Orientador: Hugo Luis Fragnito / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-13T07:01:10Z (GMT). No. of bitstreams: 1 Rieznik_AndresAnibal_D.pdf: 2453403 bytes, checksum: 66544ed487a1cb0efeea1180adac25c3 (MD5) Previous issue date: 2008 / Resumo: Apresentamos métodos para a otimização das simulações da propagação não linear da luz em fibras ópticas a través do Método de Split-Step Fourier (SSFM). Os dois efeitos considerados na modelagem da propagação são a dispersão e o efeito Kerr instantâneo. Estudamos tanto as equações acopladas considerando os dois modos principais de polarização quanto as equações escalares, estas últimas aplicáveis em situações em que o campo pode ser considerado um escalar, como em fibras isotrópicas com todos os campos linearmente polarizados e paralelos. Mostramos que o método que propomos para resolver as equações escalares é ordens de grandeza mais rápido do que outros métodos apresentados recentemente na literatura científica na modelagem de sistemas de transmissão de dados. No caso das equações acopladas, mostramos que o método proposto fornece resultados acurados na modelagem de amplificadores paramétricos e o utilizamos para validar um modelo analítico de seis ondas que nós mesmos desenvolvemos. Também utilizamos o método proposto para as equações acopladas para estudar o impacto das variações aleatórias da birrefringência sobre o ganho de amplificadores paramétricos, mostrando a importância da modelagem realista destas flutuações. Todos os códigos desenvolvidos são disponibilizados e distribuídos sob uma licença do tipo de software livre através de um portal criado na internet especialmente para esse fim. / Abstract: We introduce optimized models and algorithms for the simulation of non linear propagation in optical fibers using the split-step Fourier Method (SSFM). Dispersion and the Kerr effect are the two main effects considered in the simulations. We study the coupled equations, considering both polarization modes, as well as the scalar equation, which can be applied when the scalar approximation holds, as in isotropic fibers with all fields linearly polarized and parallels. We show that the method that we propose to solve the scalar equation is orders of magnitude faster than other methods recently introduced in the scientific literature for modeling transmission systems. In the coupled-equations case, we show that the proposed method gives accurate results for the modeling of parametric amplifiers, and use it to validate an analytical six-wave model that we developed. We also use the method for the coupled-equations to study the effects of randomly varying birefringence on parametric amplifiers gain, showing the importance of the accurate modeling of these fluctuations. All the codes developed in this thesis are available for download and distributed under a creative commons license in an internet site created specifically for this purpose. / Doutorado / Ótica / Doutor em Ciências

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho abordamos a teoria de Ginzburg-Landau da supercondutividade (teoria GL). Apresentamos suas origens, características e resultados mais importantes. A idéia fundamental desta teoria e descrever a transição de fase que sofrem alguns metais de uma fase normal para uma fase supercondutora. Durante uma transição de fase em supercondutores do tipo II é característico o surgimento de linhas de fluxo magnético em determinadas regiões de tamanho finito chamadas comumente de vórtices. A dinâmica destas estruturas topológicas é de grande interesse na comunidade científica atual e impulsiona incontáveis núcleos de pesquisa na área da supercondutividade. Baseado nisto estudamos como essas estruturas topológicas influenciam em uma transição de fase em um modelo bidimensional conhecido como modelo XY. No modelo XY vemos que os principais responsáveis pela transição de fase são os vórtices (na verdade pares de vórtice-antivórtice). Villain, observando este fato, percebeu que poderia tornar explícita a contribuição desses defeitos topológicos na função de partição do modelo XY realizando uma transformação de dualidade. Este modelo serve como inspiração para a proposta deste trabalho. Apresentamos aqui um modelo baseado em considerações físicas sobre sistemas de matéria condensada e ao mesmo tempo utilizamos um formalismo desenvolvido recentemente na referência [29] que possibilita tornar explícita a contribuição dos defeitos topológicos na ação original proposta em nossa teoria. Após isso analisamos alguns limites clássicos e finalmente realizamos as flutuações quânticas visando obter a expressão completa da função correlação dos vórtices o que pode ser muito útil em teorias de vórtices interagentes (dinâmica de vórtices). / In this work we introduced the Ginzburg-Landau theory of superconductivity (GL theory). We have shown your foundations, features and more important results. The fundamental idea of this theory is to describe the phase transition that some metals undergoes from a normal to a superconductor phase. During a phase transition in superconductors of type II is common the appearance of magnetic flux lines in given regions of finite size called of vortices. The knowledge of the dynamics of these vortices is of great importance in the current cientific community and drives many research centers to study the superconductivity. In view of this we study how these vortices changes a phase transition in a bidimensional model known as XY model.In XY model one can show that the main responsible for the phase transition are the vortices (or still, vortice-antivortice pairs). Villain, noting this fact, realized that could to turn explicit the contribution of theses topological defects in the partition function of XY model making a duality transformation. This model inspired us to study the subject of this master thesis. We presented here a model based in physical considerations about systems of condensed matter. At the same time we used a formalism developed in reference [29] that permits to turn explicit the contribution of these vortices in the original action proposed in our theory. Finally we analysed some classical limits and we looked for the quantum fluctuations to obtain the complete expression of the correlation function of vortices, whose utility is in the study of interacting vortices is wide (vortex dynamics).

