Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-05-22T14:42:33Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-05-22T14:42:51Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5) / Made available in DSpace on 2018-05-22T14:42:51Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5) Previous issue date: 2016-12-01 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we study the concept h-almost Ricci soliton introduced by Gomes-Wang-Xia which extends naturally the almost Ricci soliton studied by Pigola et al. In this setting, we show that a compact nontrivial h-almost Ricci soliton of dimension no less than three with h positive (or negative) and constant scalar curvature is isometric to a standard sphere with well defined potential function. Latter on, we also consider h-Ricci soliton which is a particular case of the h-almost Ricci soliton and a generalization of the traditional Ricci soliton. We prove that a particular case of compact gra-dient h-Ricci soliton steady or expanding, is trivial. Moreover, we give a characterization for a special class of gradient h-Ricci solitons. / Neste trabalho vamos estudar o conceito de h-quase sólitons de Ricci introduzido por Gomes-Wang-Xia o qual é uma extensão natural dos quase sólitons de Ricci estudados por Pigola et al. Com esta configuração, vamos mostrar que um h-quase sóliton de Ricci compacto de curvatura escalar constante não-trivial de dimensão maior ou igual a três e li possuindo sinal definido é isométrico a uma esfera euclidiana com função potencial explicita-mente definida. Logo após, também vamos considerar h-sólitons de Ricci os quais são casos particulares dos h-quase sólitons de Ricci e uma generalização dos tradicionais sólitons de Ricci. Vamos provar que um caso particular de h-sóliton de Ricci gradiente compacto estacionário ou expansivo, é trivial. Além disso, exibiremos uma caracterização para uma classe especial de h-sólitons de Ricci gradiente.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-10-17T13:15:34Z No. of bitstreams: 2 Dissertação - Douglas Xavier de Andrade - 2016.pdf: 8750687 bytes, checksum: b47edd6565843d8ae15e173adda15ab2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-10-17T17:16:26Z (GMT) No. of bitstreams: 2 Dissertação - Douglas Xavier de Andrade - 2016.pdf: 8750687 bytes, checksum: b47edd6565843d8ae15e173adda15ab2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-10-17T17:16:26Z (GMT). No. of bitstreams: 2 Dissertação - Douglas Xavier de Andrade - 2016.pdf: 8750687 bytes, checksum: b47edd6565843d8ae15e173adda15ab2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-10-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Among the main problems faced by Physics teachers in the Brazilian Basic Education system are: the distance of the contents studied from the daily lives of students and the lack of materials and methodologies suitable to work topics of Modern and Contemporary Physics in the classroom. Given the need to give referrals, at least in part, the problems mentioned above, the authors of this paper sought basically to work in three fundamental points: 1) Curriculum - expand undulating physics content to cover non-linear aspects of physical systems known such as the mass-spring system, the simple pendulum, waves on a string and shallow water in order to introduce the concept of soliton and some of its applications. 2) adaptable and accessible material for topics of Physics Nonlinear - talk about the educational potential of creating a website using the tools provided by "google sites"and present disclosure page (Solitons and phenomena nonlinear) and 3) methodology - report the experiences of the discussion of topics in nonlinear physics for high school students verifying the challenges and prospects of use of a website in the classroom context of a school public high school in the state of Goiás. Thus, it is _rst introduced the subject of study by presenting the research objectives and the dissertation of the structure and then we present topics of nonlinear physics based on systems which are usually treated only in a linear fashion in high school such as: the simple pendulum (when built a pendulum corresponding to na arrangement of coupled pendula), the mass-spring system (when we study a chain of particles coupled to each other