit interactions and quantum spin dynamics in cold ion-atom collisions
CERN Document Server
Tscherbul, Timur V; Buchachenko, Alexei A
2015-01-01
We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb$^+$-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-oder spin-orbit (SO) interaction as the dominant source of hyperfine relaxation and decoherence in cold Yb$^+$-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb$^+$ immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than predicted by the Langevin capture theory and display a weak $T^{-0.3}$ temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb$^+$-Li should be used to minimize hyperfine relaxation and dec...
9. UV and IR spectroscopy of cold 1,2-dimethoxybenzene complexes with alkali metal ions.
Science.gov (United States)
Inokuchi, Yoshiya; Boyarkin, Oleg V; Ebata, Takayuki; Rizzo, Thomas R
2012-04-01
We report UV photodissociation (UVPD) and IR-UV double-resonance spectra of 1,2-dimethoxybenzene (DMB) complexes with alkali metal ions, M(+)·DMB (M = Li, Na, K, Rb, and Cs), in a cold, 22-pole ion trap. The UVPD spectrum of the Li(+) complex shows a strong origin band. For the K(+)·DMB, Rb(+)·DMB, and Cs(+)·DMB complexes, the origin band is very weak and low-frequency progressions are much more extensive than that of the Li(+) ion. In the case of the Na(+)·DMB complex, spectral features are similar to those of the K(+), Rb(+), and Cs(+) complexes, but vibronic bands are not resolved. Geometry optimization with density functional theory indicates that the metal ions are bonded to the oxygen atoms in all the M(+)·DMB complexes. For the Li(+) complex in the S(0) state, the Li(+) ion is located in the same plane as the benzene ring, while the Na(+), K(+), Rb(+), and Cs(+) ions are located off the plane. In the S(1) state, the Li(+) complex has a structure similar to that in the S(0) state, providing the strong origin band in the UV spectrum. In contrast, the other complexes show a large structural change in the out-of-plane direction upon S(1)-S(0) excitation, which results in the extensive low-frequency progressions in the UVPD spectra. For the Na(+)·DMB complex, fast charge transfer occurs from Na(+) to DMB after the UV excitation, making the bandwidth of the UVPD spectrum much broader than that of the other complexes and producing the photofragment DMB(+) ion.
10. Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket
Energy Technology Data Exchange (ETDEWEB)
Gibbons, John [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Tronci, Cesare [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); TERA Foundation for Oncological Hadrontherapy, 11 V. Puccini, Novara 28100 (Italy)], E-mail: [email protected]
2008-06-02
The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are also shown to define a momentum map, which is infinitesimally equivariant. This momentum map is the dual of a Lie algebra homomorphism, defined through the Schouten bracket. Finally the moment Lie-Poisson bracket is extended to anisotropic interactions.
11. Numerical simulation of Vlasov equation with parallel tools; Simulations numeriques de l'equation de Vlasov a l'aide d'outils paralleles
Energy Technology Data Exchange (ETDEWEB)
Peyroux, J
2005-11-15
This project aims to make even more powerful the resolution of Vlasov codes through the various parallelization tools (MPI, OpenMP...). A simplified test case served as a base for constructing the parallel codes for obtaining a data-processing skeleton which, thereafter, could be re-used for increasingly complex models (more than four variables of phase space). This will thus make it possible to treat more realistic situations linked, for example, to the injection of ultra short and ultra intense impulses in inertial fusion plasmas, or the study of the instability of trapped ions now taken as being responsible for the generation of turbulence in tokamak plasmas. (author)
12. Equations of motion of test particles for solving the spin-dependent Boltzmann-Vlasov equation
CERN Document Server
Xia, Yin; Li, Bao-An; Shen, Wen-Qing
2016-01-01
A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann-Vlasov equation is presented. Though the obtained EOMs are general, they are particularly useful in simulating nucleon spinor transport in heavy-ion collisions at intermediate energies. It is shown that the nucleon transverse flow in heavy-ion collisions especially those involving polarized projectile and/or target nuclei depends strongly on the spin-orbit coupling. Future comparisons of model simulations with experimental data will help constrain the poorly known in-medium nucleon spin-orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.
13. Transient Growth in a Magnetized Vlasov Plasma
Science.gov (United States)
Ratushnaya, Valeria; Samtaney, Ravi
2015-11-01
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many tokamak instabilities, however, is still an open problem. Aiming to gain a better insight into this question, we investigate the stability properties of a collisionless Vlasov plasma for the case of: (a) stationary homogeneous magnetic field, and (b) weakly non-stationary and non-homogeneous magnetic field. We narrow the scope of our investigation to the case of a Maxwellian plasma and examine its evolution with an electrostatic approximation. We show that the linearized Vlasov operator is non-normal, which leads to an algebraic growth of perturbations in a magnetized plasma followed by exponential decay, i.e., classical Landau damping behaviour. This is a so-called transient growth phenomenon, developed in the framework of non-modal stability theory in the context of hydrodynamics. In a homogeneous magnetic field the typical time scales of the transient growth are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the initial conditions is studied. Supported by baseline research funds at KAUST.
14. Osmotic versus adrenergic control of ion transport by ionocytes of Fundulus heteroclitus in the cold
DEFF Research Database (Denmark)
Tait, Janet C; Mercer, Evan W; Gerber, Lucie;
2017-01-01
In eurythermic vertebrates, acclimation to the cold may produce changes in physiological control systems. We hypothesize that relatively direct osmosensitive control will operate better than adrenergic receptor mediated control of ion transport in cold vs. warm conditions. Fish were acclimated...... to full strength seawater (SW) at 21°C and 5°C for four weeks, gill samples and blood were taken and opercular epithelia mounted in Ussing style chambers. Short-circuit current Isc at 21°C and 5°C (measured at acclimation temperature), was significantly inhibited by the α2-adrenergic agonist clonidine...... inhibition of Isc, was higher in warm acclimated (-95%), compared to cold acclimated fish (-75%), while hypertonic stimulations were the same, indicating equal responsiveness to hyperosmotic stimuli. Plasma osmolality was significantly elevated in cold acclimated fish and, by TEM, gill ionocytes from cold...
15. Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
CERN Document Server
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
16. Rotation of cold molecular ions inside a Bose-Einstein condensate
CERN Document Server
Midya, Bikashkali; Schmidt, Richard; Lemeshko, Mikhail
2016-01-01
We use recently developed angulon theory [Phys. Rev. Lett. 114, 203001 (2015)] to study the rotational spectrum of a cyanide molecular anion immersed into Bose-Einstein condensates of rubidium and strontium. Based on $\\textit {ab initio}$ potential energy surfaces, we provide a detailed study of the rotational Lamb shift and many-body-induced fine structure which arise due to dressing of molecular rotation by a field of phonon excitations. We demonstrate that the magnitude of these effects is large enough in order to be observed in modern experiments on cold molecular ions. Furthermore, we introduce a novel method to construct pseudopotentials starting from the $\\textit {ab initio}$ potential energy surfaces, which provides a means to obtain effective coupling constants for low-energy polaron models.
17. Suppression of Emittance Growth Using a Shaped Cold Atom Electron and Ion Source
Science.gov (United States)
Thompson, D. J.; Murphy, D.; Speirs, R. W.; van Bijnen, R. M. W.; McCulloch, A. J.; Scholten, R. E.; Sparkes, B. M.
2016-11-01
We demonstrate precise control of charged particle bunch shape with a cold atom electron and ion source to create bunches with linear and, therefore, reversible Coulomb expansion. Using ultracold charged particles enables detailed observation of space-charge effects without loss of information from thermal diffusion, unambiguously demonstrating that shaping in three dimensions can result in a marked reduction of Coulomb-driven emittance growth. We show that the emittance growth suppression is accompanied by an increase in bunch focusability and brightness, improvements necessary for the development of sources capable of coherent single-shot ultrafast electron diffraction of noncrystalline objects, with applications ranging from femtosecond chemistry to materials science and rational drug design.
18. Bifurcation of BGK waves in a plasma of cold ions and electrons
Energy Technology Data Exchange (ETDEWEB)
Hannibal, L.; Rebhan, E.; Kielhorn, C. (Duesseldorf Univ. (Germany). Inst. fuer Theoretische Physik)
1994-08-01
For the simple model of cold electrons streaming against cold ions the complete set of nonlinear stationary waves is expressed in terms of elliptic functions. The conditions for their dynamical connection to a uniform neutral plasma state are taken into account, and the conditions for the neglect of the magnetic field are analysed. The range of existence of stationary waves is found to be confined to the stable regime of the two-stream instability, but covers only part of it. All nonlinear BGK waves that are found within the limits of the model can be shown to bifurcate from the two-stream instability, some of them also exhibiting secondary and further bifurcations. As an exceptional case, all bifurcations can be treated exactly. Close to the linear regime, all nonlinear modes turn out to be unstable. The corresponding instability is caused by a wave decay that transports energy from low to high wavenumbers of the Fourier modes constituting the wave. From the two-stream solutions four-stream solutions with exactly vanishing magnetic field are derived. (author).
19. Nonlinear dynamics of cold magnetized non-relativistic plasma in the presence of electron-ion collisions
Energy Technology Data Exchange (ETDEWEB)
Sahu, Biswajit, E-mail: [email protected] [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India); Sinha, Anjana, E-mail: [email protected] [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Roychoudhury, Rajkumar, E-mail: [email protected] [Department of Mathematics, Visva-Bharati, Santiniketan - 731 204, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700 075 (India)
2015-09-15
A numerical study is presented of the nonlinear dynamics of a magnetized, cold, non-relativistic plasma, in the presence of electron-ion collisions. The ions are considered to be immobile while the electrons move with non-relativistic velocities. The primary interest is to study the effects of the collision parameter, external magnetic field strength, and the initial electromagnetic polarization on the evolution of the plasma system.
20. One-dimensional Vlasov-Maxwell equilibria
Science.gov (United States)
Greene, John M.
1993-06-01
The purpose of this paper is to show that the Vlasov equilibrium of a plasma of charged particles in an electromagnetic field is closely related to a fluid equilibrium, where only a few moments of the velocity distribution of the plasma are considered. In this fluid equilibrium the electric field should be calculated from Ohm's law, rather than the Poisson equation. In practice, only one-dimensional equilibria are treated, because the symmetry makes this case tractable. The emphasis here is on gaining a better understanding of the subject, but an alternate way of doing the calculations is suggested. It is shown that particle distributions can be found that are consistent with any reasonable electromagnetic field profile.
1. Entropy production in coarse grained Vlasov equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), LPC-ISMRA, 14 - Caen (France); Walke, R. [Rostock Univ., Fachbereich Physick (Germany)
2000-07-01
The Vlasov equation is analyzed for coarse grained distributions. This coarse graining resembles a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the Vlasov equation, but with additional terms. These terms give rise to entropy production indicating dissipative features. The reason is a nonlinear mode coupling due to the finite width of the test-particles. The interchange of coarse graining and dynamical evolution is discussed with the help of an exactly solvable model and practical consequences are worked out. By calculating analytically the stationary solution we can show that a sum of modified Boltzmann-like distributions is approached dependent on the initial distribution. This behavior is independent of degeneracy and only controlled by the width of test-particles. The condition for approaching a stationary solution is derived in that the coarse graining energy given by momentum coarse graining should be smaller than a quarter of the kinetic energy. Observable consequences of this coarse graining are: (i) In the thermodynamics the coarse graining leads to spatial correlations in observables. (ii) Too large radii of nucleus in self-consistent treatments are observed and an explicit correction term appears in the Thomas Fermi equation. (iii) The momentum coarse graining translates into a structure term in the response function and resembles to a certain extent vertex correction correlations or internal structure effects. (iv) The coarse graining which is numerically unavoidable leads to a modified centroid energy and higher damping width of collective modes. The numerical codes should be revised in that a refolding is proposed. (author)
2. Diffusive Transport Particle Simulations of Cold and Hot Ions Under Northward Interplanetary Magnetic Field
Science.gov (United States)
Mata, W.; Wang, C.; Lemon, C. L.; Lyons, L. R.
2013-12-01
The main difference seen in the plasma sheet between northward interplanetary magnetic field (NIMF) and southward interplanetary magnetic field (SIMF) intervals is that the plasma sheet is colder and denser during NIMF [e.g., Terasawa et al., 1997]. The basic processes responsible for these changes in the plasma sheet during NIMF and SIMF are not fully understood. The plasma sheet densities increase gradually following a northward turning of the IMF [Wing et al., 2005], and the density change is associated with a < ~1 keV cold population near the flanks. Observations also show a large variation in density across the tail with higher densities near the flanks than at midnight [e.g., Wing and Newell.,2002; Wang et al., 2006], which suggests that there are transport processes that allow the cold particles access to the midnight sector from the flanks. It has been proposed [e.g., Terasawa et al., 1997; Antonova, 2006] that diffusion may transport cold particles from the flanks deep into the plasma sheet. Diffusive particle transport results from fluctuations in the plasma sheet flow in the presence of a spatial gradient in the particle number. In this study we add electric and magnetic field perturbations to the background Tsyganenko 2001 (T01) magnetic field and Weimer 2000 electric potential with the superposition of different waves to determine whether diffusive transport can account for the gradual cooling and densification of the plasma sheet during NIMF. We follow the guiding center drift and full particle drift, where appropriate, of over 20,000 protons with arbitrary pitch angles and energies from 32 eV-30 keV in the simulation region from X = -10 to -50 and |Y| < 20 RE .We then obtain particle distributions by mapping the phase space densities to realistic source distributions based on THEMIS and Geotail observations and compute the resulting plasma moments. We investigate if diffusion can transport colder ions more efficiently than the hotter ions from the
3. Positron-acoustic shock waves associated with cold viscous positron fluid in superthermal electron-positron-ion plasmas
Energy Technology Data Exchange (ETDEWEB)
Uddin, M. J., E-mail: [email protected]; Alam, M. S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka 1342 (Bangladesh)
2015-06-15
A theoretical investigation is made on the positron-acoustic (PA) shock waves (SHWs) in an unmagnetized electron-positron-ion plasma containing immobile positive ions, cold mobile positrons, and hot positrons and electrons following the kappa (κ) distribution. The cold positron kinematic viscosity is taken into account, and the reductive perturbation method is used to derive the Burgers equation. It is found that the viscous force acting on cold mobile positron fluid is a source of dissipation and is responsible for the formation of the PA SHWs. It is also observed that the fundamental properties of the PA SHWs are significantly modified by the effects of different parameters associated with superthermal (κ distributed) hot positrons and electrons.
4. Vlasov-Fokker-Planck modeling of magnetized plasma
Energy Technology Data Exchange (ETDEWEB)
Thomas, Alexander [Univ. of Michigan, Ann Arbor, MI (United States)
2016-08-01
Understanding the magnetic fields that can develop in high-power-laser interactions with solid-density plasma is important because such fields significantly modify both the magnitude and direction of electron heat fluxes. The dynamics of such fields evidently have consequences for inertial fusion energy applications, as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion and potentially the success of, for example, the National Ignition Facility. To study these effects, we used the code Impacta, a two-dimensional, fully implicit, Vlasov-Fokker-Planck code with self-consistent magnetic fields and a hydrodynamic ion model, designed for nanosecond time-scale laser-plasma interactions. Heat-flux effects in Ohm’s law under non-local conditions was investigated; physics that is not well captured by standard numerical models but is nevertheless important in fusion-related scenarios. Under such conditions there are numerous interesting physical effects, such as collisional magnetic instabilities, amplification of magnetic fields, re-emergence of non-locality through magnetic convection, and reconnection of magnetic field lines and redistribution of thermal energy. In this project highlights included the first full scale kinetic simulations of a magnetized hohlraum [Joglekar 2016] and the discovery of a new magnetic reconnection mechanism [Joglekar 2014] as well as a completed PhD thesis and the production of a new code for Inertial Fusion research.
5. Convergence analysis of Strang splitting for Vlasov-type equations
CERN Document Server
Einkemmer, Lukas
2012-01-01
A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step h. As an example, it is verified that the Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this analysis. Also, numerical experiments for the latter case are presented.
6. The Hamiltonian Structure of the Maxwell-Vlasov Equations.
Science.gov (United States)
1981-02-01
principle of Percival [1979). 4. By using an appropriate Darboux theorem, (see Marsden [1981], lecture 1), one can show that Of admits canonically...get the Vlasov-Poisson equation. It would also be of interest to realize both the Vlasov-Maxwell and MHD equations as limiting cases of a grand...de Vries equation, Springer Lecture Notes, #755, 1-15 and Inv. Math. 50, 219-248. J. Arms (1979]. Linearization stability of gravitational and gauge
7. Explicit Solutions of the One-dimensional Vlasov-Poisson System with Infinite Mass and Energy
CERN Document Server
Pankavich, Stephen
2010-01-01
A collisionless plasma is modeled by the Vlasov-Poisson system in one-dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as x tends to positive or negative infinity. Thus, the total positive charge and the total negative charge are infinite. In this paper, the charge density of the system is shown to be compactly supported. More importantly, both the electric field and the number density are determined explicitly for large values of x.
8. Charge breeding investigation in EBIS/T and collision study of ions with cold atoms for HITRAP
Energy Technology Data Exchange (ETDEWEB)
Sokolov, Alexey
2010-01-29
Highly charged ions (HCI) at low velocities or at rest are interesting systems for various atomic physics experiments. For investigations on HCI of heavy stable or radioactive nuclides the HITRAP (Highly charged Ion TRAP) decelerator facility has been set up at GSI to deliver cooled beams of HCI at an energy of 5 keV/q. The HCI are produced in a stripper foil at relativistic energies and are decelerated in several steps at ESR storage ring and HITRAP before they are delivered to experimental setups. One of the experiments is the investigation of multi-electron charge exchange in collisions of heavy HCI with cold atoms using novel MOTRIMS technique. Collision experiments on light ions from an ECR ion source colliding with cold atoms in a MOT have been performed and the results are described. An electron beam ion trap (EBIT) has been tested and optimized for commissioning of the HITRAP physics experiments. The process of charge breeding in the EBIT has been successfully studied with gaseous elements and with an alkaline element injected from an external ion source. (orig.)
9. Integer lattice dynamics for Vlasov-Poisson
Science.gov (United States)
Mocz, Philip; Succi, Sauro
2017-03-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving-mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.
10. Integer Lattice Dynamics for Vlasov-Poisson
CERN Document Server
Mocz, Philip
2016-01-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, ...
11. NEW INSIGHT INTO SHORT-WAVELENGTH SOLAR WIND FLUCTUATIONS FROM VLASOV THEORY
Energy Technology Data Exchange (ETDEWEB)
Sahraoui, F.; Belmont, G. [Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique-UPMC, Observatoire de Saint-Maur, 4 avenue de Neptune, 94107 Saint-Maur-des-Fosses (France); Goldstein, M. L., E-mail: [email protected] [NASA Goddard Space Flight Center, Code 673, Greenbelt, MD 20771 (United States)
2012-04-01
The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with {omega} < {omega}{sub ci}, other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode (i.e., {omega} > {omega}{sub ci}) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, typically {beta}{sub i} {approx}> {beta}{sub e} {approx} 1 and for high oblique angles of propagation 80 Degree-Sign {<=} {Theta}{sub kB} < 90 Degree-Sign as observed from the Cluster spacecraft data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation ({Theta}{sub kB} < 80 Degree-Sign ). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales k{rho}{sub i} {approx}> 1 to frequencies either larger or smaller than {omega}{sub ci}, depending on the anisotropy k{sub ||}/k . This extension into small scales is more readily called whistler ({omega} > {omega}{sub ci}) or KAW ({omega} < {omega}{sub ci}), although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings
12. Oblique propagation of solitary electrostatic waves in magnetized plasmas with cold ions and nonthermal electrons
Science.gov (United States)
Verheest, Frank; Hellberg, Manfred A.
2017-02-01
Oblique propagation of large amplitude electrostatic waves and solitary structures is investigated in magnetized plasmas, comprising cold fluid ions and Cairns nonthermally distributed electrons, by using a Sagdeev pseudopotential formalism. To perform the analysis, quasineutrality is assumed, so that in normalized variables the electrostatic potential and the occurrence of solitary structures are governed by three parameters: the Mach number M, the typical Cairns parameter β, and the angle ϑ between the directions of propagation and the static magnetic field. Below a critical β, only positive compressive solitons are possible, and their amplitudes increase with increasing β, M, and ϑ. Above the critical β, there is coexistence between negative rarefactive and positive compressive solitons, and the range of negative solitons, at increasing M, ends upon encountering a double layer or a singularity. The double layer amplitudes (in absolute value) increase with β but are independent of ϑ. Roots of the Sagdeev pseudopotential beyond the double layer are not accessible from the undisturbed conditions, because of an intervening singularity where the pseudopotential becomes infinite. Recent claims of finding supersolitons beyond a double layer appear to be based on a misinterpretation of the nature of the singularity.
13. Vlasov modelling of parallel transport in a tokamak scrape-off layer
Energy Technology Data Exchange (ETDEWEB)
Manfredi, G [Institut de Physique et Chimie des Materiaux, CNRS and Universite de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S [INRIA Nancy Grand-Est and Institut de Recherche en Mathematiques Avancees, 7 rue Rene Descartes, F-67084 Strasbourg (France); Devaux, S, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB (United Kingdom)
2011-01-15
A one-dimensional Vlasov-Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed 'asymptotic-preserving' numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.
14. Simple Approach to the Solution of a Trapped and Radiated Cold Ion Beyond the Lamb-Dicke Limit
Institute of Scientific and Technical Information of China (English)
FENG Mang; SHI Lei; GAO Ke-Lin; ZHU Xi-Wen
2002-01-01
Trapping ions outside the Lamb-Dicke limit have been proven to be useful for the laser-cooling and quantum computing.Under the supposition of the Rabi frequency much smaller than the Lamb Dicke parameter,we can use a simple method to analytically solve the system with a single cold ion trapped and radiated beyond the Lamb Dickc limit,in the absence of the rotating-wave approximation (RWA).Discussion has been made for the limitation of our approach and the comparison of our results with the solutions under the RWA.
15. The Einstein-Vlasov System/Kinetic Theory
Directory of Open Access Journals (Sweden)
Håkan Andréasson
2011-05-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
16. Preparation of cold ions in strong magnetic field and its application to gas-phase NMR spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Fuke, K., E-mail: [email protected] [Institute for Molecular Science (Japan); Ohshima, Y. [Tokyo Institute of Technology, Department of Chemistry (Japan); Tona, M. [Ayabo Co. Fukukama (Japan)
2015-11-15
Nuclear Magnetic Resonance (NMR) technique is widely used as a powerful tool to study the physical and chemical properties of materials. However, this technique is limited to the materials in condensed phases. To extend this technique to the gas-phase molecular ions, we are developing a gas-phase NMR apparatus. In this note, we describe the basic principle of the NMR detection for molecular ions in the gas phase based on a Stern-Gerlach type experiment in a Penning trap and outline the apparatus under development. We also present the experimental procedures and the results on the formation and the manipulation of cold ions under a strong magnetic field, which are the key techniques to detect the NMR by the present method.
17. Preparation of cold ions in strong magnetic field and its application to gas-phase NMR spectroscopy
Science.gov (United States)
Fuke, K.; Ohshima, Y.; Tona, M.
2015-11-01
Nuclear Magnetic Resonance (NMR) technique is widely used as a powerful tool to study the physical and chemical properties of materials. However, this technique is limited to the materials in condensed phases. To extend this technique to the gas-phase molecular ions, we are developing a gas-phase NMR apparatus. In this note, we describe the basic principle of the NMR detection for molecular ions in the gas phase based on a Stern-Gerlach type experiment in a Penning trap and outline the apparatus under development. We also present the experimental procedures and the results on the formation and the manipulation of cold ions under a strong magnetic field, which are the key techniques to detect the NMR by the present method.
18. Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas
Science.gov (United States)
Bergeson, Scott; Lyon, Mary
2016-05-01
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, and significant differences are observed. We discuss the conditions for blockaded Rydberg excitation and the subsequent spatial ordering of Rydberg atom domains. While the blockade interaction is greater than the Rabi frequency in portions of the atomic sample, no evidence for spatial ordering is observed. This research is supported in part by the Air Force Office of Scientific Research (Grant No. FA9950-12- 0308) and by the National Science Foundation (Grant No. PHY-1404488).
19. Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas
CERN Document Server
Bergeson, S D
2016-01-01
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, and significant differences are observed. We discuss the conditions for blockaded Rydberg excitation and the subsequent spatial ordering of Rydberg atom domains. While the blockade interaction is greater than the Rabi frequency in portions of the atomic sample, no evidence for spatial ordering is observed.
20. Rapid cold hardening improves recovery of ion homeostasis and chill coma recovery time in the migratory locust, Locusta migratoria.
Science.gov (United States)
Findsen, Anders; Andersen, Jonas Lembcke; Calderon, Sofia; Overgaard, Johannes
2013-05-01
Chill tolerance of insects is defined as the ability to tolerate low temperature under circumstances not involving freezing of intracellular or extracellular fluids. For many insects chill tolerance is crucial for their ability to persist in cold environments and mounting evidence indicates that chill tolerance is associated with the ability to maintain ion and water homeostasis, thereby ensuring muscular function and preventing chill injury at low temperature. The present study describes the relationship between muscle and haemolymph ion homeostasis and time to regain posture following cold shock (CS, 2 h at -4°C) in the chill-susceptible locust Locusta migratoria. This relationship was examined in animals with and without a prior rapid cold-hardening treatment (RCH, 2 h at 0°C) to investigate the physiological underpinnings of RCH. CS elicited a doubling of haemolymph [K(+)] and this disturbance was greater in locusts pre-exposed to RCH. Recovery of ion homeostasis was, however, markedly faster in RCH-treated animals, which correlated well with whole-organism performance as hardened individuals regained posture faster than non-hardened individuals following CS. The present study indicates that loss and recovery of muscular function are associated with the resting membrane potential of excitable membranes as attested by the changes in the equilibrium potential for K(+) (EK) following CS. Both hardened and non-hardened animals regained movement once K(+) homeostasis had recovered to a fixed level (EK≈-41 mV). RCH is therefore not associated with altered sensitivity to ion disturbance but instead is correlated to a faster recovery of haemolymph [K(+)].
1. From the Hartree dynamics to the Vlasov equation
DEFF Research Database (Denmark)
Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara;
2016-01-01
We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...... bounds on the 0rate of convergence....
2. On global solutions for the Vlasov-Poisson system
Directory of Open Access Journals (Sweden)
Peter E. Zhidkov
2004-04-01
Full Text Available In this article we show that the Vlasov-Poisson system has a unique weak solution in the space $L_1cap L_infty$. For this purpose, we use the method of characteristics, unlike the approach in [12].
3. The Einstein-Vlasov System/Kinetic Theory
Directory of Open Access Journals (Sweden)
Andréasson Håkan
2005-01-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einsteins equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.
4. A new explanation to the cold nuclear matter effects in heavy ion collisions
CERN Document Server
Liu, Zhi-Feng
2014-01-01
The J/Psi cross section ratios of p-A/p-p under different collision energy is calculated with cold nuclear matter effects redefined in this paper. The advantage of these new definitions is that all cold nuclear matter effects have clear physical origins.The radios are compared with the corresponding experiment data and that calculated with classic nuclear effects. The ratios calculated with new definitions can reproduce almost all existing J/Psi measurements in p-A collisions more accuratly than that calculated with classic nuclear effects. Hence, this paper presents a new approach to explain cold nuclear effects in the hardproduction of quarkonium.
5. MICRO-MOTION EFFECT OF A TRAPPED ULTRA-COLD ION IN A STANDING-WAVE LASER
Institute of Scientific and Technical Information of China (English)
JIANG YU-RONG; FENG MANG; GAO KE-LIN; ZHU XI-WEN
2001-01-01
In the absence of the requirements of the Lamb-Dicke limit and rotating wave approximation, we semi-classically investigate the dynamics of a trapped ultra-cold ion in the standing-wave laser, with the consideration of the time- dependent potential and pseudo-potential of the Paul trap. The specific calculations show that the larger the Lamb-Dicke parameter η and the Rabi frequency Ω, the greater the difference between the dynamics in the time-dependent potential and the pseudo-potential.
6. Exact nonlinear analytic Vlasov-Maxwell tangential equilibria with arbitrary density and temperature profiles
CERN Document Server
Mottez, F
2003-01-01
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell-Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.
7. Landau damping of Gardner solitons in a dusty bi-ion plasma
CERN Document Server
Misra, A P
2015-01-01
The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids {\\bf 12}, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV) or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures $(\\sigma)$ and the number densities $(\\mu)$ of hot and cold ions as well the cold to hot ion mass ratio $m$. The distinctive features of the decay rates of the ampl...
8. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Science.gov (United States)
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
9. Linear Vlasov analysis for stability of a bunched beam
Energy Technology Data Exchange (ETDEWEB)
Warnock, Robert; Stupakov, Gennady; Venturini, Marco; Ellison, James A.
2004-06-30
We study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. We rephrase the equation so that it becomes non-singular in the sense of operator theory, and has only regular solutions for coherent modes. We report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
10. Linear Vlasov Analysis for Stability of a Bunched Beam
Energy Technology Data Exchange (ETDEWEB)
Warnock, R
2004-08-12
The authors study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. The authors rephrase the equation so that it becomes non-singular in the sense of operatory theory, and has only regular solutions for coherent modes. They report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
11. Block-Structured Adaptive Mesh Refinement Algorithms for Vlasov Simulation
CERN Document Server
Hittinger, J A F
2012-01-01
Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with dimension. We propose to use high-order finite-volume techniques with block-structured adaptive mesh refinement (AMR) to reduce the computational cost. The primary complication comes from a solution state comprised of variables of different dimensions. We develop the algorithms required to extend standard single-dimension block structured AMR to the multi-dimension case. Specifically, algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail. In addition, modifications to the basic AMR algorithm that enable the use of high-order spatial and temporal discretizations are discussed. Preliminary results for a standard 1D+1V Vlasov-Poisson test problem are presented. Results indicate that there is po...
12. Variational formulations of guiding-center Vlasov-Maxwell theory
Science.gov (United States)
Brizard, Alain J.; Tronci, Cesare
2016-06-01
The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.
13. Coupled Vlasov and two-fluid codes on GPUs
CERN Document Server
Rieke, M; Grauer, R
2014-01-01
We present a way to combine Vlasov and two-fluid codes for the simulation of a collisionless plasma in large domains while keeping full information of the velocity distribution in localized areas of interest. This is made possible by solving the full Vlasov equation in one region while the remaining area is treated by a 5-moment two-fluid code. In such a treatment, the main challenge of coupling kinetic and fluid descriptions is the interchange of physically correct boundary conditions between the different plasma models. In contrast to other treatments, we do not rely on any specific form of the distribution function, e.g. a Maxwellian type. Instead, we combine an extrapolation of the distribution function and a correction of the moments based on the fluid data. Thus, throughout the simulation both codes provide the necessary boundary conditions for each other. A speed-up factor of around 20 is achieved by using GPUs for the computationally expensive solution of the Vlasov equation and an overall factor of a...
14. Vlasov versus N-body: the H\\'enon sphere
CERN Document Server
Colombi, S; Peirani, S; Plum, G; Suto, Y
2015-01-01
We perform a detailed comparison of the phase-space density traced by the particle distribution in Gadget simulations to the result obtained with a spherical Vlasov solver using the splitting algorithm. The systems considered are apodized H\\'enon spheres with two values of the virial ratio, R ~ 0.1 and 0.5. After checking that spherical symmetry is well preserved by the N-body simulations, visual and quantitative comparisons are performed. In particular we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether N-body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the N-body and the Vlasov codes, namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase-space grid in the second case, we find a spectacular agreement between both methods, even in regions of phase-space where nontrivial physical instabi...
15. Vlasov models for kinetic Weibel-type instabilities
Science.gov (United States)
Ghizzo, A.; Sarrat, M.; Del Sarto, D.
2017-02-01
The Weibel instability, driven by a temperature anisotropy, is investigated within different kinetic descriptions based on the semi-Lagrangian full kinetic and relativistic Vlasov-Maxwell model, on the multi-stream approach, which is based on a Hamiltonian reduction technique, and finally, with the full pressure tensor fluid-type description. Dispersion relations of the Weibel instability are derived using the three different models. A qualitatively different regime is observed in Vlasov numerical experiments depending on the excitation of a longitudinal plasma electric field driven initially by the combined action of the stream symmetry breaking and weak relativistic effects, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The multi-stream model offers an alternate way to simulate easily the coupling with the longitudinal electric field and particularly the nonlinear regime of saturation, making numerical experiments more tractable, when only a few moments of the distribution are considered. Thus a numerical comparison between the reduced Hamiltonian model (the multi-stream model) and full kinetic (relativistic) Vlasov simulations has been investigated in that regime. Although nonlinear simulations of the fluid model, including the dynamics of the pressure tensor, have not been carried out here, the model is strongly relevant even in the three-dimensional case.
16. Sympathetic cooling and detection of a hot trapped ion by a cold one
CERN Document Server
Guggemos, M; Herrera-Sancho, O A; Blatt, R; Roos, C F
2015-01-01
We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca$^+$ and Al$^+$ by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about dynamics of the sympathetic cooling process.
17. Properties of cold ions produced by synchrotron radiation and by charged particle impact
Science.gov (United States)
Levin, J. C.; Biedermann, C.; Cederquist, H.; O, C.-S.; Short, R. T.; Sellin, I. A.
1989-04-01
Argon recoil ions produced by beams of 0.8 MeV/u Cl 5+ have been detected by time-of-flight (TOF) techniques in coincidence with the loss of from one to five projectile electrons. Recoil-ion energies have been determined to be more than an order of magnitude higher than those of highly charged ions produced by unmonochromatized synchrotron radiation. Charge-state distributions, however, show similarities, suggesting that loss of projectile electrons corresponds, in some cases, to inner-shell target ionization producing vacancy cascades. In an essential improvement to the usual multinomial description of ionization in the independent-electron-ejection model, we find the inclusion of Auger vacancy cascades significantly alters the description of the recoil ion spectra corresponding to the projectile-electron loss. These conclusions are consistent with impact parameters inferred from determination of mean recoil energy.
18. Energy scaling of cold atom-atom-ion three-body recombination
CERN Document Server
Krükow, Artjom; Härter, Arne; Denschlag, Johannes Hecker; Pérez-Ríos, Jesús; Greene, Chris H
2015-01-01
We study three-body recombination of Ba$^+$ + Rb + Rb in the mK regime where a single $^{138}$Ba$^{+}$ ion in a Paul trap is immersed into a cloud of ultracold $^{87}$Rb atoms. We measure the energy dependence of the three-body rate coefficient $k_3$ and compare the results to the theoretical prediction, $k_3 \\propto E_{\\textrm{col}}^{-3/4}$ where $E_{\\textrm{col}}$ is the collision energy. We find agreement if we assume that the non-thermal ion energy distribution is determined by at least two different micro-motion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed into an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.
19. Yang-Mills-Vlasov system in the temporal gauge. Systeme de Yang-Mills-Vlasov en jauge temporelle
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Y.; Noutchegueme, N. (Paris-6 Univ., 75 (FR))
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction.
20. Forbidden Vibrational Transitions in Cold Molecular Ions: Experimental Observation and Potential Applications.
Science.gov (United States)
Germann, Matthias; Tonga, Xin; Willitsch, Stefan
2015-01-01
A range of interesting fundamental scientific questions can be addressed by high-precision molecular spectroscopy. A promising way towards this goal is the measurement of dipole-forbidden vibrational transitions in molecular ions. We have recently reported the first such observation in a molecular ion. Here, we give an overview of our method and our results as well as an outlook on potential future applications.
1. Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
2. Light-Assisted Cold Chemical Reactions of Barium Ions with Rubidium Atoms
CERN Document Server
Hall, Felix H J; Raoult, Maurice; Dulieu, Olivier; Willitsch, Stefan
2013-01-01
Light-assisted reactive collisions between laser-cooled Ba+ ions and Rb atoms were studied in an ion-atom hybrid trap. The reaction rate was found to strongly depend on the electronic state of the reaction partners with the largest rate constant (7(2) x 10^-11 cm^3 s^-1) obtained for the excited Ba+(6s)+Rb(5p) reaction channel. Similar to the previously studied Ca+ + Rb system, charge transfer and radiative association were found to be the dominant reactive processes. The generation of molecular ions by radiative association could directly be observed by their sympathetic cooling into a Coulomb crystal. Potential energy curves up to the Ba+(6s)+Rb(5p) asymptote and reactive-scattering cross sections for the radiative processes were calculated. The theoretical rate constant obtained for the lowest reaction channel Ba+(6s)+Rb(5s) is compatible with the experimental estimates obtained thus far.
3. Model and observations of Schottky-noise suppression in a cold heavy-ion beam.
Science.gov (United States)
Danared, H; Källberg, A; Rensfelt, K-G; Simonsson, A
2002-04-29
Some years ago it was found at GSI in Darmstadt that the momentum spread of electron-cooled beams of highly charged ions dropped abruptly to very low values when the particle number decreased to 10 000 or less. This has been interpreted as an ordering of the ions, such that they line up after one another in the ring. We report observations of similar transitions at CRYRING, including an accompanying drop in Schottky-noise power. We also introduce a model of the ordered beam from which the Schottky-noise power can be calculated numerically. The good agreement between the model calculation and the experimental data is seen as evidence for a spatial ordering of the ions.
4. Generation of Schr(o)dinger cat state of a single trapped cold ion
Institute of Scientific and Technical Information of China (English)
Zhang Miao; Jia Huan-Yu; Ji Xiao-Hui; Si Kun
2009-01-01
The fidelity of the generated Schr(o)dinger Cat state (SCS) of a single trapped ion in the Lamb-Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb-Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb-Dike approximation in laser-ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb-Dicke parameters.
5. Adaptive multiresolution semi-Lagrangian discontinuous Galerkin methods for the Vlasov equations
Science.gov (United States)
Besse, N.; Deriaz, E.; Madaule, É.
2017-03-01
We develop adaptive numerical schemes for the Vlasov equation by combining discontinuous Galerkin discretisation, multiresolution analysis and semi-Lagrangian time integration. We implement a tree based structure in order to achieve adaptivity. Both multi-wavelets and discontinuous Galerkin rely on a local polynomial basis. The schemes are tested and validated using Vlasov-Poisson equations for plasma physics and astrophysics.
6. A simple class of singular, two species Vlasov equilibria sustaining nonmonotonic potential distributions
Energy Technology Data Exchange (ETDEWEB)
Nocera, L.; Palumbo, L. J. [CNR-IPCF, Theoretical Plasma Physics, Via Moruzzi 1, I-56124 Pisa (Italy)
2013-01-15
We present new elementary, exact weak singular solutions of the steady state, two species, electrostatic, one dimensional Vlasov-Poisson equations. The distribution of the hot, finite mass, mobile ions is assumed to be log singular at the position of the electric potential's minimum. We show that the electron energy distributions on opposite sides of this minimum are not equal. This leads to a jump discontinuity of the electron distribution across its separatrix. A simple relation exists between the difference of these two electron distributions and that of the ions. The velocity Fourier transform of the electron singular distribution is smooth and appears as a simple Neumann series. Elementary, finite amplitude profiles of the electric potential result from Poisson equation, which are smoothly, but nonmonotonically and asymmetrically distributed in space. Two such profiles are given explicitly as appropriate for a nonmonotonic double layer and for a plasma bounded by a surface. The distributions of both electrons and ions supporting such potential meet smooth and kinetically stable boundary conditions at one plasma boundary. For sufficiently small potential to electron temperature ratios, the nonthermal, discontinuous electron distribution resulting at the other plasma boundary is also stable against Landau damped perturbations of the electron distribution.
7. Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation
Directory of Open Access Journals (Sweden)
Yin Xia
2016-08-01
Full Text Available A consistent derivation of the equations of motion (EOMs of test particles for solving the spin-dependent Boltzmann–Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin–orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.
8. Specific chemical reactivities of spatially separated 3-aminophenol conformers with cold Ca$^+$ ions
CERN Document Server
Chang, Yuan-Pin; Küpper, Jochen; Rösch, Daniel; Wild, Dieter; Willitsch, Stefan
2013-01-01
Many molecules exhibit multiple rotational isomers (conformers) that interconvert thermally and are difficult to isolate. Consequently, a precise characterization of their role in chemical reactions has proven challenging. We have probed the reactivity of specific conformers using an experimental technique based on their spatial separation in a molecular beam by electrostatic deflection. The separated conformers react with a target of Coulomb-crystallized ions in a trap. In the reaction of Ca$^+$ with 3-aminophenol, we find a twofold larger rate constant for the \\textit{cis}- compared to the \\textit{trans}-conformer (differentiated by the O-H bond orientation). This result is explained by conformer-specific differences in the long-range ion-molecule interaction potentials. Our approach demonstrates the possibility of controlling reactivity through selection of conformational states.
9. Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences
Science.gov (United States)
Vedenyapin, V. V.; Negmatov, M. A.; Fimin, N. N.
2017-06-01
We give a derivation of the Vlasov-Maxwell and Vlasov-Poisson-Poisson equations from the Lagrangians of classical electrodynamics. The equations of electromagnetic hydrodynamics (EMHD) and electrostatics with gravitation are derived from them by means of a hydrodynamical' substitution. We obtain and compare the Lagrange identities for various types of Vlasov equations and EMHD equations. We discuss the advantages of writing the EMHD equations in Godunov's double divergence form. We analyze stationary solutions of the Vlasov-Poisson-Poisson equation, which give rise to non-linear elliptic equations with various properties and various kinds of behaviour of the trajectories of particles as the mass passes through a critical value. We show that the classical equations can be derived from the Liouville equation by the Hamilton-Jacobi method and give an analogue of this procedure for the Vlasov equation as well as in the non-Hamiltonian case.
10. Trapping scaling for bifurcations in the Vlasov systems.
Science.gov (United States)
Barré, J; Métivier, D; Yamaguchi, Y Y
2016-04-01
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
11. A Vlasov equation with Dirac potential used in fusion plasmas
Energy Technology Data Exchange (ETDEWEB)
Bardos, Claude [Universite Paris-Diderot, Laboratoire J.-L. Lions, BP187, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Nouri, Anne [Laboratoire d' Analyse, Topologie et Probabilites (UMR 6632), Aix-Marseille Universite, 39 Rue Joliot-Curie, 13453 Marseille Cedex 13 (France)
2012-11-15
Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This pathology appears on the full nonlinear problem, well-posed locally in time with analytic initial data, but generally ill-posed in the Hadamard sense. Eventually with a very different class of solutions, mono-kinetic, which constrains the structure of the density distribution, the problem becomes locally in time well-posed.
12. Trapping scaling for bifurcations in the Vlasov systems
Science.gov (United States)
Barré, J.; Métivier, D.; Yamaguchi, Y. Y.
2016-04-01
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude—generalizing the "trapping scaling" of plasma physics—or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
13. Numerical solution to the Vlasov equation: The 2D code
Science.gov (United States)
Fijalkow, Eric
1999-02-01
The present code solves the two-dimensional Vlasov equation for a periodic in space system, in presence of an external magnetic field B O. The self coherent electric field given by Poisson equation is computed by Fast Fourier Transform (FFT). The output of the code consist of a list of diagnostics, such as total mass conservation, total momentum and energies, and of projections of the distribution function in different subspaces as the x- v x space, the x- y space and so on.
14. On the combination of a low energy hydrogen atom beam with a cold multipole ion trap
Energy Technology Data Exchange (ETDEWEB)
Borodi, Gheorghe
2008-12-09
The first part of the activities of this thesis was to develop a sophisticated ion storage apparatus dedicated to study chemical processes with atomic hydrogen. The integration of a differentially pumped radical beam source into an existing temperature variable 22- pole trapping machine has required major modifications. Since astrophysical questions have been in the center of our interest, the introduction first gives a short overview of astrophysics and -chemistry. The basics of ion trapping in temperature variable rf traps is well-documented in the literature; therefore, the description of the basic instrument (Chapter 2) is kept rather short. Much effort has been put into the development of an intense and stable source for hydrogen atoms the kinetic energy of which can be changed. Chapter 3 describes this module in detail with emphasis on the integration of magnetic hexapoles for guiding the atoms and special treatments of the surfaces for reducing H-H recombination. Due to the unique sensitivity of the rf ion trapping technique, this instrument allows one to study a variety of reactions of astrochemical and fundamental interest. The results of this work are summarized in Chapter 4. Reactions of CO{sub 2}{sup +} with hydrogen atoms and molecules have been established as calibration standard for in situ determination of H and H{sub 2} densities over the full temperature range of the apparatus (10 K-300 K). For the first time, reactions of H- and D-atoms with the ionic hydrocarbons CH{sup +}, CH{sub 2}{sup +}, and CH{sub 4}{sup +} have been studied at temperatures of interstellar space. A very interesting, not yet fully understood collision system is the interaction of protonated methane with H. The outlook presents some ideas, how to improve the new instrument and a few reaction systems are mentioned which may be studied next. (orig.)
15. Comparative study between cold plasma and hot plasma with ion beam and loss-cone distribution function by particle aspect approach
Science.gov (United States)
Patel, Soniya; Varma, P.; Tiwari, M. S.
2011-03-01
The electromagnetic ion-cyclotron (EMIC) instabilities with isotropic ion beam and general loss-cone distribution of cold and hot core plasmas are discussed. The growth rate, parallel and perpendicular resonance energies of the electromagnetic ion-cyclotron waves in a low β (ratio of plasma pressure to magnetic pressure), homogeneous plasma have been obtained using the dispersion relation for cold and hot plasmas. The wave is assumed to propagate parallel to the static magnetic field. The whole plasma is considered to consist of resonant and non-resonant particles permeated by isotropic ion beam. It is assumed that resonant particles and ion beam participate in energy exchange with the wave whereas non-resonant particles support the oscillatory motion of the wave. We determined the variation in energies and growth rate in cold and hot plasmas by the energy conservation method with a general loss-cone distribution function. The thermal anisotropy of the core plasma acts as a source of free energy for EMIC wave and enhances the growth rate. It is noted that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of up flowing ion beam and steep loss-cone distribution in the anisotropic magnetosphere. The effect of the steep loss-cone distribution is to enhance the growth rate of the EMIC wave. The heating of ions perpendicular and parallel to the magnetic field is discussed along with EMIC wave emission in the auroral acceleration region. The results are interpreted for the space plasma parameters appropriate to the auroral acceleration region of the earth's magnetoplasma.
16. ColDICE: A parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
Science.gov (United States)
Sousbie, Thierry; Colombi, Stéphane
2016-09-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65-67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.
17. ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
CERN Document Server
Sousbie, Thierry
2015-01-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density proj...
18. High-resolution spectroscopy of CH2D+ in a cold 22-pole ion trap.
Science.gov (United States)
Gärtner, Sabrina; Krieg, Jürgen; Klemann, André; Asvany, Oskar; Brünken, Sandra; Schlemmer, Stephan
2013-10-03
The method of laser-induced reaction (LIR) is used to obtain high-resolution IR spectra of CH2D(+) in collision with n-H2 at a nominal temperature of 14 K. For this purpose, a home-built optical parametric oscillator (OPO), tunable in the range of 2500-4000 cm(-1), has been coupled to a 22-pole ion trap apparatus. In total, 112 lines of the ν1 and ν4 bands have been recorded. A line list is inferred from a careful analysis of the shape of the LIR signal. Line positions have been determined to an accuracy of 1 × 10(-4) cm(-1), allowing for the prediction of pure rotational transitions with MHz accuracy. In addition, an IR-THz double-resonance LIR depletion technique is applied to H2D(+) to demonstrate the feasibility for pure rotational spectroscopy with LIR.
19. On axisymmetric and stationary solutions of the self-gravitating Vlasov system
Science.gov (United States)
Ames, Ellery; Andréasson, Håkan; Logg, Anders
2016-08-01
Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
20. On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System
CERN Document Server
Ames, Ellery; Logg, Anders
2016-01-01
Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein--Vlasov system which contain ergoregions.
1. Ion sources with arc-discharge plasma box driven by directly heated LaB(6) electron emitter or cold cathode.
Science.gov (United States)
Ivanov, Alexander A; Davydenko, Vladimir I; Deichuli, Petr P; Shulzhenko, Grigori I; Stupishin, Nikolay V
2008-02-01
In the Budker Institute, Novosibirsk, an ion source with arc-discharge plasma box has been developed in the recent years for application in thermonuclear devices for plasma diagnostics. Several modifications of the ion source were provided with extracted current ranging from 1 to 7 A and pulse duration of up to 4 s. Initially, the arc-discharge plasma box with cold cathode was used, with which pulse duration is limited to 2 s by the cathode overheating and sputtering in local arc spots. Recently, a directly heated LaB(6) electron emitter was employed instead, which has extended lifetime compared to the cold cathode. In the paper, characteristics of the beam produced with both arrangements of the plasma box are presented.
2. A Robust Scheme for Two-Qubit Grover Quantum Search Alogrithm Based on the Motional and Internal States of a Single Cold Trapped Ion
Institute of Scientific and Technical Information of China (English)
秦涛; 高克林
2003-01-01
We propose a scheme to implement a two-qubit Grover quantum search algorithm.The novelty in the proposal is that the motional state is introduced into the computation and the internal state within a single cold trapped ion.The motional and internal states of the ion are manipulated as two qubits by the laser pulses to accomplish an example of a Grover algorithm based on the two qubits.The composite laser pulses that are applied to implement the Grover algorithm have been designed in detail.The issues concerning measurement and decoherence are discussed.
3. Parallelized Vlasov-Fokker-Planck solver for desktop personal computers
Science.gov (United States)
Schönfeldt, Patrik; Brosi, Miriam; Schwarz, Markus; Steinmann, Johannes L.; Müller, Anke-Susanne
2017-03-01
The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses opencl to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of coherent synchrotron radiation will be compared to measurements that probe the effects of the microbunching instability occurring in the short bunch operation at ANKA. It will be shown that the impedance model based on the shielding effect of two parallel plates can not only describe the instability threshold, but also the presence of multiple regimes that show differences in the emission of coherent synchrotron radiation.
