Speaker
Description
Particle-based stochastic reaction-diffusion processes are widely used in modeling biological processes. There is now a well-developed set of results detailing their basic properties, how they rigorously relate to macroscopic reaction-diffusion PDE models, and a variety of numerical simulation methods for their accurate and efficient approximation. In contrast, adding drift to these models introduces a number of open questions.
In this talk, I will describe our recent work on particle-based stochastic reaction-drift-diffusion models in which drift arises from one- and two-body interactions. I will first introduce the physical formulation of these models, illustrating how satisfying detailed balance of reaction fluxes at equilibrium constrains reactive interaction functions for reversible reactions. I will then summarize our work proving the rigorous mean-field large-population limit of such particle models, and outline which types of reaction-drift-diffusion PDEs arise in this limit.
