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In dieser Arbeit wird eine systematische Methode gegeben um die Amplituden in (skalarer) Quantenelektrodynamik und nicht-Abelsche Eichtheorien in Schwinger-parametrische Form zu schreiben. Dies wird erreicht in dem der Zähler der Feynmanregeln im Impulsraum in einem Differentialoperator umgewandelt wird. Dieser Differentialoperator wirkt dann auf den parametrichen Integranden der skalaren Theorie. Für die QED ist das am einfachsten, weil die Leibnizregel hier nicht nötig ist. Im Fall der sQED und den nicht-Abelsche Eichtheorien stehen die Beiträge der Leibnizregel in Verbindung mit 4-valente Vertices. Eine andere Eigenschaft dieser Methode ist, dass mit dem hier benutzten Renormierungsschema die Subtraktionen für 1-scale Graphen signifikante Vereinfachungen verursachen. Weiterhin wurden die Ward-Identitäte für die genannten drei Theorien studiert. / In this thesis a systematic method is given for writing the amplitudes in (scalar) quantum electrodynamics and non-Abelian gauge theories in Schwinger parametric form. This is done by turning the numerator of the Feynman rules in momentum space into a differential operator. It acts then on the parametric integrand of the scalar theory. For QED it is the most straightforward, because the Leibniz rule is not involved here. In the case of sQED and non-Abelian gauge theories, the contributions from the Leibniz rule are satisfyingly related to 4-valent vertices. Another feature of this method is that in the used renormalization scheme, the subtractions for 1-scale graphs cause significant simplifications. Furthermore, the Ward identities for mentioned three theories are studied.

Neste trabalho, são caracterizadas as soluções do tipo ondas planas e modais de modelos matemáticos referentes à teoria de linhas de transmissão, com e sem perdas, e à teoria de vigas, modelo de Timoshenko e modelo não local de Eringen. Os modelos são formulados matricialmente, e as ondas em questão são determinadas em termos da base gerada pela resposta matricial fundamental de sistemas de equações diferenciais ordinárias de primeira, segunda e quarta ordem. A resposta matricial fundamental é utilizada numa forma fechada que envolve o acoplamento de um número finito de matrizes e uma função escalar geradora e suas derivadas. A função escalar geradora é bem comportada para mudanças em torno de frequências críticas e sua robustez é exibida através da técnica de Liouville. As ondas modais são decompostas em termos de uma parte que viaja para frente e uma parte que viaja para trás. Essa decomposição é utilizada para fornecer matrizes de reflexão e transmissão em descontinuidades e condições de contorno. No contexto das linhas de transmissão são consideradas uma junção de linhas com impedâncias características diferentes ou uma carga em uma extremidade da linha. Na teoria de Timoshenko são consideradas uma fissura ou condições de contorno em uma das extremidades. Exemplos numéricos com descontinuidade são considerados na viga. Na teoria de linhas de transmissão exemplos com multicondutores são considerados e observações são realizadas sobre a decomposição das ondas modais. No modelo não local de Eringen, para vigas bi-apoiadas é discutida a existência do segundo espectro de frequências. / Plane type solutions and modal waves of mathematical models, which refer to transmission lines theory, both lossless and lossy, and to beam theory, using both Timoshenko and nonlocal Eringen models, are being characterized in this work. The models are formulated in matrix form, and the waves are determined in terms of matrix basis generated by fundamental matrix response of systems of ordinary differential equations of first, second and fourth order. The fundamental matrix response is used in the closed-form, which involve the coupling between a number finite of matrices of a generating scalar function and its derivatives. The generating scalar function is well behaved for changes around critical frequencies and its robustness is exhibited through the Liouville technique. Modal waves are decomposed in forward and backward parts. This decomposition is used for providing reflection and transmission matrices when dealing with discontinuities and boundary conditions. In the context of transmission lines junction of lines with different characteristic impedances or a load at one end of the line are being considered. In Timoshenko’s theory the crack problem or boundary conditions at one end are also being considered. Numerical examples with discontinuities are considered in the context of beams. Numerical examples with discontinuities and boundary value problems were approached using modal wave decomposition. In transmission line theory examples with multiconductors are considered and observations are made about decomposition of the modal waves. In the nonlocal of Eringen model, for bi-supported beams, the existence of the second frequency spectrum is discussed.