4. On the contribution of exchange interactions to the Vlasov equation
CERN Document Server
Zamanian, J; Marklund, M
2014-01-01
Exchange effects play an important role in determining the equilibrium properties of dense matter systems, as well as for magnetic phenomena. There exists an extensive literature concerning, e.g., the effects of exchange interactions on the equation of state of dense matter. Here, a generalization of the Vlasov equation to include exchange effects is presented allowing for electromagnetic mean fields, thus incorporating some of the dynamic effects due to the exchange interactions. Treating the exchange term perturbatively, the correction to classical Langmuir waves in plasmas is found, and the results are compared with previous work. It is noted that the relative importance of exchange effects scales similarly with density and temperature as particle dispersive effects, but that the overall magnitude is sensitive to the details of the specific problem. The implications of our results are discussed.
5. PROTON KINETIC EFFECTS IN VLASOV AND SOLAR WIND TURBULENCE
Energy Technology Data Exchange (ETDEWEB)
Servidio, S.; Valentini, F.; Perrone, D.; Veltri, P. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Osman, K. T.; Chapman, S. [Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL (United Kingdom); Califano, F. [Dipartimento di Fisica and CNISM, Università di Pisa, I-56127 Pisa (Italy); Matthaeus, W. H., E-mail: [email protected] [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States)
2014-02-01
Kinetic plasma processes are investigated in the framework of solar wind turbulence, employing hybrid Vlasov-Maxwell (HVM) simulations. Statistical analysis of spacecraft observation data relates proton temperature anisotropy T /T {sub ∥} and parallel plasma beta β{sub ∥}, where subscripts refer to the ambient magnetic field direction. Here, this relationship is recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T /T {sub ∥} and β{sub ∥}, similar to solar wind sub-datasets. Moreover, both simulation and solar wind data suggest that temperature anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. This connection between non-Maxwellian kinetic effects and various types of intermittency may be a key point for understanding the complex nature of plasma turbulence.
6. Proton Kinetic Effects in Vlasov and Solar Wind Turbulence
CERN Document Server
Servidio, S; Valentini, F; Perrone, D; Califano, F; Chapman, S; Matthaeus, W H; Veltri, P
2013-01-01
Kinetic plasma processes have been investigated in the framework of solar wind turbulence, employing Hybrid Vlasov-Maxwell (HVM) simulations. The dependency of proton temperature anisotropy T_{\\perp}/T_{\\parallel} on the parallel plasma beta \\beta_{\\parallel}, commonly observed in spacecraft data, has been recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T_{\\perp}/T_{\\parallel} and \\beta_{\\parallel}, similar to solar wind sub-datasets. Moreover, both simulation and solar wind data suggest that temperature anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. This connection between non-Maxwellian kinetic effects and various types of intermittency may be a key point for understanding the complex nature of plasma turbulence.
7. High-order Hamiltonian splitting for Vlasov-Poisson equations
CERN Document Server
Casas, Fernando; Faou, Erwan; Mehrenberger, Michel
2015-01-01
We consider the Vlasov-Poisson equation in a Hamiltonian framework and derive new time splitting methods based on the decomposition of the Hamiltonian functional between the kinetic and electric energy. Assuming smoothness of the solutions, we study the order conditions of such methods. It appears that these conditions are of Runge-Kutta-Nystr{\\"o}m type. In the one dimensional case, the order conditions can be further simplified, and efficient methods of order 6 with a reduced number of stages can be constructed. In the general case, high-order methods can also be constructed using explicit computations of commutators. Numerical results are performed and show the benefit of using high-order splitting schemes in that context. Complete and self-contained proofs of convergence results and rigorous error estimates are also given.
8. Vlasov equation for long-range interactions on a lattice
CERN Document Server
Bachelard, Romain; De Ninno, Giovanni; Ruffo, Stefano; Staniscia, F
2011-01-01
We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state and a dispersion relation, that depends explicitly on the Fourier modes of the lattice, can be derived. This allows to compute the stability thresholds of the homogeneous state, which turn out to depend on the mode number. When this state is unstable, the growth rates are also function of the mode number. Explicit calculations are performed for the $\\alpha$-HMF model with $0 \\leq \\alpha <1$, for which the zero mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.
9. Vlasov equation for long-range interactions on a lattice.
Science.gov (United States)
Bachelard, R; Dauxois, T; De Ninno, G; Ruffo, S; Staniscia, F
2011-06-01
We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.
10. Local Existence and Continuation Criterion for Solutions of the Spherically Symmetric Einstein-Vlasov-Maxwell System
CERN Document Server
Noundjeu, P
2003-01-01
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
11. On Invariant Measures for the Vlasov Equation with a Regular Potential
CERN Document Server
Zhidkov, P E
2003-01-01
We consider a Vlasov equation with a smooth bounded potential of interaction between particles in a class of measure-valued solutions and construct a measure which is invariant for this problem in a sense.
12. Finite difference modeling of sinking stage curved beam based on revised Vlasov equations
Institute of Scientific and Technical Information of China (English)
张磊; 朱真才; 沈刚; 曹国华
2015-01-01
For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.
13. On Higher-order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit
Energy Technology Data Exchange (ETDEWEB)
W.W. Lee and R.A. Kolesnikov
2009-02-17
In this paper, we present a simple iterative procedure for obtaining the higher order E x B and dE/dt (polarization) drifts associated with the gyrokinetic Vlasov-Poisson equations in the long wavelength limit of k⊥ρi ~ o(ε) and k⊥L ~ o(1), where ρi is the ion gyroradius, L is the scale length of the background inhomogeneity and ε is a smallness parameter. It can be shown that these new higher order k⊥ρi terms, which are also related to the higher order perturbations of the electrostatic potential Φ, should have negligible effects on turbulent and neoclassical transport in tokamaks, regardless of the form of the background distribution and the amplitude of the perturbation. To address further the issue of a non-Maxwellian plasma, higher order finite Larmor radius terms in the gyrokinetic Poisson's equation have been studied and shown to be unimportant as well. On the other hand, the terms of o(k2⊥ρi2) ~ o(ε) and k⊥L ~ o(1) can indeed have impact on microturbulence, especially in the linear stage, such as those arising from the difference between the guiding center and the gyrocenter densities due to the presence of the background gradients. These results will be compared with a recent study questioning the validity of the commonly used gyrokinetic equations for long time simulations.
14. Vlasov Simulation of Electrostatic Solitary Structures in Multi-Component Plasmas
Science.gov (United States)
Umeda, Takayuki; Ashour-Abdalla, Maha; Pickett, Jolene S.; Goldstein, Melvyn L.
2012-01-01
Electrostatic solitary structures have been observed in the Earth's magnetosheath by the Cluster spacecraft. Recent theoretical work has suggested that these solitary structures are modeled by electron acoustic solitary waves existing in a four-component plasma system consisting of core electrons, two counter-streaming electron beams, and one species of background ions. In this paper, the excitation of electron acoustic waves and the formation of solitary structures are studied by means of a one-dimensional electrostatic Vlasov simulation. The present result first shows that either electron acoustic solitary waves with negative potential or electron phase-space holes with positive potential are excited in four-component plasma systems. However, these electrostatic solitary structures have longer duration times and higher wave amplitudes than the solitary structures observed in the magnetosheath. The result indicates that a high-speed and small free energy source may be needed as a fifth component. An additional simulation of a five-component plasma consisting of a stable four-component plasma and a weak electron beam shows the generation of small and fast electron phase-space holes by the bump-on-tail instability. The physical properties of the small and fast electron phase-space holes are very similar to those obtained by the previous theoretical analysis. The amplitude and duration time of solitary structures in the simulation are also in agreement with the Cluster observation.
15. Processing of N2O ice by fast ions: implications on nitrogen chemistry in cold astrophysical environments
Science.gov (United States)
Almeida, G. C.; Pilling, S.; de Barros, A. L. F.; da Costa, C. A. P.; Pereira, R. C.; da Silveira, E. F.
2017-10-01
Nitrous oxide, N2O, is found in the interstellar medium associated with dense molecular clouds and its abundance is explained by active chemistry occurring on N2 rich ice surfaces of dust grains. Such regions are being constantly exposed to ionizing radiation that triggers chemical processes which change molecular abundances with time. Due to its non-zero dipole moment, N2O can be used as an important tracer for the abundance of N2 in such regions as well as for characterization of nitrogen content of ices in outer bodies of Solar system. In this work, we experimentally investigate the resistance of frozen N2O molecules against radiation in attempt to estimate their half-life in astrophysical environments. All the radiolysis products, such as NO2 and NO, were identified by Fourier transform infrared spectroscopy. The infrared absorbance as a function of fluence is modified by ice compaction and by radiolysis, the compaction being dominant at the beginning of the ice processing. The N2O destruction cross-section as well the formation cross-sections of the products NxOy (x = 1-2 and y = 1-5) oxides and ozone (O3) by 1.5 MeV 14N+ ion beam are determined. The characterization of radiation resistance of N2O in cold astrophysical environments is relevant since it yields limits for the nitrogen abundance where the N2O molecule is used to indirectly derive its concentration. The half-life of solid N2O molecules dissociated by medium-mass cosmic rays at Pluto's orbit and at the interstellar medium is estimated.
16. Vlasov-Poisson simulations of electrostatic parametric instability for localized Langmuir wave packets in the solar wind
CERN Document Server
Henri, Pierre; Briand, Carine; Mangeney, André; 10.1029/2009JA014969
2013-01-01
Recent observation of large amplitude Langmuir waveforms during a Type III event in the solar wind have been interpreted as the signature of the electrostatic decay of beam-driven Langmuir waves. This mechanism is thought to be a first step to explain the generation of solar Type III radio emission. The threshold for this parametric instability in typical solar wind condition is investigated here by means of 1D-1V Vlasov-Poisson simulations. We show that the amplitude of the observed Langmuir beat-like waveforms is of the order of the effective threshold computed from the full kinetic simulations. The expected level of associated ion acoustic density fluctuations have also been computed for comparison with observations.
17. The simultaneous determination of active ingredients in cough-cold mixtures by isocratic reversed-phase ion-pair high-performance liquid chromatography.
Science.gov (United States)
Lau, O W; Chan, K; Lau, Y K; Wong, W C
1989-01-01
A simple, rapid and accurate method for the simultaneous determination of active ingredients in cough-cold mixtures using isocratic reversed-phase ion-pair high-performance liquid chromatography has been developed. It involves the use of an octadecylsilane column as the stationary phase with methanol, water, tetrahydrofuran, phosphoric acid mixtures as mobile phase including sodium dioctylsulphosuccinate as the ion-pair agent. The pH of the mobile phase was adjusted to 4.6 by means of phosphoric acid and ammonium hydroxide solutions. The proposed method involves the simple dilution of the samples with the mobile phase and the addition of metoclopramide hydrochloride as the internal standard. The active ingredients under investigation were chlorpheniramine, codeine, diphenhydramine, ephedrine, ethylmorphine, phenylephrine, phenylpropanolamine and pholcodine, which exist as various combinations in cough-cold mixtures. The optimum composition of the mobile phase and the optimum flow rate were determined and are reported. The method was applied to the determination of active ingredients in seven commercially available cough-cold mixtures.
18. Landau damping of Gardner solitons in a dusty bi-ion plasma
Science.gov (United States)
Misra, A. P.; Barman, Arnab
2015-07-01
The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold, and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely, the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids 12, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV), or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures (σ) and the number densities (μ) of hot and cold ions as well as the cold to hot ion mass ratio m. The distinctive features of the decay rates of the amplitudes of the KdV, mKdV, and Gardner solitons with a small effect of Landau damping are also studied in different parameter regimes. It is found that the Gardner soliton points to lower wave amplitudes than the KdV and mKdV solitons. The results may be useful for understanding the localization of solitary pulses and associated wave damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of Saturn), in which the number density of free electrons is much smaller than that of ions and the heavy, micron seized dust grains are highly charged.
19. A Parallelized Vlasov-Fokker-Planck-Solver for Desktop PCs
CERN Document Server
Schönfeldt,; Brosi,; Miriam,; Schwarz,; Markus,; Steinmann,; L., Johannes; Müller,; Anke-Susanne,
2016-01-01
The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses OpenCL to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of coherent synchrotron radiation will be compared to measurements that probe the effects of the micro-bunching instability occurring in the short bunch operation at ANKA. It will be shown that the impedance model based on the shielding effect of two parallel plates can not only describe the instability threshold, but also the presence of multiple regimes that show differences in the emission of coherent synchrotron radiatio...
20. Parallelized Vlasov-Fokker-Planck solver for desktop personal computers
Directory of Open Access Journals (Sweden)
Patrik Schönfeldt
2017-03-01
Full Text Available The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses opencl to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of coherent synchrotron radiation will be compared to measurements that probe the effects of the microbunching instability occurring in the short bunch operation at ANKA. It will be shown that the impedance model based on the shielding effect of two parallel plates can not only describe the instability threshold, but also the presence of multiple regimes that show differences in the emission of coherent synchrotron radiation.
1. ADI type preconditioners for the steady state inhomogeneous Vlasov equation
CERN Document Server
Gasteiger, Markus; Ostermann, Alexander; Tskhakaya, David
2016-01-01
The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov based methods like GMRES or relexation schemes) is computationally expensive. In the former case the slowest timescale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an ADI type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speedup of close to two orders of magnitude (even for intermediate grid sizes) with respect to the not preconditio...
2. Vlasov Simulations of Ionospheric Heating Near Upper Hybrid Resonance
Science.gov (United States)
Najmi, A. C.; Eliasson, B. E.; Shao, X.; Milikh, G. M.; Papadopoulos, K.
2014-12-01
It is well-known that high-frequency (HF) heating of the ionosphere can excite field- aligned density striations (FAS) in the ionospheric plasma. Furthermore, in the neighborhood of various resonances, the pump wave can undergo parametric instabilities to produce a variety of electrostatic and electromagnetic waves. We have used a Vlasov simulation with 1-spatial dimension, 2-velocity dimensions, and 2-components of fields, to study the effects of ionospheric heating when the pump frequency is in the vicinity of the upper hybrid resonance, employing parameters currently available at ionospheric heaters such as HAARP. We have found that by seeding theplasma with a FAS of width ~20% of the simulation domain, ~10% depletion, and by applying a spatially uniform HF dipole pump electric field, the pump wave gives rise to a broad spectrum of density fluctuations as well as to upper hybrid and lower hybrid oscillating electric fields. We also observe collisionless bulk-heating of the electrons that varies non-linearly with the amplitude of the pump field.
3. Synergism between rare earth cerium(IV) ion and vanillin on the corrosion of cold rolled steel in 1.0 M HCl solution
Energy Technology Data Exchange (ETDEWEB)
Li Xianghong [Department of Fundamental Courses, Southwest Forestry University, Kunming 650224 (China)], E-mail: [email protected]; Deng Shuduan [Department of Wood Science and Technology, Southwest Forestry University, Kunming 650224 (China); Fu Hui [Department of Fundamental Courses, Southwest Forestry University, Kunming 650224 (China); Mu Guannan [Department of Chemistry, Yunnan University, Kunming 650091 (China)
2008-12-15
The synergism between rare earth cerium(IV) ion and vanillin on the corrosion of cold rolled steel (CRS) in 1.0 M HCl solution was first investigated by weight loss, potentiodynamic polarization, ultraviolet and visible spectrophotometer (UV-vis), X-ray photoelectron spectroscopy (XPS) and atomic force microscope (AFM). The results revealed that vanillin had a moderate inhibitive effect, and the adsorption of vanillin obeyed the Temkin adsorption isotherm. For rare earth Ce{sup 4+}, it had a negligible effect. However, incorporation of Ce{sup 4+} with vanillin significantly improved the inhibition performance, and produced strong synergistic inhibition effect. Depending on the results, the synergism mechanism was proposed.
4. Using the Orbit Tracking Code Z3CYCLONE to Predict the Beam Produced by a Cold Cathode PIG Ion Source for Cyclotrons under DC Extraction
CERN Document Server
Forringer, Edward
2005-01-01
Experimental measurements of the emittance and luminosity of beams produced by a cold-cathode Phillips Ionization Guage (PIG) ion source for cyclotrons under dc extraction are reviewed. (The source being studied is of the same style as ones that will be used in a series of 250 MeV proton cyclotrons being constructed for cancer therapy by ACCEL Inst, Gmbh, of Bergisch Gladbach, Germany.) The concepts of 'plasma boundary' and 'plasma temperature' are presented as a useful set of parameters for describing the initial conditions used in computational orbit tracking. Experimental results for r-pr and z-pz emittance are compared to predictions from the MSU orbit tracking code Z3CYCLONE with results indicating that the code is able to predict the beam produced by these ion sources with adequate accuracy such that construction of actual cyclotrons can proceed with reasonably prudent confidence that the cyclotron will perform as predicted.
5. Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field
KAUST Repository
Ratushnaya, Valeria
2016-12-17
We investigate the stability properties of a collisionless Vlasov plasma in a weakly inhomogeneous magnetic field using non-modal stability analysis. This is an important topic in a physics of tokamak plasma rich in various types of instabilities. We consider a thin tokamak plasma in a Maxwellian equilibrium, subjected to a small arbitrary perturbation. Within the framework of kinetic theory, we demonstrate the emergence of short time scale algebraic instabilities evolving in a stable magnetized plasma. We show that the linearized governing operator (Vlasov operator) is non-normal leading to the transient growth of the perturbations on the time scale of several plasma periods that is subsequently followed by Landau damping. We calculate the first-order distribution function and the electric field and study the dependence of the transient growth characteristics on the magnetic field strength and perturbation parameters of the system. We compare our results with uniformly magnetized plasma and field-free Vlasov plasma.
6. Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field
Science.gov (United States)
Ratushnaya, Valeria; Samtaney, Ravi
2016-12-01
We investigate the stability properties of a collisionless Vlasov plasma in a weakly inhomogeneous magnetic field using non-modal stability analysis. This is an important topic in a physics of tokamak plasma rich in various types of instabilities. We consider a thin tokamak plasma in a Maxwellian equilibrium, subjected to a small arbitrary perturbation. Within the framework of kinetic theory, we demonstrate the emergence of short time scale algebraic instabilities evolving in a stable magnetized plasma. We show that the linearized governing operator (Vlasov operator) is non-normal leading to the transient growth of the perturbations on the time scale of several plasma periods that is subsequently followed by Landau damping. We calculate the first-order distribution function and the electric field and study the dependence of the transient growth characteristics on the magnetic field strength and perturbation parameters of the system. We compare our results with uniformly magnetized plasma and field-free Vlasov plasma.
7. Relativistic Vlasov-Maxwell modelling using finite volumes and adaptive mesh refinement
CERN Document Server
Wettervik, Benjamin Svedung; Siminos, Evangelos; Fülöp, Tünde
2016-01-01
The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of limited efficiency for high dimensional problems. The use of an adaptive mesh can reduce the scaling of the computational cost with the dimension of the problem. Here, we present a relativistic Eulerian Vlasov-Maxwell solver with block-structured adaptive mesh refinement in one spatial and one momentum dimension. The discretization of the Vlasov equation is based on a high-order finite volume method. A flux corrected transport algorithm is applied to limit spurious oscillations and ensure the physical character of the distribution function. We demonstrate a speed-up by a factor of five, because of the use of an adaptive mesh, in a typical scenario involving laser-plasma interaction in the self-induced transparency regime.
8. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Energy Technology Data Exchange (ETDEWEB)
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
9. Cold Stress
Science.gov (United States)
... Publications and Products Programs Contact NIOSH NIOSH COLD STRESS Recommend on Facebook Tweet Share Compartir Workers who ... cold environments may be at risk of cold stress. Extreme cold weather is a dangerous situation that ...
10. On global classical solutions of the three dimensional relativistic Vlasov-Darwin system
Science.gov (United States)
Li, Xiuting; Zhang, Xianwen
2016-08-01
We study the Cauchy problem of the relativistic Vlasov-Darwin system with generalized variables proposed by Sospedra-Alfonso et al. ["Global classical solutions of the relativistic Vlasov-Darwin system with small Cauchy data: the generalized variables approach," Arch. Ration. Mech. Anal. 205, 827-869 (2012)]. We prove global existence of a non-negative classical solution to the Cauchy problem in three space variables under small perturbation of the initial datum, and as a consequence, we obtain that nearly spherically symmetric solutions with required regularity exist globally in time.
11. Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
CERN Document Server
He, Yang; Qin, Hong; Liu, Jian
2016-01-01
In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.
12. Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
Science.gov (United States)
Chandre, C.; Perin, M.
2016-03-01
We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity. We exhibit three main families of Hamiltonian models with two, three, and four degrees of freedom aiming at modeling the complexity of the bunch of particles in the Vlasov dynamics.
13. Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Batt, J.; Rein, G. (Muenchen Univ. (Germany). Mathematisches Inst.); Morrison, P.J. (Texas Univ., Austin, TX (United States))
1993-03-01
Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e. particle, energy. The main tool in the analysis is the free energy of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.
14. Wave Propagation in an Ion Beam-Plasma System
DEFF Research Database (Denmark)
Jensen, T. D.; Michelsen, Poul; Juul Rasmussen, Jens
1979-01-01
The spatial evolution of a velocity- or density-modulated ion beam is calculated for stable and unstable ion beam plasma systems, using the linearized Vlasov-Poisson equations. The propagation properties are found to be strongly dependent on the form of modulation. In the case of velocity...
15. Ion Acoustic Waves in the Presence of Langmuir Oscillations
DEFF Research Database (Denmark)
Pécseli, Hans
1976-01-01
The dielectric function for long-wavelength, low-frequency ion acoustic waves in the presence of short-wavelength, high-frequency electron oscillations is presented, where the ions are described by the collision-free Vlasov equation. The effect of the electron oscillations can be appropriately...
16. Photoluminescence of rare earth ions coactivated Ca{sub 9}Y(VO{sub 4}){sub 7} with cold, natural and warm white emission
Energy Technology Data Exchange (ETDEWEB)
Li, Ling, E-mail: [email protected] [Ministry-of-Education Key Laboratory for the Synthesis and Applications of Organic Functional Molecules, Hubei Collaborative Innovation Center for Advanced Organochemical Materials, Hubei University, Wuhan 430062 (China); Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Liu, Xiaoguang, E-mail: [email protected] [Ministry-of-Education Key Laboratory for the Synthesis and Applications of Organic Functional Molecules, Hubei Collaborative Innovation Center for Advanced Organochemical Materials, Hubei University, Wuhan 430062 (China); Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Noh, Hyeon Mi, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Moon, Byung Kee, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Choi, Byung Chun, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Jeong, Jung Hyun, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of)
2015-05-05
It has been still a challenge to obtain a new single-component white-light phosphor with the vanadates as host lattices and with two types of ions as activators. A systematic Ln{sub 1}{sup 3+}/Ln{sub 2}{sup 3+} (Ln{sub 1}{sup 3+}/Ln{sub 2}{sup 3+} = Dy{sup 3+}/Tm{sup 3+} or Dy{sup 3+}/Sm{sup 3+} or Dy{sup 3+}/Eu{sup 3+} or Tm{sup 3+}/Eu{sup 3+} or Tm{sup 3+}/Sm{sup 3+}) coactivated Ca{sub 9}Y(VO{sub 4}){sub 7} (CYV)samples as well as their singly doped CYV phosphors have been synthesized by the traditional solid state reaction and their photoluminescence properties have been investigated. The photoluminescence properties as a function of the concentration of rare earth ions have been discussed and the tunable luminescent color was found. The warm (CYV: 1%Dy{sup 3+}, 1%Sm{sup 3+}), natural (CYV: 7% Tm{sup 3+},0.5% Eu{sup 3+}; CYV: 1.0% Tm{sup 3+}, 0.5% Sm{sup 3+}), and cold (CYV: 3% Tm{sup 3+},0.5% Eu{sup 3+}; CYV: 0.5% Dy{sup 3+},0.5% Tm{sup 3+}; CYV: 0.5% Dy{sup 3+},0.7% Tm{sup 3+}; CYV: 0.3%Dy{sup 3+}, 0.5% Tm{sup 3+}) white lights can be obtained. Generally, the emission intensity or lifetime of one rare earth ions decreases with increasing of the concentration of another rare earth ions. - Highlights: • Photoluminescence properties of rare earth ions coactivated Ca{sub 9}Y(VO{sub 4}){sub 7} were investigated. • The effects of rare earth ions concentration on photoluminescence have been discussed. • The tunable luminescent color was found. • Cold, natural and warm white emissions were obtained.
17. Magnetic reconnection and kinetic effects in Vlasov turbulence
Science.gov (United States)
Servidio, Sergio
2015-04-01
The process of magnetic reconnection is ubiquitous in nature, being typical of large scale magnetic configurations. Recently [1], reconnection has been observed to emerge locally and intermittently in plasmas, being a crucial element of turbulence itself. Systematic analysis of MHD simulations reveals the presence of a large number of X-type neutral points, where magnetic reconnection occurs. More recently, the same phenomenon has been inspected within plasma models [2]. The link between magnetic reconnection and kinetic effects in the turbulent solar-wind has been investigated by means of multi-dimensional simulations of the hybrid Vlasov-Maxwell (HVM) code [3], using 5D (2D in space and 3D in velocity space) and full 6D simulations of plasma turbulence. Kinetic effects manifest through the deformation of the proton distribution function, with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. Recent analyses [4] of solar-wind data from spacecraft aimed to quantify kinetic effects through the temperature anisotropy T⊥/T|| on the proton velocity distribution function. Values of the anisotropy range broadly, with most values between 10-1 and 101. Moreover, the distribution of temperature anisotropy depends systematically on the ambient proton parallel beta β|| (the ratio of parallel kinetic pressure to magnetic pressure), manifesting a characteristic rhomboidal shape. In order to make contact with solar-wind observations, temperature anisotropy has been evaluated from an ensemble of HVM simulations [5], obtained by varying the global plasma beta and fluctuation level, in such a way to cover distinct regions of the parameter space defined by T⊥/T|| and β||. The HVM simulations presented here demonstrate that, when the distribution function is free to explore the entire velocity subspace, new features appear as complex interactions between the particles and the turbulent background. Comparison of numerical results
18. Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
Energy Technology Data Exchange (ETDEWEB)
Barman, Arnab; Misra, A. P., E-mail: [email protected], E-mail: [email protected] [Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)
2014-07-15
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg-de Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids 12, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio (μ{sub pd}) as well as the ratios of positive to negative ion temperatures (σ) and masses (m)
19. Convergence of the Vlasov-Poisson-Fokker- Planck system to the incompressible Euler equations
Institute of Scientific and Technical Information of China (English)
2006-01-01
We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method.
20. The Cauchy Problem for the 3-D Vlasov-Poisson System with Point Charges
Science.gov (United States)
Marchioro, Carlo; Miot, Evelyne; Pulvirenti, Mario
2011-07-01
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in the presence of point charges with repulsive interaction. The present analysis extends an analogous two-dimensional result (Caprino and Marchioro in Kinet. Relat. Models 3(2):241-254, 2010).
1. The Cauchy problem for the 3-D Vlasov-Poisson system with point charges
CERN Document Server
Marchioro, Carlo; Pulvirenti, Mario
2010-01-01
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous two-dimensional result by Caprino and Marchioro [On the plasma-charge model, to appear in Kinetic and Related Models (2010)].
2. Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations
Science.gov (United States)
Han-Kwan, Daniel; Nguyen, Toan T.
2016-09-01
In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system.
3. On Local Smooth Solutions for the Vlasov Equation with the Potential of Interactions {\\pm} r^{-2}
CERN Document Server
Zhidkov, P E
2003-01-01
For the initial value problem for the Vlasov equation with the potential of interactions {\\pm} r^{-2} we prove the existence and uniqueness of a local solution with values in the Schwartz space S of infinitely differentiable functions rapidly decaying at infinity.
4. On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell system
OpenAIRE
Sospedra-Alfonso, Reinel
2010-01-01
We show that weak solutions of the relativistic Vlasov-Maxwell system preserve the total energy provided that the electromagnetic field is locally of bounded variation and, for any $\\lambda$> 0, the one-particle distribution function has a square integrable $\\lambda$-moment in the momentum variable.
5. Cosmology and gravitational waves in the Nordstrom-Vlasov system, a laboratory for Dark Energy
CERN Document Server
Corda, Christian
2013-01-01
We discuss a cosmological solution of the system which was originally introduced by Calogero and is today popularly known as "Nordstrom-Vlasov system". Although the model is un-physical, its cosmological solution results interesting for the same reasons for which the Nordstrom-Vlasov system was originally introduced in the framework of galactic dynamics. In fact, it represents a theoretical laboratory where one can rigorously study some problems, like the importance of the gravitational waves in the dynamics, which at the present time are not well understood within the physical model of the Einstein-Vlasov system. As the cosmology of the Nordstrom-Vlasov system is founded on a scalar field, a better understanding of the system is important also in the framework of the Dark Energy problem. In fact, various attempts to achieve Dark Energy by using scalar fields are present in the literature. In the solution an analytical expression for the time dependence of the cosmological evolution of the Nordstrom's scalar ...
6. Resolution of the Vlasov-Maxwell system by PIC discontinuous Galerkin method on GPU with OpenCL
Directory of Open Access Journals (Sweden)
Crestetto Anaïs
2013-01-01
Full Text Available We present an implementation of a Vlasov-Maxwell solver for multicore processors. The Vlasov equation describes the evolution of charged particles in an electromagnetic field, solution of the Maxwell equations. The Vlasov equation is solved by a Particle-In-Cell method (PIC, while the Maxwell system is computed by a Discontinuous Galerkin method. We use the OpenCL framework, which allows our code to run on multicore processors or recent Graphic Processing Units (GPU. We present several numerical applications to two-dimensional test cases.
7. Cold Urticaria
Science.gov (United States)
Diseases and Conditions Cold urticaria By Mayo Clinic Staff Cold urticaria (ur-tih-KAR-e-uh) is a skin reaction to cold. Skin that has ... in contact with cold develops reddish, itchy welts (hives). The severity of cold urticaria symptoms varies widely. ...
8. Extraction of radioactive positive ions across the surface of superfluid helium : A new method to produce cold radioactive nuclear beams
NARCIS (Netherlands)
Huang, WX; Dendooven, P; Gloos, K; Takahashi, N; Pekola, JP; Aysto, J
2003-01-01
Alpha-decay recoils Rn-219 were stopped in superfluid helium and positive ions were extracted by electric field into the vapour phase. This first quantitative observation of extraction was successfully conducted using highly sensitive radioactivity detection. The efficiency for extraction across the
9. 3D solutions of the Poisson-Vlasov equations for a charged plasma and particle-core model in a line of FODO cells
Science.gov (United States)
Turchetti, G.; Rambaldi, S.; Bazzani, A.; Comunian, M.; Pisent, A.
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribition obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances.
10. 3D solutions of the Poisson-Vlasov equations for a charged plasma and particle-core model in a line of FODO cells
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G.; Rambaldi, S.; Bazzani, A. [Dipartimento di Fisica and INFN, Via Irnerio 46, 40126, Bologna (Italy); Comunian, M.; Pisent, A. [INFN Laboratori Nazionali di Legnaro (Italy)
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribution obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances. (orig.)
11. Three-dimensional ordering of cold ion beams in a storage ring: A molecular-dynamics simulation study
Energy Technology Data Exchange (ETDEWEB)
Yuri, Yosuke, E-mail: [email protected] [Takasaki Advanced Radiation Research Institute, Japan Atomic Energy Agency, 1233 Watanuki-machi Takasaki, Gunma 370-1292 Japan (Japan)
2015-06-29
Three-dimensional (3D) ordering of a charged-particle beams circulating in a storage ring is systematically studied with a molecular-dynamics simulation code. An ion beam can exhibit a 3D ordered configuration at ultralow temperature as a result of powerful 3D laser cooling. Various unique characteristics of the ordered beams, different from those of crystalline beams, are revealed in detail, such as the single-particle motion in the transverse and longitudinal directions, and the dependence of the tune depression and the Coulomb coupling constant on the operating points.
12. Vlasov simulations of electron hole dynamics in inhomogeneous magnetic field
Science.gov (United States)
Kuzichev, Ilya; Vasko, Ivan; Agapitov, Oleksiy; Mozer, Forrest; Artemyev, Anton
2017-04-01
13. Vlasov fluid stability of a 2-D plasma with a linear magnetic field null
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S.
1984-01-01
Vlasov fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov fluid dispersion functional by using set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
14. Linear Vlasov solver for microbunching gain estimation with inclusion of CSR, LSC and linac geometric impedances
CERN Document Server
Tsai, Cheng-Ying; Li, Rui; Tennant, Chris
2015-01-01
As is known, microbunching instability (MBI) has been one of the most challenging issues in designs of magnetic chicanes for short-wavelength free-electron lasers or linear colliders, as well as those of transport lines for recirculating or energy recovery linac machines. To more accurately quantify MBI in a single-pass system and for more complete analyses, we further extend and continue to increase the capabilities of our previously developed linear Vlasov solver [1] to incorporate more relevant impedance models into the code, including transient and steady-state free-space and/or shielding coherent synchrotron radiation (CSR) impedances, the longitudinal space charge (LSC) impedances, and the linac geometric impedances with extension of the existing formulation to include beam acceleration [2]. Then, we directly solve the linearized Vlasov equation numerically for microbunching gain amplification factor. In this study we apply this code to a beamline lattice of transport arc [3] following an upstream linac...
15. Non-modal stability analysis and transient growth in a magnetized Vlasov plasma
CERN Document Server
Ratushnaya, Valeria
2014-01-01
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is s...
16. Progress on a Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits
CERN Document Server
Bassi, Gabriele; Warnock, Robert L
2005-01-01
We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates (shielding). The time evolution of the phase space distribution is determined by solving the Vlasov-Maxwell equations in the time domain. This provides lower numerical noise than the macroparticle method, and allows the study of emittance degradation and microbunching in bunch compressors. We calculate the fields excited by the bunch in the lab frame using a formula simpler than that based on retarded potentials.* We have developed an algorithm for solving the Vlasov equation in the beam frame using arc length as the independent variable and our method of local characteristics (discretized Perron-Frobenius operator).We integrate in the interaction picture in the hope that we can adopt a fixed grid. The distribution function will be represented by B-splines, in a scheme preserving positivity and normalization of the distribution. The transformation between l...
17. Vlasov simulations of self generated strong magnetic fields in plasmas and laser-plasma interaction
Directory of Open Access Journals (Sweden)
Inglebert A.
2013-11-01
Full Text Available A new formulation based on Hamiltonian reduction technique using the invariance of generalized canonical momentum is introduced for the study of relativistic Weibel-type instability. An example of application is given for the current filamentation instability resulting from the propagation of two counter-streaming electron beams in the relativistic regime of the instability. This model presents a double advantage. From an analytical point of view, the method is exact and standard fluid dispersion relations for Weibel or filamentation instabilies can be recovered. From a numerical point of view, the method allows a drastic reduction of the computational time. A 1D multi-stream Vlasov-Maxwell code is developed using such dynamical invariants in the perpendicular momentum space. Numerical comparison with a full Vlasov-Maxwell system has also been carried out to show the efficiency of this reduction technique.
18. An asymptotic preserving scheme for the relativistic Vlasov--Maxwell equations in the classical limit
CERN Document Server
Crouseilles, Nicolas; Faou, Erwan
2016-01-01
We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencies present in the numerical solution. It turns out that the choice of this implicit method is crucial as even $L$-stable methods can lead to numerical instabilities for large values of $c$. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.
19. An asymptotic preserving scheme for the relativistic Vlasov-Maxwell equations in the classical limit
Science.gov (United States)
Crouseilles, Nicolas; Einkemmer, Lukas; Faou, Erwan
2016-12-01
We consider the relativistic Vlasov-Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov-Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencies present in the numerical solution. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.
20. Vlasov Fluid stability of a 2-D plasma with a linear magnetic field null
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S.
1984-01-01
Vlasov Fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov Fluid dispersion functional by using a set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
1. Veiled singularities for the spherically symmetric massless Einstein-Vlasov system
CERN Document Server
Rendall, Alan D
2016-01-01
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was proved. Those solutions are self-similar and hence not asymptotically flat. To obtain solutions which are more physically relevant it makes sense to attempt to cut off these solutions in a suitable way so as to make them asymptotically flat. This task, which turns out to be technically challenging, will be carried out in this paper. [RV] A. D. Rendall and J. J. L. Vel\\'{a}zquez, A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Annales Henri Poincare 12, 919-964, (2011).
2. Nonlinear wave evolution in VLASOV plasma: a lie-transform analysis
Energy Technology Data Exchange (ETDEWEB)
Cary, J.R.
1979-08-01
Nonlinear wave evolution in Vlasov plasma is analyzed using the Lie transform, a powerful mathematical tool which is applicable to Hamiltonian systems. The first part of this thesis is an exposition of the Lie transform. Dewar's general Lie transform theory is explained and is used to construct Deprit's Lie transform perturbation technique. The basic theory is illustrated by simple examples.
3. On classical solutions of the relativistic Vlasov-Klein-Gordon system
Directory of Open Access Journals (Sweden)
Michael Kunzinger
2005-01-01
Full Text Available We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case.
4. The Goursat Problem for the Einstein-Vlasov System: (I) The Initial Data Constraints
CERN Document Server
2011-01-01
We show how to assign, on two intersecting null hypersurfaces, initial data for the Einstein-Vlasov system in harmonic coordinates. As all the components of the metric appear in each component of the stress-energy tensor, the hierarchical method of Rendall can not apply strictly speaking. To overcome this difficulty, an additional assumption have been imposed to the metric on the initial hypersurfaces. Consequently, the distribution function is constrained to satisfy some integral equations on the initial hypersurfaces.
5. Variational principles for the guiding-center Vlasov-Maxwell equations
CERN Document Server
Brizard, A J
2016-01-01
The Lagrange, Euler, and Euler-Poincar\\'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.
6. Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Pham, Huyên, E-mail: [email protected]; Wei, Xiaoli, E-mail: [email protected] [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)
2016-12-15
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
7. One-species Vlasov-Poisson-Landau system for soft potentials in ℝ3
Science.gov (United States)
He, Cong; Lei, Yuanjie
2016-12-01
We consider the global classical solution near a global Maxwellian to the one-species Vlasov-Poisson-Landau system in the whole space Rx 3 . It is shown that our global solvability result is obtained under the weaker smallness condition on the initial perturbation than that of Duan et al., [preprint arXiv:1112.3261 (2011)] and Lei et al., [Kinet. Relat. Models 7(3), 551-590 (2014)].
8. Geometric Integration Of The Vlasov-Maxwell System With A Variational Particle-in-cell Scheme
Energy Technology Data Exchange (ETDEWEB)
J. Squire, H. Qin and W.M. Tang
2012-03-27
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
9. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
Energy Technology Data Exchange (ETDEWEB)
Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2012-08-15
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
10. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
OpenAIRE
2014-01-01
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus, the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
11. Comparison between 1D and 1 1/2D Eulerian Vlasov codes for the numerical simulation of stimulated Raman scattering
Science.gov (United States)
Ghizzo, A.; Bertrand, P.; Lebas, J.; Shoucri, M.; Johnston, T.; Fijalkow, E.; Feix, M. R.
1992-10-01
The present 1 1/2D relativistic Euler-Vlasov code has been used to check the validity of a hydrodynamic description used in a 1D version of the Vlasov code. By these means, detailed numerical results can be compared; good agreement furnishes full support for the 1D electromagnetic Vlasov code, which runs faster than the 1 1/2D code. The results obtained assume a nonrelativistic v(y) velocity.
12. Collisional effects on the numerical recurrence in Vlasov-Poisson simulations
CERN Document Server
Pezzi, Oreste; Valentini, Francesco
2016-01-01
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456-1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through a Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales, can modify the physical features of the system evolution even in nonlinear regime. This mean...
13. Collisional effects on the numerical recurrence in Vlasov-Poisson simulations
Energy Technology Data Exchange (ETDEWEB)
Pezzi, Oreste; Valentini, Francesco [Dipartimento di Fisica and CNISM, Università della Calabria, 87036 Rende (CS) (Italy); Camporeale, Enrico [Center for Mathematics and Computer Science (CWI), 1090 GB Amsterdam (Netherlands)
2016-02-15
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.
14. Beyond single stream with the Schroedinger method - Closing the Vlasov hierarchy
Energy Technology Data Exchange (ETDEWEB)
Uhlemann, Cora; Kopp, Michael; Haugg, Thomas [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-University, Theresienstr. 37, D-80333 Munich (Germany)
2014-07-01
We investigate large scale structure formation of dark matter in the phase-space description based on the Vlasov equation whose nonlinearity is induced by gravitational interaction according to the Poisson equation. Determining the time-evolution of density and peculiar velocity demands solving the full Vlasov hierarchy for the moments of the phase-space distribution function. In the presence of long-range interaction no consistent truncation of the hierarchy is known apart from the pressureless fluid (dust) model which is incapable of describing virialization due to the occurrence of shell-crossing singularities and the inability to generate higher cumulants like vorticity and velocity dispersion. Our goal is to find a phase-space distribution function that is able to describe regions of multi-streaming and therefore can serve as theoretical N-body double. We use the coarse-grained Wigner probability distribution obtained from a wavefunction fulfilling the Schroedinger equation and show that its evolution equation bears strong resemblance to the Vlasov equation but cures the shell-crossing singularities. This feature was already employed in cosmological simulations of large-scale structure formation by Widrow and Kaiser '93. We are able to show that the coarse-grained Wigner ansatz automatically closes the corresponding hierarchy while incorporating nonzero higher cumulants which are determined self-consistently from density and velocity.
15. Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
CERN Document Server
Barman, A
2014-01-01
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\\bf 12}, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive io...
16. Cold nuclear fusion
Directory of Open Access Journals (Sweden)
Huang Zhenqiang Huang Yuxiang
2013-10-01
Full Text Available In normal temperature condition, the nuclear force constraint inertial guidance method, realize the combination of deuterium and tritium, helium and lithium... And with a magnetic moment of light nuclei controlled cold nuclear collide fusion, belongs to the nuclear energy research and development in the field of applied technology "cold nuclear collide fusion". According to the similarity of the nuclear force constraint inertial guidance system, the different velocity and energy of the ion beam mixing control, developed ion speed dc transformer, it is cold nuclear fusion collide, issue of motivation and the nuclear power plant start-up fusion and power transfer system of the important equipment, so the merger to apply for a patent
17. Common Cold
Science.gov (United States)
... nose, coughing - everyone knows the symptoms of the common cold. It is probably the most common illness. In the course of a year, people ... avoid colds. There is no cure for the common cold. For relief, try Getting plenty of rest ...
18. A conformational study of protonated noradrenaline by UV-UV and IR dip double resonance laser spectroscopy combined with an electrospray and a cold ion trap method.
Science.gov (United States)
Wako, Hiromichi; Ishiuchi, Shun-Ichi; Kato, Daichi; Féraud, Géraldine; Dedonder-Lardeux, Claude; Jouvet, Christophe; Fujii, Masaaki
2017-05-03
The conformer-selected ultraviolet (UV) and infrared (IR) spectra of protonated noradrenaline were measured using an electrospray/cryogenic ion trap technique combined with photo-dissociation spectroscopy. By comparing the UV photo dissociation (UVPD) spectra with the UV-UV hole burning (HB) spectra, it was found that five conformers coexist under ultra-cold conditions. Based on the spectral features of the IR dip spectra of each conformer, two different conformations on the amine side chain were identified. Three conformers (group I) were assigned to folded and others (group II) to extended structures by comparing the observed IR spectra with the calculated ones. Observation of the significantly less-stable extended conformers strongly suggests that the extended structures are dominant in solution and are detected in the gas phase by kinetic trapping. The conformers in each group are assignable to rotamers of OH orientations in the catechol ring. By comparing the UV-UV HB spectra and the calculated Franck-Condon spectra obtained by harmonic vibrational analysis of the S1 state, with the aid of relative stabilization energies of each conformer in the S0 state, the absolute orientations of catechol OHs of the observed five conformers were successfully determined. It was found that the 0-0 transition of one folded conformer is red-shifted by about 1000 cm(-1) from the others. The significant red-shift was explained by a large contribution of the πσ* state to S1 in the conformer in which an oxygen atom of the meta-OH group is close to the ammonium group.
19. Semiclassical Vlasov and fluid models for an electron gas with spin effects
CERN Document Server
Hurst, Jerome; Manfredi, Giovanni; Hervieux, Paul-Antoine
2014-01-01
We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.
20. Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
Directory of Open Access Journals (Sweden)
Marcel Dossa
2011-12-01
Full Text Available This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta$. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV systems.
1. Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit
CERN Document Server
Finkelshtein, Dmitri; Kutoviy, Oleksandr; Lytvynov, Eugene
2011-01-01
Let $\\Gamma$ denote the space of all locally finite subsets (configurations) in $\\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\\Gamma$ in which pairs of particles simultaneously hop over $\\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density.
2. Local null-controllability of the 2-D Vlasov-Navier-Stokes system
OpenAIRE
Moyano, Iván
2016-01-01
We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity field of the fluid from any initial state to the zero steady state, by means of an internal control. Indeed, we can modify the non-linear dynamics of the system in order to absorb the particles and let the fluid at rest. The proof is achieved thanks to the r...
3. Self-similar analysis of Vlasov-Einstein equations in spherical symmetry
Energy Technology Data Exchange (ETDEWEB)
Munier, A.; Burgan, J.R.; Feix, M.; Fijalkow, E.
1980-03-15
The Vlasov-Einstein system of equations is studied from the point of view of group transformations. Continuous groups are shown to generalize the usual infinitesimal treatment of the metric tensor to the case of a distribution function. Reduced equations are obtained, leading to a time-dependent analytical solution, which yields as a limiting case the Schwarzchild metric. The problem of a purely radial motion of null particles is discussed and leads to an expression for the redshift in a nonstatic, inhomogeneous spacetime.
4. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
Science.gov (United States)
Squire, Jonathan; Qin, Hong; Tang, William
2012-10-01
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law. This work was supported by USDOE Contract DE-AC02-09CH11466.[4pt] [1] M. Desbrun, A. N. Hirani, M. Leok, and J. E. Marsden, (2005), arXiv:math/0508341
5. Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant
CERN Document Server
Nungesser, Ernesto
2014-01-01
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.
6. Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Science.gov (United States)
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.
7. Non-modal stability analysis and transient growth in a magnetized Vlasov plasma
KAUST Repository
Ratushnaya, V.
2014-12-01
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a 3-dimensional collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma and examine its evolution with an electrostatic approximation. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.
8. Cold Sores
Science.gov (United States)
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9. Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality
CERN Document Server
Degond, Pierre; Doyen, David
2015-01-01
In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm law). The derivation of Asymptotic-Preserving methods is not straightforward since the quasi-neutral model is a singular limit of the Vlasov-Maxwell model. The key step is a reformulation of the Vlasov-Maxwell system which unifies the two models in a single set of equations with a smooth transition from one to another. As demonstrated in various and demanding numerical simulations, the Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral plasmas and non-neutral plasmas, making them particularly we...
10. Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit
Science.gov (United States)
Degond, P.; Deluzet, F.; Doyen, D.
2017-02-01
In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm law). The derivation of Asymptotic-Preserving methods is not straightforward since the quasi-neutral model is a singular limit of the Vlasov-Maxwell model. The key step is a reformulation of the Vlasov-Maxwell system which unifies the two models in a single set of equations with a smooth transition from one to another. As demonstrated in various and demanding numerical simulations, the Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral plasmas and non-neutral plasmas, making them particularly well suited for complex problems involving dense plasmas with localized non-neutral regions.
11. On local smooth solutions for the Vlasov equation with the potential of interactions ±r−2
OpenAIRE
Peter Zhidkov
2004-01-01
For the initial value problem for the Vlasov equation with the potential of interactions ±r−2, we prove the existence and uniqueness of a local solution with values in the Schwartz space S of infinitely differentiable functions rapidly decaying at infinity.
12. Gene Expression, Protein Function and Pathways of Arabidopsis thaliana Responding to Silver Nanoparticles in Comparison to Silver Ions, Cold, Salt, Drought, and Heat
Directory of Open Access Journals (Sweden)
Eisa Kohan-Baghkheirati
2015-03-01
Full Text Available Silver nanoparticles (AgNPs have been widely used in industry due to their unique physical and chemical properties. However, AgNPs have caused environmental concerns. To understand the risks of AgNPs, Arabidopsis microarray data for AgNP, Ag+, cold, salt, heat and drought stresses were analyzed. Up- and down-regulated genes of more than two-fold expression change were compared, while the encoded proteins of shared and unique genes between stresses were subjected to differential enrichment analyses. AgNPs affected the fewest genes (575 in the Arabidopsis genome, followed by Ag+ (1010, heat (1374, drought (1435, salt (4133 and cold (6536. More genes were up-regulated than down-regulated in AgNPs and Ag+ (438 and 780, respectively while cold down-regulated the most genes (4022. Responses to AgNPs were more similar to those of Ag+ (464 shared genes, cold (202, and salt (163 than to drought (50 or heat (30; the genes in the first four stresses were enriched with 32 PFAM domains and 44 InterPro protein classes. Moreover, 111 genes were unique in AgNPs and they were enriched in three biological functions: response to fungal infection, anion transport, and cell wall/plasma membrane related. Despite shared similarity to Ag+, cold and salt stresses, AgNPs are a new stressor to Arabidopsis.
13. Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas
CERN Document Server
Cheng, Bin; Tronci, Cesare
2016-01-01
We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible Navier--Stokes system for the bulk fluid; and a parabolic evolution equation, involving magnetic diffusivity, for the magnetic field. The physical derivation of our model is given. It is also shown that the weak solution, whose existence is established, has nonincreasing total energy, and that it satisfies a number of physically relevant properties, including conservation of the total momentum, conservation of the total mass, and nonnegativity of the probability density function for the energetic particles. The proof is based on a one-level approximation scheme, which is carefully devised to avoid increase of the total energy for the sequence...
