Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / A mecÃnica quÃntica desempenha um papel fundamental na descriÃÃo e entendimento dos fenÃmenos naturais. De fato, os fenÃmenos que ocorrem em uma escala muito pequena (atÃmica ou sub-atÃmica) nÃo podem ser corretamente explicados fora do contexto da mecÃnica quÃntica. AlÃm disso, existem muitos fenÃmenos em escala macroscÃpica que revelam o comportamento quÃntico da natureza. Nesse sentido, podemos dizer que a mecÃnica quÃntica à a base de todo nosso atual conhecimento sobre os fenÃmenos naturais. O estado de uma partÃcula em quÃntica à descrito matematicamente pela sua funÃÃo de onda Ψ(r,t) e a evoluÃÃo temporal de Ψ(r,t) à governada pela EquaÃÃo de SchrÃdinger dependente do tempo. Dessa forma, podemos enunciar que o problema fundamental da mecÃnica quÃntica consiste em solucionar a EquaÃÃo de SchrÃdinger numa situaÃÃo arbitrÃria. Neste trabalho, estudamos uma tÃcnica numÃrica de soluÃÃo da EquaÃÃo de SchrÃdinger dependente ou independente do tempo conhecida como Split Operator. Essa tÃcnica utiliza formas aproximadas para a exponencial da soma de operadores que nÃo comutam para implementar o operador evoluÃÃo temporal, permitindo reduzir o processo de soluÃÃo da EquaÃÃo de SchrÃdinger a sucessivos processos de simples multiplicaÃÃo e de soluÃÃo de sistemas de equaÃÃes lineares tridiagonais, que podem ser facilmente realizados por um computador. O formalismo da tÃcnica em coordenadas cartesianas foi estudado em detalhes, onde mostramos como aplicÃ-lo para sistemas com condiÃÃes de com torno periÃdicas ou com condiÃÃes de contorno finitas. Utilizamos essa forma da tÃcnica para estudar o comportamento de um elÃtron confinado numa regiÃo de energia potencial aleatÃria, onde nos deparamos com o fenÃmeno de LocalizaÃÃo de Anderson. AlÃm disso, desenvolvemos a tÃcnica Split Operator em coordenadas generalizadas, aplicando-a para estudar o problema de um elÃtron confinado na superfÃcie de um cilindro. Os resultados obtidos numericamente concordam muito bem com os resultados obtidos analiticamente, mostrando que a tÃcnica Split Operator em coordenadas generalizadas nos leva a resultados confiÃveis. / Quantum mechanics plays a fundamental role in the description and understanding of the natural phenomena. Actually, the phenomena that take place in atomic and subatomic scale can not be well explained without the quantum mechanics approach. Furthermore, there are a lot of phenomena in macroscopic scale that reveals the quantum behavior of nature. In this sense, we can say that quantum mechanics is fundamental for the understanding of all natural phenomena. In Quantum Mechanics the state of a particle is mathematically described by the wave function Ψ(r,t) and its time evolution is governed by time-dependent SchrÃdinger equation. Thus, we can state that the fundamental problem of quantum mechanics is to solve the SchrÃdinger Equation in an arbitrary situation. In this work, we study a numerical technique to solve the time-dependent and time-independent SchrÃdinger Equation known as Split Operator technique. This aproach uses approximations for the exponencial of sum of operators that do not commute in order to implement the time-evolution operator. It makes possible to reduce the solution of the SchrÃdinger equation to a successive processes of multiplication and solution of tridiagonal system of linear equations. It can be easily performed using a computer. The technique was studied in detail using cartesian coordinates, and we also explained how to use the technique with periodic or finite boundary conditions. We make use this technique to study the behavior of an electron subjected to a random potential. In this situation we face the Anderson Localization phenomena. Furthermore, we developed the Split Operator technique using generalized coordinates, and studied the problem of an electron confined to a cylinder surface. It was verified that the numerical results agree with the analytical ones. So we can conclude that the Split Operator technique using generalized coordinates produce reliable results.

