Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries

J. Batle, Armen Bagdasaryan, M. Abdel-Aty and S. Abdalla

Physica A: Statistical Mechanics and its Applications, 2016, vol. 451, issue C, 237-250

Abstract: Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the Sd−1−sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.

Keywords: Thomson model; Infinite charge system; Structures and symmetry in higher Euclidean dimensions; Non-Euclidean geometries (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:451:y:2016:i:c:p:237-250

DOI: 10.1016/j.physa.2016.01.069

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