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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:The emergence of the fractional heat equation from
a one dimensional solid (FPU-$beta$ chain) - Sara
Merino Aceituno (CCA)
DTSTART;TZID=Europe/London:20140618T160000
DTEND;TZID=Europe/London:20140618T170000
UID:TALK52350AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52350
DESCRIPTION:Justifying mathematically Fourier law (how heat is
transported from places of high temperature to pl
aces of low temperature) is one of the big challen
ges in Statistical Mechanics. But heat transfer is
not only modelled by Fourier law\; there is also
the so-called 'fractional' Fourier law. We will fo
cus on the latter.\n\nA full justification of this
law consists in deriving it from the atomic dynam
ics of the solid. This requires\, in particular\,
a multiscale analysis\, i.e.\, starting from the m
icroscopic scale model (the one dimensional FPU-$b
eta$ chain representing a solid)\, we must reach t
he macroscopic model given by the fractional Fouri
er law (fractional heat equation). The strategy is
to link these two models through an intermediate
scale model (the kinetic Boltzmann-phonon equation
) that serves as a bridge. I will comment on some
work in progress with Professor Antoine Mellet\, U
niversity of Maryland.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Vittoria Silvestri
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