Discrete Transformations in the Thomson Problem

Abstract

A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each $N$-charge solution. This raises the total energy by $N$ as an upper limit to each $(N+1)$-charge solution. Minimization of energy to $U(N+1)$ is well fit with $-0.5518(3/2)\sqrt{N}+1/2$ for up to $N=500$. The energy distribution due to this displacement exhibits correspondences with shell-filling behavior in atomic systems. This work may aid development of more efficient and innovative numerical search algorithms to obtain $N$-charge configurations having global energy minima and yield new insights to atomic structure.

7 pages, 5 figure

References in corpus (2)

• Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure
• Discrete Charge Dielectric Model of Electrostatic Energy

Cited by in corpus (2)

• Distributing many points on spheres: minimal energy and designs
• Kinetic Transition Networks for the Thomson Problem and Smale's 7th Problem