Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
Autor(a) principal: | |
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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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808129400987713536 |