General anisotropic constitutive laws and relevant dynamic equations of motion for porous media are described. The accuracy of various discretization algorithms in space and in time was surveyed. Results of these models and algorithms were compared to the exact solutions. Appropriate models and algorithms for further studies of spinal motion segments were then determined. Poroelastic axisymmetric finite element models, simulating spinal motion segments were analyzed and studied. Material properties of the intervertebral disc were derived by fitting experimental data based on porous medium theory using one-dimensional mathematical models. Structural models for the normal and degenerative processes were simulated for investigation of nutritional supply routes in the disc. Detailed structural anaalyses and failure conditions in various spinal motion segments were studied. Results of finite element analyses were consistent with the experimental observations. Nonlinear elastic material behavior of the solid skeleton was assumed and relevant formulas in creep were derived and examined. Preliminary results indicated that the nonlinear poroelastic material law used here may be useful in future analysis of the disc in finite element models of spinal motion segments.

A hp-finite element method is implemented to numerically study the modes of waveguides with two dimensional cross-section and to compute electromagnetic scattering from three dimensional objects. A method to control the chromatic dispersion properties of photonic crystal fibers using the selective hole filling technique is proposed. The method is based on a single hole-size fiber geometry, and uses an appropriate index-matching liquid to modify the effective size of the filled holes. The dependence of dispersion properties of the fiber on the design parameters such as the refractive index of the liquid, lattice constant and hole diameter are studied numerically. It is shown that very small dispersion values between 0±0.5ps/nm-km can be achieved over a bandwidth of 430-510nm in the communication wavelength region of 1300-1900nm. Three such designs are proposed with air hole diameters in the range 1.5-2.0μm. A novel multi-core fiber design strategy for obtaining a at in-phase supermode that optimizes utilization of the active medium inversion in the multiple cores is proposed. The spatially at supermode is achieved by engineering the fiber so that the total mutual coupling between neighboring active cores is equal. Different designs suitable for different fabrication processes such as stack-and-draw and drilling are proposed. An important improvement over previous methods is the design simplicity and better tolerance to perturbations. The optimal implementation of perfectly matched layer (PML) in terms of minimizing the computational overhead it introduces is studied. In one dimension it is shown that PML implementation with a single cell and a high order finite element produces minimal overhead. Estimates of optimal cell size and optimal finite element degree are given. Based on the single cell implementation of PML in three dimensions, field enhancement in metallic bowties is computed.

No description available.

Permanent magnets are today widely used in electrical machines of all sorts. With their increase in popularity, the amount of research has increased as well. In the wind power project at Uppsala University permanent magnet synchronous generators have been studied for over a decade. However, a tool for studying demagnetization has not been available. This Ph.D. thesis covers the development of a simulation model in a commercial finite element method software capable of studying demagnetization. Further, the model is also capable of simulating the connected electrical circuit of the generator. The simulation model has continuously been developed throughout the project. The simulation model showed good agreement compared to experiment, see paper IV, and has in paper III and V successfully been utilized in case studies. The main focus of these case studies has been different types of short-circuit faults in the electrical system of the generator, at normal or at an elevated temperature. Paper I includes a case study with the latest version of the model capable of handling multiple short-circuits events, which was not possible in earlier versions of the simulation model. The influence of the electrical system on the working point ripple of the permanent magnets was evaluated in paper II. In paper III and VI, an evaluation study of the possibility of creating a generator with an interchangeable rotor is presented.  A Neodymium-Iron-Boron (Nd-Fe-B) rotor was exchanged for a ferrite rotor with the electrical properties almost maintained.

Les travaux de thèse portent sur l'évaluation et la robustesse des stratégies adaptées pour la simulation de grandes structures avec non-linéarités non équitablement réparties, tels le flambage local, et des non-linéarités globales dans les structures aéronautiques. La stratégie dite de « relocalisation non-linéaire » permet l'introduction de schémas de résolution non-linéaire par sous-structure au sein des méthodes de décomposition de domaine classiques.Dans un premier temps, les performances et la robustesse de la méthode sont présentées sur des exemples de structures représentatives des cas industriels. Dans un second temps, la stratégie est complètement parallélisée et des études de « speed-up » et de « extensibilité » sont menées. Enfin, la méthode est testée sur des structures réalistes et de grandes tailles. / The thesis work focus on the evaluation and the robustness of adapted strategies for the simulation of large structures with not equitably distributed nonlinearities, like local buckling, and global nonlinearities on aeronautical structures. The nonlinear relocalization strategy allows the introduction of nonlinear solving schemes in the sub-structures of the classical domain decomposition methods.At a first step, the performances and the robustness of the method are analysed on academic examples. Then, the strategy is parallelized and studies of speed-up and extensibility are carried out. Finally, the method is tested on larger and more realistic structures.

