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Minimal mixing: Exploring the Veering Automata

Mark Bell, University of Illinois at Urbana-Champaign

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Saul Schleimer, University of Warwick; Vaibhav Gadre, University of Glasgow

To mix two things together, a collection of stirring rods are moved in a repeating pattern. The rate of mixing, also known as the entropy, can be determined from this pattern using (piecewise) linear algebra. This proposal is part of a project to find lower bounds on the entropies of stirring systems or, equivalently, to answer the question: What is the worst possible rate of mixing? To achieve this, we follow a tried and tested technique of encoding this problem as an automata and exploring the cycles within it. However, while previous automata have been too large for even the most powerful supercomputers, this proposal will explore whether these problems are now computationally tractable with a new, smaller automata developed by the investigators known as the veering automata.