O lado escuro do universo é misterioso e sua natureza é ainda desconhecida. De fato, isto talvez constitua o maior desafio da cosmologia moderna. As duas com- ponentes do setor escuro (mat´ eria escura e energia escura) correspondem hoje a cerca de noventa e cinco por cento do universo. O candidato mais simples para a energia energia é uma constante cosmológica. Contudo, esta tentativa apresenta uma enorme discrepância de 120 ordens de magnitude entre a predição teórica e os dados observados. Tal disparidade motiva os físicos a investigar modelos mais sofisticados. Isto pode ser feito tanto buscando um entendimento mais profundo de onde a constante cosmológica vem, se deseja-se derivá-la de primeiros princípios, quanto considerando outras possibilidades para a expansão acelerada, tais como modificações da relatividade geral, campos de matéria adi- cionais e assim por diante. Ainda considerando uma energia escura dinâmica, pode existir a possibilidade de interação entre energia e matéria escuras, uma vez que suas densidades são comparáveis e, dependendo do acoplamento usado, a interação pode também aliviar a questão de porquê as densidades de matéria e energia escura são da mesma ordem hoje. Modelos fenomenológicos tem sido amplamente estudados na literatura. Por outro lado, modelos de teoria de cam- pos que visam uma descrição consistente da interação energia escura/matéria escura ainda são poucos. Nesta tese, nós exploramos como candidato à energia escura um campo escalar ou vetorial em várias abordagens diferentes, levando em conta uma possível interação entre as duas componentes do setor escuro. A tese é dividida em três partes, que podem ser lidas independentemente. Na primeira parte, nós analisamos o comportamento asintótico de alguns modelos cosmológicos usando campos escalares ou vetorial como candidatos para a energia escura, à luz da teoria de sistemas dinâmicos. Na segunda parte, nós usamos um campo escalar em supergravidade para construir um modelo de energia escura dinâmico e também para incorporar um modelo de energia escura holográfica em supergravidade mínima. Finalmente, na terceira parte, nós propomos um modelo de energia escura metaestável, no qual a energia escura é um campo escalar com um potencial dado pela soma de auto-interações pares até ordem seis. Nós inserimos a energia escura metaestável em um modelo SU(2)R escuro, onde o dubleto de energia escura e o dubleto de matéria escura interagem nat- uramente. Tal interação abre uma nova janela para investigar o setor escuro do ponto-de-vista de física de partículas. Esta tese é baseada nos seguintes artigos, disponíveis também no arXiv: 1611.00428, 1605.03550, 1509.04980, 1508.07248, 1507.00902 e 1505.03243. O autor também colaborou nos trabalhos: 1607.03506 e 1605.05264. / The dark side of the universe is mysterious and its nature is still unknown. In fact, this poses perhaps as the biggest challenge in the modern cosmology. The two components of the dark sector (dark matter and dark energy) correspond today to around ninety five percent of the universe. The simplest dark energy candidate is a cosmological constant. However, this attempt presents a huge discrepancy of 120 orders of magnitude between the theoretical prediction and the observed data. Such a huge disparity motivates physicists to look into a more sophisticated models. This can be done either looking for a deeper understanding of where the cosmological constant comes from, if one wants to derive it from first principles, or considering other possibilities for accelerated expansion, such as modifications of general relativity, additional matter fields and so on. Still regarding a dynamical dark energy, there may exist a possibility of interaction between dark energy and dark matter, since their densities are comparable and, depending on the coupling used, the interaction can also alleviate the issue of why dark energy and matter densities are of the same order today. Phenomenological models have been widely explored in the literature. On the other hand, field theory models that aim a consistent description of the dark energy/dark matter interaction are still few. In this thesis, we explore either a scalar or a vector field as a dark energy candidate in several different approaches, taking into account a possible interaction between the two components of the dark sector. The thesis is divided in three parts, which can be read independently of each other. In the first part, we analyze the asymptotic behavior of some cosmological models using either scalar or vector fields as dark energy candidates, in the light of the dynamical system theory. In the second part, we use a scalar field in the supergravity framework to build a model of dynamical dark energy and also to embed a holographic dark energy model into minimal supergravity. Finally, in the third part, we propose a model of metastable dark energy, in which the dark energy is a scalar field with a potential given by the sum of even self-interactions up to order six. We insert the metastable dark energy into a dark SU(2)R model, where the dark energy doublet and the dark matter doublet naturally interact with each other. Such an interaction opens a new window to investigate the dark sector from the point-of-view of particle physics. This thesis is based on the following papers, available also in the arXiv: 1611.00428, 1605.03550, 1509.04980, 1508.07248, 1507.00902 and 1505.03243. The author also collaborated in the works 1607.03506 and 1605.05264.