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho abordamos a teoria de Ginzburg-Landau da supercondutividade (teoria GL). Apresentamos suas origens, características e resultados mais importantes. A idéia fundamental desta teoria e descrever a transição de fase que sofrem alguns metais de uma fase normal para uma fase supercondutora. Durante uma transição de fase em supercondutores do tipo II é característico o surgimento de linhas de fluxo magnético em determinadas regiões de tamanho finito chamadas comumente de vórtices. A dinâmica destas estruturas topológicas é de grande interesse na comunidade científica atual e impulsiona incontáveis núcleos de pesquisa na área da supercondutividade. Baseado nisto estudamos como essas estruturas topológicas influenciam em uma transição de fase em um modelo bidimensional conhecido como modelo XY. No modelo XY vemos que os principais responsáveis pela transição de fase são os vórtices (na verdade pares de vórtice-antivórtice). Villain, observando este fato, percebeu que poderia tornar explícita a contribuição desses defeitos topológicos na função de partição do modelo XY realizando uma transformação de dualidade. Este modelo serve como inspiração para a proposta deste trabalho. Apresentamos aqui um modelo baseado em considerações físicas sobre sistemas de matéria condensada e ao mesmo tempo utilizamos um formalismo desenvolvido recentemente na referência [29] que possibilita tornar explícita a contribuição dos defeitos topológicos na ação original proposta em nossa teoria. Após isso analisamos alguns limites clássicos e finalmente realizamos as flutuações quânticas visando obter a expressão completa da função correlação dos vórtices o que pode ser muito útil em teorias de vórtices interagentes (dinâmica de vórtices). / In this work we introduced the Ginzburg-Landau theory of superconductivity (GL theory). We have shown your foundations, features and more important results. The fundamental idea of this theory is to describe the phase transition that some metals undergoes from a normal to a superconductor phase. During a phase transition in superconductors of type II is common the appearance of magnetic flux lines in given regions of finite size called of vortices. The knowledge of the dynamics of these vortices is of great importance in the current cientific community and drives many research centers to study the superconductivity. In view of this we study how these vortices changes a phase transition in a bidimensional model known as XY model.In XY model one can show that the main responsible for the phase transition are the vortices (or still, vortice-antivortice pairs). Villain, noting this fact, realized that could to turn explicit the contribution of theses topological defects in the partition function of XY model making a duality transformation. This model inspired us to study the subject of this master thesis. We presented here a model based in physical considerations about systems of condensed matter. At the same time we used a formalism developed in reference [29] that permits to turn explicit the contribution of these vortices in the original action proposed in our theory. Finally we analysed some classical limits and we looked for the quantum fluctuations to obtain the complete expression of the correlation function of vortices, whose utility is in the study of interacting vortices is wide (vortex dynamics).

