Boundary Value Problems and Multiscale Coupling Methods for Kinetic Equations

Models of Collective Dynamics with complex orientation mechanisms

Pierre Degond

Imperial College London


We will report on recent developments on self-propelled particle models with complex orientation mechanisms. The most simple and widely studied orientation mechanism involves polar orientation and follows from the seminal work of Vicsek and co-authors. The macroscopic dynamics of this model gives rise to the SOH model (self-organized hydrodynamics) which has been shown to exhibit many surprising and unusual behavior. However, other orientation mechanisms can be found in nature such as nematic alignment or alignment of the full body configuration. We will present microscopic and macroscopic versions of these dynamics and outline some applications to bacterial colonies and flocking.