Energy minimisation of repelling particles on a toric grid
Optimization and Control
2012-03-05 v1
Abstract
We explore the minimum energy configurations of repelling particles distributed over n possible locations forming a toric grid. We conjecture that the most energy-efficient way to distribute n/2 particles over this space is to place them in a checkerboard pattern. Numerical experiments validate this conjecture for reasonable choices of the repelling force. In the present paper, we prove this conjecture in a large number of special cases---most notably, when the sizes of the torus are either two or multiples of four in all dimensions and the repelling force is a completely monotonic function of the Lee distance between the particles.
Keywords
Cite
@article{arxiv.1203.0408,
title = {Energy minimisation of repelling particles on a toric grid},
author = {Niek Bouman and Jan Draisma and Johan van Leeuwaarden},
journal= {arXiv preprint arXiv:1203.0408},
year = {2012}
}