Neste trabalho, realizamos um estudo teórico do espalhamento elástico e inelástico de elétrons por moléculas de H2. A aproximação de ondas distorcidas em segunda ordem e o método de frações continuadas multicanal foram aplicados no cálculo de seções de choque diferencial e integral (SCD e SCI) destes processos. Na aproximação de ondas distorcidas em segunda ordem, os elementos da matriz-T em primeira ordem bem como as funções de onda distorcidas foram geradas em um potencial estático-troca do estado fundamental do alvo e o método de frações continuadas ao nível monocanal foi usado para calcular a função de Green completa de ondas distorcidas. Para o espalhamento elástico, SCD e SCI na faixa de energia do elétron incidente de 1-40eV foram calculadas. Para o espalhamento inelástico, estudamos transições a partir do estado fundamental da molécula de H2 para os três primeiros estados tripletos b3 Σ+u, a3 Σ+g e c3πu e para o estado singleto B1 Σ+u para energias do elétron incidente iguais a 20 e 30eV. Nos estudos com o método de frações continuadas multicanal, foram calculadas SCD e SCI a 2 e 5 canais para transições a partir do estado fundamental da molécula de H2 para os estados tripletos tripletos b3 Σ+u, a3 Σ+g e c3πu e para os estados singletos B1Σ+u, E1Σ+g e C1>πucom energias do elétron incidente na faixa de 15-40eV. A comparação entre os resultados obtidos com a aproximação de ondas distorcidas em segunda ordem e o método de frações continuadas multicanal nos fornecerá informações sobre a convergência da série de ondas distorcidas em cálculos de seção de choque para o espalhamento inelástico e- - H2 / In this work, we report a theoretical study on elastic and inelastic electron scattering by H2 molecules. The second-order distorted-wave approximation and the multichannel formulation of the method of continued fractions were applied on the evaluation of differential and integral cross sections (DCS and ICS) of these processes. In the second-order distorted-wave approach, first-order T-matrix elements as well as distorted-wave functions were generated from the static-exchange potential of the ground state of the target and the method of continued fractions in a single-channel formulation was applied to the evaluation of the full distorted-wave Green\'s function. For elastic scattering, we have calculated DCS and ICS in the 1-40 eV incident energy range. For inelastic scattering, electronic excitation cross sections for the X1 Σ+g,→ b3 Σ+u, a3 Σ+g, c3πu and B1 Σ+u transitions in H2 by electron impact were obtained at 20 and 30 eV. In the studies with the multichannel formulation of the method of continued fractions, we have calculated DCS and ICS in both two- and five-channel formulation for transitions from the ground state of H2 to the triplet states b3Σ+u, a3Σ+g and c3πu, and to the singlet states B lEu+, E1 Eg9 and CI IIu in the 15 40 eV energy range. The comparision of the results from both methods can provide significant informations about the convergence of the distorted-wave series in inelastic e- H2 scattering calculations.

Optimal sensor placement is an important problem with many applications; placing thermostats in rooms, installing pressure sensors in chemical columns or attaching vibration detection devices to structures are just a few of the examples. Frequently, this placement problem is encountered while noise is present. The H_2-optimal control is a strategy designed for systems that have exogenous disturbing inputs. Therefore, one approach for the optimal sensor location problem is to combine it with the H_2-optimal control. In this work the H_2-optimal control is explained and combined with the sensor placement problem to create the H_2-optimal sensor location problem. The problem is examined for the one-dimensional beam equation and the two-dimensional diffusion equation in an L-shaped region. The optimal sensor location is calculated numerically for both models and multiple scenarios are considered where the location of the disturbance and the actuator are varied. The effect of different model parameters such as the weight of the state and the disturbance are investigated. The results show that the optimal sensor location tends to be close to the disturbance location.

Thesis (Ph. D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on July 18, 2008) Vita. Includes bibliographical references.

