Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevE.81.061127 http://hdl.handle.net/11449/225919 |
Resumo: | Consider N sites randomly and uniformly distributed in a d -dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last μ (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory μ1 = log2 N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems. © 2010 The American Physical Society. |
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Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systemsConsider N sites randomly and uniformly distributed in a d -dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last μ (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory μ1 = log2 N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems. © 2010 The American Physical Society.Instituto de Física Teórica (IFT) Universidade Estadual Paulista (UNESP), Caixa Postal 70532-2, 01156-970 São Paulo, SPDepartamento de Física e Matemática (DFM) Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP) National Institute of Science and Technology in Complex Systems (LNCT-SC), Avenida Bandeirantes 3900, 14040-901 Ribeirão Preto, SPInstituto de Física Teórica (IFT) Universidade Estadual Paulista (UNESP), Caixa Postal 70532-2, 01156-970 São Paulo, SPUniversidade Estadual Paulista (UNESP)National Institute of Science and Technology in Complex Systems (LNCT-SC)Berbert, Juliana Militão [UNESP]Martinez, Alexandre Souto2022-04-28T21:02:01Z2022-04-28T21:02:01Z2010-06-18info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.81.061127Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 81, n. 6, 2010.1539-37551550-2376http://hdl.handle.net/11449/22591910.1103/PhysRevE.81.0611272-s2.0-77953976916Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsinfo:eu-repo/semantics/openAccess2022-04-28T21:02:01Zoai:repositorio.unesp.br:11449/225919Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-05-23T21:06:25.219911Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
title |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
spellingShingle |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems Berbert, Juliana Militão [UNESP] |
title_short |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
title_full |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
title_fullStr |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
title_full_unstemmed |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
title_sort |
Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems |
author |
Berbert, Juliana Militão [UNESP] |
author_facet |
Berbert, Juliana Militão [UNESP] Martinez, Alexandre Souto |
author_role |
author |
author2 |
Martinez, Alexandre Souto |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) National Institute of Science and Technology in Complex Systems (LNCT-SC) |
dc.contributor.author.fl_str_mv |
Berbert, Juliana Militão [UNESP] Martinez, Alexandre Souto |
description |
Consider N sites randomly and uniformly distributed in a d -dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last μ (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory μ1 = log2 N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems. © 2010 The American Physical Society. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-06-18 2022-04-28T21:02:01Z 2022-04-28T21:02:01Z |
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://dx.doi.org/10.1103/PhysRevE.81.061127 Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 81, n. 6, 2010. 1539-3755 1550-2376 http://hdl.handle.net/11449/225919 10.1103/PhysRevE.81.061127 2-s2.0-77953976916 |
url |
http://dx.doi.org/10.1103/PhysRevE.81.061127 http://hdl.handle.net/11449/225919 |
identifier_str_mv |
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 81, n. 6, 2010. 1539-3755 1550-2376 10.1103/PhysRevE.81.061127 2-s2.0-77953976916 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803045715559055360 |