The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. Although the fundamental laws governing the behaviour of these many-body systems are believed to be known in principle, the practical solution of the equations of quantum mechanics remains a challenging area of research. This thesis is concerned with the application of quantum Monte Carlo methods to two model systems: the spin-polarised homogeneous electron gas, and a hole-doped electron gas. Electronic structure theory is briefly reviewed before discussing in more detail the quantum Monte Carlo methods used in this thesis. A study of the three-dimensional spin-polarised homogeneous electron gas (HEG) is then reported, where the relatively new technique of twist averaging is investigated in detail and accurate energies and pair correlation functions are obtained over densities $r_s = 0.5 – 20$ a.u. and the full range of spin-polarisation, allowing comparison with the Perdew-Zunger interpolation scheme used in local spin density approximation exchange-correlation functionals. Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations.

Pre-breakdown phenomena in transformer liquids have been extensively investigated. The published work can be broadly categorised into streamer and partial discharge (PD) studies, with the former focusing on physical nature and the latter being more relevant to industrial applications. Mineral oil, as the dominant candidate, has been used in power transformers for over a century. In the past decade, there has been an increasing interest in filling power transformers with alternative liquids, e.g. esters and gas-to-liquids (GTL) based oils. This work aims to correlate the PD and streamer characteristics of three transformer liquids under AC stress. The liquids include a conventional mineral oil (Gemini X), a GTL oil (Diala S4 ZX-I) and a synthetic ester (MIDEL 7131). A circuit arrangement in compliance with the IEC 60270 was used, which allowed PD measurements, wide-band current measurements and streamer shadowgraphs to be obtained simultaneously. To simulate the quasi-uniform electric fields in transformers, a plane-to-plane electrode system incorporating an adjustable needle protrusion (PNP) was employed. A needle-to-plane electrode system (NP), which is widely used in the field, was also employed to provide reference results. Based on the PD measurement results, the PD inception fields (PDIFs) of the three liquids were found to be independent of electrode geometry for the investigated tip radius. The PDIF of the synthetic ester is about 13% lower than that of the mineral oil or the GTL oil. Compared with the PD magnitude, the pulse repetition rate is more sensitive to liquid type. At the same voltage under both the NP and PNP configurations, the synthetic ester has the highest pulse repetition rate, followed by the GTL oil, and then the mineral oil. In divergent electric fields (provided by the NP electrode system), it was found that the streamers in the three liquids have a similar stopping length at the same voltage, even though the apparent charge readings are not the same. The correlations between PD and streamer characteristics indicated that the synthetic ester has the highest branching tendency, and has therefore the smallest stopping length per unit of apparent charge among the three liquids. In quasi-uniform electric fields (provided by the PNP electrode system), the streamer branching tendencies of the three liquids were largely suppressed. The change from a propagation-induced breakdown in divergent fields to an initiation-induced breakdown in quasi-uniform fields was explained. The correlations between PD and streamer characteristics revealed that the same apparent charge can indicate different levels of streamer development in the insulation, depending on the uniformity of the electric field. Overall, interpreting PD measurement results needs to take the electric field uniformity (PD location) as well as liquid type into consideration.

abstract: When ferrite materials are used in antenna designs, they introduce some interesting and unique performance characteristics. One of the attractive features, for example, is the ability to reconfigure the center frequency of the antenna. In addition, ferrite materials also introduce a number of challenges in the modeling and simulation of such antennas. In order for the ferrite material to be useful in an antenna design, it usually is subjected to an external magnetic field. This field induces the internal magnetic field inside the ferrite material. The internal field plays a pivotal role in the radiation characteristics of the antenna. Thus, from the numerical point of view, accurate computation of this field is critical to the overall accuracy of the analysis. Usually the internal field is non-uniform and its computation is often a rather complex and non-trivial task. Therefore, to facilitate the modeling, simplifying assumptions, which introduce some kind of averaging, are often made. In this study, ferrite-loaded cavity-backed slot antennas are used to demonstrate that averaging procedures can lead to very unsatisfactory results. For instance, it is common practice to assume that the external field is uniform by averaging its distribution. One of the pivotal points in this study is the demonstration that the external magnetic field plays a very significant role and should be included in the modeling without averaging, if the accurate results are to be attained. Results presented in this study clearly support this argument. A procedure which avoids such averaging is presented and verified by comparing simulations with measurements. In contrast to the previous formulations, the modeling methodology developed in this dissertation leads to accurate results which compare very well with measurements for both uniform and non-uniform field distributions. The utility of this methodology is especially evident for the case when the magnetic field is severely non-uniform. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

