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arXiv · 1203.0408

Energy minimisation of repelling particles on a toric grid

Niek Bouman·Jan Draisma·Johan van Leeuwaarden
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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.

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Niek Bouman, Jan Draisma, Johan van Leeuwaarden. 2012-03-02. Energy minimisation of repelling particles on a toric grid. https://arxiv.org/abs/1203.0408

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