by means of springs) and linear wave equation. The study of these systems leads respectively to the equation Sine-Gordon, the Toda model, and KdV equation when they are treated in a non-linear fashion. After these equations are discussed presented their solutions 1- and 2-solitons solutions using Hirota method. After analyzing the above systems, we discuss some natural physical phenomena where solitons are present and some of their technological applications. Later we perform a review of the literature, where we use theoretical concepts to support the use of Information and Communication Technologies (ICT) in science education, and presented a website built to introduce the subjects of nonlinear Physics in high school. Then we discuss a teaching sequence designed in order to provide the use of the internet page in the classroom and the results of the didactic sequence implementation are reported in the classroom indicating that the creation and use of a website is a important tool to work subjects of Nonlinear Physics in high school to allow the use of multiple virtual learning objects and motivate the continuity of the learning process outside the classroom context. / Entre os principais problemas enfrentados pelos professores de Física da Educação Básica brasileira se encontram: o distanciamento dos conteúdos estudados com o cotidiano dos estudantes e a falta de material e metodologias adequados para se trabalhar tópicos de Física Moderna e Contemporânea em sala de aula. Diante da necessidade de dar encaminhamentos, ao menos em parte, aos problemas, acima citados, os autores desta dissertação buscaram atuar basicamente em três pontos fundamentais: 1)Currículo - expandir os conteúdos de Física Ondulatória para abranger aspectos não-lineares de sistemas físicos conhecidos como o sistema massa-mola, o pêndulo simples, as ondas numa corda e em águas rasas com o intuito de introduzir o conceito de sóliton e algumas de suas aplicações para que professores da Educação Básica possam discutí-los em sala de aula; 2) Material adaptável e acessível de divulgação de tópicos de Física Não-Linear - discorrer sobre as potencialidades educacionais da criação de uma página na internet usando as ferramentas disponibilizadas pelo "google sites" e apresentar a página de divulgação "Sólitons e fenômenos não-lineares" e 3) Metodologia - relatar as experiências da discussão de tópicos de Física Não-Linear no Ensino Médio veri_cando os desa_os e potencialidades da utilização de uma página na internet no contexto de sala de aula de uma escola pública de Ensino Médio do Estado de Goiás. Dessa forma, inicialmente é introduzido o tema de estudo através da apresentação dos objetivos da pesquisa e da estrutura da dissertação e em seguida são apresentados tópicos de Física não-linear de sistemas físicos conhecidos geralmente tratados apenas em uma forma linear no Ensino Médio a saber: o pêndulo simples, o sistema massa-mola e equação de onda linear. O estudo desses sistemas em uma forma não-linear nos levam respectivamente à equação de Sine-Gordon (quando construímos um arranjo de pêndulos acoplados), ao Modelo de Toda (quando estudamos uma rede com N massa-molas ligados), e a Equação de KdV. Após discutidas essas equações são apresentadas as suas soluções para 1 e 2-sólitons utilizando o método de Hirota. Após a análise dos sistemas supracitados discorremos sobre alguns fenômenos físicos naturais onde os sólitons estão presentes e algumas aplicações tecnológicas dos mesmos. Posteriormente é feita uma revisão de literatura, onde utilizamos concepções teóricas para fundamentar a utilização das Tecnologias de Informação e Comunicação (TIC) no ensino de Ciências, e apresentada uma página na internet construída para introduzir os assuntos de Física Não-Linear no Ensino Médio. Por fim, discorre-se sobre uma sequência didática pensada de forma a propiciar o uso da página da internet em sala de aula e são relatados os resultados da implementação da sequência didática em sala de aula indicando que a criação e utilização de uma página na internet é uma importante ferramenta para se trabalhar assuntos de Física Não-Linear no Ensino Médio ao permitir o uso de diversos objetos virtuais de aprendizagem e motivar a continuidade do processo de aprendizagem fora do contexto de sala de aula.

