Break-up of invariant curves in the Fermi-Ulam model

Detalhes bibliográficos
Autor(a) principal: Hermes, Joelson D.V. [UNESP]
Data de Publicação: 2022
Outros Autores: dos Reis, Marcelo A., Caldas, Iberê L., Leonel, Edson D. [UNESP]
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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spelling 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
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