Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-13T19:45:10Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Raphael da Costa Silva.pdf: 289061 bytes, checksum: 3b5a883040e36a07a3da5fc6a355f5cd (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-13T19:45:31Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Raphael da Costa Silva.pdf: 289061 bytes, checksum: 3b5a883040e36a07a3da5fc6a355f5cd (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-13T19:45:50Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Raphael da Costa Silva.pdf: 289061 bytes, checksum: 3b5a883040e36a07a3da5fc6a355f5cd (MD5) / Made available in DSpace on 2017-02-13T19:45:50Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Raphael da Costa Silva.pdf: 289061 bytes, checksum: 3b5a883040e36a07a3da5fc6a355f5cd (MD5) Previous issue date: 2015-12-15 / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / Considering that A(q) is a di erentiable family of self-adjoint operators and that M(q0) is the eigenspace associated with a certain 0 eigenvalue of A(q), with multiplicity n. We will discuss in the following project about which results we can obtain about the space of parameters the eigenvalue that are close to 0 and keep the xed multiplicity. In order to achieve the main objective of this project, we will de ne and use the transversality idea. It is an extension for higher dimensions, in which the inverse image of a regular value forms a surface. So, with the transversality idea, we can de ne when an eigenvalue is stable. Including the idea of stability, we can nd a very important and \elegant" result for the space of parameters that maintain eigenvalues close to 0 with xed multiplicity, where it will be the main theorem of this project. / Sendo A(q) uma família de operadores diferenciáveis auto-adjuntos e M(q0) o auto-espaço associado a um certo autovalor 0 de A(q), com multiplicidade n. Dissertaremos neste trabalho quais resultados podemos obter sobre o conjunto dos parâmetros de autovalores que estão próximos de 0 e mantém a multiplicidade fixa. Para alcançarmos o objetivo principal deste trabalho iremos definir e usar a ideia de transversalidade, onde não deixa de ser uma extensão, para dimensões maiores, em que a imagem inversa de um valor regular forma uma superfície. Com o conceito de transversalidade podemos então definir quando um auto-valor é estável. Incluindo assim a ideia de estabilidade, será suficiente para encontrarmos um resultado muito importante e até "elegante" para o conjunto dos parâmetros que mantém autovalores próximos de 0 com multiplicidade fixa, onde será o teorema principal deste trabalho.

Orientador: Jaime Angulo Pava / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T02:39:00Z (GMT). No. of bitstreams: 1 Moura_RogerPeresde_D.pdf: 2234766 bytes, checksum: 9c36c9be07d4a5910fabe79366fd1e13 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho estabelecemos algumas propriedades da equação de Schr6dinger nãolinear não-local (NLSNL), em especial as relacionadas ao problema de Cauchy. Primeiramente fizemos um capítulo preliminar de notações e teoria básica utilizada no esta- belecimento dos resultados; essa parte também visa facilitar a leitura do trabalho. Em seguida apresentamos o principal resultado: boa colocação local para o problema de valor inicial (problema de Cauchy) associado à equação NLSNL para dados iniciais pequenos nos espaços de Sobolev reais usuais de ordem maior que três meios; o método permite estabelecer que a aplicação dado inicial-solução é suave. No capítulo seguinte provamos o mesmo resultado para a equação de Schr6dinger não-linear não-Iocal intermediária (INLSNL), a qual é mais geral que a outra. Depois estabelecemos boa colocação para a equação NLSNL em espaços de Sobolev com peso. Em outro capítulo apresentamos um resultado de má colocação: estabelecemos que não se pode obter boa colocação local, em espaços de Sobolev de índice negativo, para o PVI associado à equação NLSNL por meio de método iterativo de Picard; como conseqüência, a aplicação dado-solução não é suave nesses espaços. Provamos também, fazendo uso de uma identidade de Pohozaev, a não existência de soluções standing waves para a equação NLS não-local. Finalizamos com um capítulo onde exibimos alguns problemas interessantes relacionados principalmente à equação NLSNL e algumas possíveis dificuldades a serem enfrentadas em uma eventual tentativa de solucioná-Ios / Abstract: ln this work we establish some properties of the nonlocal nonlinear Schrodinger equation (NLSNL). First of alI, we present a preliminary chapter with notations and basic theory used to establish our results; that part also seeks to facilitate the reading of this work. Soon afterwards comes the main result: local welI-posedness for the initial value problem (the Cauchy problem or lVP) for the NLSNL equation with initial data in real Sobolev spaces of index larger than three and a half; the method of proof alIows to es- tablish that the data-solution map is smooth. ln the folIowing chapter we proved that previous result for the intermediate nonlocal nonlinear Schrüdinger (lNLSNL), which is more general than the NLSNL equation. After that we establish local welI-posedness for the NLSNL equation in weighted Sobolev spaces. ln another chapter the ill-posedness issue is discussed: we established that one cannot obtain local welI-posedness, in Sobolev spaces of negative index, for the lVP associated to NLSNL equation through a iterative Picard method; as a consequence, the data-solution map is not smooth in those spaces. We also proved, making use of a Pohozaev's identity, the no-existence of standing waves solutions for the NLSNL equation. We concluded with a chapter where we exhibited some interesting problems mainly related to the NLSNL equation and possible difficulties to be faced in an eventual attempt of solving them / Doutorado / Matematica / Doutor em Matemática

No description available.