14. Description of the evolution of inhomogeneities on a dark matter halo with the Vlasov equation
Science.gov (United States)
Domínguez-Fernández, Paola; Jiménez-Vázquez, Erik; Alcubierre, Miguel; Montoya, Edison; Núñez, Darío
2017-09-01
We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo in order to test its stability against perturbations. Such collection is assumed to represent a dark matter inhomogeneity which is represented by a distribution function defined in phase-space. Non-trivial stationary states are obtained and determined by the virialization of the system. We describe some features of these stationary states by means of the properties of the final distribution function and final density profile. We compare our results using the different halo models and find that the NFW halo model is the most stable of them, in the sense that an inhomogeneity in this halo model requires a shorter time to virialize.
15. From one-dimensional fields to Vlasov equilibria: Theory and application of Hermite polynomials
CERN Document Server
Allanson, O; Troscheit, S; Wilson, F
2016-01-01
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of th...
16. A Reduction of the Vlasov--Maxwell System Using Phase-Space Blobs
Science.gov (United States)
Shadwick, B. A.; Lee, Frank M.; Faeh, Luke
2011-10-01
We develop a new computational approach to solving the Vlasov-Maxwell equation by representing the distribution function by a supper-position of finite-extent phase- space blobs.'' Each blob evolves as a warm beamletdriven by the collective plasma fields. The underlying approximation treats each blob as a different plasma species and, as such, makes a counting error which we expect to be reflected in the system entropy. This approach results in a non-canonical Hamiltonian model, inheriting various properties of the original system. The primary advance of this technique over traditional Lagrangian particle methods is the near elimination of macro-particle noise.'' Since we are evolving elements of phase-space, the distribution function can be readily reconstructed at any instant. We discuss the performance and convergence of this model using a variety of standard examples. Supported by the U.S. DoE under Contract DE-FG02-08ER55000
17. Vlasov Simulations of Ladder Climbing and Autoresonant Acceleration of Langmuir Waves
Science.gov (United States)
Hara, Kentaro; Barth, Ido; Kaminski, Erez; Dodin, Ilya; Fisch, Nathaniel
2016-10-01
The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on the discreteness of the wave spectrum, this phenomenon is called ladder climbing (LC) or autroresonant acceleration (AR) of plasmons, and was first proposed by Barth et al. based on a linear fluid model. Here, we report a demonstration of LC/AR from first principles using fully nonlinear Vlasov simulations of collisionless bounded plasma. We show that, in agreement to the basic theory, plasmons survive substantial transformations of the spectrum and are destroyed only when their wave numbers become large enough to trigger Landau damping. The work was supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948 and the DTRA Grant No. HDTRA1-11-1-0037.
18. A Full Eulerian Vlasov-Maxwell Study of Turbulent Dynamics and Dissipation
Science.gov (United States)
TenBarge, J. M.; Juno, J.; Hakim, A.
2016-12-01
The development of a detailed understanding of turbulence in magnetized plasmas has been a long standing goal of the broader scientific community, both as a fundamental physics process and because of its applicability to a wide variety of phenomena. Turbulence in a magnetized plasma is the primary mechanism responsible for transforming energy at large injection scales into small-scale motions, which are ultimately dissipated as heat in systems such as the solar corona and wind. At large scales, the turbulence is well described by fluid models of the plasma; however, understanding the processes responsible for heating a weakly collisional plasma such as the solar wind requires a kinetic description. We present the first fully kinetic Eulerian Vlasov-Maxwell study of turbulence using the Gkeyll simulation code. We focus on the pristine distribution function dynamics that are possible with the Eulerian approach. We also present the signatures and form of dissipation as diagnosed via field-particle correlation functions.
19. The Hamiltonian structure and Euler-Poincare formulation of the Vlasov-Maxwell and gyrokinetic systems
Energy Technology Data Exchange (ETDEWEB)
Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Chandre, C. [Centre de Physique Theorique, CNRS - Aix-Marseille Universite, Campus de Luminy, Marseille 13009 (France)
2013-02-15
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.
20. On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field
CERN Document Server
Calogero, Simone
2016-01-01
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in fine time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.
1. Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
Science.gov (United States)
He, Yang; Sun, Yajuan; Qin, Hong; Liu, Jian
2016-09-01
In this paper, we study the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semi-discrete system that possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nédélec's mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semi-discrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. The structure-preserving nature of the algorithm ensures accuracy and fidelity of the numerical simulations over long time.
2. Canonicalizable gyrocenter and structure-preserving geometric algorithms for the Vlasov-Maxwell system
Science.gov (United States)
Qin, Hong
2016-10-01
Littlejohn's introduction of the non-canonical symplectic structure for the gyrocenter dynamics revolutionized plasma kinetic theory. The discovery of the non-canonical symplectic algorithm for gyrocenters initiated the search for symplectic algorithms for the gyrokinetic system. This effort is enforced by the recent discovery of canonical and non-canonical symplectic algorithms for the Vlasov-Maxwell (VM) system. However, symplectic algorithms for the gyrokinetic system remain elusive despite intense effort. In retrospect, the success of the symplectic algorithms for the VM system can be attributed to its global canonicalizability. Darboux's theorem ensures that any symplectic structure is locally canonicalizable, but not necessarily globally. Indeed, Littlejohn's gyrocenter is not globally canonicalizable. In this talk, I will show to construct a different gyrocenter that is globally canonicalizable. It should be a good starting point for developing symplectic algorithms for the gyrokinetic system. Research supported by the U.S. Department of Energy (DE-AC02-09CH11466).
3. On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations
Energy Technology Data Exchange (ETDEWEB)
Ghizzo, A. [Institut Jean Lamour UMR 7163, Université de Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
The saturation of the Weibel instability in the relativistic regime is investigated within the Hamiltonian reduction technique based on the multistream approach developed in paper I in the linear case and in paper II for the nonlinear saturation. In this work, the study is compared with results obtained by full kinetic 1D2V Vlasov-Maxwell simulations based on a semi-Lagrangian technique. For a temperature anisotropy, qualitatively different regimes are realized depending on the excitation of the longitudinal (plasma) electric field, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The emphasis here is on gaining a better understanding of the nonlinear aspects of the Weibel instability. The multistream model offers an alternate way to make calculations or numerical experiments more tractable, when only a few moments of the velocity distribution of the plasma are considered.
4. Vlasov simulations of kinetic Alfvén waves at proton kinetic scales
Energy Technology Data Exchange (ETDEWEB)
Vásconez, C. L. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Observatorio Astronómico de Quito, Escuela Politécnica Nacional, Quito (Ecuador); Valentini, F.; Veltri, P. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Camporeale, E. [Centrum Wiskunde and Informatica, Amsterdam (Netherlands)
2014-11-15
Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρ{sub p} and/or inertial length d{sub p} and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta β{sub p} = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to d{sub p} and β{sub p} ≃ 1 (for which ρ{sub p} ≃ d{sub p}) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects.
5. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm
CERN Document Server
Chen, Guangye
2015-01-01
For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large time steps and cell sizes, which are determined by accuracy consid...
6. An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations
CERN Document Server
Wang, Bei; Colella, Phil
2012-01-01
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.
7. The Einstein-Vlasov system with cosmological constant in a surface-symmetric cosmological model local existence and continuation criteria
CERN Document Server
Tchapnda, S B; Tchapnda, Sophonie Blaise; Noutchegueme, Norbert
2003-01-01
The Einstein-Vlasov system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with surface symmetry and a non-zero cosmological constant and prove local existence and continuation criteria in both time directions. The continuation criterion says that as long as the maximum velocity remains bounded and the lapse function remains bounded then the solution can be continued. This applies to either time direction.
8. The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria
OpenAIRE
Glass, Olivier; Han-Kwan, Daniel; Moussa, Ayman
2016-01-01
In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kineti...
9. Vlasov equation eigenvalues and eigenvectors for Fourier-Hermite dispersion matrices of order greater than 1,000
Science.gov (United States)
Grant, F. C.
1972-01-01
The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).
10. Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain
Science.gov (United States)
Boudin, Laurent; Grandmont, Céline; Moussa, Ayman
2017-02-01
In this article, we prove the existence of global weak solutions for the incompressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain with absorption boundary conditions for the kinetic part. This model arises from the study of respiratory aerosol in the human airways. The proof is based on a regularization and approximation strategy designed for our time-dependent framework.
11. Common cold
Science.gov (United States)
... have a low fever or no fever. Young children often run a fever around 100 to 102°F (37.7 to 38.8°C). Depending on which virus caused your cold, you may also have: Cough Decreased appetite Headache Muscle aches Postnasal drip Sore throat
12. Project COLD.
Science.gov (United States)
Kazanjian, Wendy C.
1982-01-01
Describes Project COLD (Climate, Ocean, Land, Discovery) a scientific study of the Polar Regions, a collection of 35 modules used within the framework of existing subjects: oceanography, biology, geology, meterology, geography, social science. Includes a partial list of topics and one activity (geodesic dome) from a module. (Author/SK)
13. A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
CERN Document Server
Rendall, Alan D
2010-01-01
In this paper the existence of a class of self-similar solutions of the Einstein-Vlasov system is proved. The initial data for these solutions are not smooth, with their particle density being supported in a submanifold of codimension one. They can be thought of as intermediate between smooth solutions of the Einstein-Vlasov system and dust. The motivation for studying them is to obtain insights into possible violation of weak cosmic censorship by solutions of the Einstein-Vlasov system. By assuming a suitable form of the unknowns it is shown that the existence question can be reduced to that of the existence of a certain type of solution of a four-dimensional system of ordinary differential equations depending on two parameters. This solution starts at a particular point $P_0$ and converges to a stationary solution $P_1$ as the independent variable tends to infinity. The existence proof is based on a shooting argument and involves relating the dynamics of solutions of the four-dimensional system to that of s...
14. Cold fusion
Energy Technology Data Exchange (ETDEWEB)
Suh, Suk Yong; Sung, Ki Woong; Kang, Joo Sang; Lee, Jong Jik [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1995-02-01
So called cold fusion phenomena are not confirmed yet. Excess heat generation is very delicate one. Neutron generation is most reliable results, however, the records are erratic and the same results could not be repeated. So there is no reason to exclude the malfunction of testing instruments. The same arguments arise in recording {sup 4}He, {sup 3}He, {sup 3}H, which are not rich in quantity basically. An experiment where plenty of {sup 4}He were recorded is attached in appendix. The problem is that we are trying to search cold fusion which is permitted by nature or not. The famous tunneling effect in quantum mechanics will answer it, however, the most fusion rate is known to be negligible. The focus of this project is on the theme that how to increase that negligible fusion rate. 6 figs, 4 tabs, 1512 refs. (Author).
15. Electron/ion whistler instabilities and magnetic noise bursts
Science.gov (United States)
Akimoto, K.; Gary, S. Peter; Omidi, N.
1987-01-01
Two whistler instabilities are investigated by means of the linear Vlasov dispersion equation. They are called the electron/ion parallel and oblique whistler instabilities, and are driven by electron/ion relative drifts along the magnetic field. It is demonstrated that the enhanced fluctuations from these instabilities can explain several properties of magnetic noise bursts in and near the plasma sheet in the presence of ion beams and/or field-aligned currents. At sufficiently high plasma beta, these instabilities may affect the current system in the magnetotail.
16. Investigation of Ion Acoustic Waves in Collisionless Plasmas
DEFF Research Database (Denmark)
Christoffersen, G. B.; Jensen, Vagn Orla; Michelsen, Poul
1974-01-01
The Green's functions for the linearized ion Vlasov equation with a given boundary value are derived. The propagation properties of ion acoustic waves are calculated by performing convolution integrals over the Green's functions. For Te/Ti less than about 3 it is concluded that the collective...... interaction is very weak and that the propagation properties are determined almost completely by freely streaming ions. The wave damping, being due to phase mixing, is determined by the width of the perturbed distribution function rather than by the slope of the undisturbed distribution function at the phase...
17. Vlasov-Fokker-Planck simulations of fast-electron transport with hydrodynamic plasma response
Energy Technology Data Exchange (ETDEWEB)
Kingham, R J; Sherlock, M; Ridgers, C P; Evans, R G, E-mail: [email protected] [Plasma Physics Group, Imperial College London, London SW7 2AZ (United Kingdom)
2010-08-01
We report on kinetic simulations of the transport of laser-produced relativistic electron beams (REB) through solid-density plasma, including the hydrodynamic response of the plasma. We consider REBs with parameters relevant to fast-ignition of compressed inertial confinement fusion capsules. We show that over the 10-20ps timescales required for fast-ignition, thermal pressure (from Ohmic heating) can significantly modify the density which in turn strongly affects the propagation of injected fast-electrons; it allows them to re-collimate into a narrow, intense beam under conditions where they initially undergo beam-hollowing. Similar static-density calculations do not show re-collimation. The re-collimation effect is attributed to PdV cooling in the pressure-induced density-channel, which in turn suppresses defocusing magnetic fields generated by resistivity gradients. These simulations have been carried out using the new 2D-3V Vlasov-Fokker-Planck (VFP) code FIDO running in hybrid mode.
18. A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures
Science.gov (United States)
Reddell, Noah
Advances are reported in the three pillars of computational science achieving a new capability for understanding dynamic plasma phenomena outside of local thermodynamic equilibrium. A continuum kinetic model for plasma based on the Vlasov-Maxwell system for multiple particle species is developed. Consideration is added for boundary conditions in a truncated velocity domain and supporting wall interactions. A scheme to scale the velocity domain for multiple particle species with different temperatures and particle mass while sharing one computational mesh is described. A method for assessing the degree to which the kinetic solution differs from a Maxwell-Boltzmann distribution is introduced and tested on a thoroughly studied test case. The discontinuous Galerkin numerical method is extended for efficient solution of hyperbolic conservation laws in five or more particle phase-space dimensions using tensor-product hypercube elements with arbitrary polynomial order. A scheme for velocity moment integration is integrated as required for coupling between the plasma species and electromagnetic waves. A new high performance simulation code WARPM is developed to efficiently implement the model and numerical method on emerging many-core supercomputing architectures. WARPM uses the OpenCL programming model for computational kernels and task parallelism to overlap computation with communication. WARPM single-node performance and parallel scaling efficiency are analyzed with bottlenecks identified guiding future directions for the implementation. The plasma modeling capability is validated against physical problems with analytic solutions and well established benchmark problems.
19. Vlasov simulations of Kinetic Alfv\\'en Waves at proton kinetic scales
CERN Document Server
Vasconez, C L; Camporeale, E; Veltri, P
2014-01-01
Kinetic Alfv\\'en waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length $d_p$ and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfv\\'en waves at proton kinetic scales, in typical conditions of the solar wind environment. In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to $d_p$ and proton plasma beta $\\bet... 20. Comparison of Semi-Lagrangian Algorithms for Solving Vlasov-type Equations Science.gov (United States) Brunner, Stephan 2005-10-01 In view of pursuing CRPP's effort in carrying out gyrokinetic simulations using an Eulerian-type approach [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)], different alternative algorithms have been considered. The issue is to identify the most appropriate time-stepping scheme, both from a point of view of numerical accuracy and numerical efficiency. Our efforts have concentrated on two semi-Lagrangian approaches: The widely used cubic B-spline interpolation scheme, based on the original work of Cheng and Knorr [C. Z. Cheng and G. Knorr, J. Comp. Phys. 22, 330 (1976)], as well as the Cubic Interpolation Propagation (CIP) scheme, based on cubic Hermite interpolation, which has only more recently been applied for solving Vlasov-type equations [T. Nakamura and T. Yabe, Comp. Phys. Comm. 120, 122 (1999)]. The systematic comparison of these algorithms with respect to their basic spectral (diffusion/dispersion) properties, as well as their ability to avoid the overshoot (Gibbs) problem, is first presented. Results from solving a guiding-center model of the two-dimensional Kelvin-Helmholtz instability are then compared. This test problem enables to address some of the key technical issues also met with the more complex gyrokinetic-type equations. 1. The exact solution of one-dimensional nonrelativistic Vlasov equation: Antitropic electron beams and Landau damping Science.gov (United States) Stepanov, Nikolay S.; Zelekson, Lev A. 2017-03-01 The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams. 2. Vlasov-Maxwell, self-consistent electromagnetic wave emission simulations of type III solar radio bursts CERN Document Server Tsiklauri, David 2010-01-01 1.5D Vlasov-Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the solar physics context. The simulations mimic the plasma emission mechanism and Larmor drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. When density gradient is removed (i.e. when plasma becomes stable to Larmor-drift instability) and a$low$density, super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, plasma emission mechanism generates non-esc... 3. Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation KAUST Repository Haji-Ali, Abdul-Lateef 2017-09-12 We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the weak solution of the limiting McKean–Vlasov SDE. To that end, our approach uses systems with finite numbers of particles and a time-stepping scheme. In this case, there are two discretization parameters: the number of time steps and the number of particles. Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of $$\\\\mathrm {TOL}$$TOL, is when using the partitioning estimator and the Milstein time-stepping scheme. We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of . Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators. 4. Identification of low-frequency kinetic wave modes in the Earth's ion foreshock Directory of Open Access Journals (Sweden) X. Blanco-Cano Full Text Available In this work we use ion and magnetic field data from the AMPTE-UKS mission to study the characteristics of low frequency (ωr « Ωp waves observed upstream of the Earth's bow shock. We test the application of various plasma-field correlations and magnetic ratios derived from linear Vlasov theory to identify the modes in this region. We evaluate (for a parameter space consistent with the ion foreshock the Alfvén ratio, the parallel compressibility, the cross-helicity, the noncoplanar ratio, the magnetic compression and the polarization for the two kinetic instabilities that can be generated in the foreshock by the interaction of hot diffuse ions with the solar wind: the left-hand resonant and the right-hand resonant ion beam instabilities. Comparison of these quantities with the observed plasma-field correlations and various magnetic properties of the waves observed during 10 intervals on 30 October 1984, where the waves are associated with diffuse ions, allows us to identify regions with Alfvénic waves and regions where the predominant mode is the right-hand resonant instability. In all the cases the waves are transverse, propagating at angles ≤ 33° and are elliptically polarized. Our results suggest that while the observed Alfvén waves are generated locally by hot diffuse ions, the right-handed waves may result from the superposition of waves generated by two different types of beam distribution (i.e. cold beam and diffuse ions. Even when there was good agreement between the values of observed transport ratios and the values given by the theory, some discrepancies were found. This shows that the observed waves are different from the theoretical modes and that mode identification based only on polarization quantities does not give a complete picture of the waves' characteristics and can lead to mode identification of waves whose polarization may agree with theoretical predictions even when 5. Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen Energy Technology Data Exchange (ETDEWEB) Le Bourdiec, S 2007-03-15 Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author) 6. Cough & Cold Medicine Abuse Science.gov (United States) ... A Week of Healthy Breakfasts Shyness Cough & Cold Medicine Abuse KidsHealth > For Teens > Cough & Cold Medicine Abuse ... DXM Why Do People Use Cough and Cold Medicines to Get High? There's an ingredient in many ... 7. Monte Carlo particle-in-cell methods for the simulation of the Vlasov-Maxwell gyrokinetic equations Science.gov (United States) Bottino, A.; Sonnendrücker, E. 2015-10-01 > The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov-Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations. 8. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm Science.gov (United States) Chen, G.; Chacón, L. 2015-12-01 For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V. 9. Generation of initial Vlasov distributions for simulation of charged particle beams with high space-charge intensity Energy Technology Data Exchange (ETDEWEB) Lund, S M; Kikuchi, T; Davidson, R C 2007-04-12 Self-consistent Vlasov simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel, both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of distributions commonly in use as initial Vlasov distributions in simulations of beams with intense space-charge fields including: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various non-equilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of usual accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial distributions are constructed using transformations that preserve linear-focusing single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for non-continuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulation applications that more precisely probe intrinsic stability properties and machine performance. 10. Self-consistent Vlasov-Maxwell description of the longitudinal dynamics of intense charged particle beams Directory of Open Access Journals (Sweden) Ronald C. Davidson 2004-02-01 Full Text Available This paper describes a self-consistent kinetic model for the longitudinal dynamics of a long, coasting beam propagating in straight (linear geometry in the z direction in the smooth-focusing approximation. Starting with the three-dimensional Vlasov-Maxwell equations, and integrating over the phase-space (x_{⊥},p_{⊥} transverse to beam propagation, a closed system of equations is obtained for the nonlinear evolution of the longitudinal distribution function F_{b}(z,p_{z},t and average axial electric field ⟨E_{z}^{s}⟩(z,t. The primary assumptions in the present analysis are that the dependence on axial momentum p_{z} of the distribution function f_{b}(x,p,t is factorable, and that the transverse beam dynamics remains relatively quiescent (absence of transverse instability or beam mismatch. The analysis is carried out correct to order k_{z}^{2}r_{w}^{2} assuming slow axial spatial variations with k_{z}^{2}r_{w}^{2}≪1, where k_{z}∼∂/∂z is the inverse length scale of axial variation in the line density λ_{b}(z,t=∫dp_{z}F_{b}(z,p_{z},t, and r_{w} is the radius of the conducting wall (assumed perfectly conducting. A closed expression for the average longitudinal electric field ⟨E_{z}^{s}⟩(z,t in terms of geometric factors, the line density λ_{b}, and its derivatives ∂λ_{b}/∂z,… is obtained for the class of bell-shaped density profiles n_{b}(r,z,t=(λ_{b}/πr_{b}^{2}f(r/r_{b}, where the shape function f(r/r_{b} has the form specified by f(r/r_{b}=(n+1(1-r^{2}/r_{b}^{2}^{n} for 0≤r 11. Vlasov - Maxwell, Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona Science.gov (United States) Tsiklauri, David 2010-12-01 1.5D Vlasov - Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the context of solar physics. The simulations mimic the plasma emission mechanism and Larmor-drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that a 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to the Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. The generated perturbations consist of two parts: i) non-escaping (trapped) Langmuir type oscillations, which are localised in the regions of density inhomogeneity, and are highly filamentary, with the period of appearance of the filaments close to electron plasma frequency in the dense regions; and ii) escaping electromagnetic radiation with phase speeds close to the speed of light. When the density gradient is removed ( i.e. when plasma becomes stable to the Larmor-drift instability) and a low density super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, the plasma emission mechanism generates non-escaping Langmuir type oscillations, which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips (the narrow-band line emission) observed in some dynamical spectra. Predictions of quasilinear theory are: i) the electron free streaming and ii) the long relaxation time of the beam, in accord with the analytic expressions. These are corroborated via direct, fully-kinetic simulation 12. Cold confusion Energy Technology Data Exchange (ETDEWEB) Chapline, G. 1989-07-01 On March 23 two chemists, Martin Fleischmann and Stanley Pons startled the world with a press conference at the University of Utah where they announced that they had achieved nuclear fusion at room temperatures. As evidence they cited the production of ''excess'' amounts of heat in an electrochemical apparatus and observation of neutron production. While the production of heat in a chemical apparatus is not in itself unusual the observation of neutrons is certainly extraordinary. As it turned out, though, careful measurements of the neutron production in electrochemical apparatus similar to that used by Fleischmann and Pons carried out at dozens of other laboratories has shown that the neutron production fails by many orders of magnitude to support the assertion by Fleischmann and Pons that their discovery represents a new and cheap source of fusion power. In particular, independent measurements of the neutron production rate suggest that the actual rate of fusion energy production probably does not exceed 1 trillionth of a watt. This paper discusses the feasibility that cold fusion is actually being achieved. 7 refs. 13. 3D Maxwell-Vlasov boundary value problem solution in stellarator geometry in ion cyclotron frequency range Energy Technology Data Exchange (ETDEWEB) Vdovin, V.; Watari, T. [National Inst. for Fusion Science, Nagoya (Japan); Fukuyama, A. 1997-12-31 In the work we formulate the basic equations to solve the above ICRF problem in flux coordinates on different equilibria. The kinetic effects like cyclotron and Cherenkov absorptions, along with excitation of kinetic Alfven waves and finite Larmor radius effects are included. The ICRF plasma heating ({omega} {approx} {omega}{sub ci}) methods are prepared for the newly constructed LHD and projected W7-X stellarators or are conducted on operating machines like W7-AS, CHS, etc. For their adequate ICRH modelling and antenna development it is needed to create more complicated in compare with tokamaks ICRF code accounting for non axis symmetrical plasmas in complicated geometry. (author) 14. Cold energy Science.gov (United States) Wallace, John P. 2015-12-01 Deviations in Q for resonant superconducting radio frequency niobium accelerator cavities are generally correlated with resistivity loss mechanisms. Field dependent Qs are not well modeled by these classical loss mechanisms, but rather can represent a form of precision cavity surface thermometry. When the field dependent Q variation shows improvement with increasing B field level the classical treatment of this problem is inadequate. To justify this behavior hydrogen as a ubiquitous impurity in niobium, which creates measurable property changes, even at very low concentrations is typically considered the cause of such anomalous behavior. This maybe the case in some instances, but more importantly any system operating with a highly coherent field with a significant time dependent magnetic component at near 2° K will have the ability to organize the remaining free spins within the London penetration depth to form a coupled energy reservoir in the form of low mass spin waves. The niobium resonant cavities are composed of a single isotope with a large nuclear spin. When the other loss mechanisms are stripped away this may be the gain medium activated by the low level residual magnetic fields. It was found that one resonant cavity heat treatment produced optimum surface properties and then functioned as a MASER extracting energy from the 2° K thermal bath while cooling the cavity walls. The cavity operating in this mode is a simulator of what can take place in the wider but not colder universe using the cosmic microwave background (CMB) as a thermal source. The low mass, long lifetimes, and the scale of the magnetic spin waves on the weakly magnetized interstellar medium allows energy to be stored that is many orders of magnitude colder than the cosmic microwave background. A linear accelerator cavity becomes a tool to explore the properties of the long wave length magnetic spin waves that populate this cold low energy regime. 15. Cold energy Energy Technology Data Exchange (ETDEWEB) Wallace, John P., E-mail: [email protected] [Casting Analysis Corp., PO Box 52, Weyers Cave, VA 24486 (United States) 2015-12-04 Deviations in Q for resonant superconducting radio frequency niobium accelerator cavities are generally correlated with resistivity loss mechanisms. Field dependent Qs are not well modeled by these classical loss mechanisms, but rather can represent a form of precision cavity surface thermometry. When the field dependent Q variation shows improvement with increasing B field level the classical treatment of this problem is inadequate. To justify this behavior hydrogen as a ubiquitous impurity in niobium, which creates measurable property changes, even at very low concentrations is typically considered the cause of such anomalous behavior. This maybe the case in some instances, but more importantly any system operating with a highly coherent field with a significant time dependent magnetic component at near 2° K will have the ability to organize the remaining free spins within the London penetration depth to form a coupled energy reservoir in the form of low mass spin waves. The niobium resonant cavities are composed of a single isotope with a large nuclear spin. When the other loss mechanisms are stripped away this may be the gain medium activated by the low level residual magnetic fields. It was found that one resonant cavity heat treatment produced optimum surface properties and then functioned as a MASER extracting energy from the 2° K thermal bath while cooling the cavity walls. The cavity operating in this mode is a simulator of what can take place in the wider but not colder universe using the cosmic microwave background (CMB) as a thermal source. The low mass, long lifetimes, and the scale of the magnetic spin waves on the weakly magnetized interstellar medium allows energy to be stored that is many orders of magnitude colder than the cosmic microwave background. A linear accelerator cavity becomes a tool to explore the properties of the long wave length magnetic spin waves that populate this cold low energy regime. 16. Kinetic description of electron-proton instability in high-intensity proton linacs and storage rings based on the Vlasov-Maxwell equations Directory of Open Access Journals (Sweden) Ronald C. Davidson 1999-05-01 Full Text Available The present analysis makes use of the Vlasov-Maxwell equations to develop a fully kinetic description of the electrostatic, electron-ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating in the z direction with average axial momentum γ_{b}m_{b}β_{b}c through a stationary population of background electrons. The ion beam has characteristic radius r_{b} and is treated as continuous in the z direction, and the applied transverse focusing force on the beam ions is modeled by F_{foc}^{b}=-γ_{b}m_{b}ω_{βb}^{0^{2}}x_{⊥} in the smooth-focusing approximation. Here, ω_{βb}^{0}=const is the effective betatron frequency associated with the applied focusing field, x_{⊥} is the transverse displacement from the beam axis, (γ_{b}-1m_{b}c^{2} is the ion kinetic energy, and V_{b}=β_{b}c is the average axial velocity, where γ_{b}=(1-β_{b}^{2}^{-1/2}. Furthermore, the ion motion in the beam frame is assumed to be nonrelativistic, and the electron motion in the laboratory frame is assumed to be nonrelativistic. The ion charge and number density are denoted by +Z_{b}e and n_{b}, and the electron charge and number density by -e and n_{e}. For Z_{b}n_{b}>n_{e}, the electrons are electrostatically confined in the transverse direction by the space-charge potential φ produced by the excess ion charge. The equilibrium and stability analysis retains the effects of finite radial geometry transverse to the beam propagation direction, including the presence of a perfectly conducting cylindrical wall located at radius r=r_{w}. In addition, the analysis assumes perturbations with long axial wavelength, k_{z}^{2}r_{b}^{2}≪1, and sufficiently high frequency that |ω/k_{z}|≫v_{Tez} and |ω/k_{z}-V_{b}|≫v_{Tbz}, where v_{Tez} and v_{Tbz} are the characteristic axial thermal speeds of the background electrons and beam ions. In this regime, Landau damping (in axial velocity space v_{z} by resonant ions and 17. Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations Energy Technology Data Exchange (ETDEWEB) Chen, Guangye [Los Alamos National Laboratory; Chacon, Luis [Los Alamos National Laboratory; Knoll, Dana Alan [Los Alamos National Laboratory; Barnes, Daniel C [Coronado Consulting 2015-07-31 A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ωpeΔt >>1, and Δx >> λD), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylov (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary. 18. Hamiltonian fluid closures of the Vlasov-Amp{\\e}re equations: from water-bags to N moment models CERN Document Server Perin, M; Morrison, P J; Tassi, E 2015-01-01 Moment closures of the Vlasov-Amp{\\e}re system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed. 19. Proof of the cosmic no-hair conjecture in the T^3-Gowdy symmetric Einstein-Vlasov setting CERN Document Server Andréasson, Håkan 2013-01-01 The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions; the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T^3-Gowdy symmetric solutions to the Einstein-Vlasov equations with a positive cosmological constant. In particular, we prove the cosmic no-hair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure... 20. Vlasov modelling of laser-driven collisionless shock acceleration of protons Energy Technology Data Exchange (ETDEWEB) Svedung Wettervik, B.; DuBois, T. C.; Fülöp, T. [Department of Applied Physics, Chalmers University of Technology, Gothenburg (Sweden) 2016-05-15 Ion acceleration due to the interaction between a short high-intensity laser pulse and a moderately overdense plasma target is studied using Eulerian Vlasov–Maxwell simulations. The effects of variations in the plasma density profile and laser pulse parameters are investigated, and the interplay of collisionless shock and target normal sheath acceleration is analyzed. It is shown that the use of a layered-target with a combination of light and heavy ions, on the front and rear side, respectively, yields a strong quasi-static sheath-field on the rear side of the heavy-ion part of the target. This sheath-field increases the energy of the shock-accelerated ions while preserving their mono-energeticity. 1. Cold stress alters transcription in meiotic anthers of cold tolerant chickpea (Cicer arietinum L.). Science.gov (United States) Sharma, Kamal Dev; Nayyar, Harsh 2014-10-11 Cold stress at reproductive phase in susceptible chickpea (Cicer arietinum L.) leads to pollen sterility induced flower abortion. The tolerant genotypes, on the other hand, produce viable pollen and set seed under cold stress. Genomic information on pollen development in cold-tolerant chickpea under cold stress is currently unavailable. DDRT-PCR analysis was carried out to identify anther genes involved in cold tolerance in chickpea genotype ICC16349 (cold-tolerant). A total of 9205 EST bands were analyzed. Cold stress altered expression of 127 ESTs (90 up-regulated, 37 down-regulated) in anthers, more than two third (92) of which were novel with unknown protein identity and function. Remaining about one third (35) belonged to several functional categories such as pollen development, signal transduction, ion transport, transcription, carbohydrate metabolism, translation, energy and cell division. The categories with more number of transcripts were carbohydrate/triacylglycerol metabolism, signal transduction, pollen development and transport. All but two transcripts in these categories were up-regulated under cold stress. To identify time of regulation after stress and organ specificity, expression levels of 25 differentially regulated transcripts were also studied in anthers at six time points and in four organs (anthers, gynoecium, leaves and roots) at four time points. Limited number of genes were involved in regulating cold tolerance in chickpea anthers. Moreover, the cold tolerance was manifested by up-regulation of majority of the differentially expressed transcripts. The anthers appeared to employ dual cold tolerance mechanism based on their protection from cold by enhancing triacylglycerol and carbohydrate metabolism; and maintenance of normal pollen development by regulating pollen development genes. Functional characterization of about two third of the novel genes is needed to have precise understanding of the cold tolerance mechanisms in chickpea anthers. 2. Long Life Cold Cathodes for Hall effect Thrusters Project Data.gov (United States) National Aeronautics and Space Administration — An electron source incorporating long life, high current density cold cathodes inside a microchannel plate for use with ion thrusters is proposed. Cathode lifetime... 3. Cold Stress and the Cold Pressor Test Science.gov (United States) Silverthorn, Dee U.; Michael, Joel 2013-01-01 Temperature and other environmental stressors are known to affect blood pressure and heart rate. In this activity, students perform the cold pressor test, demonstrating increased blood pressure during a 1- to 2-min immersion of one hand in ice water. The cold pressor test is used clinically to evaluate autonomic and left ventricular function. This… 4. Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in small wave number region CERN Document Server Feng, Q S; Wang, Q; Zheng, C Y; Liu, Z J; Cao, L H; He, X T 2016-01-01 The properties of the nonlinear frequency shift (NFS) especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas have been researched by Vlasov simulation. The pictures of the nonlinear frequency shift from harmonic generation and particles trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given and the results of Vlasov simulation are consistent to the theoretical result of multi-ion species plasmas. When the wave number$k\\lambda_{De}$is small, such as$k\\lambda_{De}=0.1$, the fluid NFS dominates in the total NFS and will reach as large as nearly$15\\%$when the wave amplitude$|e\\phi/T_e|\\sim0.1$, which indicates that in the condition of small$k\\lambda_{De}$, the fluid NFS dominates in the saturation of stimulated Brillouin scattering especially when the nonlinear IAW amplitude is large. 5. Cold and Cough Medicines Science.gov (United States) ... What can you do for your cold or cough symptoms? Besides drinking lots of fluids and getting ... medicines. There are lots of different cold and cough medicines, and they do different things. Nasal decongestants - ... 6. Cold-induced metabolism NARCIS (Netherlands) van Marken Lichtenbelt, W.D.; Daanen, A.M. 2003-01-01 Cold-induced metabolism. van Marken Lichtenbelt WD, Daanen HA. Department of Human Biology, Maastricht University, Maastricht, The Netherlands. PURPOSE OF REVIEW: Cold response can be insulative (drop in peripheral temperature) or metabolic (increase in energy expenditure). Nonshivering thermogenesi 7. Cold nuclear fusion National Research Council Canada - National Science Library Huang Zhenqiang Huang Yuxiang 2013-01-01 ...... And with a magnetic moment of light nuclei controlled cold nuclear collide fusion, belongs to the nuclear energy research and development in the field of applied technology "cold nuclear collide fusion... 8. Magnetoacoustic heating by ion Landau damping Science.gov (United States) Turner, L. 1980-01-01 The Vlasov-fluid model of Freidberg (1972) is used to study the resonance heating of a sharp-boundary screw pinch. The analysis provides the first treatment of the magnetoacoustic heating of a cylindrical plasma by means of ion Landau damping, which was identified as a viable dissipative mechanism for the conversion of magnetoacoustic wave energy into ion thermal energy. In addition, local and global energy conservation are considered, and formulae and numerical results for the thermal energy doubling time and the associated induced rf electric fields are presented. It is shown that collisionless absorption can provide a heating mechanism when an equilibrium plasma column is pumped by oscillations of the confining magnetic field at a frequency near the oblique magnetoacoustic frequency. 9. Thermalization and isotropization in heavy-ion collisions Indian Academy of Sciences (India) Michael Strickland 2015-05-01 Our current understanding of the processes driving the thermalization and isotropization of the quark gluon plasma (QGP) created in ultrarelativistic heavy-ion collisions (URHICs) is reviewed. Initially, the phenomenological evidence in favour of the creation of a thermal but momentum–space anisotropic QGP in URHICs is discussed. Further, the degree of isotropization using viscous (dissipative) hydrodynamics, weak-coupling approaches to QGP dynamics, and strong-coupling approaches to QGP dynamics are discussed. Finally, recent progress in the area of real-time non-Abelian gauge field simulations and non-Abelian Boltzmann–Vlasov-based hard-loop simulations are reported. 10. Absolute and Convective Ion Beam Instability Studied through Green's Function DEFF Research Database (Denmark) Jensen, Vagn Orla; Michelsen, Poul; Hsuan, H. C. S. 1974-01-01 A Vlasov plasma with a double‐humped, unstable ion velocity distribution function is considered. A δ function in space is assumed as the initial perturbation and the plasma response to this perturbation is calculated, i.e., the Green's function for the problem is found. The response can be divide...... into two parts: a self‐similar, damped part of the form t−1h(x/t), and an unstable, exponentially growing part. The conditions for absolute and convective growth of the latter are discussed.... 11. Estimation of cold plasma outflow during geomagnetic storms CERN Document Server Haaland, S; André, M; Maes, L; Baddeley, L; Barakat, A; Chappell, R; Eccles, V; Johnsen, C; Lybekk, B; Li, K; Pedersen, A; Schunk, R; Welling, D 2016-01-01 Low-energy ions of ionospheric origin constitute a significant contributor to the magnetospheric plasma population. Measuring cold ions is difficult though. Observations have to be done at sufficiently high altitudes and typically in regions of space where spacecraft attain a positive charge due to solar illumination. Cold ions are therefore shielded from the satellite particle detectors. Furthermore, spacecraft can only cover key regions of ion outflow during segments of their orbit, so additional complications arise if continuous longtime observations, such as during a geomagnetic storm, are needed. In this paper we suggest a new approach, based on a combination of synoptic observations and a novel technique to estimate the flux and total outflow during the various phases of geomagnetic storms. Our results indicate large variations in both outflow rates and transport throughout the storm. Prior to the storm main phase, outflow rates are moderate, and the cold ions are mainly emanating from moderately sized ... 12. The Einstein-Vlasov system in spherical symmetry: reduction of the equations of motion and classification of single-shell static solutions, in the limit of massless particles CERN Document Server Gundlach, Carsten 2016-01-01 We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable$z$(radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables$(t,r,z)$only. Similarly, in this limit the Vlasov density function$f$for static solutions depends on a single variable$Q$(energy over angular momentum). This reduction allows us to show that any given static metric which has vanishing Ricci scalar, is vacuum at the centre and for$r>3M$and obeys certain energy conditions uniquely determines a consistent$f=\\bar k(Q)$(in closed form). Vice versa, any$\\bar k(Q)$within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ODEs). Hence the space of static spherically symmetric solutions of Einstein-Vlasov is locally a space of functions of one variable. For a simple 2-parameter family of functions$\\bar k(Q)$, we construct the co... 13. Interferometry with Strontium Ions Science.gov (United States) Jackson, Jarom; Lambert, Enoch; Otterstrom, Nils; Jones, Tyler; Durfee, Dallin 2014-05-01 We describe progress on a cold ion matter-wave interferometer. Cold Strontium atoms are extracted from an LVIS. The atoms will be photo-ionized with a two-photon transition to an auto-ionizing state in the continuum. The ions will be split and recombined using stimulated Raman transitions from a pair of diode lasers injection locked to two beams from a master laser which have been shifted up and down by half the hyperfine splitting. We are developing laser instrumentation for this project including a method to prevent mode-hopping by analyzing laser frequency noise, and an inexpensive, robust wavelength meter. Supported by NSF Award No. 1205736. 14. Heavy ion storage rings Energy Technology Data Exchange (ETDEWEB) Schuch, R. 1987-01-01 A brief overview of synchrotron storage rings for heavy ions, which are presently under construction in different accelerator laboratories is given. Ions ranging from protons up to uranium ions at MeV/nucleon energies will be injected into these rings using multiturn injection from the accelerators available or being built in these laboratories. After injection, it is planned to cool the phase space distribution of the ions by merging them with cold electron beams or laser beams, or by using stochastic cooling. Some atomic physics experiments planned for these rings are presented. 15. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems CERN Document Server Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Sun, Yajuan 2015-01-01 Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially-discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a splitting method discovered by He et al., which produces five exactly-soluable sub-systems, and high-order structure- preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom ... 16. Vlasov simulations of electron heating by Langmuir turbulence near the critical altitude in the radiation-modified ionosphere Science.gov (United States) Wang, J. G.; Newman, D. L.; Goldman, M. V. 1997-12-01 One-dimensional Vlasov equations are solved numerically for conditions appropriate to the ionospheric F-region during the initial stages of HF-radiation modification experiments at two altitudes: one at the critical altitude, the other approximately 1.5 km lower. Numerical simulations of wave growth and saturation with self-consistent evolution of particle distributions are run past the point at which a statistically steady state is reached. At the critical altitude the wave turbulence is dominated by coherent collapsing wave packets or cavitons' and at the lower altitude by a combination of coherent (strong) and incoherent (weak) turbulence. Our results are consistent with the predictions of Hanssen et al. [Journal of Geophysical Research, 97, 12,073 (1992)]. Semi-open boundary conditions, in which a small fraction of the hot electrons generated by interactions with the strong localized caviton fields are replaced by electrons from the cool background distribution, are employed to model a heated region of finite length that is large compared to the simulation domain. The resultant steady-state electron distributions are characterized by power-law tails of hot electrons superposed on an approximately Maxwellian bulk distribution. The Langmuir-wave dissipation spectra are found to be in good agreement with predictions based on linear Landau damping on the nonthermal electron tails. 17. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems Energy Technology Data Exchange (ETDEWEB) Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China 2015-11-01 Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC. 18. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems Energy Technology Data Exchange (ETDEWEB) Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 (China); Qin, Hong, E-mail: [email protected] [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China) 2015-11-15 Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. 19. Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations Science.gov (United States) Silantyev, Denis A.; Lushnikov, Pavel M.; Rose, Harvey A. 2017-04-01 A nonlinear Langmuir wave in the kinetic regime k λ D ≳ 0.2 may have a filamentation instability, where k is the wavenumber and λD is the Debye length. The nonlinear stage of that instability develops into the filamentation of Langmuir waves which in turn leads to the saturation of the stimulated Raman scattering in laser-plasma interaction experiments. Here, we study the linear stage of the filamentation instability of the particular family (H. A. Rose and D. A. Russell, Phys. Plasmas 8, 4784 (2001)) of Bernstein-Greene-Kruskal (BGK) modes (I. B. Bernstein et al., Phys. Rev. 108, 546 (1957)) that is a bifurcation of the linear Langmuir wave. Performing direct 2 + 2D Vlasov-Poisson simulations of collisionless plasma, we find the growth rates of oblique modes of the electric field as a function of BGK's amplitude, wavenumber, and the angle of the oblique mode's wavevector relative to the BGK's wavevector. Simulation results are compared to theoretical predictions. 20. AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov-Poisson equation Science.gov (United States) Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; Yu, Kwangmin 2016-07-01 We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov-Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques. 1. Global well-posedness and large time behavior of classical solutions to the Vlasov-Fokker-Planck and magnetohydrodynamics equations Science.gov (United States) Jiang, Peng 2017-02-01 We are concerned with the global well-posedness of the fluid-particle system which describes the evolutions of disperse two-phase flows. The system consists of the Vlasov-Fokker-Planck equation for the dispersed phase (particles) coupled to the compressible magnetohydrodynamics equations modelling a dense phase (fluid) through the friction forcing. Global well-posedness of the Cauchy problem is established in perturbation framework, and rates of convergence of solutions toward equilibrium, which are algebraic in the whole space and exponential on torus, are also obtained under some additional conditions on initial data. The existence of global solution and decay rate of the solution are proved based on the classical energy estimates and Fourier multiplier technique, which are considerably complicated and some new ideas and techniques are thus required. Moreover, it is shown that neither shock waves nor vacuum and concentration in the solution are developed in a finite time although there is a complex interaction between particle and fluid. 2. Kinetic Simulations - Oshun (Vlasov-Fokker-Planck) and PIC (Osiris) - Physics and Open Source Software In The UCLA PICKSE Initiative Science.gov (United States) Tableman, Adam; Tzoufras, Michail; Fonseca, Ricardo; Mori, W. B. 2016-10-01 We present physics results and general updates for two plasma kinetic simulation codes developed under the UCLA PICKSE initiative. We also discuss the issues around making these codes open source such that they can be used (and contributed too) by a large audience. The first code discussed is Oshun - a Vlasov-Fokker-Planck (VFP) code. Recent simulations with the VFP code OSHUN will be presented for all of the aforementioned problems. The algorithmic improvements that have facilitated these studies will be also be discussed. The second code discussed is the PIC code Osiris. Osiris is a widely respected code used in hundreds of papers. Osiris was first developed for laser-plasma interactions but has grown into a robust framework covering most areas of plasma research. One defining feature of Osiris is that it is highly optimized for a variety of hardware configurations and scales linearly over 1 million + CPU nodes. We will discuss the recently released version 4.0 written in modern, fully-object oriented FORTRAN. Funding provided by Grants NSF ACI 1339893 and DOE DE NA 0001833. 3. AN ASYMPTOTIC PRESERVING SCHEME FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN THE HIGH FIELD REGIME Institute of Scientific and Technical Information of China (English) Shi Jin; Li Wang 2011-01-01 The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects (electrical or gravitational) are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field.We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime,namely,large time steps and coarse meshes can be used,yet the high field limit is still captured.The idea is to combine the two stiff terms and treat them implicitly.Thanks to the linearity of the collision term,using the discretization described in [Jin S,Yan B.J.Comp.Phys.,2011,230:6420-6437]we only need to invert a symmetric matrix.This method can be easily extended to higher dimensions.The method is shown to be positive,stable,mass and asymptotic preserving.Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes. 4. Kinetic study of ion acoustic twisted waves with kappa distributed electrons Science.gov (United States) Arshad, Kashif; Aman-ur-Rehman, Mahmood, Shahzad 2016-05-01 The kinetic theory of Landau damping of ion acoustic twisted modes is developed in the presence of orbital angular momentum of the helical (twisted) electric field in plasmas with kappa distributed electrons and Maxwellian ions. The perturbed distribution function and helical electric field are considered to be decomposed by Laguerre-Gaussian mode function defined in cylindrical geometry. The Vlasov-Poisson equation is obtained and solved analytically to obtain the weak damping rates of the ion acoustic twisted waves in a non-thermal plasma. The strong damping effects of ion acoustic twisted waves at low values of temperature ratio of electrons and ions are also obtained by using exact numerical method and illustrated graphically, where the weak damping wave theory fails to explain the phenomenon properly. The obtained results of Landau damping rates of the twisted ion acoustic wave are discussed at different values of azimuthal wave number and non-thermal parameter kappa for electrons. 