The Material Point Method (MPM) is a modern finite element method that is classified as a point based method or meshless method, while it takes the advantage of two kinds of spatial discretisation that are based on an arbitrary Eulerian-Lagrangian description of motion. The referenced continuum is represented by the material points, and the motions are tracked through a computational background mesh, that is an arbitrary constant mesh which does not move the material. Hence, in the MPM mesh distortion especially in the large deformation analysis is naturally avoided. However, MPM has been employed to simulate difficult problems in the literature, many are still unsatisfactory due to the lack of rigorous validation. Therefore, this thesis firstly provides a series of simple case studies which any numerical method must pass to test the validity of the MPM, and secondly demonstrate the capability of the MPM in simulating difficult problems such as degradation of highly swellable polymers during large swelling that is currently difficult to handle by the standard finite element method. Flory’s theory is incorporated into the material point method to study large swelling of polymers, and degradation of highly swellable polymers is modelled by the MPM as a random phenomenon based on the normal distribution of the volumetric strain. These numerical developments represent adaptability of the MPM and enabling the method to be used in more complicated simulations. Furthermore, the advantages of this powerful numerical tool are studied in the modelling of an additive manufacturing technology called Selective Laser Melting (SLM). It is shown the MPM is an ideal numerical method to study SLM manufacturing technique. The focus of this thesis is to validate the MPM and exhibit the simplicity, strength, and accuracy of this numerical tool compared with standard finite element method for very complex problems which requires a complicated topological system.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Lehmer (1929) analisa matematicamente o método do passo uniforme para construção de quadrados mágicos de ordem impar. Ele divide sua análise em várias etapas. Na primeira delas, envolvendo a discussão de condições necessárias e suficientes para o preenchimento do quadrado pelo método, o autor afirma que se dois números guardarem entre si uma certa relação, eles serão designados a ocupar a mesma célula do quadrado causando seu não preenchimento. A análise do preenchimento pelo método do passo uniforme envolve a resolução de um sistema linear módulo n. Nesse trabalho, discutimos o comportamento das soluções desse sistema quando o método falha no preenchimento. Como consequência, concluímos que números que guardam a relação mencionada nunca ocupam a mesma célula. A análise das condições necessárias e suficientes para obter quadrados mágicos segundo a definição de Lehmer (1929) envolve a resolução de equações de congruências lineares a duas variáveis. Nesse trabalho, detalhamos os resultados de Lehmer (1929). A análise das condições necessárias e suficientes para obtenção de quadrados mágicos, como são reconhecidos usualmente, também envolve a resolução de equações de congruências lineares a duas variáveis. Discutimos o comportamento das soluções dessas equações para obter diagonais principais mágicas. Como consequência, mostramos que diagonais principais mágicas são obtidas se e somente se as coordenadas iniciais guardarem certas relações / Lehmer (1929) mathematically analyzes the uniform step method for constructing magic squares of odd order. He divides his analysis into several steps. In the first, involving a discussion of necessary and sufficient conditions for completing the square, the author states that if two numbers keep a certain relationship to each other, they will be designated to occupy the same cell of the square causing its non fulfillment. The analysis of the uniform step method involves solving a linear system module n. In this monograph, we discuss the behavior of solutions of this system when the method fails in fulfilling the square. Consequently, we conclude that numbers guarding the mentioned relationship never occupy the same cell. The analysis of necessary and sufficient conditions for obtaining magic square (as defined by Lehmer (1929)) involves solving linear congruences in two variables. In this work, we detail the results of Lehmer (1929). The analysis of the necessary and sufficient conditions for magic squares (as usually defined) also involves solving linear congruences in two variables. We discuss the behavior of solutions of these equations to obtain magic main diagonals. Then, we show that magic main diagonals are obtained if and only if the initial coordinates keep certain relationships

