2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

From microscopic to macroscopic models in self-organized dynamics

Sébastien Motsch

University of Maryland

In many biological systems, we observe the emergence of self-organized dynamics (e.g. flock of birds, school of fish, aggregation of bacteria). Modeling is an essential tool to better understand their behavior. Based on experimental data, we introduce some recent models which have been proposed to explain such dynamics. Since those biological systems can reach up to millions of individuals, we discuss in a second part how we can derive "macroscopic models" from these microscopic models using kinetic theory. In contrast with particle systems in physics, models of self-organized dynamics do not conserve momentum or energy. This lack of conservation requires to introduce new tools to derive macroscopic models. For instance, a new type of "collisional invariant" allows us to derive the hydrodynamic limit of a large class of microscopic models. The macroscopic models obtained are non-conservative hyperbolic systems. We present a numerical scheme to investigate the behavior of such systems.