Hydrodynamical behavior of symmetric exclusion with slow bonds
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/16881 |
Resumo: | We consider the exclusion process in the one-dimensional discrete torus with $N$ points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter $\beta$. If $\beta\in [0,1)$, the hydrodynamic limit is given by the usual heat equation. If $\beta=1$, it is given by a parabolic equation involving an operator $\frac{d}{dx}\frac{d}{dW}$, where $W$ is the Lebesgue measure on the torus plus the sum of the Dirac measure supported on each macroscopic point related to the slow bond. If $\beta\in(1,\infty)$, it is given by the heat equation with Neumann's boundary conditions, meaning no passage through the slow bonds in the continuum. |
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Hydrodynamical behavior of symmetric exclusion with slow bondsExclusion with slow bondsHydrodynamical behaviorDynamical phase transitionHydrodynamic limitExclusion processSlow bondsScience & TechnologyWe consider the exclusion process in the one-dimensional discrete torus with $N$ points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter $\beta$. If $\beta\in [0,1)$, the hydrodynamic limit is given by the usual heat equation. If $\beta=1$, it is given by a parabolic equation involving an operator $\frac{d}{dx}\frac{d}{dW}$, where $W$ is the Lebesgue measure on the torus plus the sum of the Dirac measure supported on each macroscopic point related to the slow bond. If $\beta\in(1,\infty)$, it is given by the heat equation with Neumann's boundary conditions, meaning no passage through the slow bonds in the continuum.Fundação para a Ciência e a Tecnologia (FCT)ElsevierUniversidade do MinhoFranco, TertulianoGonçalves, PatríciaNeumann, Adriana20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/16881eng0246-020310.1214/11-AIHP445http://www.e-publications.org/ims/submission/index.php/AIHP/user/submissionFile/9315?confirm=1e8d3afeinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:25:06Zoai:repositorium.sdum.uminho.pt:1822/16881Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:19:16.818709Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
title |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
spellingShingle |
Hydrodynamical behavior of symmetric exclusion with slow bonds Franco, Tertuliano Exclusion with slow bonds Hydrodynamical behavior Dynamical phase transition Hydrodynamic limit Exclusion process Slow bonds Science & Technology |
title_short |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
title_full |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
title_fullStr |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
title_full_unstemmed |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
title_sort |
Hydrodynamical behavior of symmetric exclusion with slow bonds |
author |
Franco, Tertuliano |
author_facet |
Franco, Tertuliano Gonçalves, Patrícia Neumann, Adriana |
author_role |
author |
author2 |
Gonçalves, Patrícia Neumann, Adriana |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Franco, Tertuliano Gonçalves, Patrícia Neumann, Adriana |
dc.subject.por.fl_str_mv |
Exclusion with slow bonds Hydrodynamical behavior Dynamical phase transition Hydrodynamic limit Exclusion process Slow bonds Science & Technology |
topic |
Exclusion with slow bonds Hydrodynamical behavior Dynamical phase transition Hydrodynamic limit Exclusion process Slow bonds Science & Technology |
description |
We consider the exclusion process in the one-dimensional discrete torus with $N$ points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter $\beta$. If $\beta\in [0,1)$, the hydrodynamic limit is given by the usual heat equation. If $\beta=1$, it is given by a parabolic equation involving an operator $\frac{d}{dx}\frac{d}{dW}$, where $W$ is the Lebesgue measure on the torus plus the sum of the Dirac measure supported on each macroscopic point related to the slow bond. If $\beta\in(1,\infty)$, it is given by the heat equation with Neumann's boundary conditions, meaning no passage through the slow bonds in the continuum. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 2013-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/16881 |
url |
http://hdl.handle.net/1822/16881 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0246-0203 10.1214/11-AIHP445 http://www.e-publications.org/ims/submission/index.php/AIHP/user/submissionFile/9315?confirm=1e8d3afe |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132651181834240 |