Bruning considered sets of isospectral Schrodinger operators with smooth real potentials on a compact manifold of dimension three. He showed the set of potentials associated to an isospectral set is compact in the topology of smooth functions by relating the spectrum to the trace of the heat semi-group. Similarly, we can consider the resonances of Schrodinger operators with real valued potentials on Euclidean space of whose support lies inside a ball of fixed radius that generate the same resonances as some fixed Schrodinger operator, an ``isoresonant" set of potentials. This isoresonant set of potentials is also compact in the topology of smooth functions for dimensions one and three. The basis of the result stems from the relation of a regularized wave trace to the resonances via the Poisson formula (also known as the Melrose trace formula). The second link is the small-t asymptotic expansion of the regularized wave trace whose coefficients are integrals of the potential function and its derivatives. For an isoresonant set these coefficients are equal due to the Poisson formula. The equivalence of coefficients allows us to uniformly bound the potential functions and their derivatives with respect to the isoresonant set. Finally, taking a sequence of functions in the isoresonant set we use the uniform bounds to construct a convergent subsequence using the Arzela-Ascoli theorem.

Water waves are an important design consideration for engineers wishing to design structures in the offshore environment. Designers need to know the size and shape of the waves which any structure is likely to encounter. Engineers have developed approaches to predict these, based on a combination of field and laboratory measurements, as well theoretical analysis. However some aspects of this are still poorly understood; in particular there is growing evidence that there are rare "freak" waves which do not fit with our current understanding of wave physics or statistics. In the first part of this thesis a new approach is developed for measuring the directional spreading of a sea-state, when the free surface time-history at a single point is the only available information. We use the magnitude of the second order "bound" waves to infer this information. This is validated using fully non-linear simulations, for random waves in a wave-basin, and for field data recorded in the North Sea. We also apply this to the famous Draupner wave, which our analysis suggests was caused by two wave systems, propagating at approximate 120 degrees to each other. The second part of the thesis looks at the non-linear evolution of Gaussian wave-groups. Whilst much work has previously been done to investigate these numerically, we instead derive an approximate analytical model for describing the non-linear changes to the group, based on the conserved quantities of the non-linear Schrodinger equation. These are validated using a numerical model. There is excellent agreement for uni-directional waves. The analytical model is generally good for predicting change in shape of directionally spread groups, but less good for predicting peak elevation. Nevertheless, it is still useful for typical sea-state parameters. Finally we consider the effect of wind on the local modeling of extreme waves. We insert a negative damping term into the non-linear Schrodinger equation, and consider the evolution of "NewWave" type wave-groups. We find that energy input accentuates the non-linear dynamics of wave-group evolution which suggests it may be important in the formation of "freak" waves.

Introduzimos um método não-relativístico para estudar a espectroscopia de estados ligados hadrônicos compostos por quatro quarks charme, na figura de diquark-antidiquark. Resolvendo numericamente a equação de Schrödinger com dois potenciais diferentes inspirados no potencial de Cornell, de uma maneira semelhante aos modelos de quarkonium pesado para mésons, nós fatoramos o problema de 4 corpos em três sistemas de 2 corpos: primeiro o diquark e o antidiquark, que são compostos por dois quarks (antiquarks) em um estado de antitripleto de cor. No próximo passo eles são considerados como os blocos para construir o tetraquark, onde a sua interação leva a um singleto de cor. Termos dependentes de spin (spin-spin, spin-órbita e tensor) são usados para descrever o desdobramento do espectro e a separação entre estados com diferentes números quânticos. Atenção especial é dada à interação do tensor entre duas partículas de spin 1, com uma discussão detalhada da estratégia adotada. A interação spin-spin é tratada perturbativamente no primeiro modelo e incluída no potencial de ordem zero no segundo. A contribuição de cada termo de interação também é analisada e comparada. Dados experimentais recentes de estados bem estabelecidos de mésons de charmonium são utilizados para fixar os parâmetros de ambos os modelos (em um procedimento de ajuste minimizando chi quadrado), obtendo uma reprodução satisfatória do espectro do charmonium. As diferenças entre modelos são discutidas no contexto do charmonium, diquarks e tetraquarks. Nós concluímos que quase todas as ondas S e P (e as respectivas primeiras excitações radiais) do todo-charme tetraquark composto por diquarks de spin 1 estão entre 5.8 e 7 GeV, acima do limite de dissociação espontânea em pares de charmonium de baixa energia como dois eta_c ou J/psi, o que sugere que esses poderiam ser os canais ideais para procurar por esses estados, e desenvolver o atual conhecimento de estados multiquarks. / We introduce a non-relativistic framework to study the spectroscopy of hadronic bound states composed of four charm quarks in the diquark-antidiquark picture. By numerically solving the Schrödinger equation with two different Cornell-inspired potentials in a similar way of heavy quarkonium models of mesons, we factorize the 4-body problem into three 2-body systems: first the diquark and the antidiquark, which are composed of 2 quarks (antiquarks) into a color antitriplet state. In the next step they are considered as the tetraquark building blocks, where their interaction leads to a color singlet. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the spectrum and account for different quantum numbers of each state. Special attention is given to the tensor interaction between two particles of spin 1, with a detailed discussion of the adopted strategy. The spin-spin interaction is addressed perturbatively in the first model and included in the zeroth-order potential in the second one. The contribution of each interaction term is also analysed and compared. Recent experimental data of reasonably well-established charmonium mesons are used to fix the parameters of both models (with a fitting procedure minimizing chi square), obtaining a satisfactory reproduction of charmonium spectrum. The differences between models are discussed in the charmonium, diquark and tetraquark context. We conclude that almost all the S and P waves (and respective first radial excitations), of the all-charm tetraquark composed by spin 1 diquarks are in the range between 5.8 to 7 GeV, above the threshold of spontaneous decay in low-lying charmonium pairs, like two eta_c or J/psi, what suggests that this could be the ideal channels to look for these states, and develop the current understanding of multiquark states.