Dans ces travaux, nous avons étudié numériquement la croissance du décollement de l'interface fibre / matrice d'un composite UD avec garnissage hexagonale de fibre sous charge longitudinal et transversal. Nous avons mis l'accent en particulier sur l'influence des fibres voisines sur sa croissance. Dans la présente étude, le taux de libération d'énergie (ERR) est considéré comme la force motrice de la croissance du décollement et a été calculé sur la base de Integral J et de la technique de fermeture virtuelle de fissures (VCCT) à l'aide du logiciel de calcul par éléments finis ANSYS. Dans la présente recherche de thèse, nous avons étudier d’abord l'influence des fibres voisines sur ERR d'une décohésion émanant d'une rupture de fibre en condition de chargement longitudinal. Dans le cas du chargement longitudinal, la croissance du décollement est gouvernée par le mode II. Comme point de départ l’étude, nous avons mis place un modèle axisymétrique composé de 5 cylindres concentriques représentant la fibre endommagée, la matrice environnante, les fibres voisines, la matrice environnante et le composite effectif généré. On constate qu'il y a deux stades de croissance, la première étape correspond à une longueur courte du décollement, l'ERR diminue à mesure que l'angle du décollement augmente, et la présence de voisins augmente significativement la décohésion de l'ERR. Pour une décohésion relativement longue, le décollement se situe dans une région de croissance en état stationnaire lorsque l'ERR est pratiquement constant quelle que soit la longueur du décollement. À l’état stationnaire de la croissance du défaut, la présence de fibres voisines n'a que peu d'effet sur l'ERR. Les travails ultérieurs, nous avons mis en place un modèle 3-D (explicite) avec la fibre endommagée et ses 6 fibres les plus proches dans un composite UD compacté hexagonal, entourées par le composite homogénéisé. Sur la base des résultats obtenus, nous avons montré que l'ERR varie le long de la face frontale et a son maximum à l'endroit circonférentiel où la distance entre deux centres de fibre est la plus petite. Cela indique que le front du décollement n’est pas circulaire. Pour l'état stable du décollement, la présence de fibres a peu d'effet sur l'ERR qui progresse le long du front du décollement. Pour un décollement court, la présence de fibres augmente l'ERRS moyenné, et cette augmentation est plus significative lorsque la distance entre fibre est la plus petite. Après l’étude du la décollement fibre / matrice en charge longitudinale, nous avons commencé à étudier la croissance du décollement fibre / matrice le long de la circonférence de la fibre sous charge transversale. On constate que la croissance de la du décollement est en mode mixte, et les composants ERR du mode I et du mode II augmentent avec l'augmentation de l'angle de déformation puis diminuent. La croissance du décollement démarre principalement en mode I pour les petits angles de décollement et se poursuit en mode II. La présence de fibres voisines a un effet d’accroissement sur la croissance du décollement jusqu'à certains petits angles et change ensuite en effet protecteur. En fin, nous avons étudié l'interaction entre deux décollement sous chargement transversale. Nous avons constaté que lorsque deux décollements sont proches l'un de l'autre, l'interaction entre devient beaucoup plus forte et conduit à l'augmentation significative de l'ERR de chaque décollement, ce qui facilite la croissance du décollement / In the presence thesis, the growth of fiber/matrix interface debond of a UD composite with hexagonal fiber packing under longitudinal and transverse tensile loading was investigated numerically, with the special focus on the influence of neighboring fibers on its growth. In the current study, energy release rate (ERR) is considered as the driving force for debond growth and was calculated based on J Integral and Virtual Crack Closure Technique (VCCT) using finite element software ANSYS. In the present thesis research, we started with investigating the influence of neighboring fibers on ERR of a debond emanating from a fiber break in longitudinal loading condition. In longitudinal loading case, debond growth is mode II dominated. As the starting point for the research, an axisymmetric model consisting 5 concentric cylinders that represent broken fiber with debond, surrounding matrix, neighboring fibers, surrounding matrix and effective composites was generated. It’s found that there are two stages of debond growth, the first stage is when debond length is short, the ERR decreases with increasing debond angle, and the presence of neighboring significantly increase the ERR of debond. For relatively long debond, the debond is in a steady state growth region when ERR is almost constant regardless of debond length. In steady state of debond growth, the presence of neighboring fibers have little effect on the ERR. In the later research, a 3-D model was generated with broken fiber and its 6 nearest fibers in a hexagonal packed UD composite were modelled explicitly, surrounded by the homogenized composite. Based on the obtained results, it’s shown that ERR is varying along debond front, and has its maximum at the circumferential location where the distance between two fiber center is the smallest. This indicates the debond front is not a circle. For steady state debond, the presence of fibers have little effect on ERR that averages along debond front. For short debond, the presence of fibers increases the averaged ERRS, and that the increase is more significant when inter-fiber distance are the smallest. When we conclude our investigation on fiber/matrix debonding under longitudinal loading, we began studying the growth of a fiber/matrix debond along fiber circumference under transverse loading. It’s found that debond growth is mixed-mode, and both mode I and mode II ERR components increase with increasing debond angle and then decreases. Debond growth is mode I dominated for small debond angle and then switch to mode II dominated. The presence of neighboring fibers have an enhancement effect on debond growth up to certain small debond angle and then changes to a protective effect. Finally, the interaction between two arc-size debond under transverse loading is investigated. It’s found that when two debonds are close to each other, the interaction between two debond becomes much stronger, and that interaction leads to the increase of ERR of each debond significantly, which facilitates further debond growth for both debond

