Tangent Method and Some Dynamical Properties of an Oval-Like Billiard

Detalhes bibliográficos
Autor(a) principal: Costa, Diogo Ricardo da [UNESP]
Data de Publicação: 2022
Outros Autores: Hansen, Matheus, Silva, Mario Roberto [UNESP], Leonel, Edson D. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1142/S0218127422500523
http://hdl.handle.net/11449/218853
Resumo: In this paper, we consider the evolution of an ensemble of noninteracting classical particles confined in a closed region. Each one of these particles experiences several elastic collisions with a rigid-smooth oval-like boundary. As known in the literature, numerical simulations for this kind of system demand too much time, mostly because of the time spent in solving transcendental equations. To deal with that, we highlight an alternative approach to speed up the search of solutions for the transcendental equations via the tangent method, which has proved to be a faster way to solve this problem when compared with other methods, like the bisection one. The methods applied here are generic and can be used or adapted for other billiard boundaries.
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spelling Tangent Method and Some Dynamical Properties of an Oval-Like BilliardChaosnonlinear dynamicsbilliardnumerical methodIn this paper, we consider the evolution of an ensemble of noninteracting classical particles confined in a closed region. Each one of these particles experiences several elastic collisions with a rigid-smooth oval-like boundary. As known in the literature, numerical simulations for this kind of system demand too much time, mostly because of the time spent in solving transcendental equations. To deal with that, we highlight an alternative approach to speed up the search of solutions for the transcendental equations via the tangent method, which has proved to be a faster way to solve this problem when compared with other methods, like the bisection one. The methods applied here are generic and can be used or adapted for other billiard boundaries.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Center for Scientific Computing (NCC/GridUNESP) of the Sao Paulo State University (UNESP)Univ Fed Parana UFPR, Dept Fis, BR-80060000 Curitiba, Parana, BrazilUniv Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP, BrazilUniv Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP, BrazilUniv Fed Sao Paulo, Inst Ciencia & Tecnol, BR-12247014 Sao Jose Dos Campos, SP, BrazilUniv Estadual Paulista, Dept Estat Matemat Aplicada & Comp, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, Dept Estat Matemat Aplicada & Comp, BR-13506900 Rio Claro, SP, BrazilFAPESP: 2020/02415-7FAPESP: 2019/09150-1FAPESP: 2019/14038-6CNPq: 162944/20209CNPq: 301318/2019-0World Scientific Publ Co Pte LtdUniversidade Federal do Paraná (UFPR)Universidade de São Paulo (USP)Universidade Estadual Paulista (UNESP)Universidade Federal de São Paulo (UNIFESP)Costa, Diogo Ricardo da [UNESP]Hansen, MatheusSilva, Mario Roberto [UNESP]Leonel, Edson D. [UNESP]2022-04-28T17:23:24Z2022-04-28T17:23:24Z2022-03-30info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article15http://dx.doi.org/10.1142/S0218127422500523International Journal Of Bifurcation And Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 32, n. 04, 15 p., 2022.0218-1274http://hdl.handle.net/11449/21885310.1142/S0218127422500523WOS:000776249200017Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal Of Bifurcation And Chaosinfo:eu-repo/semantics/openAccess2022-04-28T17:23:24Zoai:repositorio.unesp.br:11449/218853Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:40:54.404038Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
title Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
spellingShingle Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
Costa, Diogo Ricardo da [UNESP]
Chaos
nonlinear dynamics
billiard
numerical method
title_short Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
title_full Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
title_fullStr Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
title_full_unstemmed Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
title_sort Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
author Costa, Diogo Ricardo da [UNESP]
author_facet Costa, Diogo Ricardo da [UNESP]
Hansen, Matheus
Silva, Mario Roberto [UNESP]
Leonel, Edson D. [UNESP]
author_role author
author2 Hansen, Matheus
Silva, Mario Roberto [UNESP]
Leonel, Edson D. [UNESP]
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Federal do Paraná (UFPR)
Universidade de São Paulo (USP)
Universidade Estadual Paulista (UNESP)
Universidade Federal de São Paulo (UNIFESP)
dc.contributor.author.fl_str_mv Costa, Diogo Ricardo da [UNESP]
Hansen, Matheus
Silva, Mario Roberto [UNESP]
Leonel, Edson D. [UNESP]
dc.subject.por.fl_str_mv Chaos
nonlinear dynamics
billiard
numerical method
topic Chaos
nonlinear dynamics
billiard
numerical method
description In this paper, we consider the evolution of an ensemble of noninteracting classical particles confined in a closed region. Each one of these particles experiences several elastic collisions with a rigid-smooth oval-like boundary. As known in the literature, numerical simulations for this kind of system demand too much time, mostly because of the time spent in solving transcendental equations. To deal with that, we highlight an alternative approach to speed up the search of solutions for the transcendental equations via the tangent method, which has proved to be a faster way to solve this problem when compared with other methods, like the bisection one. The methods applied here are generic and can be used or adapted for other billiard boundaries.
publishDate 2022
dc.date.none.fl_str_mv 2022-04-28T17:23:24Z
2022-04-28T17:23:24Z
2022-03-30
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/10.1142/S0218127422500523
International Journal Of Bifurcation And Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 32, n. 04, 15 p., 2022.
0218-1274
http://hdl.handle.net/11449/218853
10.1142/S0218127422500523
WOS:000776249200017
url http://dx.doi.org/10.1142/S0218127422500523
http://hdl.handle.net/11449/218853
identifier_str_mv International Journal Of Bifurcation And Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 32, n. 04, 15 p., 2022.
0218-1274
10.1142/S0218127422500523
WOS:000776249200017
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal Of Bifurcation And Chaos
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 15
dc.publisher.none.fl_str_mv World Scientific Publ Co Pte Ltd
publisher.none.fl_str_mv World Scientific Publ Co Pte Ltd
dc.source.none.fl_str_mv Web of Science
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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