Dirhodium complexes such as carboxylates and carboxylamidates are very efficient metal catalysts used in the synthesis of pharmaceuticals and agrochemicals. Recent experimental work has indicated that there are significant differences in the isomeric ratios obtained among the possible products when synthesizing these complexes. The relative stabilities of the Rh2(NPhCOCH3)4 tolunitrile complexes, Rh2(NPhCOCH3)4(NCC6H4CH3)2, were determined at the HF/LANL2DZ ECP, 6-31G and DFT/B3LYP/LANL2DZ ECP, 6-31G levels of theory using NWChem 6.3. The LANL2DZ ECP (effective core potential) basis set was used for the rhodium atoms and 6-31G basis set was used for all other atoms. Specifically, the o-tolunitrile, m-tolunitrile, and p-tolunitrile complexes of the 2,2-trans and the 4,0- isomers of Rh2(NPhCOCH3)4 were compared.

Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods. Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational structure. For such an equation or system, a weak solution can be found through finding the critical point of a corresponding energy functional. If this equation or system is also invariant under a certain symmetric group, multiple solutions are often expected. In this work, an integer-valued function that measures symmetries of CNLS was used to determine critical values. Besides variational methods, bifurcation methods may also be used to find solutions of a differential equation or system, if some trivial solution branch exists and the system is degenerate somewhere on this branch. If local bifurcations exist, then new solutions can be found in a neighborhood of each bifurcation point. If global bifurcation branches exist, then there is a continuous solution branch emanating from each bifurcation point. We consider two types of CNLS. First, for a fully symmetric system, we introduce a new index and use it to construct a sequence of critical energy levels. Using variational methods and the symmetric structure, we prove that there is at least one solution on each one of these critical energy levels. Second, we study the bifurcation phenomena of a two-equation asymmetric system. All these bifurcations take place with respect to a positive solution branch that is already known. The locations of the bifurcation points are determined through an equation of a coupling parameter. A few nonexistence results of positive solutions are also given

No description available.

Variational structure plays an important role in critical point theory and methods. However many differential problems are non-variational i.e. they are not the Euler- Lagrange equations of any variational functionals, which makes traditional critical point approach not applicable. In this thesis, two types of non-variational problems, a nonlinear eigen solution problem and a non-variational semi-linear elliptic system, are studied. By considering nonlinear eigen problems on their variational energy profiles and using the implicit function theorem, an implicit minimax method is developed for numerically finding eigen solutions of focusing nonlinear Schrodinger equations subject to zero Dirichlet/Neumann boundary condition in the order of their eigenvalues. Its mathematical justification and some related properties, such as solution intensity preserving, bifurcation identification, etc., are established, which show some significant advantages of the new method over the usual ones in the literature. A new orthogonal subspace minimization method is also developed for finding multiple (eigen) solutions to defocusing nonlinear Schrodinger equations with certain symmetries. Numerical results are presented to illustrate these methods. A new joint local min orthogonal method is developed for finding multiple solutions of a non-variational semi-linear elliptic system. Mathematical justification and convergence of the method are discussed. A modified non-variational Gross-Pitaevskii system is used in numerical experiment to test the method.