Dr. Justin Tzou

Biography

Justin Tzou's research is aimed at obtaining quantitative descriptions of critical thresholds in diffusive processes. His area of focus includes mean passage time problems and the presence of small absorbing traps, commonly known as the narrow capture problem. A significant direction of his work involves analyzing mobile traps within cellular processes, particularly in predator-prey dynamics. The challenges in this field include deriving the correct partial differential equations (PDEs) for various problems and solving these using asymptotic or numerical methods. A critical question that arises is under what conditions a mobile trap becomes more effective than a stationary one. His major focus is on stability dynamics of patterns in reaction-diffusion systems across various spatial dimensions, especially near and far from the linear regime. He employs asymptotic and numerical continuation techniques to construct and characterize steady-state patterns, blending both analytic and numerical methods to derive critical thresholds and types of instabilities. Delayed bifurcations and their qualitative effects have been analyzed particularly in the context of ordinary differential equations (ODEs) near the linear regime. The overarching theme of Tzou's techniques includes asymptotic methods, PDE techniques, numerical continuation methods, and Monte Carlo simulations, yielding quantitative results that provide rich qualitative insights into the underlying phenomena.

Research Interests