O conhecimento das reações nucleares que ocorrem no interior das estrelas permite estudar como será a evolução destes astros e as relações de abundância entre os isótopos de alguns elementos. Em alguns casos, a detecção de elementos traços pode ser útil para inferir a ocorrência de eventos explosivos, como novas e supernovas. Um destes elementos é o 22Na, cuja abundância depende da reação de captura de próton 22Na(p, ?)23Mg. Assim, o estudo dos estados de ressonância do 23Mg, é importante para compreender o mecanismo de reação e determinar a abundância do 22Na. O núcleo de 23Mg ainda participa do ciclo NeNa na fase AGB da evolução de estrelas de massa média. Com essa motivação propomos o estudo espectroscópico do núcleo 23Mg por meio da reação de transferência 24Mg(3He, 4He)23Mg, cujos dados experimentais foram obtidos no laboratório Tandem-Orsay (França), com o uso de um feixe de 3He de 25 MeV. As ressonâncias de interesse do núcleo 23Mg estudadas nesse trabalho estão compreendidas na faixa de energia de excitação 7.5 MeV a 9.5 MeV. Os estados de ressonância do 23Mg foram populados com a interação do feixe com o alvo de natMg, e as partículas de 4He foram analisadas com o espectrógrafo Split-pole. Os espectros de posição das partículas de 4He foram então calibrados em rigidez magnética, por meio de um polinômio de segunda ordem. Após a calibração os espectros de rigidez magnética foram transformados em espectros de energia de excitação. Nesses espectros pudemos identificar e estudar a presença de contaminantes. Vários estados abaixo e alguns estados acima do limiar de decaimento foram observados e identificados. Dentre os estados acima do limiar estão os estados: 7.586, 7.648, (7.782 e 7.786), 7.855, 8.076, 8.163, 8.420, 8.453, 8.943 e 8.990 MeV do 23Mg. Sendo que apenas os estados 7.586 e 8.163 tem o spin J=5/2+ estabelecido. Ao final apresentamos uma discussã / The knowledge of the nuclear reactions that take place inside the stars allows to study how the evolution of this star will be and the relations of abundance between the isotopes of some elements. In some cases the detection of trace elements can be useful to infer about the occurrence of explosive events, as novae and the supernovae. One of these elements is the 22Na, whose abundance depends on the proton capture reaction 22Na(p, ?)23Mg. The gamma radiation photon with energy 1.275 MeV emitted by 22Na may be a novae type event indicator. Thus, the study of the resonance states of 23Mg is important to understand the mechanism of reaction and determine the 22Na abundance. The nucleus of 23Mg still participate in the cycle NeNa in the AGB phase of the evolution of average stars. With this motivation, we propose to study the spectroscopy of the 23Mg by the 24Mg(3He, 4He)23Mg neutron transfer reaction, whose experimental data were obtained in the Tandem-Orsay facility (France), using the 3He beam of energy 25 MeV. The resonances of interest for this work are in the range of 7.5 MeV up to 9.5 MeV, above the decay threshold for protons. The resonance states of 23Mg were obtained with the interaction of the beam with the natMg target, and the 4He particles were analyzed in a Split-pole spectrograph. The position spectra were then calibrated in magnetic rigidity by means of a second-order polynomial function. The effects of the contaminants were analyzed by converting the spectra into excitation energy, in which it was possible to separate the states 7.586, 7.648, (7.782 e 7.786), 7.855, 8.076, 8.163, 8.420, 8.453, 8.943 e 8.990 MeV of 23Mg. Finally we present a qualitative discussion of the angular distribution for some states and we discuss the possibilities for the future.

