Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | , , , |
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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Repositório Institucional da UNESP |
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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) |
repository.mail.fl_str_mv |
|
_version_ |
1808129270716825600 |