Espalhamento de gaussons em acopladores ópticos direcionais
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/7270 |
Resumo: | This dissertation presents the research that was focused on the study of solitons in nonintegrable systems governed by effective models of partial differential equations (PDEs) of (1+1) dimensions, that is, one spatial and one time dimension. In the main research line, we considered a model of two fields given by nonlinear Schrödinger equations with logarithmic nonlinearity and linear coupling, the main aspects of the collision dynamics of two Gaussian solitons (gaussons) were investigated, addressing the stability of the solutions, the interaction mechanisms, and the regularity of the scattering. The study of gaussons collisions in this model was performed via two approaches: semianalytic (variational/reduced model) and direct numerical simulation. For the system considered in this work, both approaches provided similar results which revealed the existence of a chaotic and fractal dynamics involving the initial conditions and the post-collisional properties of the solitons, which were verified by the analysis of the correlations between the input and output parameters. The fractal patterns are constituted by regularity windows that are positioned accordingly to a well defined rule, which was obtained via a linearization model that was found to be very similar in both approaches (i.e., the windows arrangement was well described by the variational model). In such windows the solitons collision dynamic turns out to be not chaotic (regular collision), it becomes predictable and very well defined, hence the width of these windows provides the conditions in which the control of the interaction is possible. Besides, by analyzing the dynamics of the variational parameters of the reduced model and also the dynamics of the most relevant physical quantities in the exact approach via PDEs (namely the total kinetic and potential energies), we attested that these windows arise due to a resonant mechanism of energy exchange between translational and vibrational soliton modes. By studying the linear stability of the solitary waves, we proved that the vibrational modes originate from shape oscillations induced by internal modes and also, possibly, by instability modes excited during the collisions. We verified that these oscillations are well defined in all regular collisions. The viability of the variational method in the system studied is due to the suitable description of the vibrational modes by the reduced model, and also the low influence of the emitted nonlinear radiation in the regular collision processes found in the direct simulations. |
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Cardoso, Wesley Buenohttp://lattes.cnpq.br/6845416823133684Avelar, Ardiley TorresRamos, Jorge Gabriel Gomes de Souzahttp://lattes.cnpq.br/8713492477336011Teixeira, Rafael Marques Paes2017-05-05T12:55:46Z2017-04-10TEIXEIRA, Rafael Marques Paes. Espalhamento de gaussons em acopladores ópticos direcionais. 2017. 128 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2017.http://repositorio.bc.ufg.br/tede/handle/tede/7270This dissertation presents the research that was focused on the study of solitons in nonintegrable systems governed by effective models of partial differential equations (PDEs) of (1+1) dimensions, that is, one spatial and one time dimension. In the main research line, we considered a model of two fields given by nonlinear Schrödinger equations with logarithmic nonlinearity and linear coupling, the main aspects of the collision dynamics of two Gaussian solitons (gaussons) were investigated, addressing the stability of the solutions, the interaction mechanisms, and the regularity of the scattering. The study of gaussons collisions in this model was performed via two approaches: semianalytic (variational/reduced model) and direct numerical simulation. For the system considered in this work, both approaches provided similar results which revealed the existence of a chaotic and fractal dynamics involving the initial conditions and the post-collisional properties of the solitons, which were verified by the analysis of the correlations between the input and output parameters. The fractal patterns are constituted by regularity windows that are positioned accordingly to a well defined rule, which was obtained via a linearization model that was found to be very similar in both approaches (i.e., the windows arrangement was well described by the variational model). In such windows the solitons collision dynamic turns out to be not chaotic (regular collision), it becomes predictable and very well defined, hence the width of these windows provides the conditions in which the control of the interaction is possible. Besides, by analyzing the dynamics of the variational parameters of the reduced model and also the dynamics of the most relevant physical quantities in the exact approach via PDEs (namely the total kinetic and potential energies), we attested