User talk:PAR/archive 3

Learning about contact and symplectic geometry

Since you posted the link to the paper you're trying to understand, I see now that you're approaching things from more of a physics point of view than a pure math one. (I suppose I could have guessed that if I had looked at your user page earlier!) In that case, I recommend the book Mathematical Methods of Classical Mechanics by V.I. Arnold. It has enough mathematical rigor to teach the subject properly but uses examples from classical dynamics. Also recommended is Ted Frankel's book The Geometry of Physics which takes a slightly slower pace than Arnold. Frankel's book, that I recall, doesn't spend much time on contact stuff, whereas Arnold's book has a huge and very well-written appendix on contact geometry. I haven't personally seen the connection between contact geometry and thermodynamics before, but then again, I'm a pure math guy. I'm sure someone has written on it; you may want to try a Google search and see what comes up. VectorPosse 09:05, 15 December 2006 (UTC)

Hi.

You might look for papers by Mrugala, Chen (e.g. Chen "On the geometric structure of thermodynamics") or Differential Geometry books by Hermann, e.g. "Geometry, Physics and System"

The old idea is to use the Differential Geometric Picture to convert PDE's of first order to a system of ode's. A thermodynamical state is then interpreted in this picture and it's evolution over time as well. This takes its origin already in ideas by Caratheodory.

good luck. Stscho 07:03, 24 April 2007 (UTC)

Your edits to Thermodynamic Equations are unacceptable.

Your edits to Thermodynamic Equations remove vast amounts of work done by large numbers of people over long periods of time. The page was a valuable reference, much like the tables of integrals and tables of derivatives Wikipedia manages, and were depended on by many people. I intend to revert your alterations within a few days unless there is a substantial consensus against it. And no, the suggested page "Brigdeman Equations", in addition to not being obvious to the person looking for a reference, also does not contain most of the same information in spite of your claims otherwise. --Pmetzger 23:59, 18 December 2006 (UTC)

Can you please tell me what equations are missing that are so important? Before, this page was a hodge-podge of random equations, many of which used undefined symbols. I brought some order to the page and included 95 percent of the old equations, leaving out unintelligible ones, and perhaps five intelligible ones. I will be glad to restore those five, put them in the structure, but I cannot believe that the original mess was better than it is now. I will leave a note at Wikipedia talk:WikiProject Physics and see what others think. PAR 02:09, 19 December 2006 (UTC)

As I said elsewhere, my apologies for being too angry about it. I would have much preferred if you had discussed your proposed changes first so we could have done them in a more orderly way. An article containing the content you wrote was a good thing, but it conflicted with what went before -- I would have suggested that we rename the original article to "Table of thermodynamic equations" (as has now been done after the fact) and we would then have started a new article with the content you produced, but that's all water under the bridge now. I'm probably going to take this as an opportunity to do lots of cleanup on the table of thermodynamic equations anyway -- they could be presented more consistently and more reasonably than is currently the case. --Pmetzger 18:46, 20 December 2006 (UTC)

Ok, no problem. I was thinking there would be no objection, which is why I acted so abruptly. PAR 22:56, 20 December 2006 (UTC)

Further work

More importantly, I'd like to work together to fix a few things since you clearly have an interest in this area as do I. For example, it would be nice to decide on a single convention across the Wikipedia articles on thermodynamics for the sign of work (i.e. is positive work to represent work on a system or work by a system). As I am currently mostly a chemist I am naturally biased towards the "positive is work on, negative is work by" definition, and of course physicists would be biased in the other direction, but it really doesn't matter so long as we can hyperlink to an explanation in one place about the convention. Having one convention means that all our equations will be consistent across pages and across explanations, which would be nice. Presumably this would be a reasonable thing to discuss on the Wikipedia chemistry and physics project pages.

Also, I note that the article on Maxwell relations does not show the four Gibbs equations that they correspond to. This makes the article somewhat more opaque than it needs to be -- given the Euler reciprocity relation and the Gibbs equations the Maxwell relations just pop out with no effort. Thoughts? --Pmetzger 18:46, 20 December 2006 (UTC)

Well, I am of the dU=TdS-PdV school, so we agree on that. All of the articles I have seen use this convention and I try to use it when editing, but maybe I missed some. Regarding the Maxwell relations, I thought it was pretty simple to see each one as equating two expressions for the second derivative of a thermodynamic potential, using Euler reciprocity. For example, the first one is really just saying that

