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.

Este trabalho trata de fissura, uma das principais patologias que podem ocorrer em edifícios residenciais em alvenaria estrutural, visando identificar os locais onde elas aparecem com mais frequência, para assim procurar formas de evitá-las. Inicialmente foram realizadas visitas a vários edifícios em alvenaria estrutural de forma a levantar as principais fissuras encontradas nesse tipo de estrutura. Identificou-se que as fissuras são mais frequentes nos contornos de aberturas, diante disse foi realizado um estudo teórico, com a utilização de um programa computacional, para se determinar algumas das principais causas prováveis dessas patologias através de modelos numéricos adequados. Finalmente, foram analisadas algumas das soluções para as patologias encontradas, tentando sugerir as melhores soluções para cada caso. / This paper deals with fissure, one of major diseases that can occur in a structural masonry residential buildings, in order to identify the locals they usually occur, to seek ways to avoid them. Initially were realized visits a several structural masonry buildings to analise the principals fissures in this type of structure. Was identified that the fissures are more frequently in the contours of openings, given this, was realized a theoretical study using a finite element computer program to identify some of the main possible causes of these pathologies through adequate numerical models. Finally, some possible solutions for the conditions found were analyzed, trying to suggest the best solutions for each case.

Este trabalho tem como objetivos complementar os requisitos para obtenção do grau de mestre em engenharia e propiciar um texto para os que se iniciam no estudo do método dos elementos finitos. Apresentam-se, no primeiro capítulo, conceitos básicos da teoria da elasticidade importantes no desenvolvimento do tema. No segundo capítulo desenvolvem-se os teoremas variacionais da teoria da elasticidade. Estabelecem-se os teoremas da energia potencial total, da energia potencial complementar total e um conjunto de outros teoremas, com destaque para o de dois campos, devido a Reissner, e o três campos, devido a Oliveira. Introduz-se no terceiro capítulo, o conceito de solução aproximada contínua. Inicialmente apresenta-se um modelo genérico, análogo a todos os modelos contínuos. Em seguida avalia-se o erro global das soluções aproximadas contínuas, no caso de serem compatíveis ou equilibradas, estabelecendo extremos superior e inferior para a energia de deformação da solução exata. Dedica-se o quarto capítulo ao método dos elementos finitos aplicado às estruturas de comportamento linear. Apresenta-se uma visão panorâmica do estágio atual do método, referindo-se aos vários processos e modelos derivados. Estabelecem-se, relativamente ao processo dos deslocamentos, a técnica de discretização propriamente dita e sua justificativa. Finalmente desenvolve-se a formulação de vários elementos, correspondentes aos possíveis modelos derivados do processo dos deslocamentos.Ressalta-se a importância das obras de Oliveira (13) a (20) no desenvolvimento de todo o trabalho, e as de Fung (4) e Sokolnikoff (32), no primeiro capítulo, de Washizu (34), no segundo capítulo, de Prager (30) no terceiro capítulo e Pedro (22), no quarto capítulo. O autor deseja expressar os seus agradecimentos aos professores Decio Leal de Zagottis, Maurício Gertsenchtein e Victor Manuel de Souza Lima, da Escola Politécnica da Universidade de São Paulo, ao professor Jairo Porto, da Escola de Engenharia de Lins, e aos engenheiros José de Oliveira Pedro e Manuel Pinho de Miranda, do Laboratório Nacional de Engenharia Civil de Lisboa, que colaboraram no desenvolvimento deste trabalho. / The purpose of this work is completing the requirements for obtaining the master degree in engineering and providing a text for those who are initiating in the study of the finite-element method. The first chapter refers to the basic concepts of the theory of elasticity being important to the development of this theme. In chapter 2 the variational theorems of the theory of elasticity are developed. The total potential energy theorem, the total complementary potential energy theorem, and a group of other theorems, are established, emphasis being placed on the ones of two fields, due to Reissner, and the ones of three fields, due to Oliveira. It is introduced, in the third chapter, the concept of approximate continuos solution. Initially is presented a general model, analogous to all continuos models. Following, the overall error of the approximate continuous solutions is evaluated, whether compatible or in equilibrium, by establishing upper and lower extremes for the deformation energy of the exact solution. The fourth chapter is dedicated to the finite-element method as applied to structures of linear behavior. An overall view of the present stage of the method, referring to the various processes and models derived, is presented. It is established, as refers the displacement process, the discreting technique proper and its justification. Finally, the formulation of various elements corresponding to the possible models derived from the displacement process, is developed. It must be emphasized the importance of the works published by Oliveira (13) to (20) for the development of the entire work, as well as those by Fung (4) and Sokolnikoff (32), in the first chapter, those by Washizu (34), in the second chapter, those by Prager (30), in the third chapter, and Pedro (22), in the fourth chapter.

