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SUMMARY:Nonuniform mixing: filters\, swimmers\, and floaters - Jean-Luc Th
 iffeault\, University of Wisconsin
DTSTART:20220211T160000Z
DTEND:20220211T170000Z
UID:TALK168440@talks.cam.ac.uk
CONTACT:Prof. Jerome Neufeld
DESCRIPTION:Fluid mixing involves the interplay between advection and diff
 usion\, which together cause any initial distribution of passive scalar to
  homogenize and ultimately reach a uniform state.  However\, this scenario
  only holds when the velocity field is non-divergent and has no normal com
 ponent to the boundary.  If either condition is unmet\, such as for active
  particles in a bounded region\, floating particles\, or for filters\, the
  ultimate state after a long time is not uniform\, and may be time depende
 nt.  We show that in those cases of nonuniform mixing it is preferable to 
 characterize the degree of mixing in terms of an f-divergence\, which is a
  generalization of relative entropy. Unlike concentration variance (L2 nor
 m)\, the f-divergence always decays monotonically\, even for nonuniform mi
 xing\, which facilitates measuring the rate of mixing.  We show by an exam
 ple that flows that mix well for the nonuniform case can be drastically di
 fferent from efficient uniformly mixing flows.  We also discuss Some conne
 ctions to the acceleration of convergence of Markov chains on graphs.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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