Undergraduate Submissions for the SIAM 2008 Annual Meeting Poster Session

Organizers: Andrew Bernoff, Harvey Mudd College, and Chad Topaz, Macalester College

Undergraduates are invited to participate in the poster session to be held at the 2008 SIAM Annual Meeting in San Diego. The poster session is from 8:00 PM – 10:00 PM on Tuesday, July 8, 2008.

Prizes will be awarded to the three best posters demonstrating research done by undergraduates in applied and computational mathematics. Students who have not received a bachelor's degree before January 1, 2008 are eligible. The undergraduate portion of the poster session and prizes are sponsored by the SIAM Education Committee.

Submissions should be sent to [email protected] and must include the following information:

The deadline for submission is Monday, April 21, 2008. Receipt and acceptance of the submissions will be communicated via e-mail by May 1, 2008.

A specimen abstract is below:

Title: An Integro-differential Equation Model for Biological Swarms

Authors: Ima Student, Department of Mathematics, Harvey Mudd College ([email protected]) and Johnny Mnemonic, Department of Physics, Macalester College ([email protected])

Advisors: Andrew Bernoff, Department of Mathematics, Harvey Mudd College ([email protected]) and Chad Topaz, Department of Mathematics, Macalester College ([email protected])

Abstract: We explore an integrodifferential equation that models one- dimensional biological swarms. In this model, the swarm motion is determined by pairwise interactions, which in a continuous setting corresponds to a convolution of the swarm density with a pairwise interaction kernel. As the swarm spreads, we show the density $\rho (x,t)$, satisfies a non-linear diffusion equation, $\rho_t = (\rho \rho_x)_x)$,which allows us to predict the approximate shape and scaling of a similarity profile. We verify this prediction numerically.

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