Homogenization for advection-diffusion in a perforated domain
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 diffus...
| Egile Nagusiak: | , , , |
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| Formatua: | Journal article |
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2010
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| _version_ | 1826263275270045696 |
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| author | Haynes, P Hoang, V Norris, J Zygalakis, K |
| author_facet | Haynes, P Hoang, V Norris, J Zygalakis, K |
| author_sort | Haynes, P |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T19:49:09Z |
| format | Journal article |
| id | oxford-uuid:235be16c-6f05-46f4-ad05-0d8da8aa6811 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:49:09Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:235be16c-6f05-46f4-ad05-0d8da8aa68112022-03-26T11:43:59ZHomogenization for advection-diffusion in a perforated domainJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:235be16c-6f05-46f4-ad05-0d8da8aa6811Mathematical Institute - ePrints2010Haynes, PHoang, VNorris, JZygalakis, KThe 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. |
| spellingShingle | Haynes, P Hoang, V Norris, J Zygalakis, K Homogenization for advection-diffusion in a perforated domain |
| title | Homogenization for advection-diffusion in a perforated domain |
| title_full | Homogenization for advection-diffusion in a perforated domain |
| title_fullStr | Homogenization for advection-diffusion in a perforated domain |
| title_full_unstemmed | Homogenization for advection-diffusion in a perforated domain |
| title_short | Homogenization for advection-diffusion in a perforated domain |
| title_sort | homogenization for advection diffusion in a perforated domain |
| work_keys_str_mv | AT haynesp homogenizationforadvectiondiffusioninaperforateddomain AT hoangv homogenizationforadvectiondiffusioninaperforateddomain AT norrisj homogenizationforadvectiondiffusioninaperforateddomain AT zygalakisk homogenizationforadvectiondiffusioninaperforateddomain |