Homogenization for advection-diffusion in a perforated domain
Abstract
The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random and positive asymptotic rate of growth. This is used to establish the existence of a homogenized limit for such a diffusion when subject to Dirichlet conditions on the boundaries of a sparse and independent array of obstacles. There is a constant effective long-time loss rate at the obstacles. The dependence of this rate on the form and intensity of the obstacles and on the velocity field is investigated. A Monte Carlo algorithm for the computation of the volume growth rate of the sausage is introduced and some numerical results are presented for the Taylor--Green velocity field.
Keywords
Cite
@article{arxiv.1003.3990,
title = {Homogenization for advection-diffusion in a perforated domain},
author = {P. H. Haynes and V. H. Hoang and J. R. Norris and K. C. Zygalakis},
journal= {arXiv preprint arXiv:1003.3990},
year = {2010}
}
Comments
19 pages, 7 figures, To appear in Bingham, N. H., and Goldie, C. M. (eds), Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman. London Math. Soc. Lecture Note Series. Cambridge: Cambridge Univ. Press