Paddy Gidney is a final year undergraduate student majoring in philosophy and applied mathematics at the University of Sydney. The areas of mathematics that most interest him are dynamical systems and differential equations, and the project he will be working on this summer is concerned with spectral analysis of reaction-diffusion PDEs.
Spectral Dynamics Of Periodic Wavetrains In Reaction Diffusion Equations
The aim of this project is to compute (analytically if possible, but numerically as necessary) the spectrum of periodic wave trains in two relatively famous reaction diffusion equations. The Fisher-KPP equation and the Bistable/Allen-Cahn equation. Following on this, we will numerically simulate what happens to the periodic waves. Finally, this project aims to consider what happens to both the spectral and temporal dynamics with the addition of small noise to the PDE.