Speaker: Chad Topaz, Mathematics, Macalester College
Title: Biological aggregation patterns and social interactions

Abstract: Biological aggregations such as insect swarms, bird flocks, and fish schools are some of the most common and least understood patterns in nature. Through two modeling studies, I will discuss the connection between macroscopic properties of aggregations and the microscopic rules for social interactions that constituent members obey. The first model is a discrete description of locust groups. The statistical mechanical properties of the attractive-repulsive social interaction potential control whether or not locusts form a rolling migratory swarm pattern similar to those observed in nature. A continuum approximation and variational analysis lead to exact solutions for the vertical structure of swarms; these agree closely with simulations of the underlying discrete problem. The second model is a conservation-type partial integrodifferential equation for a moving animal group. Long- and short-wave analyses give rise to conditions that social interactions must satisfy for the population to asymptotically spread, contract, or reach steady state.

Time: Friday, Nov. 5, 2010, 1:30-2:30 p.m.

Place: Science and Tech 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