The generalized Thomson Problem

Abstract: 

The question of "How to optimally arrange N repulsive particles on a spherical shell?" can be applied to problems such as virus-morphology, crystallization, discretization of manifolds (e.g. wings of airplanes, numerical integration and optimal placement problems. Finding the most stable ground state energy configuration of N classical electrons (whose pairwise interaction is governed by Coulomb law) constrained to move on the unit sphere in R^ is known as Thomson's problem. We give a survey of the discrete energy problem associated with the energy functional induced by a logarithmic potential log(1/r) or a Riesz s-potential 1/r^s and present joint work with Ed Saff and Doug Hardin (Vanderbilt) and Peter Dragnev (IPFW).