5. Atomic absorption spectroscopy in ion channel screening. Science.gov (United States) Stankovich, Larisa; Wicks, David; Despotovski, Sasko; Liang, Dong 2004-10-01 This article examines the utility of atomic absorption spectroscopy, in conjunction with cold flux assays, to ion channel screening. The multiplicity of ion channels that can be interrogated using cold flux assays and atomic absorption spectroscopy is summarized. The importance of atomic absorption spectroscopy as a screening tool is further elaborated upon by providing examples of the relevance of ion channels to various physiological processes and targeted diseases. 6. Nonlinear Evolution of the Ion-Ion Beam Instability DEFF Research Database (Denmark) Pécseli, Hans; Trulsen, J. 1982-01-01 The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates... 7. Cold suppresses agonist-induced activation of TRPV1. Science.gov (United States) Chung, M-K; Wang, S 2011-09-01 Cold therapy is frequently used to reduce pain and edema following acute injury or surgery such as tooth extraction. However, the neurobiological mechanisms of cold therapy are not completely understood. Transient receptor potential vanilloid 1 (TRPV1) is a capsaicin- and heat-gated nociceptive ion channel implicated in thermosensation and pathological pain under conditions of inflammation or injury. Although capsaicin-induced nociception, neuropeptide release, and ionic currents are suppressed by cold, it is not known if cold suppresses agonist-induced activation of recombinant TRPV1. We demonstrate that cold strongly suppressed the activation of recombinant TRPV1 by multiple agonists and capsaicin-evoked currents in trigeminal ganglia neurons under normal and phosphorylated conditions. Cold-induced suppression was partially impaired in a TRPV1 mutant that lacked heat-mediated activation and potentiation. These results suggest that cold-induced suppression of TRPV1 may share a common molecular basis with heat-induced potentiation, and that allosteric inhibition may contribute, in part, to the cold-induced suppression. We also show that combination of cold and a specific antagonist of TRPV1 can produce an additive suppression. Our results provide a mechanistic basis for cold therapy and may enhance anti-nociceptive approaches that target TRPV1 for managing pain under inflammation and tissue injury, including that from tooth extraction. 8. Cooling of ions and antiprotons with magnetized electrons CERN Document Server Mollers, B; Walter, M; Zwicknagel, G; Carli, Christian; Nersisyan, H 2004-01-01 Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. More recently antiprotons have been cooled in traps, first by electrons and then by positrons in order to produce antihydrogen atoms as simplest form of antimatter for CPT-tests. During these cooling processes the light particles are guided by strong external magnetic fields which imposes a challenge to the theoretical description. Within the binary collision model we treat the Coulomb interaction as second-order perturbation to the helix motion of the light particles and also by numerical simulations. In the complementary dielectric theory we calculate the polarization of the light particles by solving the nonlinear Vlasov-Poisson equation as well as linear response. It turns out that the linearization becomes dubious at low ion velocities. In the presence of a strong magnetic field the numerically expensive solution of the Vlasov-Poisson equation is the method of choice, alternatively one may empl... 9. Normal modes of confined cold ionic systems Energy Technology Data Exchange (ETDEWEB) Schiffer, J.P.; Dubin, D.H. [Univ. of California, San Diego, CA (United States) 1995-08-01 The normal modes of a cloud of confined ions forming a strongly-correlated plasma were investigated. The results of molecular-dynamics simulations were compared to predictions of a cold fluid mode. Mode frequencies are observed to shift slightly compared to the cold fluid predictions, and the modes are also observed to damp in time. Simulations also reveal a set of torsional oscillations which have no counterpart in cold fluid theory. The frequency shift, damping, and torsional effects are compared to a model that treats trapped plasmas as a visco-elastic spheroid. It may be possible to measure high-frequency bulk and shear moduli of a strongly-correlated plasma from mode excitation experiments on trapped non-neutral plasmas. An example of the results of the calculation is presented. 10. COLD-WORKED HARDWARE Directory of Open Access Journals (Sweden) N. M. Strizhak 2007-01-01 Full Text Available The different types of cold-worked accessory are examined in the article. The necessity of development of such type of accessory in the Republic of Belarus due to requirements of market is shown. High emphasis is placed on the methods of increase of plasticity of cold-worked accessory from usual mill of RUP and CIS countries. 11. Cold Sores (HSV-1) Science.gov (United States) ... A Week of Healthy Breakfasts Shyness Cold Sores (HSV-1) KidsHealth > For Teens > Cold Sores (HSV-1) A A A What's in this article? ... or around a person's lips, are caused by herpes simplex virus-1 (HSV-1) . But they don't ... 12. Working in the Cold Centers for Disease Control (CDC) Podcasts 2016-02-08 During the winter, many workers are outdoors, working in cold, wet, icy, or snowy conditions. Learn how to identify symptoms that tell you there may be a problem and protect yourself from cold stress. Created: 2/8/2016 by National Institute for Occupational Safety and Health (NIOSH). Date Released: 2/8/2016. 13. Cold fusion research Energy Technology Data Exchange (ETDEWEB) None 1989-11-01 I am pleased to forward to you the Final Report of the Cold Fusion Panel. This report reviews the current status of cold fusion and includes major chapters on Calorimetry and Excess Heat, Fusion Products and Materials Characterization. In addition, the report makes a number of conclusions and recommendations, as requested by the Secretary of Energy. 14. Cold-Weather Sports Science.gov (United States) ... Surgery? A Week of Healthy Breakfasts Shyness Cold-Weather Sports KidsHealth > For Teens > Cold-Weather Sports A A A What's in this article? ... Equipment Ahh, winter! Shorter days. Frigid temperatures. Foul weather. What better time to be outdoors? Winter sports ... 15. Coping with Colds Science.gov (United States) ... have heard that chicken soup can cure a cold. There's no real proof of this, but sick people have been swearing by it for more than 800 years. When Should I Go to the Doctor? Teens who catch colds usually don't get very sick or need ... 16. How Cold is Cold Dark Matter? CERN Document Server Armendariz-Picon, Cristian 2013-01-01 If cold dark matter consists of particles, these must be non-interacting and non-relativistic by definition. In most cold dark matter models, however, dark matter particles inherit a non-vanishing velocity dispersion from interactions in the early universe, a velocity that redshifts with cosmic expansion but certainly remains non-zero. In this article, we place model-independent constraints on the dark matter temperature to mass ratio, whose square root determines the dark matter velocity dispersion. We only assume that dark matter particles decoupled kinetically while non-relativistic, when galactic scales had not entered the horizon yet, and that their momentum distribution has been Maxwellian since that time. Under these assumptions, using cosmic microwave background and matter power spectrum observations, we place upper limits on the temperature to mass ratio of cold dark matter. The latter imply that its velocity dispersion extrapolated to the present has to be smaller than 56 m/s. Cold dark matter has t... 17. New Insight into Short-Wavelength Solar Wind Fluctuations from Vlasov Theory Science.gov (United States) Sahraoui, Fouad; Belmont, G.; Goldstein, M. L. 2012-01-01 The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with omega omega (sub ci)) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, Typically Beta(sub i) approx. > Beta (sub e) 1 and for high oblique angles of propagation 80 deg 1 to frequencies either larger or smaller than omega (sub ci), depending on the anisotropy kappa (parallel )/ kappa(perpendicular). This extension into small scales is more readily called whistler (omega > omega (sub ci)) or KAW (omega < omega (sub ci)) although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW. 18. New Insight into Short-wavelength Solar Wind Fluctuations from Vlasov Theory Science.gov (United States) Sahraoui, F.; Belmont, G.; Goldstein, M. L. 2012-04-01 The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfvén waves (KAWs) at sub-ion scales with ω ωci) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, typically β i >~ β e ~ 1 and for high oblique angles of propagation 80° ~ 1 to frequencies either larger or smaller than ωci, depending on the anisotropy k par/k . This extension into small scales is more readily called whistler (ω > ωci) or KAW (ω < ωci), although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW. 19. New insight into short wavelength solar wind fluctuations from Vlasov theory CERN Document Server Sahraoui, Fouad; Goldstein, Melvyn 2011-01-01 The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays. Although recent observations gave evidence of the dominance of Kinetic Alfv\\'en Waves (KAW) at sub-ion scales with$\\omega\\omega_{ci}$) is more relevant. Here, we propose to study key properties of the short wavelength plasma modes under realistic SW conditions, typically$\\beta_i\\gtrsim \\beta_e\\sim 1$and for high oblique angles of propagation$80^\\circ\\leq \\Theta_{\\bf kB}\\omega_{ci}$) or a KAW mode (with$\\omega<\\omega_{ci}$) depending on the anisotropy$k_\\parallel/ k_\\perp. This contrasts with the well-accepted idea that the whistler branch develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter a more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy co... 20. Ion–Cyclotron Resonance Frequency Interval Dependence on the O VI Ion Number Density in the North Polar Coronal Hole 1.5–3 Region Indian Academy of Sciences (India) Özgür Gültekin; Emine Rızaoǧlu; K. Gediz Akdeniz 2013-12-01 The frequency intervals in which O VI ions get in resonance with ion–cyclotron waves are calculated using the kinetic model, for the latest six values found in literature on O VI ion number densities in the 1.5–3 region of the NPCH. It is found that the common resonance interval is 1.5 kHz to 3 kHz. The -variations of wave numbers necessary for the above calculations are evaluated numerically, solving the cubic dispersion relation with the dielectric response derived from the quasi-linear Vlasov equation for the left-circularly polarized ion-cyclotron waves. 1. Einstein-Vlasov system in spherical symmetry: Reduction of the equations of motion and classification of single-shell static solutions in the limit of massless particles Science.gov (United States) Gundlach, Carsten 2016-12-01 We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable z (radial over angular momentum). This regularizes the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables (t ,r ,z ) only. Similarly, in this limit the Vlasov density function f for static solutions depends on a single variable Q (energy over angular momentum). This reduction allows us to show that any given static metric that has vanishing Ricci scalar, is vacuum at the center and for r >3 M and obeys certain energy conditions uniquely determines a consistent f =k ¯(Q ) (in closed form). Vice versa, any k ¯(Q ) within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ordinary differential equations). Hence the space of static spherically symmetric solutions of the Einstein-Vlasov system is locally a space of functions of one variable. For a simple two-parameter family of functions k ¯(Q ), we construct the corresponding static spherically symmetric solutions, finding that their compactness is in the interval 0.7 ≲maxr(2 M /r )≤8 /9 . This class of static solutions includes one that agrees with the approximately universal type-I critical solution recently found by Akbarian and Choptuik (AC) in numerical time evolutions. We speculate on what singles it out as the critical solution found by fine-tuning generic data to the collapse threshold, given that AC also found that all static solutions are one-parameter unstable and sit on the threshold of collapse. 2. Flows of non-smooth vector fields and degenerate elliptic equations with applications to the Vlasov-Poisson and semigeostrophic systems CERN Document Server Colombo, Maria 2017-01-01 The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows. 3. Uniformly accurate Particle-in-Cell method for the long time solution of the two-dimensional Vlasov-Poisson equation with uniform strong magnetic field Science.gov (United States) Crouseilles, Nicolas; Lemou, Mohammed; Méhats, Florian; Zhao, Xiaofei 2017-10-01 In this work, we focus on the numerical resolution of the four dimensional phase space Vlasov-Poisson system subject to a uniform strong external magnetic field. To do so, we consider a Particle-in-Cell based method, for which the characteristics are reformulated by means of the two-scale formalism, which is well-adapted to handle highly-oscillatory equations. Then, a numerical scheme is derived for the two-scale equations. The so-obtained scheme enjoys a uniform accuracy property, meaning that its accuracy does not depend on the small parameter. Several numerical results illustrate the capabilities of the method. 4. Ion-atom hybrid systems CERN Document Server Willitsch, Stefan 2014-01-01 The study of interactions between simultaneously trapped cold ions and atoms has emerged as a new research direction in recent years. The development of ion-atom hybrid experiments has paved the way for investigating elastic, inelastic and reactive collisions between these species at very low temperatures, for exploring new cooling mechanisms of ions by atoms and for implementing new hybrid quantum systems. The present lecture reviews experimental methods, recent results and upcoming developments in this emerging field. 5. Cold Suppresses Agonist-induced Activation of TRPV1 OpenAIRE 2011-01-01 Cold therapy is frequently used to reduce pain and edema following acute injury or surgery such as tooth extraction. However, the neurobiological mechanisms of cold therapy are not completely understood. Transient receptor potential vanilloid 1 (TRPV1) is a capsaicin- and heat-gated nociceptive ion channel implicated in thermosensation and pathological pain under conditions of inflammation or injury. Although capsaicin-induced nociception, neuropeptide release, and ionic currents are suppress... 6. Cold Vacuum Drying Facility Data.gov (United States) Federal Laboratory Consortium — Located near the K-Basins (see K-Basins link) in Hanford's 100 Area is a facility called the Cold Vacuum Drying Facility (CVDF).Between 2000 and 2004, workers at the... 7. Cold-induced metabolism NARCIS (Netherlands) Lichtenbelt, W. van Marken; Daanen, H.A.M. 2003-01-01 Purpose of review Cold response can be insulative (drop in peripheral temperature) or metabolic (increase in energy expenditure). Nonshivering thermogenesis by sympathetic, norepinephrine-induced mitochondrial heat production in brown adipose tissue is a well known component of this metabolic 8. The cold reading technique. Science.gov (United States) Dutton, D L 1988-04-15 For many people, belief in the paranormal derives from personal experience of face-to-face interviews with astrologers, palm readers, aura and Tarot readers, and spirit mediums. These encounters typically involve cold reading, a process in which a reader makes calculated guesses about a client's background and problems and, depending on the reaction, elaborates a reading which seems to the client so uniquely appropriate that it carries with it the illusion of having been produced by paranormal means. The cold reading process is shown to depend initially on the Barnum effect, the tendency for people to embrace generalized personality descriptions as idiosyncratically their own. Psychological research into the Barnum effect is critically reviewed, and uses of the effect by a professional magician are described. This is followed by detailed analysis of the cold reading performances of a spirit medium. Future research should investigate the degree to which cold readers may have convinced themselves that they actually possess psychic or paranormal abilities. 9. A Cold Alarm Institute of Scientific and Technical Information of China (English) 2010-01-01 Since the end of 2009, north China has been repeatedly struck by arctic-like blasts of cold weather. As temperatures have plummeted to historic lows, they have inflicted considerable suffering as well. 10. A Cold Alarm Institute of Scientific and Technical Information of China (English) ZHOU JIANXIONG 2010-01-01 @@ Since the end of 2009, north China has been repeatedly struck by arctic-like blasts of cold weather. As temperatures have plummeted to historic lows, they have inflicted considerable suffering as well. 11. Hemolymph metabolites and osmolality are tightly linked to cold tolerance of Drosophila species DEFF Research Database (Denmark) Olsson, Trine; MacMillan, Heath A.; Nyberg, Nils 2016-01-01 Drosophila, like most insects, are susceptible to low temperatures, and will succumb to temperatures above the freezing point of their hemolymph. For these insects, cold exposure causes a loss of extracellular ion and water homeostasis, leading to chill injury and eventually death. Chill...... that the larger contribution of classical cryoprotectants in chill-tolerant Drosophila plays a non-colligative role for cold tolerance that contributes to osmotic and ion homeostasis during cold exposure and, in addition, we discuss how these comparative differences may represent an evolutionary pathway toward...... more extreme cold tolerance of insects.... 12. QCD Factorization Approach to Cold Nuclear Matter Effects Science.gov (United States) Qiu, Jianwe 2016-09-01 Cold nuclear matter effects exist in all high energy collisions involving identified nucleus (or nuclei). They have been manifested in very significant ways in e-A and p-A, as well as A-A collisions, where the cold nuclear effect is a part of the initial condition which plays a critical role in determining the outcome of heavy ion collisions. In this talk, I will discuss if it is possible to consistently calculate or extract the cold nuclear effect, the advantage and limitation of QCD factorization approach, and the predictive power or the testability of the QCD calculations. 13. KCNQ channels in nociceptive cold-sensing trigeminal ganglion neurons as therapeutic targets for treating orofacial cold hyperalgesia. Science.gov (United States) Abd-Elsayed, Alaa A; Ikeda, Ryo; Jia, Zhanfeng; Ling, Jennifer; Zuo, Xiaozhuo; Li, Min; Gu, Jianguo G 2015-07-31 Hyperexcitability of nociceptive afferent fibers is an underlying mechanism of neuropathic pain and ion channels involved in neuronal excitability are potentially therapeutic targets. KCNQ channels, a subfamily of voltage-gated K(+) channels mediating M-currents, play a key role in neuronal excitability. It is unknown whether KCNQ channels are involved in the excitability of nociceptive cold-sensing trigeminal afferent fibers and if so, whether they are therapeutic targets for orofacial cold hyperalgesia, an intractable trigeminal neuropathic pain. Patch-clamp recording technique was used to study M-currents and neuronal excitability of cold-sensing trigeminal ganglion neurons. Orofacial operant behavioral assessment was performed in animals with trigeminal neuropathic pain induced by oxaliplatin or by infraorbital nerve chronic constrictive injury. We showed that KCNQ channels were expressed on and mediated M-currents in rat nociceptive cold-sensing trigeminal ganglion (TG) neurons. The channels were involved in setting both resting membrane potentials and rheobase for firing action potentials in these cold-sensing TG neurons. Inhibition of KCNQ channels by linopirdine significantly decreased resting membrane potentials and the rheobase of these TG neurons. Linopirdine directly induced orofacial cold hyperalgesia when the KCNQ inhibitor was subcutaneously injected into rat orofacial regions. On the other hand, retigabine, a KCNQ channel potentiator, suppressed the excitability of nociceptive cold-sensing TG neurons. We further determined whether KCNQ channel could be a therapeutic target for orofacial cold hyperalgesia. Orofacial cold hyperalgesia was induced in rats either by the administration of oxaliplatin or by infraorbital nerve chronic constrictive injury. Using the orofacial operant test, we showed that retigabine dose-dependently alleviated orofacial cold hyperalgesia in both animal models. Taken together, these findings indicate that KCNQ channel plays a 14. Electron-ion collisional effect on Weibel instability in a Kappa distributed unmagnetized plasma Energy Technology Data Exchange (ETDEWEB) Kumar Kuri, Deep, E-mail: [email protected]; Das, Nilakshi, E-mail: [email protected] [Department of Physics, Tezpur University, Tezpur, Assam 784 028 (India) 2014-04-15 Weibel instability has been investigated in the presence of electron-ion collisions by using standard Vlasov-Maxwell equations. The presence of suprathermal electrons has been included here by using Kappa distribution for the particles. The growth rate γ of Weibel instability has been calculated for different values of spectral index κ, collision frequency ν{sub ei}, and temperature anisotropy parameter β. A comparative study between plasma obeying Kappa distribution and that obeying Maxwellian distribution shows that the growth of instability is higher for the Maxwellian particles. However, in the presence of collisions, the suprathermal particles result in lower damping of Weibel mode. 15. Effects of Magnetic Shear on Ion-Cyclotron Modes. Science.gov (United States) Ganguli, Gurudas Effects of Magnetic Shear on electrostatic Ion -Bernstein Modes (IBM) are examined. Shear affects the mode structure in 3 principal ways: (i) Local effect, (ii) Global effect and (iii) Orbital effect. The role of shear at the above three levels is investigated for IBM in general and in the context of parametric instability of two Ion-Bernstein modes by a magnetosonic wave in a multispecies plasma in particular. An improved marginal stability criterion is presented at Local and Global levels and the region where the Orbital effects are influential is defined and discussed. An electron drift relative to the ions is introduced parallel to the external magnetic field giving rise to Current Driven Ion Cyclotron Instability (CDICI). An improved theory of CDICI in a sheared magnetic field is given. For temperature ratios (tau) = T(,i)/T(,e) > .25, the imaginary part of the local dispersion relation, (as a function of k(,(PARLL)) (('x)), the local parallel wavevector), can be approximated by a parabola, while for weaker (tau) it can be approximated by a pair of straight lines; in each case a second order differential equation is solved for complex roots, (omega). Growth rates ((gamma)/(OMEGA)), are plotted against the square of the normalized pependicular wavevector ((TURN)b) for various values of shear, temperature ratios and electron drift strengths. The main effect of shear is to localize this instability in x-space around some x(,0) such that k(,(PARLL))('0) = ('s)k(,y)x(,0), (('s) being inverse shear length), corresponds to the ((gamma)/(OMEGA))(,max) in the absence of shear. Shear also reduces the growth rate in general: however, ((gamma)/(OMEGA)) for the b values away from the value corresponding to the maximum growth rate are affected more than those which are closer, thereby making the instability more coherent in b. Operator methods employing the Vlasov operator to obtain orbits and velocities in external magnetic fields are studied. Particle orbits and 16. Ionic mechanisms of spinal neuronal cold hypersensitivity in ciguatera. Science.gov (United States) Patel, Ryan; Brice, Nicola L; Lewis, Richard J; Dickenson, Anthony H 2015-12-01 Cold hypersensitivity is evident in a range of neuropathies and can evoke sensations of paradoxical burning cold pain. Ciguatoxin poisoning is known to induce a pain syndrome caused by consumption of contaminated tropical fish that can persist for months and include pruritus and cold allodynia; at present no suitable treatment is available. This study examined, for the first time, the neural substrates and molecular components of Pacific ciguatoxin-2-induced cold hypersensitivity. Electrophysiological recordings of dorsal horn lamina V/VI wide dynamic range neurones were made in non-sentient rats. Subcutaneous injection of 10 nm ciguatoxin-2 into the receptive field increased neuronal responses to innocuous and noxious cooling. In addition, neuronal responses to low-threshold but not noxious punctate mechanical stimuli were also elevated. The resultant cold hypersensitivity was not reversed by 6-({2-[2-fluoro-6-(trifluoromethyl)phenoxy]-2-methylpropyl}carbamoyl)pyridine-3-carboxylic acid, an antagonist of transient receptor potential melastatin 8 (TRPM8). Both mechanical and cold hypersensitivity were completely prevented by co-injection with the Nav 1.8 antagonist A803467, whereas the transient receptor potential ankyrin 1 (TRPA1) antagonist A967079 only prevented hypersensitivity to innocuous cooling and partially prevented hypersensitivity to noxious cooling. In naive rats, neither innocuous nor noxious cold-evoked neuronal responses were inhibited by antagonists of Nav 1.8, TRPA1 or TRPM8 alone. Ciguatoxins may confer cold sensitivity to a subpopulation of cold-insensitive Nav 1.8/TRPA1-positive primary afferents, which could underlie the cold allodynia reported in ciguatera. These data expand the understanding of central spinal cold sensitivity under normal conditions and the role of these ion channels in this translational rat model of ciguatoxin-induced hypersensitivity. 17. Cold asymmetrical fermion superfluids Energy Technology Data Exchange (ETDEWEB) Caldas, Heron 2003-12-19 The recent experimental advances in cold atomic traps have induced a great amount of interest in fields from condensed matter to particle physics, including approaches and prospects from the theoretical point of view. In this work we investigate the general properties and the ground state of an asymmetrical dilute gas of cold fermionic atoms, formed by two particle species having different densities. We have show in a recent paper, that a mixed phase composed of normal and superfluid components is the energetically favored ground state of such a cold fermionic system. Here we extend the analysis and verify that in fact, the mixed phase is the preferred ground state of an asymmetrical superfluid in various situations. We predict that the mixed phase can serve as a way of detecting superfluidity and estimating the magnitude of the gap parameter in asymmetrical fermionic systems. 18. Cold regions isotope applications Energy Technology Data Exchange (ETDEWEB) Perrigo, L.D.; Divine, T.E. 1976-04-01 Pacific Northwest Laboratories (PNL) started the Cold Regions Isotope Applications Program in FY-1975 to identify special conditions in the Arctic and similar geographic areas (Cold Regions) where radioisotope power, heater, or sterilization systems would be desirable and economically viable. Significant progress was made in the first year of this program and all objectives for this initial 12-month period were achieved. The major conclusions and recommendations resulting for this effort are described below. The areas of interest covered include: radiosterilization of sewage; heating of septic tanks; and radioisotope thermoelectric generators as power sources for meteorological instruments and navigational aids. (TFD) 19. Ion Behavior and Gas Mixing in electron cyclotron resonance plasmas as sources of highly charged ions (concept OpenAIRE Melin, G.; Drentje, A. G.; Girard, A; Hitz, D. 1999-01-01 Abstract: An ECR ion source is basically an ECR heated plasma confinement machine, with hot electrons and cold ions. The main parameters of the ion population have been analyzed, including temperature, losses, and confinement time. The "gas mixing" effect has been studied in this context. An expression is derived for determining the ion temperature from the values of all extracted ion currents. One aim is to study the ion temperature behavior in argon plasmas without and with mixing different... 20. How cold is it? TRPM8 and TRPA1 in the molecular logic of cold sensation Directory of Open Access Journals (Sweden) McKemy David D 2005-04-01 Full Text Available Abstract Recognition of temperature is a critical element of sensory perception and allows us to evaluate both our external and internal environments. In vertebrates, the somatosensory system can discriminate discrete changes in ambient temperature, which activate nerve endings of primary afferent fibers. These thermosensitive nerves can be further segregated into those that detect either innocuous or noxious (painful temperatures; the latter neurons being nociceptors. We now know that thermosensitive afferents express ion channels of the transient receptor potential (TRP family that respond at distinct temperature thresholds, thus establishing the molecular basis for thermosensation. Much is known of those channels mediating the perception of noxious heat; however, those proposed to be involved in cool to noxious cold sensation, TRPM8 and TRPA1, have only recently been described. The former channel is a receptor for menthol, and links the sensations provided by this and other cooling compounds to temperature perception. While TRPM8 almost certainly performs a critical role in cold signaling, its part in nociception is still at issue. The latter channel, TRPA1, is activated by the pungent ingredients in mustard and cinnamon, but has also been postulated to mediate our perception of noxious cold temperatures. However, a number of conflicting reports have suggested that the role of this channel in cold sensation needs to be confirmed. Thus, the molecular logic for the perception of cold-evoked pain remains enigmatic. This review is intended to summarize our current understanding of these cold thermoreceptors, as well as address the current controversy regarding TRPA1 and cold signaling. 1. How cold is it? TRPM8 and TRPA1 in the molecular logic of cold sensation. Science.gov (United States) McKemy, David D 2005-04-22 Recognition of temperature is a critical element of sensory perception and allows us to evaluate both our external and internal environments. In vertebrates, the somatosensory system can discriminate discrete changes in ambient temperature, which activate nerve endings of primary afferent fibers. These thermosensitive nerves can be further segregated into those that detect either innocuous or noxious (painful) temperatures; the latter neurons being nociceptors. We now know that thermosensitive afferents express ion channels of the transient receptor potential (TRP) family that respond at distinct temperature thresholds, thus establishing the molecular basis for thermosensation. Much is known of those channels mediating the perception of noxious heat; however, those proposed to be involved in cool to noxious cold sensation, TRPM8 and TRPA1, have only recently been described. The former channel is a receptor for menthol, and links the sensations provided by this and other cooling compounds to temperature perception. While TRPM8 almost certainly performs a critical role in cold signaling, its part in nociception is still at issue. The latter channel, TRPA1, is activated by the pungent ingredients in mustard and cinnamon, but has also been postulated to mediate our perception of noxious cold temperatures. However, a number of conflicting reports have suggested that the role of this channel in cold sensation needs to be confirmed. Thus, the molecular logic for the perception of cold-evoked pain remains enigmatic. This review is intended to summarize our current understanding of these cold thermoreceptors, as well as address the current controversy regarding TRPA1 and cold signaling. 2. Commemoration of a cold war DEFF Research Database (Denmark) Farbøl, Rosanna 2015-01-01 This article brings together the fields of Cold War studies and memory studies. In Denmark, a remarkable institutionalisation of Cold War memory has taken place in the midst of a heated ideological battle over the past and whether to remember the Cold War as a ‘war’. Using Danish Cold War museums...... and heritage sites as case studies, this article sheds new light on the politics of history involved in Cold War commemoration. It suggests that the Cold War is commemorated as a war, yet this war memory is of a particular kind: it is a war memory without victims.... 3. Detection of cold pain, cold allodynia and cold hyperalgesia in freely behaving rats Directory of Open Access Journals (Sweden) Woolf Clifford J 2005-12-01 Full Text Available Abstract Background Pain is elicited by cold, and a major feature of many neuropathic pain states is that normally innocuous cool stimuli begin to produce pain (cold allodynia. To expand our understanding of cold induced pain states we have studied cold pain behaviors over a range of temperatures in several animal models of chronic pain. Results We demonstrate that a Peltier-cooled cold plate with ± 1°C sensitivity enables quantitative measurement of a detection withdrawal response to cold stimuli in unrestrained rats. In naïve rats the threshold for eliciting cold pain behavior is 5°C. The withdrawal threshold for cold allodynia is 15°C in both the spared nerve injury and spinal nerve ligation models of neuropathic pain. Cold hyperalgesia is present in the spared nerve injury model animals, manifesting as a reduced latency of withdrawal response threshold at temperatures that elicit cold pain in naïve rats. We also show that following the peripheral inflammation produced by intraplantar injection of complete Freund's adjuvant, a hypersensitivity to cold occurs. Conclusion The peltier-cooled provides an effective means of assaying cold sensitivity in unrestrained rats. Behavioral testing of cold allodynia, hyperalgesia and pain will greatly facilitate the study of the neurobiological mechanisms involved in cold/cool sensations and enable measurement of the efficacy of pharmacological treatments to reduce these symptoms. 4. Stabilit\\'e orbitale pour le syst\\eme de Vlasov-Poisson gravitationnel, d'apr\\es Lemou-M\\'ehats-Rapha\\"el, Guo, Lin, Rein et al. [Orbital stability for the gravitational Vlasov-Poisson system, after Lemou-M\\'ehats-Rapha\\"el, Guo, Lin, Rein et al. CERN Document Server Mouhot, Clément 2012-01-01 This paper reviews the recent mathematical progresses made on the study of the orbital stability properties for the gravitational Vlasov-Poisson system. We present in details the paper of Lemou, M\\'ehats and Rapha\\"el (Inventiones 2011) and we review also the previous works by Dolbeault, Guo, Hadzic, Lin, Rein, S\\'anchez, Soler, Wan, Wolansky. We also include a discussion of the history of this topic and the pioneering works by physicists like Antonov, Lynden-Bell and Aly. This is the text of a Bourbaki seminar given in november 2011 (in french). 5. Cold spray nozzle design Science.gov (United States) Haynes, Jeffrey D.; Sanders, Stuart A. 2009-06-09 A nozzle for use in a cold spray technique is described. The nozzle has a passageway for spraying a powder material, the passageway having a converging section and a diverging section, and at least the diverging section being formed from polybenzimidazole. In one embodiment of the nozzle, the converging section is also formed from polybenzimidazole. 6. Finger cold induced vasodilation NARCIS (Netherlands) Daanen, H.A.M. 2007-01-01 There are indications that subjects with a reduced finger CIVD response are more prone to get local cold injuries, but more epidemiological research is needed to establish a firm relationship. Although it was observed that an early CIVD onset was associated with initially superior manual performance 7. Teaching "In Cold Blood." Science.gov (United States) Berbrich, Joan D. 1967-01-01 The Truman Capote nonfiction novel, "In Cold Blood," which reflects for adolescents the immediacy of the real world, illuminates (1) social issues--capital punishment, environmental influence, and the gap between the "haves" and "have-nots," (2) moral issues--the complexity of man's nature, the responsibility of one… 8. Cold Weather Pet Safety Science.gov (United States) ... they can be knocked over, potentially starting a fire. Check your furnace before the cold weather sets in to make ... avoided because of the risk of burns or fire. Heated pet mats should also be used ... to burrow, get them back inside quickly because they are showing signs of ... 9. Cold-induced metabolism NARCIS (Netherlands) Lichtenbelt, W. van Marken; Daanen, H.A.M. 2003-01-01 Purpose of review Cold response can be insulative (drop in peripheral temperature) or metabolic (increase in energy expenditure). Nonshivering thermogenesis by sympathetic, norepinephrine-induced mitochondrial heat production in brown adipose tissue is a well known component of this metabolic respon 10. Chilling Out With Colds Science.gov (United States) ... some feel-better tips if you get a cold: Bring on the heat. Hot drinks soothe coughs and sore throats while also clearing mucus. So eat (or drink) your chicken soup! Get steamed up. A steamy shower helps stuffy or irritated noses. Or run a ... 11. Out in the cold. Science.gov (United States) Bates, Jane 2016-05-04 Every now and then, you say something to a patient and wonder whether you should have kept quiet. On this occasion, a female patient and I were indulging in a moment of shared empathy over an annoying symptom we both experience - permanently cold feet. 12. Cold War Propaganda. Science.gov (United States) Bennett, Paul W. 1988-01-01 Briefly discusses the development of Cold War propaganda in the United States, Canada, and the USSR after 1947. Presents two movie reviews and a Canadian magazine advertisement of the period which illustrate the harshness of propaganda used by both sides in the immediate postwar years. (GEA) 13. Recent Cold War Studies Science.gov (United States) Pineo, Ronn 2003-01-01 Cold War historiography has undergone major changes since the 1991 collapse of the Soviet Union. For two years (1992-1993) the principal Soviet archives fell open to scholars, and although some of the richest holdings are now once again closed, new information continues to find its way out. Moreover, critical documentary information has become… 14. A fast and efficient determination of amines and preservatives in cough and cold liquid and suspension formulations using a single isocratic ion-pairing high performance [correction of power] liquid chromatography method. Science.gov (United States) Paciolla, M D; Jansen, S A; Martellucci, S A; Osei, A A 2001-08-01 A single, highly selective ion-pairing reverse phase-high power liquid chromatography (RP-HPLC) method has been developed for the determination of amines and preservatives in a wide range of Tylenol((R)) liquid and suspension liquid products. As with many OTC products, the challenge is to quantitatively extract the analytes from difficult matrices and specifically analyze them in the presence of various excipients and flavors. Historically, separate analytical methods were used for each class of analytes (acids, bases and neutral compounds). In this method a mobile phase consisting of a buffered ion-pairing agent with acetonitrile, methanol and tetrahydrofuran was used to separate the charged amines from neutral and acidic compounds on a Phenomenex LUNA C8(2) 75 x 4.6 mm i.d. analytical column with a 3-microm particle size. The analytes include acids (benzoic acid), bases (pseudoephedrine, chlorpheniramine, dextromethorphan, doxylamine and diphenhydramine) and a neutral compound (butylparaben). The effects of pH, the chain length of the ion-pairing reagent, ionic strength and organic modifiers on the separation are discussed. The method is linear from 15 to 150% of the target amounts. The optimized method proves to be specific, robust and accurate for the analysis of the compounds. 15. Herpes Simplex Virus (Cold Sores) Science.gov (United States) ... Print Share Cold Sores in Children: About the Herpes Simplex Virus Page Content A child's toddler and ... Cold sores (also called fever blisters or oral herpes) start as small blisters that form around the ... 16. The dynamics of electron and ion holes in a collisionless plasma Directory of Open Access Journals (Sweden) B. Eliasson 2005-01-01 Full Text Available We present a review of recent analytical and numerical studies of the dynamics of electron and ion holes in a collisionless plasma. The new results are based on the class of analytic solutions which were found by Schamel more than three decades ago, and which here work as initial conditions to numerical simulations of the dynamics of ion and electron holes and their interaction with radiation and the background plasma. Our analytic and numerical studies reveal that ion holes in an electron-ion plasma can trap Langmuir waves, due the local electron density depletion associated with the negative ion hole potential. Since the scale-length of the ion holes are on a relatively small Debye scale, the trapped Langmuir waves are Landau damped. We also find that colliding ion holes accelerate electron streams by the negative ion hole potentials, and that these streams of electrons excite Langmuir waves due to a streaming instability. In our Vlasov simulation of two colliding ion holes, the holes survive the collision and after the collision, the electron distribution becomes flat-topped between the two ion holes due to the ion hole potentials which work as potential barriers for low-energy electrons. Our study of the dynamics between electron holes and the ion background reveals that standing electron holes can be accelerated by the self-created ion cavity owing to the positive electron hole potential. Vlasov simulations show that electron holes are repelled by ion density minima and attracted by ion density maxima. We also present an extension of Schamel's theory to relativistically hot plasmas, where the relativistic mass increase of the accelerated electrons have a dramatic effect on the electron hole, with an increase in the electron hole potential and in the width of the electron hole. A study of the interaction between electromagnetic waves with relativistic electron holes shows that electromagnetic waves can be both linearly and nonlinearly 17. Trainability of cold induced vasodilation NARCIS (Netherlands) Daanen, H.A.M.; Raymann, R.J.E.M.; Stoop, M. 2007-01-01 Peripheral cold injuries are often reported in mountaineers. Not only low ambient temperatures, but also the hypobaric circumstances are known to be major environmental risk factors. When the fingers are exposed to extreme cold for several minutes, cold induced vasodilation (CIVD) occurs, that is 18. Trainability of cold induced vasodilation NARCIS (Netherlands) Daanen, H.A.M.; Raymann, R.J.E.M.; Stoop, M. 2007-01-01 Peripheral cold injuries are often reported in mountaineers. Not only low ambient temperatures, but also the hypobaric circumstances are known to be major environmental risk factors. When the fingers are exposed to extreme cold for several minutes, cold induced vasodilation (CIVD) occurs, that is re 19. Differential kinetic dynamics and heating of ions in the turbulent solar wind CERN Document Server Valentini, F; Stabile, S; Pezzi, O; Servidio, S; De Marco, R; Marcucci, F; Bruno, R; Lavraud, B; De Keyser, J; Consolini, G; Brienza, D; Sorriso-Valvo, L; Retinò, A; Vaivads, A; Salatti, M; Veltri, P 2016-01-01 The solar wind plasma is a fully ionized and turbulent gas ejected by the outer layers of the solar corona at very high speed, mainly composed by protons and electrons, with a small percentage of helium nuclei and a significantly lower abundance of heavier ions. Since particle collisions are practically negligible, the solar wind is typically not in a state of thermodynamic equilibrium. Such a complex system must be described through self-consistent and fully nonlinear models, taking into account its multi-species composition and turbulence. We use a kinetic hybrid Vlasov-Maxwell numerical code to reproduce the turbulent energy cascade down to ion kinetic scales, in typical conditions of the uncontaminated solar wind plasma, with the aim of exploring the differential kinetic dynamics of the dominant ion species, namely protons and alpha particles. We show that the response of different species to the fluctuating electromagnetic fields is different. In particular, a significant differential heating of alphas w... 20. Kinetically modified parametric instabilities of circularly-polarized Alfven waves: Ion kinetic effects CERN Document Server Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru 2006-01-01 Parametric instabilities of parallel propagating,circularly polarized Alfv\\'en waves in a uniform background plasma is studied, within a framework of one-dimensional Vlasov equation for ions and massless electron fluid, so that kinetic perturbations in the longitudinal direction (ion Landau damping) are included. The present formulation also includes the Hall effect. The obtained results agree well with relevant analysis in the past, suggesting that kinetic effects in the longitudinal direction play essential roles in the parametric instabilities of Alfven waves when the kinetic effects react "passively". Furthermore, existence of the kinetic parametric instabilities is confirmed for the regime with small wave number daughter waves. Growth rates of these instabilities are sensitive to ion temperature. 1. WISPy cold dark matter Energy Technology Data Exchange (ETDEWEB) Arias, Paola [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pontificia Univ. Catolica de Chile, Santiago (Chile). Facultad de Fisica; Cadamuro, Davide; Redondo, Javier [Max-Planck-Institut fuer Physik, Muenchen (Germany); Goodsell, Mark [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); European Organization for Nuclear Research (CERN), Geneva (Switzerland); Jaeckel, Joerg [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; Ringwald, Andreas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2012-01-15 Very weakly interacting slim particles (WISPs), such as axion-like particles (ALPs) or hidden photons (HPs), may be non-thermally produced via the misalignment mechanism in the early universe and survive as a cold dark matter population until today. We find that, both for ALPs and HPs whose dominant interactions with the standard model arise from couplings to photons, a huge region in the parameter spaces spanned by photon coupling and ALP or HP mass can give rise to the observed cold dark matter. Remarkably, a large region of this parameter space coincides with that predicted in well motivated models of fundamental physics. A wide range of experimental searches - exploiting haloscopes (direct dark matter searches exploiting microwave cavities), helioscopes (searches for solar ALPs or HPs), or light-shining-through-a-wall techniques - can probe large parts of this parameter space in the foreseeable future. (orig.) 2. "Miniature Cold War?" Institute of Scientific and Technical Information of China (English) 2004-01-01 @@ Fu: Relations between America and Russia are one of the most important bilateral ties that could affect the trend of world situation.What's the matter with U. S. -Russia ties? What's wrong with their bilateral relations? People tend to ask these days. Some observers on both sides suggest that post 9/11 honeymoon has turned sour when joint effort against challenges from nontraditional security issues failed to remove original bilateral contradictions over traditional security concerns.Japanese Jiji News Agency saw "a miniature Cold War" evolving and the British Guardian even bluntly pronounced "a new Cold War" on January 3, asserting that disintegration of the former Soviet Union did not terminate bilateral contention, which has only been performed on an international stage more complicated than ever before, with covert scheming against each other replacing overt, direct confrontation. How about starting our discussion with those comments? 3. Engine Cold Start Science.gov (United States) 2015-09-01 14. ABSTRACT These fuels were used for testing a GEP 6.5L turbocharged V-8 diesel engine operation in a cold box. This engine architecture is... engines . The U.S. military currently uses petroleum-based jet fuels in diesel engine -powered ground vehicles and is studying the use of alternative jet...to identify a window, or range, of cetane number which would be acceptable to ensure the reliable operation of diesel engine -powered military ground 4. Electronic Equipment Cold Plates Science.gov (United States) 1976-04-01 equations for such a flow regiae. For laainar flow and Moderate teaperature differwwe« between the well «nd coolant, a aodifled Sieder -Tate...con- figuration. The heat-transfer coefficients, therefore, were determined by using both the Sieder -Tate and McAdams equations and the coaputed...values used In the analytical predictions. As with th* previous cold Plates, the Sieder -Tate equation gave too low of values for the heat- transfer 5. The CMS COLD BOX CERN Multimedia Brice, Maximilien 2015-01-01 The CMS detector is built around a large solenoid magnet. This takes the form of a cylindrical coil of superconducting cable that generates a field of 3.8 Tesla: about 100,000 times the magnetic field of the Earth. To run, this superconducting magnet needs to be cooled down to very low temperature with liquid helium. Providing this is the job of a compressor station and the so-called “cold box”. 6. 稀土离子和香兰素在H2SO4溶液中对冷轧钢的缓蚀协同效应%Synergistic Inhibition Effect of Rare Earth Ions and Vanillin on Corrosion of Cold Rolled Steel in H2SO4 Solution Institute of Scientific and Technical Information of China (English) 李向红; 邓书端; 付惠; 木冠南 2009-01-01 用失重法研究了四种稀土离子(La3+,Ce3+,Ce4+,Nd3+)和香兰素(4-羟基-3-甲氧基-苯甲醛)在1.0 mol/LH2SO4介质中对冷轧钢的缓蚀协同效应.结果表明,香兰素对冷轧钢有中等程度的缓蚀作用,缓蚀率随其浓度的增加而增大;四种稀土离子对冷轧钢的缓蚀作用均较差,最大缓蚀率仅为20%左右.香兰素和稀土Ce4+复配后对冷轧钢产生了明显的缓蚀协同效应,最大缓蚀率可达95%左右;而与La3+,Ce3+和Nd3+复配后均无缓蚀协同效应.%The synergistic inhibition effect of four rare earth ions (La3+, Ce3+, Ce4+, Nd3+) and vanillin (4-hydroxy-3-methoxy-benzaldehyde) on the corrosion of cold rolled steel (CRS) in 1.0 mol/L H2SO4 solution was studied by weight loss method. The present study revealed that vanillin had a moderate inhibitive effect on the corrosion of CRS in 1.0 mol/L H2SO4 solution, and the inhibition efficiency increased with the concentration. The rare earth ions of La3+,Ce3+,Ce4+ and Nd3+ had a negligible effect in 1.0 mol/L H2SO4, and the maximum inhibition efficiency was not more than 20%. The experiments of incorporation of rare earth ions and vanillin, indicated that Ce4+ and vanillin produced strong synergistic effect on corrosion inhibition for CRS, and the maximum inhibition efficiency was about 95%. However, there was no synergistic inhibition effect between other rare earth ions (La3+, Ce3+ and Nd3+) and vanillin. 7. Cold Atmosphere Plasma in Cancer Therapy Science.gov (United States) Keidar, Michael 2012-10-01 Plasma is an ionized gas that is typically generated in high-temperature laboratory conditions. Recent progress in atmospheric plasmas led to the creation of cold plasmas with ion temperature close to room temperature. Areas of potential application of cold atmospheric plasmas (CAP) include dentistry, drug delivery, dermatology, cosmetics, wound healing, cellular modifications, and cancer treatment. Various diagnostic tools have been developed for characterization of CAP including intensified charge-coupled device cameras, optical emission spectroscopy and electrical measurements of the discharge propertied. Recently a new method for temporally resolved measurements of absolute values of plasma density in the plasma column of small-size atmospheric plasma jet utilizing Rayleigh microwave scattering was proposed [1,2]. In this talk we overview state of the art of CAP diagnostics and understanding of the mechanism of plasma action of biological objects. The efficacy of cold plasma in a pre-clinical model of various cancer types (long, bladder, and skin) was recently demonstrated [3]. Both in-vitro and in-vivo studies revealed that cold plasmas selectively kill cancer cells. We showed that: (a) cold plasma application selectively eradicates cancer cells in vitro without damaging normal cells. For instance a strong selective effect was observed; the resulting 60--70% of lung cancer cells were detached from the plate in the zone treated with plasma, whereas no detachment was observed in the treated zone for the normal lung cells under the same treatment conditions. (b) Significantly reduced tumor size in vivo. Cold plasma treatment led to tumor ablation with neighbouring tumors unaffected. These experiments were performed on more than 10 mice with the same outcome. We found that tumors of about 5mm in diameter were ablated after 2 min of single time plasma treatment. The two best known cold plasma effects, plasma-induced apoptosis and the decrease of cell migration 8. Ionization of Sodium Cluster by Heavy Ion Impact Institute of Scientific and Technical Information of China (English) 2001-01-01 Energetic ions have recently been used as an efficient means to produce highly charged cold clusters~[1]. There are two ways to obtain highly-charged clusters: low-fluence nano-second lasers irradiation and energetic highly charged ions impact. Compared to the low-density laser, heavy ions, e.g. delivered by ECR sources, have the 9. Paroxysmal cold hemoglobinuria. Science.gov (United States) Shanbhag, Satish; Spivak, Jerry 2015-06-01 Paroxysmal cold hemoglobinuria is a rare cause of autoimmune hemolytic anemia predominantly seen as an acute form in young children after viral illnesses and in a chronic form in some hematological malignancies and tertiary syphilis. It is a complement mediated intravascular hemolytic anemia associated with a biphasic antibody against the P antigen on red cells. The antibody attaches to red cells at colder temperatures and causes red cell lysis when blood recirculates to warmer parts of the body. Treatment is mainly supportive and with red cell transfusion, but immunosuppressive therapy may be effective in severe cases. 10. Exception in Cold War Institute of Scientific and Technical Information of China (English) 2004-01-01 @@ In the Cold War, India mainly focused its Southeast Asia Strategy on preserving the regional peace and stability, fearing that changes in Southeast Asia would impact India. Generally speaking, India would like to see a relatively strong, stable and independent Southeast Asia, which would guarantee the stability of its east wing. However, fettered by its limited power, its non-alignment policy and its special relation with Soviet Union, India's policy toward Southeast Asia remained relatively passive and its relation with Southeast Asia was, to some extent, trapped in a historical "intermission." 11. Ion Behavior and Gas Mixing in electron cyclotron resonance plasmas as sources of highly charged ions (concept NARCIS (Netherlands) Melin, G.; Drentje, A. G.; Girard, A.; Hitz, D. 1999-01-01 Abstract: An ECR ion source is basically an ECR heated plasma confinement machine, with hot electrons and cold ions. The main parameters of the ion population have been analyzed, including temperature, losses, and confinement time. The "gas mixing" effect has been studied in this context. An express 12. Chill-tolerant Gryllus crickets maintain ion balance at low temperatures. Science.gov (United States) Coello Alvarado, Litza E; MacMillan, Heath A; Sinclair, Brent J 2015-06-01 Insect cold tolerance is both phenotypically-plastic and evolutionarily labile, but the mechanisms underlying this variation are uncertain. Chill-susceptible insects lose ion and water homeostasis in the cold, which contributes to the development of injuries and eventually death. We thus hypothesized that more cold-tolerant insects will better maintain ion and water balance at low temperatures. We used rapid cold-hardening (RCH) and cold acclimation to improve cold tolerance of male Gryllus pennsylvanicus, and also compared this species to its cold-tolerant relative (Gryllus veletis). Cold acclimation and RCH decreased the critical thermal minimum (CTmin) and chill coma recovery time (CCR) in G. pennsylvanicus, but while cold acclimation improved survival of 0 °C, RCH did not; G. veletis was consistently more cold-tolerant (and had lower CCR and CTmin) than G. pennsylvanicus. During cold exposure, hemolymph water and Na(+) migrated to the gut of warm-acclimated G. pennsylvanicus, which increased hemolymph [K(+)] and decreased muscle K(+) equilibrium potentials. By contrast, cold-acclimated G. pennsylvanicus suffered a smaller loss of ion and water homeostasis during cold exposure, and this redistribution did not occur at all in cold-exposed G. veletis. The loss of ion and water balance was similar between RCH and warm-acclimated G. pennsylvanicus, suggesting that different mechanisms underlie decreased CCR and CTmin compared to increased survival at 0 °C. We conclude that increased tolerance of chilling is associated with improved maintenance of ion and water homeostasis in the cold, and that this is consistent for both phenotypic plasticity and evolved cold tolerance. Copyright © 2015 Elsevier Ltd. All rights reserved. 