that these windows arise due to a resonant mechanism of energy exchange between translational and vibrational soliton modes. By studying the linear stability of the solitary waves, we proved that the vibrational modes originate from shape oscillations induced by internal modes and also, possibly, by instability modes excited during the collisions. We verified that these oscillations are well defined in all regular collisions. The viability of the variational method in the system studied is due to the suitable description of the vibrational modes by the reduced model, and also the low influence of the emitted nonlinear radiation in the regular collision processes found in the direct simulations.Essa dissertação apresenta o trabalho de pesquisa que teve como foco o estudo de sólitons em sistemas não-integráveis governados por modelos efetivos de equações diferenciais parciais (EDPs) de dimensão (1+1), isto é, uma dimensão espacial e uma temporal. Na linha de pesquisa principal, foi considerado um modelo de dois campos dado por equações de Schrödinger com não-linearidade logarítmica e acoplamento linear, em que foram investigados os principais aspectos da colisão de dois sólitons gaussianos (gaussons), considerando a estabilidade das soluções, seus mecanismos de interação e a regularidade do espalhamento. O estudo de colisões de gaussons nesse modelo foi realizado a partir de duas abordagens: semianalítica (modelo variacional/reduzido) e simulação numérica direta. Para o sistema considerado nesse trabalho, as duas abordagens renderam resultados semelhantes que revelam a existência de uma dinâmica caótica e fractal envolvendo as condições iniciais e as propriedades pós-colisionais dos sólitons, que foi constatada pela análise das correlações entre os parâmetros de entrada e saída. Os padrões fractais são constituídos por janelas de regularidade, cujo posicionamento segue uma regra bem definida que foi obtida via um modelo de linearização que se mostrou muito semelhante nas duas abordagens (i.e., a distribuição de janelas foi bem descrita variacionalmente). Em tais janelas a dinâmica de colisão dos sólitons deixa de ser caótica (colisão regular), tornando-se previsível e bem definida, por isso a largura dessas janelas fornece as condições em que o controle da interação é possível. Além disso, pela análise da dinâmica dos parâmetros variacionais do modelo reduzido e das quantidades físicas mais relevantes na abordagem exata via EDPs (energia total cinética e potencial), verificou-se que essas janelas surgem devido a um mecanismo ressonante de troca de energia entre os modos translacionais e vibracionais dos sólitons. Pelo estudo da estabilidade linear das ondas solitárias, verificou-se que os modos vibracionais decorrem de oscilações de forma induzidas por modos internos e também, possivelmente, por modos de instabilidade excitados durante as colisões. Constatou-se que essas oscilações são bem definidas em todas as colisões regulares. A viabilidade do método variacional no sistema estudado se deve à adequada descrição dos modos vibracionais pelo modelo reduzido e à baixa influência da radiação não-linear emitida sobre os processos de colisão regulares encontrados via simulações diretas.Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-05-04T18:54:25Z No. of bitstreams: 2 Dissertação - Rafael Marques Paes Teixeira - 2017.pdf: 12639296 bytes, checksum: a0fc40914d28a4f117459a9314e27b7a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-05-05T12:55:45Z (GMT) No. of bitstreams: 2 Dissertação - Rafael Marques Paes Teixeira - 2017.pdf: 12639296 bytes, checksum: a0fc40914d28a4f117459a9314e27b7a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2017-05-05T12:55:46Z (GMT). No. of bitstreams: 2 Dissertação - Rafael Marques Paes Teixeira - 2017.pdf: 12639296 bytes, checksum: a0fc40914d28a4f117459a9314e27b7a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-04-10Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqapplication/pdfporUniversidade Federal de GoiásPrograma de Pós-graduação em Fisica (IF)UFGBrasilInstituto de Física - IF (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessSólitonsFibras ópticasEspalhamento fractalCaosSolitonsOptical fibersFractal scatteringChaosMATEMATICA APLICADA::FISICA MATEMATICAEspalhamento de gaussons em acopladores ópticos direcionaisScattering of gaussons in optical directional couplersinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis3162138865744262028600600600600-4029658853652049306-5516461120698566022-2555911436985713659reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
Espalhamento de gaussons em acopladores ópticos direcionais |
dc.title.alternative.eng.fl_str_mv |
Scattering of gaussons in optical directional couplers |
title |
Espalhamento de gaussons em acopladores ópticos direcionais |
spellingShingle |
Espalhamento de gaussons em acopladores ópticos direcionais Teixeira, Rafael Marques Paes Sólitons Fibras ópticas Espalhamento fractal Caos Solitons Optical fibers Fractal scattering Chaos MATEMATICA APLICADA::FISICA MATEMATICA |
