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arXiv · 2502.06256

Dynamical Spreading and Memory Retention Under Power Law Potential

Ido Fanto·Yuval Rosenblum·Ori Harel·M. Y. Ben Zion·Naomi Oppenheimer
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Abstract

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.

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Ido Fanto, Yuval Rosenblum, Ori Harel, M. Y. Ben Zion, Naomi Oppenheimer. 2025-02-10. Dynamical Spreading and Memory Retention Under Power Law Potential. https://doi.org/10.1103/v1nk-pfzj

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