13. Ion-Ion Neutralization. Science.gov (United States) 1980-12-31 plasma were identified using a downstream quadrupole mass spectrometer. In these experimento it is a simple matter to establish H+(H 2 0):f as the...pressure as predicted by the Thomson t2rnary mechanism whicK hzr been suownr to be valid experimentally at hiTh rrsurs (,han and Peron, 1:EI4 hereafter t...of NO , NO2 ions in various gases and the ternary recombination coefficients of these ions in the higher pres:;ure ( Thomson ) re"ie. Equation (5) cr>n 14. Effect of a short weak prepulse on laser-triggered front-surface heavy-ion acceleration Energy Technology Data Exchange (ETDEWEB) Bochkarev, S. G.; Bychenkov, V. Yu. [P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow (Russian Federation); Golovin, G. V.; Uryupina, D. S.; Shulyapov, S. A.; Savel' ev, A. B. [M. V. Lomonosov Moscow State University, International Laser Centre and Faculty of Physics, Moscow (Russian Federation); Andriyash, A. V. [The All-Russia Research Institute of Automatics, Moscow (Russian Federation) 2012-10-15 A suppression of light-ion acceleration (from surface water contaminants) was observed when a moderate-intensity subpicosecond laser pulse was focused on a thick metal target. Simultaneously, an effective generation of high-energy multicharge ions of the target material (Fe) was experimentally observed. A numerical simulation based on the Boltzmann-Vlasov-Poisson model revealed that this is due to the very specific regime of cleaning contaminants from the target surface by the short weak prepulse preceding the main pulse by more than 10 ns and having an intensity below the surface breakdown threshold. Because this prepulse causes the contaminant layer to boil explosively, a low-density gap forms above the target surface. These conditions are consequently favorable for boosting the energy of heavy ions. 15. Cold nuclear matter CERN Document Server Dorso, C O; Nichols, J I; López, J A 2012-01-01 We study the behavior of cold nuclear matter near saturation density (\\rho 0) and very low temperature using classical molecular dynamics. We used three different (classical) nuclear interaction models that yield medium' or stiff' compressibilities. For high densities and for every model the ground state is a classical crystalline solid, but each one with a different structure. At subsaturation densities, we found that for every model the transition from uniform (crystal) to non-uniform matter occurs at \\rho ~ 0.12 fm^(-3) = 0.75 \\rho 0. Surprisingly, at the non-uniform phase, the three models produce pasta-like' structures as those allegedly present in neutron star matter but without the long-range Coulomb interaction and with different length scales. 16. Cold dark matter resuscitated? CERN Document Server White, M; Silk, J; Davis, M; White, Martin; Scott, Douglas; Silk, Joe; Davis, Marc 1995-01-01 The Cold Dark Matter (CDM) model has an elegant simplicitly which makes it very predictive, but when its parameters are fixed at their canonical' values its predictions are in conflict with observational data. There is, however, much leeway in the initial conditions within the CDM framework. We advocate a re-examination of the CDM model, taking into account modest variation of parameters from their canonical values. We find that CDM models with n=0.8--0.9 and h=0.45--0.50 can fit the available data. Our best fit'' CDM model has n=0.9, h=0.45 and C_2^{T}/C_2^{S}=0.7. We discuss the current state of observations which could definitely rule out this model. 17. Cold gelation of globular proteins NARCIS (Netherlands) Alting, A.C. 2003-01-01 Keywords : globular proteins, whey protein, ovalbumin, cold gelation, disulfide bonds, texture, gel hardnessProtein gelation in food products is important to obtain desirable sensory and textural properties. Cold gelation is a novel method to produce protein-based gels. It is a two step process in w 18. Cold gelation of globular proteins NARCIS (Netherlands) Alting, A.C. 2003-01-01 Keywords : globular proteins, whey protein, ovalbumin, cold gelation, disulfide bonds, texture, gel hardnessProtein gelation in food products is important to obtain desirable sensory and textural properties. Cold gelation is a novel method to produce protein-based gels. It is a two step process in w 19. The status of cold fusion Science.gov (United States) Storms, E. This report attempts to update the status of the phenomenon of cold fusion. The new field is continuing to grow as a variety of nuclear reactions are discovered to occur in a variety of chemical environments at modest temperatures. However, it must be cautioned that most scientists consider cold fusion as something akin to UFO's, ESP, and numerology. 20. Cold Crystal Reflector Filter Concept CERN Document Server Muhrer, G 2014-01-01 In this paper the theoretical concept of a cold crystal reflector filter will be presented. The aim of this concept is to balance the shortcoming of the traditional cold polycrystalline reflector filter, which lies in the significant reduction of the neutron flux right above (in energy space) or right below (wavelength space) the first Bragg edge. 1. The Vlasov formalism for extended relativistic mean field models: the crust-core transition and the stellar matter equation of state CERN Document Server Pais, Helena 2016-01-01 The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear\\omega\\rho$and$\\sigma\\rho$coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of$1.36\\pm 0.06$km for a 1.4$M_\\odot$star. 2. High Order Vlasov Solvers for the Simulation of KEEN Wavea Including the L-B and F-P Collision Models Science.gov (United States) Sonnendrucker, Eric; Crouseilles, Nicolas; Afeyan, Bedros 2012-10-01 Since the discovery of KEEN waves in 2002, it has been an open question whether the detailed phase space structures found in those well resolved simulations of Afeyan et al., would survive (essentially) intact, if instead of cubic splines, higher order interpolation schemes were used, up to spectral accuracy. In this work, the Vlasov-Poisson system is solved using Fourier-Fourier descriptions in phase space, and Fourier spline. The splines can be any order approaching spectral accuracy quickly. These simulations show what the role of numerical dissipation is for the stable simulation of driven KEEN waves, how delicate structures found in low order simulations survive and persist even when the microscope with which they are being scrutinized is much more powerful. The Fourier capability also allows truncated descriptions for the theoretical advancement of reduced models of fully formed KEEN waves, as described previously by Afeyan et al. The partitioned phase space structures they found is further tested by the use of a Lenard-Bernstein collision model on the way to including the full Fokker Planck collision operator in cylindrical (in velocity space) geometry, advanced by Greengard et al. 3. Accuracy analysis of a 2D Poisson-Vlasov PIC solver and estimates of the collisional effects in space charge dynamics CERN Document Server Bazzani, A; Franchi, A; Rambaldi, S; Turchetti, G 2005-01-01 We analyze the accuracy of a 2D Poisson-Vlasov PIC integrator, taking the KV as a reference solution for a FODO cell. The particle evolution is symplectic and the Poisson solver is based on FFT. The numerical error, evaluated by comparing the moments of the distribution and the electric field with the exact solution, shows a linear growth. This effect can be modeled by a white noise in the envelope equations for the KV beam. In order to investigate the collisional effects we have integrated the Hamilton's equations for N charged macro-particles with a hard-core r/sub H/ reducing the computational complexity to N/sup 3/2/. In the constant focusing case we observed that a KV beam, matched or mismatched relaxes to the Maxwell-Boltzmann self consistent distribution on a time interval, which depends on r/sub H/ and has a finite limit, for r/sub H/ to 0. A fully 3D PIC code for short bunches was developed for the ADS linac design at LNL (Italy). A 3D particle-core model, based on Langevin's equations with the drift... 4. A high-resolution global Vlasov simulation of a small dielectric body with a weak intrinsic magnetic field on the K computer Science.gov (United States) Umeda, Takayuki; Fukazawa, Keiichiro 2015-04-01 The interaction between the solar wind and solar system bodies, such as planets, satellites, and asteroids, is one of the fundamental global-scale phenomena in space plasma physics. In the present study, the electromagnetic environment around a small dielectric body with a weak intrinsic magnetic field is studied by means of a first-principle kinetic plasma simulation, which is a challenging task in space plasma physics as well as high-performance computing. Due to several computational limitations, five-dimensional full electromagnetic Vlasov simulations with two configuration space and three velocity space coordinates are performed with two different spatial resolutions. The Debye-scale charge separation is not solved correctly in the simulation run with a low spatial resolution, while all the physical processes in collisionless plasma are included in the simulation run with a high spatial resolution. The direction comparison of electromagnetic fields between the two runs shows that there is small difference in the structure of magnetic field lines. On the other hand, small-scale fine structures of electrostatic fields are enhanced by the electric charge separation and the charge accumulation on the surface of the body in the high-resolution run, while these structures are absent in the low-resolution runs. These results are consistent with the conventional understanding of plasma physics that the structure and dynamics of global magnetic fields, which are generally described by the magneto-hydro-dynamics (MHD) equations, are not affected by electron-scale microphysics. 5. A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation CERN Document Server Myers, Andrew; Van Straalen, Brian 2016-01-01 Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements. 6. Complex Korteweg-de Vries equation and Nonlinear dust-acoustic waves in a magnetoplasma with a pair of trapped ions CERN Document Server Misra, A P 2015-01-01 The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of positive and negative ions. 7. Cough and Cold Medicine Abuse (For Parents) Science.gov (United States) ... Old Feeding Your 1- to 2-Year-Old Cough and Cold Medicine Abuse KidsHealth > For Parents > Cough ... cough and cold medicine. Why Do Kids Abuse Cough and Cold Remedies? Before the U.S. Food and ... 8. Cold-Weather Sports and Your Family Science.gov (United States) ... Feeding Your 1- to 2-Year-Old Cold-Weather Sports and Your Family KidsHealth > For Parents > Cold- ... once the weather turns frosty. Beating the Cold-Weather Blahs Once a chill is in the air, ... 9. Understanding Colds: Anatomy of the Nose Science.gov (United States) ... at least one-half of colds. (5) Cold viruses can only multiply when they are inside of living cells. When on an environmental surface, cold viruses cannot multiply. However, they are still infectious if ... 10. Cold plasma decontamination of foods. Science.gov (United States) Niemira, Brendan A 2012-01-01 Cold plasma is a novel nonthermal food processing technology that uses energetic, reactive gases to inactivate contaminating microbes on meats, poultry, fruits, and vegetables. This flexible sanitizing method uses electricity and a carrier gas, such as air, oxygen, nitrogen, or helium; antimicrobial chemical agents are not required. The primary modes of action are due to UV light and reactive chemical products of the cold plasma ionization process. A wide array of cold plasma systems that operate at atmospheric pressures or in low pressure treatment chambers are under development. Reductions of greater than 5 logs can be obtained for pathogens such as Salmonella, Escherichia coli O157:H7, Listeria monocytogenes, and Staphylococcus aureus. Effective treatment times can range from 120 s to as little as 3 s, depending on the food treated and the processing conditions. Key limitations for cold plasma are the relatively early state of technology development, the variety and complexity of the necessary equipment, and the largely unexplored impacts of cold plasma treatment on the sensory and nutritional qualities of treated foods. Also, the antimicrobial modes of action for various cold plasma systems vary depending on the type of cold plasma generated. Optimization and scale up to commercial treatment levels require a more complete understanding of these chemical processes. Nevertheless, this area of technology shows promise and is the subject of active research to enhance efficacy. 11. Cold nuclear fusion reactor and nuclear fusion rocket Directory of Open Access Journals (Sweden) Huang Zhenqiang 2013-10-01 Full Text Available "Nuclear restraint inertial guidance directly hit the cold nuclear fusion reactor and ion speed dc transformer" [1], referred to as "cold fusion reactor" invention patents, Chinese Patent Application No. CN: 200910129632.7 [2]. The invention is characterized in that: at room temperature under vacuum conditions, specific combinations of the installation space of the electromagnetic field, based on light nuclei intrinsic magnetic moment and the electric field, the first two strings of the nuclei to be bound fusion on the same line (track of. Re-use nuclear spin angular momentum vector inherent nearly the speed of light to form a super strong spin rotation gyro inertial guidance features, to overcome the Coulomb repulsion strong bias barrier to achieve fusion directly hit. Similar constraints apply nuclear inertial guidance mode for different speeds and energy ion beam mixing speed, the design of ion speed dc transformer is cold fusion reactors, nuclear fusion engines and such nuclear power plants and power delivery systems start important supporting equipment, so apply for a patent merger 12. Laser ablation production of Ba, Ca, Dy, Er, La, Lu, and Yb ions CERN Document Server Olmschenk, S 2016-01-01 We use a pulsed nitrogen laser to produce atomic ions by laser ablation, measuring the relative ion yield for several elements, including some that have only recently been proposed for use in cold trapped ion experiments. For barium, we monitor the ion yield as a function of the number of applied ablation pulses for different substrates. We also investigate the ion production as a function of the pulse energy, and the efficiency of loading an ion trap as a function of radiofrequency voltage. 13. Friendly units for coldness CERN Document Server Fraundorf, P 2006-01-01 Measures of temperature that center around human experience get lots of use. Of course thermal physics insights of the last century have shown that reciprocal temperature (1/kT) has applications that temperature addresses less well. In addition to taking on negative absolute values under population inversion (e.g. of magnetic spins), bits and bytes turn 1/kT into an informatic measure of the thermal ambient for developing correlations within any complex system. We show here that, in the human-friendly units of bytes and food Calories, water freezes when 1/kT ~200 ZB/Cal or kT ~5 Cal/YB. Casting familiar benchmarks into these terms shows that habitable human space requires coldness values (part of the time, at least) between 0 and 40 ZB/Cal with respect body temperature ~100 degrees F, a range in kT of ~1 Cal/YB. Insight into these physical quantities underlying thermal equilibration may prove useful for budding scientists, as well as the general public, in years ahead. 14. Zitterbewegung in Cold Atoms Science.gov (United States) Penteado, Poliana; Egues, J. Carlos 2013-03-01 In condensed matter systems, the coupling between spatial and spin degrees of freedom through the spin-orbit (SO) interaction offers the possibility of manipulating the electron spin via its orbital motion. The proposal by Datta and Das of a `spin transistor' for example, highlights the use of the SO interaction to control the electron spin via electrical means. Recently, arrangements of crossed lasers and magnetic fields have been used to trap and cool atoms in optical lattices and also to create light-induced gauge potentials, which mimic the SO interactions in real solids. In this work, we investigate the Zitterbewegung in cold atoms by starting from the effective SO Hamiltonian derived in Ref.. Cross-dressed atoms as effective spins can provide a proper setting in which to observe this effect, as the relevant parameter range of SO strengths may be more easily attainable in this context. We find a variety of peculiar Zitterbewegung orbits in real and pseudo-spin spaces, e.g., cycloids and ellipses - all of which obtained with realistic parameters. This work is supported by FAPESP, CAPES and CNPq. 15. Understanding the conductivity in ion propulsion devices Energy Technology Data Exchange (ETDEWEB) Garrigues, L.; Boeuf, J.P.; Pitchford, L.C. [Univ. Paul Sabatier, Toulouse (France) 1996-12-31 A SPT (stationary plasma thruster) is a type of ion source developed primarily in Russian over the past 30 years and used as an electromagnetic propulsion device in applications requiring a low to moderate thrust with a high efficiency (satellite station keeping, for example). Although SPTs have been used in space, the principles of operation are far from clear. One of the outstanding issues is the identification of the mechanisms leading to the observed high conductivity in these devices. The neutral density is low and the plasma at the cathode end is fully ionized. Electron-neutral and electron-ion collisions are insufficient to account for the observed conductivity across the magnetic field lines. Bohm diffusion resulting from turbulence is a possible explanation for the observed high conductivity but other effects such as electron-wall interaction seem to play a very important role, due to the particular structure of this device where magnetic field lines are directed toward the walls. Electron collisions with the dielectric walls can enhance the conductivity in SPTs. Because the B field is perpendicular to the walls, the electron current is forced to the walls and secondary electron emission can occur for electron energies greater than about 30 eV on these surfaces. The authors have performed Monte Carlo calculations to study the effect of reflection and secondary emission on the calculated conductivity. Results from the Monte Carlo simulation are used to estimate the electron conductivity and energy loss in the device. These data are used as input in a self-consistent quasi-neutral hybrid model of the discharge where ions are described by a Vlasov equation, and the electric field distribution is deduced from the electron momentum equation, assuming quasi-neutrality. 16. Cold-formed steel design CERN Document Server Yu, Wei-Wen 2010-01-01 The definitive text in the field, thoroughly updated and expanded Hailed by professionals around the world as the definitive text on the subject, Cold-Formed Steel Design is an indispensable resource for all who design for and work with cold-formed steel. No other book provides such exhaustive coverage of both the theory and practice of cold-formed steel construction. Updated and expanded to reflect all the important developments that have occurred in the field over the past decade, this Fourth Edition of the classic text provides you with more of the detailed, up-to-the-minute techni 17. Quantum logic with molecular ions CERN Document Server Wolf, Fabian; Heip, Jan C; Gebert, Florian; Shi, Chunyan; Schmidt, Piet O 2015-01-01 Laser spectroscopy of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants, the laboratory test for their possible variation, and the search for a possible electric dipole moment of the electron. Optical clocks based on molecular ions sensitive to some of these effects are expected to achieve uncertainties approaching the$10^{-18}$level. While the complexity of molecular structure facilitates these applications, the absence of cycling transitions poses a challenge for direct laser cooling, quantum state control, and detection. Previously employed state detection techniques based on photo-dissociation or chemical reactions are destructive and therefore inefficient. Here we experimentally demonstrate non-destructive state detection of a single trapped molecular ion through its strong Coulomb coupling to a well-controlled co-trapped atomic ion. An algorithm based on a state-dependent optical dipole force(ODF) changes the internal state... 18. Tunneling process in heavy-ion fusion and fission Energy Technology Data Exchange (ETDEWEB) Iwamoto, Akira [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kondratyev, V.; Bonasera, A. 1998-10-01 We present a model towards the many-body description of sub-barrier fusion and spontaneous fission based on the semiclassical Vlasov equation and the Feynman path integral method. We define suitable collective variables from the Vlasov solution and use the imaginary time technique for the dynamics below the Coulomb barrier. (author) 19. Operant behavioral responses to orofacial cold stimuli in rats with chronic constrictive trigeminal nerve injury: effects of menthol and capsazepine Science.gov (United States) 2013-01-01 Both spinal and trigeminal somatosensory systems use the TRPM8 channel as a principal transducer for detecting cold stimuli. It is currently unclear whether this cold transducer may play a role in trigeminal neuropathic pain manifesting cold allodynia and hyperalgesia. In the present study, trigeminal neuropathy was induced by chronic constrictive nerve injury of the infraorbital nerve (ION-CCI). Behavioral responses to cold stimuli in orofacial regions were assessed by the newly developed orofacial operant test in the ION-CCI rats. We tested menthol and capsazepine, two compounds that can activate and inhibit TRPM8 respectively, on orofacial operant responses to cold stimuli in ION-CCI rats. Testing animals performed operant tasks by voluntarily contacting their orofacial regions to a cold stimulation module in order to access sweetened milk as a reward, and contact time and number of the operant behaviors were automatically recorded. Total contact time was significantly reduced at the cooling temperatures of 17°C and 12°C in ION-CCI group in comparison with sham group, indicating the presence of cold allodynia and hyperalgesia in ION-CCI rats. When menthol was administered to ION-CCI rats, total contact time was further reduced and total contact number increased at the cooling temperatures. In contrast, after administration of capsazepine to ION-CCI rats, total contact time was significantly increased at the cooling temperatures. The behavioral outcomes support the idea that TRPM8 plays a role in cold allodynia and hyperalgesia following chronic trigeminal nerve injury. PMID:23767981 20. PANDA: Cold three axes spectrometer Directory of Open Access Journals (Sweden) Astrid Schneidewind 2015-08-01 Full Text Available The cold three axes spectrometer PANDA, operated by JCNS, Forschungszentrum Jülich, offers high neutron flux over a large dynamic range keeping the instrumental background comparably low. 1. Flu and Colds: In Depth Science.gov (United States) ... studies have evaluated the use of American ginseng (Panax quinquefolius) to prevent colds. A 2011 evaluation of ... E561. Seida JK, Durec T, Kuhle S. North American (Panax quinquefolius) and Asian ginseng (Panax ginseng) preparations for ... 2. Cold nuclear fusion Energy Technology Data Exchange (ETDEWEB) Tsyganov, E.N., E-mail: [email protected] [Cold Fusion Power, International (United States); Bavizhev, M.D. [LLC “Radium”, Moscow (Russian Federation); Buryakov, M.G. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation); Dabagov, S.B. [RAS P.N. Lebedev Physical Institute, Leninsky pr. 53, 119991 Moscow (Russian Federation); National Research Nuclear University MEPhI, Kashirskoe shosse 31, 115409 Moscow (Russian Federation); Golovatyuk, V.M.; Lobastov, S.P. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation) 2015-07-15 If target deuterium atoms were implanted in a metal crystal in accelerator experiments, a sharp increase in the probability of DD-fusion reaction was clearly observed when compared with the reaction’s theoretical value. The electronic screening potential, which for a collision of free deuterium atoms is about 27 eV, reached 300–700 eV in the case of the DD-fusion in metallic crystals. These data leads to the conclusion that a ban must exist for deuterium atoms to be in the ground state 1s in a niche filled with free conduction electrons. At the same time, the state 2p whose energy level is only 10 eV above that of state 1s is allowed in these conditions. With anisotropy of 2p, 3p or above orbitals, their spatial positions are strictly determined in the lattice coordinate system. When filling out the same potential niches with two deuterium atoms in the states 2p, 3p or higher, the nuclei of these atoms can be permanently positioned without creating much Coulomb repulsion at a very short distance from each other. In this case, the transparency of the potential barrier increases dramatically compared to the ground state 1s for these atoms. The probability of the deuterium nuclei penetrating the Coulomb barrier by zero quantum vibration of the DD-system also increases dramatically. The so-called cold nuclear DD-fusion for a number of years was registered in many experiments, however, was still rejected by mainstream science for allegedly having no consistent scientific explanation. Finally, it received the validation. Below, we outline the concept of this explanation and give the necessary calculations. This paper also considers the further destiny of the formed intermediate state of {sup 4}He{sup ∗}. 3. Garlic for the common cold. Science.gov (United States) Lissiman, Elizabeth; Bhasale, Alice L; Cohen, Marc 2014-11-11 Background Garlic is alleged to have antimicrobial and antiviral properties that relieve the common cold, among other beneficial effects. There is widespread usage of garlic supplements. The common cold is associated with significant morbidity and economic consequences. On average, children have six to eight colds per year and adults have two to four.Objectives To determine whether garlic (Allium sativum) is effective for the prevention or treatment of the common cold, when compared to placebo, no treatment or other treatments.Search methods We searched CENTRAL (2014, Issue 7),OLDMEDLINE (1950 to 1965),MEDLINE (January 1966 to July week 5, 2014), EMBASE(1974 to August 2014) and AMED (1985 to August 2014).Selection criteria Randomised controlled trials of common cold prevention and treatment comparing garlic with placebo, no treatment or standard treatment.Data collection and analysis Two review authors independently reviewed and selected trials from searches, assessed and rated study quality and extracted relevant data.Main results In this updated review, we identified eight trials as potentially relevant from our searches. Again, only one trial met the inclusion criteria.This trial randomly assigned 146 participants to either a garlic supplement (with 180 mg of allicin content) or a placebo (once daily)for 12 weeks. The trial reported 24 occurrences of the common cold in the garlic intervention group compared with 65 in the placebo group (P value garlic group compared with the placebo group (111 versus 366). The number of days to recovery from an occurrence of the common cold was similar in both groups (4.63 versus 5.63). Only one trial met the inclusion criteria, therefore limited conclusions can be drawn. The trial relied on self reported episodes of the common cold but was of reasonable quality in terms of randomisation and allocation concealment. Adverse effects included rash and odour. Authors' conclusions There is insufficient clinical trial evidence 4. Proton and heavy ion acceleration by stochastic fluctuations in the Earth's magnetotail Energy Technology Data Exchange (ETDEWEB) Catapano, Filomena; Zimbardo, Gaetano; Perri, Silvia; Greco, Antonella [Calabria Univ., Rende (Italy). Dept. of Physics; Artemyev, Anton V. [Russian Academy of Science, Moscow (Russian Federation). Space Research Inst.; California Univ., Los Angeles, CA (United States). Dept. of Earth, Planetary, and Space Science and Inst. of Geophysics and Planetary Physics 2016-07-01 Spacecraft observations show that energetic ions are found in the Earth's magnetotail, with energies ranging from tens of keV to a few hundreds of keV. In this paper we carry out test particle simulations in which protons and other ion species are injected in the Vlasov magnetic field configurations obtained by Catapano et al. (2015). These configurations represent solutions of a generalized Harris model, which well describes the observed profiles in the magnetotail. In addition, three-dimensional time-dependent stochastic electromagnetic perturbations are included in the simulation box, so that the ion acceleration process is studied while varying the equilibrium magnetic field profile and the ion species. We find that proton energies of the order of 100 keV are reached with simulation parameters typical of the Earth's magnetotail. By changing the ion mass and charge, we can study the acceleration of heavy ions such as He{sup ++} and O{sup +}, and it is found that energies of the order of 100-200 keV are reached in a few seconds for He{sup ++}, and about 100 keV for O{sup +}. 5. Ion acoustic solitons/double layers in two-ion plasma revisited Energy Technology Data Exchange (ETDEWEB) Lakhina, G. S., E-mail: [email protected]; Singh, S. V., E-mail: [email protected]; Kakad, A. P., E-mail: [email protected] [Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai 410218 (India) 2014-06-15 Ion acoustic solitons and double layers are studied in a collisionless plasma consisting of cold heavier ion species, a warm lighter ion species, and hot electrons having Boltzmann distributions by Sagdeev pseudo-potential technique. In contrast to the previous results, no double layers and super-solitons are found when both the heavy and lighter ion species are treated as cold. Only the positive potential solitons are found in this case. When the thermal effects of the lighter ion species are included, in addition to the usual ion-acoustic solitons occurring at M > 1 (where the Mach number, M, is defined as the ratio of the speed of the solitary wave and the ion-acoustic speed considering temperature of hot electrons and mass of the heavier ion species), slow ion-acoustic solitons/double layers are found to occur at low Mach number (M < 1). The slow ion-acoustic mode is actually a new ion-ion hybrid acoustic mode which disappears when the normalized number density of lighter ion species tends to 1 (i.e., no heavier species). An interesting property of the new slow ion-acoustic mode is that at low number density of the lighter ion species, only negative potential solitons/double layers are found whereas for increasing densities there is a transition first to positive solitons/double layers, and then only positive solitons. The model can be easily applicable to the dusty plasmas having positively charged dust grains by replacing the heavier ion species by the dust mass and doing a simple normalization to take account of the dust charge. 6. Finger and toe temperature response to cold water and cold air exposure NARCIS (Netherlands) Struijs, N.R. van der; Es, E.M. van; Raymann, R.J.E.M.; Daanen, H.A.M. 2008-01-01 Introduction: Subjects with a weak cold-induced vasodilatation response (CIVD) to experimental cold-water immersion of the fingers in a laboratory setting have been shown to have a higher risk for local cold injuries when exposed to cold in real life. Most of the cold injuries in real life, however, 7. 2D fluid simulations of interchange turbulence with ion dynamics DEFF Research Database (Denmark) Nielsen, Anders Henry; Madsen, Jens; Xu, G. S. 2013-01-01 In this paper we present a first principle global two-dimensional fluid model. The HESEL (Hot Edge SOL Electrostatic) model is a 2D numerical fluid code, based on interchange dynamics and includes besides electron also the ion pressure dynamic. In the limit of cold ions the model almost reduces... 8. Feedback cooling of a single trapped ion CERN Document Server Bushev, P; Wilson, A; Dubin, F; Becher, C; Eschner, J; Blatt, R; Steixner, V; Rabl, P; Zoller, P; Bushev, Pavel; Rotter, Daniel; Wilson, Alex; Dubin, Francois; Becher, Christoph; Eschner, Juergen; Blatt, Rainer; Steixner, Viktor; Rabl, Peter; Peter Zoller 2005-01-01 Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electro-mechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical Master Equation. 9. Ion Colliders CERN Document Server Fischer, W 2014-01-01 High-energy ion colliders are large research tools in nuclear physics to study the Quark-Gluon-Plasma (QGP). The range of collision energy and high luminosity are important design and operational considerations. The experiments also expect flexibility with frequent changes in the collision energy, detector fields, and ion species. Ion species range from protons, including polarized protons in RHIC, to heavy nuclei like gold, lead and uranium. Asymmetric collision combinations (e.g. protons against heavy ions) are also essential. For the creation, acceleration, and storage of bright intense ion beams, limits are set by space charge, charge change, and intrabeam scattering effects, as well as beam losses due to a variety of other phenomena. Currently, there are two operating ion colliders, the Relativistic Heavy Ion Collider (RHIC) at BNL, and the Large Hadron Collider (LHC) at CERN. 10. Laser spectroscopy of cold molecules CERN Document Server Borri, Simone 2016-01-01 This paper reviews the recent results in high-resolution spectroscopy on cold molecules. Laser spectroscopy of cold molecules addresses issues of symmetry violation, like in the search for the electric dipole moment of the electron and the studies on energy differences in enantiomers of chiral species; tries to improve the precision to which fundamental physical constants are known and tests for their possible variation in time and space; tests quantum electrodynamics, and searches for a fifth force. Further, we briefly review the recent technological progresses in the fields of cold molecules and mid-infrared lasers, which are the tools that mainly set the limits for the resolution that is currently attainable in the measurements. 11. COLD-SAT dynamic model Science.gov (United States) Adams, Neil S.; Bollenbacher, Gary 1992-01-01 This report discusses the development and underlying mathematics of a rigid-body computer model of a proposed cryogenic on-orbit liquid depot storage, acquisition, and transfer spacecraft (COLD-SAT). This model, referred to in this report as the COLD-SAT dynamic model, consists of both a trajectory model and an attitudinal model. All disturbance forces and torques expected to be significant for the actual COLD-SAT spacecraft are modeled to the required degree of accuracy. Control and experimental thrusters are modeled, as well as fluid slosh. The model also computes microgravity disturbance accelerations at any specified point in the spacecraft. The model was developed by using the Boeing EASY5 dynamic analysis package and will run on Apollo, Cray, and other computing platforms. 12. A linear dispersion relation for the hybrid kinetic-ion/fluid-electron model of plasma physics CERN Document Server Told, Daniel; Astfalk, Patrick; Jenko, Frank 2016-01-01 A dispersion relation for a commonly used hybrid model of plasma physics is developed, which combines fully kinetic ions and a massless-electron fluid description. Although this model and variations of it have been used to describe plasma phenomena for about 40 years, to date there exists no general dispersion relation to describe the linear wave physics contained in the model. Previous efforts along these lines are extended here to retain arbitrary wave propagation angles, temperature anisotropy effects, as well as additional terms in the generalized Ohm's law which determines the electric field. A numerical solver for the dispersion relation is developed, and linear wave physics is benchmarked against solutions of a full Vlasov-Maxwell dispersion relation solver. This work opens the door to a more accurate interpretation of existing and future wave and turbulence simulations using this type of hybrid model. 13. Insect capa neuropeptides impact desiccation and cold tolerance. Science.gov (United States) Terhzaz, Selim; Teets, Nicholas M; Cabrero, Pablo; Henderson, Louise; Ritchie, Michael G; Nachman, Ronald J; Dow, Julian A T; Denlinger, David L; Davies, Shireen-A 2015-03-03 The success of insects is linked to their impressive tolerance to environmental stress, but little is known about how such responses are mediated by the neuroendocrine system. Here we show that the capability (capa) neuropeptide gene is a desiccation- and cold stress-responsive gene in diverse dipteran species. Using targeted in vivo gene silencing, physiological manipulations, stress-tolerance assays, and rationally designed neuropeptide analogs, we demonstrate that the Drosophila melanogaster capa neuropeptide gene and its encoded peptides alter desiccation and cold tolerance. Knockdown of the capa gene increases desiccation tolerance but lengthens chill coma recovery time, and injection of capa peptide analogs can reverse both phenotypes. Immunohistochemical staining suggests that capa accumulates in the capa-expressing Va neurons during desiccation and nonlethal cold stress but is not released until recovery from each stress. Our results also suggest that regulation of cellular ion and water homeostasis mediated by capa peptide signaling in the insect Malpighian (renal) tubules is a key physiological mechanism during recovery from desiccation and cold stress. This work augments our understanding of how stress tolerance is mediated by neuroendocrine signaling and illustrates the use of rationally designed peptide analogs as agents for disrupting protective stress tolerance. 14. Development of cold neutron depth profiling system at HANARO Energy Technology Data Exchange (ETDEWEB) Park, B.G. [Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of); Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-355 (Korea, Republic of); Sun, G.M., E-mail: [email protected] [Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-355 (Korea, Republic of); Choi, H.D. [Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of) 2014-07-01 A neutron depth profiling (NDP) system has been designed and developed at HANARO, a 30 MW research reactor at the Korea Atomic Energy Research Institute (KAERI). The KAERI-NDP system utilizes cold neutrons that are transported along the CG1 neutron guide from the cold neutron source and it consists of a neutron beam collimator, a target chamber, a beam stopper, and charged particle detectors along with NIM-standard modules for charged particle pulse-height analysis. A 60 cm in diameter stainless steel target chamber was designed to control the positions of the sample and detector. The energy distribution of the cold neutron beam at the end of the neutron guide was calculated by using the Monte Carlo simulation code McStas, and a neutron flux of 1.8×10{sup 8} n/cm{sup 2} s was determined by using the gold foil activation method at the sample position. The performance of the charged particle detection of the KAERI-NDP system was tested by using Standard Reference Materials. The energy loss spectra of alpha particles and Li ions emitted from {sup 10}B, which was irradiated by cold neutrons, were measured. The measured peak concentration and the areal density of {sup 10}B in the Standard Reference Material are consistent with the reference values within 1% and 3.4%, respectively. 15. Development of cold neutron depth profiling system at HANARO Science.gov (United States) Park, B. G.; Sun, G. M.; Choi, H. D. 2014-07-01 A neutron depth profiling (NDP) system has been designed and developed at HANARO, a 30 MW research reactor at the Korea Atomic Energy Research Institute (KAERI). The KAERI-NDP system utilizes cold neutrons that are transported along the CG1 neutron guide from the cold neutron source and it consists of a neutron beam collimator, a target chamber, a beam stopper, and charged particle detectors along with NIM-standard modules for charged particle pulse-height analysis. A 60 cm in diameter stainless steel target chamber was designed to control the positions of the sample and detector. The energy distribution of the cold neutron beam at the end of the neutron guide was calculated by using the Monte Carlo simulation code McStas, and a neutron flux of 1.8×108 n/cm2 s was determined by using the gold foil activation method at the sample position. The performance of the charged particle detection of the KAERI-NDP system was tested by using Standard Reference Materials. The energy loss spectra of alpha particles and Li ions emitted from 10B, which was irradiated by cold neutrons, were measured. The measured peak concentration and the areal density of 10B in the Standard Reference Material are consistent with the reference values within 1% and 3.4%, respectively. 16. Insect capa neuropeptides impact desiccation and cold tolerance Science.gov (United States) Terhzaz, Selim; Teets, Nicholas M.; Cabrero, Pablo; Henderson, Louise; Ritchie, Michael G.; Nachman, Ronald J.; Dow, Julian A. T.; Denlinger, David L.; Davies, Shireen-A. 2015-01-01 The success of insects is linked to their impressive tolerance to environmental stress, but little is known about how such responses are mediated by the neuroendocrine system. Here we show that the capability (capa) neuropeptide gene is a desiccation- and cold stress-responsive gene in diverse dipteran species. Using targeted in vivo gene silencing, physiological manipulations, stress-tolerance assays, and rationally designed neuropeptide analogs, we demonstrate that the Drosophila melanogaster capa neuropeptide gene and its encoded peptides alter desiccation and cold tolerance. Knockdown of the capa gene increases desiccation tolerance but lengthens chill coma recovery time, and injection of capa peptide analogs can reverse both phenotypes. Immunohistochemical staining suggests that capa accumulates in the capa-expressing Va neurons during desiccation and nonlethal cold stress but is not released until recovery from each stress. Our results also suggest that regulation of cellular ion and water homeostasis mediated by capa peptide signaling in the insect Malpighian (renal) tubules is a key physiological mechanism during recovery from desiccation and cold stress. This work augments our understanding of how stress tolerance is mediated by neuroendocrine signaling and illustrates the use of rationally designed peptide analogs as agents for disrupting protective stress tolerance. PMID:25730885 17. Sampling of ions at atmospheric pressure: ion transmission and ion energy studied by simulation and experiment Science.gov (United States) Große-Kreul, Simon; Hübner, Simon; Benedikt, Jan; von Keudell, Achim 2016-04-01 Mass spectrometry of ions from atmospheric pressure plasmas is a challenging diagnostic method that has been applied to a large variety of cold plasma sources in the past. However, absolute densities can usually not be obtained, moreover, the process of sampling of ions and neutrals from such a plasma inherently influences the measured composition. These issues are studied in this contribution by a combination of experimental and numerical methods. Different numerical domains are sequentially coupled to calculate the ion transmission from the source to the mass analyzer. It is found that the energy of the sampled ions created by a radio-frequency microplasma operated in a He-N2 mixture at atmospheric pressure is of the order of 0.1 eV and that it depends linearly on the ion mass in good agreement with the expectation for seeded particles accelerated in a supersonic expansion. Moreover, the measured ion energy distribution from an afterglow of an atmospheric pressure plasma can be reproduced on basis of the particle trajectories in the sampling system. Eventually, an estimation of the absolute flux of ions to the detector is deduced. 18. Cold Tolerance of Plants Used for Cold-Regions Revegetation Science.gov (United States) 1990-10-01 from tempted to transfer the rye cold-tolerance genome to increased concentrations of solutes in cells and extra- wheat in hybrids. While the gene...Journal, 76: 516-517. Tryon, E.H. and R.P. True (1952) Blister shake of Yelenosky, G. (1988) Capacity of citrus flowers to yellow poplar. Bulletin of the 19. Adiabatic Cooling for Rovibrational Spectroscopy of Molecular Ions DEFF Research Database (Denmark) Fisher, Karin 2017-01-01 The field of cold molecular ions is a fast growing one, with applications in high resolution spectroscopy and metrology, the search for time variations of fundamental constants, cold chemistry and collisions, and quantum information processing, to name a few. The study of single molecular ions...... is attractive as it enables one to push the limits of spectroscopic accuracy. Non-destructive spectroscopic detection of molecular ions can be achieved by co-trapping with an easier to detect atomic ion. The ion chain has coupled motion, and transitions which change both the internal and motional states...... to the measured heating rates, almost perfectly fitting existing heating rate theory. Further, the same model successfully predicted the heating rates of the in-phase mode of a two-ion crystal, indicating that we can use it to predict the heating rates in experiments on molecule-atom chains. Adiabatic cooling... 20. Avionics Box Cold Plate Damage Prevention Science.gov (United States) Stambolian, Damon B.; Larchar, Steven W.; Henderson, Gena; Tran, Donald; Barth, Tim 2012-01-01 Problem Introduction: 1. Prevent Cold Plate Damage in Space Shuttle. 1a. The number of cold plate problems had increased from an average of 16.5 per/year between 1990 through 2000, to an average of 39.6 per year between 2001through 2005. 1b. Each complete set of 80 cold plates cost approximately$29 million, an average of $362,500 per cold plate. 1c It takes four months to produce a single cold plate. 2. Prevent Cold Plate Damage in Future Space Vehicles. 1. Excitation of nonlinear ion acoustic waves in CH plasmas CERN Document Server Feng, Q S; Liu, Z J; Xiao, C Z; Wang, Q; He, X T 2016-01-01 Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number$ k\\lambda_{De} $increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of$ T_i/T_e < 0.2 $in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with$k\\lambda_{De}$increasing. When$k\\lambda_{De}$is not large, such as$k\\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when$k\\lambda_{De}$is large, such as$k\\lambda_{De}=0.7, the linear ... 2. Phonon forces and cold denaturatio DEFF Research Database (Denmark) Bohr, Jakob 2003-01-01 the molecule Is a continuum. The frequencies of the vibrational modes depend on the molecular dimensionality; hence, the zero-point energies for the folded and the denatured protein are estimated to differ by several electron volts. For a biomolecule such an energy is significant and may contribute to cold... 3. Images of the Cold War. Science.gov (United States) Chomsky, Noam 1989-01-01 The conventional U.S. picture traces the Cold War to Soviet violation of wartime agreements, while the U.S.S.R. defends its actions as responses to American violations and foreign adventurism. An understanding of how ideology is shaped by national self-interest will help students see beyond propaganda and myth in interpreting past and current… 4. Encyclopedia of the Cold War NARCIS (Netherlands) van Dijk, R. 2008-01-01 Between 1945 and 1991, tension between the USA, its allies, and a group of nations led by the USSR, dominated world politics. This period was called the Cold War - a conflict that stopped short to a full-blown war. Benefiting from the recent research of newly open archives, the Encyclopedia of the C 5. Encyclopedia of the Cold War NARCIS (Netherlands) van Dijk, R. 2008-01-01 Between 1945 and 1991, tension between the USA, its allies, and a group of nations led by the USSR, dominated world politics. This period was called the Cold War - a conflict that stopped short to a full-blown war. Benefiting from the recent research of newly open archives, the Encyclopedia of the 6. Vaccines for the common cold. Science.gov (United States) Simancas-Racines, Daniel; Franco, Juan Va; Guerra, Claudia V; Felix, Maria L; Hidalgo, Ricardo; Martinez-Zapata, Maria José 2017-05-18 The common cold is a spontaneously remitting infection of the upper respiratory tract, characterised by a runny nose, nasal congestion, sneezing, cough, malaise, sore throat, and fever (usually Register of Controlled Trials (CENTRAL) (September 2016), MEDLINE (1948 to September 2016), Embase (1974 to September 2016), CINAHL (1981 to September 2016), and LILACS (1982 to September 2016). We also searched three trials registers for ongoing studies and four websites for additional trials (February 2017). We included no language or date restrictions. Randomised controlled trials (RCTs) of any virus vaccines compared with placebo to prevent the common cold in healthy people. Two review authors independently evaluated methodological quality and extracted trial data. We resolved disagreements by discussion or by consulting a third review author. We found no additional RCTs for inclusion in this update. This review includes one RCT dating from the 1960s with an overall high risk of bias. The RCT included 2307 healthy participants, all of whom were included in analyses. This trial compared the effect of an adenovirus vaccine against placebo. No statistically significant difference in common cold incidence was found: there were 13 (1.14%) events in 1139 participants in the vaccines group and 14 (1.19%) events in 1168 participants in the placebo group (risk ratio 0.95, 95% confidence interval 0.45 to 2.02; P = 0.90). No adverse events related to the live vaccine were reported. The quality of the evidence was low due to limitations in methodological quality and a wide 95% confidence interval. This Cochrane Review was based on one study with low-quality evidence. We found no conclusive results to support the use of vaccines for preventing the common cold in healthy people compared with placebo. We identified a need for well-designed, adequately powered RCTs to investigate vaccines for the common cold in healthy people. Any future trials on medical treatments for preventing the 7. Common cold - how to treat at home Science.gov (United States) ... this page: //medlineplus.gov/ency/patientinstructions/000466.htm Common cold - how to treat at home To use ... this page, please enable JavaScript. Colds are very common. A visit to your health care provider's office ... 8. The cold equation of state of tantalum Energy Technology Data Exchange (ETDEWEB) Greeff, Carl W [Los Alamos National Laboratory; Rudin, Sven P [Los Alamos National Laboratory; Corckett, Scott D [Los Alamos National Laboratory; Wills, John M [Los Alamos National Laboratory 2009-01-01 In high-pressure isentropic compression experiments (ICE), the pressure is dominated by the cold curve. In order to obtain an accurate semi-empirical cold curve for Ta, we calculate the thermal pressure from ab initio phonon and electronic excitation spectra. The cold curve is then inferred from ultrasonic and shock data. Our empirical cold pressure is compared to density functional calculations and found to be closer to GGA results at low pressure and to approach LDA at high pressure. 9. SCIENCES IN COLD AND ARID REGIONS Institute of Scientific and Technical Information of China (English) 2008-01-01 Aims and Scope Sciences in Cold and Arid Regions, an international Engiish-language journal, is devoted to publishing the latest research achievements on the process and the pattern of Earth surface system in cold and arid regions. Researches in cold regions 1) emphasize particularly on the cold-region-characterized physical, chemical and biological processes and their interactions, and on the response of Cryosphere to Global change and Human activities as well as its effect to environment and the acclimatizable 10. Ion Chromatography. Science.gov (United States) Mulik, James D.; Sawicki, Eugene 1979-01-01 Accurate for the analysis of ions in solution, this form of analysis enables the analyst to directly assay many compounds that previously were difficult or impossible to analyze. The method is a combination of the methodologies of ion exchange, liquid chromatography, and conductimetric determination with eluant suppression. (Author/RE) 11. Common Cold in Babies: Symptoms and Causes Science.gov (United States) Common cold in babies Symptoms and causes By Mayo Clinic Staff The first indication of the common cold in a baby is often: A congested ... or green Other signs and symptoms of a common cold in a baby may include: Fever Sneezing ... 12. 1. contribution of the dynamics on the reactions mechanisms in the heavy ions collisions at the intermediary energies (20-100 MeV/A) for the light systems. 2. management of radioactive wastes by new options: nuclear data measurement programme between 20 and 150 MeV; 1. role de la dynamique sur les mecanismes de reactions dans les collisions d'ions lourds aux energies intermediaires (20-100 MeV/A) pour des systemes legers. 2. gestion des dechets radioactifs par des options nouvelles: programme de mesures de donnees nucleaires entre 20 et 150 MeV Energy Technology Data Exchange (ETDEWEB) Eudes, Ph 2000-09-22 The first part concerns the features of emitted charged particles in heavy ions reactions that have been studied in the framework of the semi classical Landau-Vlasov approach for the light system Ar + Al at 65 MeV/nucleon incident energy. The second part is devoted to the radioactive waste management (transmutation), but it was necessary to increase the data banks evaluated in neutrons up to 150-200 MeV and to create a data bank in protons. In the European framework it was decide to focus on three representative elements: lead (spallation target), iron (structure material) and uranium (actinide). (N.C.) 13. 77 FR 43117 - Meeting of the Cold War Advisory Committee for the Cold War Theme Study Science.gov (United States) 2012-07-23 ... National Park Service Meeting of the Cold War Advisory Committee for the Cold War Theme Study AGENCY... with the Federal Advisory Committee Act, 5 U.S.C. Appendix, that the Cold War Advisory Committee for the Cold War Theme Study will conduct a teleconference meeting on August 3, 2012. Members of the... 14. Observation of a power-law energy distribution in atom-ion hybrid system Science.gov (United States) Meir, Ziv; Akerman, Nitzan; Sikorsky, Tomas; Ben-Shlomi, Ruti; Dallal, Yehonatan; Ozeri, Roee 2016-05-01 Understanding atom-ion collision dynamics is at the heart of the growing field of ultra-cold atom-ion physics. The naive picture of a hot ion sympathetically-cooled by a cold atomic bath doesn't hold due to the time dependent potentials generated by the ion Paul trap. The energy scale of the atom-ion system is determined by a combination of the atomic bath temperature, the ion's excess micromotion (EMM) and the back action of the atom-ion attraction on the ion's position in the trap. However, it is the position dependent ion's inherent micromotion which acts as an amplifier for the ion's energy during random consecutive collisions. Due to this reason, the ion's energy distribution deviates from Maxwell-Boltzmann (MB) characterized by an exponential tail to one with power-law tail described by Tsallis q-exponential function. Here we report on the observation of a strong deviation from MB to Tsallis energy distribution of a trapped ion. In our experiment, a ground-state cooled 88 Sr+ ion is immersed in an ultra-cold cloud of 87 Rb atoms. The energy scale is determined by either EMM or solely due to the back action on the ion position during a collision with an atom in the trap. Energy distributions are obtained using narrow optical clock spectroscopy. 15. Cold Stress at High Altitudes Directory of Open Access Journals (Sweden) N. C. Majumdar 1983-04-01 Full Text Available The problem of cold at high altitudes has been analysed from a purely physical standpoint. It has been shown that Siple's Wind-Chill Index is not reliable because (i it does not make use of the well established principles governing the physical processes of heat transfer by convection and radiation, and (ii it assumes that the mean radiant temperature of the surroundings is the same as the ambient dry bulb temperature. A Cold Stress Index has been proposed which is likely to be a more reliable guide for assessing the climatic hazards of high altitude environments. The Index can be quickly estimated with the help of two nomograms devised for the purpose. 16. Ultra-cold molecule production. Energy Technology Data Exchange (ETDEWEB) Ramirez-Serrano, Jamie; Chandler, David W.; Strecker, Kevin; Rahn, Larry A. 2005-12-01 The production of Ultra-cold molecules is a goal of many laboratories through out the world. Here we are pursuing a unique technique that utilizes the kinematics of atomic and molecular collisions to achieve the goal of producing substantial numbers of sub Kelvin molecules confined in a trap. Here a trap is defined as an apparatus that spatially localizes, in a known location in the laboratory, a sample of molecules whose temperature is below one degree absolute Kelvin. Further, the storage time for the molecules must be sufficient to measure and possibly further cool the molecules. We utilize a technique unique to Sandia to form cold molecules from near mass degenerate collisions between atoms and molecules. This report describes the progress we have made using this novel technique and the further progress towards trapping molecules we have cooled. 17. Pseudoneutropenia from cold agglutinin leucoagglutination Directory of Open Access Journals (Sweden) Momin M 2015-01-01 Full Text Available Pseudoneutropenia or low leucocyte count secondary to leucoagglutination is caused by ethylene diamine tetra acetic acid (EDTA or cold agglutinins and is seen in benign and malignant disorders. We report a 34-year-old lady who was admitted with fever, vomiting, respiratory distress and productive cough. Complete blood count (CBC at initial presentation revealed low haemoglobin (11.6 g/dL, total leucocyte count (TLC (5900/mm3 with 50% polymorphs. Peripheral blood smear showed leucocytes in clusters. Another sample was asked for in citrate anticoagulant which showed a TLC of 5900/mm3 with 50% polymorphs and evidence of auto agglutination. Another collected in a prewarmed ethylene diamine tetra acetic acid (EDTA tube, CBC showed a TLC of 9800/mm3 with 39% neutrophils suggestive of pseudoneutropenia due to cold agglutinins. 