Diferentes tipos de sólitons têm sido observados em meios ópticos não-lineares, e seus comportamentos individuais descritos pela equação não-linear de Schrödinger e pela equação não-linear de Schrödinger generalizada, em diferentes dimensões e geometrias. Entretando, há situações onde muitos sólitons são gerados formando uma densa rede de sólitons. Nestes casos, é impossível desprezar as interações entre os sólitons e temos que considerar a evolução da estrutura como um todo. A teoria das ondas de choque dispersivas em meios fotorrefrativos e a teoria da difração não-linear de intensos feixes de luz propagando-se em meios fotorrefrativos com um fio refletor incorporado a esse meio foi desenvolvida, e verificamos que está em excelente acordo com nossas simulações numéricas. No caso da formação de sólitons em condensados, fizemos cálculos numéricos realísticos dentro da aproximação de campo médio usando a equação de Gross-Pitaevskii, incluindo também um potencial de confinamento, um potencial móvel e um potencial dipolar. A maioria dos resultados puderam ser comparados com experimentos recentes. / Different kinds of solitons have already been observed in various nonlinear optical media, and their behavior has been explained in the frameworks of such mathematical models as the nonlinear Schrödinger and generalized nonlinear Shrödinger equations for different dimensions and geometries. However, there are situations when many solitons are generated so that they can comprise a dense soliton train. In such situations, it is impossible to neglect interactions between solitons and one has to consider the evolution of the structure as a whole rather than to trace the evolution of each soliton separately. The theory of optical shock waves in photorefractive media and the theory of nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire was developed and agrees very well with our numerical simulations. In the condensate soliton formation case, we did numerical calculations in the mean field approach using the Gross-Pitaevskii equation, adding a trap potential and a moving potential and a potential of the dipole-dipole interaction. The main results were also checked by recent experiments.

The reflection and transmission of an electromagnetic TE-polarized plane wave at a dielectric film between two linear semi-infinite media (substrate and cladding) is considered. All media are assumed to be homogeneous in x- and z- direction, isotropic, and non-magnetic. The permittivity of the film is assumed to be characterized by a continuously differentiable function of the transverse coordinate and the field. To obtain solutions of Maxwell´s equations that satisfy the boundary conditions the problem is reduced to a Helmholtz equation, which is transformed to a Volterra integral equation for the field intensity inside the film. The Volterra equation is solved by iteration subject to the appropriate boundary conditions. The (iteration) solutions for the linear case and for the nonlinear case are expressed in terms of a uniformly convergent series and a uniformly convergent sequence, respectively. The uniform convergence is proved using the Banach Fixed-Point Theorem. The condition for its applicability leads to a condition for the parameters of the problem. By iterating the Volterra equation an approximate solution for the intensity inside the film is presented. The mathematical basis of the procedure is outlined in detail. Using an approximate solution, the phase function,the phase shifts on reflection and transmission, the reflectivity and the absorptance are determined.Further iterations of the Volterra equation are possible.Semianalytical and numerical examples illustrate the main features of the approach. The method is succesfully applied to different permittivity functions (real, complex, Kerr-like and saturable nonlinear). The agreement between the approximate analytical solutions and numerical solutions is satisfactory. It seems that the method proposed can serve as a means to optimize certain parameters of the problem (material and/or geometrical) for particular purposes.

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No description available.

