Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Detalhes bibliográficos
Autor(a) principal: Livorati, André L. P.
Data de Publicação: 2012
Outros Autores: Kroetz, Tiago, Dettmann, Carl P. [UNESP], Caldas, Iberê Luiz, Leonel, Edson D. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1103/PhysRevE.86.036203
http://hdl.handle.net/11449/226969
Resumo: Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter ε and experiences a transition from integrable (ε=0) to nonintegrable (ε0). For small values of ε, the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter ε increases and reaches a critical value ε c, all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large ε, the survival probability decays exponentially when it turns into a slower decay as the control parameter ε is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity. © 2012 American Physical Society.
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spelling Stickiness in a bouncer model: A slowing mechanism for Fermi accelerationSome phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter ε and experiences a transition from integrable (ε=0) to nonintegrable (ε0). For small values of ε, the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter ε increases and reaches a critical value ε c, all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large ε, the survival probability decays exponentially when it turns into a slower decay as the control parameter ε is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity. © 2012 American Physical Society.Instituto de Física IFUSP Universidade de São Paulo, USP Rua do Matão, Tr. R 187, 05314-970, São Paulo, SPDepartamento de Física Universidade Tecnológica Federal Do Paraná UTFPR Campus Pato Branco, 85503-390, Pato Branco, PRSchool of Mathematics University of Bristol, Bristol BS8 1TWDepartamento de Estatística Matemática Aplicada e Computação UNESP Univ Estadual Paulista, Av. 24A, 1515 Bela Vista, 13506-900, Rio Claro, SPAbdus Salam ICTP, 34151 TriesteDepartamento de Estatística Matemática Aplicada e Computação UNESP Univ Estadual Paulista, Av. 24A, 1515 Bela Vista, 13506-900, Rio Claro, SPUniversidade de São Paulo (USP)UTFPR Campus Pato BrancoUniversity of BristolUniversidade Estadual Paulista (UNESP)ICTPLivorati, André L. P.Kroetz, TiagoDettmann, Carl P. [UNESP]Caldas, Iberê LuizLeonel, Edson D. [UNESP]2022-04-29T04:35:28Z2022-04-29T04:35:28Z2012-09-06info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.86.036203Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 86, n. 3, 2012.1539-37551550-2376http://hdl.handle.net/11449/22696910.1103/PhysRevE.86.0362032-s2.0-84866361316Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsinfo:eu-repo/semantics/openAccess2022-04-29T04:35:28Zoai:repositorio.unesp.br:11449/226969Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:58:37.346592Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
title Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
spellingShingle Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
Livorati, André L. P.
title_short Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
title_full Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
title_fullStr Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
title_full_unstemmed Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
title_sort Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
author Livorati, André L. P.
author_facet Livorati, André L. P.
Kroetz, Tiago
Dettmann, Carl P. [UNESP]
Caldas, Iberê Luiz
Leonel, Edson D. [UNESP]
author_role author
author2 Kroetz, Tiago
Dettmann, Carl P. [UNESP]
Caldas, Iberê Luiz
Leonel, Edson D. [UNESP]
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
UTFPR Campus Pato Branco
University of Bristol
Universidade Estadual Paulista (UNESP)
ICTP
dc.contributor.author.fl_str_mv Livorati, André L. P.
Kroetz, Tiago
Dettmann, Carl P. [UNESP]
Caldas, Iberê Luiz
Leonel, Edson D. [UNESP]
description Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter ε and experiences a transition from integrable (ε=0) to nonintegrable (ε0). For small values of ε, the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter ε increases and reaches a critical value ε c, all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large ε, the survival probability decays exponentially when it turns into a slower decay as the control parameter ε is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity. © 2012 American Physical Society.
publishDate 2012
dc.date.none.fl_str_mv 2012-09-06
2022-04-29T04:35:28Z
2022-04-29T04:35:28Z
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/10.1103/PhysRevE.86.036203
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 86, n. 3, 2012.
1539-3755
1550-2376
http://hdl.handle.net/11449/226969
10.1103/PhysRevE.86.036203
2-s2.0-84866361316
url http://dx.doi.org/10.1103/PhysRevE.86.036203
http://hdl.handle.net/11449/226969
identifier_str_mv Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 86, n. 3, 2012.
1539-3755
1550-2376
10.1103/PhysRevE.86.036203
2-s2.0-84866361316
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
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)
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