Weathered rock has been located at over 450 sites in northeast Scotland. Depths of weathering locally exceed 30m but the weathering front is often highly irregular. The incidence of weathering is spatially variable and weathering zones are identified which reflect the influence of geology, fracturing, slopes and patterns of glacial erosion. Two weathering types, grusses and clayey grusses, are recognised after examination of granulometry, geochemistry and clay mineralogy. The grusses have low clay contents, high proportions of little-altered felspar and biotite, modest soluble base losses and heterogeneous clay mineral assemblages. The grusses are equivalent to the 'sandy weathering type' of Bakker (1967) and were formed mainly under the temperate environments of the late Pliocene and the early Pleistocene. The clayey grusses have elevated clay contents, high proportions of detrital quartz, high soluble base losses, kaolinite-illite bi-mineralic assemblages and may be rubefied. The clayey grusses formed under warmer environments than at present, probably in the Miocene. The Buchan Gravels consist of two formations of separate age. The Windyhills Formation comprises fluvial gravels of Middle to Late Pliocene age. The Buchan Ridge Formation includes glacially- disturbed masses of fluviatile deposits of Late Miocene to Early Pliocene age. The denudational history of the region is reconstructed using evidence from morphology, weathering types, and onshore and offshore geology. In the Late Cretaceous, transgression into the Buchan area left a cover of Greensand and Chalk. In the Palaeocene, the eastern Grampians were uplifted and tilted but the eastern lowlands were simultaneously downwarped towards the outer Moray Firth. Western areas subsided after the Early Eocene, the Chalk was exposed and the Mid-Palaeogene etchplain developed under tropical environments. Differential movements recurred at the Oligo-Miocene boundary, with uplift and tilting west of the Bennachie-Fare Fracture and initiation of basin development. Further etching in the warm and stable Middle Miocene period led to the establishment of the main erosion surfaces. The Eastern Grampian Surface (450 - 750m) is an etchsurface produced by lowering of the Mid-Palaeogene etchplain. The Marginal Surface (280 - 370m) is derived from a Miocene etchplain that was raised and tilted gently eastwards in the late Neogene. Fragments of this surface are associated with clayey grusses and the Buchan Ridge gravels in central Buchan and the Buchan Surface (60 - 140m) has developed by lowering of this relief in the Pliocene. Drainage incision in the early Pleistocene led to development of younger forms along valleys. Repeated glaciation failed to greatly modify pre-existing relief.

Neste trabalho, realizamos um estudo teórico do espalhamento elástico e inelástico de elétrons por moléculas de H2. A aproximação de ondas distorcidas em segunda ordem e o método de frações continuadas multicanal foram aplicados no cálculo de seções de choque diferencial e integral (SCD e SCI) destes processos. Na aproximação de ondas distorcidas em segunda ordem, os elementos da matriz-T em primeira ordem bem como as funções de onda distorcidas foram geradas em um potencial estático-troca do estado fundamental do alvo e o método de frações continuadas ao nível monocanal foi usado para calcular a função de Green completa de ondas distorcidas. Para o espalhamento elástico, SCD e SCI na faixa de energia do elétron incidente de 1-40eV foram calculadas. Para o espalhamento inelástico, estudamos transições a partir do estado fundamental da molécula de H2 para os três primeiros estados tripletos b3 Σ+u, a3 Σ+g e c3πu e para o estado singleto B1 Σ+u para energias do elétron incidente iguais a 20 e 30eV. Nos estudos com o método de frações continuadas multicanal, foram calculadas SCD e SCI a 2 e 5 canais para transições a partir do estado fundamental da molécula de H2 para os estados tripletos tripletos b3 Σ+u, a3 Σ+g e c3πu e para os estados singletos B1Σ+u, E1Σ+g e C1>πucom energias do elétron incidente na faixa de 15-40eV. A comparação entre os resultados obtidos com a aproximação de ondas distorcidas em segunda ordem e o método de frações continuadas multicanal nos fornecerá informações sobre a convergência da série de ondas distorcidas em cálculos de seção de choque para o espalhamento inelástico e- - H2 / In this work, we report a theoretical study on elastic and inelastic electron scattering by H2 molecules. The second-order distorted-wave approximation and the multichannel formulation of the method of continued fractions were applied on the evaluation of differential and integral cross sections (DCS and ICS) of these processes. In the second-order distorted-wave approach, first-order T-matrix elements as well as distorted-wave functions were generated from the static-exchange potential of the ground state of the target and the method of continued fractions in a single-channel formulation was applied to the evaluation of the full distorted-wave Green\'s function. For elastic scattering, we have calculated DCS and ICS in the 1-40 eV incident energy range. For inelastic scattering, electronic excitation cross sections for the X1 Σ+g,→ b3 Σ+u, a3 Σ+g, c3πu and B1 Σ+u transitions in H2 by electron impact were obtained at 20 and 30 eV. In the studies with the multichannel formulation of the method of continued fractions, we have calculated DCS and ICS in both two- and five-channel formulation for transitions from the ground state of H2 to the triplet states b3Σ+u, a3Σ+g and c3πu, and to the singlet states B lEu+, E1 Eg9 and CI IIu in the 15 40 eV energy range. The comparision of the results from both methods can provide significant informations about the convergence of the distorted-wave series in inelastic e- H2 scattering calculations.

