We extend an efficient cone beam transform inversion formula, proposed earlier for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much in a certain sense, and do not admit lines which are tangent to C at one point and intersect C at another point. A domain U is found where reconstruction is possible with a filtered backprojection type algorithm. Results of numerical experiments demonstrate very good image quality. The algorithm developed is useful for image reconstruction in computerized tomography.

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Thermoelectric materials have been used for cooling and heating systems for over a hundred years. Today practical applications of thermoelectric devices include cooling car seats, power generation, and refrigeration. Thermoelectric materials are special for their ability to convert temperature imbalances into electricity. Their applications can inform the discourse about the transition to renewable energy sources---something that our Earth most desperately needs. The goal of this dissertation is to describe how the effective tensors of two-dimensional thermoelectric composites made from two isotropic materials depend on thermoelectric parameters of the constituents. Using the theory of exact relations and links developed by Grabovsky and his collaborators, we describe all equations satisfied by the thermoelectric effective tensor of a composite without the explicit knowledge of its microstructure. In some special cases, the effective tensor can be determined completely. Even in the general case, four out of 10 components of the two-dimensional thermoelectric tensor can be expressed in terms of the remaining 6, regardless of the microstructure. We started with special cases and worked our way up to the more general ones. / Mathematics

Semi-active suspension systems promise to significantly reduce the necessary trade-off be-tween handling and passenger comfort present in conventional suspension systems by enabling active chassis and wheel control. Öhlins Racing AB have developed a semi-active suspension technology known as CES, Continuously controlled Electronic Suspension, based on solenoid control valves which are integrated into specially designed hydraulic dampers, and are currently developing control and estimation systems which will enable their application in advanced motorcycle suspensions. In these systems an important aspect is being able to accurately control the forces produced. Öhlins’ current system uses an open loop control strategy in which currents sent through the solenoid valves, to achieve the requested damping force under the prevailing circumstances, is calculated using experimentally derived static lookup tables. In this thesis a new closed loop control system, based on the direct measurement of the damper force, is developed and its performance is evaluated in comparison to the old one’s. Sufficient understanding of the system requires extensive modeling and therefore two different models have been developed; a simpler one used for model based control design and a more extensive, high fidelity model used for high accuracy simulations. The developed simulation model is the first of its kind that is able to capture the studied systems behavior with satisfactory accuracy, as demonstrated against real dynamometer measurements. The valves and damper behave in a highly non linear manner and the final controller design uses a combination of exact linearization, non linear state estimation, dynamical inversion and classical control theory. Simulation results indicate that the new controller reduces the root mean square force tracking error to about 63% of that of the existing controller in the evaluation scenarios used. Cascaded within the system is also closed loop current controllers. A developed model based controller is shown to reduce the rise time to less than 30% of that of the existing PID-controllers, reduce the overshoot and provide online estimates of the winding series resistance, providing the basis for future solenoid diagnosis and temperature tracking systems.

General relativity has a small number of known, exact solutions which model astronomically relevant systems. These models are highly idealized situations. Either perturbation theory or numerical simulations are typically needed to produce more realistic models. Numerical simulations are time-consuming and suffer from a difficulty in interpreting the results. In addition, global properties of numerical solutions are nearly impossible to uncover. On the other hand, standard perturbation methods are very difficult to implement beyond the second order, which means they barely scratch the surface of non-linear phenomena which distinguishes general relativity from Newtonian gravity. This work develops a method of finding exact solutions, inspired by perturbation theory, which have energy-momentum tensor components that approximately satisfy desired relationships. We find a spherical lump of matter which has a density profile $\mu \propto r^{-2}$ in a Robertson-Walker background; it looks like a galaxy in an expanding universe. We also find a plane-symmetric perturbation of a Bianchi type I metric with a density profile $\mu \propto z^{-2}$; it models a jet impacting a sheet-like structure. The former solution involves a wormhole while the latter involves a two dimensional singularity. These are both non-linear structures which perturbation theory can never produce.

Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation of an undirected graph, has rank equal to the maximum number of vertices covered by a matching in the associated graph. The branching matrix, a representation of a directed graph, has rank equal to the maximum number of vertices covered by a branching in the associated graph. A mixed graph has both undirected and directed edges, and the matching forest problem for mixed graphs, introduced by Giles, is a generalization of the matching problem and the branching problem. A mixed graph can be represented by the matching forest matrix, and the rank of the matching forest matrix is related to the size of a matching forest in the associated mixed graph. The Tutte matrix and the branching matrix have indeterminate entries, and we describe algorithms that evaluate the indeterminates as rationals in such a way that the rank of the evaluated matrix is equal to the rank of the indeterminate matrix. Matroids in the context of graphs are discussed, and matroid formulations for the matching, branching, and matching forest problems are given.

The supLM test for structural change is embedded into a permutation test framework for a simple location model. The resulting conditional permutation distribution is compared to the usual (unconditional) asymptotic distribution, showing that the power of the test can be clearly improved in small samples. Furthermore, generalizations are discussed for binary and multivariate dependent variables as well as model-based permutation testing for structural change. The procedures suggested are illustrated using both artificial and real-world data (number of youth homicides, employment discrimination data, structural-change publications, and stock returns). / Series: Research Report Series / Department of Statistics and Mathematics

Polímeros conjugados semicondutores tem atraído grande interesse nas últimas décadas devido às possíveis aplicações como componentes ativos em aplicações optoeletrônicas. A adequação destes semicondutores orgânicos para a fabricação de dispositivos depende do entendimento e controle de propriedades eletrônicas básicas: gap fundamental (Eg) e potencial de ionização (IP). Nesse contexto, estudos teóricos baseados em cálculos de primeiros princípios tem se mostrado muito úteis, uma vez que possibilitam a simulação de processos físicos em condições ideais, onde se pode analisar as propriedades eletrônicas de polímeros desconsiderando efeitos do ambiente ou desordem estrutural. A Teoria do Funcional da Densidade (DFT) tem se tornado o método mais comum para o cálculo da estrutura eletrônica do estado fundamental de uma ampla variedade de materiais orgânicos complexos. Embora cálculos DFT baseados na diferença de energias totais tem sido aplicados com sucesso para estimar IPs de moléculas pequenas, este método falha nas propriedades de sistemas conjugados longos. Realmente, a capacidade preditiva da DFT padrão com respeito as propriedades espectroscópicas é frequentemente limitada, entretanto o tratamento adequado das excitações eletrônicas através de abordagens de muitos corpos é ainda muito difícil para materiais orgânicos complexos. Funcionais híbridos que misturam uma fração () de troca exata (EX) não-local ao correspondente semi-local representam uma boa alternativa, embora a quantidade ideal de EX seja, em geral, dependente do sistema. Neste trabalho, adotamos um esquema não-empírico baseado na aproximação G0W0 para identificar o valor ótimo de para o funcional híbrido PBE no qual a correção de autoenergia para o orbital mais alto ocupado (HOMO) de Kohn-Sham generalisado é minimizado. Estudamos, com base nessa estratégia, a dependência com o comprimento das propriedades eletrônicas básicas em uma família de oligômeros conjugados 1D de trans-poliacetileno (TPA). Nossos cálculos mostram que a fração EX ótima (dependente do tamanho) incorporada ao PBEh reproduz com precisão os IPs experimentais determinados em fase gasosa, / Semiconducting conjugated polymers have attracted considerable interest over the past decades due to the promising applications as active components for optoelectronic applications. The suitability of such organic semiconductors for device fabrication relies on quantitative understanding and control of basic electronic properties: fundamental gap (Eg) and ionization potential (IP). In this context, theoretical studies based on first principles approaches have proven useful, through simulating physical processes in ideal conditions, in which one might analyse the electronic properties of polymers apart from the effects of the surrounding environment or structural disorder. Density Functional Theory (DFT) has become an usual choice for calculating the ground state electronic structure of a wide variety of complex organic materials. Although DFT calculations based on total energy differences have been successfully applied to estimate IPs of small molecules, they fail for properties of long conjugated systems. Indeed, the predictive ability of standard DFT with respect to spectroscopic properties is often limited, however a proper treatment of the electronic excitations through many-body approaches is still very difficult for complex organic materials. Hybrid functionals that mix a fraction (_) of nonlocal exact exchange (EX) with the semilocal counterpart represent a good alternative, although the ideal amount of EX is usually system dependent. In this work, we adopt a non-empirical scheme based on the G0W0 approximation to identify the optimum _ value for the PBE hybrid functional for which the self-energy correction to the generalized Kohn-Sham highest occupied molecular orbital (HOMO) is minimized. Based on this strategy we study the size dependence of the basic electronic properties in a family of 1D _-conjugated oligomers of trans-polyacetylene (TPA). Our calculations demonstrate that the size dependent optimal EX fraction incorporated in PBEh accurately reproduces IPs from experimental gas phase data, although no particular constraint has been imposed a priori. Furthermore, we note that the optimum _-value decreases exponen tially with chain length going from _ w0.85 for the smaller oligomer (ethylene, n=1) up to _ w0.75 extrapolated for an isolated TPA chain. The accuracy of our optimized PBEh in predicting IPs and Eg is superior to other conventional mean field approaches, as demonstrated for a selected set of conjugated molecules such as acenes and phenylenes. As a result, we can obtain good estimations for the energy barriers of electron transfer in organic/organic interfaces. On the other extreme, we analyse the influence of exact exchange on the electronic structure of the prototypical metal system gold (Au), commonly used as electrode in organic devices. In this case, we confirm the expected result that the insertion of even a small fraction of EX into PBE functional distorts the Au band structure, worsening the description of electronic properties compared to regular PBE. We then proceed to analyse the factibility of studying polymer/metal interface systems using pure DFT. Our calculations reveal that the result is too system-dependent: for the TPA/Au(111) interface, an artificial charge transfer takes place at interface due to an underestimation of the IPs of the conjugated system inherent to the underlying DFT approximation. Finally, our study emphasizes the importance of a physically motivated choice of EX fraction in hybrid functionals for accurately predicting both ionization potentials and fundamental gaps of organic semiconductors relevant for nanoelectronics.

