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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Diffusion in arrays of obstacles: beyond homogenis
ation - Alexandra Tzella (University of Birmingham
)
DTSTART;TZID=Europe/London:20220309T133000
DTEND;TZID=Europe/London:20220309T143000
UID:TALK170693AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170693
DESCRIPTION:We revisit the classical problem of diffusion of a
scalar (or heat) released in a two-dimensional me
dium with an embedded periodic array of impermeabl
e obstacles such as perforations. Homogenisation t
heory provides a coarse-grained description of the
scalar at large times and predicts that it diffus
es with a certain effective diffusivity\, so the c
oncentration is approximately Gaussian. We improve
on this by developing a large-deviation approxima
tion which also captures the non-Gaussian tails of
the con- centration through a rate function obtai
ned by solving a family of eigenvalue problems. We
focus on cylindrical obstacles and on the dense l
imit\, when the obstacles occupy a large area frac
tion and non-Gaussianity is most marked. We derive
an asymptotic approximation for the rate function
in this limit\, valid uniformly over a wide range
of distances. We use finite-element implementatio
ns to solve the eigenvalue problems yielding the r
ate function for arbitrary obstacle area fractions
and an elliptic boundary-value problem arising in
the asymptotics calculation. Comparison between n
umerical results and asymptotic predictions confir
m the validity of the latter.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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