Dynamical Spreading and Memory Retention of Particle Suspensions under Power Law Potential

We study the overdamped dynamic spreading of a suspension of particles under a repulsive power law potential. We predict that the suspension spreads in a self-similar form, with its radius growing in time with a power independent of the dimension. We confirm this prediction experimentally using magnetized colloids with dipolar repulsion. Numerical simulations corroborate the experiments and further predict a categorically different behavior at a critical power, below which the initial distribution is no longer concentrated at the origin. Instead, particles accumulate at the perimeter and retain a long-lived memory of their original pattern. Below this threshold, the initial distribution seeds the resulting pattern, encoding the future structure of a dynamically evolving system.