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Lehmer (1929) analisa matematicamente o método do passo uniforme para construção de quadrados mágicos de ordem impar. Ele divide sua análise em várias etapas. Na primeira delas, envolvendo a discussão de condições necessárias e suficientes para o preenchimento do quadrado pelo método, o autor afirma que se dois números guardarem entre si uma certa relação, eles serão designados a ocupar a mesma célula do quadrado causando seu não preenchimento. A análise do preenchimento pelo método do passo uniforme envolve a resolução de um sistema linear módulo n. Nesse trabalho, discutimos o comportamento das soluções desse sistema quando o método falha no preenchimento. Como consequência, concluímos que números que guardam a relação mencionada nunca ocupam a mesma célula. A análise das condições necessárias e suficientes para obter quadrados mágicos segundo a definição de Lehmer (1929) envolve a resolução de equações de congruências lineares a duas variáveis. Nesse trabalho, detalhamos os resultados de Lehmer (1929). A análise das condições necessárias e suficientes para obtenção de quadrados mágicos, como são reconhecidos usualmente, também envolve a resolução de equações de congruências lineares a duas variáveis. Discutimos o comportamento das soluções dessas equações para obter diagonais principais mágicas. Como consequência, mostramos que diagonais principais mágicas são obtidas se e somente se as coordenadas iniciais guardarem certas relações / Lehmer (1929) mathematically analyzes the uniform step method for constructing magic squares of odd order. He divides his analysis into several steps. In the first, involving a discussion of necessary and sufficient conditions for completing the square, the author states that if two numbers keep a certain relationship to each other, they will be designated to occupy the same cell of the square causing its non fulfillment. The analysis of the uniform step method involves solving a linear system module n. In this monograph, we discuss the behavior of solutions of this system when the method fails in fulfilling the square. Consequently, we conclude that numbers guarding the mentioned relationship never occupy the same cell. The analysis of necessary and sufficient conditions for obtaining magic square (as defined by Lehmer (1929)) involves solving linear congruences in two variables. In this work, we detail the results of Lehmer (1929). The analysis of the necessary and sufficient conditions for magic squares (as usually defined) also involves solving linear congruences in two variables. We discuss the behavior of solutions of these equations to obtain magic main diagonals. Then, we show that magic main diagonals are obtained if and only if the initial coordinates keep certain relationships

Made available in DSpace on 2015-05-15T11:46:12Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 804145 bytes, checksum: 80e03dda4533d0039f991cc668ca2c87 (MD5) Previous issue date: 2012-08-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We consider a dynamical one-dimensional nonlinear Von Kármán model for beams depending on the parameter " > 0 and we study their asymptotic behavior for t large, when " ! 0. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponential uniform with respect to the parameter ". In order for this to be true the damping mechanism has to have the appropriate scale with respect to ". In the limit as " ! 0 we obtain damped Berger- Timoshenko beam model for which the energy tends exponentially to zero. This is done both in the case of internal and boundary damping . / Consideramos a dinâmica unidimensional não linear do modelo de Von Kármán para vigas dependendo de um parâmetro " > 0, e estudamos o seu comportamento assintótico para t grande, quando " ! 0. Introduzindo mecanismos adequados de amortecimento, mostramos que a energia de soluções do correspondente modelo amortecido possui decaimento exponencial uniforme com respeito ao parâmetro ". Afim de que seja verdadeiro, o mecanismo de amortecimento tem que ter a escala apropriada em relação a ". No limite, quando " ! 0 obtemos o modelo de Berger-Timoshenko para viga amortecida, bem como quando a energia tende exponencialmente para zero. Isso é feito tanto no caso de amortecimento interno e na fronteira.

Real time convolution has many applications among others simulating room reverberation in audio processing. Non-uniformly partitioning filters could satisfy the both desired features of having a low latency and less computational complexity for an efficient convolution. However, distributing the computation to have an uniform demand on Central Processing Unit (CPU) is still challenging. Moreover, computational cost for very long filters is still not acceptable. In this thesis, a new algorithm is presented by taking advantage of the broad memory on Graphics Processing Units (GPU). Performing the computations of a non-uniformly partitioned block convolution on GPU could solve the problem of work load on CPU. It is shown that the computational time in this algorithm reduces for the filters with long length.

