Escaping from cycles through a glass transition
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/101364 |
Resumo: | A random walk is performed over a disordered media composed of N sites random and uniformly distributed inside a d-dimensional hypercube. The walker cannot remain in the same site and hops to one of its n neighboring sites with a transition probability that depends on the distance D between sites according to a cost function E(D). The stochasticity level is parametrized by a formal temperature T. In the case T=0, the walk is deterministic and ergodicity is broken: the phase space is divided in a O(N) number of attractor basins of two-cycles that trap the walker. For d=1, analytic results indicate the existence of a glass transition at T1=1/2 as N->∞. Below T1, the average trapping time in two-cycles diverges and an out-of-equilibrium behavior appears. Similar glass transitions occur in higher dimensions when the right cost function is chosen. We also present some results for the statistics of distances for Poisson spatial point processes. |
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Gusman, Sebastian RisauMartinez, Alexandre SoutoKinouchi, Osame2014-08-19T02:10:30Z20031539-3755http://hdl.handle.net/10183/101364000503833A random walk is performed over a disordered media composed of N sites random and uniformly distributed inside a d-dimensional hypercube. The walker cannot remain in the same site and hops to one of its n neighboring sites with a transition probability that depends on the distance D between sites according to a cost function E(D). The stochasticity level is parametrized by a formal temperature T. In the case T=0, the walk is deterministic and ergodicity is broken: the phase space is divided in a O(N) number of attractor basins of two-cycles that trap the walker. For d=1, analytic results indicate the existence of a glass transition at T1=1/2 as N->∞. Below T1, the average trapping time in two-cycles diverges and an out-of-equilibrium behavior appears. Similar glass transitions occur in higher dimensions when the right cost function is chosen. We also present some results for the statistics of distances for Poisson spatial point processes.application/pdfengPhysical review. E, Statistical, nonlinear, and soft matter physics. Vol. 68, no. 1 (July 2003), 016104, 11 p.Sistemas dinâmicos não-linearesTransicao vitreaProcessos estocásticosHipercuboFuncao custoProcessos espaciaisestatisticas de distanciasEscaping from cycles through a glass transitionEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000503833.pdf000503833.pdfTexto completo (inglês)application/pdf136701http://www.lume.ufrgs.br/bitstream/10183/101364/1/000503833.pdfd9a6eef60ad8d82babce0cb406e0b9d2MD51TEXT000503833.pdf.txt000503833.pdf.txtExtracted Texttext/plain47481http://www.lume.ufrgs.br/bitstream/10183/101364/2/000503833.pdf.txt44c087d1d1f6f2798c3b218d3f4ddf48MD52THUMBNAIL000503833.pdf.jpg000503833.pdf.jpgGenerated Thumbnailimage/jpeg1994http://www.lume.ufrgs.br/bitstream/10183/101364/3/000503833.pdf.jpg6373c48ca4d4ffb8f24785b9b45b22a6MD5310183/1013642022-02-22 05:07:24.456945oai:www.lume.ufrgs.br:10183/101364Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2022-02-22T08:07:24Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Escaping from cycles through a glass transition |
title |
Escaping from cycles through a glass transition |
spellingShingle |
Escaping from cycles through a glass transition Gusman, Sebastian Risau Sistemas dinâmicos não-lineares Transicao vitrea Processos estocásticos Hipercubo Funcao custo Processos espaciais estatisticas de distancias |
title_short |
Escaping from cycles through a glass transition |
title_full |
Escaping from cycles through a glass transition |
title_fullStr |
Escaping from cycles through a glass transition |
title_full_unstemmed |
Escaping from cycles through a glass transition |
title_sort |
Escaping from cycles through a glass transition |
author |
Gusman, Sebastian Risau |
author_facet |
Gusman, Sebastian Risau Martinez, Alexandre Souto Kinouchi, Osame |
author_role |
author |
author2 |
Martinez, Alexandre Souto Kinouchi, Osame |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Gusman, Sebastian Risau Martinez, Alexandre Souto Kinouchi, Osame |
dc.subject.por.fl_str_mv |
Sistemas dinâmicos não-lineares Transicao vitrea Processos estocásticos Hipercubo Funcao custo Processos espaciais estatisticas de distancias |
topic |
Sistemas dinâmicos não-lineares Transicao vitrea Processos estocásticos Hipercubo Funcao custo Processos espaciais estatisticas de distancias |
description |
A random walk is performed over a disordered media composed of N sites random and uniformly distributed inside a d-dimensional hypercube. The walker cannot remain in the same site and hops to one of its n neighboring sites with a transition probability that depends on the distance D between sites according to a cost function E(D). The stochasticity level is parametrized by a formal temperature T. In the case T=0, the walk is deterministic and ergodicity is broken: the phase space is divided in a O(N) number of attractor basins of two-cycles that trap the walker. For d=1, analytic results indicate the existence of a glass transition at T1=1/2 as N->∞. Below T1, the average trapping time in two-cycles diverges and an out-of-equilibrium behavior appears. Similar glass transitions occur in higher dimensions when the right cost function is chosen. We also present some results for the statistics of distances for Poisson spatial point processes. |
publishDate |
2003 |
dc.date.issued.fl_str_mv |
2003 |
dc.date.accessioned.fl_str_mv |
2014-08-19T02:10:30Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
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publishedVersion |
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http://hdl.handle.net/10183/101364 |
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1539-3755 |
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000503833 |
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http://hdl.handle.net/10183/101364 |
dc.language.iso.fl_str_mv |
eng |
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eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear, and soft matter physics. Vol. 68, no. 1 (July 2003), 016104, 11 p. |
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openAccess |
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