A quadrotor is a type of small unmanned aerial vehicle (UAV) with four rotors. Various control techniques have been successfully applied to the quadrotor. In this thesis, two control methods, including linear quadratic regulator (LQR) and H2-optimal control, are applied to the autonomous navigation and control of a quadorotor named QBall-X4 that is developed by Quanser. The continuous-time dynamic model is established using the Euler-Lagrange approach. Due to the nonlinearities in the quadrotor dynamics, we propose a simplified linear model, which is further used for the controller design in this thesis. According to the simplified quadrotor dynamics, we design an LQR controller to regulate the quadrotor system from its initial position to the desired position. The effectiveness of the controller is verified by simulation studies. However, the LQR control system is operated in the nominal model, and it can not present guaranteed performance when system uncertainties exist. The main emphasis is placed on designing an H2-optimal controller that minimizes the H2-norm of the transfer function. The solution is obtained by using the state-space approach and linear matrix inequality (LMI) method, respectively. In contrast to LQR control method, which is normally applied to a system with no disturbance, the H2-optimal controller takes the form of an observer together with a state feedback control gain to deal with the system uncertainties and disturbances. The simulation results and experimental study verify that the proposed H2-optimal controller is an effective option for the quadrotor with the attendance of uncertainties and disturbances. / Graduate