title_short |
Espalhamento de gaussons em acopladores ópticos direcionais |
title_full |
Espalhamento de gaussons em acopladores ópticos direcionais |
title_fullStr |
Espalhamento de gaussons em acopladores ópticos direcionais |
title_full_unstemmed |
Espalhamento de gaussons em acopladores ópticos direcionais |
title_sort |
Espalhamento de gaussons em acopladores ópticos direcionais |
author |
Teixeira, Rafael Marques Paes |
author_facet |
Teixeira, Rafael Marques Paes |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Cardoso, Wesley Bueno |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6845416823133684 |
dc.contributor.referee1.fl_str_mv |
Avelar, Ardiley Torres |
dc.contributor.referee2.fl_str_mv |
Ramos, Jorge Gabriel Gomes de Souza |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/8713492477336011 |
dc.contributor.author.fl_str_mv |
Teixeira, Rafael Marques Paes |
contributor_str_mv |
Cardoso, Wesley Bueno Avelar, Ardiley Torres Ramos, Jorge Gabriel Gomes de Souza |
dc.subject.por.fl_str_mv |
Sólitons Fibras ópticas Espalhamento fractal Caos |
topic |
Sólitons Fibras ópticas Espalhamento fractal Caos Solitons Optical fibers Fractal scattering Chaos MATEMATICA APLICADA::FISICA MATEMATICA |
dc.subject.eng.fl_str_mv |
Solitons Optical fibers Fractal scattering Chaos |
dc.subject.cnpq.fl_str_mv |
MATEMATICA APLICADA::FISICA MATEMATICA |
description |
This dissertation presents the research that was focused on the study of solitons in nonintegrable systems governed by effective models of partial differential equations (PDEs) of (1+1) dimensions, that is, one spatial and one time dimension. In the main research line, we considered a model of two fields given by nonlinear Schrödinger equations with logarithmic nonlinearity and linear coupling, the main aspects of the collision dynamics of two Gaussian solitons (gaussons) were investigated, addressing the stability of the solutions, the interaction mechanisms, and the regularity of the scattering. The study of gaussons collisions in this model was performed via two approaches: semianalytic (variational/reduced model) and direct numerical simulation. For the system considered in this work, both approaches provided similar results which revealed the existence of a chaotic and fractal dynamics involving the initial conditions and the post-collisional properties of the solitons, which were verified by the analysis of the correlations between the input and output parameters. The fractal patterns are constituted by regularity windows that are positioned accordingly to a well defined rule, which was obtained via a linearization model that was found to be very similar in both approaches (i.e., the windows arrangement was well described by the variational model). In such windows the solitons collision dynamic turns out to be not chaotic (regular collision), it becomes predictable and very well defined, hence the width of these windows provides the conditions in which the control of the interaction is possible. Besides, by analyzing the dynamics of the variational parameters of the reduced model and also the dynamics of the most relevant physical quantities in the exact approach via PDEs (namely the total kinetic and potential energies), we attested that these windows arise due to a resonant mechanism of energy exchange between translational and vibrational soliton modes. By studying the linear stability of the solitary waves, we proved that the vibrational modes originate from shape oscillations induced by internal modes and also, possibly, by instability modes excited during the collisions. We verified that these oscillations are well defined in all regular collisions. The viability of the variational method in the system studied is due to the suitable description of the vibrational modes by the reduced model, and also the low influence of the emitted nonlinear radiation in the regular collision processes found in the direct simulations. |
publishDate |
2017 |
dc.date.accessioned.fl_str_mv |
2017-05-05T12:55:46Z |
dc.date.issued.fl_str_mv |
2017-04-10 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
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masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
TEIXEIRA, Rafael Marques Paes. Espalhamento de gaussons em acopladores ópticos direcionais. 2017. 128 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2017. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/7270 |
identifier_str_mv |
TEIXEIRA, Rafael Marques Paes. Espalhamento de gaussons em acopladores ópticos direcionais. 2017. 128 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2017. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/7270 |
dc.language.iso.fl_str_mv |
por |
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por |
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600 600 600 600 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Física - IF (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
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