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arXiv · 0804.2520

Topology of Chaotic Mixing Patterns

Jean-Luc Thiffeault·Matthew D. Finn·Emmanuelle Gouillart·Toby Hall
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Abstract

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.

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Jean-Luc Thiffeault, Matthew D. Finn, Emmanuelle Gouillart, Toby Hall. 2008-08-26. Topology of Chaotic Mixing Patterns. https://doi.org/10.1063/1.2973815

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