In this thesis, we study two stochastic reaction diffusion models - the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching the boundary of a properly embedded open set, termed the reaction region (or more generally some fixed lower dimensional sub-manifold). The Doi model uses reaction potentials, supported in the reaction region, whereby two molecules react with a fixed probability per unit time, λ, upon entering the reaction region. The problem considered is that of obtaining estimates for convergence rates, in λ, of the Doi model to the Smoluchowski model. This problem fits into the theory of singular perturbation or optimization, depending on which reactive boundary conditions one considers, and we solve it - at least for the bimolecular reaction with one stationary target.

No description available.

CAPES / Neste estudo, os espectros Raman ressonante das moléculas de H2 e O2 foram computados através da resolução numérica da equação de Schrödinger vibracional utilizando potenciais completamente anarmônicos, obtidos através de métodos ab initio multiconfiguracionais. O problema vibracional foi resolvido através da simulação de Monte Carlo Quântico Variacional Modificado (MCQVM) e do método de Interação de Configurações Vibracional (VCI). As intensidades RR foram calculadas através da teoria independente do tempo do efeito RR. Exceto pela PES do estado eletrônico excitado B3Σ− u da molécula de O2, a qual não pôde ser plenamente descrita devido a um cruzamento evitado entre estados eletrônicos, as demais PESs apresentaram uma boa concordância com os valores experimentais das constantes espectroscópicas (Re, Te, De, Be, We e WeXe). Constatou-se através do desvio teórico-experimental que as energias vibracionais geradas via simulação de MCQVM são, de maneira geral, bastante acuradas para os estados vibracionais de mais baixa energia. Entretanto, à medida que necessitou-se otimizar um número elevado de estados vibracionais de energia superior, necessários para o cálculo da polarizabilidade RR, houve um acréscimo significativo no tempo computacional dos cálculos MCQVM, motivando a adoção do método VCI, no intuito de tentar reduzir o tempo de processamento e também conseguir resultados mais acurados. No que tange ao cálculo da seção de choque RR das moléculas de H2 e O2, constatou-se que a convergência das seções de choque, com relação ao número de estados vibracionais intermediários, é mais rápida quando o potencial de interação é harmônico. A adição da correção vibrônica de Herzberg-Teller (HT) foi bastante pronunciada para as duas moléculas avaliadas, e tendem a atenuar as intensidades das transições RR com relação aos valores obtidos com a aproximação de Franck-Condon. Constatou-se que a meialargura à meia-altura (Γ) do estado vibrônico excitado tem pouca influência sobre a magnitude das seções de choque RR dos sistemas estudados, podendo ser variado em mais de uma ordem de grandeza sem que isso afete substancialmente as intensidades RR. Por fim, verificou-se que a obtenção das intensidades RR por meio de funções de onda vibracionais anarmônicas demanda um número elevado de estados vibracionais intermediários (algumas dezenas) para que haja uma boa convergência nas seções de choque. Esse número é bastante superior ao observado nos cálculos harmônicos. / In this study, the resonance Raman spectra of H2 and O2 molecules were computed by the numerical resolution of the vibrational Schrödinger equation employing fully anharmonic potentials, obtained by Multiconfigurational ab initio methods. The vibrational problem was solved through the Modified Variational Quantum Monte Carlo (MVQMC) simulation and the Vibrational Configurations Interaction (VCI) methods. The time independent framework of the RR effect was used to compute the RR intensities. The Potential Energy Surfaces (PESs) were in good agreement with the experimental values of the spectroscopic constants (Re, Te, De, Be, We e WeXe), except for the excited electronic state B3Σ− u PES of the O2 molecule, which could not be fully described due to an avoided crossing between electronic states. It was verified through the theoretical-experimental deviation values that the vibrational energies generated by MVQMC simulations are, in general, very accurate for the lowest energy vibrational states. However, as it was necessary to optimize higher energy states, required in the calculation of the RR polarizability, the computational time of MVQMC method was greatly increased, motivating the use of VCI method in order to try to reduce processing time and achieve results that are more accurate. Regarding to calculating the RR cross sections of the H2 and O2 molecules, results have showed that the convergence is faster when using the harmonic potential instead of the anharmonic potential. The addition of vibronic coupling effects was quite impactful for both molecular systems evaluated, and tended to attenuate the RR transition intensities relative to the values obtained with the Franck–Condon contribution. It was verified that the bandwidth variation of the excited electronic state (Γ parameter) pose little influence in the RR cross sections of the addressed molecular systems, therefore being able to vary Γ in more than an order of magnitude without substantially affecting the RR intensities. Ultimately, the target property is largely influenced by the number of vibrational wave functions, requiring considerable quantities of intermediate vibrational states (dozens) for a good convergence of the anharmonic RR cross sections, which is a much larger quantity compared to the harmonic calculations.