M.Ing. / Optical fibre Bragg gratings are a periodic variation of the refractive index in the core of an optical fibre andmay be formed by exposure to intense UV laser light under specific conditions. Light at a certain wavelength, called the Bragg wavelength, is reflected back when illuminating the grating with a light source. Bragg gratings can relatively easily be employed as strain and temperature sensors, but have small sensitivity for pressure. Special transducers are required to increase the sensitivity. A pressure sensor was manufactured by coating a fibre Bragg grating with a polymer. The polymer coating converts transverse pressure into longitudinal strain through the Poisson effect inside the polymer coating. This thesis investigates the sensitivity of themanufactured Bragg grating pressure sensor, by using the method of finite element analysis. An account of the experimental setup, whereby the Bragg grating is written with a frequency tripled Nd:YAG laser, is given. The process whereby the fibre is coated with the polymer is described. The sensor is characterized through experimental results and a comparison is made between theoretical and experimental results. Uses for this sensor and ways with which the sensitivity may be increased are suggested as future work.

<p></p><p>Granular material blending plays an important role in many industries ranging from those that manufacture pharmaceuticals to those producing agrochemicals. The ability to create homogeneous powder blends can be critical to the final product quality. For example, insufficient blending of a pharmaceutical formulation may have serious consequences on product efficacy and safety. Unfortunately, tools for quantitatively predicting particulate blending processes are lacking. Most often, parameters that produce an acceptable degree of blending are determined empirically.</p> <p> </p> <p>The objective of this work was to develop a validated model for predicting the magnitude and rate of granular material mixing and segregation for binary mixtures of granular material in systems of industrial interest. The model utilizes finite element method simulations to determine the bulk-level granular velocity field, which is then combined with particle-level diffusion and segregation correlations using the advection-diffusion-segregation equation. </p> <p> </p> <p>An important factor to the success of the finite element method simulation used in the current work is the material constitutive model used to represent the granular flow behavior. In this work, the Mohr-Coulomb elastoplastic (MCEP) model was used. The MCEP model parameters were calibrated both numerically and experimentally and the procedure is described in the current work. Additionally, the particle-level diffusion and segregation correlations are important to the accurate prediction of mixing and segregation rates. The current work derived the diffusion and segregation correlations from published literature and determined a methodology for obtaining the particle diffusion and segregation parameters from experiments.</p> <p> </p> <p>The utility of this modelling approach is demonstrated by predicting mixing patterns in a rotating drum and Tote blender as well as segregation patterns in a rotating drum and during the discharge of conical hoppers. Indeed, a significant advantage of the current modeling approach compared to previously published models is that arbitrary system geometries can be modeled.</p> <p> </p> <p>The model predictions were compared with both DEM simulation and experiment results. The model is able to quantitatively predict the magnitude and rate of powder mixing and segregation in two- and three-dimensional geometries and is computationally faster than DEM simulations. Since the numerical approach does not directly model individual particles, this new modeling approach is well suited for predicting mixing and segregation in large industrial-scale systems.</p><br><p></p>

