Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Detalhes bibliográficos
Autor(a) principal: Leonel, Edson Denis [UNESP]
Data de Publicação: 2009
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1155/2009/367921
http://hdl.handle.net/11449/24944
Resumo: A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map. Copyright (C) 2009 Edson D. Leonel.
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spelling Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical ExponentsA phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map. Copyright (C) 2009 Edson D. Leonel.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação para o Desenvolvimento da UNESP (FUNDUNESP)Univ Estadual Paulista, Dept Estatist Matemat Aplicada & Computacao, Inst Geociencias & Ciencias Exatas, BR-13506700 Rio Claro, SP, BrazilUniv Estadual Paulista, Dept Estatist Matemat Aplicada & Computacao, Inst Geociencias & Ciencias Exatas, BR-13506700 Rio Claro, SP, BrazilHindawi Publishing CorporationUniversidade Estadual Paulista (Unesp)Leonel, Edson Denis [UNESP]2013-09-30T18:50:35Z2014-05-20T14:16:24Z2013-09-30T18:50:35Z2014-05-20T14:16:24Z2009-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article22application/pdfhttp://dx.doi.org/10.1155/2009/367921Mathematical Problems In Engineering. New York: Hindawi Publishing Corporation, p. 22, 2009.1024-123Xhttp://hdl.handle.net/11449/2494410.1155/2009/367921WOS:000271739500001WOS000271739500001.pdf61306442327186100000-0001-8224-3329Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematical Problems in Engineering1.145info:eu-repo/semantics/openAccess2024-01-05T06:24:37Zoai:repositorio.unesp.br:11449/24944Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:11:00.415899Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
title Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
spellingShingle Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
Leonel, Edson Denis [UNESP]
title_short Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
title_full Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
title_fullStr Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
title_full_unstemmed Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
title_sort Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
author Leonel, Edson Denis [UNESP]
author_facet Leonel, Edson Denis [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Leonel, Edson Denis [UNESP]
description A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map. Copyright (C) 2009 Edson D. Leonel.
publishDate 2009
dc.date.none.fl_str_mv 2009-01-01
2013-09-30T18:50:35Z
2013-09-30T18:50:35Z
2014-05-20T14:16:24Z
2014-05-20T14:16:24Z
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/10.1155/2009/367921
Mathematical Problems In Engineering. New York: Hindawi Publishing Corporation, p. 22, 2009.
1024-123X
http://hdl.handle.net/11449/24944
10.1155/2009/367921
WOS:000271739500001
WOS000271739500001.pdf
6130644232718610
0000-0001-8224-3329
url http://dx.doi.org/10.1155/2009/367921
http://hdl.handle.net/11449/24944
identifier_str_mv Mathematical Problems In Engineering. New York: Hindawi Publishing Corporation, p. 22, 2009.
1024-123X
10.1155/2009/367921
WOS:000271739500001
WOS000271739500001.pdf
6130644232718610
0000-0001-8224-3329
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mathematical Problems in Engineering
1.145
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 22
application/pdf
dc.publisher.none.fl_str_mv Hindawi Publishing Corporation
publisher.none.fl_str_mv Hindawi Publishing Corporation
dc.source.none.fl_str_mv Web of Science
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
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