Alethea Barbaro (Case Western Reserve University): Kinetics of socially interacting particles
Wednesday, 03.07.2013 16:15 im Raum M5
Abstract: Interacting particles models are often used to describe the dynamics of interacting molecules or other inanimate physical bodies. These models can be justified directly by considering the physical interactions of the bodies with one another. However, since such microscopic models do not serve well for very large numbers of such particles, the evolution is generally modeled at the kinetic or hydrodynamic scale by considering limits of these models (examples include the Boltzmann, Euler, and Navier-Stokes equations). More recently, researchers have been applying these interacting particle models in a much broader context, modeling everything from polymers to insects to birds and fish and even people! In this talk, I will discuss applications of such particle models in the context of socially interacting animals. These models can be quite close to the physical reality but are limited in practice by their computational intensity. In the second half of my talk, I will discuss a kinetic PDE corresponding to this type of interacting particle model and focus on the derivation of macroscopic models from the kinetic model. At the level of the compressible Euler system, we prove that a noise-driven phase transition can occur between a diffusion equation and self-organized hydrodynamics. We then examine diffusive corrections to this system, leading to a wider range of Navier-Stokes-type models for socially interacting animals.