A general multidisciplinary design problem features coupling and feedback between contributing analyses. This feedback may lead to convergence issues requiring significant iteration in order to obtain a feasible design. This work casts the multidisciplinary design problem as a dynamical system in order to leverage the benefits of dynamical systems theory in a new domain. Three areas from dynamical system theory are chosen for investigation: stability analysis, optimal control, and estimation theory. Stability analysis is used to investigate the existence of a solution to the design problem and how that solution can be found. Optimal control techniques allow consideration of contributing analysis output and design variables constraints at the same level of the optimization hierarchy. Finally, estimation methods are employed to rapidly evaluate the robustness of the multidisciplinary design. These three dynamical system techniques are then combined in a methodology for the rapid robust design of linear multidisciplinary systems. While inherently linear, the developed robust design methodology is shown to be extensible to nonlinear systems. The applicability and performance of the developed technique is demonstrated through linear and nonlinear test problems including the design of a hypersonic aerodynamic surface for a system in which an increase in range or improvement in landed accuracy is sought. In addition, it is shown that the developed robust design methodology scales well compared to other methods.

O lado escuro do universo é misterioso e sua natureza é ainda desconhecida. De fato, isto talvez constitua o maior desafio da cosmologia moderna. As duas com- ponentes do setor escuro (mat´ eria escura e energia escura) correspondem hoje a cerca de noventa e cinco por cento do universo. O candidato mais simples para a energia energia é uma constante cosmológica. Contudo, esta tentativa apresenta uma enorme discrepância de 120 ordens de magnitude entre a predição teórica e os dados observados. Tal disparidade motiva os físicos a investigar modelos mais sofisticados. Isto pode ser feito tanto buscando um entendimento mais profundo de onde a constante cosmológica vem, se deseja-se derivá-la de primeiros princípios, quanto considerando outras possibilidades para a expansão acelerada, tais como modificações da relatividade geral, campos de matéria adi- cionais e assim por diante. Ainda considerando uma energia escura dinâmica, pode existir a possibilidade de interação entre energia e matéria escuras, uma vez que suas densidades são comparáveis e, dependendo do acoplamento usado, a interação pode também aliviar a questão de porquê as densidades de matéria e energia escura são da mesma ordem hoje. Modelos fenomenológicos tem sido amplamente estudados na literatura. Por outro lado, modelos de teoria de cam- pos que visam uma descrição consistente da interação energia escura/matéria escura ainda são poucos. Nesta tese, nós exploramos como candidato à energia escura um campo escalar ou vetorial em várias abordagens diferentes, levando em conta uma possível interação entre as duas componentes do setor escuro. A tese é dividida em três partes, que podem ser lidas independentemente. Na primeira parte, nós analisamos o comportamento asintótico de alguns modelos cosmológicos usando campos escalares ou vetorial como candidatos para a energia escura, à luz da teoria de sistemas dinâmicos. Na segunda parte, nós usamos um campo escalar em supergravidade para construir um modelo de energia escura dinâmico e também para incorporar um modelo de energia escura holográfica em supergravidade mínima. Finalmente, na terceira parte, nós propomos um modelo de energia escura metaestável, no qual a energia escura é um campo escalar com um potencial dado pela soma de auto-interações pares até ordem seis. Nós inserimos a energia escura metaestável em um modelo SU(2)R escuro, onde o dubleto de energia escura e o dubleto de matéria escura interagem nat- uramente. Tal interação abre uma nova janela para investigar o setor escuro do ponto-de-vista de física de partículas. Esta tese é baseada nos seguintes artigos, disponíveis também no arXiv: 1611.00428, 1605.03550, 1509.04980, 1508.07248, 1507.00902 e 1505.03243. O autor também colaborou nos trabalhos: 1607.03506 e 1605.05264. / The dark side of the universe is mysterious and its nature is still unknown. In fact, this poses perhaps as the biggest challenge in the modern cosmology. The two components of the dark sector (dark matter and dark energy) correspond today to around ninety five percent of the universe. The simplest dark energy candidate is a cosmological constant. However, this attempt presents a huge discrepancy of 120 orders of magnitude between the theoretical prediction and the observed data. Such a huge disparity motivates physicists to look into a more sophisticated models. This can be done either looking for a deeper understanding of where the cosmological constant comes from, if one wants to derive it from first principles, or considering other possibilities for accelerated expansion, such as modifications of general relativity, additional matter fields and so on. Still regarding a dynamical dark energy, there may exist a possibility of interaction between dark energy and dark matter, since their densities are comparable and, depending on the coupling used, the interaction can also alleviate the issue of why dark energy and matter densities are of the same order today. Phenomenological models have been widely explored in the literature. On the other hand, field theory models that aim a consistent description of the dark energy/dark matter interaction are still few. In this thesis, we explore either a scalar or a vector field as a dark energy candidate in several different approaches, taking into account a possible interaction between the two components of the dark sector. The thesis is divided in three parts, which can be read independently of each other. In the first part, we analyze the asymptotic behavior of some cosmological models using either scalar or vector fields as dark energy candidates, in the light of the dynamical system theory. In the second part, we use a scalar field in the supergravity framework to build a model of dynamical dark energy and also to embed a holographic dark energy model into minimal supergravity. Finally, in the third part, we propose a model of metastable dark energy, in which the dark energy is a scalar field with a potential given by the sum of even self-interactions up to order six. We insert the metastable dark energy into a dark SU(2)R model, where the dark energy doublet and the dark matter doublet naturally interact with each other. Such an interaction opens a new window to investigate the dark sector from the point-of-view of particle physics. This thesis is based on the following papers, available also in the arXiv: 1611.00428, 1605.03550, 1509.04980, 1508.07248, 1507.00902 and 1505.03243. The author also collaborated in the works 1607.03506 and 1605.05264.