Notre étude porte sur la caractérisation expérimentale et numérique de la dynamique des ondes de détonation dans des prémélanges gazeux non-uniformément distribués dont les gradients de composition sont orientés selon la direction de propagation de la détonation. Elle vise à améliorer la compréhension des phénomènes complexes présents dans une chambre de combustion de moteur à détonations pulsées (PDE) ou rotatives (RDE) et dans des situations de fuites accidentelles de combustibles. Nous rappelons d’abord le contexte de notre étude, la phénoménologie de la détonation dans les gaz et les travaux antérieurs sur la propagation de la détonation dans des compositions non-uniformes. Nous décrivons ensuite le banc expérimental que nous avons conçu pour satisfaire à la contrainte de génération contrôlée de gradients de composition dans une chambre d’étude de section carrée 50⇥50 mm2 et de longueur 665 mm, et les diagnostics que nous avons mis en œuvre : sondes à oxygène, capteurs de pression dynamique, enregistrements sur plaques recouvertes d’un dépôt de carbone, strioscopie et spectroscopie par chimiluminescence ultra-rapides. Nous présentons alors les résultats de nos expériences dans des compositions de propane ou d’éthane et d’oxygène à la pression et à la température initiales 200 mbar et 290 K. Nous avons considéré des distributions monotones, de richesse décroissante, et des distributions non-monotones, de richesse décroissante puis croissante. Dans les distributions monotones, nous avons identifié deux types d’extinction de la détonation, l’un brusque, par découplage choc-flamme, pour des gradients suffisamment forts, l’autre progressif, par transition vers des modes marginaux de propagation, pour des gradients plus faibles. Nous avons proposé et validé des critères d’existence de la détonation fondés sur les échelles caractéristiques du problème. Nous avons démontré, pour ces distributions, la capacité de simulations numériques avec cinétique chimique détaillée à représenter nos expériences, dans le cadre d’une collaboration avec l’Université Keio. Dans les distributions non-monotones, nous avons identifié des comportements super-critique, critique et sous-critique, selon que la détonation est transmise ou non de la zone où la richesse diminue vers celle où elle augmente. Nous avons en particulier identifié les conditions de réamorçage d’une détonation éteinte dans la zone de richesse décroissante. Notre étude souligne l’intérêt de travaux futurs sur des non-uniformités de compositions initiales constitués de gaz brûlés et de gaz frais et donc, également, des non-uniformités de température initiale. Elle souligne aussi la nécessité de diagnostics optiques et d’outils numériques performants, et de schémas détaillés de cinétique chimique adaptés aux hautes pressions et températures caractérisant la dynamique des détonations. / Our study is an experimental and numerical work on the dynamical behaviours of detonation waves in non-uniformly distributed premixed gases with composition gradients parallel to the direction of the detonation propagation. The study aims at improving the understanding of the complex phenomena involved in the combustion chambers of pulsed or rotating detonation engine (PDE, RDE) and after accidental leaks of fuels. We first remind the context of our study, the phenomenology of gaseous detonation and the previous works on detonation propagation in non-uniform compositions. We then describe the experimental set-up that we have designed in order to meet the constraint of a controlled generation of composition gradients in a 50⇥50 mm2 square-section, 665-mm length test chamber, and the diagnoses that we have implemented : oxygen probes, fast pressure transducers, carbon-sooted plates and ultrafast Schlieren and chemiluminescence spectroscopy. Next, we present the results of our experiments in mixtures of propane or ethane and oxygen with initial pressure and temperature 200 mbar and 290 K, respectively. We have considered monotonic distributions, with decreasing equivalence ratio, and non- monotonic distributions, with decreasing then increasing equivalence ratio. In the monotonic distributions, we have identified two types of detonation quenching, one sudden, with a shock-flame decoupling, for the steeper gradients, the other progressive, with a transition through marginal modes of detonation propagation, for the weaker gradients. We have proposed and validated criteria for detonation, based on the characteristic scales of the problem. We have demonstrated, for these monotonic distributions, the ability of numerical simulations with detailed schemes of chemical kinetics to represent our experimental observations, through a collaboration with Keio University. In the non-monotonic distributions, we have identified super-critical, critical and sub-critical behaviours, depending on whether the detonation is transmitted or not from the domain where the equivalence ratio decreases to that where it increases. In particular, we have identified the re-initiation conditions for a detonation that was quenched in the domain of decreasing equivalence ratio. Our study stresses the interest for future works to consider non-uniform distributions of mixtures comprising burnt gases and fresh reactants, and, consequently, non-uniform distributions of temperature. It also stresses the need for performing optical diagnoses and numerical capacities and for detailed schemes of chemical kinetics adapted to the high pressures and temperatures characterizing detonation dynamics.