<p>We consider existence and stability of breather solutions to discrete nonlinear Schrodinger (dNLS) and discrete Klein-Gordon (dKG) equations near the anti-continuum limit, the limit of the zero coupling constant. For sufficiently small coupling, discrete breathers can be uniquely extended from the anti-continuum limit where they consist of periodic oscillations on excited sites separated by "holes" (sites at rest).</p> <p>In the anti-continuum limit, the dNLS equation linearized about its discrete breather has a spectrum consisting of the zero eigenvalue of finite multiplicity and purely imaginary eigenvalues of infinite multiplicities. Splitting of the zero eigenvalue into stable and unstable eigenvalues near the anti-continuum limit was examined in the literature earlier. The eigenvalues of infinite multiplicity split into bands of continuous spectrum, which, as observed in numerical experiments, may in turn produce internal modes, additional eigenvalues on the imaginary axis. Using resolvent analysis and perturbation methods, we prove that no internal modes bifurcate from the continuous spectrum of the dNLS equation with small coupling.</p> <p>Linear stability of small-amplitude discrete breathers in the weakly-coupled KG lattice was considered in a number of papers. Most of these papers, however, do not consider stability of discrete breathers which have "holes" in the anti-continuum limit. We use perturbation methods for Floquet multipliers and analysis of tail-to-tail interactions between excited sites to develop a general criterion on linear stability of multi-site breathers in the KG lattice near the anti-continuum limit. Our criterion is not restricted to small-amplitude oscillations and it allows discrete breathers to have "holes" in the anti-continuum limit.</p> / Doctor of Philosophy (PhD)

Au long de ce manuscrit de thèse je présenterai des effets non linéaires émergents dans les condensats d'exciton-polaritons spineurs. Après un chapitre d'introduction amenant les notions de bases nécessaires, je me concentrerai dans une première partie sur les défauts topologiques quantifiés par des nombres demi-entiers et discuterai leur stabilité, accélération et nucléation en présence de champs magnétiques effectifs. Nous verrons que ces objets se comportent comme des charges magnétiques manipulables démontrant une analogie fascinante avec les monopoles de Dirac. De manière remarquable nous verrons également que ces objets peuvent être utilisés comme des signaux stables pour sonder la physique d'analogues acoustiques de trous noirs. Dans une seconde partie j'étudierai des structures de basse dimensions. Plus particulièrement, je décrirai la formation de solitons de bande interdite et les oscillations de Bloch des exciton-polaritons dans des microfils comportant des structures périodiques et d'autre part les oscillations Josephson à température ambiante dans des paires de micropilliers couplés. / Along this thesis manuscript I shall present some emergent nonlinear phenomena in spinor exciton polariton condensates. After an introductory chapter bringing the necessary background, I will in a first part focus on half-integer topological defects discussing their stability, acceleration and nucleation in the presence of effective magnetic fields. We will see that these objects behave as magnetic charges being fascinating dirac's monopole analogues. Remarkably we will see as well how they can be used as stable signals allowing to seed the physics acoustic black holes analogues. In a second part I will concentrate on low dimensional structures. Especially, I'll describe the formation of gap solitons and the Bloch oscillations of exciton-polaritons in periodically patterned microwires, and besides, the room temperature Josephson oscillations within pairs of coupled micropillars.

Cette thèse est dédiée à l'étude de l'analogue du rayonnement de Hawking dans les condensats de Bose-Einstein. Le premier chapitre présente de nouvelles configurations d'intérêt expérimental permettant de réaliser l'équivalent acoustique d'un trou noir gravitationnel dans l'écoulement d'un condensat atomique unidimensionnel. Nous donnons dans chaque cas une description analytique du profil de l'écoulement, des fluctuations quantiques associées et du spectre du rayonnement de Hawking. L'analyse des corrélations à deux corps de la densité dans l'espace des positions et des impulsions met en évidence l'émergence de signaux révélant l'effet Hawking dans nos systèmes. En démontrant une règle de somme vérifiée par la matrice densité à deux corps connexe, on montre que les corrélations à longue portée de la densité doivent être associées aux modifications diagonales de la matrice densité à deux corps lorsque l'écoulement du condensat présente un horizon acoustique. Motivés par des études expérimentales récentes de profils d'onde générés dans des condensats de polaritons en microcavité semi-conductrice, nous analysons dans un second chapitre les caractéristiques superfluides et dissipatives de l'écoulement autour d'un obstacle localisé d'un condensat de polaritons unidimensionnel obtenu par pompage incohérent. Nous examinons la réponse du condensat dans la limite des faibles perturbations et au moyen de la théorie de Whitham dans le régime non-linéaire. On