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Exponential growth in two-dimensional topological fluid dynamics

Presented by: 
P Boyland University of Florida
Monday 23rd July 2012 - 16:00 to 16:40
INI Seminar Room 1
Session Chair: 
Jean-Luc Thiffeault
In two-dimensional multi-connected fluid regions the Thurston-Nielsen (TN) theory implies that the essential topological length of material lines grows either exponentially or linearly; the TN theory and subsequent results provide many procedures for determining which growth rate occurs. Our first application is to Euler flows. The main theorem is that there are periodic stirring protocols for which generic initial vorticity yields a solution to Euler's equations which is not periodic and further, the sup norm of the gradient of the vorticity grows exponentially in time. The second application investigates which stirring protocols maximize the efficiency of mixing in the precise, topological sense of the maximal exponential growth of per unit generator of certain push-point mapping classes on the punctured disk. Related Links - my paper's page
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons