Salvato in:
| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2502.06256 |
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Sommario:
- Power law potentials dictate interactions across scales and matter, controlling the structure and dynamics of inanimate, and living systems. Though the equilibrium distributions of particles with a power law repulsion were extensively studied, their unconfined dynamical evolution gained far less attention -- Yet, living matter is inherently out of equilibrium and is seldom static. Here, we investigate the overdamped dynamic spreading of a dense suspension of particles under repulsive pair-potential of the form $1/r^k$. Coarse graining the pair interactions, we predict that the suspension spreads in a self-similar form, with its radius growing in time as $t^{1/(k+2)}$, independent of the spatial dimension ($d$). We confirm this prediction experimentally in quasi-two dimensions using perpendicularly magnetized colloids with dipolar repulsion ($k=3$). Numerical simulations corroborate the experiments for the $k=3$ case and further predict a categorically different behavior at a critical power law: when $k<d-2$, 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. We demonstrate that below this threshold, the initial distribution seeds the resulting pattern, encoding the future structure of an unconfined, and dynamically evolving system.