On the Bulk Velocity of Brownian Ratchets
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10316/44427 https://doi.org/10.1137/15M1016205 |
Resumo: | In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential. |
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7160 |
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On the Bulk Velocity of Brownian RatchetsIn this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential.Society for Industrial and Applied Mathematics (SIAM)2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44427http://hdl.handle.net/10316/44427https://doi.org/10.1137/15M1016205https://doi.org/10.1137/15M1016205enghttp://epubs.siam.org/doi/10.1137/15M1016205Kondratyev, StanislavUrbano, José MiguelVorotnikov, Dmitryinfo: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:RCAAP2021-06-29T10:03:20Zoai:estudogeral.uc.pt:10316/44427Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:23.185233Repositório 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 |
On the Bulk Velocity of Brownian Ratchets |
title |
On the Bulk Velocity of Brownian Ratchets |
spellingShingle |
On the Bulk Velocity of Brownian Ratchets Kondratyev, Stanislav |
title_short |
On the Bulk Velocity of Brownian Ratchets |
title_full |
On the Bulk Velocity of Brownian Ratchets |
title_fullStr |
On the Bulk Velocity of Brownian Ratchets |
title_full_unstemmed |
On the Bulk Velocity of Brownian Ratchets |
title_sort |
On the Bulk Velocity of Brownian Ratchets |
author |
Kondratyev, Stanislav |
author_facet |
Kondratyev, Stanislav Urbano, José Miguel Vorotnikov, Dmitry |
author_role |
author |
author2 |
Urbano, José Miguel Vorotnikov, Dmitry |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Kondratyev, Stanislav Urbano, José Miguel Vorotnikov, Dmitry |
description |
In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 |
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/10316/44427 http://hdl.handle.net/10316/44427 https://doi.org/10.1137/15M1016205 https://doi.org/10.1137/15M1016205 |
url |
http://hdl.handle.net/10316/44427 https://doi.org/10.1137/15M1016205 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
http://epubs.siam.org/doi/10.1137/15M1016205 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics (SIAM) |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics (SIAM) |
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 |
repository.mail.fl_str_mv |
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1799133821092757504 |