O objetivo deste trabalho é o desenvolvimento do modelo de uma microturbina a gás do tipo split-shaft com sistema de controle por retro-alimentação. Uma revisão bibliográfica dos trabalhos sobre controle de turbinas a gás indicou que praticamente inexistem trabalhos focando este tipo de turbina. O modelo foi desenvolvido a partir da geometria básica da turbina, aplicando-se os fundamentamentos de termodinâmica, mecânica newtoniana e mecânica dos fluidos mencionando os usos da primeira lei da termodinâmica, teoria de momento angular e atrito viscoso entre outros. O trabalho descreve os componentes, materiais e controles que podem ser usados em uma turbina split-shaft. O modelo foi simulado primeiramente sem controle e posteriormente com controle. Através dos resultados da simulação do modelo sem controle puderam ser vistos fenômenos que podem ocorrer em um sistema desse tipo como picos de temperatura, influência de uma turbina sobre a outra e a variação de injeção de combustível devido à variação de pressão na câmara de combustão entre outros. Para o modelo controlado, foram testados os controles PI, PID, PI-D, I-PD e PI-PD com feedback negativo. A escolha dos parâmetros de cada controle foi determinada pelo método ITAE dentro de um intervalo para cada parâmetro. O controle escolhido foi o PI-D por seu melhor desempenho e maior simplicidade. O controle fez com que as temperaturas de pico abaixassem em relação ao sistema sem controle e a rotação do gerador de energia elétrica foi mantida com uma variação máxima menor que 1% em relação à rotação de referência. Uma modelagem foi feita para um sistema lubrificante seguindo os mesmos princípios da modelagem da turbina split-shaft. Usou-se fundamentos de mecânica newtoniana e mecânica dos fluidos, com o equacionamento da conservação da quantidade de movimento, perdas de pressão localizada e distribuída entre outros. O modelo foi simulado primeiramente sem controle e posteriormente com controle. Através do modelo sem controle viu-se os efeitos do aumento da perda de carga em um dos ramos do sistema e os efeitos de uma entrada de referência em degrau. Esses efeitos são as variações das perdas no sistema e a variação do fluxo nos ramos do sistema. Para o modelo controlado foram testados os controles PI e PI-D com feedback negativo. Utilizou-se o método ITAE dentro de um intervalo para escolha dos parâmetros. O controle escolhido foi o PI porque a diferença de desempenho não foi significativa e a parte derivativa poderia tornar o erro maior devido à forma como o sistema foi modelado. A variável de processo foi controlada e os efeitos da variação de perda de carga em um dos ramos do sistema pôde ser observada. Os modelos são constituídos de várias partes simples, cada qual pode ser substituída por um modelo mais preciso. Assim, a modelagem funciona como um guia, mostrando as partes principais do sistema e podendo fornecer dados para a elaboração de novos modelos. / The objective of the present work is the development of the model of a split-shaft micro gas turbine with feed back control system. A bibliographical review of the works on control of gas turbines indicated that there are very few works dealing this type of gas turbines. The model was developed starting from the basic geometry of the turbine and applying the fundamentals of thermodynamics, newtonian mechanics and fluid mechanics. The components, materials and controls which can be used in a split-shaft turbine are described. The model is simulated firstly without control and later with control. The results showed that, for the uncontrolled model, typical phenomena which may happen in this type of system are seen such as temperature peaks, influence of one turbine on the other and fuel injection variation due to combustion chamber pressure variation amongst others. For the controlled model, the controls PI, PID, PI-D, I-PD and PI-PD with negative feedback are tested. The parameters choice of each control is determined by the ITAE method within an interval for each parameter. The PI-D control was chosen for its best performance and simplicity. The control made the peak temperatures lower than the uncontrolled system and the electricity generator rotation error was kept under 1% with respect to the reference value. A modeling is done for a lubrification system following the same principles of the split-shaft turbine modeling. Conservation laws of mechanics and fluid mechanics are used, such as momentum conservation and energy conservation equations (pressure loss). The model is simulated firstly without control and later with control. For the uncontrolled model, the effects on increasing the head loss in one branch of the system and the effects for a step reference was showed. These effects are the variations of system losses and the flow variation in the system branches. For the controlled model, the PI and PI-D controls with negative feedback were tested. The parameters choice of each control is determined by the ITAE method within an interval for each parameter. The PI control was chosen because the performance difference was not significant and the derivative part could turn the error bigger due to the way the system was modelled. The process variable was controlled and the effects on the variation head loss in one of the system branches was observed. The models have many simple parts; each one can be replaced by a more complex one if necessary. Thus, the present modeling may be used as guide for future improvements.

