Northwestern Events Calendar

Apr
21
2014

Chad Topaz, Biological aggregations: Nonlocal PDE, random walks and bugs

When: Monday, April 21, 2014
4:00 PM - 5:00 PM CT

Where: Technological Institute, M416, 2145 Sheridan Road, Evanston, IL 60208 map it

Audience: Faculty/Staff - Student - Public

Contact: Beth Siculan   (847) 491-3345

Group: McCormick-Colloquia Engineering Sciences and Applied Mathematics

Category: Lectures & Meetings

Description:

Title: Biological aggregations: Nonlocal PDE, random walks, and bugs

Speaker: Chad Topaz, Macalester College

Abstract: From bird flocks to ungulate herds to fish schools, nature abounds with biological aggregations that arise from social interactions. These interactions take place over finite (rather than infinitesimal) distances, giving rise to nonlocal models. In this mathematical modeling talk, I will discuss two projects on insect swarms in which nonlocal social interactions play a key role. The first project examines desert locusts. The model is a system of nonlinear partial integrodifferential equations of advection-reaction type. I find conditions for the formation of population density clumps, demonstrate transiently traveling pulses of insects, and find hysteresis in the aggregation's existence. The second project examines the pea aphid. Based on experiments that motion track aphids walking in a circular arena, I extract a discrete, stochastic model for the group. Each aphid transitions randomly between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid’s nearest neighbor. For large nearest neighbor distances, when an aphid is isolated, its motion is ballistic and it is less likely to stop. In contrast, for short nearest neighbor distances, aphids move diffusively and are more likely to become stationary; this behavior constitutes a simple aggregation mechanism.

-----

To subscribe to the Applied Mathematics Colloquia List send a message to seminar-join@esam.northwestern.edu

Add to Calendar

Add Event To My Group:

Please sign-in