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Dynamical Systems Seminar: Rebecca Mitchell

Optimizing Mixing of Area Preserving Maps

Rebecca Mitchell

Applied Mathematics,Ìý

Date and time:Ìý

Thursday, October 15, 2015 - 2:00pm

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ECCR 257

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We seek to better understand how to induce efficient mixing by applying area preserving maps to an incompressible fluid in a two dimensional periodic domain. Mixing is controlled by modifying parameters in the map at each step, which we call stirring parameters. Given an initial concentration of a passive scalar, our goal is to determine a progression of stirring parameters that will most uniformly distribute the concentration over some finite time. The talk will explain how the maps can be applied using Fourier decompositions or the Perron-Frobenius method and how mixing is quantified by taking a negative Sobolev norm of the concentration. A Monte Carlo algorithm is used to determine stirring parameters which induce the best mixing given an energy constraint and a fixed number of steps of the map.