Compact expansion of a repulsive suspension

Repulsive interactions govern the dynamics of matter from atoms to animals. Using theory, simulations, and experiments, we find that an ensemble of repulsive particles spreads compactly with a sharp boundary, in contrast to the diffusive spreading of Brownian particles. Starting from the pair interactions, at high densities, the many-body dynamics follow nonlinear diffusion with a self-similar expansion. We give theoretical predictions that we verify experimentally and numerically for the scaling of the dynamics for various forms of potentials. When the interactions are long-ranged, the system retains a long-lived memory of the original pattern. We demonstrate that below a threshold, the initial distribution seeds the resulting pattern, encoding the future structure of an unconfined and dynamically evolving system.