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Mathematical modeling of self-organized dynamics: from microscopic to macroscopic description

PDE and Applied Math Seminar

Speaker: Sebastian Motsch, University of Maryland
Location: 1147 MSB
Start time: Tue, Mar 6 2012, 4:10PM

In many biological systems, we observe the emergence of self-organized dynamics (e.g. flock of birds, school of fish, aggregation of bacteria). To model these phenomena, we can either use "microscopic models" describing the motion of each individual or "macroscopic models" describing the evolution of the density of individuals. In this talk, we discuss how we can "link" the two approaches using kinetic theory. In contrast with particle systems in physics, models of self-organized dynamics do not conserve momentum and 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.

Download slides from the presentation (PDF).