Possible Global Minimum Lattice Configurations for Thomson's Problem of Charges on a Sphere
Abstract
What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J. J. Thomson posed this question in 1904. For N<=112, numerical methods have found apparent global minimumenergy configurations; but the number of local minima appears to grow exponentially with N, making many such methods impractical. Here we describe a topological/numerical procedure that we believe gives the global energy minimum lattice configuration for N of the form N = 10\(m^{2}+n^{2}+mn\)+2 ( m, n positive integers). For those N with more than one lattice, we give a rule to choose the minimum one.
 Publication:

Physical Review Letters
 Pub Date:
 April 1997
 DOI:
 10.1103/PhysRevLett.78.2681
 Bibcode:
 1997PhRvL..78.2681A