Extreme value theory and Quantitative Poincare recurrence in fluid mixing problems

The importance and relevance of fluid mixing in modern science is clear, both from the range of industrial and environmental situations in which it appears, and from the explosion of research articles connected with mixing by chaotic advection that have appeared in the last thirty years. Similarly well-established is extreme value theory (EVT) – the study of large deviations in probabilistic systems, where it has been employed to predict floods, freak waves and tornados. Much more recent is the application of EVT to deterministic systems, but this has met with success in apparently simple dynamical systems (for example, the Cat Map, a fundamental model of hyperbolic behaviour), which happen to also model a wide class of fluid mixing device. In this project we propose to extend this work by considering EVT in related maps, arguably closer to modelling physical phenomena in mixing problems. A basic tool is quantitative Poincare recurrence – an analysis of the distributions of time returns to a `good’ mixing region. The project relies on dynamical systems theory, with much scope for careful numerical work.