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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-242@lptms.universite-paris-saclay.fr
DTSTART:20140311T110000Z
DTEND:20140311T120000Z
DTSTAMP:20140307T085633Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
s-5/
SUMMARY:Séminaire du LPTMS: Enrique Abad - LPTMS\, salle 201\, 2ème étag
e\, Bât 100\, Campus d'Orsay - 11 Mar 14 11:00
DESCRIPTION:Fractional equation approaches to subdiffusion problems: a tale
of tails\nEnrique Abad\, Dpto. de Física Aplicada (Univ. de Extremadura)
\nAnomalous transport (in the sense of a nonlinear growth of the mean squa
re displacement) is ubiquitous in nature\, notably in biological systems.
A widely used model to mimic anomalous transport processes with a large di
spersion of waiting times is the celebrated Continuous Time Random Walk (C
TRW). The CTRW with a long-tailed waiting time distribution and a jump len
gth distribution of finite variance (both decoupled from one another) is k
nown to become equivalent to a fractional diffusion equation in the long-t
ime limit. While the fractional diffusion equation is an integrodifferenti
al equation\, it is nevertheless amenable to exact solution via Laplace tr
ansform methods or a variable separation ansatz.\nWe consider a number of
first-passage problems of interest involving the solution of the fractiona
l diffusion equation with absorbing boundary conditions. The solutions are
characterized by a very detailed memory of the initial condition persisti
ng even in the long-time regime\; the solutions are also peculiar from a m
athematical viewpoint as a) the long-time decay modes can be used to const
ruct new polynomial approximations for Bessel functions and b) for a prope
r choice of the system parameters divergent series are seen to emerge in t
he solution. Such series must be suitably regularized to recover the physi
cally correct solutions.\nFinally\, we shall also give an overview on how
to deal with problems where the absorption process is not constrained to a
boundary\, but is delocalized in space. In this case one must use highly
non-intuitive reaction-subdiffusion equations which find a proper justific
ation in the framework of a mesoscopic approach. We shall discuss the appl
ication of this type of equations to understand a key process in developme
ntal biology\, namely\, the formation of morphogen concentration gradients
by means of subdiffusive transport.
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15
Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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