Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916145496326144 |
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| author | Fradon, Myriam Kern, Julian Roelly, Sylvie Zass, Alexander |
| author_facet | Fradon, Myriam Kern, Julian Roelly, Sylvie Zass, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02672 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect Fradon, Myriam Kern, Julian Roelly, Sylvie Zass, Alexander Probability 60K35, 60H10, 60J55, 82D99 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. |
| title | Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect |
| topic | Probability 60K35, 60H10, 60J55, 82D99 |
| url | https://arxiv.org/abs/2306.02672 |