# Classifying minimum energy states for interacting particles (II) -- regular simplices

@inproceedings{Davies2021ClassifyingME, title={Classifying minimum energy states for interacting particles (II) -- regular simplices}, author={Cameron Davies and Tongseok Lim and Robert J. McCann}, year={2021} }

Consider densities of particles on R which interact pairwise through an attractive-repulsive power-law potential Wα,β(x) = |x|/α − |x|/β in the mildly repulsive regime α ≥ β ≥ 2. For n ≥ 2, we show there exists βn ∈ (2, 4) and a decreasing homeomorphism α∆n of [2, βn] onto [βn, 4] which can be extended (non-homeomorphically) by setting α∆n(β) = β for β > βn such that: distributing the particles uniformly over the vertices of a regular unit diameter n-simplex minimizes the potential energy if… Expand

#### 2 Citations

Classifying minimum energy states for interacting particles (I) -- spherical shells

- Mathematics, Physics
- 2021

Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the… Expand

Minimizers for a one-dimensional interaction energy

- Physics, Mathematics
- 2021

We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a… Expand

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