DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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