18. Cold dark matter heats up. Science.gov (United States) Pontzen, Andrew; Governato, Fabio 2014-02-13 A principal discovery in modern cosmology is that standard model particles comprise only 5 per cent of the mass-energy budget of the Universe. In the ΛCDM paradigm, the remaining 95 per cent consists of dark energy (Λ) and cold dark matter. ΛCDM is being challenged by its apparent inability to explain the low-density 'cores' of dark matter measured at the centre of galaxies, where centrally concentrated high-density 'cusps' were predicted. But before drawing conclusions, it is necessary to include the effect of gas and stars, historically seen as passive components of galaxies. We now understand that these can inject heat energy into the cold dark matter through a coupling based on rapid gravitational potential fluctuations, explaining the observed low central densities. 19. THOR Cold Solar Wind (CSW) instrument Science.gov (United States) Lavraud, Benoit 2017-04-01 Turbulence Heating ObserveR (THOR) is the first mission concept dedicated to the study of plasma turbulence. We present the Cold Solar Wind (CSW) instrument that is being designed for THOR. CSW will measure the full three dimensional distribution function of solar wind protons and alphas with unprecedented accuracies. It will measure solar wind proton distributions down to at least 50 ms with energy resolution of 7% and angular resolution of 1.5°. CSW is based on a top-hat electrostatic analyzer (with very large geometric factor) design with deflectors at the entrance. The particle detection system uses Channel Electron Multipliers (CEM) associated with an analog front end Application-Specific Integrated Circuit (ASIC). CSW electronics comprises a fast sweeping high voltage board, as well as an FPGA and low voltage power supply boards to perform its operations. CSW is designed to address many of the key science objectives of THOR, in particular regarding ion-scale kinetic aspects of solar wind turbulence. 20. Symmetry energy in cold dense matter Energy Technology Data Exchange (ETDEWEB) Jeong, Kie Sang, E-mail: [email protected]; Lee, Su Houng, E-mail: [email protected] 2016-01-15 We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment. 1. Superheavy nuclei – cold synthesis and structure Indian Academy of Sciences (India) Raj K Gupta 2001-08-01 The quantum mechanical fragmentation theory (QMFT), given for the cold synthesis of new and superheavy elements, is reviewed and the use of radioactive nuclear beams (RNB) and targets (RNT) is discussed. The QMFT is a complete theory of cold nuclear phenomena, namely, the cold fission, cold fusion and cluster radioactivity. Also, the structure calculations based on the axially deformed relativistic mean field (DRMF) approach are presented which predict new regions of spherical magicity, namely = 120 and = 172 or 184, for superheavy nuclei. This result is discussed in the light of recent experiments reporting the cold synthesis of = 118 element. 2. Acclimatization to cold in humans Science.gov (United States) Kaciuba-Uscilko, Hanna; Greenleaf, John E. 1989-01-01 This review focuses on the responses and mechanisms of both natural and artificial acclimatization to a cold environment in mammals, with specific reference to human beings. The purpose is to provide basic information for designers of thermal protection systems for astronauts during intra- and extravehicular activities. Hibernation, heat production, heat loss, vascular responses, body insulation, shivering thermogenesis, water immersion, exercise responses, and clinical symptoms and hypothermia in the elderly are discussed. 3. Superheated rubber for cold storage Energy Technology Data Exchange (ETDEWEB) Katzenberg, Frank; Heuwers, Benjamin; Tiller, Joerg Christian [Biomaterials and Polymer Science, Department of Biochemical and Chemical Engineering, TU Dortmund, D-44221 Dortmund (Germany) 2011-04-26 Highly stretched rubber cools down upon relaxation. A natural rubber material that stores high elongations up to 1000% strain upon strain-induced crystallization at room temperature is reported. The strain recovered and, with this, the stored ''cold'' is released only by a thermal or athermal trigger. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) 4. Micro-Kelvin cold molecules. Energy Technology Data Exchange (ETDEWEB) Strecker, Kevin E.; Chandler, David W. 2009-10-01 We have developed a novel experimental technique for direct production of cold molecules using a combination of techniques from atomic optical and molecular physics and physical chemistry. The ability to produce samples of cold molecules has application in a broad spectrum of technical fields high-resolution spectroscopy, remote sensing, quantum computing, materials simulation, and understanding fundamental chemical dynamics. Researchers around the world are currently exploring many techniques for producing samples of cold molecules, but to-date these attempts have offered only limited success achieving milli-Kelvin temperatures with low densities. This Laboratory Directed Research and Development project is to develops a new experimental technique for producing micro-Kelvin temperature molecules via collisions with laser cooled samples of trapped atoms. The technique relies on near mass degenerate collisions between the molecule of interest and a laser cooled (micro-Kelvin) atom. A subset of collisions will transfer all (nearly all) of the kinetic energy from the 'hot' molecule, cooling the molecule at the expense of heating the atom. Further collisions with the remaining laser cooled atoms will thermally equilibrate the molecules to the micro-Kelvin temperature of the laser-cooled atoms. 5. Quantum-State-Resolved Ion-Molecule Chemistry Science.gov (United States) Chen, Gary; Yang, Tiangang; Campbell, Wesley; Hudson, Eric 2016-05-01 We propose a method to achieve quantum-state-resolved ion-molecule chemistry by utilizing cryogenic buffer gas cooling techniques and a combination of ion imaging and mass spectrometry of targets in an RF Paul trap. Cold molecular species produced by a cryogenic buffer gas beam (CBGB) are introduced to target ion species in an linear quadrupole trap (LQT) where ion imaging techniques and time of flight mass spectrometry (ToF) are then used to observe the target ions and the charged reaction products [1,2]. By taking advantage of the large ion-neutral interaction cross sections and characteristically long ion trap lifetimes, we can utilize the precision control over quantum states allowed by an ion trap to resolve state-to-state quantum chemical reactions without high-density molecular sample production, well within proposed capabilities. The combination of these two very general cold species production techniques allows for production and observation of a broad range of ion-neutral reactions. We initially plan to study chemical reactions between sympathetically cooled carbon ions (via laser cooled beryllium ions) with buffer gas cooled water. This work is supported by the US Air Force Office of Scientific Research. 6. Charge transfer in the cold Yb^+$+ Rb collisions CERN Document Server Sayfutyarova, Elvira R; Yakovleva, Svetlana A; Belyaev, Andrey K 2013-01-01 Charge-transfer cold Yb$^+$+ Rb collision dynamics is investigated theoretically using high-level {\\it ab initio} potential energy curves, dipole moment functions and nonadiabatic coupling matrix elements. Within the scalar-relativistic approximation, the radiative transitions from the entrance$A^1\\Sigma^+$to the ground$X^1\\Sigma^+$state are found to be the only efficient charge-transfer pathway. The spin-orbit coupling does not open other efficient pathways, but alters the potential energy curves and the transition dipole moment for the$A-X$pair of states. The radiative, as well as the nonradiative, charge-transfer cross sections calculated within the$10^{-3}-10$cm$^{-1}$collision energy range exhibit all features of the Langevin ion-atom collision regime, including a rich structure associated with centrifugal barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two Yb isotopes agree well with those measured by immersing Yb$^+$ion in an ultracold Rb ensemble in a hybrid trap.... 7. Atomic physics experiments with cooled stored ions Science.gov (United States) Schuch, Reinhold 2004-10-01 This presentation contains examples of recent atomic physics experiments with stored and cooled ion beams from the CRYRING facility in Stockholm. One of these experiments uses the high luminosity of a cooled MeV proton beam in a He COLTRIMS apparatus (COLd supersonic He gas-jet Target for Recoil Ion Momentum Spectroscopy) for measuring correlation effects in transfer ionization. Another class of experiments exploits the cold electron beam available in the CRYRING electron cooler and cooled heavy-ion beams for recombination experiments. A section concerns the still rather open question of the puzzling recombination enhancement over the radiative recombination theory. Dielectronic resonances at meV-eV energy are measured with a resolution in the order of 10-3-10-2 eV with highly charged ions stored at several hundreds of MeV kinetic energy in the ring. These resonances provide a serious challenge to theories for describing correlation, relativistic, QED effects, and isotope shifts in highly ionized ions. Applications of recombination rates with complex highly charged ions for fusion and astrophysical plasmas are shown. 8. Atomic physics experiments with cooled stored ions Energy Technology Data Exchange (ETDEWEB) Schuch, Reinhold E-mail: [email protected] 2004-10-11 This presentation contains examples of recent atomic physics experiments with stored and cooled ion beams from the CRYRING facility in Stockholm. One of these experiments uses the high luminosity of a cooled MeV proton beam in a He COLTRIMS apparatus (COLd supersonic He gas-jet Target for Recoil Ion Momentum Spectroscopy) for measuring correlation effects in transfer ionization. Another class of experiments exploits the cold electron beam available in the CRYRING electron cooler and cooled heavy-ion beams for recombination experiments. A section concerns the still rather open question of the puzzling recombination enhancement over the radiative recombination theory. Dielectronic resonances at meV-eV energy are measured with a resolution in the order of 10{sup -3}-10{sup -2} eV with highly charged ions stored at several hundreds of MeV kinetic energy in the ring. These resonances provide a serious challenge to theories for describing correlation, relativistic, QED effects, and isotope shifts in highly ionized ions. Applications of recombination rates with complex highly charged ions for fusion and astrophysical plasmas are shown. 9. Ion focusing Energy Technology Data Exchange (ETDEWEB) Cooks, Robert Graham; Baird, Zane; Peng, Wen-Ping 2017-01-17 The invention generally relates to apparatuses for focusing ions at or above ambient pressure and methods of use thereof. In certain embodiments, the invention provides an apparatus for focusing ions that includes an electrode having a cavity, at least one inlet within the electrode configured to operatively couple with an ionization source, such that discharge generated by the ionization source is injected into the cavity of the electrode, and an outlet. The cavity in the electrode is shaped such that upon application of voltage to the electrode, ions within the cavity are focused and directed to the outlet, which is positioned such that a proximal end of the outlet receives the focused ions and a distal end of the outlet is open to ambient pressure. 10. Interaction of cosmic rays with cold clouds in galactic haloes Science.gov (United States) Wiener, Joshua; Oh, S. Peng; Zweibel, Ellen G. 2017-05-01 We investigate the effects of cosmic ray (CR) dynamics on cold, dense clouds embedded in a hot, tenuous galactic halo. If the magnetic field does not increase too much inside the cloud, the local reduction in Alfvén speed imposes a bottleneck on CRs streaming out from the star-forming galactic disc. The bottleneck flattens the upstream CR gradient in the hot gas, implying that multiphase structure could have global effects on CR-driven winds. A large CR pressure gradient can also develop on the outward-facing edge of the cloud. This pressure gradient has two independent effects. The CRs push the cloud upwards, imparting it with momentum. On smaller scales, the CRs pressurize cold gas in the fronts, reducing its density, consistent with the low densities of cold gas inferred in recent Cosmic Origins Spectrograph (COS) observations of local L* galaxies. They also heat the material at the cloud edge, broadening the cloud-halo interface and causing an observable change in interface ionic abundances. Due to the much weaker temperature dependence of CR heating relative to thermal-conductive heating, CR mediated fronts have a higher ratio of low-to-high ions compared to conduction fronts, in better agreement with observations. We investigate these effects separately using 1D simulations and analytic techniques. 11. Interaction of Cosmic Rays with Cold Clouds in Galactic Halos Science.gov (United States) Wiener, Joshua; Peng Oh, S.; Zweibel, Ellen G. 2017-01-01 We investigate the effects of cosmic ray (CR) dynamics on cold, dense clouds embedded in a hot, tenuous galactic halo. If the magnetic field does not increase too much inside the cloud, the local reduction in Alfvén speed imposes a bottleneck on CRs streaming out from the star-forming galactic disk. The bottleneck flattens the upstream CR gradient in the hot gas, implying that multi-phase structure could have global effects on CR driven winds. A large CR pressure gradient can also develop on the outward-facing edge of the cloud. This pressure gradient has two independent effects. The CRs push the cloud upward, imparting it with momentum. On smaller scales, the CRs pressurize cold gas in the fronts, reducing its density, consistent with the low densities of cold gas inferred in recent COS observations of local L★ galaxies. They also heat the material at the cloud edge, broadening the cloud-halo interface and causing an observable change in interface ionic abundances. Due to the much weaker temperature dependence of cosmic ray heating relative to thermal conductive heating, CR mediated fronts have a higher ratio of low to high ions compared to conduction fronts, in better agreement with observations. We investigate these effects separately using 1D simulations and analytic techniques. 12. Cold inactivation and dissociation into dimers of Escherichia coli tryptophanase and its W330F mutant form. Science.gov (United States) Erez, T; Gdalevsky GYa; Torchinsky, Y M; Phillips, R S; Parola, A H 1998-05-19 The kinetics and mechanism of reversible cold inactivation of the tetrameric enzyme tryptophanase have been studied. Cold inactivation is shown to occur slowly in the presence of K+ ions and much faster in their absence. The W330F mutant tryptophanase undergoes rapid cold inactivation even in the presence of K+ ions. In all cases the inactivation is accompanied by a decrease of the coenzyme 420-nm CD and absorption peaks and a shift of the latter peak to shorter wavelengths. The spectral changes and the NaBH4 test indicate that cooling of tryptophanase leads to breaking of the internal aldimine bond and release of the coenzyme. HPLC analysis showed that the ensuing apoenzyme dissociates into dimers. The dissociation depends on the nature and concentration of anions in the buffer solution. It readily occurs at low protein concentrations in the presence of salting-in anions Cl-, NO3- and I-, whereas salting-out anions, especially HPO4(2-), hinder the dissociation. K+ ions do not influence the dissociation of the apoenzyme, but partially protect holotryptophanase from cold inactivation. Thus, the two processes, cold inactivation of tryptophanase and dissociation of its apoform into dimers exhibit different dependencies on K+ ions and anions. 13. EDITORIAL: Focus on Cold and Ultracold Molecules FOCUS ON COLD AND ULTRACOLD MOLECULES Science.gov (United States) Carr, Lincoln D.; Ye, Jun 2009-05-01 öhlich, A Griesmaier, T Pfau, H Saito, Y Kawaguchi and M Ueda High-energy-resolution molecular beams for cold collision studies L P Parazzoli, N Fitch, D S Lobser and H J Lewandowski Collisional effects in the formation of cold guided beams of polar molecules M Motsch, C Sommer, M Zeppenfeld, L D van Buuren, P W H Pinkse and G Rempe Towards sympathetic cooling of large molecules: cold collisions between benzene and rare gas atoms P Barletta, J Tennyson and P F Barker Efficient formation of ground-state ultracold molecules via STIRAP from the continuum at a Feshbach resonance Elena Kuznetsova, Marko Gacesa, Philippe Pellegrini, Susanne F Yelin and Robin Côté Emergent timescales in entangled quantum dynamics of ultracold molecules in optical lattices M L Wall and L D Carr Rotational state resolved photodissociation spectroscopy of translationally and vibrationally cold MgH+ ions: toward rotational cooling of molecular ions K Højbjerre, A K Hansen, P S Skyt, P F Staanum and M Drewsen Collective transverse cavity cooling of a dense molecular beam Thomas Salzburger and Helmut Ritsch A Stark decelerator on a chip Samuel A Meek, Horst Conrad and Gerard Meijer Deceleration of molecules by dipole force potential: a numerical simulation Susumu Kuma and Takamasa Momose Ultracold molecules: vehicles to scalable quantum information processing Kathy-Anne Brickman Soderberg, Nathan Gemelke and Cheng Chin Magnetic field modification of ultracold molecule-molecule collisions T V Tscherbul, Yu V Suleimanov, V Aquilanti and R V Krems Spectroscopy of 39K85Rb triplet excited states using ultracold a 3Σ+ state molecules formed by photoassociation J T Kim, D Wang, E E Eyler, P L Gould and W C Stwalley Pumping vortex into a Bose-Einstein condensate of heteronuclear molecules Z F Xu, R Q Wang and L You Intense atomic and molecular beams via neon buffer-gas cooling David Patterson, Julia Rasmussen and John M Doyle Dynamical properties of dipolar Fermi gases T Sogo, L He, T Miyakawa, S Yi, H Lu 14. Cold dark matter by heavy double charged leptons? CERN Document Server Fargion, D; Stephan, C A 2005-01-01 A new candidate of cold dark matter arises by a novel elementary particle model that is adding two heavy leptons, each one sharing a double opposite electric charge and an own lepton flavor number: the almost-commutative (AC)-geometrical framework. In this scenario two new heavy ($ m_L \\geq 100 GeV$), oppositely double charged leptons (E,P), (E with charge -2 and P with charge +2 and opposite Z-charge), are born with no twin quark companions. Their final cosmic relics are bounded into "neutral" stable atoms (EP) forming the mysterious cold dark matter, in the spirit of the Glashow's Sinister model. An (EP) state is reached in the early Universe along a tail of a few secondary frozen exotic components. They should be now here somehow hidden in the surrounding matter. The two main secondary manifest relics are P (mostly hidden in a neutral (e e P) "anomalous helium" atom, at a 10^{-8} ratio) and a corresponding "ion" E bounded with an ordinary helium ion which preserves the leptons to later recombine with neutr... 15. Biodiversity and cold adaptive mechanisms of psychrophiles Directory of Open Access Journals (Sweden) Yuhua Xin 2013-07-01 Full Text Available Cold-adapted bacteria and archaea are widely distributed in cold environments on Earth, such as permafrost, cold soils and deserts, glaciers, lakes, sea ice in the Arctic, Antarctic and high mountains, as well as the deep sea, ice caves and the atmospheric stratosphere etc. Cold-adapted organisms inhabiting these environments exhibit rich diversity. Studies on the biogeography of psychrophiles will enable us to understand their biodiversity, distribution and origins. Due to long-term living in cold regions, cold-adapted bacteria and archeae have developed specific physiological mechanisms of adaptation to cold environments. These mechanisms include: regulating the fluidity of the cytoplasmic membrane through adjusting the composition of membrane lipids; achieving low-temperature protection through compatibility solute, antifreeze proteins, ice-binding proteins, ice-nucleation proteins and anti-nucleating proteins; production of heat-shock and coldshock proteins, cold acclimation protein and DEAD-box RNA helicase at low temperatures; production of cold-active enzymes; increasing energy generation and conservation. With the rapid development of sequencing technology, various omics-based approaches have been used to reveal cold-adaptive mechanisms of psychrophiles at the genomic level. 16. Cooling of highly charged ions in a Penning trap Energy Technology Data Exchange (ETDEWEB) Gruber, L 2000-03-31 Highly charged ions are extracted from an electron beam ion trap and guided to Retrap, a cryogenic Penning trap, where they are merged with laser cooled Be{sup +} ions. The Be{sup +} ions act as a coolant for the hot highly charged ions and their temperature is dropped by about 8 orders of magnitude in a few seconds. Such cold highly charged ions form a strongly coupled nonneutral plasma exhibiting, under such conditions, the aggregation of clusters and crystals. Given the right mixture, these plasmas can be studied as analogues of high density plasmas like white dwarf interiors, and potentially can lead to the development of cold highly charged ion beams for applications in nanotechnology. Due to the virtually non existent Doppler broadening, spectroscopy on highly charged ions can be performed to an unprecedented precision. The density and the temperature of the Be{sup +} plasma were measured and highly charged ions were sympathetically cooled to similar temperatures. Molecular dynamics simulations confirmed the shape, temperature and density of the highly charged ions. Ordered structures were observed in the simulations. 17. Probing Cold Dense Nuclear Matter Energy Technology Data Exchange (ETDEWEB) Subedi, Ramesh; Shneor, R.; Monaghan, Peter; Anderson, Bryon; Aniol, Konrad; Annand, John; Arrington, John; Benaoum, Hachemi; Benmokhtar, Fatiha; Bertozzi, William; Boeglin, Werner; Chen, Jian-Ping; Choi, Seonho; Cisbani, Evaristo; Craver, Brandon; Frullani, Salvatore; Garibaldi, Franco; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Hansen, Jens-Ole; Higinbotham, Douglas; Holmstrom, Timothy; Ibrahim, Hassan; Igarashi, Ryuichi; De Jager, Cornelis; Jans, Eddy; Jiang, Xiaodong; Kaufman, Lisa; Kelleher, Aidan; Kolarkar, Ameya; Kumbartzki, Gerfried; LeRose, John; Lindgren, Richard; Liyanage, Nilanga; Margaziotis, Demetrius; Markowitz, Pete; Marrone, Stefano; Mazouz, Malek; Meekins, David; Michaels, Robert; Moffit, Bryan; Perdrisat, Charles; Piasetzky, Eliazer; Potokar, Milan; Punjabi, Vina; Qiang, Yi; Reinhold, Joerg; Ron, Guy; Rosner, Guenther; Saha, Arunava; Sawatzky, Bradley; Shahinyan, Albert; Sirca, Simon; Slifer, Karl; Solvignon, Patricia; Sulkosky, Vince; Sulkosky, Vincent; Sulkosky, Vince; Sulkosky, Vincent; Urciuoli, Guido; Voutier, Eric; Watson, John; Weinstein, Lawrence; Wojtsekhowski, Bogdan; Wood, Stephen; Zheng, Xiaochao; Zhu, Lingyan 2008-06-01 The protons and neutrons in a nucleus can form strongly correlated nucleon pairs. Scattering experiments, in which a proton is knocked out of the nucleus with high-momentum transfer and high missing momentum, show that in carbon-12 the neutron-proton pairs are nearly 20 times as prevalent as proton-proton pairs and, by inference, neutron-neutron pairs. This difference between the types of pairs is due to the nature of the strong force and has implications for understanding cold dense nuclear systems such as neutron stars. 18. Probing Cold Dense Nuclear Matter CERN Document Server Subedi, R; Monaghan, P; Anderson, B D; Aniol, K; Annand, J; Arrington, J; Benaoum, H; Benmokhtar, F; Bertozzi, W; Boeglin, W; Chen, J -P; Choi, Seonho; Cisbani, E; Craver, B; Frullani, S; Garibaldi, F; Gilad, S; Gilman, R; Glamazdin, O; Hansen, J -O; Higinbotham, D W; Holmstrom, T; Ibrahim, H; Igarashi, R; De Jager, C W; Jans, E; Jiang, X; Kaufman, L; Kelleher, A; Kolarkar, A; Kumbartzki, G; LeRose, J J; Lindgren, R; Liyanage, N; Margaziotis, D J; Markowitz, P; Marrone, S; Mazouz, M; Meekins, D; Michaels, R; Moffit, B; Perdrisat, C F; Piasetzky, E; Potokar, M; Punjabi, V; Qiang, Y; Reinhold, J; Ron, G; Rosner, G; Saha, A; Sawatzky, B; Shahinyan, A; Širca, S; Slifer, K; Solvignon, P; Sulkosky, V; Urciuoli, G; Voutier, E; Watson, J W; Weinstein, L B; Wojtsekhowski, B; Wood, S; Zheng, X -C; Zhu, L; 10.1126/science.1156675 2009-01-01 The protons and neutrons in a nucleus can form strongly correlated nucleon pairs. Scattering experiments, where a proton is knocked-out of the nucleus with high momentum transfer and high missing momentum, show that in 12C the neutron-proton pairs are nearly twenty times as prevalent as proton-proton pairs and, by inference, neutron-neutron pairs. This difference between the types of pairs is due to the nature of the strong force and has implications for understanding cold dense nuclear systems such as neutron stars. 19. The Herschel Cold Debris Disks CERN Document Server Gaspar, Andras 2013-01-01 The Herschel "DUst around NEarby Stars (DUNES)" survey has found a number of debris disk candidates that are apparently very cold, with temperatures near 22K. It has proven difficult to fit their spectral energy distributions with conventional models for debris disks. Given this issue we carefully examine the alternative explanation, that the detections arise from confusion with IR cirrus and/or background galaxies that are not physically associated with the foreground star. We find that such an explanation is consistent with all of these detections. 20. Cold atoms close to surfaces DEFF Research Database (Denmark) Krüger, Peter; Wildermuth, Stephan; Hofferberth, Sebastian 2005-01-01 Microscopic atom optical devices integrated on atom chips allow to precisely control and manipulate ultra-cold (T atoms and Bose-Einstein condensates (BECs) close to surfaces. The relevant energy scale of a BEC is extremely small (down to ... be utilized as a sensor for variations of the potential energy of the atoms close to the surface. Here we describe how to use trapped atoms as a measurement device and analyze the performance and flexibility of the field sensor. We demonstrate microscopic magnetic imaging with simultaneous high spatial... 1. Harmonics Effect on Ion-Bulk Waves in CH Plasmas CERN Document Server Feng, Q S; Liu, Z J; Cao, L H; Xiao, C Z; Wang, Q; He, X T 2016-01-01 The harmonics effect on ion-bulk (IBk) waves has been researched by Vlasov simulation. The condition of excitation of a large-amplitude IBk waves is given to explain the phenomenon of strong short-wavelength electrostatic activity in solar wind. When$k$is much lower than$k_{lor}/2$($k_{lor}$is the wave number at loss-of-resonance point), the IBk waves will not be excited to a large amplitude, because a large part of energy will be spread to harmonics. The nature of nonlinear IBk waves in the condition of$k
2. Cold hardiness increases with age in juvenile Rhododendron populations
Directory of Open Access Journals (Sweden)
Rajeev eArora
2014-10-01
Full Text Available Winter survival in woody plants is controlled by environmental and genetic factors that affect the plant's ability to cold acclimate. Because woody perennials are long-lived and often have a prolonged juvenile (pre-flowering phase, it is conceivable that both chronological and physiological age factors influence adaptive traits such as stress tolerance. This study investigated annual cold hardiness (CH changes in several hybrid Rhododendron populations based on Tmax, an estimate of the maximum rate of freezing injury (ion leakage in cold-acclimated leaves from juvenile progeny. Data from F2 and backcross populations derived from R. catawbiense and R. fortunei parents indicated significant annual increases in Tmax ranging from 3.7 to to 6.4 C as the seedlings aged from 3 to 5 years old. A similar yearly increase (6.7° C was observed in comparisons of 1- and 2-year-old F1 progenies from a R. catawbiense x R. dichroanthum cross. In contrast, CH of the mature parent plants (> 10 years old did not change significantly over the same evaluation period. In leaf samples from a natural population of R. maximum, CH evaluations over two years resulted in an average Tmax value for juvenile 2- to 3- year- old plants that was 9.2 C lower than the average for mature (~30 years old plants. . A reduction in CH was also observed in three hybrid rhododendron cultivars clonally propagated by rooted cuttings (ramets - Tmax of 4-year-old ramets was significantly lower than the Tmax estimates for the 30- to 40-year-old source plants (ortets. In both the wild R. maximum population and the hybrid cultivar group, higher accumulation of a cold-acclimation responsive 25kDa leaf dehydrin was associated with older plants and higher CH. The feasibility of identifying hardy phenotypes at juvenile period and research implications of age-dependent changes in CH are discussed.
3. Synthesis of the heaviest nuclei in cold fusion reactions
Science.gov (United States)
Münzenberg, G.; Morita, K.
2015-12-01
Cold fusion of heavy ions paved the way to superheavy elements. It was proposed by Yu.Ts. Oganessian more than forty years ago in 1974 [1,2]. First experiments were carried out at JINR Dubna, starting with the reaction 40Ar + 208Pb → 248Fm* where several hundreds to thousand atoms were produced on one day. The large production rate indicating an enhancement of the fusion cross section, especially for the evaporation of two or three neutrons, proved the concept of cold-fusion with the use of the doubly magic nucleus 208Pb as a target. The Dubna experiments were extended to the transactinide region beyond rutherfordium. The breakthrough came with the separation in-flight. Two different approaches were used: kinematic separation with the velocity filter SHIP [3] at GSI Darmstadt, and with the gasfilled separator GARIS [4,5] at RIKEN. With SHIP the concept of cold fusion of massive nuclear systems was convincingly confirmed by the observation of the one-neutron evaporation channel in the production of 247Rf in an irradiation of 208Pb with 50Ti [6] in 1981 which opened the way to the transactinide region. At SHIP the elements bohrium (107) to copernicium (112) were discovered [7]. A new closed shell region around hassium was found. The RIKEN experiments started in 2002. They confirmed the GSI results and in addition improved the data on structure and production of elements hassium to copernicium significantly. The heaviest element ever created in a cold fusion reaction, Z = 113, was observed at GARIS [8,9].
4. 2D fluid simulations of interchange turbulence with ion dynamics
DEFF Research Database (Denmark)
Nielsen, Anders Henry; Madsen, Jens; Xu, G. S.
2013-01-01
In this paper we present a first principle global two-dimensional fluid model. The HESEL (Hot Edge SOL Electrostatic) model is a 2D numerical fluid code, based on interchange dynamics and includes besides electron also the ion pressure dynamic. In the limit of cold ions the model almost reduces......B vorticity as well as the ion diamagnetic vorticity. The 2D domain includes both open and closed field lines and is located on the out-board midplane of a tokamak. On open field field lines the parallel dynamics are parametrized as sink terms depending on the dynamic quantities; density, electron and ion...
5. International workshop on cold neutron sources
Energy Technology Data Exchange (ETDEWEB)
Russell, G.J.; West, C.D. (comps.) (Los Alamos National Lab., NM (United States))
1991-08-01
The first meeting devoted to cold neutron sources was held at the Los Alamos National Laboratory on March 5--8, 1990. Cosponsored by Los Alamos and Oak Ridge National Laboratories, the meeting was organized as an International Workshop on Cold Neutron Sources and brought together experts in the field of cold-neutron-source design for reactors and spallation sources. Eighty-four people from seven countries attended. Because the meeting was the first of its kind in over forty years, much time was spent acquainting participants with past and planned activities at reactor and spallation facilities worldwide. As a result, the meeting had more of a conference flavor than one of a workshop. The general topics covered at the workshop included: Criteria for cold source design; neutronic predictions and performance; energy deposition and removal; engineering design, fabrication, and operation; material properties; radiation damage; instrumentation; safety; existing cold sources; and future cold sources.
6. Diagnosis and management of cold urticaria.
Science.gov (United States)
Singleton, Reid; Halverstam, Caroline P
2016-01-01
Cold urticaria is a physical urticaria characterized by a localized or systemic eruption of papules upon exposure of the skin to cold air, liquids, and/or objects. In some cases, angioedema and anaphylaxis also may occur. The symptoms of cold urticaria can have a negative impact on patients' quality of life. Second-generation H1 antihistamines are the first line of treatment in cold urticaria; however, patients who are unresponsive to initial treatment with H1 antihistamines may require further management options. Avoidance of cold exposure is the most effective prophylactic measure. In mild to moderate cases, the primary goal of therapy is to improve the patient's quality of life. In more severe cases, treatment measures to protect the patient's airway, breathing, and circulation may be necessary. We report the case of a 23-year-old man with cold urticaria who was refractory to initial therapy with H1 antihistamines. A review of the literature also is provided.
7. Cognitive Egocentrism Differentiates Warm and Cold People
OpenAIRE
Ryan L. Boyd; Bresin, Konrad; Ode, Scott; Robinson, Michael D.
2013-01-01
Warmth-coldness is a fundamental dimension of social behavior. Cold individuals are egocentric in their social relations, whereas warm individuals are not. Previous theorizing suggests that cognitive egocentrism underlies social egocentrism. It was hypothesized that higher levels of interpersonal coldness would predict greater cognitive egocentrism. Cognitive egocentrism was assessed in basic terms through tasks wherein priming a lateralized self-state biased subsequent visual perceptions in ...
8. Electrical shielding box measurement of the negative hydrogen beam from Penning ion gauge ion source.
Science.gov (United States)
Wang, T; Yang, Z; Dong, P; long, J D; He, X Z; Wang, X; Zhang, K Z; Zhang, L W
2012-06-01
The cold-cathode Penning ion gauge (PIG) type ion source has been used for generation of negative hydrogen (H(-)) ions as the internal ion source of a compact cyclotron. A novel method called electrical shielding box dc beam measurement is described in this paper, and the beam intensity was measured under dc extraction inside an electrical shielding box. The results of the trajectory simulation and dc H(-) beam extraction measurement were presented. The effect of gas flow rate, magnetic field strength, arc current, and extraction voltage were also discussed. In conclusion, the dc H(-) beam current of about 4 mA from the PIG ion source with the puller voltage of 40 kV and arc current of 1.31 A was extrapolated from the measurement at low extraction dc voltages.
9. On the Stability of Pick-up Ion Ring Distributions in the Outer Heliosheath
Science.gov (United States)
Summerlin, Errol J.; Viñas, Adolfo F.; Moore, Thomas E.; Christian, Eric R.; Cooper, John F.
2014-10-01
The "secondary energetic neutral atom (ENA)" hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of <1° are sufficient to damp the self-generated waves associated with the ring beam. Thus, at least from the perspective of linear Vlasov dispersion analysis of parallel propagating waves, there is no reason to expect that the ring distributions necessary to produce the
10. On the stability of pick-up ion ring distributions in the outer heliosheath
Energy Technology Data Exchange (ETDEWEB)
Summerlin, Errol J.; Viñas, Adolfo F.; Moore, Thomas E.; Christian, Eric R.; Cooper, John F., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Heliophysics Science Division, NASAs Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD (United States)
2014-10-01
The 'secondary energetic neutral atom (ENA)' hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of <1° are sufficient to damp the self-generated waves associated with the ring beam. Thus, at least from the perspective of linear Vlasov dispersion analysis of parallel propagating waves, there is no reason to expect that the ring distributions necessary to
11. The North Atlantic Cold Bias
Science.gov (United States)
Greatbatch, Richard; Drews, Annika; Ding, Hui; Latif, Mojib; Park, Wonsun
2016-04-01
The North Atlantic cold bias, associated with a too zonal path of the North Atlantic Current and a missing "northwest corner", is a common problem in coupled climate and forecast models. The bias affects the North Atlantic and European climate mean state, variability and predictability. We investigate the use of a flow field correction to adjust the path of the North Atlantic Current as well as additional corrections to the surface heat and freshwater fluxes. Results using the Kiel Climate Model show that the flow field correction allows a northward flow into the northwest corner, largely eliminating the bias below the surface layer. A surface cold bias remains but can be eliminated by additionally correcting the surface freshwater flux, without adjusting the surface heat flux seen by the ocean model. A model version in which only the surface fluxes of heat and freshwater are corrected continues to exhibit the incorrect path of the North Atlantic Current and a strong subsurface bias. Removing the bias impacts the multi-decadal time scale variability in the model and leads to a better representation of the SST pattern associated with the Atlantic Multidecadal Variability than the uncorrected model.
12. Ion accelerator system mounting design and operating characteristics for a 5 kW 30-cm xenon ion engine
Science.gov (United States)
Aston, Graeme; Brophy, John R.
1987-01-01
Results from a series of experiments to determine the effect of accelerator grid mount geometry on the performance of the J-series ion optics assembly are described. Three mounting schemes, two flexible and one rigid, are compared for their relative ion extraction capability over a range of total accelerating voltages. The largest ion beam current, for the maximum total voltage investigated, is shown to occur using one of the flexible grid mounting geometries. However, at lower total voltages and reduced engine input power levels, the original rigid J-series ion optics accelerator grid mounts result in marginally better grid system performance at the same cold interelectrode gap.
13. Prediction of cold flow properties of Biodiesel
Directory of Open Access Journals (Sweden)
Parag Saxena
2016-08-01
Full Text Available Biodiesel being environmentally friendly is fast gaining acceptance in the market as an alternate diesel fuel. But compared to petroleum diesel it has certain limitations and thus it requires further development on economic viability and improvement in its properties to use it as a commercial fuel. The cold flow properties play a major role in the usage of biodiesel commercially as it freezes at cold climatic conditions. In the present study, cold flow properties of various types of biodiesel were estimated by using correlations available in literature. The correlations were evaluated based on the deviation between the predicted value and experimental values of cold flow properties.
14. Review on Cold-Formed Steel Connections
Science.gov (United States)
Tan, Cher Siang; Mohammad, Shahrin; Md Tahir, Mahmood; Shek, Poi Ngian
2014-01-01
The concept of cold-formed light steel framing construction has been widespread after understanding its structural characteristics with massive research works over the years. Connection serves as one of the important elements for light steel framing in order to achieve its structural stability. Compared to hot-rolled steel sections, cold-formed steel connections perform dissimilarity due to the thin-walled behaviour. This paper aims to review current researches on cold-formed steel connections, particularly for screw connections, storage rack connections, welded connections, and bolted connections. The performance of these connections in the design of cold-formed steel structures is discussed. PMID:24688448
15. Cold vacuum drying facility design requirements
Energy Technology Data Exchange (ETDEWEB)
IRWIN, J.J.
1999-07-01
This document provides the detailed design requirements for the Spent Nuclear Fuel Project Cold Vacuum Drying Facility. Process, safety, and quality assurance requirements and interfaces are specified.
16. Cold panniculitis: delayed onset in an adult.
Science.gov (United States)
Lipke, Michelle M; Cutlan, Jonathan E; Smith, Ann C
2015-01-01
The panniculitides are a complex dermatologic entity for both dermatologists and dermatopathologists. Panniculitis is an inflammation of the subcutaneous adipose tissue and can be associated with systemic diseases. We present a case of cold panniculitis, a form of traumatic panniculitis, in a 37-year-old woman that was caused by a cold therapy unit. Our patient did not develop lesions until 10 days following initiation of therapy, which is a unique presentation of cold panniculitis, as lesions usually develop 1 to 3 days after cold exposure.
17. Collisional Cooling of Light Ions by Cotrapped Heavy Atoms.
Science.gov (United States)
Dutta, Sourav; Sawant, Rahul; Rangwala, S A
2017-03-17
We experimentally demonstrate cooling of trapped ions by collisions with cotrapped, higher-mass neutral atoms. It is shown that the lighter ^{39}K^{+} ions, created by ionizing ^{39}K atoms in a magneto-optical trap (MOT), when trapped in an ion trap and subsequently allowed to cool by collisions with ultracold, heavier ^{85}Rb atoms in a MOT, exhibit a longer trap lifetime than without the localized ^{85}Rb MOT atoms. A similar cooling of trapped ^{85}Rb^{+} ions by ultracold ^{133}Cs atoms in a MOT is also demonstrated in a different experimental configuration to validate this mechanism of ion cooling by localized and centered ultracold neutral atoms. Our results suggest that the cooling of ions by localized cold atoms holds for any mass ratio, thereby enabling studies on a wider class of atom-ion systems irrespective of their masses.
18. IMPROVED, FAVORABLE FOR ENVIRONMENT POLYURETHANE COLD-BOX-PROCESS (COLD BOX «HUTTENES-ALBERTUS» .
Directory of Open Access Journals (Sweden)
A. Sergini
2005-01-01
Full Text Available The results of the laboratory and industrial investigations, the purpose of which is improvement of the classical Cold-box-process, i.e. the process of the slugs hardening in cold boxes, are presented.
19. Cold neutral atoms via charge exchange from excited state positronium: a proposal
CERN Document Server
Bertsche, W A; Eriksson, S
2016-01-01
We present a method for generating cold neutral atoms via charge exchange reactions between trapped ions and Rydberg positronium. The high charge exchange reaction cross section leads to efficient neutralisation of the ions and since the positronium-ion mass ratio is small, the neutrals do not gain appreciable kinetic energy in the process. When the original ions are cold the reaction produces neutrals that can be trapped or further manipulated with electromagnetic fields. Because a wide range of species can be targeted we envisage that our scheme may enable experiments at low temperature that have been hitherto intractable due to a lack of cooling methods. We present an estimate for achievable temperatures, neutral number and density in an experiment where the neutrals are formed at a milli-Kelvin temperature from either directly or sympathetically cooled ions confined on an ion chip. The neutrals may then be confined by their magnetic moment in a co-located magnetic minimum well also formed on the chip. We ...
20. Polarized ion source operation at IUCF
Energy Technology Data Exchange (ETDEWEB)
Derenchuk, V. [Indiana University Cyclotron Facility, Bloomington, Indiana 47408 (United States); Belov, A. [Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, 117312, Russian Federation (Russian Federation); Brown, R.; Collins, J.; Sowinski, J.; Stephenson, E.; Wedekind, M. [Indiana University Cyclotron Facility, Bloomington, Indiana 47408 (United States)
1995-07-15
The IUCF high intensity polarized ion source (HIPIOS), based on the source in operation at TUNL (1) and employing cold ({similar_to}30 K) atomic beam technology with an electron cyclotron resonance ionizer, has recently delivered beam to the first users. The results of the development work required to make the source operate reliably, with reasonable beam parameters are described. Methods used to measure the polarization and possible sources of unpolarized background are also discussed. | {"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": 0.8541108965873718, "perplexity": 2859.7285854503702}, "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-2018-09/segments/1518891812959.48/warc/CC-MAIN-20180220125836-20180220145836-00136.warc.gz"} |
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https://en.wikibooks.org/wiki/User:Daviddaved/On_inhomogeneous_string_of_Krein | # User:Daviddaved/On inhomogeneous string of Krein
The following physical model of a vibrating inhomogeneous string (or string w/with beads) by Krein provides mechanical interpretation for the study of Stieltjes continued fractions. The model is one-dimensional, but it arises as a restriction of n-dimensional inverse problems with rotational symmetry.
The string is represented by a non-decreasing positive mass function m(x) on a possibly infinite interval [0, l]. The right end of the string is fixed. The ratio of the forced oscillation to an applied periodic force @ the left end of the string is the function of frequency, called coefficient of dynamic compliance of the string.
The small vertical vibration of the string is described by the following differential equation:
${\displaystyle {\frac {1}{\rho (x)}}{\frac {\partial ^{2}f(x,\lambda )}{\partial x^{2}}}=\lambda f(x,\lambda ),}$
where
${\displaystyle \rho (x)={\frac {dm}{dx}}}$
is the density of the string, possibly including atomic masses. One can express the coefficient in terms of the fundamental solution of the ODE:
${\displaystyle H(\lambda )={\frac {f'(0,\lambda )}{f(0,\lambda )}},}$
where, ${\displaystyle f(l,\lambda )=0.}$
A fundamental theorem of Krein and Kac, see [10], & also [19] essentially states that an analytic function ${\displaystyle H(\lambda )}$ is the coefficient of dynamic compliance of a string if and only if the function
${\displaystyle \beta (\lambda )=\lambda H(-\lambda ^{2})}$
is an analytic automorphism of the right half-plane C+, that is real on the real line.
Exercise(**). Use the theorem above, Fourier transform and a change of variables to characterize the set of Dirichlet-to-Neumann maps for a unit disc with conductivity depending only on radius. | {"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": 0.9089757204055786, "perplexity": 506.0018941432968}, "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-2017-13/segments/1490218190134.67/warc/CC-MAIN-20170322212950-00580-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://poesophicalbits.blogspot.com/2013/03/three-paths-to-becoming-mathematical.html | ## Sunday, March 3, 2013
### Three paths to becoming a mathematical anti-platonist
It may be the case that "no good arguments exist either for or against mathematical platonism" (Platonism and Anti-Platonism in Mathematics by Mark Balaguer). Mathematical anti-platonists may come from a certain naturalistic belief that there's nothing outside nature, so if it's the case that there are no infinities in nature, how can one believe in platonist mathematical objects like infinite sets and the real number continuum?
The three paths below are not arguments against mathematical platonism. They are just ways mathematical anti-platonists can travel. (The first path is complete in the sense that it actually gets to a goal of a truly non-platonistic alternative to interpreting standard mathematics. The other two are incomplete in the sense that they result either with a somewhat restrictive or a non-standard mathematics.)
1. Finite mathematics (of indefinitely large size sets)*
In Understanding the Infinite, Shaughan Lavine describes the mathematics of Jan Mycielski ("The meaning of pure mathematics", "Locally finite theories"). In this approach, the quantifiers (∀, ∃) within the sentences of standard mathematics are replaced with indexed quantifiers (∀i, ∃j), and the interpretation of these quantifiers is that the variables they govern range over finite sets (Ωi, Ωj) with the same index. The key to this approach is that the finite sets can be of different sizes (unlike in the standard interpretation where the variables range over the same set). This indexing of quantifiers in sentences of a standard-mathematical theory T is done by process called relativization, and the result of applying this process to a sentence φ of standard mathematics is called a regular relativization φ' of φ. Beginning with a standard theory T, the result is the corresponding finitary theory Fin(T). The key theorem of this approach is:
"If φ is a sentence in the language of T and φ' is a regular relativization of φ, then φ is a theorem of T if and only if φ' is a theorem of Fin(T)."
Thus every theorem of T (interpreted with possibly infinite sets) has a corresponding theorem of Fin(T) (interpreted with only finite sets).
Note: Mycielski calls this interpretation intentionalism (which is different from intuitionism), in contrast with formalism and platonism. For some examples, see:
Mathematica materialis, or How not to be lured into Plato's cave
Persons without infinities
Plato's cave is closed
Transfinity
* or MIFS: Mathematics of Indefinitely-large Finite Sets
The other two paths I mention briefly.
2. Computable analysis
Can computable numbers be used instead of the reals?
Computable analysis
Constructive mathematics
E.g., only consider numbers and methods of analysis that can be represented by computer programs. It would interesting to link path 2 to path 1.
3. Paraconsistent mathematics (with finite models)
Inconsistent mathematics
Paraconsistent Logic
"One interesting implication of the existence of inconsistent models of arithmetic is that some of them are finite (unlike the classical non-standard models)."
Inconsistent models of arithmetic:
Part I: Finite models, Part II: The general case | {"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": 0.9271174669265747, "perplexity": 1732.636510064063}, "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/1502886124662.41/warc/CC-MAIN-20170823225412-20170824005412-00017.warc.gz"} |
http://www.guitaretab.com/t/three-days-grace/196764.html | Song name
# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
# Three Days Grace - Time Of Dying drum
```C=Crash
Sp=Splash
R=Ride
H=Hi-hats
S=Snare
FT=Floor tom/Low tom
B=Bass
x=closed hi-hat
X=normal strike/open hi-hat
o=normal hit
f=flam
g=ghost note
d=double hit
h=double ghost
r=roll
Intro 0:03
S |rd--o------o--o-| |o--o-dooo-oo----|
B |o--oo---o-------| |o---o---o-------|
C |X---X---X---X---| |X---X-------X---|
Sp |----------------| |--------X-------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---|
FT |--------------o-|
S |----o-------ooo-|
B |o-------o-------|
|1e+a2e+a3e+a4e+a|
S |----o---g---o---| |----o---g---o---|
B |o-o---o--o—-go--| |o-o--o---o--go--|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Verse 0:13
S |----o---g---o---| |----f-------f---|
B |o-o--o--o--o-o--| |o--o----o--o----|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---------------| |----------------|
H |--x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---oo-o-----o|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |x-x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---o-o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
PreChorus 0:33
R |g---g---g---g-gg| |g---g---gg--gg--|
B |----------------| |o---------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
R |g---g---g---gh--| |g---------------|
FT |----------------| |-------------f--|
B |o---------------| |o---------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Chorus 0:43
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-----|
ST |----------------| |------------d---|
MT |----------------| |-------------d--|
FT |----------------| |--------------o-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o--f|
B |o---o-ooo—--o-oo| |o---o-ooo---o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Post-Chorus 1:02
S |-------------f--|
B |-------------ooo|
|1e+a2e+a3e+a4e+a|
Verse 1:05
C |X---------------| |----------------|
H |--x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---oo-o-----o|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |x-x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---o-o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---------------| |----------------|
H |--x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---oo-o-----o|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |x-x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---o-o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
PreChorus 1:23
R |g---g---g---g-gg| |g---g---gg--gg--|
FT |------------o---| |o-----------o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
[ Tab from: http://www.guitaretab.com/t/three-days-grace/196764.html ]
R |g---g---g---gh--| |X---------------|
S |----------------| |-------------f--|
FT |o-----------o---| |----------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Chorus 1:34
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Bridge 1:53 (I couldn’t get the timing perfect but it locks in with the riff)
R |x--xx-x--xxxxx--| |x---x---xxx-xx--|
S |o---------------| |----------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
S |o---o-o----o----| |o--o-dooo-oo----|
B |o--oo---o-------| |o---o---o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---| |X---X-------X---|
Sp |----------------| |--------X-------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---|
S |----o-------o-f-|
B |o-------o-------|
|1e+a2e+a3e+a4e+a|
Chorus 2:08
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o--d|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-----|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Outro 2:46
C |X---X---X---X---| |X---X-------X---|
Sp |----------------| |--------X-------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---| |----X---X---X---|
Sp |----------------| |X---------------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---| |----------------|
Sp |----------------| |----------------|
S |o---o-do----o---| |o--o-dooo-oo----|
B |o-------o-------| |o-------o-------|
```
Related for Time Of Dying drum
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"Time Of Dying" | {"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": 0.8489445447921753, "perplexity": 548.1736283619371}, "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/1466783392159.3/warc/CC-MAIN-20160624154952-00027-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/3976/on-the-binary-decimal-expansion-of-the-reciprocal-primes | # On the binary decimal expansion of the reciprocal prime's
I have been thinking a little bit about the binary decimal expansion of reciprocal prime numbers; and I have a few questions.
I found this neat table which lists the binary expansion of many fractions, and I was trying to find some patterns.
Here are my questions, for brevity I say a natural number has a period N if the binary decimal expansion of it's reciprocal has period N: (for example, 1/7 = .001001... has period 3)
1. Given an arbitrary natural number N, does there exist a prime number of minimum period N?
(By minimum period I mean to exclude the case that one prime has a period which is a multiple of the period of another prime. For example, 1/3 = .0101... has period 2, and 1/5 = .00110011... has period 4; so while 1/3 has period 4, what I call it's "minimum period" is 2)
2. Can two prime numbers have the same minimum period?
A useful result which I believe is well known, is that a natural number has a period N if and only if it is a factor of 2N - 1.
Does anyone know of a good reference that describes some theory behind the relationship between the period of the reciprocal of a natural number, and the prime factorization of that number?
-
I recommend changing the phrase "inverse prime numbers" to "reciprocals of prime numbers". The latter has a clear meaning, the former does not. – Arturo Magidin Sep 3 '10 at 19:41
I edited the OP, thanks for the suggestion. – Matt Calhoun Sep 3 '10 at 19:46
If you look at my answer together with mau's answer on this question, adjusting the base form 10 to 2, that gives you the criteria you're looking for or at least a start on it. – Isaac Sep 3 '10 at 19:51
For the second question: both 1/41 & 1/271 have period 5; 1/7 & 1/13 have period 6; 1/73 & 1/137 have period 8, ... Relevant Mathematica code: Sort[{Length[Nest[First, RealDigits[1/#], 2]], #} & /@ Prime[Range[500]]] – J. M. Sep 3 '10 at 20:04
From the table I linked: 1/7 = .001 (repeating); 1/13 = .000100111011 (repeating); so although it's true that 7 and 13 have the same period (12), they do not have the same minimum period, so this is not what I am looking for, sorry for the confusing way I stated the question, I am happy to make any edits which are suggested for clarity. Actually I noticed most primes p have a repeating sequence which is p-1 digits long (such as 13, but not 7)... – Matt Calhoun Sep 3 '10 at 22:47
(In the below post there are several links with the apostrophes omitted; fill them in if the links don't work.)
The phenomenon you are studying is a phenomenon in modular arithmetic. If a prime $p$ has period $n$, this means that there is some numerator $N$ such that $\frac{N}{2^n - 1} = \frac{1}{p}$. This is equivalent to $Np = 10^n - 1$, or $p | 2^n - 1$, or $2^n \equiv 1 \bmod p$. The smallest $n$ for which this is true is called the order of $2 \bmod p$, sometimes denoted $\text{ord}_p(2)$ (although this is confusingly also used to denote the greatest power of $p$ which divides $2$...).
Fermat's little theorem guarantees that $\text{ord}_p(2)$ always divides $p-1$; you have already observed this yourself. However, predicting the exact order is very difficult to do in general. For example, knowing that the order is actually equal to $p-1$ is equivalent to knowing that $2$ is a primitive root, and it is not currently even known whether this is true infinitely often. In any case, you should be able to find basic information about order in any good textbook on elementary number theory.
With that background out of the way...