${\frac {\partial }{\partial S}}\,\left({\frac {\partial U}{\partial V}}\right)={\frac {\partial }{\partial V}}\,\left({\frac {\partial U}{\partial S}}\right)$

The other three are the same, only using A, H, and G instead of U. Could you tell me the derivation involving the Gibbs equations and the Euler reciprocity relation? (I'm not sure what "Gibbs equations" are). Thanks - PAR 22:56, 20 December 2006 (UTC)

You are quoting the derivation in terms of the Gibbs equations. The Gibbs equations are

dU = TdS-PdV

dH = TdS+VdP

dA =-SdT-PdV

dG =-SdT+VdP

However the explanation on the page doesn't explicitly list them or explain explicitly that the Euler reciprocity relation then implies that because, say, dH=TdS+VdP that $T={\frac {\partial H}{\partial S}}$. It would be nice if these things, which we understand very well, were made explicit rather than implict. It is obvious if you know it, but if you don't know it you need to have the intermediate steps in the reasoning spelled out. I might perhaps do that work myself. --Pmetzger 15:45, 21 December 2006 (UTC)

Ok, I can't do much today, but I will do it tomorrow, unless you get there first. PAR 17:47, 21 December 2006 (UTC)

I've just added a section to Maxwell relations to clarify the derivation. Please let me know if you have any changes to propose in it. (We might want to hyperlink some of the steps to explanations of the math.) --Pmetzger 19:17, 21 December 2006 (UTC)

Efficient algorithm for polylog

Hi,

I just posted a paper An efficient algorithm for computing the polylogarithm and the Hurwitz zeta functions (11 pages) with the following abstract:

This paper develops an extension of the techniques given by Borwein's paper "An efficient algorithm for computing the Riemann zeta function", to the polylogarithm and the Hurwitz zeta function. The algorithm provides a rapid means of evaluating Li_s(z) for general values of complex s and the region of complex z values given by |z²/(z-1)|<3.3. This region includes the the Hurwitz zeta ζ(s,q) for general complex s and real 1/4≤ q ≤3/4. By using the duplication formula, the range of convergence for the Hurwitz zeta can be extended to the whole real interval 0<q<1, although the algorithm does run logarithmically slower as it approaches the endpoints. In particular, this algorithm allows the exploration of the Hurwitz zeta in the critical strip, where fast algorithms are otherwise unavailable.

I thought you might be interested; if so, please take a look, let me know what you think. linas 05:55, 28 December 2006 (UTC)

Moved my comments to your talk page

After much work, its now retitled as An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions, has bloated to 31 pages, and is nearing completion. Its got oodles of pretty pictures, which you might enjoy.

However, I've yet another question to pester you with: have you ever seen a clear, simple discussion of the cuts/branches/monodromy for the polylog? It seems easy enough, but the details have tripped me up for a while. My article now includes a longer section on this, but the notation I'm introducing is akward ... linas 05:02, 5 February 2007 (UTC)

I dont think I have. I remember when writing the polylog article, that was the number one issue which caused me the most headaches. I'm a physicist, not a mathematician, so it was a double headache. I believe I finally got it right, including the places where it tripped up people like Erdelyi, but the best I can say is that all known errors have been removed. I will take a look at your paper, particularly the notation part. I always have believed that getting the notation right was half the battle. PAR 06:52, 5 February 2007 (UTC)

Thanks. I may have failed to copy the latest draft over to the web site when I posted the above note. The monodromy is Z+Z not Z as the WP article implies: there are two branch points, not one. You can't see the second branch point on the main sheet. That's one of the subtlities that tripped me up for a while. linas 15:11, 5 February 2007 (UTC)

Where is the second branch point? I only remember one (finite) branch point. PAR 16:30, 5 February 2007 (UTC)

TfD nomination of Template:Standard test

Template:Standard test has been nominated for deletion. You are invited to comment on the discussion at the template's entry on the Templates for Deletion page. Thank you. --Oden 21:14, 12 January 2007 (UTC)

No personal attacks

Please see Wikipedia's no personal attacks policy. Comment on content, not on contributors; personal attacks damage the community and deter users. Note that continued personal attacks may lead to blocks for disruption. Please stay cool and keep this in mind while editing. Thank you. --Oden 01:17, 13 January 2007 (UTC)

I'm not attacking you. I am pointing out that you made a mistake. Thats not the same as a personal attack. stay cool yourself. PAR 16:23, 13 January 2007 (UTC)