Introduction: Unicompartmental knee replacements (UKRs) are an alternative to total knee replacements (TKRs) for treating isolated medial compartment knee osteoarthritis. However, revision rates are consistently higher than for TKR and UKRs are commonly revised for “unexplained” pain, a possible cause of which is elevated proximal tibial bone strain. The influence of implant design on this strain has not been previously investigated. Aims: The aims of this thesis are to determine the effect of medial UKR tibial component design on proximal tibial strain and ongoing pain. Methods: A retrospective clinical cohort study was performed comparing patient reported outcome and implant survival of a metal backed mobile bearing UKR implant (n=289) and an all-polyethylene (AP) fixed bearing UKR implant (n=111) with minimum 5 year follow up. A method of digital radiological densitometry, the greyscale ratio b (GSRb), was developed, validated and applied to plain radiographs to measure changes in bone density over 5 years in both the metal backed (n=173) and all-polyethylene (n=72) UKR patients. A finite element model (FEM) was validated against previous mechanical testing data and was used to analyse the effect of metal backing and implant thickness on proximal tibial cancellous bone strain in fixed bearing UKR implants. Results: There were no significant differences in patient reported outcomes between implants throughout follow up. Ten year all cause survival was 90.2 (95%CI 86-94) for the metal backed implant and 79.9 (60.7 to 99) for the all-polyethylene. Revision for unexplained pain was significantly greater in the AP implant where revisions were performed significantly earlier. Overall, the mean GSRb reduced following medial UKR with no difference between implants. In those patients where GSRb increased, patient reported outcomes were worse with an association with ongoing pain. A finite element model was successfully validated using acoustic emission and digital image correlation data. This model confirmed that the volume of cancellous bone exposed to compressive and tensile strains in excess of 3000 (pathological overloading) and 7000 (fracture) microstrain were higher in the AP implants, as were peak tensile and compressive strains. Varying polyethylene insert thickness did not affect these strain parameters in the metal backed implant, but varying polyethylene thickness in the AP implants had significant effects at all loads with elevated strains in thinner implants. Increasing the AP thickness to 10mm did not reduce strains to the levels found under metal backed implants, and imminent cancellous bone failure was implied when AP thickness was reduced to 6mm. Conclusion: UKRs with all-polyethylene tibial components are associated with greater proximal tibial strains than metal backed implants and this is exacerbated in thinner implants. The clinical consequences of this are uncertain. Medial UKR implantation does alter proximal tibial GSRb, though this is not uniform and is independent of implant type. When GSRb increases it is associated with ongoing pain.

