Stochastic approach to diffusion inside the chaotic layer of a resonance

Autores
Mestre, Martin Federico; Bazzani, Armando; Cincotta, Pablo Miguel; Giordano, Claudia Marcela
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics.
Fil: Mestre, Martin Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Bazzani, Armando. Infn, Sezione Di Bologna; Italia. Dipartimento Di Fisica; Italia
Fil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Giordano, Claudia Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
Materia
STOCHASTIC ANALYSIS METHODS
NUMERICAL SIMULATIONS OF CHAOTIC SYSTEMS
CLASSICAL TRANSPORT
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/82374
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Stochastic approach to diffusion inside the chaotic layer of a resonanceMestre, Martin FedericoBazzani, ArmandoCincotta, Pablo MiguelGiordano, Claudia MarcelaSTOCHASTIC ANALYSIS METHODSNUMERICAL SIMULATIONS OF CHAOTIC SYSTEMSCLASSICAL TRANSPORThttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics.Fil: Mestre, Martin Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Bazzani, Armando. Infn, Sezione Di Bologna; Italia. Dipartimento Di Fisica; ItaliaFil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Giordano, Claudia Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaAmerican Physical Society2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/82374Mestre, Martin Federico; Bazzani, Armando; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Stochastic approach to diffusion inside the chaotic layer of a resonance; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 89; 1; 1-2014; 12911-129111539-3755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.89.012911info:eu-repo/semantics/altIdentifier/url/http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.012911info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:03:57Zoai:ri.conicet.gov.ar:11336/82374instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:03:57.542CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stochastic approach to diffusion inside the chaotic layer of a resonance
title Stochastic approach to diffusion inside the chaotic layer of a resonance
spellingShingle Stochastic approach to diffusion inside the chaotic layer of a resonance
Mestre, Martin Federico
STOCHASTIC ANALYSIS METHODS
NUMERICAL SIMULATIONS OF CHAOTIC SYSTEMS
CLASSICAL TRANSPORT
title_short Stochastic approach to diffusion inside the chaotic layer of a resonance
title_full Stochastic approach to diffusion inside the chaotic layer of a resonance
title_fullStr Stochastic approach to diffusion inside the chaotic layer of a resonance
title_full_unstemmed Stochastic approach to diffusion inside the chaotic layer of a resonance
title_sort Stochastic approach to diffusion inside the chaotic layer of a resonance
dc.creator.none.fl_str_mv Mestre, Martin Federico
Bazzani, Armando
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author Mestre, Martin Federico
author_facet Mestre, Martin Federico
Bazzani, Armando
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author_role author
author2 Bazzani, Armando
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author2_role author
author
author
dc.subject.none.fl_str_mv STOCHASTIC ANALYSIS METHODS
NUMERICAL SIMULATIONS OF CHAOTIC SYSTEMS
CLASSICAL TRANSPORT
topic STOCHASTIC ANALYSIS METHODS
NUMERICAL SIMULATIONS OF CHAOTIC SYSTEMS
CLASSICAL TRANSPORT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics.
Fil: Mestre, Martin Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Bazzani, Armando. Infn, Sezione Di Bologna; Italia. Dipartimento Di Fisica; Italia
Fil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Giordano, Claudia Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
description We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/82374
Mestre, Martin Federico; Bazzani, Armando; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Stochastic approach to diffusion inside the chaotic layer of a resonance; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 89; 1; 1-2014; 12911-12911
1539-3755
CONICET Digital
CONICET
url http://hdl.handle.net/11336/82374
identifier_str_mv Mestre, Martin Federico; Bazzani, Armando; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Stochastic approach to diffusion inside the chaotic layer of a resonance; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 89; 1; 1-2014; 12911-12911
1539-3755
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.89.012911
info:eu-repo/semantics/altIdentifier/url/http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.012911
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842980118189834240
score 13.004268

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