Calendar

Join us in person for refreshments beginning at 1:30 p.m. outside Beckman 3151, Samuel Isaacson will speak at 2 p.m. in Beckman 3269.

Title: Adding Drift to Stochastic Reaction-Diffusion Processes: Model Formulation and Numerical Approximations

Abstract: Particle-based stochastic reaction-diffusion processes are foundational for modeling biological systems. While their basic properties, relation to macroscopic reaction-diffusion PDEs, and numerical approximation methods are now well-established, adding drift to these models introduces significant open questions. Resolving these questions is fundamentally necessary for accurately modeling physical phenomena like volume exclusion and short-range interactions.
 
This talk presents our recent work on particle-based stochastic reaction-drift-diffusion models where drift arises from one- and two-body interactions. We will begin with the physical formulation of these models, demonstrating how satisfying the detailed balance of reaction fluxes at equilibrium constrains reactive interaction functions for reversible reactions. From there, we outline the derivation of convergent jump process approximations for numerical simulations, effectively generalizing the Reaction-Diffusion Master Equation to a convergent model that includes drift. Ultimately, the focus will be on constructing methods that preserve the detailed balance of both drift-diffusion and reaction fluxes, ensuring discrete equilibrium distributions that remain fully consistent with the underlying particle model.