Dynamical thermalization in time-dependent billiards

Detalhes bibliográficos
Autor(a) principal: Hansen, Matheus
Data de Publicação: 2019
Outros Autores: Ciro, David, 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/10.1063/1.5120023
http://hdl.handle.net/11449/198028
Resumo: Numerical experiments of the statistical evolution of an ensemble of noninteracting particles in a time-dependent billiard with inelastic collisions reveals the existence of three statistical regimes for the evolution of the speed ensemble, namely, diffusion plateau, normal growth/exponential decay, and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Furthermore, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations, the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for an intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for thermalization, where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space toward a stationary distribution function with a kind of reservoir temperature determined by the boundary oscillation amplitude and the restitution coefficient.
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spelling Dynamical thermalization in time-dependent billiardsNumerical experiments of the statistical evolution of an ensemble of noninteracting particles in a time-dependent billiard with inelastic collisions reveals the existence of three statistical regimes for the evolution of the speed ensemble, namely, diffusion plateau, normal growth/exponential decay, and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Furthermore, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations, the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for an intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for thermalization, where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space toward a stationary distribution function with a kind of reservoir temperature determined by the boundary oscillation amplitude and the restitution coefficient.Instituto de Física Universidade de São PauloInstituto de Astronomia Geofísica e Ciências Atmosféricas Universidade de São PauloDepartamento de Física UNESPDepartamento de Física UNESPUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Hansen, MatheusCiro, DavidCaldas, Iberê L.Leonel, Edson D. [UNESP]2020-12-12T00:56:55Z2020-12-12T00:56:55Z2019-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1063/1.5120023Chaos, v. 29, n. 10, 2019.1054-1500http://hdl.handle.net/11449/19802810.1063/1.51200232-s2.0-85073591954Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengChaosinfo:eu-repo/semantics/openAccess2021-10-23T07:53:22Zoai:repositorio.unesp.br:11449/198028Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:42:14.595611Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Dynamical thermalization in time-dependent billiards
title Dynamical thermalization in time-dependent billiards
spellingShingle Dynamical thermalization in time-dependent billiards
Hansen, Matheus
title_short Dynamical thermalization in time-dependent billiards
title_full Dynamical thermalization in time-dependent billiards
title_fullStr Dynamical thermalization in time-dependent billiards
title_full_unstemmed Dynamical thermalization in time-dependent billiards
title_sort Dynamical thermalization in time-dependent billiards
author Hansen, Matheus
author_facet Hansen, Matheus
Ciro, David
Caldas, Iberê L.
Leonel, Edson D. [UNESP]
author_role author
author2 Ciro, David
Caldas, Iberê L.
Leonel, Edson D. [UNESP]
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Hansen, Matheus
Ciro, David
Caldas, Iberê L.
Leonel, Edson D. [UNESP]
description Numerical experiments of the statistical evolution of an ensemble of noninteracting particles in a time-dependent billiard with inelastic collisions reveals the existence of three statistical regimes for the evolution of the speed ensemble, namely, diffusion plateau, normal growth/exponential decay, and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Furthermore, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations, the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for an intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for thermalization, where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space toward a stationary distribution function with a kind of reservoir temperature determined by the boundary oscillation amplitude and the restitution coefficient.
publishDate 2019
dc.date.none.fl_str_mv 2019-10-01
2020-12-12T00:56:55Z
2020-12-12T00:56:55Z
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/10.1063/1.5120023
Chaos, v. 29, n. 10, 2019.
1054-1500
http://hdl.handle.net/11449/198028
10.1063/1.5120023
2-s2.0-85073591954
url http://dx.doi.org/10.1063/1.5120023
http://hdl.handle.net/11449/198028
identifier_str_mv Chaos, v. 29, n. 10, 2019.
1054-1500
10.1063/1.5120023
2-s2.0-85073591954
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Chaos
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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