The answer to question 1 is no. The only exception is $n = 6$ by Zsigmondy's theorem.
The answer to question 2 is yes. If $p$ and $n$ are relatively prime, then $p$ has period $n$ if and only if $p$ divides $\Phi_n(2)$, where $\Phi_n(x)$ is the $n^{th}$ cyclotomic polynomial. (This is more or less a restatement of the condition that $p | 2^n - 1$ but $p$ doesn't divide $2^k - 1$ for $k < n$.) So it suffices to show that some number of this form has more than one prime factor relatively prime to $n$. There are two cases here which are particularly classical:
• $n$ is a prime $q$. In this case $\Phi_q(2) = 2^q - 1$ is a Mersenne number, and $2^{11} - 1 = 23 \cdot 89$ is the smallest composite Mersenne number, hence $23$ and $89$ both have period $11$.
• $n = 2^k$ for some $k$. In this case $\Phi_{2^k}(2) = 2^{2^{k-1}} + 1$ is a Fermat number, and $\Phi_{64}(2) = 2^{32} + 1 = 641 \cdot 6700417$ is the smallest composite Fermat number, hence $641$ and $6700417$ both have period $64$.
The answer to question 3 is the following.
Lemma: If $n, m$ are relatively prime odd numbers, then $\text{ord}_{mn}(2) = \text{lcm}(\text{ord}_n(2), \text{ord}_m(2))$.
Proof. $\text{ord}_{mn}(2)$ is the order of the element $2$ in the multiplicative group of $\mathbb{Z}/mn\mathbb{Z}$, which we will denote $U(mn)$. By the Chinese remainder theorem, $U(mn)$ is isomorphic to the direct product $U(m) \times U(n)$, so the order of $2$ in $U(mn)$ must be the $\text{lcm}$ of the orders of $2$ in $U(m)$ and $U(n)$.
It follows that to compute $\text{ord}_m(2)$ for arbitrary $m$ it suffices to compute it for the odd prime power factors of $m$ and then to take the $\text{lcm}$ of the resulting numbers. (Note that if $m$ is divisible by a power of $2$ this only contributes a leading string of zeroes to the binary expansion of $\frac{1}{m}$ and hence does not affect the computation of the period.) Again, you can find a discussion of the Chinese remainder theorem in any good textbook on elementary number theory. (I am particularly bad at recommending textbooks on elementary number theory because I learned mine through a summer program, not a textbook...)
-
@Matt: as a general rule, you should wait maybe a day or so to accept answers. That makes it easier for other answers to accrue which might offer additional insights (as well as specific references, which I haven't provided), and it also allows the relevant answers to receive more votes. (Finally, it allows people to correct anything wrong I might've said :P) – Qiaochu Yuan Sep 4 '10 at 1:16 | {"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": 0.8731280565261841, "perplexity": 194.57070711687084}, "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-2016-18/segments/1461860115836.8/warc/CC-MAIN-20160428161515-00135-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://alihosseiny.com/statistical-field-theory/ | An introduction to the quantum field theory and its application in statistical physics.
Topics are as follows:
• A review on the critical phenomena
• Landau Ginsburg theory
• Perturbation and Feynman diagrams
• Renormalization
Textbooks:
Quantum and Statistical Field Theory, M. Le Bellac
Statistical theory of fields, M. Kardar | {"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": 0.8040381669998169, "perplexity": 3492.9631085089322}, "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/1679296945287.43/warc/CC-MAIN-20230324144746-20230324174746-00685.warc.gz"} |
http://mathhelpforum.com/algebra/31864-factoring-again.html | # Math Help - Factoring again
1. ## Factoring again
Factor:
$27x^2+64$
I am completely lost...
2. $
27x^2+64
$
this is a binomial expression- an expression with two terms, the variable, x is only present in the first term and thus you cannot factor it. We are only left with the constants 27 and 64. These numbers do not have a common favtor hence we cannot factor again. Thus the expression canot be factored
3. Originally Posted by mt_lapin
Factor:
$27x^2+64$
I am completely lost...
I'll assume you're required to factorise over the complex number field. Otherwise, as has been previously correctly noted, it can't be done and the question is pointless.
Recall: $A^2 + B^2 = (A + iB)(A - iB)$.
In your case, $A = \sqrt{27} \, x = 3 \sqrt{3} \, x$ and B = 8 ....
4. Oh dear. I meant $27^3+64$. Does that make it solvable now? Really sorry :/
5. Originally Posted by mt_lapin
Oh dear. I meant $27^3+64$. Does that make it solvable now? Really sorry :/
$= (27)^3 + (4)^3$.
Factorise using the sum of two cubes formula.
6. I keep missing things. It's supposed to be $27x^3+64$
I promise this is correct.
7. Would I then need $(3x)^3+4^3$ and to factorise using the sum of two cubes formula?
8. The answer would be: $(3x+4)(9x^2-12x+16)$
Is this correct?
9. Originally Posted by mt_lapin
The answer would be: $(3x+4)(9x^2-12x+16)$
Is this correct?
Yes. | {"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": 12, "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": 0.9518529772758484, "perplexity": 927.3930940085212}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042986615.83/warc/CC-MAIN-20150728002306-00086-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://la.mathworks.com/help/ident/ref/iddata.greyest.html;jsessionid=c10fa192f5c1577a5fd1d40a007d | # greyest
Linear grey-box model estimation
## Syntax
```sys = greyest(data,init_sys) sys = greyest(data,init_sys,opt) [sys,x0] = greyest(___) ```
## Description
`sys = greyest(data,init_sys)` estimates a linear grey-box model, `sys`, using time or frequency domain data, `data`. The dimensions of the inputs and outputs of `data` and `init_sys`, an `idgrey` model, must match. `sys` is an identified `idgrey` model that has the same structure as `init_sys`.
`sys = greyest(data,init_sys,opt)` estimates a linear grey-box model using the option set, `opt`, to configure the estimation options.
`[sys,x0] = greyest(___)` returns the value of the initial states computed during estimation. You can use this syntax with any of the previous input-argument combinations.
## Input Arguments
`data` Estimation data. The dimensions of the inputs and outputs of `data` and `init_sys` must match. For time-domain estimation, `data` is an `iddata` object containing the input and output signal values. For frequency domain estimation, `data` can be one of the following: Recorded frequency response data (`frd` (Control System Toolbox) or `idfrd`)`iddata` object with its `Domain` property set to `'Frequency'` `init_sys` Identified linear grey-box model that configures the initial parameterization of `sys`. `init_sys`, an `idgrey` model, must have the same input and output dimensions as `data`. `opt` Estimation options. `opt` is an option set, created using `greyestOptions`, which specifies options including: Estimation objectiveInitialization choiceDisturbance model handlingNumerical search method to be used in estimation
## Output Arguments
`sys`
Estimated grey-box model, returned as an `idgrey` model. This model is created using the specified initial system, and estimation options.
Information about the estimation results and options used is stored in the `Report` property of the model. ``` Report``` has the following fields:
Report FieldDescription
`Status`
Summary of the model status, which indicates whether the model was created by construction or obtained by estimation.
`Method`
Estimation command used.
`InitialState`
Handling of initial states during estimation, returned as one of the following:
• `'model'` — The initial state is parameterized by the ODE file used by the `idgrey` model.
• `'zero'` — The initial state is set to zero.
• `'estimate'` — The initial state is treated as an independent estimation parameter.
• `'backcast'` — The initial state is estimated using the best least squares fit.
• Vector of doubles of length Nx, where Nx is the number of states. For multiexperiment data, a matrix with Ne columns, where Ne is the number of experiments.
This field is especially useful to view how the initial states were handled when the `InitialState` option in the estimation option set is `'auto'`.
`DisturbanceModel`
Handling of the disturbance component (K) during estimation, returned as one of the following values:
• `'model'`K values are parameterized by the ODE file used by the `idgrey` model.
• `'fixed'` — The value of the `K` property of the `idgrey` model is fixed to its original value.
• `'none'`K is fixed to zero.
• `'estimate'`K is treated as an independent estimation parameter.
This field is especially useful to view the how the disturbance component was handled when the `DisturbanceModel` option in the estimation option set is `'auto'`.
`Fit`
Quantitative assessment of the estimation, returned as a structure. See Loss Function and Model Quality Metrics for more information on these quality metrics. The structure has the following fields:
FieldDescription
`FitPercent`
Normalized root mean squared error (NRMSE) measure of how well the response of the model fits the estimation data, expressed as the percentage `fit` = 100(1-NRMSE).
`LossFcn`
Value of the loss function when the estimation completes.
`MSE`
Mean squared error (MSE) measure of how well the response of the model fits the estimation data.
`FPE`
Final prediction error for the model.
`AIC`
Raw Akaike Information Criteria (AIC) measure of model quality.
`AICc`
Small sample-size corrected AIC.
`nAIC`
Normalized AIC.
`BIC`
Bayesian Information Criteria (BIC).
`Parameters`
Estimated values of model parameters.
`OptionsUsed`
Option set used for estimation. If no custom options were configured, this is a set of default options. See `greyestOptions` for more information.
`RandState`
State of the random number stream at the start of estimation. Empty, `[]`, if randomization was not used during estimation. For more information, see `rng`.
`DataUsed`
Attributes of the data used for estimation, returned as a structure with the following fields:
FieldDescription
`Name`
Name of the data set.
`Type`
Data type.
`Length`
Number of data samples.
`Ts`
Sample time.
`InterSample`
Input intersample behavior, returned as one of the following values:
• `'zoh'` — Zero-order hold maintains a piecewise-constant input signal between samples.
• `'foh'` — First-order hold maintains a piecewise-linear input signal between samples.
• `'bl'` — Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.
`InputOffset`
Offset removed from time-domain input data during estimation. For nonlinear models, it is `[]`.
`OutputOffset`
Offset removed from time-domain output data during estimation. For nonlinear models, it is `[]`.
`Termination`
Termination conditions for the iterative search used for prediction error minimization, returned as a structure with the following fields:
FieldDescription
`WhyStop`
Reason for terminating the numerical search.
`Iterations`
Number of search iterations performed by the estimation algorithm.
`FirstOrderOptimality`
$\infty$-norm of the gradient search vector when the search algorithm terminates.
`FcnCount`
Number of times the objective function was called.
`UpdateNorm`
Norm of the gradient search vector in the last iteration. Omitted when the search method is `'lsqnonlin'` or `'fmincon'`.
`LastImprovement`
Criterion improvement in the last iteration, expressed as a percentage. Omitted when the search method is `'lsqnonlin'` or `'fmincon'`.
`Algorithm`
Algorithm used by `'lsqnonlin'` or `'fmincon'` search method. Omitted when other search methods are used.
For estimation methods that do not require numerical search optimization, the `Termination` field is omitted.
For more information on using `Report`, see Estimation Report.
`x0`
Initial states computed during the estimation, returned as a matrix containing a column vector corresponding to each experiment.
This array is also stored in the `Parameters` field of the model `Report` property.
## Examples
collapse all
Estimate the parameters of a DC motor using the linear grey-box framework.
Load the measured data.
```load(fullfile(matlabroot, 'toolbox', 'ident', 'iddemos', 'data', 'dcmotordata')); data = iddata(y, u, 0.1, 'Name', 'DC-motor'); data.InputName = 'Voltage'; data.InputUnit = 'V'; data.OutputName = {'Angular position', 'Angular velocity'}; data.OutputUnit = {'rad', 'rad/s'}; data.Tstart = 0; data.TimeUnit = 's';```
`data` is an `iddata` object containing the measured data for the outputs, the angular position, the angular velocity. It also contains the input, the driving voltage.
Create a grey-box model representing the system dynamics.
For the DC motor, choose the angular position (rad) and the angular velocity (rad/s) as the outputs and the driving voltage (V) as the input. Set up a linear state-space structure of the following form:
`$\underset{}{\overset{˙}{x}}\left(t\right)=\left[\begin{array}{cc}0& 1\\ 0& -\frac{1}{\tau }\end{array}\right]x\left(t\right)+\left[\begin{array}{c}0\\ \frac{G}{\tau }\end{array}\right]u\left(t\right)$`
`$y\left(t\right)=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]x\left(t\right).$`
$\tau$ is the time constant of the motor in seconds, and $G$ is the static gain from the input to the angular velocity in rad/(V*s) .
```G = 0.25; tau = 1; init_sys = idgrey('motorDynamics',tau,'cd',G,0);```
The governing equations in state-space form are represented in the MATLAB® file `motorDynamics.m`. To view the contents of this file, enter `edit motorDynamics.m` at the MATLAB command prompt.
$G$ is a known quantity that is provided to `motorDynamics.m` as an optional argument.
$\tau$ is a free estimation parameter.
`init_sys` is an `idgrey` model associated with `motor.m`.
Estimate $\tau$.
`sys = greyest(data,init_sys);`
`sys` is an `idgrey` model containing the estimated value of $\tau$.
To obtain the estimated parameter values associated with `sys`, use `getpvec(sys)`.
Analyze the result.
```opt = compareOptions('InitialCondition','zero'); compare(data,sys,Inf,opt)```
`sys` provides a 98.35% fit for the angular position and an 84.42% fit for the angular velocity.
Estimate the parameters of a DC motor by incorporating prior information about the parameters when using regularization constants.
The model is parameterized by static gain `G` and time constant $\tau$. From prior knowledge, it is known that `G` is about 4 and $\tau$ is about 1. Also, you have more confidence in the value of $\tau$ than `G` and would like to guide the estimation to remain close to the initial guess.
`load regularizationExampleData.mat motorData`
The data contains measurements of motor's angular position and velocity at given input voltages.
Create an `idgrey` model for DC motor dynamics. Use the function `DCMotorODE` that represents the structure of the grey-box model.
```mi = idgrey(@DCMotorODE,{'G', 4; 'Tau', 1},'cd',{}, 0); mi = setpar(mi, 'label', 'default');```
If you want to view the `DCMotorODE` function, type:
`type DCMotorODE.m`
```function [A,B,C,D] = DCMotorODE(G,Tau,Ts) %DCMOTORODE ODE file representing the dynamics of a DC motor parameterized %by gain G and time constant Tau. % % [A,B,C,D,K,X0] = DCMOTORODE(G,Tau,Ts) returns the state space matrices % of the DC-motor with time-constant Tau and static gain G. The sample % time is Ts. % % This file returns continuous-time representation if input argument Ts % is zero. If Ts>0, a discrete-time representation is returned. % % See also IDGREY, GREYEST. % Copyright 2013 The MathWorks, Inc. A = [0 1;0 -1/Tau]; B = [0; G/Tau]; C = eye(2); D = [0;0]; if Ts>0 % Sample the model with sample time Ts s = expm([[A B]*Ts; zeros(1,3)]); A = s(1:2,1:2); B = s(1:2,3); end ```
Specify regularization options Lambda.
```opt = greyestOptions; opt.Regularization.Lambda = 100;```
Specify regularization options R.
`opt.Regularization.R = [1, 1000];`
You specify more weighting on the second parameter because you have more confidence in the value of $\tau$ than `G`.
Specify the initial values of the parameters as regularization option $\theta$*.
`opt.Regularization.Nominal = 'model';`
Estimate the regularized grey-box model.
`sys = greyest(motorData, mi, opt);` | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "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": 0.8417780995368958, "perplexity": 1627.6063713975827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039563095.86/warc/CC-MAIN-20210422221531-20210423011531-00602.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/11/lesson/11.2.2/problem/11-68 | ### Home > INT3 > Chapter 11 > Lesson 11.2.2 > Problem11-68
11-68.
For each of the following equations, list every point where its three-dimensional graph intersects one of the coordinate axes. That is, what are the $x$, $y$, and $z$‑intercepts? Express your answers in $\left(x, y, z\right)$ form.
1. $6y+15z=60$
To find the intercept of a given axis, set all other variables to zero.
For example, the $y$-intercept will be $\left(0, ?, 0\right)$.
To find the $y$-intercept, let $x = 0$ and $z = 0$
Repeat the process to find the $z$-intercept. $\left(0, 0, ?\right)$.
$\left(0, 10, 0\right)$ and $\left(0, 0, 4\right)$
1. $3x+4y+2z=24$
See part (a):
1. $(x+3)^2+z^2=25$
See part (a).
Note: You will have two $x$-intercepts and two $z$-intercepts. Why?
1. $z=6$
See part (a):
Use the eTool below to test your solutions to parts (a), (b) and (c) above.
Click on the link at right for the full eTool version: INT3 11-68 HW eTool | {"extraction_info": {"found_math": true, "script_math_tex": 19, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 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": 0.8135543465614319, "perplexity": 1994.780153853718}, "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/1631780057158.19/warc/CC-MAIN-20210921041059-20210921071059-00498.warc.gz"} |
http://www.theincredibletruths.com/2018/08/duality-of-light.html | # DUAL-NATURE OF LIGHT
From the very beginning we know that light is a wave. A wave travels through a medium. But it was found that light can travel even through vacuum or empty space. Before Einstein, scientists thought that “ether” is a thing which is present everywhere in this universe, even in the empty space or vacuum. That’s why light can travel through vacuum. But Einstein said that the whole concept about ether is meaningless. Rather he proposed that light has a dual-nature.
More specifically we can say that light behaves in two different ways depending upon situations. Like in medium light behaves like wave and in vacuum light behaves like particle. This is called the dual nature of light.
## WAVE NATURE
The wave nature of light says how light can bent. In 17th century, Isaac Newton believed light is composed of a stream of corpuscles. Then a Dutch physicist and astronomer Christiaan Huygens thought that light is a wave vibrating in some sort of ether.
Some experiments like diffraction, interference, refraction etc. proves that light has a wave property.
Wavelength is the parameter which can differentiate between waves. In case of refraction we can differentiate mediums by their refractive Indexes. The Refractive Index of every medium is different. It is defined as
n = c/v
Where, n= Refractive index of the medium
c= speed of light in vacuum
v= speed of the light in the medium
List of Refractive Index of some mediums –
MEDIUM n Vacuum 1 Air 1.00029 Water 1.33 Diamond 2.417 Amber 1.55 Ice 1.31 glass 1.52 Human lens 1.386-1.406 Germanium 4.05-4.01
## PARTICLE NATURE
The fundamental particle of light is photon. We can define light as a packet of photons. Photon is a mass less particle but it has energy. It was first found by Albert Einstein in his Photoelectric effect experiment. In this experiment a high energy photon strikes a metal surface and an electron is ejected from the metal and the photon disappears. When the frequency of the light increases, the speed of the electron being ejected, increases. This experiment shows the particle nature of light.
The energy (E) of photon is defined as –
E = hf
Where, h = Plank’s constant
f = frequency of the light
Quantum Theory: In Quantum theory light is taken as a particle. It means we study the particle nature of light in quantum physics. Light is an energy packet or packet of photon. Particle nature of light explains how light travels in straight lines or reflects.
ETHER : http://www.theincredibletruths.com/search/label/ether | {"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": 0.8732212781906128, "perplexity": 833.3601963418137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370493684.2/warc/CC-MAIN-20200329015008-20200329045008-00315.warc.gz"} |
http://math.stackexchange.com/questions/153302/summation-of-frac12-frac34-frac78-frac1516-cdots | # Summation of $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$ till $n$ terms
What is the pattern in the following?
• Sum to $n$ terms of the series: $$\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$$
-
Hint: The $k$th term is $1-\frac1{2^k}$. – Did Jun 3 '12 at 15:39
## 2 Answers
Hint:
Write it as $(1-{1\over2})+(1-{1\over4})+(1-{1\over 8})+\cdots+(1-{1\over 2^n}).$
-
Here is the pattern:
\begin{align*} \frac{1}{2} + \frac{3}{4} + \cdots &= \biggl(1-\frac{1}{2}\biggr) + \biggl(1-\frac{1}{2^2}\biggr) + \cdots \\\ &= (1+1+\cdots + 1) - \biggl(\frac{1}{2}+\frac{1}{2^2} + \cdots +\frac{1}{2^n}\biggr) \end{align*}
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.999998927116394, "perplexity": 4039.5246820533844}, "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-2015-06/segments/1422118973352.69/warc/CC-MAIN-20150124170253-00247-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://iris.unibs.it/handle/11379/567206 | The production of J/psi is measured at midrapidity (vertical bar y vertical bar < 0.9) in proton-proton collisions at root s = 5.02 and 13 TeV, through the dielectron decay channel, using the ALICE detector at the Large Hadron Collider. The data sets used for the analyses correspond to integrated luminosities of L-int = 19.4 +/- 0.4 nb(-1 )and L-int = 32.2 +/- 0.5 nb(-1) at root s = 5.02 and 13 TeV, respectively. The fraction of non-prompt J/psi mesons, i.e. those originating from the decay of beauty hadrons, is measured down to a transverse momentum p(T) = 2 GeV/c (1GeV/c) at root s = 5.02 TeV (13 TeV). The p(T) and rapidity (y) differential cross sections, as well as the corresponding values integrated over p(T) and y, are carried out separately for prompt and non-prompt J/psi mesons. The results are compared with measurements from other experiments and theoretical calculations based on quantum chromodynamics (QCD). The shapes of the p(T) and y distributions of beauty quarks predicted by state-of-the-art perturbative QCD models are used to extrapolate an estimate of the b (b) over bar pair cross section at midrapidity and in the total phase space. The total b (b) over bar cross sections are found to be sigma(b (b) over bar) = 541 +/- 45 (stat.) +/- 69 (syst.)(-12)(+10) (extr.) mu b and sigma(b (b) over bar) = 218 +/- 37 (stat.)+/- 31 (syst.)(-9.1)(+8.2) (extr.) mu b at root s = 13 and 5.02 TeV, respectively. The value obtained from the combination of ALICE and LHCb measurements in pp collisions at root s = 13 TeV is also provided.
### Prompt and non-prompt J/?? production cross sections at midrapidity in proton-proton collisions at $$\sqrt{\mathrm{s}}$$ = 5.02 and 13 TeV
#### Abstract
The production of J/psi is measured at midrapidity (vertical bar y vertical bar < 0.9) in proton-proton collisions at root s = 5.02 and 13 TeV, through the dielectron decay channel, using the ALICE detector at the Large Hadron Collider. The data sets used for the analyses correspond to integrated luminosities of L-int = 19.4 +/- 0.4 nb(-1 )and L-int = 32.2 +/- 0.5 nb(-1) at root s = 5.02 and 13 TeV, respectively. The fraction of non-prompt J/psi mesons, i.e. those originating from the decay of beauty hadrons, is measured down to a transverse momentum p(T) = 2 GeV/c (1GeV/c) at root s = 5.02 TeV (13 TeV). The p(T) and rapidity (y) differential cross sections, as well as the corresponding values integrated over p(T) and y, are carried out separately for prompt and non-prompt J/psi mesons. The results are compared with measurements from other experiments and theoretical calculations based on quantum chromodynamics (QCD). The shapes of the p(T) and y distributions of beauty quarks predicted by state-of-the-art perturbative QCD models are used to extrapolate an estimate of the b (b) over bar pair cross section at midrapidity and in the total phase space. The total b (b) over bar cross sections are found to be sigma(b (b) over bar) = 541 +/- 45 (stat.) +/- 69 (syst.)(-12)(+10) (extr.) mu b and sigma(b (b) over bar) = 218 +/- 37 (stat.)+/- 31 (syst.)(-9.1)(+8.2) (extr.) mu b at root s = 13 and 5.02 TeV, respectively. The value obtained from the combination of ALICE and LHCb measurements in pp collisions at root s = 13 TeV is also provided.
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• ND
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• 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": 0, "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": 0.9850140810012817, "perplexity": 4902.904008250036}, "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-2023-14/segments/1679296949107.48/warc/CC-MAIN-20230330070451-20230330100451-00407.warc.gz"} |
https://www.physicsforums.com/threads/evaluation-of-a-parabolic-line-integral-with-respect-to-arc-length.298756/ | # Homework Help: Evaluation of a (parabolic) line integral with respect to arc length
1. Mar 10, 2009
### GelatinousFur
1. The problem statement, all variables and given/known data
Evaluate the line integral $$$\int_c yz\,ds.$$$
where C is a parabola with z=y^2 , x=1 for 0<=y<=2
2. Relevant equations
A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts.
I also know from other line integrals with respect to arc length that:
ds=sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)
3. The attempt at a solution
I think that from the information given, the beginning and end points are (1,0,0) to (1,2,4).
My first guess is:
x(t) = t
y(t) = 2t
z(t) = t^2
This will be when t goes from 0 to 2.
So after I have parameterized the curve, I would substitute the functions of t back into the integral to get:
int((2t)^3*sqrt(1^2+2^2+(2t)^2),t,0,2)
=8*int(t^3*sqrt(4t^2+5),t,0,2)
=12032/3
This doesn't look right to me though. Any help would be appreciated!
Last edited: Mar 10, 2009
2. Mar 11, 2009
### tiny-tim
Welcome to PF!
Hi GelatinousFur! Welcome to PF!
No, x is constant
x(t) = 1
(and your y and z don't fit each other)
3. Mar 11, 2009
### GelatinousFur
Re: Welcome to PF!
Ah, I see. Thanks for the help (and the welcome)!
So then...
X(t) is constant, so x(t)=1
y(t) =t
z(t) = t^2
when t goes from 0 to 2.
The line integral would then become:
int(y^3,s) over the curve C, because z=y^2.
=int(t^3*sqrt(0^2+1^2+(2t)^2),t,0,2)
=int(t^3*2t,t,0,2)
=2*int(t^4,t,0,2)
=64/5
This answer feels a bit more correct but I still cannot see why the teacher gave us the hint to use integration by parts, as I didn't have to when I just performed that integral.
4. Mar 11, 2009
### lanedance
Re: Welcome to PF!
Hi
in you integrand you have
$$t^3\sqrt{1+4t^2}$$
I think you simplified away the one from the squareroot
5. Mar 11, 2009
### GelatinousFur
Re: Welcome to PF!
Thanks, you are correct.
The correct integral is:
int(t^3*sqrt(1+4*t^2),t,0,2)
So here's where I use integration by parts, but when I integrate sqrt(1+4*t^2) I have to go to an integral table.
I punched int(t^3*sqrt(1+4*t^2),t,0,2) into MATLAB and it spits this answer out:
-1/64/pi^(1/2)*(-3128/15*pi^(1/2)*17^(1/2)-8/15*pi^(1/2))
Is this the wrong answer? Looks a bit weird to me. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9948546886444092, "perplexity": 1685.0311921845296}, "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-2018-30/segments/1531676589536.40/warc/CC-MAIN-20180716232549-20180717012549-00156.warc.gz"} |
http://www.fields.utoronto.ca/programs/scientific/07-08/liegroups/abstracts.html | # SCIENTIFIC PROGRAMS AND ACTIVITIES
September 2, 2014
## CRM-Fields-MITACS Workshop on Lie Groups, Group Transforms and Image Processing
### Abstracts
Jirí Hrivnák, University of Montreal
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
We consider recently introduced symmetric or antisymmetric exponential and trigonometric functions. These are defined as determinants or antideterminants of matrices whose elements are corresponding functions of one variable. To each of these multivariate functions correspond expansion into Fourier series, integral Fourier transform and finite Fourier transform. We give explicit formulas of these functions, expansions and Fourier transforms in dimension two. We also present some examples and discuss possible applications of these functions and transforms.
Frederic Lesage, École Polytechnique de Montréal
Compressed sensing in photo-acoustic tomography, a potential application for Lie Algebra bases.
Recent work in photo-acoustic tomography indicates that this modality might bring high resolution imaging at low cost. The technique however is hampered by long acquisition times. In this work we describe new image acquisition techniques based on the theory of compressed sensing are able to partly solve this problem. Here the choice of basis is crucial in having the compressed sensing work properly and Lie Algebra bases could provide an avenue to extend to new applications.
Maryna Nesterenko, Université de Montréal
Computing with almost periodic functions
Computational Fourier analysis of functions defined on quasicrystals is developed. A key point is to build the analysis around the emergent
theory of quasicrystals and diffraction based on local hulls and dynamical systems. Numerically computed approximations arising in this way are built out of the precise Fourier module of the quasicrystal in question, and approximate their target functions uniformly on the entire infinite space. This is in striking contrast with numerical approximations based on periodization of some finite part of the crystal. The methods are practical and computable. Examples of functions based on the standard Fibonacci quasicrystal serve to illustrate the method.
Jiri Petera, University of Montreal
Morning short course
Discrete and continuous multidimensional transforms based on $C$-, $S$-, and $E$-functions of a compact semisinple Lie group
References:
J. Patera, {\it Compact simple Lie groups and theirs $C$-, $S$-, and
$E$-transforms,\/} SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) {\bf 1} (2005) 025, 6 pages, math-ph/0512029.
R.V. Moody, J.~Patera, {\it Orthogonality within the families of \ $C$-,
$S$-, and $E$-functions of any compact semisimple Lie group,\/} SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) {\bf 2} (2006) 076, 14 pages, math-ph/0611020.
A. Klimyk, J. Patera, {\it Orbit functions,\/} SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) {\bf 2} (2006), 006, 60 pages, math-ph/0601037
A. Klimyk, J. Patera, {\it Antisymmetric orbit functions,\/} SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) {\bf 3} (2007), paper 023, 83 pages; math-ph/0702040v1
A. Klimyk, J. Patera, {\it $E$-orbit functions,\/} SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) {\bf 4} (2008), 002, 57 pages; arXiv:0801.0822
Matthieu Voorons, Université de Montréal
Interpolation based on Lie group theory and comparison with standard techniques
New interpolation algorithms, based on the Lie group theory, were recently developed by Mr Patera and his team. The Continuous Extension of the Discrete Orbit Function Transform (CEDOFT) based on the C-functions of the Lie groups leading to square lattices were considered as interpolators. More precisely, Lie groups SU(2)xSU(2) and O(5) were used to interpolate 2-dimensional data, and the cubic lattice SU(2)xSU(2)xSU(2) for 3-dimensional data. All algorithms presented for 2 and 3-dimensional data have the advantage to give the exact value of the original data at the points of the grid lattice, and interpolate well the data values between the grid points. The quality and speed of the interpolation are comparable with the most efficient classical interpolation techniques. Interpolation results for many application are presented, from simple zooming and filtering of still images to video interpolation and refinement of volume estimation in medical imagery.
Yusong Yan and Hongmei Zhu, York University
Integer Lie group transforms
The C- or S-functions derived from the Lie Group C2 form an orthogonal basis in its corresponding fundamental region F. Discretizing such a basis results in a class of discrete orthogonal transforms. Using the lifting schemes, we develop the integer-to-integer transforms associated to these discrete orthogonal transforms on a discrete grid FM of F of density defined by a positive integer M. Since these integer transforms are invertible, it has potential applications such as lossless image compression and encryption.
Hongmei Zhu, York University
Interpolation using the discrete group transforms
Interpolation methods are often used in many applications for image generation and processing, such as image resampling and zooming.
Here, we introduce a new family of interpolation algorithms based on a compact semisimple Lie groups of rank n, although here we explore mainly the cases n = 2. The performance of the algorithms is compared with the other commonly used interpolation methods. | {"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": 0.821983277797699, "perplexity": 1263.6470729300609}, "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-2014-35/segments/1409535921872.11/warc/CC-MAIN-20140909032458-00146-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://pure.knaw.nl/portal/en/publications/forms-of-density-regulation-and-quasi-stationary-distributions-of | # Forms of density regulation and (quasi-) stationary distributions of population sizes in birds
B-E. Sæther, S. Engen, V. Grøtan, T. Bregnballe, C. Both, P. Tryjanowski, A. Leivits, J. Wright, A.P. Møller, M.E. Visser, W. Winkel
Research output: Contribution to journal/periodicalArticleScientificpeer-review
## Abstract
The theta-logistic model of density regulation is an especially flexible class of density regulation models where different forms of non-linear density regulation can be expressed by only one parameter, θ. Estimating the parameters of the theta-logistic model is, however, challenging. This is mainly due to the need for information concerning population growth at low densities as well as data on fluctuations around the carrying capacity K in order to estimate the strength of density regulation. Here we estimate parameters of the theta-logistic model for 28 populations of three species of birds that have grown from very small population sizes followed by a period of fluctuations around K. We then use these parameters to estimate the quasi-stationary distribution of population size. There were often large uncertainties in these parameters specifying the form of density regulation that were generally independent of the duration of the study period. In contrast, precision in the estimates of environmental variance increased with the length of the time series. In most of the populations, a large proportion of the probability density of the (quasi-) stationary distribution of population sizes was located at intermediate population sizes relative to K. Thus, we suggest that the (quasi-) stationary distribution of population sizes represents a useful summary statistic that in many cases provides a more robust characterisation of basic population dynamics (e.g. range of variation in population fluctuations or proportion of time spent close to K) than can be obtained from analyses of single model parameters.
Original language English 1197-1208 Oikos 117 8 https://doi.org/10.1111/j.0030-1299.2008.16420.x Published - 2008
## Fingerprint
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http://www.emis.de/classics/Erdos/cit/01201004.htm | ## Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 012.01004
Autor: Erdös, Pál
Title: On the density of some sequences of numbers. (In English)
Source: J. London Math. Soc. 10, 120-125 (1935).
Review: Let f(m) be a non-negative arithmetical function satisfying
f(m1m2) = f(m1)+f(m2) if (m1,m2) = 1, (1)
f(p1) \ne f(p2) (2)
for two different primes p1,p2; and let
N(f; c,d) = sum \Sb{m \leq n}
{c \leq f(m) \leq d}\endSb 1, N(f; c) = N(f; c,oo).
The main result of this paper, which constitutes a wide generalization of the author's work on abundant numbers (Zbl 010.10303), is that limn ––> oo N (f; c)/n exists and is a continuous function of c. The case of the abundant numbers is obtained by taking f(m) = log {\sigma(m) \over m}, c = log 2.
Suppose first f(m) satisfies the more stringent conditions: (3) f(p\alpha) = f(p), (4) sump {f(p)\over p} converges. Defining fp(m) = sum{p|m, {p \leq P}} f(p) it is easily seen that limn ––> oo N(fp; c)/n = Ap exists, and as Ap in non-decreasing and \leq 1, limp ––> oo Ap = A exists. That limn ––> oo N(f; c)/n = A follows easily from the two lemmas:
(I) For any \epsilon > 0 there exists a \delta such that N(f; c,c+\delta) < \epsilon n for all sufficiently large n;
(II) For any \epsilon,\delta > 0 there exists a P(\epsilon,\delta) such that for P > P(\epsilon,\delta) and all n, the number of integers m \leq n for which f(m)-fp(m) > \delta is less than \epsilon n. The main difficulty lies in the proof of (I), which uses the same idea as the paper already cited.
The author then sketches the proof when (3) is not assumed. As regards (4), he shows that it can be replaced by a weaker condition (4') and that if (4') does not hold, then limn ––> oo N(f; c)/n = 1.
Reviewer: Davenport (Cambridge)
Classif.: * 11N60 Distribution functions (additive and positive multipl. functions)
Index Words: Number theory
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag | {"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": 0.9922338724136353, "perplexity": 4692.010869584833}, "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/1448398447913.86/warc/CC-MAIN-20151124205407-00118-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://shibaura.pure.elsevier.com/en/publications/on-supersymmetric-fermion-lattice-systems | # On Supersymmetric Fermion Lattice Systems
Hajime Moriya
Research output: Contribution to journalArticlepeer-review
4 Citations (Scopus)
## Abstract
This note provides a C*-algebraic framework for supersymmetry. Particularly, we consider fermion lattice models satisfying the simplest supersymmetry relation. Namely, we discuss a restricted sense of supersymmetry without a boson field involved. We construct general supersymmetric C*-dynamics in terms of a superderivation and a one-parameter group of automorphisms on the CAR algebra. (We do not introduce Grassmann numbers into our formalism.) We show several basic properties of superderivations on the fermion lattice system. Among others, we establish that superderivations defined on the strictly local algebra are norm-closable. We show a criterion of superderivations on the fermion lattice system for being nilpotent. This criterion can be easily checked and hence yields new supersymmetric fermion lattice models.
Original language English 2199-2236 38 Annales Henri Poincare 17 8 https://doi.org/10.1007/s00023-016-0461-1 Published - 2016 Aug 1
## ASJC Scopus subject areas
• Statistical and Nonlinear Physics
• Nuclear and High Energy Physics
• Mathematical Physics
## Fingerprint
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https://datascience.stackexchange.com/questions/51456/best-way-to-classify-plots-which-are-overlapping | Best way to classify plots which are overlapping?
I have an experiment in which it was done under two conditions. For each condition, the experiment was performed 26 times. The output of the experiment is a plot with 70 time indices. I would like to train a classifier to predict, given a plot, to which condition it belongs. The image below shows the output of the conducted experiment under the two conditions recognised by different colors. The actual experiment begins at index 35, and thus it can be seen there is no difference in the outcome of the experiment before that regardless of the condition. The plots represent power spectral density of EEG from one channel (electrode).
I am trying to train an svm classifer ignoring the features below 35. The classifier is having hard time doing so considering the high variability of each condition. One thing is, averaging the red plots and blue plots yield a noticeably different behaviour, as can be seen from the second figure. I would like to improve the accuracy of my classifier, beyond 65%. Is LSTM suitable for this type of problem? Any other suggestions?
• Is it possible to have some information on the physical nature of the experiment so as to have a better understanding? That will help in giving you some constructive feedback. May 6 '19 at 4:29
• The plots represent power spectral densities of EEG data. I edited the question to clarify that May 6 '19 at 4:35
• Hmm... if its PSD of EEG on a single channel, I don't think simply feeding this data to any ML algorithm will not give you any sensible results. From what I understand, that it is an around the normalised frequency beyond 35 (x-axis) the EEG signature is prominent. Physically this simply means the major signal power is at those frequencies. I would rather suggest building some nice frequency related features rather than go for LSTM or even simply feeding in the psd to any ML. You should also use other channels like C1/C2 or even PO3 depending on the type experiment to do a classification. May 6 '19 at 11:29
• Thanks for the recommendation. The experiment was done 96 times for each subject under each condition, averaging out trials improves the SNR and I have done that. The other thing is I am testing the SVM classifier on 58 channels separately, however, many of the channels are irrelevant. I identified 5 to 6 channels which are performing relatively good. They reach mean accuracy of 60%. I am trying to improve my accuracy. Additionally, I am focusing on one frequency band as the rest of the bands seems irrelevant. Note that x-axis is time while y-axis is PSD of certain frequency band. May 6 '19 at 12:49 | {"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": 0.8276470899581909, "perplexity": 479.8391484637135}, "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-2021-39/segments/1631780057227.73/warc/CC-MAIN-20210921191451-20210921221451-00548.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/93059-determining-matrix-size.html | # Math Help - determining matrix size
1. ## determining matrix size
Show that if A is an [m x n] matrix and A(BA) is defined, then B is an [n x m] matrix.
2. If A has order $m\times n$ look at BA first of all
For be BA to be defined B must have order $k\times m$ in turn BA must have order $k\times n$
Now for A(BA) to be defined $k=n$ therefore B has order $n\times m$
3. thank you, easy to understand when its right in front of me | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9352315664291382, "perplexity": 1872.7494977268107}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398468396.75/warc/CC-MAIN-20151124205428-00245-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/177326 | Infoscience
Thesis
# Hermitian Forms over Algebras with Involution and Hermitian Categories
This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involution. The second, which consists of the last two chapters, generalizes several classical properties of unimodular hermitian forms over rings with involution to the setting of sesquilinear forms in hermitian categories. The original results established in this thesis are joint work with Professor Eva Bayer-Fluckiger. The first chapter contains an introduction to the algebraic theory of unimodular ε-hermitian forms over fields with involution. One knows that if L/K is an extension of odd degree (where char(K) ≠ 2) then the restriction map rL/K : W(K) →W(L) is injective. In addition, if the extension is purely inseparable then the map rL/K is bijective. In the second chapter we first introduce the basic notions and techniques of the theory of unimodular ε-hermitian forms over algebras with involution, in particular the technique of Morita equivalence. Let L/K be a finite field extension, τ an involution on L and A a finite-dimensional K-algebra endowed with an involution α such that αœK = τœK. E. Bayer-Fluckiger and H.W. Lenstra proved that if L/K is of odd degree and αœK = idK then the restriction map rL/Kε : Wε(A, α) → Wε(A ⊗K L, α ⊗ τ) is injective for any ε = ±1. This holds also if αœK ≠ idK. We prove that if, in addition, L/K is purely inseparable and A is a central simple K-algebra, then the above map is actually bijective. The proof proceeds via induction on the degree of the algebra and uses in an essential way an exact sequence of Witt groups due to R. Parimala, R. Sridharan and V. Suresh, later extended by N. Gernier-Boley and M.G. Mahmoudi. The third chapter contains a survey of the theory of hermitian and quadratic forms in hermitian categories. In particular, we cover the transfer between two hermitian categories, the reduction by an ideal, the transfer into the endomorphism ring of an object, as well as the Krull-Schmidt-Azumaya theorem and some of its applications. In the fourth chapter we prove, adapting the ideas developed by E. Bayer-Fluckiger and L. Fainsilber, that the category of sesquilinear forms in a hermitian category ℳ is equivalent to the category of unimodular hermitian forms in the category of double arrows of ℳ. In order to obtain this equivalence of categories we associate to a sesquilinear form the double arrow consisting of its two adjoints, equipped with a canonical unimodular hermitian form. This equivalence of categories allows us to define a notion of Witt group for sesquilinear forms in hermitian categories. This generalizes the classical notion of a Witt group of unimodular hermitian forms over rings with involution. Using the above equivalence of categories we deduce analogues of the Witt cancellation theorem and Springer's theorem for sesquilinear forms over certain algebras with involution. We also extend some finiteness results due to E. Bayer-Fluckiger, C. Kearton and S.M. J. Wilson. In addition, we study the weak Hasse-Minkowski principle for sesquilinear forms over skew fields with involution over global fields. We prove that this principle holds for systems of sesquilinear forms over a skew field over a global field and endowed with a unitary involution. Two systems of sesquilinear forms are hence isometric if and only if they are isometric over all the completions of the base field. This result has already been known for unimodular hermitian and skew-hermitian forms over rings with involution, under the same hypothesis. Finally, we study the behaviour of the Witt group of a linear hermitian category under extension of scalars. Let K be a field of characteristic different from 2, L a finite extension of K and ℳ a K-linear hermitian category. We define the extension of ℳ to L as being the category with the same objects as ℳ and with morphisms given by the morphisms of ℳ extended to L. We obtain an L-linear hermitian category, denoted by ℳL. The canonical functor of scalar extension ℛL/K : ℳ → ℳL induces for any ε = ±1 a group homomorphism Wε(ℳ) →Wε(ℳL). We prove that if all the idempotents of the category ℳ split and the extension L/K is of odd degree then this homomorphism is injective. This result has already been known in the case when ℳ is the category of finite-dimensional K-vector spaces.
Thèse École polytechnique fédérale de Lausanne EPFL, n° 5371 (2012)
Programme doctoral Mathématiques
Faculté des sciences de base
Institut de mathématiques de géométrie et applications
Chaire des structures algébriques et géométriques
#### Reference
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=50&t=39793&p=135546 | ## 7th Edition Problem 5.35
Posts: 82
Joined: Thu Sep 27, 2018 11:16 pm
Been upvoted: 2 times
### 7th Edition Problem 5.35
Does anyone know why all the pressure values are divided by 100 in the K expression in problem 5.35 (7th edition)?
Chem_Mod
Posts: 16494
Joined: Thu Aug 04, 2011 12:53 pm
Has upvoted: 349 times
### Re: 7th Edition Problem 5.35
Will you write out the question for those who don't have the 7th edition?
Matthew Tran 1H
Posts: 127
Joined: Thu Sep 27, 2018 11:16 pm
### Re: 7th Edition Problem 5.35
The question showed a graph of the decomposition of compound A into compounds B and C that reach equilibrium. The partial pressure is on the y-axis, in kPa. A changed from a partial pressure of 28 to 18, B from 0 to 5, and C from 0 to 10. Part (a) asked to write the balanced chemical equation for the reaction, but the part in question is part(b), where it asks to calculate K for the reaction. I was initially confused why the pressures had to be divided by 100, but I think it's because the value of Kp depends on the units of pressure. The textbook calculates Kp using atm or bar (1atm ~ 1bar). Since the pressure was given in kPa, you had to convert kPa to atm, and 1kPa ~ 0.01 atm, which is why you had to divide by 100. I'm not sure if we'll be given conversion factors like that on the test though, I had to look it up myself. | {"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": 0.8346274495124817, "perplexity": 1110.581888660138}, "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-2019-09/segments/1550247504594.59/warc/CC-MAIN-20190221111943-20190221133943-00400.warc.gz"} |
https://www.physicsforums.com/threads/how-far-can-light-travel.206196/ | # How far can light travel?
1. Dec 27, 2007
### InfinateLoop
I am hoping someone could let me know how far light can travel?
2. Dec 27, 2007
### ok123jump
If light (as in photons) were in a vacuum, it would travel forever in a given direction.
In reality however, it is far more probable that light will experience disturbances (absorption, reflection, refraction, etc..) as it moves through space - thus, it's distance of travel is limited to some finite distance. I do not think that there is any good estimation for this realistic finite distance. Clearly, this finite distance depends on the situation of the light being transmitted, direction and regions of space through which it will travel.
Last edited: Dec 27, 2007
3. Dec 27, 2007
### InfinateLoop
So do these disturbances destroy the light? I'm a little confused to what actually happens to the energy/photons.
4. Dec 27, 2007
### belliott4488
Photons can be "destroyed", although the more usual term is "absorbed". Their energy is then transferred to the material (particles) that absorbed them. They might also be reflected (or re-radiated, if you prefer the quantum-mechanical version), in which case they might have lost some energy to the reflective surface.
Classically, light is simply absorbed, much as a sound wave can be absorbed by a soft material. In Quantum Theory, there are fundamental interactions wherein a photon interacts with a charged particle, e.g. an electron, and the photon is absorbed. Another way this is stated is that "photon number is not conserved", i.e. you can create and destroy photons.
That was somewhat rambling - I hope it helped.
5. Dec 27, 2007
### InfinateLoop
So on a quantum level is this a massive collision? A photon is traveling at c and comes to a screeching halt?
6. Dec 27, 2007
### ok123jump
[Removed Text] I wasn't correct about the facts.
Last edited: Dec 27, 2007
7. Dec 27, 2007
### belliott4488
I'm not sure what you mean by a "massive collision".
Unfortunately, Quantum Field Theory stops short of describing in detail what happens to the fields that correspond to the particles participating in an interaction like this. One thing that is for sure, however, is that you have to leave behind the classical picture of a particle as a discrete object; the photon and the electron are both represented by quantum fields that carry certain properties. The energy and momentum of the photon are transferred to the electron, and the photon field is no more. I'm speaking very loosely here, and if you want a better picture, I think you'll have to post a question specifically about particle interactions in Quantum Field Theory.
Alternatively, you could just stay in the classical realm, where light is only a wave form of an electromagnetic field (no photons). In this case, the EM field exerts forces on the electrons in the absorbent material, which react by absorbing the energy of the incoming field. Since the electrons have EM fields of their own, you could think of these fields as "swallowing up" the incoming field, although I've never heard a physicist describe it this way!
8. Dec 27, 2007
### belliott4488
Sorry, I don't think that's right. EM fields most definitely carry momentum and can transfer it to massive particles. Invoking F=ma isn't quite appropriate since it describes the acceleration of a massive particle, which, as you've said, the photon is not. Better is to use F=dp/dt, i.e. a force produces a proportional change in momentum (which reduces to ma for a particle with constant non-zero mass).
In any case, the momentum transfer from light (i.e. EM waves) to massive objects is well-known, and is responsible for the solar radiation pressure that is exerted on satellites in orbit, or which would drive the solar sails that have been suggested as a form of propulsion in space.
9. May 22, 2010
### thomas pesek
OK so light will stop if some force interacts with it.
but what about light that misses an event, and keeps traveling in the vacuum of space ?
was just wondering, in SETI, instead of searching for sound, wouldn't it be wiser to search for light ? wouldn't that travel farther and faster ?
instead of looking out wards, why don't we look in wards ?
I mean, why not send out messages ourselves, piggy backed on lazer beams ?
if found, maybe they'll reply ?
maybe green men are out there and are just waiting for us to call them first ?
10. May 22, 2010
### dgtech
So then it is possible for the observable universe to be limited by distance rather than time?
11. May 22, 2010
### Kynnath
It's limited by both, in a sense. Light travels at a fixed speed. So you can describe the observable universe in terms of the distance the light we can see travelled, or the time it took it to travel that distance. The result is the same either way.
12. May 22, 2010
### dgtech
But how do we make sure? The only thing we know for sure is light gets absorbed and decays, everything else is just unproven hypothesis.
13. May 22, 2010
### Kynnath
We don't need to be sure, and proving is not possible. So long as the model we have is internally consistent and agrees with observations, it's good enough.
I'm don't know myself, but astronomers have figured out ways to measure the distance of the farthest emissions we can see (observable universe is, after all, how much of the universe we can see). Then again, for astronomers, a couple orders of magnitude of error is 'precise'. But seeing as I don't want to do the math myself, I'm happy to take them at their word.
14. May 22, 2010
### dgtech
Yes, I know that, but those ways of measuring are also based on plenty of assumptions, plus there was so much controversial evidence discovered, which was hurried to be "reevaluated" and reinterpreted in a more convenient form. IMO there is a strong element of "believing" and wishful thinking in that area :)
15. May 22, 2010
### pallidin
Does a photon, given enough space and time(and totally unimpeded), eventually "flat line"?
16. May 22, 2010
### dgtech
It's not a practical question, perfect vacuum likely does not exist
However, even in perfect vacuum gravity will affect photons - a very weak effect but present, at least in the current model
17. May 22, 2010
### pallidin
OK, unimpeded with respect to physical blocking atoms/objects.
What happens to that photon over VERY EXTENDED time? Decrease in wavelength?
18. May 22, 2010
### dgtech
you mean redshift?
19. May 22, 2010
### pallidin
No. Redshift requires that the emmiter and observer be separate and moving away from each other.