Recently it has been shown that N = 4 super Yang-Mills theory is integrable in the planar limit. Past arguments suggest the integrability is only present in the planar limit. However, this conclusion was shown to be incorrect. Two speci c classes of operators were studied in the O(N) sector. The rst were labelled by Young diagrams having two long columns. The second were labelled by Young diagrams having two long rows. This result was then generalized to p long rows or columns with p xed to be O(1) as N ! 1. For this case, the non-planar limit was found to be integrable. In this dissertation, we extend this work by considering p to be O(N). We have calculated the dilation operator for the case with two impurities.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. March 2013. / In the past decade, the gauge/gravity duality has been extensively explored in the large N limit. In particular, the spectrum of anomalous dimensions have been compared with the energy spectrum of the dual string theory showing remarkable agreement. In this limit, for operators with a bare dimension of order 1, planar diagrams give the leading contribution to the anomalous dimension. To obtain the anomalous dimensions, one needs to diagonalize the dilatation operator. One of the methods used to accomplish this is integrability. This allows an exact computation of the spectrum of the anomalous dimensions. There is by now a great deal of evidence that N = 4 supersymmetric Yang-Mills (SYM) theory and N = 6 superconformal Chern Simons (ABJ(M)) theory are integrable in the planar limit. In this thesis we probe the gauge gravity duality at finite N using novel tools developed from the representation theory of symmetric and unitary groups. We start by studying the action of the nonplanar dilatation operator of N = 4 SYM theory and ABJ(M) theory. The gauge invariant operators we consider are the restricted Schur polynomials. In the case of N = 4 SYM theory, we obtain the spectrum of the anomalous dimension beyond the SU(2) sector at one loop, and in the SU(2) sector at two loops. In both cases, we obtain the spectrum at arbitrary (finite) N. We then obtain the spectrum of anomalous dimensions in the SU(2) sector of ABJ(M) theory at two loops. The class of gauge invariant operators we consider have classical dimension of order O(N). In both theories, the spectrum of the anomalous dimensions reduces to a set of decoupled harmonic oscillators at large N. This indicates, for the first time, that N = 4 SYM theory and ABJ(M) theory exhibit nonplanar integrability. We expect to recover non-perturbative quantum gravity effects, from the gauge/gravity duality, when N is finite. The non-planar integrability we discover here may play an important role in finite N studies of the gauge/gravity duality, and hence may play an important role in understanding non-perturbative string stringy physics. In addition, we study various classes of correlators in ABJ(M) theory. In this context, we derive extremal n-point correlators in ABJ(M) theory and we probe the giant graviton dynamics in these theories.

Cette thèse présente la modélisation de l’effet magnéto-électrique dans les matériaux composites par la méthode des éléments finis. Les matériaux composites magnéto-électriques sont la combinaison de matériaux piézoélectriques et magnétostrictifs. Les lois de comportement ont été établies en associant les lois de comportement piézoélectrique et magnétostrictive. Le modèle piézoélectrique a été supposée linéaire, contrairement au magnétostrictif qui est non-linéaire. Afin de modéliser des dispositifs dans lequel il y a coexistence d’un champ statique et d’un champ dynamique de faible amplitude, nous avons proposé une étape de linéarisation des lois de comportement. Cette étape consiste à déterminer le point de fonctionnement fixé par le champ statique pour ensuite calculer la variation autour de ce point associée au champ dynamique. Les deux lois de comportement ont ensuite été intégrées dans un code éléments finis 2D. Le code de calcul éléments finis a ensuite été exploité pour différents dispositifs déjà mis en ?uvre expérimentalement dans la littérature. La première application est une inductance variable contrôlée par un champ électrique. Malgré une méconnaissance de certaines valeurs des propriétés des matériaux, le calcul numérique et les résultats expérimentaux sont en bon accord d’un point de vue qualitatif. Les travaux nous ont permis de modéliser des capteurs de champ magnétique. Ces capteurs ont pour but de détecter précisément un champ magnétique statique dans le plan de travail. La comparaison des résultats numériques et expérimentaux a montré à nouveau une bonne concordance qualitative. Quelques améliorations de la structure du dispositif ont été proposées et évaluées à l’aide du modèle développé. / This thesis deals with the modelling of magnetoelectric effect in composite materials using finite element method. The magnetoelectric composite materials result from the combination of piezoelectric and magnetostrictive materials. The magnetoelectric constitutive laws were established by combining piezoelectric and magnetostrictive constitutive laws. The piezoelectric behaviour is assumed to be linear. Unlike the piezoelectric material, the magnetostrictive behaviour is nonlinear. In order to model the smart devices with the coexistence of static and low amplitude dynamic field, a linearization of constitutive laws is proposed. This step is to determine the polarisation point given by static field, then calculate the variation around this point associated with dynamic field. The static and linearized constitutive laws are then integrated in a 2D finite element code using Galerkin method.The finite element program is then used for modeling different devices in experimental. The first application is a tunable inductor controlled by a electric field. The numerical results are closed to experimental results despite unknown material properties. The model is then implemented in the case of magnetic sensor. This sensor is to detect accurately the static magnetic field in working plane. The comparison between numerical and experimental results shows again good qualitative agreement. Some improvements of sensor structure are purposed thanks to the developed model.