Tangent Method and Some Dynamical Properties of an Oval-Like Billiard
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808129233579409408 |