O uso de simulações computacionais no campo da engenharia vem se tornando cada vez mais freqüente. Este trabalho aplica diferentes tipos de análise, Método Multicorpos e Método dos Elementos Finitos, para estudos dinâmicos e estruturais, como ferramenta de auxílio no desenvolvimento de veículos terrestres. Através de métodos de integração numérica e posteriormente a utilização do método dos multicorpos, uma suspensão independente dianteira de um veículo foi isolada, considerada como um conjunto de corpos unidos por juntas, movidos por forças e restringidos por batentes. O comportamento dinâmico do sistema foi determinado submetendo o modelo a entradas provenientes do pavimento. O Método dos Elementos Finitos já é considerado como ferramenta potente para o cálculo estrutural. Para abordar tal tema, foi construído um modelo discretizado em Elementos Finitos de um veículo comercial completo. Este modelo foi submetido a simulações de situações de situações reais quasi-estáticas e dinâmicas, utilizando algoritmos implícito e explícito, dependendo do fenômeno considerado. A partir destes, puderam ser verificadas a performance estrutural e a segurança passiva do veículo arremessado a obstáculos cotidianos. O último estudo retrata que com a fusão dos métodos é possível, através de programas dedicados, prever a dinâmica de um modelo encriptado de um boneco tipo HYBRIDIII, quando submetido a um pulso de desaceleração no interior de um veículo com e sem bolsa de segurança(airbag). Todos os resultados obtidos foram comparados à realidade ou \"benchmark\". Os obstáculos enfrentados permitiram definir qual ferramenta melhor se encaixa num contexto de desenvolvimento dentro de uma corporação. / The use of computational tools in various engineering fields has increased over the last years. Mathematical modelling is identified as being the most adequate tool for simulating real service conditions along several product development phases. This work investigates different dynamic and structural analysis used for ground vehicle development tools. By numerical integration using the Multibody system method, an independent suspension was isolated from the car and considered as bodies connected by joints, moved by forces and constrained by stoppers. The dynamic behaviour of the systems was predicted when submitted to input exclusively from the ground. The Finite Element Method is already considered a very powerful simulation tool. In order to study the method, a full vehicle model was built and submitted to quasi-static and dynamic inputs. Both implicit and explicit methods were used to simulate different situations. The vehicle had its structural performance analysed related to durability and safety aspects. The last analysis that shows the fusion of methods is possible using dedicated computational tools to simulate the passenger kinematics by using an encrypted dummy and an airbag model under a deceleration pulse as input. AlI the results were compared to experimental and benchmark results. Also the difficulties emerged from each tool were pointed out in order to define which is the most appropriate within the development context.

A ideia de realizar este trabalho surgiu durante do curso de pós-graduação, ministrado pelo Prof. M. Drigas, \"Tópicos especiais sobre máquinas elétricas\", realizado no 2º semestre de 1980 na EPUSP, onde foi observada a necessidade do conhecimento das distribuições de campos magnéticos em dispositivos eletromecânicos com o objetivo de se prever seu desempenho na fase de projeto. Nesta época, já havia sido apresentada a tese do Prof. Janiszewski, o primeiro trabalho, de nosso conhecimento realizado no Brasil nesta área, onde foi desenvolvida a técnica de resolução de problemas de Campos Magnéticos em Regime Estacionário, que, evidentemente, não pode ser aplicada na resolução de problemas onde a variável tempo está envolvida; baseado neste tese, em 1982 o Prof. Luiz Lebensztajn, reproduziu o trabalho do Dr. Janiszewski o qual foi aplicado para verificar a consistência dos resultados práticos na tese de Livre Docência do Prof.. Dr. Aurio Gilberto Falcone. As formulações mais frequentes do Método dos Elementos Finitos (MEF), publicada nos periódicos internacionais, são baseadas no Cálculo Variacional, onde o sistema de equações algébricas não linear resultante, é derivado a partir da obtenção do extremo de uma funcional que em algumas situações