Energy minimisation of repelling particles on a toric grid

Details Energy minimisation of repelling particles on a toric grid Energy minimisation of repelling particles on a toric grid

2012-03-02

arxiv.org/abs/1203.0408v1

Mathematics

Optimization and Control

Scientific paper

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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