Image:Airplane24.png listed for deletion

An image or media file that you uploaded or altered, Image:Airplane24.png, has been listed at Wikipedia:Images and media for deletion. Please look there to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Oden 14:12, 14 January 2007 (UTC) --Oden 14:12, 14 January 2007 (UTC)

The same applies for:

• Image:Boats24.png
• Image:Goldhill24.png
• Image:Mouse.png
• Image:Zelda24.png
• Image:Barbara24.png
• Image:Masuda2.png
• Image:Masuda1.png
• Image:Sailboat24.png
• Image:House24.png
• Image:Peppers2.png
• Image:Peppers.png
• Image:Tiffany24.png
• Image:Baboon24.png

--Oden 00:52, 15 January 2007 (UTC)

You have violated the 3-revert rule on Standard test image page

You said: No formal report this time. Next time I file a formal report. PAR 03:40, 15 January 2007 (UTC)

3RR does not apply to removing vandalism. Also don't threaten action, if you believe in it go ahead and do it. Just read WP:OWN first. --Oden 03:43, 15 January 2007 (UTC)

PI in Plankian locus

Hate to disappoint you but ther is PI. It's either source where you looked formula up, or ISO standard is wrong. ISO standard gives formula in the form c1*lambda^-5*... and c1 value, but if you divide c1 by 2ch (like you insist) you will have exactly 3.141592... so PI is there. —The preceding unsigned comment was added by 195.137.203.137 (talk) 13:32, 15 January 2007 (UTC).

I'm rather sure there is no pi. Where is the ISO standard you mention? Is it on the web somewhere so I can look at it? PAR 17:20, 15 January 2007 (UTC)

Oh yeah it's in many places, but they kinda live from selling it (I happen to have a free hard copy). See http://www.iso.org/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=30604 Meanwhile I will try to find more info on this PI and where it came from. 82.207.27.24

Looky here, also PI for some reason 82.207.27.24

more 82.207.27.24

derivation, gives formula with PI after "The flux radiated from the surface of a black body is related to the energy density" at page 2 (do you realize if this is so, plank's law main article will also have to be edited ?) 82.207.27.24

more PIs - this one is interesting in the way that it has this law in exactly the same form it is given in ISO standard section 7.1 I was referring to (via c1 and c2 constants)... did I made my point yet? 82.207.27.24

one thing bothers me, they use CGS units but I don't think that's the cause (because numbers match) 82.207.27.24

Ok, thanks for those references, this is interesting. What they are displaying is the flux F(λ,T), which is the total power going through a unit area on a black body, per unit wavelength. What is shown in this article is the intensity I(λ,T), which is the flux per unit solid angle. The two are related by:

$F(\lambda ,T)=\pi \,I(\lambda ,T)$

I could derive that if you are interested. Anyway, I did not realize the flux expression was so widely used, so this is something that is new to me. Thanks again for the references, especially the derivation one. PAR 06:07, 16 January 2007 (UTC)

but then, shouldn't either F or I have steradian somewhere in their units? Neither seem to have one? 195.137.203.137

The intensity I does, its dimensions are power per unit area per unit solid angle per unit wavelength. If you use SI units, that comes out to watts per meter squared per steradian per meter. In the Planck's law of black body radiation it says "per unit solid angle" and if you click on that, you see that steradians are the units that are usually used to measure solid angle. PAR 20:07, 16 January 2007 (UTC)

It doesnt say so anywhere in Planckian locus 195.137.203.137

Well, it should. I will fix that. Also - it is bad form to erase a talk page. You should have left the discussion on the Planckian locus page, even if is evidence of a mistake. Everybody makes mistakes, so its no big deal. (See added discussion on that page). PAR 18:27, 17 January 2007 (UTC)

Info on the sailboat

Hi! Do you know where the sailboat test image comes from? I like it very much! It's the 50's style colouring and scene (I envision a trip with the family to the lake on a Sunday) that captivates me. Thanks. —Bromskloss 10:50, 17 January 2007 (UTC)

Hello - its availiable from various test image sites, but if you download the Wikipedia version it will be the same image, since it is a standardized image. PAR 20:26, 21 January 2007 (UTC)

Ah, yes, but I thought that if I could find the origin of the image, I could perhaps get it in a higher-quality version. You see, I do not intend to use it as a test image, only enjoy myself looking at it. —Bromskloss 08:44, 25 January 2007 (UTC)

No, sorry, I don't have any more information on it. Its been used as a test image in the image processing literature, so if you could find where it was first used, that author might be helpful. Actually, any author might be helpful. Thats how I would start tracking it down. PAR 14:11, 25 January 2007 (UTC)

SVG

Hey PAR, I just wanted to comment on your statment over at Talk:Bohr model

"I use Adobe Illustrator which can save an SVG file, but it is not compatible with Wikipedia, so I convert to a pixel picture and save as PNG."

