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SUMMARY:Stochastic partial differential fluid equations as a diffusive lim
 it of deterministic Lagrangian multi-time dynamics - Darryl Holm (Imperial
  College London)
DTSTART:20170922T092000Z
DTEND:20170922T100000Z
UID:TALK80651@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Colin J Cotter		(Imperial College London)\, 
 Georg A Gottwald		(University of Sydney)        <br></span><br>In [Holm\, 
 Proc. Roy. Soc. A 471 (2015)] stochastic fluid equations were derived by e
 mploying a variational principle with an assumed stochastic Lagrangian par
 ticle dynamics. Here we show that the same stochastic Lagrangian dynamics 
 naturally arises in a multi-scale decomposition of the deterministic Lagra
 ngian flow map into a slow large-scale mean and a rapidly fluctuating smal
 l scale map. We employ homogenization theory to derive effective slow stoc
 hastic particle dynamics for the resolved mean part\, thereby justifying s
 tochastic fluid partial equations in the Eulerian formulation. To justify 
 the application of rigorous homogenization theory\, we assume mildly chaot
 ic fast small-scale dynamics\, as well as a centering condition. The latte
 r requires that the mean of the fluctuating deviations is small\, when pul
 led back to the mean flow. <br><span><br>Joint work with Colin J Cotter (I
 mperial College London) Georg A Gottwald (University of Sydney).</span>
LOCATION:Seminar Room 1\, Newton Institute
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