Swarms in bounded domains

Document Type

Presentation Abstract

Presentation Date

5-2-2016

Abstract

Swarms of animals, fish, birds, locusts etc. are a common experience and their coherence and dynamics have been the focus of research in mathematics and biology in the last 20 years. A number of different models for the onset of coherent swarming and the shapes of the swarms have been proposed but studies of the dynamics of these swarms and their interaction with other swarms or boundaries are lacking. This talk will present recent research on scattering at boundaries and collisions between two swarms for two swarming models, the Vicsek and the Attraction-Repulsion model. We will show that, while individual particles are specularly reflected at a boundary, the swarm as a whole is reflected inelastically. A fundamental refraction law for a swarm, impacting on a planar boundary is derived. Inelastic collisions lead to alignment with the wall and to damped pulsating oscillations of the swarm as well as new dynamical swarm solutions. Setting two identical flocks on a collision course is studied in a simplified form analytically and for large swarms numerically. Depending on the scattering parameters swarms will diverge, converge or form bound states where the translational kinetic energy is converted into a rotational kinetic energy.

Additional Details

Monday, May 2, 2016 at 3:10 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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