So, SVG does work on Wikipedia, like as used in,

• Compton_scattering
• Mandelstam_variables
• Double_pendulum

Perhaps it's a browser issue with you? I know firefox 2.0 seems to work the best with them.

For all other browsers, there's one issue that I've seen cause SVG images not to show up in Wikipedia correctly, and that's if the image is forced to have a size that doesn't have the same height/width ratio as it was uploaded with. Like, take the Double pendulum image listed above, it's displayed with the code

[[Image:Double-Pendulum.svg|thumb|right|272px|An example of a double pendulum.]]

If you change that "272px" to certain, specific values (AND you're not using firefox 2.0), then the image doesn't show up for reasons I can't explain. Does this help any? Or were you having other problems with SVG? JabberWok 02:52, 26 January 2007 (UTC)

Principle of maximum work

moved to: Talk:Principle of maximum work for reference purposes.

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thanks

thanks for fixing up the math in axis angle, it was my first time trying to use the markup Kborer 22:04, 31 January 2007 (UTC)

Could you check the equation for ω under the section axis angle#Log map from SO(3) to so(3)? I think its wrong, it should be R not r, and the indices are wrong. Thanks - PAR 23:00, 2 February 2007 (UTC)

Pressure/density variation article

Hi PAR, what do you think of this article? I just posted it. I thought you might like it? Talk later. --Sadi Carnot 08:45, 2 February 2007 (UTC)

Hi - I looked at it, and I see I will have to read it more closely. I'm trying to remember now how my high school was laid out. PAR 06:55, 5 February 2007 (UTC)

Yes, I just thought you might like it, in that it gives an interesting angle on thinking about how macroscopic pressure arises from microscopic atomic and molecular interactions. P.S. you might like to comment on this recent image revert. Talk later. --Sadi Carnot

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I added permissions and source, and removed the templates. PAR 06:31, 8 February 2007 (UTC)

Naming of the categories for Entropy

There's a discussion at Wikipedia:Categories_for_discussion/Log/2007_March_7#Category:Entropy_in_thermodynamics on the appropriate names for the categories for entropy. I'd be interested to read your input. I still waver as to whether Category:Entropy in thermodynamics or Category:thermodynamic entropy is preferable; but there are other people who don't like the way I've split up the categories at all, never mind what they get called. Would be good to hear what you think. -- Jheald 00:50, 12 March 2007 (UTC)

Hi- Sorry, I've been away for a while, but looking at the results of the discussion, I am in favor of the rename result.

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Zipf's law infobox

I just corrected what I believe must've been mistakes in the "support" and "mode" entries in the infoboxes on Zipf's law and Zipf-Mandelbrot distribution. Since you were the one who added those infoboxes in the first place, I thought I should let you know, just in case I may have made some stupid mistake myself. Anyway, thanks for your contributions to those articles, and to our mathematics articles in general. —Ilmari Karonen (talk) 01:37, 13 May 2007 (UTC)

van der Waals equation

Hi PAR, I noticed that you entered quite some time ago an equation for the Helmholtz free energy in the article van der Waals equation. I could understand your equation (for the special case of an ideal gas) if ${\hat {c}}_{v}$ were 3/2. Usually one takes 3Nk/2 for the specific heat of an ideal gas, but if your value is per particle, then there is still a factor k too much. I tried to find your formula in some textbooks, but I failed. I am intending to introduce a derivation of the vdW equation in the manner of T.L. Hill (Statistical Thermodynamics) and I would like to have it seamless with your equation. To that end I need ${\hat {c}}_{v}=3/2$. Any comments?--P.wormer 13:40, 13 May 2007 (UTC)

• Addendum: looking at the article ideal gas I saw that indeed ${\hat {c}}_{v}=3/2$ (for a monoatomic gas, which is the situation for the van der Waals equation). To me this notation was quite confusing and seems unnecessary in this context. A propos thermodynamical notation. I saw that you are somewhat involved in it. I noticed F and A for Helmholtz free energy, p and P for pressure, k and k_B for Boltzmann (should be k_B).--P.wormer 15:58, 13 May 2007 (UTC)

