DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Sebastien Motsch, University of Maryland

**Title: ***
Mathematical modeling of self-organized dynamics
*

**Abstract:**
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.

**Time:** Friday, November 9, 2012, 1:30-2:30 p.m.

**Place:** Planetary Hall (formerly S & T I), Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491