Ordinary differential equations (ODEs) play an important role in mathematics. Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are considered as maps from one function space to another, common numerical algorithms for ODEs discretise problems early on in the solution process. This thesis is about continuous analogues of such discrete algorithms for the numerical solution of ODEs. This thesis shows how Newton's method for finite dimensional system can be generalised to function spaces, where it is known as Newton-Kantorovich iteration. It presents affine invariant damping strategies for increasing the chance of convergence for the Newton-Kantorovich iteration. The derivatives required in this continuous setting are Fréchet derivatives, the continuous analogue of Jacobian matrices. In this work, we present how automatic differentiation techniques can be applied to compute Fréchet derivatives. We introduce chebop, a Matlab solver for nonlinear boundary-value problems, which combines damped Newton iteration in function space and automatic Fréchet differentiation. By proving that affine operators have constant Fréchet derivatives, it is demonstrated how automatic linearity detection of computed quantities can be implemented. This is valuable for black-box solvers, which can use the information to determine whether an iteration scheme has to be employed for solving a problem. Like nonlinear systems of equations, nonlinear boundary-value problems can have multiple solutions. This thesis present two techniques for obtaining multiple solutions of operator equations: deflation and path-following. An algorithm combining the two techniques is proposed.

In an effort to assess the predictive ability of exchange rate models when data on African countries is sampled, this paper studies nonlinear modelling and prediction of the nominal exchange rate series of the United States dollar to currencies of thirty-eight African states using the smooth transition autoregressive (STAR) model. A three step analysis is undertaken. One, it investigates nonlinearity in all nominal exchange rate series examined using a chain of credible statistical in-sample tests. Significantly, evidence of nonlinear exponential STAR (ESTAR) dynamics is detected across all series. Two, linear models are provided another chance to make it right by shuffling to data on African countries to investigate their predictive power against the tough random walk without drift model. Linear models again failed significantly. Lastly, the predictive ability of nonlinear models against both the random walk without drift and the corresponding linear models is investigated. Nonlinear models display useful forecasting gains over all contending models.

Une solution pertinente afin d'alimenter des capteurs isolés consiste à récupérer l'énergie disponible dans leur environnement immédiat. Parmi les sources d'énergie envisageables, notre choix s'est porté sur les vibrations mécaniques ambiantes. Notre contribution porte sur l'étude et la réalisation, par un procédé de fabrication collective, d'un transducteur électrostatique sans électrets en technologie MEMS Silicium. Nous proposons une étude analytique permettant d'optimiser l'efficacité du générateur électrostatique, tout en considérant une limite sur la tension maximale aux bornes du transducteur afin de ne pas endommager le circuit de conditionnement. Le design proposé prend également en compte d'éventuelles variations de l'amplitude des vibrations externes. Le dispositif a été fabriqué au sein de ESIEE Paris et présente un volume total de moins de 100 mm3.Les tests expérimentaux ont montré un comportement fortement non-linéaire de la structure. Nous avons obtenu une conversion d'énergie mécanique en énergie électrique correspondant à une puissance maximale de 2.3 μW à 260 Hz, pour une accélération de 1 g et à une pression de 0.15 Torr, lorsque le système est pré-chargé avec une tension de 10 V. Une fois implémenté dans un circuit de pompe de charge et pour les mêmes conditions d'accélération et de pression, le système peut fonctionner en complète autonomie pendant plus de 500 secondes pendant lesquelles la puissance délivrée varie de 1.4 μW à 940 nW avec une tension de pré-charge de 10.6 V / A relevant solution to power isolated sensors is to harvest the energy available in their immediate environment. Among the possible sources of energy, our choice was made on ambient mechanical vibrations. We have designed and fabricated a silicon-based and batch-processed MEMS electrostatic transducer which does not use an electret. We present an analytical method to optimize the efficiency of the electrostatic generator, while a voltage limitation on the transducer's terminal is set to prevent any damage in the conditioning electronics. The proposed design also takes into account some possible variations in the amplitude of external vibration. The device was fabricated in ESIEE Paris and its volume is less than 100 mm3. The device was tested experimentally and exhibits a strong non-linear behavior. We obtained a conversion of mechanical energy into electrical energy corresponding to a power of 2.3 μW at 260 Hz, with an acceleration of 1 g and a pressure of 0.15 Torr, when the system is pre-charged with a voltage of10 V. When the device is implemented in a charge pump circuit and under the same parameters of acceleration and pressure, the system can operate in autonomous mode for more than 500 seconds during which the output power varies from 1.4 μW to 940 nW when the pre-charge voltage is 10.6 V