Hi - I take it that everything is clear now, except for the symbols? IUPAC is the standard for symbols, A should be used always for Helmholtz free energy, P for pressure, I'm not sure about Boltzmann's constant. I admit I am lax about some of these. If the article uses k for Boltzmann's constant, I use it too, rather than change every occurrence in the article. PAR 23:45, 14 May 2007 (UTC)

In my own papers I'm fairly lax too. In Wikipedia it is different, one clicks from article to article and it were nice if one would find the same notation everywhere. I try to follow SI, IUPAC, and APS as much as possible. (BTW pressure is lowercase p).--P.wormer 08:12, 15 May 2007 (UTC)

Checking IUPAC Gold Book, yes, pressure is lowercase p. I totally agree we should have consistent, IUPAC notation everywhere, except perhaps for certain contentious cases (e.g. "Helmholtz free energy", rather than "Helmholtz energy"). I intend my future edits to follow IUPAC even more closely. PAR 01:00, 16 May 2007 (UTC)

I'm still observing the "Helmholtz (free) energy" issue from afar  ;-)p

Sorry to digress, PAR, but I would also like to voice my appreciation for your many and varied contributions to a number of articles.

—DIV (128.250.204.118 05:49, 9 July 2007 (UTC))

Well, I haven't been making any contributions lately, but I still check in to see how things are going. PAR 19:09, 10 July 2007 (UTC)

Image:Airplane24.png

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Image:Baboon24.png

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Image:Barbara24.png

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Image:Boats24.png

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Image:Goldhill24.png

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Image:House24.png

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w

Planck's Law

I'm a little confused by opening section on Planck's Law page.

A little rusty on LaTeX. Rusty on my physics, too, maybe that is why I have this question.

$\int I(\nu ,T)\,d\nu =\int I(\lambda ,T)\,d\lambda$, meaning total energy is same for both.

However, $I(\nu ,T)\,d\nu =I(\lambda ,T)\,d\lambda$ is not true in the general case, since these are just rectangles summed by the integration, and while the sum is equal, individual rectangles need not be equal, unless they happen to be the same rectangle.

It seems that the second equation should be obtained by substituting $\nu ={\frac {c}{\lambda }}$ and $d\nu ={\frac {-c}{\lambda ^{2}}}\,d\lambda$ into first one, so why does minus sign not appear until third equation?

Wjifkri 16:30, 6 September 2007 (UTC)

Image:Lognormal distribution PDF.png

σ=10 seems like it could be positive at x=0

How hard would it be to change the color of the σ=10 line in Image:Lognormal distribution PDF.png from black to e.g. brown so that readers can see that it originates at (0,0) like all the others? I hope you still have the source for whatever you used to draw it. Thanks for all your excellent work on those stats articles. ←Ben^B4 03:32, 7 September 2007 (UTC)

Move means move

I note the edit summary on Francis Marion McDowell of "New Page - moved from Francis M. McDowell, and added to". You did not move the page, you did a copy and paste which threw away the edit history. There was nothing to stop you moving the article. Please use move in future, not copy&paste.

In fact given that all the links point to Francis M. McDowell, I would suggest moving the article back (which is something that you can do). -- RHaworth 23:48, 26 October 2007 (UTC)

Sorry, I have never tried to effectively change the name of an article, and I guess I did it wrong. But assuming that I am willing to do the work to edit all the links, what is the best thing to do here? I am of the opinion that the article should have the full name as its title, rather than just having the middle initial. Sometimes middle initial is the best that can be done, but not in this case. Do you agree? PAR 14:40, 27 October 2007 (UTC)

If you are willing to change all the links, go ahead and do so. I don't think we have any rules. I would say use the form more commonly used in the newspapers of his day. Google would seem to prefer Francis M. McDowell but that may simply be a result of Wikipedia scraping sites. -- RHaworth 17:07, 27 October 2007 (UTC)

I will edit the links. As long as Francis M. McDowell redirects here, I think there should be no problem. PAR 17:13, 27 October 2007 (UTC)

Image:Mae West Signature.png

I have tagged Image:Mae West Signature.png as {{no rationale}}, because it does not provide a fair use rationale. If you believe the image to be acceptable for fair use according to Wikipedia policy, please provide a rationale explaining as much, in accordance with the fair use rationale guideline, on the image description page. Please also consider using {{non-free fair use in|article name}} or one of the other tags listed at Wikipedia:Image copyright tags#Fair_use. Thank you. Armedanode 11:54, 11 November 2007 (UTC)

I have put the rationale in the image, and removed the tag from the signature and the article. PAR 17:29, 11 November 2007 (UTC)