Scaling limits for a population model with growth, division and cross-diffusion
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915091594608640 |
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| author | Doumic, Marie Hecht, Sophie Hoffmann, Marc Peurichard, Diane |
| author_facet | Doumic, Marie Hecht, Sophie Hoffmann, Marc Peurichard, Diane |
| contents | Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic stochastic model, write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. Under smoothness and symmetry assumptions for the interaction kernel, we then obtain entropy estimates, which provide us with a localization limit at the macroscopic level. Finally, we perform a thorough numerical study in order to compare the three modeling scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling limits for a population model with growth, division and cross-diffusion Doumic, Marie Hecht, Sophie Hoffmann, Marc Peurichard, Diane Analysis of PDEs Probability Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic stochastic model, write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. Under smoothness and symmetry assumptions for the interaction kernel, we then obtain entropy estimates, which provide us with a localization limit at the macroscopic level. Finally, we perform a thorough numerical study in order to compare the three modeling scales. |
| title | Scaling limits for a population model with growth, division and cross-diffusion |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2410.13329 |