não pode ser obtida, limitando assim sua aplicação. Em decorrência deste fato, o primeiro objetivo deste trabalho foi organizar os procedimentos para obtenção do sistema de equações de MEF aplicado à resolução de problemas de campo descritos por equações diferenciais não lineares, sem a necessidade. Algumas contribuições interessantes são encontradas no Capítulo II, referente à formulação do MEF para problemas de campo descrito por operadores diferenciais não auto-adjuntos.No Capítulo III são apresentadas as técnicas de montagem das matrizes, bem como aquelas de introdução das condições de contorno, originárias deste método, que muito embora sejam técnicas de aplicação corriqueiras, ajudarão em muito o pesquisador iniciante nesta área, sem a necessidade de recorrer a outro texto. No Capítulo VI são apresentadas as formulações necessárias para a solução de problemas de campos eletromagnéticos estáticos, para elementos de quatro lados retos (e curvos) assim como a técnica utilizada na obtenção da relutividade em meios não lineares. No Capítulo V são tratados os problemas de campo, onde a variável tempo está envolvida, permitindo assim a resolução de uma série enorme de problemas referentes aos campos de natureza eletromagnética, tais como os fenômenos transitórios e o Regime Permanente Senoidal. Os aspectos computacionais ligados ao trabalho estão expostos no Capítulo VI, onde são apresentadas as rotinas de resolução do sistema de equações resultante adaptadas às particularidades do problema, e as rotinas de integração numérica de problemas descrito por equações diferenciais dependentes do tempo de primeira e segunda ordem. Algumas técnicas apresentadas nestes Capítulos, são aplicadas espe3cificamente para a obtenção da distribuição de campo magnético no Capitulo VII deste trabalho, com o objetivo de analisar o desempenho de um transformador em regime transitório, onde é confirmada a consistência do método. / The idea of making this work came during a graduation course, \" Special topics on electric machines\", lectured by Prof. Dr. M. Drigas during the 2nd semester of 1980 at EPUSP, when the need of knowing the distribution of magnetic fields in electromechanics devices was notices, in order to foresse its performance during design. At that time, the first work about this subject realized made in Brazil was presented in prof. Janiszewski\'s thesis, where a technique was developed to solve Steady-State Magnetic Fields. However, it is clear that when the time variable is considered, this technique cannot be applied. The usual formulations of the Finite Element Method, published in international journals, was based on Variational Calculations, where the resulting non-linear algebraic equations system is derived from the extreme of a functional, which sometimes cannot be obtained, limiting in this way its application. Consequently, the first aim of this work is to organize procedures to obtain the Finite Method equations system, in order solve non-linear differential equations of fields, without the need of a previous functional for the problem. In Chapter II, one will find some interesting contributions referred to the Finite Element Method formulation, in the description of field problems by the use of non self-adjacent differentials operations.Matrix building techniques are presented in Chapter III, as well as the introduction of boundary conditions in this method. In spite of being an ordinary technique, it will help the beginners a lot, eliminating the need of other sources. Chapter IV presents the necessary formulations, which solve static electromagnetic fields for elements of four square (and curved) sides, and the technique used in the determination of non-linear media reluctivity. In Chapter V, the time variable of electromagnetic fields is treated, making possible the solution of problems of this nature, such as transient phenomena and sinusoidal steady-state. Computer aspects of the work are shown in Chapter VI, presenting resolution routines of the equation system fitted to the problem, and numeric integration routines described by first and second order differential equations, which depend on the time. Some techniques showed in those previous Chapters are specifically used in Chapter VII to obtain the magnetic field distribution, which analyses transformer performance during transients. The coherence of the method is also confirmed.

