Minimum-Energy Distribution of Point Charges Confined To a Square

Abstract

The minimum-energy configurations of N(2 <= N <= 160) identical classical point charges confined within a square under the effect of a Coulombic 1/r potential have been determined by performing steepest-descent simulations. The energies of the final optimized configurations are given, along with their corresponding structural charge distributions. When all systems evolve in time to reach a minimum-energy configuration, local or global, they are all seen to be in quest of symmetry.