Diffusion of finite-size particles and application to heterogeneous domains

Maria Bruna (University of Cambridge)

23-Oct-2020, 07:00-08:00 (3 years ago)

Abstract: In this talk, I will discuss nonlinear Fokker-Planck models describing diffusion processes with particle interactions. These models are motivated by the study of many-particle systems in biology and arise as the population-level description of a stochastic particle-based model. While mean-field approximations are valid for long-range interactions, here I will show how to tackle the case of short-range interactions such as finite-size or excluded-volume effects. In the second part of the talk, I will discuss how this method can be used to derive an effective transport equation in heterogeneous domains, such as porous media or crowded environments. A nice feature of this approach is that it can easily account for macroscopic gradients in porosity or crowding. I will compare this with an alternative homogenisation method for periodic porous media and show an industrial application concerning filters.

Mathematics

Audience: researchers in the discipline


Barcelona Mathematical Days 2020

Series comments: Note that registration is free but mandatory, and available until Oct 22nd.

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Organizers: Amadeu Delshams, NĂºria Fuster, Marc Masdeu*, Josep Vives
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