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Weerapat Pittayakanchit

Picture of Weerapat Pittayakanchit.

Thesis

The Global Stability of the Solution to the Morse Potential in a Catastrophic Regime

Advisor
Andrew J. Bernoff
Second Reader(s)
Chad M. Topaz (Macalester College)

Abstract

Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in \citep{BerTop2013}. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single component. We are still examining the local minimizers with multiple components to determine whether the candidate solution is the minimum-energy configuration.

Additional Materials

Poster