The total wind power capacity installed in the world has substantially grown during the last few years, mainly due to the increasing number of horizontal axis wind turbines (HAWT). Consequently, a big effort was employed to increase HAWT\'s power capacity, which is directly associated to the size of blades. Then, novel designs of blades may lead to very fexible structures, susceptive to large deformation, not only during extreme events, but also for operational conditions. In this context, this thesis aims to compare two geometrically nonlinear structural modeling approaches that handle large deformation of blade structures: 3D geometrically-exact beam and shell finite element models. Regarding the beam model, due to geometric complexity of typical cross-sections of wind turbine blades it is adopted a theory that allows creation of arbitrary multicellular cross-sections. Two typical blade geometries are tested, and comparisons between the models are done in statics and dynamics, always inducing large deformation and exploring the accuracy limits of beam models, when compared to shells. Results showed that the beam and shell models present very similar behavior, except when violations occur on the beam formulation hypothesis, such as when shell local buckling phenomena takes place. / A capacidade total de energia eólica instalada no mundo cresceu substancialmente nos últimos anos, principalmente devido ao número crescente de turbinas eólicas de eixo horizontal. Consequentemente, um grande esforço foi empregado com o intuito de aumentar a capacidade de produção das turbinas eólicas, que está diretamente associada ao tamanho das pás. Assim, surgiram projetos inovadores quanto à concepção de pás de turbinas eólicas levando a estruturas bastante flexíveis, susceptíveis a grandes deslocamentos, não apenas em eventos extremos, mas também em condições normais de operação. Nesse contexto, a presente dissertação tem por objetivo comparar duas abordagens de modelos estruturais geometricamente não-lineares capazes de lidar com grandes deslocamentos de pás de turbinas eólicas: elementos finitos geometricamente exatos 3D de vigas e cascas. Em relação ao modelo de viga, devido à complexidade geométrica das seções transversais típicas de pás de turbinas eólicas, adota-se uma teoria que permite a criação de seções transversais arbitrárias multicelulares. Duas geometrias de pás s~ao testadas e comparações entre os modelos s~ao feitas em análises estáticas e dinâmicas, sempre induzindo grandes deslocamentos e explorando os limites de precisão do modelo de viga, quando comparado ao modelo de cascas. Os resultados indicam que os modelos de viga e casca apresentam comportamento muito similar, exceto quando ocorrem violações em hipóteses do modelo de viga, tal como quando ocorre flambagem local do modelo de casca.

The purpose of this paper was to present the exact analysis of variance with unequal variances. Bishop presented the new procedure for the r-way layout ANOVA. In this paper, one and two way layout ANOVA were explained and Bishop's method and Standard method were compared by using a Monte Carlo method.