On s'intéresse à la dynamique électronique de systèmes atomiques soumis à une impulsion laser brève et intense ou à l'impact d'un ion positivement chargé. On procède alors à une comparaison détaillée des descriptions classique et quantique de ces interactions. Sur la base de cette comparaison, on développe une méthode auto-cohérente de trajectoires quantiques, basée sur l'approche hydrodynamique de Bohm. Cette méthode permet d'obtenir des observables très précises tout en conservant le caractère illustratif des méthodes de trajectoires classiques. / We are interested in the electronic dynamic of atomic system under influence of a short and intense laser pulse or induced by impact of positively charged ion. We then proceeds in a deeper comparative study of classical and quantal description of these interactions. On the basis of this study, we developped a self-consistent quantum trajectory method, based on the hydrodynamical formulation of Bohm. This method allow to obtain very precise observable while retaining the illustrative character of classical trajectory method.

Cette thèse contient deux parties. Je décris une approche pour construire une réalisation physique d'un ordinateur quantique par Résonance Magnétique Nucléaire (RMN). Je propose un nouveau cadre pour la RMN dans les réalisations physiques d'un ordinateur quantique. Je construis une description de la RMN à partir de la mécanique quantique avec laquelle je peux construire les opérateurs élémentaires essentiels pour le calcul quantique. Je décris les expériences pour construire ces opérateurs. Je propose un algorithme quantique en temps polynomial pour résoudre des équations de Pell simultanées comme extension de l'algorithme de Hallgren pour des équations de Pell simples.

In this thesis, having in mind applications to the fault-detection/diagnosis of electrical networks, we consider some inverse scattering problems for the Zakharov-Shabat equations and time-independent Schrödinger operators over star-shaped graphs. The first chapter is devoted to describe reflectometry methods applied to electrical networks as an inverse scattering problems on the star-shaped network. Reflectometry methods are presented and modeled by the telegrapher's equations. Reflectometry experiments can be written as inverse scattering problems for Schrödinger operator in the lossless case and for Zakharov-Shabat system for the lossy transmission network. In chapter 2 we introduce some elements of the inverse scattering theory for 1 d Schrödinger equations and the Zakharov-Shabat system. We recall the basic results for these two systems and we present the state of art of scattering theory on network. The third chapter deals with some inverse scattering for the Schrödinger operators. We prove the identifiability of the geometry of the star-shaped graph: the number of the edges and their lengths. Next, we study the potential identification problem by inverse scattering. In the last chapter we focus on the inverse scattering problems for lossy transmission star-shaped network. We prove the identifiability of some geometric informations by inverse scattering and we present a result toward the identification of the heterogeneities, showing the identifiability of the loss line factor.

The fully quantum mechanical 'direct-potential-fit' (DPF) method has become increasingly widely used in the reduction of diatomic spectra. The central problem of this method is the representation of the potential energy and Born-Oppenheimer breakdown (BOB) correction functions. There are a number of problems associated with the existing method and potential forms. This thesis delineates these problems and finds solutions to some of them. In particular, it is shown that use of a different expansion variable and a new treatment of some of the expansions resolves most of the problems. These techniques have been successfully tested on the ground electronic states of the coinage metal hydrides and the Rb2 molecule. To address the problem of representing 'barrier' potential curves, a flexible new functional form, the 'double-exponential long-range' (DELR) potential function, is introduced and applied to the B barrier state of Li2. In addition, the Lambda-doubling level splitting which occurs for singlet Pi electronic states has been taken into account by extending the effective Schrodinger equation. The computer program DSPotFit developed in our laboratory for performing DPF analyses has been extended to incorporate the ability to fit the analytical potential energy functions to tunneling predissociation line widths for quasibound levels. Finally, an attempt is made to investigate whether there exists a hump in the ground state rotationless potential curve of beryllium hydride.