Dmitri Vainchtein, Nyheim Plasma Institute, Drexel University
In my talk I discuss several aspects of transport phenomena in the near-integrable multi-scale dynamical systems. In the first part of the talk I consider mixing via resonances-induced chaotic advection in microdroplets. Using the method of averaging and the theory of adiabatic invariants, I show that proper characterization of the mixing quality requires introduction of two different metrics. The first metric determines the relative volumes of the domain of chaotic and regular dynamics. The second metric describes the time for homogenization inside the chaotic domain. In the second part of the talk I illustrate how the capture into resonance, that by itself is random in nature can be made into an effective mechanism of regular transport . As a model problem I consider dynamics of a charged particle in an electromagnetic field.