Este trabalho apresenta um estudo qualitativo das equações diferenciais nãolineares que descrevem o sincronismo de fase nos PLLs de 3ª ordem que compõem redes OWMS de topologia mista, Estrela Simples e Cadeia Simples. O objetivo é determinar, através da Teoria de Bifurcações, os valores ou relações entre os parâmetros constitutivos da rede que permitam a existência e a estabilidade do estado síncrono, quando são aplicadas, no oscilador mestre, duas funções de excitação muito comuns na prática: o degrau e a rampa de fase. Na determinação da estabilidade dos pontos de equilíbrio, sob o ponto de vista de Lyapunov, a existência de pontos de equilíbrio não-hiperbólicos não permite uma aproximação linear e, nesses casos, é aplicado o Teorema da Variedade Central. Essa técnica de simplificação de sistemas dinâmicos permite fazer uma aproximação homeomórfica em torno desses pontos, preservando a orientação no espaço de fases e possibilitando determinar localmente suas estabilidades. / This work presents a qualitative study of the non-linear differential equations that describe the synchronous state in 3rd order PLLs that compose One-way masterslave time distribution networks with Single Star and Single Chain topologies. Using bifurcation theory, the dynamical behavior of third-order phase-locked loops employed to extract the syncronous state in each node is analyzed depending on constitutive node parameters when two usual inputs, the step and the ramp phase pertubations, are supposed to appear in the master node. When parameter combinations result in non hyperbolic synchronous states, from Lyapunov point of view, the linear approximation does not provide any information about the local behavior of the system. In this case, the center manifold theorem permits the construction of an equivalent vector field representing the asymptotic behavior of the original system in the neighborhood of these points. Thus, the local stability can be determined.

In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models. Comparative numerical results are also provided for each model.

