The h-theory: universality classes of hierarchical complex systems

Detalhes bibliográficos
Autor(a) principal: ROA GONZÁLEZ, Iván René
Data de Publicação: 2017
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFPE
Texto Completo: https://repositorio.ufpe.br/handle/123456789/25596
Resumo: ROA GONZÁLEZ, Iván René, também é conhecido em citações bibliográficas por: GONZÁLEZ, Iván René Roa
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spelling ROA GONZÁLEZ, Iván Renéhttp://lattes.cnpq.br/3567090559095962http://lattes.cnpq.br/7160030619369816MACÊDO, Antônio Murilo Santos2018-08-15T22:43:09Z2018-08-15T22:43:09Z2017-04-28https://repositorio.ufpe.br/handle/123456789/25596ROA GONZÁLEZ, Iván René, também é conhecido em citações bibliográficas por: GONZÁLEZ, Iván René RoaComplex dynamical systems can be characterized through the time series associated with dynamical variables, which yield important information on the underlying stochastic process. The probability density function, the temporal correlation function, the power spectrum, and the memory function are examples of statistical properties that can be extracted from the time series. In this thesis, we are particularly interested in describing complex phenomena in which the stationary distribution of the time series of the main dynamical variable (the signal) exhibits large deviations from Gaussian statistics, possibly showing long and heavy tails. This kind of phenomena is present in many areas of physics, biology, and economics. However, our interest is focused on spectral fluctuations in non-integrable ballistic cavities, intensity fluctuations in random lasers, turbulence in fluids, stock prices fluctuations in financial markets. We shall attempt to describe these phenomena as a composition of distributions with distinct space/time scales which arise from a hierarchical dynamics with a coupling between contiguous scales. The model to be used, denominated H-Theory, was recently proposed by our research group and consists of a set of coupled stochastic differential equations, whose stationary solution leads to a parametric family of distributions represented by Fox H-function. This result unifies and generalizes the universality classes of superstatistics, which is a formalism that has been successfully used to describe systems with two separated time scales.CNPqna caracterização de sistemas complexos nos quais a distribuição estacionária da série temporal da variável dinâmica principal (o sinal) desvia-se substancialmente da gaussiana, podendo exibir caudas longas e pesadas. Exemplos de sistemas deste tipo podem ser encontrados em diversas áreas da física, da biologia e da economia. Contudo, centraremos nosso foco nos fenômenos de flutuações espectrais em turbulência em fluidos, variações nos preços de ações no mercado financeiro, flutuações de intensidade em lasers aleatórios em fibra óptica e estatística espectral de cavidades balísticas não-integráveis. Caracterizamos esses fenômenos como resultado da composição de distribuições com distintas escalas espaçiais/temporais que resultam de uma dinâmica hierárquica com acoplamento entre escalas contíguas. O modelo a ser usado, denominado teoria H, foi recentemente proposto por nosso grupo de pesquisa e consiste de um sistema de equações diferenciais estocásticas acopladas, cuja solução estacionária produz uma família paramétrica de distribuições representadas por funções H de Fox. Este resultado unifica e estende para múltiplas escalas as classes de universalidade da superestatística, que é um formalismo que tem sido usado com sucesso para descrever sistemas dinâmicos complexos com duas escalas temporais separadas.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessMecânica estatísticaSistemas complexosProcessos estocásticosTurbulênciaThe h-theory: universality classes of hierarchical complex systemsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Iván René Roa González.pdf.jpgTESE Iván René Roa González.pdf.jpgGenerated Thumbnailimage/jpeg1212https://repositorio.ufpe.br/bitstream/123456789/25596/5/TESE%20Iv%c3%a1n%20Ren%c3%a9%20Roa%20Gonz%c3%a1lez.pdf.jpgb862ae9b504c1bb2ffb8a18b262dbf4eMD55ORIGINALTESE Iván René Roa González.pdfTESE Iván René Roa González.pdfapplication/pdf10499894https://repositorio.ufpe.br/bitstream/123456789/25596/1/TESE%20Iv%c3%a1n%20Ren%c3%a9%20Roa%20Gonz%c3%a1lez.pdffc4dd4d7bc530a34f5f3bf20698efba5MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv The h-theory: universality classes of hierarchical complex systems
title The h-theory: universality classes of hierarchical complex systems
spellingShingle The h-theory: universality classes of hierarchical complex systems
ROA GONZÁLEZ, Iván René
Mecânica estatística
Sistemas complexos
Processos estocásticos
Turbulência
title_short The h-theory: universality classes of hierarchical complex systems
title_full The h-theory: universality classes of hierarchical complex systems
title_fullStr The h-theory: universality classes of hierarchical complex systems
title_full_unstemmed The h-theory: universality classes of hierarchical complex systems
title_sort The h-theory: universality classes of hierarchical complex systems
author ROA GONZÁLEZ, Iván René
author_facet ROA GONZÁLEZ, Iván René
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/3567090559095962
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/7160030619369816
dc.contributor.author.fl_str_mv ROA GONZÁLEZ, Iván René
dc.contributor.advisor1.fl_str_mv MACÊDO, Antônio Murilo Santos
contributor_str_mv MACÊDO, Antônio Murilo Santos
dc.subject.por.fl_str_mv Mecânica estatística
Sistemas complexos
Processos estocásticos
Turbulência
topic Mecânica estatística
Sistemas complexos
Processos estocásticos
Turbulência
description ROA GONZÁLEZ, Iván René, também é conhecido em citações bibliográficas por: GONZÁLEZ, Iván René Roa
publishDate 2017
dc.date.issued.fl_str_mv 2017-04-28
dc.date.accessioned.fl_str_mv 2018-08-15T22:43:09Z
dc.date.available.fl_str_mv 2018-08-15T22:43:09Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
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status_str publishedVersion
dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/25596
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dc.language.iso.fl_str_mv eng
language eng
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Fisica
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dc.publisher.country.fl_str_mv Brasil
publisher.none.fl_str_mv Universidade Federal de Pernambuco
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