# Joint Mathematical Biology and Applied Math Seminar

### Sebastien Motsch

University of Maryland

#### Kinetic and macroscopic models for complex systems

#### Friday, January 8, 2013, at 4:00pm

LCB 225

In complex systems such as a flock of birds or a school of fish, we observe at large
scales the formation of complex structures. To model these phenomena, we can either use
"microscopic models" describing the motion of each individual or "macroscopic models"
(PDEs) describing the evolution of the density of individuals. In this talk, we discuss
how we can "link" the two approaches using kinetic theory.
One of the main difficulty to study those systems is the lack of conserved quantities
(e.g. momentum, energy). To overcome this difficulty, we introduce of new type of
"collisional invariant" that allows us to derive the macroscopic limit of a large class
of "microscopic models". Based on this method, we develop accurate numerical schemes for
both kinetic and macroscopic models. We observe numerically new types of solutions that
remain to be understood analytically.