Compact expansion of a repulsive suspension

Short-range repulsion governs 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 non-linear diffusion with a self-similar expansion, growing as $t^{1\mathrm{/}4}$; At longer times, thermal motion dominates with the classic $t^{1\mathrm{/}2}$ expansion. A logarithmic growth controlled by nearest-neighbor interactions connects the two self-similar regimes.