Ma Mun Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 86-88). / Abstract also in Chinese. / Abstract --- p.i / Declaration --- p.ii / Acknowledgement --- p.iii / List of Figures --- p.iv / List of Tables --- p.ix / Table of Contents --- p.x / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Motivation --- p.1 / Chapter 1.2. --- Thesis Roadmap --- p.3 / Chapter 1.3. --- Contribution / Chapter 2. --- System Architecture --- p.6 / Chapter 2.1. --- Tracker system --- p.6 / Chapter 2.1.1. --- Spatial Information --- p.6 / Chapter 2.1.2. --- Transmitter (Xmtr) --- p.6 / Chapter 2.1.3. --- Receiver (Recvr) --- p.7 / Chapter 2.2. --- Glove System --- p.7 / Chapter 2.2.1. --- CyberGlove Interface Unit (CGIU) --- p.7 / Chapter 2.2.2. --- Bend Sensors --- p.7 / Chapter 2.3. --- Integrating the tracker and the glove system --- p.9 / Chapter 2.3.1. --- System Layout --- p.9 / Chapter 3. --- Deformable Model --- p.11 / Chapter 3.1. --- Elastic models in computer --- p.11 / Chapter 3.2. --- Virtual object model --- p.17 / Chapter 3.3. --- Force displacement relationship --- p.18 / Chapter 3.3.1. --- Stress-strain relationship --- p.19 / Chapter 3.3.2. --- Stiffness matrix formulation --- p.20 / Chapter 3.4. --- Solving the linear system --- p.24 / Chapter 3.5. --- Implementation --- p.26 / Chapter 3.5.1. --- Data structure --- p.26 / Chapter 3.5.2. --- Global stiffness matrix formulation --- p.27 / Chapter 3.5.3. --- Re-assemble of nodal displacement --- p.30 / Chapter 4. --- Collision Detection --- p.32 / Chapter 4.1. --- Related Work --- p.31 / Chapter 4.2. --- Spatial Subdivision --- p.37 / Chapter 4.3. --- Hierarchy construction --- p.38 / Chapter 4.3.1. --- Data structure --- p.39 / Chapter 4.3.2. --- Initialisation --- p.41 / Chapter 4.3.3. --- Expanding the hierarchy --- p.42 / Chapter 4.4. --- Collision detection --- p.45 / Chapter 4.4.1. --- Hand Approximation --- p.45 / Chapter 4.4.2. --- Interference tests --- p.47 / Chapter 4.4.3. --- Searching the hierarchy --- p.51 / Chapter 4.4.4. --- Exact interference test --- p.51 / Chapter 4.5. --- Grasping mode --- p.53 / Chapter 4.5.1. --- Conditions for Finite Element Analysis (FEA) --- p.53 / Chapter 4.5.2. --- Attaching conditions --- p.53 / Chapter 4.5.3. --- Collision avoidance --- p.54 / Chapter 4.6. --- Repeating deformation in different orientation --- p.56 / Chapter 5. --- Enhancing performance --- p.59 / Chapter 5.1. --- Data communication --- p.60 / Chapter 5.1.1. --- Client-server model --- p.60 / Chapter 5.1.2. --- Internet protocol suite --- p.61 / Chapter 5.1.3. --- Berkeley socket --- p.61 / Chapter 5.1.4. --- Checksum problem --- p.62 / Chapter 5.2. --- Use of parallel tool --- p.62 / Chapter 5.2.1. --- Parallel code generation --- p.63 / Chapter 5.2.2. --- Optimising parallel code --- p.64 / Chapter 6. --- Implementation and Results --- p.65 / Chapter 6.1. --- Supporting functions --- p.65 / Chapter 6.1.1. --- Read file --- p.66 / Chapter 6.1.2. --- Keep shape --- p.67 / Chapter 6.1.3. --- Save as --- p.67 / Chapter 6.1.4. --- Exit --- p.67 / Chapter 6.2. --- Visual results --- p.67 / Chapter 6.3. --- An operation example --- p.75 / Chapter 6.4. --- Performance of parallel algorithm --- p.78 / Chapter 7. --- Conclusion and Future Work --- p.84 / Chapter 7.1. --- Conclusion --- p.84 / Chapter 7.2. --- Future Work --- p.84 / Reference --- p.86 / Appendix A Matrix Inversion --- p.89 / Appendix B Derivation of Equation 6.1 --- p.92 / Appendix C Derivation of (6.2) --- p.93

Ding, Ning. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 215-225). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.