A critical maneuver for a heavy vehicle is braking with different friction on the left and right hand side of the vehicle, called μ-split. This results in an unwanted yaw torque acting on the vehicle. During this situation, the driver maintains the lateral stability and follows the desired path by corrective steering. In anautonomous heavy vehicle the system must handle this situation by itself. The purpose of this thesis is to analyze how an autonomous vehicle can detect a μ-split situation and then use steering control to maintain its path and stability. Two methods for detecting a μ-split situation are presented where one is based on vehicle kinematics, this detector utilizes the difference in wheel speed between the left and right hand side of the vehicle. The other detector is based on lateral vehicle dynamics, this method uses a sliding mode observer to detect unexpected changes in the yaw rate signal. The detectors were tested in a real vehicle and the results showed that the kinematic detector was fast but had a small risk of false detection, while the dynamic detector was slower but more robust. An analysis of the desired steering behavior showed that the steady state during μ-split braking is to drive with a non zero body slip. If a kinematic path follower is used with kinematic error dynamics this will lead to a contradicting behavior since the body slip is equal to the heading error during straight line braking, assuming that the velocity vector of the vehicle is parallel to the path. Simulations showed that during a μ-split situation the Linear Quadratic pathfollower based on kinematic error dynamics manages to follow the path with a non zero body slip while keeping the path errors small. It has also been shown how the detection of a μ-split situation can be used to change control strategy. By introducing active yaw control or change the tuning on the controller after a detection a better result could be achieved.

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Master of Science / Department of Statistics / Christopher I. Vahl / In the classic split-plot design where whole plots have a completely randomized design, the conventional analysis approach assumes a compound symmetry (CS) covariance structure for the errors of observation. However, often this assumption may not be true. In this report, we examine using different covariance models in PROC MIXED in the SAS system, which are widely used in the repeated measures analysis, to model the covariance structure in the split-plot data in which the simple compound symmetry assumption does not hold. The comparison of the covariance structure models in PROC MIXED and the conventional split-plot model is illustrated through a simulation study. In the example analyzed, the heterogeneous compound symmetry (CSH) covariance model has the smallest values for the Akaike and Schwarz’s Bayesian information criteria fit statistics and is therefore the best model to fit our example data.

Previous research about the acquisition of the case-marking systems of ergative languages suggests that children acquire ergative and accusative languages equally easily (Van Valin 1992), depending on the degree to which the case morphology is consistently ergative or accusative and the degree to which adults use the morphology (Pye 1990). However, split-ergative languages incorporate both accusative and ergative systems, some in the midst of a shift away from ergativity, thus providing variable and inconsistent input for children. Yet previous research suggests that children can acquire variable linguistic forms at early stages, reflecting frequencies in which the forms occur in caregiver input (Henry 1998, 2002, Miller 2006, 2007, Westergaard 2009). This study examines the acquisition of split-ergativity in Kurmanji Kurdish, where the direct case is used with both present-tense agents and past-tense patients and the oblique case is used with past-tense agents and present-tense patients. However, recent research suggests the weakening of ergativity in Kurmanji (Dorleijn 1996), resulting in variable use of case-marking. This study examines the acquisition of split-ergativity in Kurmanji when considering the split systems and inconsistent adult input. Data from children (n=12) and caretakers (n=24) include spontaneous speech samples and results from a modified Agent-Patient test (Slobin 1985). Four children from three age groups, 1;6, 2;6, and 3;6, were recorded interacting with caretakers every three months for one hour over a 12-month period. Statistical analyses were conducted focusing on adult patterns (input for children) and children’s production at different ages. Results suggest that Kurmanji may be shifting away from a split-ergative system, with the past tense extending to a double oblique pattern and nouns gradually losing oblique case-marking altogether, resulting in variable case-marking. Data show that children first use ergative case as early as 2;0 and show evidence of repeated use of split-ergative case-marking by 2;6. Even at these early ages, children use similar variability and frequency in case-marking as their caretakers, closer to usage of younger adults versus older adults. Thus children seem to use ergative case-marking early, and when faced with inconsistent input, they ultimately conform to the patterns modeled by the adult community. / text