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arXiv · 2410.13329

Scaling limits for a population model with growth, division and cross-diffusion

Marie Doumic·Sophie Hecht·Marc Hoffmann·Diane Peurichard
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Abstract

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.

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Marie Doumic, Sophie Hecht, Marc Hoffmann, Diane Peurichard. 2024-10-17. Scaling limits for a population model with growth, division and cross-diffusion. https://arxiv.org/abs/2410.13329

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