La creciente demanda energética por el crecimiento demográfico y el desarrollo de países antes no industrializados, ocurrido en las últimas décadas, ha derivado en la imperiosa necesidad de obtener combustibles nuevos, limpios y eficientes. En esta búsqueda ha surgido el hidrógeno como potencial vector energético para el futuro. Es conocida ya la alta eficiencia del hidrógeno como recurso energético, como así también la baja contaminación ambiental que el mismo produce. Sin embargo, su utilización como combustible todavía conlleva dificultades técnicas no resueltas. Por ello es conveniente pensar en un combustible alternativo, versátil, y de fácil aplicación en su uso cotidiano, como lo es el metanol, para así disminuir el consumo de combustibles derivado de los hidrocarburos. En esta tesis se estudian, por un lado, todos los pasos para la síntesis de metanol a partir del gas CO en superficies catalíticas de óxidos de Cerio, Galio y Zinc. Complementariamente, se desarrolla una metodología teórica que puede ser extendida al estudio y análisis de otras reacciones superficiales. En los primeros capítulos se estudia la adsorción y reactividad de las moléculas de CO, CO2 y H2 sobre las superficies de CeO2 con cortes (111) y (331), Ga2O3(100) y ZnO(0001), perfectas y con vacancias de oxígeno. Las mismas reacciones se estudian en las superficies soportadas ZnO/CeO2(111) y Ga2O3/CeO2(111), como modelado del crecimiento epitaxial de una monocapa de ZnO y Ga2O3, respectivamente. Luego se estudia la síntesis de metanol a partir de reacciones de hidrogenación progresiva de CO. Se calculan las barreras de activación en cada paso de la síntesis y se describen también las posibles direcciones de cada reacción. Se concluye que la metodología de estudio es óptima para reacciones similares en un conjunto de óxidos. / The growing demand for energy due to population growth and development of non-industrialized countries in recent decades has led to the urgent need for new, clean and efficient fuels. In this search hydrogen an energy vector potential for the future. It is already known the high efficiency of hydrogen as an energy source is widely known, as the well as low environmental pollution it produces. However, its use as a fuel has difficulties still unresolved. Therefore it is convenient to think of an alternative fuel, versatile, and easy to apply in daily use (such as methanol) to reduce the consumption of oil-derived fuels. In this thesis, studies- on the one hand, all the steps for the synthesis of methanol from CO gas in catalytic surfaces of oxides of cerium, gallium and zinc; and on the other hand, it develops a theoretical methodology that can be extended to the study and analysis of other surface reactions. The early chapters, study the adsorption and reactivity of molecules of CO, CO2 and H2 on surfaces CeO2 with cuts (111) and (331), Ga2O3(100) and ZnO(0001)-perfect and with oxygen vacancies. The same reactions are studied on surfaces supported ZnO / CeO2 (111) and Ga2O3 / CeO2 (111)as a modeling of epitaxial growth of a monolayer of ZnO and Ga2O3, respectively. Then, the methanol synthesis is studied from reactions of progressive hydrogenation of CO. Activation barriers at each step of the synthesis are calculated the possible directions of each reaction are describe. In conclusion, the methodology used in this thesis is appropriate for similar reactions in a set of oxides.

Dynamical systems and their numerical simulation are very important for investigating physical and technical problems. The more accuracy is desired, the more equations are needed to reach the desired level of accuracy. This leads to large-scale dynamical systems. The problem is that computations become infeasible due to the limitations on time and/or memory in large-scale settings. Another important issue is numerical ill-conditioning. These are the main reasons for the need of model reduction, i.e. replacing the original system by a reduced system of much smaller dimension. Then one uses the reduced models in order to simulate or control processes. The main goal of this thesis is to investigate an interpolation-based approach to the weighted-H2 model reduction problem. Nonetheless, first we will discuss the regular (unweighted) H2 model reduction problem. We will re-visit the interpolation conditions for H2-optimality, also known as Meier-Luenberger conditions, and discuss how to obtain an optimal reduced order system via projection. After having introduced the H2-norm and the unweighted-H2 model reduction problem, we will introduce the weighted-H2 model reduction problem. We will first derive a new error expression for the weighted-H2 model reduction problem. This error expression illustrates the significance of interpolation at the mirror images of the reduced system poles and the original system poles, as in the unweighted case. However, in the weighted case this expression yields that interpolation at the mirror images of the poles of the weighting system is also significant. Finally, based on the new weighted-H2 error expression, we will propose an iteratively corrected interpolation-based algorithm for the weighted-H2 model reduction problem. Moreover we will present new optimality conditions for the weighted-H2 approximation. These conditions occur as structured orthogonality conditions similar to those for the unweighted case which were derived by Antoulas, Beattie and Gugercin. We present several numerical examples to illustrate the effectiveness of the proposed approach and compare it with the frequency-weighted balanced truncation method. We observe that, for virtually all of our numerical examples, the proposed method outperforms the frequency-weighted balanced truncation method. / Master of Science

