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SUMMARY:The emergence of the fractional heat equation from a one dimension
 al solid (FPU-$beta$ chain) - Sara Merino Aceituno (CCA)
DTSTART:20140618T150000Z
DTEND:20140618T160000Z
UID:TALK52350@talks.cam.ac.uk
CONTACT:Vittoria Silvestri
DESCRIPTION:Justifying mathematically Fourier law (how heat is transported
  from places of high temperature to places of low temperature) is one of t
 he big challenges in Statistical Mechanics. But heat transfer is not only 
 modelled by Fourier law\; there is also the so-called 'fractional' Fourier
  law. We will focus on the latter.\n\nA full justification of this law con
 sists in deriving it from the atomic dynamics of the solid. This requires\
 , in particular\, a multiscale analysis\, i.e.\, starting from the microsc
 opic scale model (the one dimensional FPU-$beta$ chain representing a soli
 d)\, we must reach the macroscopic model given by the fractional Fourier l
 aw (fractional heat equation). The strategy is to link these two models th
 rough an intermediate scale model (the kinetic Boltzmann-phonon equation) 
 that serves as a bridge. I will comment on some work in progress with Prof
 essor Antoine Mellet\, University of Maryland.
LOCATION:MR14\, Centre for Mathematical Sciences
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