CAREER: Anomalous Diffusion, Homogenization and Averaging

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This project studies various phenomena related to diffusive tracer particles in a strong array of opposing vorticies. One particularly interesting aspect is a seemingly anomalous diffusive behaviour exhibited on "intermediate" time scales. On long time scales this anomalous diffusive behaviour should "average" to an effectively Brownian behaviour, recovering classical homogenization results. The project crucially uses tools from both Probability and PDE. The educational component of this project aims to further interaction between these two areas from the undergraduate to the post-graduate level.Observing the movement of gravel particles shows intermittent periods of rest and travel. One aspect of this project studies an idealised system modelling this behaviour with the eventual aim of rigorously quantifying the "rest and travel". This is closely related to questions about homogenization -- the approximation of inhomogeneous media with microscopic inhomogeneities by a homogeneous one. This project crucially uses tools from two connected but different areas in Mathematics: Probability and PDE. The educational component of this project aims to further interaction between these two areas from the undergraduate level all the way to the post-graduate level.