Stochastic, Multiscale Modeling, and Computation Seminar by Jeremy Wu: Mean Field Limit for Congestion Dynamics in One Dimension
Speaker: , assistant professor of mathematics, University of Manitoba
Title: Mean Field Limit for Congestion Dynamics in One Dimension
Abstract: In this talk, I will present joint work with Inwon Kim and Antoine Mellet in which we derive a model for congested transport (a PDE at a macroscopic scale) from particle dynamics (a system of ODEs at the microscopic scale). Such PDEs appear very naturally in the description of crowd motion, tumour growth, and general aggregation phenomena. We begin with a system where the particle trajectories evolve according to a gradient flow with a non-overlapping constraint; the particles have a fixed finite distance of separation from each other. This constraint leads to a Lagrange multiplier which, in the mean field limit (infinite number of particles), generates a pressure variable to enforce the hard-congestion constraint. We rely on both the Eulerian and Lagrangian perspectives for the continuum limit.
Multiscale Modeling and Computation