A Mexican hat dance: Clustering in spatially non-exclusive particle systems.

Abstract

The dynamics and spontaneous organization of coupled particles is a classic problem in modeling and applied mathematics. Here, we examine the behavior of particles coupled by a Mexican hat type potential-one exhibiting finite local repulsion transitioning to distal attraction, leading to an energy-minimizing "preferred distance." When confined by a background potential well, these particles exhibit intricate self-organization into "stacks" with varying sizes and positions. We examine bifurcations of these high-dimensional arrangements, yielding tantalizing glimpses into a rich dynamical zoo of behavior.