Le but de cette thèse est d’obtenir des informations sur le spectre discret d’opérateurs non auto-adjoints définis par des perturbations relativement compactes d’opérateurs auto-adjoints. Ces opérateurs auto-adjoints sont choisis parmi les opérateurs classiques de mécanique quantique. Il s’agit des opérateurs de Dirac, de Klein-Gordon et le laplacien fractionnaire qui généralise l’opérateur de Schrödinger habituellement considéré pour de tels problèmes. La principale méthode utilisée ici relève d’un théorème d’analyse complexe donnant une condition de type Blaschke sur les zéros d’une fonction holomorphe du disque unité. Cette condition traduit lecomportement des valeurs propres de l’opérateur perturbé sous forme d’inégalités de type Lieb-Thirring. Une autre méthode venant d’analyse fonctionnelle a été employée pour obtenir de telles inégalités et les deux méthodes sont comparées entre elles. / The topic of this thesis concerns the discrete spectrum of non-selfadjoint operators defined by relatively compact perturbation of selfadjoint operators. These selfadjoint operators are choosen among classical operators of quantum mechanics. These areDirac operator, Klein-Gordon operator, and the fractional Laplacian who generalize the Schrödinger operator. The main method is based on a theorem of complex analysis which gives Blaschke-type condition on the zeros of a holomorphic function on the unit disc. This Blaschke condition gives the information on the behaviour of eigenvalues of the perturbed operator by mean of Lieb-Thirring-type inequalities. Another method using functional analysis is also used to obtain these kind of inequalities and both methods are compared to each other.

This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries. The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders with non-compact Riemann surfaces of finite area as cross sections. For these cylinders, we present a detailed investigation of the Bunke-Olbrich extension operator under the assumption that the cross section of the cylinder has one cusp. We establish the meromorphic continuation of the extension of Eisenstein series and incomplete theta series through the limit set. Furthermore, we derive explicit formulas for the residues of the extension operator in terms of boundary values of automorphic eigenfunctions. The motivation for the second paper comes from conformal geometry in Lorentzian signature. We prove the existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti de Sitter spaces.

The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and extension arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. Qualitatively, a good agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. Quantitatively, the results are compared with that of ANSYS finite element analysis software. The effect of crack size, crack position and beam thickness variation on SIF values and mode mixity is investigated.

Wireless communications have been an indispensable aspect of everyday life, and there is an increasing consumer demand for accessing several wireless communication technologies from a single, compact, mobile device. System-on-package (SOP) technology is an advanced packaging technology that has been proven to realize the convergence of multiple functions into miniaturized, high-performance systems to meet this demand. With the advancements in the SOP technology, the miniaturization of the front-end module has been achieved using embedded passives in multilayer packages. However, the integration of the antenna directly on the module package is still the barrier to achieve a fully-integrated, high-performance RF SOP system. The main reason for this missing link is that integrating the antenna on the package requires miniaturizing the antenna, which is a difficult task. The focus of this dissertation is to design high-performance antennas along with developing techniques for miniaturization and system-on-package (SOP) integration of these antennas to achieve fully-integrated SOP systems using advanced multilayer organic substrates and thin-film magneto-dielectric materials. The targeted spectrum for the antenna designs are 2.4/5 GHz WLAN/WiMAX and 60 GHz WPAN bands. Several novel antenna designs and configurations to integrate the antenna on the package along with the module are discussed in this dissertation. The advanced polymers used in this research are Liquid Crystalline Polymer (LCP), RXP, and thin-film magneto-dielectrics.

