Brownian motion limit of random walks in symmetric non-homogeneous media
Autor(a) principal: | |
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Data de Publicação: | 1999 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Brazilian Journal of Physics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97331999000300014 |
Resumo: | The phenomenon of macroscopic homogenization is illustrated with a simple example of diffusion. We examine the conditions under which a d-dimensional simple random walk in a symmetric random media converges to a Brownian motion. For d = 1, both the macroscopic homogeneity condition and the diffusion coeficient can be read from an explicit expression for the Green's function. Except for this case, the two available formulas for the effective diffusion matrix kappa do not explicit show how macroscopic homogenization takes place. Using an electrostatic analogy due to Anshelevich, Khanin and Sinai [AKS], we discuss upper and lower bounds on the diffusion coeficient kappa for d >1. |
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Brazilian Journal of Physics |
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spelling |
Brownian motion limit of random walks in symmetric non-homogeneous mediaThe phenomenon of macroscopic homogenization is illustrated with a simple example of diffusion. We examine the conditions under which a d-dimensional simple random walk in a symmetric random media converges to a Brownian motion. For d = 1, both the macroscopic homogeneity condition and the diffusion coeficient can be read from an explicit expression for the Green's function. Except for this case, the two available formulas for the effective diffusion matrix kappa do not explicit show how macroscopic homogenization takes place. Using an electrostatic analogy due to Anshelevich, Khanin and Sinai [AKS], we discuss upper and lower bounds on the diffusion coeficient kappa for d >1.Sociedade Brasileira de Física1999-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97331999000300014Brazilian Journal of Physics v.29 n.3 1999reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97331999000300014info:eu-repo/semantics/openAccessMarchetti,Domingos H. U.Silva,Roberto daeng2000-08-07T00:00:00Zoai:scielo:S0103-97331999000300014Revistahttp://www.sbfisica.org.br/v1/home/index.php/pt/ONGhttps://old.scielo.br/oai/scielo-oai.phpsbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br1678-44480103-9733opendoar:2000-08-07T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Brownian motion limit of random walks in symmetric non-homogeneous media |
title |
Brownian motion limit of random walks in symmetric non-homogeneous media |
spellingShingle |
Brownian motion limit of random walks in symmetric non-homogeneous media Marchetti,Domingos H. U. |
title_short |
Brownian motion limit of random walks in symmetric non-homogeneous media |
title_full |
Brownian motion limit of random walks in symmetric non-homogeneous media |
title_fullStr |
Brownian motion limit of random walks in symmetric non-homogeneous media |
title_full_unstemmed |
Brownian motion limit of random walks in symmetric non-homogeneous media |
title_sort |
Brownian motion limit of random walks in symmetric non-homogeneous media |
author |
Marchetti,Domingos H. U. |
author_facet |
Marchetti,Domingos H. U. Silva,Roberto da |
author_role |
author |
author2 |
Silva,Roberto da |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Marchetti,Domingos H. U. Silva,Roberto da |
description |
The phenomenon of macroscopic homogenization is illustrated with a simple example of diffusion. We examine the conditions under which a d-dimensional simple random walk in a symmetric random media converges to a Brownian motion. For d = 1, both the macroscopic homogeneity condition and the diffusion coeficient can be read from an explicit expression for the Green's function. Except for this case, the two available formulas for the effective diffusion matrix kappa do not explicit show how macroscopic homogenization takes place. Using an electrostatic analogy due to Anshelevich, Khanin and Sinai [AKS], we discuss upper and lower bounds on the diffusion coeficient kappa for d >1. |
publishDate |
1999 |
dc.date.none.fl_str_mv |
1999-09-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97331999000300014 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97331999000300014 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0103-97331999000300014 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Brazilian Journal of Physics v.29 n.3 1999 reponame:Brazilian Journal of Physics instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Brazilian Journal of Physics |
collection |
Brazilian Journal of Physics |
repository.name.fl_str_mv |
Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
sbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br |
_version_ |
1754734858770317312 |