Os galpões de concreto pré-moldado, formados por pórticos atirantados, são muito utilizados, no Brasil. Porém, para o projeto dessas estruturas, a bibliografia é limitada. Além disso, vários critérios de projeto são adaptados dos relativos a estruturas de concreto moldado no local e de múltiplos pavimentos. O objetivo deste trabalho é contribuir para a análise desse tipo de estrutura, introduzindo conceitos que dificilmente são considerados na prática, tais como: rigidez da ligação viga-pilar, análise não-linear física e geométrica, deformação excessiva e fluência. A pesquisa foi desenvolvida por meio de análises estruturais, usando modelos de galpões comuns na prática. Cada conceito citado anteriormente foi analisado em exemplos. A rigidez da ligação viga-pilar foi avaliada com base no parâmetro de restrição à rotação, \'alfa\'R. A não-linearidade física (NLF) do concreto foi considerada pelo método de Branson. Para a não-linearidade geométrica (NLG), foram utilizados os parâmetros \'alfa\' e o processo P.\'delta\'. A deformação excessiva, incluindo a fluência, foi discutida tendo em conta os aspectos normativos. Constatou-se que a ligação viga-pilar pode ter comportamento semi-rígido em alguns casos, mas, se corretamente dimensionada, apresenta, de fato, comportamento rígido. A consideração da NLF apresentou resultados melhores que a análise elástica linear, sendo possível, para o exemplo estudado, utilizar um coeficiente redutor de inércia igual a 0,5, para as vigas e para os pilares do pórtico. Concluiu-se, também, que a consideração da NLG deve ser feita sistematicamente para esse tipo de estrutura, uma vez que alguns exemplos apresentaram acréscimos de momentos superiores a 10% e \'alfa\' > \'alfa\' lim. Além disso, observou-se que a verificação do estado limite de deformação excessiva (ELS-DEF) pode ser determinante na escolha das seções transversais do pórtico, sendo obrigatória a consideração da fluência. Nesse sentido, o presente trabalho contribui para a literatura técnica sobre a análise estrutural dos galpões atirantados, auxiliando projetistas no cálculo dessas estruturas e servindo de referência nos cursos sobre esse assunto. / Sheds of precast concrete formed by tied portal frames are widely used in Brazil. However, there are few works on the design of these structures. In addition, several design criteria are adapted from those relative to the structures of cast in place concrete and multi-storey buildings. The objective of this work is to contribute to the analysis of this type of structure, introducing concepts that are hardly seen in practice, such as: rigidity of beam-column connection, physics and geometric nonlinear analysis, excessive deformation, and creep. The research was developed by mean of structural analysis, using models of sheds common in practice. Each concept previously mentioned was analyzed in examples. The stiffness of the beam-column connection was evaluated with base on the restriction parameter of the rotation, \'alfa\'R. The physics non-linearity (PNL) of concrete was considered by the method of Branson. For the geometric non-linearity (GNL) the parameter \'alfa\' and the process P.\'delta\' were used. The excessive deformation including creep was discussed taking in account the aspects of brazilian codes. It was found that the beam-column connection may have semi-rigid behavior in some cases, but, if properly designed, it has in fact rigid behavior. The consideration of the PNL had better results than the linear elastic analysis, and, for the sample studied, was possible to use a reduction coefficient of inertia equal to 0.5 for the beams and columns of the portal frame. It was also concluded that the consideration of GNL should be done systematically for this type of structure, since as some examples showed increase of moments above 10% and \'alfa\' > \'alfa\' lim. Furthermore, it was observed that the verification of deflection serviceability can be decisive in the choice of the portal frame cross sections, being obligatory the consideration of creep. In this sense, the present work contributes to the technical literature on the structural analysis of the tied portal frame sheds, helping engineers in the design of these structures and serving as reference in courses about this subject.

Dans le cadre des théories stables, il a été prouvé qu'une courbe pseudolinéaire était toujours, spécifiquement, linéaire (ce qui correspond dans ce cadre également à localement modulaire): on peut alors caractériser la géométrie de l'ensemble associé, qui est soit projective (avec le type associé à la courbe non-trivial et modulaire), soit affine (quand le type est non-modulaire) sur un corps gauche; lorsque le type associé est trivial, la géométrie est dégénérée. Cela nous permet donc de déduire de la simple pseudolinéarité d'un type la structure de l'ensemble sous-jacent: cette thèse étend ce résultat au cadre des théories simples, ce qui nous permettra à nouveau de détermé de la théorie), mais en se restreignant au cas où k < 4 / In the context of stable theories, it has been proven that a plane curve which is pseudolinear must be linear; it is then possible to deduce the geometry of the associated set, which is either projective (when the type associated to the plane curve is non-trivial and modular), or affine (when the type is non-modular) on a division ring; if the associated type is trivial, the geometry is degenerate. This means we can infer, from a type's pseudolinearity, the structure of the underlying set; this thesis extends this result to the context of simple theories, allowing us to determine the set's geometry (with several differences to account for the fact that the theory is simple and not stable) if we restrict ourselves to k < 4