I just want to know what happens to a photon if it goes on, and on, and on.
Does it change?
20. May 22, 2010
### dgtech
if there is nothing to take away its energy potential theoretically it shouldn't decay
or at least I think so
I don't really have an idea what the photon actually is made of, maybe it can decay if there are some internal dynamics in it, that interact with each other and displace some form of energy | {"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": 0.8166542649269104, "perplexity": 858.2467821665533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660181.83/warc/CC-MAIN-20160924173740-00300-ip-10-143-35-109.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/6649/geometric-intuition-behind-convergence-of-fourier-series/6674 | # Geometric intuition behind convergence of Fourier series
I've been trying to work out the best way to understand why Fourier series converge, and it's a little embarrassing but I don't even know a rigorous proof. Can someone please help put me on the right track to thinking about these issue's in the proper way? I am especially interested any geometric ways to think about the convergence issue (something I suppose which takes advantage of the fact that each component $e^{in\theta}$ corresponds to some point along the unit circle).
Thanks!
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I would be interested in hearing someone address geometric interpretations of this convergence as well... – angela o. Oct 13 '10 at 2:48
...here is how I've always thought of it. The key thing is to show that no function is orthogonal to all of $\cos(n \theta), \sin (n \theta)$ for all $n$. Thinking of integrals as analogous to Riemann sums, we can think of each orthogonality condition as saying that a certain linear combination of the function values is zero. There is a certain independence among these linear combinations, so that they allow one to conclude that the function itself must be zero. – angela o. Oct 13 '10 at 2:50
...I realize this is quite fuzzy, especially on the integrals vs linear combinations analogy, and I hope someone will give a better answer. – angela o. Oct 13 '10 at 2:55
@angela: I am a little confused by your comment #2; I don't see how the orthogonality is related to convergence. Can you elaborate on why you say "the key thing" is to show that there is no function orthogonal to $cos(n\theta)$ and $sin(n\theta)$ for all n? – Matt Calhoun Oct 13 '10 at 3:20
But Fourier series don't converge; at least in general they don't converge pointwise. You need extra conditions to ensure pointwise convergence. – Robin Chapman Oct 13 '10 at 8:05
I don't know about a geometric interpretation, but here is a brief sketch of a proof. First we need to be precise about what we mean by "convergence." In the naive sense, Fourier series don't always converge - that is, pointwise. (If you change the value of a function at a single point, the Fourier series remains unchanged.) The sense in which they do always converge is in the Hilbert space $L^2([0, 1])$, which has inner product defined by $\langle f, g \rangle = \int_0^1 \overline{g(x)} f(x) dx$ inducing a norm, which induces a metric. In $L^2([0, 1])$ let $X$ be the subspace spanned by the functions $e^{2\pi i nx}, n \in \mathbb{Z}$. It is fairly straightforward to verify that the functions $e^{2\pi i nx}$ are orthogonal and have norm $1$; generally I think about this in a representation-theoretic way, as a special case of the orthogonality relations for characters.
Then the statement that Fourier series converge is equivalent to the statement that $X$ is dense in $L^2([0, 1])$. Why? Given a sequence in $X$ converging to an element of $L^2([0, 1])$ we can compute the Fourier coefficients, which depend continuously on the sequence and hence which converge to a limit. That these coefficients actually represent the element of $L^2([0, 1])$ is a standard Hilbert space argument and you should take a course in functional analysis if you want to learn this kind of stuff thoroughly.
Now, something else you need to know about $L^2([0, 1])$ is that the subspace $Y$ consisting of all step functions is dense in it. (If you have trouble believing this, first convince yourself that $Y$ is dense in the continuous functions on $[0, 1]$ and then believe me that the continuous functions are dense in $L^2([0, 1])$. In fact, $L^2([0, 1])$ can be defined as the completion of $C([0, 1])$ with respect to the $L^2$ norm.) So to show that $X$ is dense, it suffices to show that the closure of $X$ contains $Y$. In fact, it suffices to show that $X$ has as a limit point a step function with a single bump, say
$$a(x) = \begin{cases} 0 \text{ if } 0 \le x \le \frac{1}{3}, \frac{2}{3} \le x \le 1 \\ 1 \text{ otherwise} \end{cases}$$
and to take linear combinations, translations, and dilations of this. In other words, it suffices to prove convergence for square waves. But one can do the computations directly here. There is a standard picture to stare at, and of course if you have ever actually heard a square wave you should believe that audio engineers, at least, are perfectly capable of approximating square waves by sines and cosines.
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This is great! I am going to go through my functional analysis books and make sure I understand this proof thoroughly, thanks for the road map. – Matt Calhoun Oct 13 '10 at 18:44
You can write the partial sum $S_n(x)$ as an integral $${1\over 2\pi}\int_{-\pi}^\pi D_n(t) f(x-t)dt,$$ where the weight function or "kernel" $D_n(t)$ can be easily computed and graphed once and for all. One obtains $$D_n(t)={\sin((n+1/2)t)\over \sin(t/2)}.$$ So $S_n(x)$ is an "average" of $f$-values from the neighborhood of $x$. The essential point is that $D_n(t)$ is heavily concentrated around $t=0$ and oscillates quickly far away from $0$.
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The way I see Fourier series (especially the trigonometric expansions) you simply draw the initial sine and cosine lines at the macro level, and then you start dealing with higher frequencies that correct the smaller details.
So in the case of an infinite sum, you always go about correcting a bit more on a smaller scale, and at the limit point you have your original function.
(I'm pretty sure I wasn't clear about it, and that I need to wave my arms around, so I've set this CW so if anyone gets the idea and thinks they can clarify it will be easier to do so.)
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I see the trigonometric Fourier series in the same way as you. Here is a graph of the square wave expansion problemasteoremas.files.wordpress.com/2008/05/… – Américo Tavares Oct 13 '10 at 11:26
I really like this answer for the "geometric intuition" part of the OP. The lack of rigor is a bit obscene, but my main goal was to find the best way to use geometry to explain the convergence issue to a non-expert. In my opinion, geometric insights like this one should come before rigorous arguments. – Matt Calhoun Oct 13 '10 at 18:50
@Matt: As I wrote, I made it CW so people could somewhat correct and add the much needed rigor. However, intuition was asked upon so that was what I could write about. – Asaf Karagila Oct 13 '10 at 19:41
I think the main issue here is that although the picture of the convergence is nice, it doesn't really explain why an infinite series of sines and cosines should converge. I think a by considering a geometrical interpretation of Christian's answer, regarding the error term of the partial fourier sums, we could argue that adding additional terms will approximate the function more closely. I will have to think about this much more thoroughly before editing this answer however. – Matt Calhoun Oct 14 '10 at 17:24
Since your question was about the geometry behind convergence, I'll chime in with a very geometric way to think about these concepts. However, as Qiaochu Yuan mentions, in order to do so, we must first nail down in what sense we mean convergence. I'll discuss the "big three" types of convergence: pointwise, uniform, and mean-square (also called $L^2$) convergence.
Let's begin with defining a notion of $error$ between $f(x)$ and the $N$th partial sum of its Fourier series, denoted by $F_N(x)$, on $-\ell<x<\ell$. Define the (absolute) pointwise error, $p(x)$, by $$p(x)=|f(x)-F_N(x)|, \quad -\ell<x<\ell.$$ The geometry of the situation belies its name: $p(x)$ represents the point-by-point difference (or error) between $f(x)$ and $F_N(x)$.
We can then define the following three types of convergence based on the behavior of $p(x)$ as $N\to\infty$.
• $F_N(x)$ converges pointwise to $f(x)$ on $-\ell<x<\ell$ if $$p_N(x)\to 0 \text{ as } N\to\infty \text{ for each fixed }x\in(-\ell,\ell).$$
• $F_N(x)$ converges uniformly to $f(x)$ on $-\ell<x<\ell$ if $$\sup_{-\ell<x<\ell}p_N(x)\to 0 \text{ as } N\to\infty.$$
• $F_N(x)$ converges in the mean-square or $L^2$ sense to $f(x)$ on $-\ell<x<\ell$ if $$\int_{-\ell}^\ell p_N^2(x)\,dx\to 0 \text{ as } N\to\infty.$$
Think of each of these in terms of what is happening with the pointwise error as $N\to \infty$. The first says that at a fixed $x$, the difference between $f(x)$ and $F_N(x)$ is going to zero. This may happen for some $x$ in the interval and fail for others. On the other hand, uniform convergence says that the supremum of all pointwise errors tends to zero. Finally, the mean-square error says that the area under $p^2(x)$ must tend to zero as $N\to\infty$.
The first is a very local way to measure error (at a point), whereas the second two are global ways to measure the error (across the entire interval).
We can formulate this in terms of norms by setting $$\|f-F_N\|_\infty:=\sup_{-\ell<x<\ell}|f(x)-F_N(x)|$$ Then, $F_N(x)\to f(x)$ uniformly on $-\ell<x<\ell$ provided $\|f-F_N\|_\infty\to 0$ as $N\to\infty$. (This is why we call it the uniform norm!)
On the other hand, if we set $$\|f-F_N\|_{L^2}:=\sqrt{\int_{-\ell}^\ell |f(x)-F_N(x)|^2\,dx},$$ then $F_N(x)\to f(x)$ in the $L^2$ sense on $-\ell<x<\ell$ provided $\|f-F_N\|_{L^2}\to 0$ as $N\to\infty$. (This is called the $L^2$ norm on $-\ell<x<\ell$.)
To illustrate this geometrically, here's $f(x)=x^2$ (black) and its Fourier sine series $F_N(x)$ (blue) on $0<x<1$ for $N=5,\dots,50$ and the corresponding pointwise error (red). We can see this series converges pointwise but not uniformly on $0<x<1$. You can also get an idea of the $L^2$ convergence by envisioning the area under the square of the red curve and seeing it tend to zero also. I was going to post that picture as well, put the shaded area is so thin it is difficult to see.
These illustrations are of course not a proof of the convergences, but simply a way to interpret them geometrically.
For the sake of completeness, here's an example which does converge uniformly: the same function and interval as above, but $F_N(x)$ is the Fourier cosine series.
Hope that helps.
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https://www.physicsforums.com/threads/cmb-and-prefered-lorentz-frames.115989/ | # CMB and prefered lorentz frames
1. Mar 30, 2006
### DavidK
Consider two farmes of reference moving relative each other. In one of the frames the CMD is fully isotropic, i.e., it looks the same in all directions. In the other frame however, the CMD should be red shifted in one direction and blue shifted in the other direction. Thus, the first frame can be considered to be at rest relative the CMD, and therefore, in some sence, constitute a prefered lorenz frame.
How can this be?
2. Mar 30, 2006
### marcus
That is perfectly correct.
It is not forbidden to have preferred frames in that sense.
One way to think about why it can be is to say this to yourself:
special relativity says that the LAWS of physics must be Lor. inv.
So we expect the EQUATIONS like the Maxwell eqns. to be Lor. inv.
But we do not expect particular SOLUTIONS of those equations to have this same symmetry.
So, well, the universe is a particular solution to the Einstein General Relativity equation. This solution is approximately the Friedman solution (called various things, Friedman-Lemaitre, FRW metric, various names....)
this particular solution, call it Friedman solution or whatever you like, is NOT Lorentz invariant. It has a concept of being at REST which was already discovered by Hubble back in 1930s (if I remember history right) long before people knew about CMB!
One can be at rest with respect to the expansion------sometimes they call it being at rest with respet to the "Hubble flow". So that the recession speed of distant galaxies looks the same in all directions.
That idea of being at rest turns out to be the SAME as being at rest with respect to the CMB, as you described.
If you are not at rest then it will look to you as if the galaxies in one direction are receding FASTER from you than the galaxies the same distance away in the opposite direction.
If you adjust your velocity so the Hubble expansion looks the same in all directions, then you will also find that the CMB looks on average the same in all directions (I mean has no dipole, it still can have small irregularities but think of them as averaged out).
Last edited: Mar 30, 2006
3. Mar 30, 2006
### DavidK
Thanks for the very informative answer. A natural follow up question is: why is the earth at rest relative the CMB? Is it something one should expect?
4. Mar 30, 2006
### marcus
It is not at rest. If I remember, the solarsystem is moving some 370 km/second with respect CMB.
the direction we are going is in the direction of the constellation Leo.
this motion w.r.t. CMB has to be deducted and compensated when people analyse the data.
The orbital motion of WMAP satellite, which is roughly similar to earth's motion, also has to be deducted but that is only about 30 km/sec and varies seasonally. The main motion thing they need to get rid of is the overall motion of the solar system w.r.t. CMB.
============
Here is a paper about measuring the speed and direction of sun relative CMB
http://arxiv.org/astro-ph/9601151 [Broken]
Sep 1996 The Dipole Observed in the COBE DMR Four-YearData
C. H. Lineweaver et al
"The largest anisotropy in the cosmic microwave background (CMB) is the ~3mK dipole assumed to be due to our velocity with respect to the CMB. ..."
this will give the coordinates of the direction and the speed (in case i have forgotten the speed)
Last edited by a moderator: May 2, 2017
5. Mar 31, 2006
### DavidK
Ahhh...now it all makes sence again .
6. Apr 2, 2006
### Chronos
I prefer to think of the CMB as a convenient reference frame, not absolute. The danger of that assumption is buried in Maxwell's equations.
Similar Discussions: CMB and prefered lorentz frames | {"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": 0.9100230932235718, "perplexity": 858.6719321027169}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806586.6/warc/CC-MAIN-20171122122605-20171122142605-00244.warc.gz"} |
http://planetmath.org/Trigonometry | trigonometry
Primary tabs
Defines:
sine,cosine,tangent,secant,cosecant,cotangent
Type of Math Object:
Topic
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
basic trigonometric entry
to my surprise there wasn't an entry defining and dealing and defining the elementary trigonometric functions, so I went and created this.
I know this entry is the kind of entry that will generate a long thread about comments, suggestions criticism and all that jazz, so why don't someone better sets up an asteroidmeta page for this so we can avoid polluting the page (and making it a lot larger and slower to load ;)
It's incomplete as it stands right now, but I'm making it world editable so anyone can work on it directly. Ah, and I'd like it to keep it as real trig mostly entru, so please do not dwell too much into complex analysis (perhaps just some mention and references)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f
Re: basic trigonometric entry
Actually, THERE IS already an entry defining elementary trigonometric functions:
http://planetmath.org/encyclopedia/DefinitionsInTrigonometry.html
Re: basic trigonometric entry
Another entry defining geometrically the sine and cosine of all real numbers is
Re: basic trigonometric entry
does cyclometric functions one really defines them?
it seems a bit circular to me if you want them to define sin, cos, etc
(unless you use the power series at the bottom to define arcsin first and then define sin as the inverse of arcsin, but then it gets all too contrived)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f
Re: basic trigonometric entry
The first section of your entry is a repeat of "definitions in trigonometry" and as a matter of fact the previous entry is a little clearer in the exposition (for my taste). And that entry defines (i.e. they are in the "also defines" list) sine, cosine and the kind.
I like the idea of extending the topic and adding a bunch of things that "defs in trig. " is missing though, that is why I suggested making your entry a child of that one.
Alvaro
Re: basic trigonometric entry
Ok I'll attach it, but keep in mind I said the entry as it stands is far from complete, right now I'm redoing the picture so I can fill the correction you still have opened, and many other things need to be added
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f
Re: basic trigonometric entry
Thanks!
And again, thanks for adding this entry to the collection, I have also noticed that Planetmath was a little weak in trigonometry.
Alvaro
Re: basic trigonometric entry
As I see it, there really should be both definitions available. The definition in terms of sides and angles is uitable for beginners studying geometry and the definition in terms of power series and invers functions is more suitable for more advanced people.
Hoewever, this discussion should never have happened here, so I am going to build the wiki so we can carry out the discussion in a more suitable place.
Trigonometry discussion page
Please post all further discussion of this entry to the following webpage:
http://oddwiki.taoriver.net/wiki.pl/AsteroidMeta/Discussion_of_Trigonometry
Re: basic trigonometric entry
Maybe, it seems a bit circular. In fact the 'defining' of sine and cosine (for all real numbers) is only a subplot in explaining the old names arcsin and arccos -- you will see it if you read anew the whole article. But possibly I shall improve the order of things there. - The power series here is not any definition of arcsin, but only a formula.
Jussi
Re: basic trigonometric entry
all I pointed is that I can't see the cyclometric entry defining the trig functions, just making use of them
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f
All right =o) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 143, "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": 0.9715301394462585, "perplexity": 1685.0021317013372}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246639325.91/warc/CC-MAIN-20150417045719-00097-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://blogformathematics.blogspot.com/2011/03/discriminant-of-quadratic-equation.html | ## Pages
### Discriminant of a quadratic equation
The discriminant can be considered as a property of a quadratic equation. It is calculated from the quadratic equation in the general form. The discriminant value is very important in determining the nature of roots of a quadratic equation, even before calculating the roots themselves. This gives us the advantage of not having to calculate the roots of a quadratic equation, when knowing their nature is sufficient.
The nature of roots of a quadratic equation means the possible set of values that the roots can be. This tells us whether the roots are real numbers, imaginary numbers, complex numbers, or rational numbers, and so on..
Knowing the nature of roots of a quadratic equation is especially useful in graphing parabolas, and in checking the answers.
The discriminant can be calculated when the quadratic equation is in the general form:
ax^2 + bx + c = 0
In the above equation, the discriminant D is calculated by:
D = b^2 - 4ac
Example: In the equation
2x^2 + 3x + 5 = 0,
the discriminant is
D = 3^2 - 4(2)(5) = -31
The discriminant value in a quadratic is especially useful in determining the nature of the roots of a quadratic 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": 0.8009121417999268, "perplexity": 196.10024898157806}, "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-2017-22/segments/1495463609404.11/warc/CC-MAIN-20170528004908-20170528024908-00361.warc.gz"} |
http://www.ipam.ucla.edu/abstract/?tid=10905&pcode=MDWS3 | Computations and Experiments of Grain Evolution in Four Dimensions
Peter VoorheesNorthwestern University
Recent advances in computational and experimental techniques now permit the evolution of a microstructure to be determined in three dimensions and as a function of time. It is thus possible to employ an experimentally measured microstructure as an initial condition in a simulation and to then compare the predicted structure to that measured experimentally at some later time. Such an approach is a particularly stringent test of simulation and can be used to identify important phenomena that are lost in an averaging process. We shall illustrate this approach using experiments and simulations of solid-state grain growth. Using an experimentally measured grain structure as an initial condition in a phase field model, we compare the shapes of individual grains measured experimentally to those predicted by the simulation at some later time. We find that the phase field simulations reproduce quite accurately the grain morphology and topology in regions of the sample with isotropic grain boundary properties. However, in other regions, we find a clear influence of grain boundary energy anisotropy on the morphological evolution of grains and a disagreement between simulation and experiment.
Back to Workshop III: Mesoscale and Continuum Scale Modeling of Materials Defects | {"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": 0.9766721725463867, "perplexity": 688.7778024250111}, "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-2017-43/segments/1508187825057.91/warc/CC-MAIN-20171022022540-20171022042540-00416.warc.gz"} |
https://www.birs.ca/events/2017/5-day-workshops/17w5059/videos/watch/201711301531-Phan.html | ## Video From 17w5059: Partial Order in Materials: at the Triple Point of Mathematics, Physics and Applications
Thursday, November 30, 2017 15:31 - 16:16
Gradient estimates of weak solutions of quasi-linear parabolic equations with... | {"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": 0.8832307457923889, "perplexity": 2282.2972736000297}, "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-2022-05/segments/1642320305266.34/warc/CC-MAIN-20220127133107-20220127163107-00591.warc.gz"} |
https://www.arxiv-vanity.com/papers/1301.7536/ | UT-13-03
IPMU 13-0024
Axino dark matter with R-parity violation and
130 GeV gamma-ray line
Motoi Endo, Koichi Hamaguchi, Seng Pei Liew,
Kyohei Mukaida and Kazunori Nakayama
Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8583, Japan
We show that decaying axino dark matter with R-parity violation can explain the observed excess of the 130GeV gamma-ray line from the Galactic center in the Fermi data. The branching fraction of the axino decay into monochromatic photons can be , and constraints from continuum gamma-rays and the anti-proton flux are ameliorated. The Peccei-Quinn scale of GeV and the R-parity violation parameter of are cosmologically favored.
## 1 Introduction
Recently, there is increasing evidence of the excess of the 130 GeV gamma-ray line from the Galactic Center (GC) in the four-year Fermi data [1, 2, 3, 4, 5, 6, 7, 8, 9]. This may be interpreted as a signal of the dark matter (DM), which annihilates or decays around the GC. An obstacle to construct a model of the annihilating/decaying DM which explains the observed gamma-ray line excess is that the branching ratio of the monochromatic photon production must be fairly large. It should be larger than around 0.01 [10, 11, 12]. Otherwise, continuum gamma-rays would hide the line gamma, and anti-protons may be overproduced. For instance, if the DM annihilation into photons takes place through loops of the standard model (SM) particles, it is difficult to realize such a large branching ratio [13].
In this letter, we propose a model of the decaying DM which naturally explains the gamma-ray line excess without producing too much continuum gammas and anti-protons. A supersymmetric (SUSY) axion model [14] is considered to solve the strong CP problem in the framework of the minimal SUSY SM (MSSM). The axino, which is a fermionic superpartner of the axion, is a suitable candidate of the DM, if it is the lightest SUSY particle (LSP). By introducing small R-parity violations, the axino decays into a photon plus a neutrino, and the Fermi gamma-ray line excess can be explained. It is stressed that the branching fraction of the axino decay into monochromatic photons typically becomes , and the constraints from the overproductions of the continuum gamma-ray and the antiproton are satisfied. This is in contrast to the decaying gravitino DM scenario, where the branching fraction of the monochromatic photon production is suppressed [10]. Moreover, the present scenario is cosmologically favored, because the lightest SUSY particle of the MSSM (MSSM-LSP), e.g., the lightest neutralino, decays by the R-parity violating effects before the big-bang nucleosynthesis (BBN) begins. This avoids the cosmological problem associated with a late decay of the MSSM-LSP when the gravitino is lighter than the MSSM-LSP.#1#1#1 Light axino DM with R-parity violations was considered in Refs. [15, 16, 17]. Ref. [18] considered the gravitino LSP with the axino heavier than MSSM-LSP. On the other hand, the morphology of the gamma-ray line signature from the GC seems to favor the annihilating DM scenario rather than that of the decaying DM [10]. Although relatively large gamma-ray signals are expected from the Galactic halo in the decaying DM scenario, no such excesses have been observed. However, since there are potentially large uncertainties in the gamma-ray data and the DM density profile around the GC, it is premature to specify the DM model by the morphology [10, 19].
In the next section, the axino DM model will be introduced, and properties of the model will be explained, particularly paying attention to the R-parity violating effects. We consider the KSVZ axion models [20]. It will be shown that the model can explain the gamma-ray line excess. In addition, several cosmological aspects will be discussed. The last section will be devoted to the conclusion and discussion.
## 2 Axino dark matter with R-parity violation
### 2.1 Axino decay rate with R-parity violation
Let us first introduce R-parity violations. In this letter, we consider a bilinear type of the R-parity violation [21], which is characterized by the superpotential,
W=μiLiHu, (2.1)
where and are chiral superfields of the lepton doublet and the up-type Higgs doublet, respectively. The index denotes the generation, and is a parameter with a mass dimension. Here and hereafter, summation over is implicitly promised. By redefining and the down-type Higgs superfield as and with , where is the higgsino mass parameter appearing in the superpotential as , the R-parity violating superpotential (2.1) is eliminated. Hereafter, for notational simplicity, the primes on the redefined fields are omitted. After the redefinition, the SUSY breaking potential becomes
−LRPV=Bi~LiHu+m2LiHd~LiH∗d+h.c., (2.2)
where is a scalar component of the superfield . The coefficients are and , where , and represent soft SUSY breaking parameters in the MSSM, . Due to the R-parity violating scalar potential (2.2), sneutrinos obtain non-zero vacuum expectation values (VEVs) as
⟨~νi⟩=−m2LiHdcosβ+Bisinβm2~νiv, (2.3)
where is a ratio of the VEVs of the up- and down-type Higgs fields, GeV, and is a sneutrino mass.
Before proceeding to discuss phenomenological aspects, several comments are in order. It is possible to introduce the bilinear R-parity violating soft terms, and in addition to (2.1), before the field redefinition. The coefficients in (2.2) then have additional contributions, but the following analysis will not be affected as far as the R-parity violation is parametrized by the the sneutrino VEV (2.3). Next, trilinear R-parity violating terms, and , are also generated by the field redefinition. They are subdominant and will be ignored in the following study, because the terms are multiplied by the Yukawa couplings.
The sneutrino VEVs (2.3) induce mixings between the SM leptons and the gauginos. The SM neutrinos mix with the bino and the neutral wino, and the SM charged leptons mix with the charged winos. Hence, the R-parity violating parameters are constrained. The neutrinos obtain masses of , where is a bino (wino) mass [22, 23, 24]. For gaugino masses of GeV, is imposed to satisfy the experimental bound on the neutrino masses. Also, the cosmological asymmetry is preserved for [25, 26, 27, 28]. Other constraints are known to be weaker (see e.g., Ref. [21]). As we will see, the size of the R-parity violation favored by the Fermi gamma-ray line excess is much smaller as . #2#2#2 See e.g., Refs. [29, 30, 31] for models to explain such a tiny R-parity violation parameter.
The R-parity violation destabilizes the LSP. In this letter, we consider the axino LSP scenario in the KSVZ axion models [20]. The relevant interaction terms of the axino are
L~aλA=iαYCY16πfa¯~aγ5[γμ,γν]~BBμν+iαWCW16πfa¯~aγ5[γμ,γν]~WaWaμν (2.4)
where and are model-dependent coupling constants of order unity, is the fine structure constant of U(1), is that of SU(2), is the PQ scale, denotes the axino, is the bino (wino), and is the field strength of the U(1) (SU(2)) gauge boson. The axino LSP is stable as long as the R-parity is conserved, whereas it decays via the operators (2.4) with the gaugino mixings with the SM leptons, once the R-parity violation is turned on.
First, let us consider the case of (see Sec. 2.2 for an explicit realization). The first term in (2.4) provides interactions of and . The R-parity violation opens a decay of the axino through the mixing as and . In the limit of , the axino decay rate becomes
Γ(~a→γνi)≃C2Yα2Y128π3m3~af2a(g2Y⟨~νi⟩22m2~Bcos2θW), (2.5)
where is the axino mass, and is the weak mixing angle. Here and hereafter, denotes a sum of the partial decay rates into and . The factor in the parenthesis comes from the bino-neutrino mixing, and from the U(1) gauge boson-photon mixing. Similarly, we obtain
Γ(~a→Zνi)≃C2Yα2Y128π3m3~af2a(g2Y⟨~νi⟩22m2~Bsin2θW)(1−m2Zm2~a)(1−m2Z2m2~a−m4Z2m4~a), (2.6)
where is the mass of the boson. For , the branching fractions are given by . From the above results, the axino lifetime is estimated as
τ~a≃8×1026sec C−2Y(m~a260GeV)−3(fa1013GeV)2(m~B1TeV)2(κ10−11)−2, (2.7)
where the R-parity violating parameter is defined as .
The two-body decay of the axino into a photon contributes to the monochromatic gamma signal of the Fermi observation. If the axino mass is around 260 GeV, the photon produced by has an energy of about 130 GeV. According to Ref. [10], the observed excess of the gamma-ray line is accounted for by a decaying DM, when its lifetime and the branching ratio are in the range of sec and . The astrophysical constraints from the diffuse gamma-rays [32] and neutrinos [33] are also satisfied for such a parameter region. In the present model, the branching ratio is around 0.8 for , while the hadronic branch from is sufficiently small. Thus, the lifetime and the branching fraction which are required to explain the gamma-ray line excess from the GC are realized by the axino DM.
Next, let us focus on the case of and neglect the contribution from the first term in (2.4), i.e., . The second term in (2.4) provides interactions of , and . The decays, and , proceed by these interactions with the mixings of and . In the limit of , the decay rate of the axino into a photon and a neutrino is given by
Γ(~a→γνi)≃C2Wα2W128π3m3~af2a⎛⎝g22⟨~νi⟩22m2~Wsin2θW⎞⎠, (2.8)
where the factor in the parenthesis is the mixing between the wino and the neutrino, and the mixing between and the photon. Similarly, the decay rate of becomes
Γ(~a→Zνi)≃C2Wα2W128π3m3~af2a⎛⎝g22⟨~νi⟩22m2~Wcos2θW⎞⎠(1−m2Zm2~a)(1−m2Z2m2~a−m4Z2m4~a), (2.9)
while that of , which is a sum of the rates of and , is
Γ(~a→Wli)≃C2Wα2W128π3m3~af2a⎛⎝g22⟨~νi⟩2m2~W⎞⎠(1−m2Wm2~a)(1−m2W2m2~a−m4W2m4~a), (2.10)
where is the mass of the boson, and the factor represents the mixing between the charged wino and the lepton. Thus, we obtain for . This results in the branching fraction of of around .
In the case of , both the first and second terms in Eq. (2.4) contribute to the axino decay. The decay rates in such a generic case are summarized in App. A. As shown there, the branching fractions are determined by a combination of for . Fig. 1 shows the branching ratios of the axino decay into , and as a function of for (left) and as a function of for (right). One can confirm that the branching ratio of becomes for , while it becomes for large . In the intermediate regime, the branching ratio of decreases due to an interference effect and eventually vanishes at [cf. Eq. (A.7)]. In most of the parameter space, however, and hence the model can explain the gamma-line without overproducing continuum gamma-ray and antiprotons.
### 2.2 A model of SUSY axion
Here, we briefly describe an explicit model of the SUSY axion. Let us introduce PQ superfields, and , with PQ charges of and , respectively. Also, PQ quarks, and , are added, which have fundamental and anti-fundamental representations of the SM SU(3), respectively, and both of which have a PQ charge of . The superpotential is given by
WPQ=λX(Φ¯Φ−V2)+kΦQ¯Q+W0, (2.11)
where is a singlet superfield, and are coupling constants, and is a constant term with the gravitino mass and the reduced Planck scale . The coupling constants are taken to be real and positive. Including the SUSY breaking terms, and , the relevant terms of the scalar potential are
VPQ=m2Φ|Φ|2+m2¯Φ|¯Φ|2+λ2|Φ¯Φ−V2|2+λ2|X|2(|Φ|2+|¯Φ|2)+(2λm3/2V2X+h.c.), (2.12)
where we have assumed the minimal Kähler potential, for simplicity. The VEVs of the PQ scalars are given by , which is related to the PQ scale as , and the PQ quarks obtain a mass of . The axion, which is a goldstone boson associated with the VEVs of the PQ scalars, has an anomaly-induced coupling to the gluon via PQ quark loops, because the PQ symmetry is anomalous under the QCD. Thus it solves the strong CP problem. The coupling constants, and , depend on assignments of the U(1) and SU(2) charge on the PQ quarks. If they are a singlet under SU(2) but have (opposite) U(1) charges, we obtain and . If they are embedded in the SU(5) representation, both and are nonzero and satisfy . For instance, if the PQ quarks are embedded in of SU(5), the coefficients become .
In this model, the axino, that is a fermionic component of a linear combination of and , obtains a mass of , where the VEV of is derived from (2.12). Several additional effects can make the axino heavier or lighter. There can be other SUSY breaking contributions to the tadpole term of in (2.12), which change the VEV of and hence the axino mass. Radiative correction from the loops can also modify the axino mass [34]. In this letter, we assume that these effects slightly reduce the axino mass, and the axino becomes the LSP.
### 2.3 Cosmology
In this section, we discuss several cosmological constraints on the decaying axino DM scenario.
#### 2.3.1 Lightest neutralino
Let us assume that the lightest neutralino is mostly composed of the bino and that it is the MSSM-LSP. In the presence of the R-parity violation, the bino decays into and due to the sneutrino VEV. The decay rate of the bino is given by [35]
1Γ(RPV)~B≃2×10−3sec(κ10−11)−2(m~B1TeV)−1. (2.13)
In order for the bino decay not to disturb the BBN, i.e., for the bino lifetime shorter than 0.1 sec, we need for .
The bino also decays into the axino through the R-parity conserving operators (2.4) as and . If this dominates the bino decays, the produced axinos may exceed the observed DM abundance. In order to avoid the axino overproduction, the production rate should be much less than . The decay rate of the bino into axinos with photons or bosons is totally given by [36]
1Γ(PQ)~B≃3×102sec C−2Y(fa1015GeV)2(m~B1TeV)−3. (2.14)
The axino abundance produced by the bino decay in terms of the density parameter , where is the present energy density of the axino and is the present critical energy density, becomes
Ω(~B)~ah2=m~am~BΓ(PQ)~BΓ(PQ)~B+Γ(RPV)~BΩ~Bh2, (2.15)
where is the present Hubble parameter in units of 100 km/s/Mpc, and is the bino abundance after the thermal decoupling evaluated as if the bino were stable. Since the bino abundance is large in general, the axion abundance becomes too large, unless the branching ratio of the bino decay into the axino is suppressed, i.e., .
#### 2.3.2 Axino and axion
Axinos are produced by scatterings of the gluons and the gluinos from the thermal bath at the reheating. The thermally produced axino abundance is given by [37, 38]
Ω(th)~ah2≃6×10−3g63ln(3g3)(m~a260GeV)(TR106GeV)(fa1015GeV)−2, (2.16)
where is the running QCD coupling constant at the scale, and is the reheating temperature after the inflation. This is valid as long as is larger than the axino mass. Thus, the axino can be a dominant component of the DM for .
The abundance of the axion coherent oscillation is estimated as [40]
Ωah2≃0.2θ2a(fa1012GeV)1.19, (2.17)
where denotes the axion initial misalignment angle. For GeV, we need in order for the axion abundance to be lower than the DM abundance.
#### 2.3.3 Saxion
The saxion, , belongs to a flat direction in the scalar potential (2.12), which satisfies . It obtains a mass, , from the SUSY breaking effect.
Let us estimate the saxion abundance. The saxion sits around the minimum during the inflation, which is slightly displaced from the low-energy true minimum, and begins to oscillate around the true minimum when the Hubble parameter decreases to with an initial amplitude of . The abundance of saxion coherent oscillation is
ρσs=18TR(σiMP)2≃2×10−2GeV(TR106GeV)(fa1015GeV)2(σifa)2, (2.18)
where is the saxion energy density, and is the entropy density. Here, we have assumed that the saxion oscillation starts before the reheating process of the inflation is finished, which is the case for . The saxion dominantly decays into the axion pair. The lifetime becomes [41]
τσ=(ξ232πm3σf2a)−1≃0.5sec(fa1015GeV)2(mσ500GeV)−3ξ−2, (2.19)
with . Note that the saxion also decays into a pair of the gluons with a branching fraction of [42], but it does not affect the BBN as long as GeV is satisfied for GeV.#3#3#3 We assume that the saxion is lighter than twice the mass of the axino. Otherwise, the axino LSPs are overproduced by the saxion decay, . This indicates GeV.
The axions produced by the saxion decay contribute to the extra effective number of the neutrino species, [43, 44, 42, 45, 46, 47, 48, 49], which is given by
where
with denoting the temperature at which the saxion decays and being the radiation energy density. It is estimated as
ΔNeff≃1.2(fa1015GeV)3(TR104GeV)(mσ500GeV)−3/2(σifa)2ξ−1. (2.22)
The contribution should satisfy . In other words, the recent claims of the existence of the extra light species, [50], can be explained by the non-thermal axions from the saxion decay. We assume for simplicity.
#### 2.3.4 Combined constraints
The combined constraints on a plane of are shown in Fig. 2. In the top panel, we have taken , , GeV, TeV, GeV and . In the light blue band, the Fermi 130 GeV gamma-ray line excess is explained. On the right side of the black dashed line, the bino lifetime is shorter than sec, and the decay has no effects on the BBN. Above the orange dot-dashed line, we have , and the axino abundance produced by the bino decay is sufficiently small. Here, is taken as a reference value of the bino abundance as inferred from Ref. [51]. Below the red horizontal line, is obtained from the axions produced by the saxion decay. In the figure, is set so that is realized for each . Above the blue dotted horizontal line, and the axino DM is thermally produced.
In the bottom panel, we have taken and and assumed that the wino is the MSSM-LSP with its mass of TeV. Note that since the thermal relic wino abundance is small, there is no constraint from the axino overproduction by the wino decay.#4#4#4Similar conclusions hold for the case of the stau MSSM-LSP. In both cases, it is found that the Fermi 130 GeV gamma-ray line excess is accounted for without suffering from the cosmological constraints for and GeV.
Here we briefly mention parameter dependences on these constraints. For larger neutralino mass, the axino lifetime becomes longer and the light-blue band moves to the bottom-right. Also, the axino abundance from the neutralino decay (2.15) becomes larger and the orange dot-dashed line moves to the top-right. For smaller saxion mass or larger initial amplitude of the saxion, the bound from (2.22) becomes stronger and the red line moves to the bottom. For general values of and , the branching ratio of the axino decay into photon may become smaller, as shown in Fig. 1, and hence the light-blue band moves to the bottom-right to make the axino lifetime smaller.
Before closing this section, let us comment on the gravitino. The gravitinos are also produced by scatterings of the gluons and the gluinos from the thermal bath at the reheating. If the gravitino is lighter than the MSSM-LSP, then it dominantly decays into the axino and the axion, and hence there is no BBN constraint [39]. The nonthermal production of axinos by the gravitino decay is negligible, since the abundance of the thermally produced gravitino is less than that of the axino. On the other hand, if the gravitino is heavier than the MSSM-LSP, its decay affects the BBN. The parameter range corresponding to GeV (just below the red horizontal line in Fig. 2) is constrained depending on the gravitino mass and the MSSM mass spectrum [51].
## 3 Conclusion
We have proposed the decaying axino DM scenario as a model to explain the Fermi 130 GeV gamma-ray line excess from the GC. It is based on the SUSY KSVZ axion model with the bilinear R-parity violation. The model realizes a fairly large branching fraction of the axino decay into a photon plus a neutrino. It was found that the Fermi excess is accounted for while satisfying the other cosmological constraints for GeV and .
Compared to another well–motivated decaying DM, i.e., the decaying gravitino DM, the decaying axino DM typically has a larger branching fraction into the monochromatic gamma. The gravitino universally couples to the lepton and the Higgs superfields, and hence the gravitino’s decay into , and cannot be suppressed in the presence of the bilinear R-parity violation. Thus, the decaying gravitino DM is severely constrained by the observation of the antiproton flux [10].
Let us touch on the collider phenomenology. The MSSM-LSP is stable in the detectors for the R-parity violation of (see e.g., Ref. [52]). Thus, when the MSSM-LSP is neutral, the SUSY events would be detected by searching for signals with a large missing transverse momentum. If the MSSM-LSP is a charged particle, it leaves a charged track, which is a characteristic signal in the detector. The sensitivities of the LHC searches are the same as the standard SUSY searches.
As mentioned in the introduction, the morphology of the observed gamma-ray signature is still premature to refute the decaying DM scenario. If the uncertainties will be understood in future, such an analysis can be used for distinguishing the DM models particularly between the decaying and annihilating DM models. If the former scenario will become favored, the decaying axino DM model can be an attractive candidate.
## Acknowledgment
This work was supported by JSPS KAKENHI Grant No. 23740172 (M.E.), No. 21740164 (K.H.), No. 22244021 (K.H.), No. 22244030 (K.N.) and by the MEXT Grant-in-Aid No. 21111006 (K.N.). The work of K.M. is supported in part by JSPS Research Fellowships for Young Scientists. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.
## Appendix A Formulae for the axino decay rate
In this appendix, we provide the general formulae for the axino decay rate in the presence of the R-parity violation. The interaction between the axion and the SU(2)U(1) gauge supermultiplets is given by
L=αYCY4√2πfa∫d2θAWBWB+αWCW4√2πfa∫d2θAWaWWaW+h.c., (A.1)
where stands for the fine structure constant of U(1) (SU(2)), is the PQ scale, is the axion superfield, , and () is the supersymmetric field strength of U(1) (SU(2)). The coefficients and are model-dependent constants of order unity. In terms of the component fields, the axino interactions become
L=iαYCY16πfa¯~aγ5[γμ,γν]~BBμν+iαWCW16πfa¯~aγ5[γμ,γν]~WaWaμν, (A.2)
where is the axino, () is the gauge boson of U(1) (SU(2)), and and denote the bino and the wino, respectively.
Due to the sneutrino VEV induced by the bilinear R-parity violation, the SM leptons and the gauginos mix with each other, and the axino LSP, , can decay into , and . The mass matrix of the neutralino and the neutrino becomes
MN=⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝m~B0−mZsWcβmZsWsβ−gY⟨~νi⟩/√20m~WmZcWcβ−mZcWsβg2⟨~νi⟩/√2−mZsWcβmZcWcβ0−μ0mZsWsβ−mZcWsβ−μ00−gY⟨~νi⟩/√2g2⟨~νi⟩/√2000⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠, (A.3)
for with . Here, the subscript stands for the generation, , , and with the weak mixing angle . The upper-left matrix is identical to the neutralino mass matrix of the MSSM, and the neutrino masses are approximated to be zero. On the other hand, the mass matrix of the chargino and the lepton is given by
MC=⎛⎜ ⎜⎝m~W√2mWsβ0√2mWcβμ−Yli⟨~νi⟩g2⟨~νi⟩0mli⎞⎟ ⎟⎠, (A.4)
for with and . Here, is the lepton Yukawa coupling constant, and the upper-left matrix is identical to the chargino mass matrix of the MSSM. Neglecting the small SM lepton masses in the phase space, one finds the decay rates as
Γ(~a→GL)=1128π3m3~af2a(1−m2Gm2~a)(1−m2G2m2~a−m4G2m4~a)FGL(CY,CW,m~B,m~W) (A.5)
with
FGL (CY,CW,m~B,m~W)≡ ⎧⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪⎩∣∣αYCYcosθWUνi~B+αWCWsinθWUνi~W∣∣2for (G,L)=(γ,νi),∣∣−αYCYsinθWUνi~B+αWCWcosθWUνi~W∣∣2for (G,L)=(Z,νi),α2WC2W(∣∣ULli~W∣∣2+∣∣URli~W∣∣2).for (G,L)=(W,li). (A.6)
where is a mass of the gauge boson, and , and are the mixings that diagonalize the mass matrices of Eqs. (A.3) and (A.4).
In the limit of , the mixings between the gauginos and the higgsinos become irrelevant. Assuming that the R-parity violation is small, , and in Eq. (A.6) are approximated as
FGL (CY,CW,m~B,m~W)≃ ⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩∣∣ ∣∣αYCYcosθWgY⟨~νi⟩√2m~B−αWCWsinθWg2⟨~νi⟩√2m~W∣∣ ∣∣2for (G,L)=(γ,νi),∣∣ ∣∣αYCYsinθWgY⟨~νi⟩√2m~B+αWCWcosθWg2⟨~νi⟩√2m~W∣∣ ∣∣2for (G,L)=(Z,νi),α2WC2W∣∣∣g2⟨~νi⟩m~W∣∣∣2for (G,L)=(W,li), (A.7)
where is the sneutrino VEV induced by the R-parity violation.
As can be seen from (A.7), the branching fractions are determined by . When either or is sufficiently small, the decay rates are reduced to the expressions in Sec. 2.1. If the PQ quarks are embedded in a complete vector-like multiplet of the GUT, they become . Moreover, if the GUT relation is assumed for the gaugino masses, they satisfy | {"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": 0.9850772619247437, "perplexity": 1646.283815793802}, "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/1664030334332.96/warc/CC-MAIN-20220925004536-20220925034536-00346.warc.gz"} |
https://rupress.org/jem/article/79/3/267/4766/THE-SIZE-OF-INFLUENZA-VIRUS | The sedimentation behavior of influenza virus in dilute solutions of electrolyte was found to be quite variable. At times the virus activity appeared to sediment at a rate comparable with that of particles about 80 to 120 mµ in diameter, at other times at a rate comparable with that of particles about 10 mµ in diameter, and at still other times the bulk of the activity appeared to sediment at a rate comparable with that of the larger particles and the residual activity at a rate comparable with that of the smaller particles. However, in the presence of a sucrose density gradient, the virus activity was always found to sediment with a rate comparable to that of particles about 80 to 120 mµ in diameter; hence it appeared that the variable sedimentation behavior in dilute electrolyte solution was due to convection or mechanical disturbances during centrifugation.
About 30 per cent of the high molecular weight protein present in the allantoic fluid of chick embryos infected with the F 12 strain of influenza virus was found to consist of a component having a sedimentation constant of about 30 S, and hence a probable particle diameter of about 10 mµ. The residual protein of high molecular weight was present in the form of a component having a sedimentation constant of about 600 S, and hence a probable particle diameter of about 70 mµ. The proportion of the 30 S component in allantoic fluid of chick embryos infected with the PR8 strain of influenza virus was found to be considerably less. The 600 S and 30 S components of F 12 allantoic fluid were purified and separated by differential centrifugation. The purified preparations of the 600 S component were found to possess a specific virus activity from 100 to over 10,000 times that of the purified preparations of the 30 S component, the difference in activity apparently depending only on the degree of fractionation of the two components. The purified 30 S component was found to sediment normally in the presence of 12 per cent sucrose, whereas the small residual virus activity of such preparations was found to sediment in the presence of a sucrose density gradient with a rate comparable to that of much heavier particles. It is concluded that influenza virus activity is not associated with material having a particle diameter of about 10 mµ, but is associated solely with material having a sedimentation constant of about 600 S and hence a probable particle diameter of about 70 mµ.
This content is only available as a PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8156417608261108, "perplexity": 1060.357313048192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988927.95/warc/CC-MAIN-20210508211857-20210509001857-00286.warc.gz"} |
https://www.physicsforums.com/threads/plasma-frequency.311444/ | # Plasma frequency
1. May 3, 2009
### Thierry12
Why are electromagnetic waves reflected when they comme in contact with a plasma ( with a frequency lower then the plasma frequency, and im trying to find precisely why the wave cannot pass ). I was also wondering if conductors (metals) are considered to have a plasma frequency
ty
2. May 3, 2009
### Born2bwire
A plasma is a sea of ions and electrons that is generally neutral in charge. Generally, we assume that the ions have much larger mass than the negative charges, being that the ions are the nucleus and electrons of an ionized atom and the negative charges the stripped electrons. When an electromagnetic wave hits a conductor, the electric and magnetic fields induce currents in the conductor. These currents produce their own electromagnetic waves that cancel the incident wave. In a perfect conductor, there is no resistance to these currents and so they perfectly cancel the incident wave in the conductor, causing the incident wave to reflect.
When an electromagnetic wave travels through a plasma, the electric field also induces currents due to the Lorentz force, just like with a conductor. We do not consider the ions to move though, because the frequency of the fields are too high. The heavy ions have too much inertia to move along with the high frequency fields. However, the light electrons do move with the fields. The electrons thus induce the same currents as we would find in a conductor giving rise to the cancelling and reflected fields.
However, there are secondary effects on the electrons in the plasma from the magnetic field of the electromagnetic wave. This gives rise to what is called the ponderamotive force. If I recall correctly, the ponderamotive force is what allows the wave to eventually propagate. The ponderamotive force is like a dispersion force, it is a force that acts on the electrons towards the volume of weakest electric field. So without the ponderamotive force, the electrons will be able to produce the wave cancelling currents willy-nilly. However, the ponderamotive force will create a drift in the electrons, upsetting the desired currents and thus allow higher frequency waves to propagate.
Yes, some metals, I don't know if all, do behave as plasmas. The plasma frequency is very high though, for example, silver has a plasma frequency in the terahertz. As I recall most of the plasma modes are surface modes though.
Last edited: May 3, 2009
3. May 3, 2009
### Thierry12
ty for the information | {"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": 0.9737969636917114, "perplexity": 479.4460644551512}, "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/1502886116921.70/warc/CC-MAIN-20170823000718-20170823020718-00545.warc.gz"} |
https://planetmath.org/exampleoffibreproduct | example of fibre product
Let $G$, $G^{\prime}$, and $H$ be groups, and suppose we have homomorphisms $f:G\to H$ and $f^{\prime}:G^{\prime}\to H$. Then we can construct the fibre product $G\times_{H}G^{\prime}$. It is the following group:
$\left\{(g,g^{\prime})\in G\times G^{\prime}\text{ such that }f(g)=f^{\prime}(g% ^{\prime})\right\}.$
Observe that since $f$ and $f^{\prime}$ are homomorphisms, it is closed under the group operations.
Note also that the fibre product depends on the maps $f$ and $F^{\prime}$, although the notation does not reflect this.
Title example of fibre product ExampleOfFibreProduct 2013-03-22 14:08:38 2013-03-22 14:08:38 archibal (4430) archibal (4430) 4 archibal (4430) Example msc 14A15 Group Homomorphism CartesianProduct | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 11, "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": 0.995336651802063, "perplexity": 766.1320874350225}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202689.76/warc/CC-MAIN-20190322200215-20190322222215-00133.warc.gz"} |
https://uwaterloo.ca/graduate-studies-academic-calendar/node/7140 | # Symmetric Functions
Subject:
Combinatorics & Optimization (CO)
Catalog number:
631
Unit weight:
0.50
Meet type:
LEC
NUM
Cross-listing(s):
N/A
Requisites:
N/A
Description:
The ring of symmetric functions, standard bases, the Hall inner product. Young tableaux. The Robinson-Schensted-Knuth correspondence, the hook-length formula, the Jacobi-Trudi formula, the Pieri rule, the Littlewood-Richardson rule. Representation theory of the symmetric groups. Enumeration of plane partitions. Enumeration of maps on surfaces. Other topics.
Topic titles:
N/A
Faculty:
Mathematics (MAT) | {"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": 0.8152496814727783, "perplexity": 4302.540584549399}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991737.39/warc/CC-MAIN-20210514025740-20210514055740-00557.warc.gz"} |
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