Καθώς η εξέλιξη της βιοϊατρικής επιστήμης και τεχνολογίας είναι συνεχής και ραγδαία, η έρευνα επικεντρώνεται τόσο στη βελτίωση των κλινικών τεχνικών όσο και στην ανάπτυξη νέων με κυριότερο σκοπό την ακριβέστερη και ασφαλέστερη διάγνωση και θεραπεία. Στην παρούσα διπλωματική εργασία, μελετάται η χρήση δύο περιοχών του φάσματος, των μικροκυματικών και των ηχητικών συχνοτήτων για διαγνωστικές λειτουργικές εφαρμογές εγκεφάλου. Παρόλο που η χρήση των υπερήχων έχει αξιοποιηθεί στην κλινική εφαρμογή, οι αναφορές για τη χρήση των ηχητικών κυμάτων στις βιοιατρικές εφαρμογές είναι περιορισμένες στη διεθνή βιβλιογραφία. Στην παρούσα διπλωματική εργασία μελετάται η ανάπτυξη ενός συστήματος για διαγνωστικές εφαρμογές εγκεφάλου στις ηχητικές συχνότητες. Στα δύο πρώτα κεφάλαια περιγράφονται οι βασικές αρχές που διέπουν την επιστήμη του ήχου (ακουστική) αλλά και οι φυσικές αρχές αλληλεπίδρασης των ηχητικών κυμάτων με τους βιολογικούς ιστούς (δημιουργία και εξέλιξη των φυσικών φαινομένων ανάκλασης, διάθλασης, μετάδοσης και απορρόφησης της ηχητικής δέσμης). Πιο συγκεκριμένα μοντελοποιείται και μελετάται θεωρητικά το πρόβλημα της αλληλεπίδρασης των ηχητικών κυμάτων με τον ανθρώπινο εγκέφαλο. Στο τρίτο κεφάλαιο παρατίθεται η θεωρητική ανάλυση και οι βασικές αρχές της προτεινόμενης μεθόδου για μέτρηση της εγκεφαλικής δραστηριότητας στις ηχητικές συχνότητες καθώς και τα βασικά στοιχεία της πρακτικής της υλοποίησης που περιλαμβάνουν ανάλυση του πιεζοηλεκτρικού φαινομένου και των αντίστοιχων μετατροπέων καθώς και το αντίστοιχο σύστημα λήψης ηχητικών σημάτων. Τα μικροκύματα έχουν χρησιμοποιηθεί σε πλήθος διαγνωστικών και θεραπευτικών τεχνικών τόσο σε επίπεδο έρευνας όσο και στην κλινική πράξη. Στην παρούσα εργασία πραγματοποιείται θεωρητική μελέτη δύο πολυσυχνοτικών κυρτών προσαρμόσιμων μικροταινιακών τυπωμένων κεραιών για χρήση τους με συστήματα ευαίσθητων δεκτών μικροκυματικής ραδιομετρίας. Στο κεφάλαιο 4 περιγράφονται η βασική τεχνολογία και οι βασικές αρχές λειτουργίας της παθητικής μεθόδου διάγνωσης με μικροκύματα, της μικροκυματικής ραδιομετρίας. Οι προτεινόμενες κυρτές κεραίες μοντελοποιήθηκαν (κεφάλαιο 5) και μελετήθηκαν με τη βοήθεια του ηλεκτρομαγνητικού προσομοιωτικού λογισμικού πακέτου HFSS που χρησιμοποιεί τη μέθοδο των πεπερασμένων στοιχείων. Παρουσιάζονται αναλυτικά οι ιδιότητες εστίασης των κεραιων αυτών σε δύο διαφορετικά μοντέλα κεφαλιού στος εύρος συχνοτήτων 2 – 3.5 GHz. / As the evolution in the field of biomedical science and technology is continuous, the research focuses mainly on the improvement of existent clinical techniques and the development of new ones, aiming to the most accurate and safe diagnosis and treatment. In the present thesis, the usage of two frequency bands is investigated, the microwave and sound frequencies for diagnostic functional brain applications. Despite the fact that ultrasounds have been utilized in clinical practice, the references regarding the application of sound frequencies in medical diagnosis are restrained in international literature. In the present thesis the development of a system for diagnostic brain applications operating at sound frequencies is studied. In the first two chapters the basic principles of acoustics and the physical principles of the interaction of sound waves with biological tissue (including physical phenomena of reflection, diffraction, transmission and absorption of sound) are described. More specifically, the problem of the interaction of sound waves with the human brain tissues is theoretically modeled and studied. In the third chapter theoretical analysis and basic principles of the suggested method are given together with the basic points of its practical implementation that include analysis of the piezoelectric phenomenon, the respective piezoelectric transducers and sound signal receiver. Microwaves have been used in many diagnostic and therapeutic techniques both at research level and in clinical practice. Herein, a theoretical study of two multi-frequency conformal microstrip patch antennas is performed, in order to use them in conjunction with sensitive microwave radiometry receivers. In chapter 4 the basic technology and the basic operation principles of the passive diagnostic method with microwaves (microwave radiometry) are described. The suggested conformal antennas are modeled (chapter 5) and studied using the electromagnetic simulation tool HFSS that implements the finite element method (FEM). The properties of these antennas and their focusing ability on specific brain areas are presented at 2 – 3.5 GHz in two different head models.

The continuous miniaturization of electronic systems using the three-dimensional (3D) integration technique has brought in new challenges for the computer-aided design and modeling of 3D integrated circuits (ICs) and systems. The major challenges for the modeling and analysis of 3D integrated systems mainly stem from four aspects: (a) the interaction between the electrical and thermal domains in an integrated system, (b) the increasing modeling complexity arising from 3D systems requires the development of multiscale techniques for the modeling and analysis of DC voltage drop, thermal gradients, and electromagnetic behaviors, (c) efficient modeling of microfluidic cooling, and (d) the demand of performing fast thermal simulation with varying design parameters. Addressing these challenges for the electrical/thermal modeling and analysis of 3D systems necessitates the development of novel numerical modeling methods. This dissertation mainly focuses on developing efficient electrical and thermal numerical modeling and co-simulation methods for 3D integrated systems. The developed numerical methods can be classified into three categories. The first category aims to investigate the interaction between electrical and thermal characteristics for power delivery networks (PDNs) in steady state and the thermal effect on characteristics of through-silicon via (TSV) arrays at high frequencies. The steady-state electrical-thermal interaction for PDNs is addressed by developing a voltage drop-thermal co-simulation method while the thermal effect on TSV characteristics is studied by proposing a thermal-electrical analysis approach for TSV arrays. The second category of numerical methods focuses on developing multiscale modeling approaches for the voltage drop and thermal analysis. A multiscale modeling method based on the finite-element non-conformal domain decomposition technique has been developed for the voltage drop and thermal analysis of 3D systems. The proposed method allows the modeling of a 3D multiscale system using independent mesh grids in sub-domains. As a result, the system unknowns can be greatly reduced. In addition, to improve the simulation efficiency, the cascadic multigrid solving approach has been adopted for the voltage drop-thermal co-simulation with a large number of unknowns. The focus of the last category is to develop fast thermal simulation methods using compact models and model order reduction (MOR). To overcome the computational cost using the computational fluid dynamics simulation, a finite-volume compact thermal model has been developed for the microchannel-based fluidic cooling. This compact thermal model enables the fast thermal simulation of 3D ICs with a large number of microchannels for early-stage design. In addition, a system-level thermal modeling method using domain decomposition and model order reduction is developed for both the steady-state and transient thermal analysis. The proposed approach can efficiently support thermal modeling with varying design parameters without using parameterized MOR techniques.

Dumb holes (also known as acoustic black holes) are fluid flows which include an "acoustic horizon:" a surface, analogous to a gravitational horizon, beyond which sound may pass but never classically return. Soundwaves in these flows will therefore experience "effective geometries" which are identical to black hole spacetimes up to a conformal factor. By adjusting the parameters of the fluid flow, it is possible to create an effective geometry which is conformal to the Anti-de Sitter black hole spacetime- a geometry which has recieved a great deal of attention in recent years due to its conjectured holographic duality to Conformal Field Theories. While we would not expect an acoustic analogue of the AdS-CFT correspondence to exist, this dumb hole provides a means, at least in principle, of experimentally testing the theoretical properties of the AdS spacetime. In particular, I have calculated the quasinormal mode spectrum of this acoustic geometry. / Graduate / 0986 / 0753 / jpbabb@yahoo.ca

The Archimedean spiral antenna is well-known for its broadband characteristics with circular polarization and has been investigated for several decades. Since their development in the late 1950's, establishing an analytical expression for the characteristics of spiral antenna has remained somewhat elusive. This has been studied qualitatively and evaluated using numerical and experimental techniques with some success, but many of these methods are not convenient in the design process since they do not impart any physical insight into the effect each design parameter has on the overall operation of the spiral antenna. This work examines the operation of spiral antennas and obtains a closed-form analytical solution by conformal mapping and transmission line model with high precision in a wide frequency band. Based on the analysis of spiral antenna, we propose two novel design processes for the stripline-fed Archimedean spiral antenna. This includes a stripline feed network integrated into one of the spiral arms and a broadband tapered impedance transformer that is conformal to the spiral topology for impedance matching the nominally-high input impedance of the spiral. A Dyson-style balun located at the center facilitates the transition between guided stripline and radiating spiral modes. Measured and simulated results for a probe-fed design operating from 2 GHz to over 20 GHz are in excellent agreements to illustrate the synthesis and performance of a demonstration antenna. The research in this work also provides the possibility to achieve conformal integration and planar structural multi-functionality for an Unmanned Air Vehicle (UAV) with band coverage across HF, UHF, and VHF. The proposed conformal mapping analysis can also be applied on periodic coplanar waveguides for integrated circuit applications.