identifie un régime dépendant du temps séparant deux types d'écoulement stationnaire et dissipatif : un principalement visqueux à faible vitesse et un autre caractérisé par un rayonnement de Cherenkov d'ondes de densité à grande vitesse. Nous présentons enfin des effets de polarisation obtenus en incluant le spin des polaritons dans la description du condensat et montrons dans le troisième chapitre que des effets similaires en présence d'un horizon acoustique pourraient être utilisés pour démontrer expérimentalement le rayonnement de Hawking dans les condensats de polaritons. / This thesis is devoted to the study of the analogue of Hawking radiation in Bose-Einstein condensates. The first chapter presents new configurations of experimental interest making it possible to realize the acoustic equivalent of a gravitational black hole in the flow of a one-dimensional atomic condensate. In each case we give an analytical description of the flow pattern, the associated quantum fluctuations, and the spectrum of Hawking radiation. Analysis of the two-body density correlations in position and momentum space emphasizes the occurrence of signals revealing the Hawking effect in our systems. By demonstrating a sum rule verified by the connected two-body density matrix we show that the long-range density correlations have to be associated to the diagonal modifications of the two-body density matrix when the flow of the condensate presents an acoustic horizon. Motivated by recent experimental studies of wave patterns generated in semiconductor microcavity polariton condensates we analyze in a second chapter superfluid and dissipative characteristics of the flow of a nonresonantly pumped one-dimensional polariton condensate past a localized obstacle. We examine the response of the condensate in the weak-perturbation limit and by means of Whitham theory in the nonlinear regime. We identify a time-dependent regime separating two types of stationary and dissipative flow: a mostly viscous one at low velocity and another one characterized by Cherenkov radiation of density waves at large velocity. Finally we present polarization effects obtained by including the spin of polaritons in the description of the condensate and show in the third chapter that similar effects in the presence of an acoustic horizon could be used to experimentally demonstrate Hawking radiation in polariton condensates.

Ces travaux de thèse rapportent l’étude des instabilités non-linéaires et des évènements extrêmesse développant lors de la propagation guidée d’un champ électromagnétique au sein de fibresoptiques. Après un succinct rappel des divers processus linéaires et non-linéaires menant à lagénération de super continuum optique, nous montrons que le spectre de celui-ci peut présenterde larges fluctuations, incluant la formation d’événements extrêmes, dont les propriétés statistiqueset l’analogie avec les vagues scélérates hydrodynamiques sont abordées en détail. Nous présentonsune preuve de principe de l’application de ces fluctuations spectrales à la génération de nombres etde marches aléatoires et identifions le phénomène d’instabilité de modulation, ayant lieu lors de laphase initiale d’expansion spectrale du super continuum, comme principale contribution à la formationd’événements extrêmes. Ce mécanisme est étudié numériquement et analytiquement, en considérantune catégorie de solutions exactes de l’équation de Schrödinger non-linéaire présentant descaractéristiques de localisations singulières. Les résultats obtenus sont vérifiés expérimentalement,notamment grâce à un système de caractérisation spectrale en temps réel et à l’utilisation conjointede métriques statistiques innovantes (ex : cartographie de corrélations spectrales). L’excellent accordentre simulations et expériences a permis de valider les prédictions théoriques et d’accéder àune meilleure compréhension des dynamiques complexes inhérentes à la propagation non-linéaired’impulsions optiques. / This thesis reports the study of nonlinear instabilities and extreme events occurring during the guidedpropagation of an electromagnetic field into optical fibers. After a short overview of the various linearand nonlinear processes leading to optical supercontinuum generation, we show that its spectrumcan exhibit large fluctuations, including the formation of extreme events, whose statistical propertiesas well as hydrodynamic rogue waves analogy are studied in detail. We provide a proof of principle ofusing these spectral fluctuations for random number and random walk generation and identify modulationinstability, associated with the onset phase of supercontinuum spectral broadening, as themain phenomenon leading to extreme event formation. This mechanism is studied both numericallyand analytically, considering a class of exact solutions of nonlinear Schrödinger equation which exhibitsingular localization characteristics. The results are experimentally verified, especially througha real-time spectral characterization system along with the use of innovative statistical metrics (e.g.spectral correlation maps). The excellent agreement between simulations and experiments allowedus to validate the theoretical predictions and get further insight into the complex dynamics associatedto nonlinear optical pulse propagation.