Talk:Thomson problem

annotations wanted
Where did the table come from? What is $$\mathbf{r}_{i}$$? &mdash;Tamfang 06:02, 28 March 2007 (UTC)

Yes, whoever put up this list should have added some explanations...! I guess I've figured it out by now. r_i of course are the positions of the points (charges), thus \sum r_i is essentially the center of mass. Theta_1 must be the smallest angle between any 2 points, no? Then we imagine to make each configuration into a (convex) polyhedron, thus nu_3, nu_4 etc are the numbers of vertices where 3,4... edges meet, e the total number of edges, f_3, f_4 number of triangle and quadrilateral faces.

Yes, and where did the list come from? (I take it that only for small numbers it is proven that these are the actual mimimum energy configuration...!) Also in order would be a link for the symmetry type notation, e.g. the article on point groups in 3D: Point groups in three dimensions [Also: From 160 on there are gaps in the list. No data, or simply C_1 (no symmetry)?]85.0.224.208 (talk) 20:49, 1 February 2008 (UTC)

I've now added a paragraph at the top of the table, explaining the table entries. (Hope it's ok...) 85.3.160.49 (talk) 12:50, 26 February 2008 (UTC)


 * I think every entry on the table should be referenced as I doubt that most of the data is current. I believe the most accurate and current data are to be found (interactively) on the Thomson Problem applet at Syracuse University's webpage (otherwise, feel free to hunt down and compare every article published with current numerical solutions). This table of data should not be 'static' unless it cites the source of each energy solution -- these have changed, and will change (slowly) over time. It should be made specifically clear that these data are obtained (primarily) by numerical minimization of the total energy and are subject to change. I have never liked this table beyond the occasional note of symmetry group(s) and have thus never cited it in my work. TJ LaFave (talk) 03:47, 12 February 2014 (UTC)

polyhedra
There must be a better word than equivalent for two polyhedra having the same topology. Tamfang (talk) 05:21, 17 October 2009 (UTC)

value for 7 charges
Is the energy value for 7 charges correct? I think there might be a typo (i.e. it should be ...977... instead of ...997...).


 * Wow, how did you spot that? I get 14.452977414221342.  I'll change it.  —Tamfang (talk) 18:25, 30 May 2012 (UTC)

I'm doing a project on this right now (using a genetic algorithm to find the best configuration) and this was the only result (so far) I couldn't reproduce to within my numerical accuracy. — Preceding unsigned comment added by 128.131.48.66 (talk) 12:54, 31 May 2012 (UTC)

Did JJ Thomson *really* pose the Thomson problem?
I think the claim on this page, that J.J. Thomson posed this problem in 1904 as part of his proposal for an atomic model, is NOT true. I know that several papers cite the 1904 paper as a reference for background information on the Thomson Problem. However, I don't think this specific mathematical problem is described in the 1904 paper.

It is my understanding that the name of this problem is attributed to JJ Thomson as it is similar to the plum pudding model (which, by the way, Thomson did not himself label!).

I changed the word "created" -- 1) because JJ Thomson didn't create the "plum pudding model", but mostly because, 1) he merely proposed it as an atomic model based on the available knowledge of the day (which I've clarified in the introductory paragraph -- and will likely dig into my papers and books to include some useful citations).

If my memory serves me well, it was Whyte who may have first attributed Thomson to this problem. However, there may be a more extant source. Does anyone have information this? — Preceding unsigned comment added by Tjlafave (talk • contribs) 03:55, 12 February 2014 (UTC)

ambiguity
This article currently mentions

vs.
 * "The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration ..."
 * "Related problems include the study of the geometry of the minimum energy configuration ..."

That sounds like exactly the same problem stated in different words. What exactly is the distinction between them, if any? --DavidCary (talk) 03:43, 2 May 2014 (UTC)
 * I would interpret that as identifying transformations/subgroups in the solution; vs. just numerical solutions.

Rrogers314 (talk) 15:53, 31 January 2019 (UTC)

contradiction
This article implies that "known solutions" exist only for N = 1 through 6, and N = 12.

However, the Kevin Brown reference seems to be saying that it is known that there is only one stable local equilibrium (which therefore must be the unique global minimal-energy configuration) for N = 1 through 15. That reference also seems to be saying that "known solutions" exist for N = 1 through 32.

How can we fix this (apparent) contradiction? --DavidCary (talk) 03:43, 2 May 2014 (UTC)

obscure vandalism
An anonymous user changed the number of edges in #5 (triangular dipyramid) from 9 to 8. I reverted. Since the change was hard to find, I shoulda said in the edit summary what it was. —Tamfang (talk) 05:52, 21 May 2014 (UTC)

distance on the sphere
What happens if distance is measured on the sphere (along a great circle) rather than on a straight line? Do the optimal configurations remain the same? If there is literature on this, some mention in the article would be nice. Zerotalk 02:05, 26 July 2014 (UTC)


 * Hm! In that case I'd want to change the energy function from 1/d to something like cosecant(d/2). —Tamfang (talk) 07:21, 26 July 2014 (UTC)

e_i = e_j
It's a detail, but it is somehow "contradictory" to introduce e_i and e_j when stating at the same time, right from the beginning, that they are equal, and nonetheless to continue writing e_i e_j in the subsequent displayed formula, before finally setting both of them equal to 1 (lol...) &mdash; MFH:Talk 04:58, 1 June 2018 (UTC)

latitudes

 * ... The great circle is often considered to define an equator about the sphere and the two points perpendicular to the plane are often considered poles to aid in discussions about the electrostatic configurations of many-N electron solutions. ...

I dunno, an arrangement can have dihedral symmetry without having any electrons on either the 'poles' or the 'equator'; and with no dihedral symmetry, do these terms even mean anything? I'd cut the sentence. —Tamfang (talk) 18:22, 18 April 2024 (UTC)