Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevE.99.012202 http://hdl.handle.net/11449/187257 |
Resumo: | The dynamics of a classical point particle confined to an asymmetric time-dependent potential well is investigated under the framework of scaling. The potential corresponds to a reduced version of a particle moving along an infinitely periodic sequence of synchronously oscillating potential barriers. The dynamics of the model is described by a two-dimensional nonlinear and area preserving map in energy and phase variables. The asymmetric potential well is defined by two regions: Region I with fixed null potential and region II with an oscillating potential. The time-dependent potential of region II makes, for certain initial conditions, the particle to undergo a number of multiple reflections η at the border of the two regions and stay trapped in region I. Such trappings are described by histograms of multiple reflections η, obeying the power-law H(η) η-ν with ν≈3, which are scale invariant with a scaling parameter depending of the control parameters of the mapping. We identify the location of the sets of initial conditions in phase space producing the multiple reflections and show that they generate well defined self-similar structures in density plots of trajectories in energy space. The self-similar structures can be enhanced by properly tuning the system parameters. |
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Repositório Institucional da UNESP |
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Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential wellThe dynamics of a classical point particle confined to an asymmetric time-dependent potential well is investigated under the framework of scaling. The potential corresponds to a reduced version of a particle moving along an infinitely periodic sequence of synchronously oscillating potential barriers. The dynamics of the model is described by a two-dimensional nonlinear and area preserving map in energy and phase variables. The asymmetric potential well is defined by two regions: Region I with fixed null potential and region II with an oscillating potential. The time-dependent potential of region II makes, for certain initial conditions, the particle to undergo a number of multiple reflections η at the border of the two regions and stay trapped in region I. Such trappings are described by histograms of multiple reflections η, obeying the power-law H(η) η-ν with ν≈3, which are scale invariant with a scaling parameter depending of the control parameters of the mapping. We identify the location of the sets of initial conditions in phase space producing the multiple reflections and show that they generate well defined self-similar structures in density plots of trajectories in energy space. The self-similar structures can be enhanced by properly tuning the system parameters.Departamento de Física UNESP - Universidade Estadual Paulista, Av. 24A, 1515, Bela VistaDepartamento de Matemática e Estatística - UEPGInstituto de Física Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48Departamento de Física UNESP - Universidade Estadual Paulista, Av. 24A, 1515, Bela VistaUniversidade Estadual Paulista (Unesp)Universidade Estadual de Ponta Grossa (UEPG)Benemérita Universidad Autónoma de PueblaDa Costa, Diogo R. [UNESP]Méndez-Bermúdez, J. A.Leonel, Edson D. [UNESP]2019-10-06T15:30:31Z2019-10-06T15:30:31Z2019-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.99.012202Physical Review E, v. 99, n. 1, 2019.2470-00532470-0045http://hdl.handle.net/11449/18725710.1103/PhysRevE.99.0122022-s2.0-85059805485Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Einfo:eu-repo/semantics/openAccess2021-10-23T17:30:23Zoai:repositorio.unesp.br:11449/187257Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:01:28.624894Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
title |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
spellingShingle |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well Da Costa, Diogo R. [UNESP] |
title_short |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
title_full |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
title_fullStr |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
title_full_unstemmed |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
title_sort |
Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well |
author |
Da Costa, Diogo R. [UNESP] |
author_facet |
Da Costa, Diogo R. [UNESP] Méndez-Bermúdez, J. A. Leonel, Edson D. [UNESP] |
author_role |
author |
author2 |
Méndez-Bermúdez, J. A. Leonel, Edson D. [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Estadual de Ponta Grossa (UEPG) Benemérita Universidad Autónoma de Puebla |
dc.contributor.author.fl_str_mv |
Da Costa, Diogo R. [UNESP] Méndez-Bermúdez, J. A. Leonel, Edson D. [UNESP] |
description |
The dynamics of a classical point particle confined to an asymmetric time-dependent potential well is investigated under the framework of scaling. The potential corresponds to a reduced version of a particle moving along an infinitely periodic sequence of synchronously oscillating potential barriers. The dynamics of the model is described by a two-dimensional nonlinear and area preserving map in energy and phase variables. The asymmetric potential well is defined by two regions: Region I with fixed null potential and region II with an oscillating potential. The time-dependent potential of region II makes, for certain initial conditions, the particle to undergo a number of multiple reflections η at the border of the two regions and stay trapped in region I. Such trappings are described by histograms of multiple reflections η, obeying the power-law H(η) η-ν with ν≈3, which are scale invariant with a scaling parameter depending of the control parameters of the mapping. We identify the location of the sets of initial conditions in phase space producing the multiple reflections and show that they generate well defined self-similar structures in density plots of trajectories in energy space. The self-similar structures can be enhanced by properly tuning the system parameters. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T15:30:31Z 2019-10-06T15:30:31Z 2019-02-01 |
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.99.012202 Physical Review E, v. 99, n. 1, 2019. 2470-0053 2470-0045 http://hdl.handle.net/11449/187257 10.1103/PhysRevE.99.012202 2-s2.0-85059805485 |
url |
http://dx.doi.org/10.1103/PhysRevE.99.012202 http://hdl.handle.net/11449/187257 |
identifier_str_mv |
Physical Review E, v. 99, n. 1, 2019. 2470-0053 2470-0045 10.1103/PhysRevE.99.012202 2-s2.0-85059805485 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review E |
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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1808128305950359552 |