O objetivo principal desta dissertação é estudar a ressonância $\\k$, um méson escalar ainda hoje bastante controverso na comunidade científica. Estudamos o espalhamento elástico $K\\pi$, pois é neste subsistema que o $\\k$ se manifesta como um estado intermediário. A partir de uma lagrangiana efetiva quiral $SU(3)\\times SU(3)$, envolvendo termos de contato e ressonâncias, calculamos a amplitude $K\\pi$ projetada no canal de isospin $1/2$ e em seguida a unitarizamos por meio de {\\it loops} mesônicos. Investigamos os pólos físicos da amplitude, dados pelos zeros do seu denominador que se encontram na segunda superfície de Riemann. Esses zeros podem ser obtidos numericamente, mas a análise estrita desta solução não fornece informações a respeito da dinâmica que produz os pólos. Como alternativa, uma descrição qualitativa dos pólos foi obtida considerando o limite de $SU(2) \\Leftrightarrow M_\\p=0$ e a aproximação da matriz K, que corresponde a unitarizar a amplitude com {\\it loops} de $K\\p$ na camada de massa. Essas simplificações reduzem o denominador da amplitude a um polinômio de segundo grau, que dá origem a dois pólos físicos, posteriormente identificados como sendo o $K^*_0(1430)$ e o $\\k$. Este modelo simplificado permite uma boa interpretação da origem dinâmica dos pólos. O $\\k$ mostrou-se estável na variação dos acoplamentos da ressonância explícita, o que indica que ele é produzido pelo diagrama de contato. Já a ressonância identificada como o $K^*_0(1430)$ varia de um estado ligado a um pólo não físico, dependendo dos valores atribuídos aos parâmetros da ressonância, o que sugere fortemente que a natureza destes pólos é distinta. Esses diferentes comportamentos dinâmicos também foram observados no programa numérico, indicando que a essência dos pólos foi mantida no modelo simplificado. % Com o programa numérico obtivemos a posição do pólo do $\\k$ em $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, o que está em pleno acordo com diversos modelos quirais muito mais complicados. / This work aims mostly at studying the $\\k$ resonance, which is still a controversial scalar meson nowadays within the scientific community. We studied the $K\\pi$ elastic scattering, because the $\\k$ appears as an intermediate state in this subsystem. From an effective chiral lagrangian $SU(3)\\times SU(3)$, involving contact terms and resonances, we calculated the $K\\pi$ amplitude projected on the $1/2$ isospin channel and then unitarized by means of mesonic {\\it loops}. The physical poles of the amplitude were investigated, given by the zeros of its denominator which are encountered on the Riemanns surface. Although these zeros can be numerically obtained, the strict analysis of this solution does not supply information about the poles producing dynamics. Alternatively, a qualitative description of the poles was obtained considering the $SU(2) \\Leftrightarrow M_\\p=0$ limit and the K matrix approximation, which corresponds to the unitarizing of the amplitude with {\\it loops} of $K\\p$ on shell. These simplifications reduce the amplitude denominator to a second grade polynomial that originates two physical poles, later identified as being $K^*_0(1430)$ and $\\k$. This simplified model allows for a good interpretation of the poles dynamic origin. The $\\k$ has been stable on the explicit resonance coupling, showing that it is produced by the contact diagram. The $K^*_0(1430)$ identified resonance, on the other hand, varies from a bounded state to a non-physical pole, depending on the resonance parameters attributed values, which strongly suggest that the nature of this poles is distinct. These different dynamic behaviors have also been observed in the numerical programs, indicating that the essence of the poles was maintained in the simplified model. With the numerical programs we obtained the position of pole $\\k$ in $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, which is in accordance with various more complex chiral models.

