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\title{Entropy-Based Numerical Investigation of Transport and Mixing in Flows}
\tocauthor{K. Padberg-Gehle} \author{} \institute{}
{\large Kathrin Padberg-Gehle}\\
Technische Universit\"at Dresden\\
Transport and mixing processes in flows can typically only be studied computationally. Finite-time Lyapunov exponents (FTLEs) or related stretching indicators are frequently used as a means to estimate transport barriers \cite{haller_11,shadden_lekien_marsden_05}. Alternatively, dominant eigenvectors \cite{dellnitz_junge_99} or singular vectors \cite{froyland_santi_monahan_10} of numerical transfer operators detect regions in phase space that are minimally dispersed under the dynamics.
Here we attempt to combine these two approaches. We introduce the concept of finite-time entropy (FTE) as a simple and flexible way to capture nonlinear stretching directly from the entropy growth experienced by a small localized density evolved by the transfer operator \cite{froyland_padberg_2012}.
We develop a simple and numerically efficient method of constructing an estimate of the FTE field within a set-oriented framework. Our novel approach is illustrated by several examples and compared to other approaches.
This is joint work with Gary Froyland (University of New South Wales, Australia).
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{\sc G. Froyland and K. Padberg-Gehle}. {Finite-time entropy: a probabilistic approach for measuring nonlinear stretching}. submitted (2011).