An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action
Autor(a) principal: | |
---|---|
Data de Publicação: | 2018 |
Outros Autores: | |
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. |
id |
UNSP_9ab5ef1f2a51d76e550d24ec6aef5dec |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/170381 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
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 |
|
_version_ |
1808129067752357888 |