Chaotic Diffusion in Non-Dissipative Mappings
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Capítulo de livro |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-981-16-3544-1_10 http://hdl.handle.net/11449/233488 |
Resumo: | We discuss in this Chapter three different procedures to investigate the chaotic diffusion for a family of discrete mappings. The first of them involves a phenomenological investigation obtained from scaling hypotheses leading to a scaling law relating three critical exponents among them. The second one transforms the equation of differences into an ordinary differential equation which integration for short time leads to a good description of the time evolution obtained analytically and the numerical findings. For long enough time the stationary state is obtained via the localization of the lowest action invariant spanning curve allowing the determination of the critical exponents. Finally the third one considers the analytical solution of the diffusion equation, furnishing then the probability to observe a particle with a certain action at a given instant of time. From the knowledge of the probability all the momenta of the distribution are obtained including the three critical exponents describing the scaling properties of the dynamics. |
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Chaotic Diffusion in Non-Dissipative MappingsWe discuss in this Chapter three different procedures to investigate the chaotic diffusion for a family of discrete mappings. The first of them involves a phenomenological investigation obtained from scaling hypotheses leading to a scaling law relating three critical exponents among them. The second one transforms the equation of differences into an ordinary differential equation which integration for short time leads to a good description of the time evolution obtained analytically and the numerical findings. For long enough time the stationary state is obtained via the localization of the lowest action invariant spanning curve allowing the determination of the critical exponents. Finally the third one considers the analytical solution of the diffusion equation, furnishing then the probability to observe a particle with a certain action at a given instant of time. From the knowledge of the probability all the momenta of the distribution are obtained including the three critical exponents describing the scaling properties of the dynamics.Departmamento de Física Sao Paulo State UniversityDepartmamento de Física Sao Paulo State UniversityUniversidade Estadual Paulista (UNESP)Leonel, Edson Denis [UNESP]2022-05-01T08:45:05Z2022-05-01T08:45:05Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart143-161http://dx.doi.org/10.1007/978-981-16-3544-1_10Nonlinear Physical Science, p. 143-161.1867-84591867-8440http://hdl.handle.net/11449/23348810.1007/978-981-16-3544-1_102-s2.0-85114320627Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Physical Scienceinfo:eu-repo/semantics/openAccess2022-05-01T08:45:05Zoai:repositorio.unesp.br:11449/233488Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:57:52.189227Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Chaotic Diffusion in Non-Dissipative Mappings |
title |
Chaotic Diffusion in Non-Dissipative Mappings |
spellingShingle |
Chaotic Diffusion in Non-Dissipative Mappings Leonel, Edson Denis [UNESP] |
title_short |
Chaotic Diffusion in Non-Dissipative Mappings |
title_full |
Chaotic Diffusion in Non-Dissipative Mappings |
title_fullStr |
Chaotic Diffusion in Non-Dissipative Mappings |
title_full_unstemmed |
Chaotic Diffusion in Non-Dissipative Mappings |
title_sort |
Chaotic Diffusion in Non-Dissipative Mappings |
author |
Leonel, Edson Denis [UNESP] |
author_facet |
Leonel, Edson Denis [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Leonel, Edson Denis [UNESP] |
description |
We discuss in this Chapter three different procedures to investigate the chaotic diffusion for a family of discrete mappings. The first of them involves a phenomenological investigation obtained from scaling hypotheses leading to a scaling law relating three critical exponents among them. The second one transforms the equation of differences into an ordinary differential equation which integration for short time leads to a good description of the time evolution obtained analytically and the numerical findings. For long enough time the stationary state is obtained via the localization of the lowest action invariant spanning curve allowing the determination of the critical exponents. Finally the third one considers the analytical solution of the diffusion equation, furnishing then the probability to observe a particle with a certain action at a given instant of time. From the knowledge of the probability all the momenta of the distribution are obtained including the three critical exponents describing the scaling properties of the dynamics. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01-01 2022-05-01T08:45:05Z 2022-05-01T08:45:05Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/bookPart |
format |
bookPart |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-981-16-3544-1_10 Nonlinear Physical Science, p. 143-161. 1867-8459 1867-8440 http://hdl.handle.net/11449/233488 10.1007/978-981-16-3544-1_10 2-s2.0-85114320627 |
url |
http://dx.doi.org/10.1007/978-981-16-3544-1_10 http://hdl.handle.net/11449/233488 |
identifier_str_mv |
Nonlinear Physical Science, p. 143-161. 1867-8459 1867-8440 10.1007/978-981-16-3544-1_10 2-s2.0-85114320627 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Nonlinear Physical Science |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
143-161 |
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_ |
1808129004871352320 |