Os galpões de concreto pré-moldado, formados por pórticos atirantados, são muito utilizados, no Brasil. Porém, para o projeto dessas estruturas, a bibliografia é limitada. Além disso, vários critérios de projeto são adaptados dos relativos a estruturas de concreto moldado no local e de múltiplos pavimentos. O objetivo deste trabalho é contribuir para a análise desse tipo de estrutura, introduzindo conceitos que dificilmente são considerados na prática, tais como: rigidez da ligação viga-pilar, análise não-linear física e geométrica, deformação excessiva e fluência. A pesquisa foi desenvolvida por meio de análises estruturais, usando modelos de galpões comuns na prática. Cada conceito citado anteriormente foi analisado em exemplos. A rigidez da ligação viga-pilar foi avaliada com base no parâmetro de restrição à rotação, \'alfa\'R. A não-linearidade física (NLF) do concreto foi considerada pelo método de Branson. Para a não-linearidade geométrica (NLG), foram utilizados os parâmetros \'alfa\' e o processo P.\'delta\'. A deformação excessiva, incluindo a fluência, foi discutida tendo em conta os aspectos normativos. Constatou-se que a ligação viga-pilar pode ter comportamento semi-rígido em alguns casos, mas, se corretamente dimensionada, apresenta, de fato, comportamento rígido. A consideração da NLF apresentou resultados melhores que a análise elástica linear, sendo possível, para o exemplo estudado, utilizar um coeficiente redutor de inércia igual a 0,5, para as vigas e para os pilares do pórtico. Concluiu-se, também, que a consideração da NLG deve ser feita sistematicamente para esse tipo de estrutura, uma vez que alguns exemplos apresentaram acréscimos de momentos superiores a 10% e \'alfa\' > \'alfa\' lim. Além disso, observou-se que a verificação do estado limite de deformação excessiva (ELS-DEF) pode ser determinante na escolha das seções transversais do pórtico, sendo obrigatória a consideração da fluência. Nesse sentido, o presente trabalho contribui para a literatura técnica sobre a análise estrutural dos galpões atirantados, auxiliando projetistas no cálculo dessas estruturas e servindo de referência nos cursos sobre esse assunto. / Sheds of precast concrete formed by tied portal frames are widely used in Brazil. However, there are few works on the design of these structures. In addition, several design criteria are adapted from those relative to the structures of cast in place concrete and multi-storey buildings. The objective of this work is to contribute to the analysis of this type of structure, introducing concepts that are hardly seen in practice, such as: rigidity of beam-column connection, physics and geometric nonlinear analysis, excessive deformation, and creep. The research was developed by mean of structural analysis, using models of sheds common in practice. Each concept previously mentioned was analyzed in examples. The stiffness of the beam-column connection was evaluated with base on the restriction parameter of the rotation, \'alfa\'R. The physics non-linearity (PNL) of concrete was considered by the method of Branson. For the geometric non-linearity (GNL) the parameter \'alfa\' and the process P.\'delta\' were used. The excessive deformation including creep was discussed taking in account the aspects of brazilian codes. It was found that the beam-column connection may have semi-rigid behavior in some cases, but, if properly designed, it has in fact rigid behavior. The consideration of the PNL had better results than the linear elastic analysis, and, for the sample studied, was possible to use a reduction coefficient of inertia equal to 0.5 for the beams and columns of the portal frame. It was also concluded that the consideration of GNL should be done systematically for this type of structure, since as some examples showed increase of moments above 10% and \'alfa\' > \'alfa\' lim. Furthermore, it was observed that the verification of deflection serviceability can be decisive in the choice of the portal frame cross sections, being obligatory the consideration of creep. In this sense, the present work contributes to the technical literature on the structural analysis of the tied portal frame sheds, helping engineers in the design of these structures and serving as reference in courses about this subject.

