Diffusion of finite-size particles: multiple species and confined geometries Seminar

We discuss nonlinear Fokker-Planck models describing diffusion processes with particle interactions. These models are motivated by the study of systems in biology and ecology composed of many interacting individuals, and arise as the population-level description of a stochastic particle-based model. In particular, we consider a system finite-sized hard-core interacting Brownian particles and use the method of matched asymptotic expansions to obtain a systematic model reduction.

The result is a nonlinear Fokker-Planck equation, with the nonlinear term accounting for the size-exclusion interactions. We will present two
applications: the diffusion of heterogeneous species (e.g. two types of cell populations), and the diffusion in confined domains (e.g. ion transport in channels).