<p>The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency virus (HIV) and mycobacterium tuberculosis (TB) are among the leading causes of morbidity and mortality. It is found that infection with HIV increases the risk of reactivating latent TB infection, and HIV-infected individuals who acquire new TB infections have high rates of disease progression. Research has shown that these two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models.&nbsp / Comparative numerical results are also provided for each model.</p>

<p>The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency virus (HIV) and mycobacterium tuberculosis (TB) are among the leading causes of morbidity and mortality. It is found that infection with HIV increases the risk of reactivating latent TB infection, and HIV-infected individuals who acquire new TB infections have high rates of disease progression. Research has shown that these two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models.&nbsp / Comparative numerical results are also provided for each model.</p>

In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models. Comparative numerical results are also provided for each model.

Este trabalho apresenta um estudo qualitativo das equações diferenciais nãolineares que descrevem o sincronismo de fase nos PLLs de 3ª ordem que compõem redes OWMS de topologia mista, Estrela Simples e Cadeia Simples. O objetivo é determinar, através da Teoria de Bifurcações, os valores ou relações entre os parâmetros constitutivos da rede que permitam a existência e a estabilidade do estado síncrono, quando são aplicadas, no oscilador mestre, duas funções de excitação muito comuns na prática: o degrau e a rampa de fase. Na determinação da estabilidade dos pontos de equilíbrio, sob o ponto de vista de Lyapunov, a existência de pontos de equilíbrio não-hiperbólicos não permite uma aproximação linear e, nesses casos, é aplicado o Teorema da Variedade Central. Essa técnica de simplificação de sistemas dinâmicos permite fazer uma aproximação homeomórfica em torno desses pontos, preservando a orientação no espaço de fases e possibilitando determinar localmente suas estabilidades. / This work presents a qualitative study of the non-linear differential equations that describe the synchronous state in 3rd order PLLs that compose One-way masterslave time distribution networks with Single Star and Single Chain topologies. Using bifurcation theory, the dynamical behavior of third-order phase-locked loops employed to extract the syncronous state in each node is analyzed depending on constitutive node parameters when two usual inputs, the step and the ramp phase pertubations, are supposed to appear in the master node. When parameter combinations result in non hyperbolic synchronous states, from Lyapunov point of view, the linear approximation does not provide any information about the local behavior of the system. In this case, the center manifold theorem permits the construction of an equivalent vector field representing the asymptotic behavior of the original system in the neighborhood of these points. Thus, the local stability can be determined.

Made available in DSpace on 2016-03-15T19:38:09Z (GMT). No. of bitstreams: 1 Marcos Kleber Soares Kunyosi.pdf: 2418852 bytes, checksum: ab6795f8d39445430da1eca23e865c56 (MD5) Previous issue date: 2006-09-11 / Instituto Presbiteriano Mackenzie / Recognition of patterns can be performed by using neural networks built with oscillators, like phase-locked loops (PLLs). These networks are modeled with differential equation systems and can be studied by using Dynamical System Theory, which is used in this work in order to investigate the dynamical behavior related to a synaptic configuration of a neural network. As a result of such an investigation, two methods (Brute Force and Algebric) that help to build neural networks formed by PLLs are presented. These methods aim to relate the synaptic configuration of the network to the corresponding basin of attraction of fixed points, which represent the stored patterns on the network. Also general properties of synaptic configuration are presented in order to generate other useful configurations. Then a model of an image recognition machine able to store in its memory a monochromatic image and able to determine if other image is similar to the memorized one is proposed. / Reconhecimento de padrões pode ser feito usando redes neurais construídas com osciladores, como malhas de sincronismo de fase (PLLs). Essas redes são modeladas por sistemas de equações diferenciais e podem ser estudas pela Teoria de Sistemas Dinâmicos, que é usada neste trabalho para investigar o comportamento dinâmico associado a uma configuração sináptica de uma rede neural. Como resultado dessa investigação, são apresentados dois métodos (Força Bruta e Algébrico) que auxiliam na construção de redes neurais formadas por PLLs. Esses métodos têm como objetivo relacionar a configuração sináptica da rede às respectivas bacias de atração de pontos atratores, os quais representam os padrões memorizados na rede. Também são apresentadas propriedades gerais da configuração sináptica que podem ser usadas para compor outras configurações de interesse. Por fim, é proposto um modelo de máquina reconhecedora de imagem capaz de armazenar em sua memória uma figura monocromática e determinar se uma imagem qualquer apresentada a ela é semelhante à memorizada.