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Mathematical Sciences

Thesis Presentations

Date: 3:30pm PDT April 17, 2012 Location: JRR Howard Hall, Room 114

JRR Howard Hall, Room 114

Mathematical Sciences Honors Thesis Presentations:

Alison Fankhauser ‘12,  Numerical Evolution of Reaction-Diffusion Equations Arising in the Oscillating, Chemical Belousov-Zhabotinsky Reaction

The Belousov-Zhabotinsky (BZ) reaction is a chemical reaction in which the concentrations of intermediates oscillate instead of immediately tending toward equilibrium. We make use of the Oregonator model of the Field-Körös-Noyes mechanism to model the unusual behavior of this reaction in two-dimensional and three-dimensional space by combining ordinary differential equations (ODEs) to represent the reaction and partial differential equations (PDEs) to represent the diffusion components of the process. We apply numerical methods to examine the oscillatory behavior in the ODE case and the effects of diffusion on oscillatory reactions in the PDE case. We find traveling wave solutions present in the two-dimensional PDE system arising from Murray’s model.

Ana Rodenberg, ‘12, “Numerical Analysis of a Quasilinear Wave Equation Arising from Relativity”

We look into the quasilinear wave equation which describes the timelike minimal subsurfaces embedded in Minkowski space. We wish to numerically calculate threshold values on the L2 norm of the initial profile and its initial time derivative so that we can predict the long term behavior of the resulting surface. Using numerical methods, we develop a program which will both evolve the surface and check different geometric quantities to differentiate between a coordinate breakdown and the actuality of the surface going null or blowing up.