Graduation Year
2016
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Second Department
Physics
Reader 1
Andrew J. Bernoff
Reader 2
Chad M. Topaz
Terms of Use & License Information
Rights Information
© 2016 Weerapat Pittayakanchit
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 A Primer of Swarm Equilibria. 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.
Recommended Citation
Pittayakanchit, Weerapat, "The Global Stability of the Solution to the Morse Potential in a Catastrophic Regime" (2016). HMC Senior Theses. 72.
https://scholarship.claremont.edu/hmc_theses/72
Included in
Dynamic Systems Commons, Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons, Statistical, Nonlinear, and Soft Matter Physics Commons
