Break-up of invariant curves in the Fermi-Ulam model
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.chaos.2022.112410 http://hdl.handle.net/11449/241404 |
Resumo: | The transport of particles in the phase space is investigated in the Fermi-Ulam model. The system consists of a particle confined to move within two rigid walls with which it collides. One is fixed and the other is periodically moving in time. In this work we investigate, for this model, the location of invariant curves that separate chaotic areas in the phase space. Applying the Slater's theorem we verify that the mapping presents a family of invariant spanning curves with a rotation number whose expansion into continued fractions has an infinite tail of the unity, acting as local transport barriers. We study the destruction of such curves and find the critical parameters for that. The determination of the rotation number in the vicinity of one of the considered spanning curves allowed us to understand the dynamics in the vicinity of the considered curve, both before and after criticality. The rotation number profile showed us the fractal character of the region close to the curve, since this profile has a structure similar to a “Devil's Staircase”. |
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Repositório Institucional da UNESP |
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Break-up of invariant curves in the Fermi-Ulam modelChaosHamiltonian systemsMappingsNonlinear dynamicsThe transport of particles in the phase space is investigated in the Fermi-Ulam model. The system consists of a particle confined to move within two rigid walls with which it collides. One is fixed and the other is periodically moving in time. In this work we investigate, for this model, the location of invariant curves that separate chaotic areas in the phase space. Applying the Slater's theorem we verify that the mapping presents a family of invariant spanning curves with a rotation number whose expansion into continued fractions has an infinite tail of the unity, acting as local transport barriers. We study the destruction of such curves and find the critical parameters for that. The determination of the rotation number in the vicinity of one of the considered spanning curves allowed us to understand the dynamics in the vicinity of the considered curve, both before and after criticality. The rotation number profile showed us the fractal character of the region close to the curve, since this profile has a structure similar to a “Devil's Staircase”.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Federal Institute of Education Science and Technology of South of Minas Gerais - IFSULDEMINASDepartamento de Física Universidade Estadual Paulista (UNESP), Campus Rio Claro, Av. 24A, 1515, SPEscola Preparatória de Cadetes do Exército - EsPCEx Campinas, SPPhysics Institute University of São Paulo, São PauloDepartamento de Física Universidade Estadual Paulista (UNESP), Campus Rio Claro, Av. 24A, 1515, SPFAPESP: 2018-03211-6CNPq: 302665-2017-0CNPq: 407299-2018-1Science and Technology of South of Minas Gerais - IFSULDEMINASUniversidade Estadual Paulista (UNESP)CampinasUniversidade de São Paulo (USP)Hermes, Joelson D.V. [UNESP]dos Reis, Marcelo A.Caldas, Iberê L.Leonel, Edson D. [UNESP]2023-03-01T21:00:52Z2023-03-01T21:00:52Z2022-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.chaos.2022.112410Chaos, Solitons and Fractals, v. 162.0960-0779http://hdl.handle.net/11449/24140410.1016/j.chaos.2022.1124102-s2.0-85134748064Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengChaos, Solitons and Fractalsinfo:eu-repo/semantics/openAccess2023-03-01T21:00:53Zoai:repositorio.unesp.br:11449/241404Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:06:15.811246Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Break-up of invariant curves in the Fermi-Ulam model |
title |
Break-up of invariant curves in the Fermi-Ulam model |
spellingShingle |
Break-up of invariant curves in the Fermi-Ulam model Hermes, Joelson D.V. [UNESP] Chaos Hamiltonian systems Mappings Nonlinear dynamics |
title_short |
Break-up of invariant curves in the Fermi-Ulam model |
title_full |
Break-up of invariant curves in the Fermi-Ulam model |
title_fullStr |
Break-up of invariant curves in the Fermi-Ulam model |
title_full_unstemmed |
Break-up of invariant curves in the Fermi-Ulam model |
title_sort |
Break-up of invariant curves in the Fermi-Ulam model |
author |
Hermes, Joelson D.V. [UNESP] |
author_facet |
Hermes, Joelson D.V. [UNESP] dos Reis, Marcelo A. Caldas, Iberê L. Leonel, Edson D. [UNESP] |
author_role |
author |
author2 |
dos Reis, Marcelo A. Caldas, Iberê L. Leonel, Edson D. [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Science and Technology of South of Minas Gerais - IFSULDEMINAS Universidade Estadual Paulista (UNESP) Campinas Universidade de São Paulo (USP) |
dc.contributor.author.fl_str_mv |
Hermes, Joelson D.V. [UNESP] dos Reis, Marcelo A. Caldas, Iberê L. Leonel, Edson D. [UNESP] |
dc.subject.por.fl_str_mv |
Chaos Hamiltonian systems Mappings Nonlinear dynamics |
topic |
Chaos Hamiltonian systems Mappings Nonlinear dynamics |
description |
The transport of particles in the phase space is investigated in the Fermi-Ulam model. The system consists of a particle confined to move within two rigid walls with which it collides. One is fixed and the other is periodically moving in time. In this work we investigate, for this model, the location of invariant curves that separate chaotic areas in the phase space. Applying the Slater's theorem we verify that the mapping presents a family of invariant spanning curves with a rotation number whose expansion into continued fractions has an infinite tail of the unity, acting as local transport barriers. We study the destruction of such curves and find the critical parameters for that. The determination of the rotation number in the vicinity of one of the considered spanning curves allowed us to understand the dynamics in the vicinity of the considered curve, both before and after criticality. The rotation number profile showed us the fractal character of the region close to the curve, since this profile has a structure similar to a “Devil's Staircase”. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-09-01 2023-03-01T21:00:52Z 2023-03-01T21:00:52Z |
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/10.1016/j.chaos.2022.112410 Chaos, Solitons and Fractals, v. 162. 0960-0779 http://hdl.handle.net/11449/241404 10.1016/j.chaos.2022.112410 2-s2.0-85134748064 |
url |
http://dx.doi.org/10.1016/j.chaos.2022.112410 http://hdl.handle.net/11449/241404 |
identifier_str_mv |
Chaos, Solitons and Fractals, v. 162. 0960-0779 10.1016/j.chaos.2022.112410 2-s2.0-85134748064 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Chaos, Solitons and Fractals |
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_ |
1808129284701683712 |