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Diffusion of finite-size particles and application to heterogeneous domains

Presented by: 
Maria Bruna
Date: 
Monday 20th June 2016 - 11:45 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Co-author: Jonathan Chapman (University of Oxford)

We 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. In particular, we consider a system of impenetrable diffusing spheres and use the method of matched asymptotic expansions to obtain a systematic model reduction. In the second part of the talk, we 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons