Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

The introduction of the use of Tire Pressure Control Systems (TPCS) to improve the productivity of the Canadian trucking industry is gaining momentum. The imposition of seasonal load restrictions (SLR) on the thaw-weakened secondary roads interrupts the transportation of raw materials to processing facilities For the forestry industry in particular, this has very significant impacts on productivity and costs. FPInnovations-Feric Division (Feric) has investigated the potential for TPCS-equipped trucks to travel with full, legal loading during the SLR period without accelerating road wear and tear. The TPCS monitors and adjusts the inflation pressure of the trucks’ tires while driving and allows the operator to optimize the inflations for changes in loading, travel speed, or road quality encountered in the trip. This thesis describes an investigation to determine whether TPCS can be used to mitigate traffic generated damage to secondary roads and also reduce the need to implement load restrictions. The project involves a partnership with the Ontario Ministry of Transportation Ontario (MTO), Forest Engineering Research Institute of Canada (FERIC), Ontario Ministry of Natural Resources (MNR) and the Centre for Pavement and Transportation Technology (CPATT) located at the University of Waterloo. The thesis will describe the methodology, design, and instrumentation of the two test sites which are located in Dryden, Ontario and Chapleau, Ontario. In addition, repeated Portable Falling Weight Deflectometer (PFWD) testing is being carried out at these sites and the initial results of this examination and associated impacts of the environment and traffic on the road will be presented. This study also involves looking into the reliability of using the portable FWD, offering a lower cost alternative instead of the trailer mounted FWD to monitor pavement strength for the identification the SLR period. The use of innovative sensors and data collection techniques are proving to be very informative and are advancing pavement engineering knowledge. Moreover, the thesis is aimed at exploring the possibilities of achieving the current objectives of the government DOTs such as TPCS potential for addressing the timber industry in crisis, reduced road maintenance budgets, and global warming increasing road damage.

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

Linear springs with variable stiffnesses find some key roles in robotic applications. They are implemented into robotic devices for two main reasons, to increase energy efficiency of walking-running robots and prosthesis, and to get safe human-robot interaction at industrial robots. Being inspired from the human actuation system, a mathematical method to get mechanically adjustable linear springs is noted in the literature / antagonistically working two quadratic springs method. But the proposed solution requires two non-linear springs with quadratic spring characteristics and they are not readily available. Several solutions have been noted in the literature for the acquisition of such non-linear springs. At this thesis work, the solution is realized with a string wrapping around cam mechanism. Two different prototypes were designed and constructed and the second one was physically tested to validate the linear spring behavior. The results displayed good linear spring characteristics with different levels of adjustable spring stiffness. Beside the antagonistically working two quadratic springs method, three novel methods to get mechanically adjustable linear springs are introduced at this thesis. They are based on using hanging weights, an exponential characteristic spring and a linear translation spring respectively. The real prototypes were not manufactured but sample designs using string wrapping around cam mechanisms are made.

This thesis investigates the potential of wafer-scale integration (WSI) for the implementation of low-cost fine-grain parallel processing computer systems. As WSI is a relatively new subject, there was little work on which to base investigations. Indeed, most WSI architectures existed only as untried and sometimes vague proposals. Accordingly, the research strategy approached this problem by identifying a representative WSI structure and architecture on which to base investigations. An analysis of architectural proposals identified associative memory to be general purpose parallel processing component used in a wide range of WSI architectures. Furthermore, this analysis provided a set of WSI-level design requirements to evaluate the sustainability of different architectures as research vehicles. The WSI-ASP (WASP) device, which has a large associative memory as its main component is shown to meet these requirements and hence was chosen as the research vehicle. Consequently, this thesis addresses WSI potential through an in-depth investigation into the feasibility of implementing a large associative memory for the WASP device that meets the demanding technological constraints of WSI. Overall, the thesis concludes that WSI offers significant potential for the implementation of low-cost fine-grain parallel processing computer systems. However, due to the dual constraints of thermal management and the area required for the power distribution network, power density is a major design constraint in WSI. Indeed, it is shown that WSI power densities need to be an order of magnitude lower than VLSI power densities. The thesis demonstrates that for associative memories at least, VLSI designs are unsuited to implementation in WSI. Rather, it is shown that WSI circuits must be closely matched to the operational environment to assure suitable power densities. These circuits are significantly larger than their VLSI equivalents. Nonetheless, the thesis demonstrates that by concentrating on the most power intensive circuits, it is possible to achieve acceptable power densities with only a modest increase in area overheads.

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Cette thèse traite des aspects géométriques et d'intégrabilité associés aux modèles de matrices aléatoires. Son but est de présenter diverses applications des modèles de matrices aléatoires allant de la géométrie algébrique aux équations aux dérivées partielles des systèmes intégrables. Ces différentes applications permettent en particulier de montrer en quoi les modèles de matrices possèdent une grande richesse d'un point de vue mathématique. Ainsi, cette thèse abordera d'abord l'étude de la jonction de deux intervalles du support de la densité des valeurs propres au voisinage d'un point singulier. On montrera plus précisément en quoi ce régime limite particulier aboutit aux équations universelles de la hiérarchie de Painlevé II des systèmes intégrables. Ensuite, l'approche des polynômes (bi)-orthogonaux, introduite par Mehta pour le calcul des fonctions de partition, permettra d'énoncer des problèmes de Riemann-Hilbert et d'isomonodromies associés aux modèles de matrices, faisant ainsi le lien avec la théorie de Jimbo-Miwa-Ueno. On montrera en particulier que le cas des modèles à deux matrices hermitiens se transpose à un cas dégénéré de la théorie isomonodromique de Jimbo-Miwa-Ueno qui sera alors généralisé. La méthode des équations de boucles avec ses notions centrales de courbe spectrale et de développement topologique permettra quant à elle de faire le lien avec les invariants symplectiques de géométrie algébrique introduits récemment par Eynard et Orantin. Ce dernier point fera également l'objet d'une généralisation aux modèles de matrices non-hermitien (beta quelconque) ouvrant ainsi la voie à la ``géométrie algébrique quantique'' et à la généralisation de ces invariants symplectiques pour des courbes ``quantiques''. Enfin, une dernière partie sera consacrée aux liens étroits entre les modèles de matrices et les problèmes de combinatoire. En particulier, l'accent sera mis sur les aspects géométriques de la théorie des cordes topologiques avec la construction explicite d'un modèle de matrices aléatoires donnant le dénombrement des invariants de Gromov-Witten pour les variétés de Calabi-Yau toriques de dimension complexe trois utilisées en théorie des cordes topologiques. L'étendue des domaines abordés étant très vaste, l'objectif de la thèse est de présenter de façon la plus simple possible chacun des domaines mentionnés précédemment et d'analyser en quoi les modèles de matrices peuvent apporter une aide précieuse dans leur résolution. Le fil conducteur étant les modèles matriciels, chaque partie a été conçue pour être abordable pour un spécialiste des modèles de matrices ne connaissant pas forcément tous les domaines d'application présentés ici. / This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to ``quantum algebraic geometry'' and to the generalization of symplectic invariants to ``quantum curves''. Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold. Since the range of the applications encountered is large, we try to present every domain in a simple way and explain how random matrix models can bring new insights to those fields. The common element of the thesis being matrix models, each part has been written so that readers unfamiliar with the domains of application but familiar with matrix models should be able to understand it. / Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard.

This Thesis is concerned with three particular aspects of extended cosmic strings and domain walls in cosmology: their dynamics, gravitation and interaction with a black hole. In Chapter 3, we study the dynamics of an abelian-Higgs cosmic string. We find its equations of motion from an effective action and compare, for three test trajectories, the resulting motion with that observed in the Nambu-Gotō approximation. We also present a general argument showing that the corrected motion of any string is generically antirigid. We pursue the investigation of the dynamics of topological defects in Chapter 5, where we find (from integrability conditions rather than an effective action) the effective equations governing the motion of a gravitating curved domain wall. In Chapter 4 we investigate the spacetime of a gravitating domain wall in a theory with a general potential V(ɸ). We show that, depending on the gravitational coupling e of the scalar ɸ, all nontrivial solutions fall into two categories interpretable as describing respectively domain wall and false vacuum-de Sitter solutions. Wall solutions cannot exist beyond a value (^4)(_3)ɛmax, and vacuum-de Sitter solutions are unstable to decaying into wall solutions below ɛmax at ɛmax we observe a phase transition between the two types of solution. We finally specialize for the Goldstone and sine-Gordon potentials. In Chapter 6 we consider a Nielsen-Olesen vortex whose axis passes through the centre of an extremal Reissner-Nordstr0m black hole. We examine in particular the existence of piercing and expelled solutions (where the string respectively does and does not penetrate the black hole's horizon) and determine that while thin strings penetrate the horizon — and therefore can be genuinely called hair — thick strings are expelled; the two kinds of solution are separated by a phase transition.