Moduladores espaciais de luz são elementos que fazem a modulação de uma frente de onda de modo a resultar em uma distribuição de luz desejada. Eles operam por difração, de acordo com o princípio de Huygens-Fresnel, e por este motivo são chamados Elementos Ópticos Difrativos (EODs). O foco deste trabalho é o estudo da modulação de frentes de onda, através da Teoria Escalar da Difração. O objetivo inicial foi o domínio do cálculo dos moduladores espaciais de luz, através da implementação do Algoritmo Iterativo da Transformada de Fourier. São calculados três EODs de fase: fase contínua, 4 níveis de fase e fase binária. Os resultados são avaliados através do cálculo da eficiência difrativa e da relação sinal-ruído. Para verificação do cálculo, hologramas binários foram fabricados usando filme fotográfico, de maneira simples e baixo custo. Algumas reconstruções simuladas e ópticas são apresentadas, demonstrando a viabilidade do uso do algoritmo na codificação de EODs. Em seguida, é feita a análise das frequências de ressonância de moduladores de ferroeletretos com canaleta, através de uma montagem experimental baseada no interferômetro de Michelson. Os ferroeletretos apresentam o efeito piezoelétrico e vêm sendo produzidos através de novas técnicas de fabricação. No campo da óptica tem-se o interesse em caracterizar ferroeletretos de modo a utilizá-los como possíveis moduladores de luz. São apresentados a montagem interferométrica em detalhes e o procedimento usado para medir as frequências de ressonância. Os resultados obtidos e as discussões demonstram a viabilidade do uso da montagem interferométrica proposta na caracterização de ferroeletretos. / Spatial light modulators perform the modulation of wavefront so that the desired light distribution is acquired. They work by diffraction, according to the Huygens-Fresnel principie, and for that they are called Diffractive Optical Elements (DOEs). The focus of this work is the study of light modulators through Scalar Diffraction Theory. The initial objective was to execute the calculation of spatial light modulators through the implementation of the so-called Iterative Fourier Transform AIgorithm. The calculation of three phase holograms is made: analog phase, 4 leveI phase and binary phase. The results are evaluated by calculating the diffraction efficiency and by signal to noise ratio. To verify the calculation, binary holograms were fabricated using photographic film in a simple and low cost way. Simulated and optical reconstructions are presented, showing the viability for the use of the algorithm in the coding of DOEs. Next, the resonance frequencies analysis in open tubular channels ferroelectrets is made through an experimental setup based in the Michelson interferometer. The ferroelectrets present the piezoelectric effect and are continuously produced through new techniques. In optics there is in interest in feroelectrets characterization in order to use them as spatial light modulators. The interferometric setup and the procedure used to measure the resonance frequencies are shown. The obtained results and discussion demonstrate the viability of the use of optical measurements in the characterization of ferroelectrets.

Nesta tese apresentamos a análise da absorção e do espalhamento de partículas não massivas de spins 0 e 1 por buracos negros de Schwarzschild, assim como a absorção e espalhamento por análogos acústicos destes buracos negros. Apresentamos também a análise da absorção e do espalhamento do campo escalar não massivo por buracos negros de Reissner-Nordström. A presente pesquisa se baseia no método de decomposição em ondas parciais. Devido a estes espaços-tempos serem estáticos e esfericamente simétricos, as partes temporal e angular das soluções das equações de campo se reduzem a funções conhecidas. O mesmo não acontece com a parte radial, o que nos leva a abordar o problema, principalmente, por meio de métodos numéricos. Cálculos analíticos também são realizados, geralmente para podermos verificar a precisão dos resultados numéricos. Os principais resultados analíticos mostrados aqui são a seção de choque de absorção em baixas e altas frequências e a seção de choque diferencial de espalhamento para ângulos próximos a 180 (efeito glória). Mostramos, de forma analítica, que as principais características das seções de choque de absorção e diferencial de espalhamento estão diretamente relacionadas à existência da órbita instável de partículas não massivas. Os nossos resultados numéricos estão em excelente concordância com os resultados obtidos por meio de cálculos analíticos. Com relação ao espaço-tempo de Reissner-Nordström, mostramos qual o comportamento das seções de choque com a variação da intensidade de carga do buraco negro. No caso de buracos negros descarregados, fazemos comparações das seções de choque obtidas para partículas de diferentes spins. / We present an analysis of the absorption and scattering of massless particles of spin 0 and 1 by Schwarzschild black holes, and the absorption and scattering by analogues of these black holes. We present also the analysis of the massless scalar field absorption and scattering by Reissner-Nordström black holes. This research is based on the partial wave methods. Since these spacetimes are static and spherically symmetric, the time and angular dependence of the field equation solutions can be written in terms of well known functions. The same does not happen with the radial part of the field equation solutions, so that we apply numerical methods to solve the absorption and scattering problem. Analytical computations are also performed and we use them to verify the precision of our numerical computations. The main analytical results obtained here are the low- and high-frequency absorption cross sections and the dierential scattering cross section for angles near 180 (the glory eect). We use our analytical results to show that the main cross sections properties are related to the existence of an unstable orbit for massless particles. We compare our numerical results with semiclassical approximations from a geodesic analysis, and find excellent agreement. In the Reissner-Nordström spacetime case, we show how the cross sections behave as we vary the black hole charge. For uncharged black holes, we compare cross sections for particles with dierent spins.

<p>In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D).</p><p>In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively.</p><p>In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels.</p><p>Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity.</p><p>These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.</p>

QC 20110926

In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D). In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively. In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels. Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity. These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.