Defect free global minima in Thomson's problem of charges on a sphere

Details Defect free global minima in Thomson's problem of charges on a sphere Defect free global minima in Thomson's problem of charges on a sphere

2005-09-19

arxiv.org/abs/cond-mat/0509501v2

Phys. Rev. E, 73, 036108 (2006)

Physics

Condensed Matter

Other Condensed Matter

Revisions in Tables and References

Scientific paper

10.1103/PhysRevE.73.036108

Given $N$ unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy $\sum_{i>j=1}^N 1/r_{ij}$? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For \hbox{$N = 10(h^2+hk+k^2)+ 2$} recent theoretical work based on elasticity theory, and subsequent numerical work has shown, that for $N \sim >500$--1000 adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy. Here we show that in fact this approach holds for all $N$, and we give a complete or near complete catalogue of defect free global minima.

Affiliated with

Also associated with

No associations

Rating

Defect free global minima in Thomson's problem of charges on a sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Defect free global minima in Thomson's problem of charges on a sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Defect free global minima in Thomson's problem of charges on a sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-299150