The activation of the innate immune system is the first line of host defence against infection. Nucleic acids can potently stimulate this response and trigger a series of signalling cascades leading to cytokine production and the establishment of an inflammatory state. Mutations in genes encoding nucleases have been identified in patients with autoimmune diseases, including Aicardi-Goutières syndrome (AGS). This rare childhood inflammatory disorder is characterised by the presence of high levels of the antiviral cytokine interferon-α in the cerebrospinal fluid and blood, which is thought to be produced as a consequence of the activation of the innate immunity by unprocessed self-nucleic acids. This thesis therefore aimed to define the role of one of the AGS nucleases, the Ribonuclease H2 (RNase H2) complex, in innate immunity, and to establish if nucleic acid substrates of this enzyme were able to induce type I interferon production in vitro. The AGS nucleases may function as components of the innate immune response to nucleic acids. Consistent with this hypothesis, RNase H2 was constitutively expressed in immune cells, however, its expression was not upregulated in response to type I interferons. RNase H2-deficient cells responded normally to a range of nucleic acid PAMPs, which implied that a role for RNase H2 as a negative regulator of the immune response was unlikely, in contrast to the reported cellular functions of two other AGS proteins, TREX1 and SAMHD1. Therefore, no clear evidence was found for the direct involvement of RNase H2 in the innate immune response to nucleic acids. An alternative model for the pathogenesis of disease hypothesises that decreased RNase H2 activity within the cell results in an accumulation of RNA:DNA hybrids. To investigate the immunostimulatory potential of such substrates, RNA:DNA hybrids with different physiochemical properties were designed and synthesised. Methods to purify the hybrids from other contaminating nucleic acid species were established and their capacity as activators of the innate immune response tested using a range of in vitro cellular systems. A GU-rich 60 bp RNA:DNA hybrid was shown to be an effective activator of a pro-inflammatory cytokine response exclusively in Flt3-L bone marrow cultures. This response was completely dependent on signalling involving MyD88 and/or Trif, however the specific receptor involved remains to be determined. Reduced cellular RNase H2 activity did not affect the ability of Flt3-L cultures to mount a cytokine response against the RNA:DNA hybrid. These in vitro studies suggested that RNA:DNA hybrids may be a novel nucleic acid PAMP. Taken together, the data in this thesis suggest that the cellular function of RNase H2 is in the suppression of substrate formation rather than as a component of the immune response pathways. Future studies to identify endogenous immunostimulatory RNA:DNA hybrids and the signalling pathways activated by them should provide a detailed understanding of the molecular mechanisms involved in the pathogenesis of AGS and related autoimmune diseases.

Mathematical models of physical systems are pervasive in engineering. These models can be used to analyze properties of the system, to simulate the system, or synthesize controllers. However, many of these models are too complex or too large for standard analysis and synthesis methods to be applicable. Hence, there is a need to reduce the complexity of models. In this thesis, techniques for reducing complexity of large linear time-invariant (lti) state-space models and linear parameter-varying (lpv) models are presented. Additionally, a method for synthesizing controllers is also presented. The methods in this thesis all revolve around a system theoretical measure called the H2-norm, and the minimization of this norm using nonlinear optimization. Since the optimization problems rapidly grow large, significant effort is spent on understanding and exploiting the inherent structures available in the problems to reduce the computational complexity when performing the optimization. The first part of the thesis addresses the classical model-reduction problem of lti state-space models. Various H2 problems are formulated and solved using the proposed structure-exploiting nonlinear optimization technique. The standard problem formulation is extended to incorporate also frequency-weighted problems and norms defined on finite frequency intervals, both for continuous and discrete-time models. Additionally, a regularization-based method to account for uncertainty in data is explored. Several examples reveal that the method is highly competitive with alternative approaches. Techniques for finding lpv models from data, and reducing the complexity of lpv models are presented. The basic ideas introduced in the first part of the thesis are extended to the lpv case, once again covering a range of different setups. lpv models are commonly used for analysis and synthesis of controllers, but the efficiency of these methods depends highly on a particular algebraic structure in the lpv models. A method to account for and derive models suitable for controller synthesis is proposed. Many of the methods are thoroughly tested on a realistic modeling problem arising in the design and flight clearance of an Airbus aircraft model. Finally, output-feedback H2 controller synthesis for lpv models is addressed by generalizing the ideas and methods used for modeling. One of the ideas here is to skip the lpv modeling phase before creating the controller, and instead synthesize the controller directly from the data, which classically would have been used to generate a model to be used in the controller synthesis problem. The method specializes to standard output-feedback H2 controller synthesis in the lti case, and favorable comparisons with alternative state-of-the-art implementations are presented.