An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

Detalhes bibliográficos
Autor(a) principal: Leonel, Edson D. [UNESP]
Data de Publicação: 2018
Outros Autores: Kuwana, Célia M. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s10955-017-1920-x
http://hdl.handle.net/11449/170381
Resumo: The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ= 0 to non-integrable for ϵ≠ 0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠ 0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.
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spelling An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly ActionCritical exponentsDiffusion equationPhase transitionScaling lawsThe chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ= 0 to non-integrable for ϵ≠ 0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠ 0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Departamento de Física UNESP - Univ Estadual Paulista, Av. 24A 1515Abdus Salam International Center for Theoretical Physics, Strada Costiera 11Departamento de Física UNESP - Univ Estadual Paulista, Av. 24A 1515FAPESP: 2012/23688-5CNPq: 303707/2015-1Universidade Estadual Paulista (Unesp)Abdus Salam International Center for Theoretical PhysicsLeonel, Edson D. [UNESP]Kuwana, Célia M. [UNESP]2018-12-11T16:50:34Z2018-12-11T16:50:34Z2018-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article69-78application/pdfhttp://dx.doi.org/10.1007/s10955-017-1920-xJournal of Statistical Physics, v. 170, n. 1, p. 69-78, 2018.0022-4715http://hdl.handle.net/11449/17038110.1007/s10955-017-1920-x2-s2.0-850342181092-s2.0-85034218109.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Statistical Physics0,930info:eu-repo/semantics/openAccess2023-12-03T06:19:10Zoai:repositorio.unesp.br:11449/170381Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:25:59.389148Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
title An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
spellingShingle An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
Leonel, Edson D. [UNESP]
Critical exponents
Diffusion equation
Phase transition
Scaling laws
title_short An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
title_full An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
title_fullStr An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
title_full_unstemmed An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
title_sort An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
author Leonel, Edson D. [UNESP]
author_facet Leonel, Edson D. [UNESP]
Kuwana, Célia M. [UNESP]
author_role author
author2 Kuwana, Célia M. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Abdus Salam International Center for Theoretical Physics
dc.contributor.author.fl_str_mv Leonel, Edson D. [UNESP]
Kuwana, Célia M. [UNESP]
dc.subject.por.fl_str_mv Critical exponents
Diffusion equation
Phase transition
Scaling laws
topic Critical exponents
Diffusion equation
Phase transition
Scaling laws
description The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ= 0 to non-integrable for ϵ≠ 0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠ 0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.
publishDate 2018
dc.date.none.fl_str_mv 2018-12-11T16:50:34Z
2018-12-11T16:50:34Z
2018-01-01
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/10.1007/s10955-017-1920-x
Journal of Statistical Physics, v. 170, n. 1, p. 69-78, 2018.
0022-4715
http://hdl.handle.net/11449/170381
10.1007/s10955-017-1920-x
2-s2.0-85034218109
2-s2.0-85034218109.pdf
url http://dx.doi.org/10.1007/s10955-017-1920-x
http://hdl.handle.net/11449/170381
identifier_str_mv Journal of Statistical Physics, v. 170, n. 1, p. 69-78, 2018.
0022-4715
10.1007/s10955-017-1920-x
2-s2.0-85034218109
2-s2.0-85034218109.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Statistical Physics
0,930
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 69-78
application/pdf
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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