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arXiv · 2306.02672

Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect

Myriam Fradon·Julian Kern·Sylvie Roelly·Alexander Zass
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Abstract

We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in $\mathbb{R}^d$, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is the occurrence of an attractive short-range dynamical interaction -- known in the physics literature as a depletion interaction -- between the large spheres, which is induced by the hidden presence of the small ones. By considering the asymptotic limit for such a system when the density of the particles is high, we also obtain a constructive dynamical approach to the famous discrete geometry problem of maximisation of the contact number of $n$ identical spheres in $\mathbb{R}^d$. As support material, we propose numerical simulations in the form of movies.

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Myriam Fradon, Julian Kern, Sylvie Roelly, Alexander Zass. 2024-02-25. Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect. https://doi.org/10.1016/j.spa.2024.104319

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