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SUMMARY:Diffusion in arrays of obstacles: beyond homogenisation - Alexandr
 a Tzella (University of Birmingham)
DTSTART:20220309T133000Z
DTEND:20220309T143000Z
UID:TALK170693@talks.cam.ac.uk
DESCRIPTION:We revisit the classical problem of diffusion of a scalar (or 
 heat) released in a two-dimensional medium with an embedded periodic array
  of impermeable obstacles such as perforations. Homogenisation theory prov
 ides a coarse-grained description of the scalar at large times and predict
 s that it diffuses with a certain effective diffusivity\, so the concentra
 tion is approximately Gaussian. We improve on this by developing a large-d
 eviation approximation which also captures the non-Gaussian tails of the c
 on- centration through a rate function obtained by solving a family of eig
 envalue problems. We focus on cylindrical obstacles and on the dense limit
 \, when the obstacles occupy a large area fraction and non-Gaussianity is 
 most marked. We derive an asymptotic approximation for the rate function i
 n this limit\, valid uniformly over a wide range of distances. We use fini
 te-element implementations to solve the eigenvalue problems yielding the r
 ate function for arbitrary obstacle area fractions and an elliptic boundar
 y-value problem arising in the asymptotics calculation. Comparison between
  numerical results and asymptotic predictions confirm the validity of the 
 latter.
LOCATION:Seminar Room 1\, Newton Institute
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