Esta dissertação tem como objetivo principal o desenvolvimento de uma formulação, via método dos elementos finitos (MEF), para a identificação e solução do impacto não linear bidimensional entre estruturas anelares reticuladas e anteparo rígido fixo. O comportamento dinâmico não linear geométrico é feito por meio de uma formulação posicional classificada como Lagrangiana total com cinemática exata. Utiliza-se o integrador temporal de Newmark modificado para descrever o comportamento dinâmico, de forma a garantir a estabilidade na análise do impacto. Desenvolveu-se um algoritmo de identificação da ocorrência do impacto, utilizando-se segmentos auxiliares que definem uma região formada por pontos passíveis de impacto. A solução do impacto é feita com um algoritmo de retorno geométrico segundo superfície curva com aproximação qualquer para o anteparo rígido, considerando situações com e sem atrito. Faz-se uma comparação entre a técnica adotada e a técnica dos multiplicadores de Lagrange e das penalidades, mostrando a equivalência entre as mesmas. Por fim, são apresentados exemplos numéricos gerais utilizando a técnica desenvolvida, onde se fez um estudo de convergência para discretização geométrica e temporal. / This work has as main goal the development of a formulation, based on the finite element method (FEM), for the identification and solution of the bidimensional nonlinear impact between reticulated cyclics structures and fixed rigid wall. The dynamic geometrically nonlinear behavior is treated with a positional formulation classified as total Lagrangean with exact kinematics. The time integrator of modified Newmark is used, to describe the dynamic behavior, to assure the stability in the analysis of the impact. An algorithm of identification of the occurrence of the impact was developed, using auxiliary segments that define a region formed for feasible points of impact. The solution of the impact is made with an algorithm of geometric return as curve surface with any approach for the rigid wall, considering situations with and without friction. A comparison between the technique adopted and Lagrange multipliers and penalty is made. Finally, general numerical examples are presented, where a study of convergence was made.

Among the parametric nonlinear time series model families, the smooth transition regression (STR) model has recently received attention in the literature. The considerations in this dissertation focus on the univariate special case of this model, the smooth transition autoregression (STAR) model, although large parts of the discussion can be easily generalised to the more general STR case. Many nonlinear univariate time series models can be described as consisting of a number of regimes, each one corresponding to a linear autoregressive parametrisation, between which the process switches. In the STAR models, as opposed to certain other popular models involving multiple regimes, the transition between the extreme regimes is smooth and assumed to be characterised by a bounded continuous function of a transition variable. The transition variable, in turn, may be a lagged value of the variable in the model, or another stochastic or deterministic observable variable. A number of other commonly discussed nonlinear autoregressive models can be viewed as special or limiting cases of the STAR model. The applications presented in the first two chapters of this dissertation, Chapter I: Another look at Swedish Business Cycles, 1861-1988 Chapter II: Modelling asymmetries and moving equilibria in unemployment rates, make use of STAR models. In these two studies, STAR models are used to provide insight into dynamic properties of the time series which cannot be be properly characterised by linear time series models, and which thereby may be obscured by estimating only a linear model in cases where linearity would be rejected if tested. The applications being of interest in their own right, an important common objective of these two chapters is also to develop, suggest, and give examples of various methods that may be of use in discussing the dynamic properties of estimated STAR models in general.Chapter III, Testing linearity against smooth transition autoregression using a parametric bootstrap, reports the result of a small simulation study considering a new test of linearity against STAR based on bootstrap methodology. / <p>Diss. Stockholm : Handelshögskolan, 1999</p>

Karl-Birger Blomdahl (1916-1968) and Ingvar Lidholm (1921- ) were two leading figures in modern Swedish music. While studying in Stockholm they created a study circle known as the Monday Group. Regarded as anti-romanticists, Blomdahl and Lidholm revitalized musical creation by prioritizing compositional technique (as in hantverk, i.e. craft), melodic line and Gestalt concepts such as organicism. Following a study of this shared historical, aesthetic and theoretical framework, this thesis proposes a detailed analysis of thirty works by Blomdahl and Lidholm, dating from the 1940s. Based on the initial aesthetic and theoretical context and also on the theories of Schenker and Meyer, the analytical method used enables a graphical and textual representation of the compositional coherence and dynamic of the respective works. This thesis establishes the essential melodic, tonal and organic divergences in the musical languages of Blomdahl and Lidholm. Additionally, this thesis shows that the notions of linearity, dissonance and counterpoint have a deeper significance in Blomdahl’s and Lidholm’s respective musical languages than is to be found in many texts dating from this period. Finally, this thesis highlights aesthetic and compositional components that significantly invigorate modern music in Sweden.

In this thesis, high performance torque and speed control for a surface-mounted permanent magnet synchronous machine (PMSM) is designed, simulated and implemented. A three-phase two-level pulse width modulation voltage-source inverter (PWM-VSI) with power MOSFETs is used to feed the PMSM. The study has three objectives. The first is to compensate the voltage disturbance caused by nonideal characteristics of the voltage-source inverter (VSI). The second is to decouple the coupled variables in the synchronous reference frame model of the PMSM. The last is to design a load torque estimator in order to increase the disturbance rejection capability of the speed control. The angular acceleration required for load torque estimation is extracted through a Kalman filter from noisy velocity measurements. Proposed methods for improved torque and speed control performance are verified through simulations and experimental tests. The drive system is modeled in Matlab/Simulink, and control algorithms are developed based on this model. The experimental drive system comprises a three-phase VSI and a 385 W surface-mounted PMSM. Control algorithms developed in the study have been implemented in a digital signal processor (DSP) board and tested comprehensively. With the use of the proposed methods, a considerable improvement of torque and speed control performance has been achieved.