Transport Models for Collective Dynamics in Biological Systems

Phase transitions for self-organized dynamics and sweeping networks

Jian-Guo Liu

Duke University

For some classes of self-organized dynamics and sweeping networks such as flocking of birds, pedestrian flow in corridors, I will present some theoretical derivations from large particle system to the master equation, then to the kinetic equation for the one-particle marginal distribution, then to the hydrodynamic equations. I will then show that both first order and second order phase transitions could appear in these kinetic equations and these hydrodynamics models. Hysteresis behavior will be studied both theoretically and numerically. This is a joint work with Amic Frouvelle of University Paris Dauphine and Pierre Degond of Toulouse.