Diffusion and Lyapunov timescales in the Arnold model

Autores
Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Shevchenko, Ivan
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present work, we focus on two dynamical timescales in the Arnold Hamiltonian model: the Lyapunov time and the diffusion time when the system is confined to the stochastic layer of its dominant resonance (guiding resonance). Following Chirikov's formulation, the model is revisited, and a discussion about the main assumptions behind the analytical estimates for the diffusion rate is given. On the other hand, and in line with Chirikov's ideas, theoretical estimations of the Lyapunov time are derived. Later on, three series of numerical experiments are presented for various sets of values of the model parameters, where both timescales are computed. Comparisons between the analytical estimates and the numerical determinations are provided whenever the parameters are not too large, and those cases are in fact in agreement. In particular, the case in which both parameters are equal is numerically investigated. Relationships between the diffusion time and the Lyapunov time are established, like an exponential law or a power law in the case of large values of the parameters.
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
Fil: Giordano, Claudia Marcela. 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
Fil: Shevchenko, Ivan. Saint Petersburg State University; Rusia
Materia
CHAOTIC DIFFUSION
LYAPUNOV TIME
INSTABILITY TIME
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:11336/210884
Acceder
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spelling Diffusion and Lyapunov timescales in the Arnold modelCincotta, Pablo MiguelGiordano, Claudia MarcelaShevchenko, IvanCHAOTIC DIFFUSIONLYAPUNOV TIMEINSTABILITY TIMEhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In the present work, we focus on two dynamical timescales in the Arnold Hamiltonian model: the Lyapunov time and the diffusion time when the system is confined to the stochastic layer of its dominant resonance (guiding resonance). Following Chirikov's formulation, the model is revisited, and a discussion about the main assumptions behind the analytical estimates for the diffusion rate is given. On the other hand, and in line with Chirikov's ideas, theoretical estimations of the Lyapunov time are derived. Later on, three series of numerical experiments are presented for various sets of values of the model parameters, where both timescales are computed. Comparisons between the analytical estimates and the numerical determinations are provided whenever the parameters are not too large, and those cases are in fact in agreement. In particular, the case in which both parameters are equal is numerically investigated. Relationships between the diffusion time and the Lyapunov time are established, like an exponential law or a power law in the case of large values of the parameters.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; ArgentinaFil: Giordano, Claudia Marcela. 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; ArgentinaFil: Shevchenko, Ivan. Saint Petersburg State University; RusiaAmerican Physical Society2022-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/210884Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Shevchenko, Ivan; Diffusion and Lyapunov timescales in the Arnold model; American Physical Society; Physical Review E; 106; 4; 10-2022; 1-152470-00452470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevE.106.044205info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.106.044205info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:21:43Zoai:ri.conicet.gov.ar:11336/210884instacron: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:34982025-09-29 10:21:43.297CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Diffusion and Lyapunov timescales in the Arnold model
title Diffusion and Lyapunov timescales in the Arnold model
spellingShingle Diffusion and Lyapunov timescales in the Arnold model
Cincotta, Pablo Miguel
CHAOTIC DIFFUSION
LYAPUNOV TIME
INSTABILITY TIME
title_short Diffusion and Lyapunov timescales in the Arnold model
title_full Diffusion and Lyapunov timescales in the Arnold model
title_fullStr Diffusion and Lyapunov timescales in the Arnold model
title_full_unstemmed Diffusion and Lyapunov timescales in the Arnold model
title_sort Diffusion and Lyapunov timescales in the Arnold model
dc.creator.none.fl_str_mv Cincotta, Pablo Miguel
Giordano, Claudia Marcela
Shevchenko, Ivan
author Cincotta, Pablo Miguel
author_facet Cincotta, Pablo Miguel
Giordano, Claudia Marcela
Shevchenko, Ivan
author_role author
author2 Giordano, Claudia Marcela
Shevchenko, Ivan
author2_role author
author
dc.subject.none.fl_str_mv CHAOTIC DIFFUSION
LYAPUNOV TIME
INSTABILITY TIME
topic CHAOTIC DIFFUSION
LYAPUNOV TIME
INSTABILITY TIME
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the present work, we focus on two dynamical timescales in the Arnold Hamiltonian model: the Lyapunov time and the diffusion time when the system is confined to the stochastic layer of its dominant resonance (guiding resonance). Following Chirikov's formulation, the model is revisited, and a discussion about the main assumptions behind the analytical estimates for the diffusion rate is given. On the other hand, and in line with Chirikov's ideas, theoretical estimations of the Lyapunov time are derived. Later on, three series of numerical experiments are presented for various sets of values of the model parameters, where both timescales are computed. Comparisons between the analytical estimates and the numerical determinations are provided whenever the parameters are not too large, and those cases are in fact in agreement. In particular, the case in which both parameters are equal is numerically investigated. Relationships between the diffusion time and the Lyapunov time are established, like an exponential law or a power law in the case of large values of the parameters.
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
Fil: Giordano, Claudia Marcela. 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
Fil: Shevchenko, Ivan. Saint Petersburg State University; Rusia
description In the present work, we focus on two dynamical timescales in the Arnold Hamiltonian model: the Lyapunov time and the diffusion time when the system is confined to the stochastic layer of its dominant resonance (guiding resonance). Following Chirikov's formulation, the model is revisited, and a discussion about the main assumptions behind the analytical estimates for the diffusion rate is given. On the other hand, and in line with Chirikov's ideas, theoretical estimations of the Lyapunov time are derived. Later on, three series of numerical experiments are presented for various sets of values of the model parameters, where both timescales are computed. Comparisons between the analytical estimates and the numerical determinations are provided whenever the parameters are not too large, and those cases are in fact in agreement. In particular, the case in which both parameters are equal is numerically investigated. Relationships between the diffusion time and the Lyapunov time are established, like an exponential law or a power law in the case of large values of the parameters.
publishDate 2022
dc.date.none.fl_str_mv 2022-10
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/11336/210884
Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Shevchenko, Ivan; Diffusion and Lyapunov timescales in the Arnold model; American Physical Society; Physical Review E; 106; 4; 10-2022; 1-15
2470-0045
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/210884
identifier_str_mv Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Shevchenko, Ivan; Diffusion and Lyapunov timescales in the Arnold model; American Physical Society; Physical Review E; 106; 4; 10-2022; 1-15
2470-0045
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevE.106.044205
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.106.044205
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
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
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score 13.070432

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