Eduard G. Nikonov, Rashid G. Nazmitdinov, Pavel I. Glukhovtsev
The problem of finding equilibrium configurations of one-component charged particles, induced byexternal electrostatic fields in planar systems, is a subject of active studies in fundamental as well in experimentalinvestigations. In this paper the results of numerical analysis of the equilibrium configurations of chargedparticles (electrons), confined in a circular region by an infinite external potential at its boundary are presented.Equilibrium configurations with minimal energy are searched by means of special calculation scheme. Thiscomputational scheme consists of the following steps. First, the configuration of the system with the energy asclose as possible to the expected energy value in the ground equilibrium state is found using a model of stableconfigurations. Next, classical Newtonian molecular dynamics is used using viscous friction to bring the systeminto equilibrium with a minimum energy. With a sufficient number of runs, we obtain a stable configurationwith an energy value as close as possible to the global minimum energy value for the ground stable state fora given number of particles. Our results demonstrate a significant efficiency of using the method of classicalmolecular dynamics (MD) when using the interpolation formulas in comparison with algorithms based on MonteCarlo methods and global optimization. This approach makes it possible to significantly increase the speed atwhich an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to theMetropolis annealing simulation algorithm and other algorithms based on global optimization methods.