Les textures directionnelles forment la classe particulière des images texturées représentant des hypersurfaces (lignes dermiques, fibres de matériaux, horizons sismiques, etc.). Pour ce type de textures, la reconstruction d'hypersurfaces permet ainsi d'en décrire la géométrie et la structure. À partir du calcul préalable du champ d'orientation, des reconstructions peuvent être obtenues au moyen de la minimisation d'une équation aux dérivées partielles sous contraintes, linéarisée et résolue itérativement de manière optimale dans le domaine de Fourier.Dans ce travail, les reconstructions d'hypersurfaces sont considérées comme un moyen de description à la fois amont et aval de la géométrie des textures directionnelles. Dans une démarche amont, la reconstruction de faisceaux locaux et denses d'hypersurfaces conduit à un modèle de transformation d'espace permettant de déplier localement la texture ou son champ de gradient et d'améliorer l'estimation du champ d'orientation par rapport au classique tenseur de structure. Dans une démarche aval, des reconstructions d'hypersurfaces effectuées sur des supports polygonaux quelconques, isolés ou imbriqués, permettent d'obtenir des reconstructions plus pertinentes que par les méthodes existantes. Les démarches proposées mettent en œuvre des chaînes de transformations d'espace conformes (transformation de Schwarz-Christoffel, de Möbius, etc.) afin de respecter les contraintes et d'accéder à des schémas de résolution rapide. / Directional textures are the particular class of textured images representing hypersurfaces (dermal lines, material fibers, seismic horizons, etc.). For this type of textures, the reconstruction of hypersurfaces describes their geometry and structure. From the preliminary estimation of the orientation field, reconstructions can be obtained by means of the minimization of a partial differential equation under constraints, linearized and iteratively resolved in the Fourier domain.In this work, the reconstructions of hypersurfaces are considered as means of description both upstream and downstream of the geometry of the directional textures. In an upstream approach, the reconstruction of local and dense streams of hypersurfaces leads to a spatial transformation model to locally unfold the texture or its gradient field and to improve the estimation of the orientation field compared with the classic tensor structure. In a downstream approach, reconstructions of hypersurfaces carried out on any polygonal supports, either isolated or imbricated, lead to more accurate reconstructions than existing methods. The proposed approaches implement chains of conformal space transformations (transformation of Schwarz-Christoffel, Möbius, etc.) in order to respect the constraints and to access fast PDE solution schemes.

In this work, we make a brief review of the Conformal Field Theory in two dimensions,in order to understand some basic definitions in the study of the Liouville Field Theory, which has many application in theoretical physics like string theory, general relativity and supersymmetric gauge field theories. In particular, we focus on the analytic continuation of the Liouville Field Theory, context in which an interesting relation with the Chern-Simons Theory arises as an extension of its well-known relation with the Wess-Zumino-Witten model. Thus, calculating correlation functions by using the complex solutions of the Liouville Theory will be crucial aim in this work in order to test the consistency of this analytic continuation. We will consider as an application the time-like version of the Liouville Theory, which has several applications in holographic quantum cosmology and in studying tachyon condensates. Finally, we calculate the three-point function for the Wess-Zumino-Witten model for the standard Kac-Moody level k > 2 and the particular case 0 < k < 2, the latter has an interpretation in time-dependent scenarios for string theory. Here we will find an analogue relation we find by comparing the correlation function of the time-like and space-like Liouville Field Theory. / Neste trabalho, nós fazemos uma breve revisão da Teoria de Campo Conforme em duas dimensões, a fim de entender algumas denições básicas do estudo da Teoria de Campo de Liouville, que tem muitas aplicações em física teórica como a teoria das cordas, a relatividade geral e teorias de campo de calibre supersimétricas. Em particular, vamos nos concentrar sobre a continuação analítica da Teoria de Campo de Liouville, contexto no qual uma interessante relação com a Teoria de Chern-Simons surge como uma extensão de sua relação conhecida com o modelo de Wess-Zumino-Witten. Assim, o cálculo das funções de correlação usando as soluções complexas da Teoria Liouville será o objectivo fundamental neste trabalho, a fim de testar a consistência da continuação analítica. Vamos considerar como uma aplicação a versão time-like da Teoria de Liouville, que tem várias aplicações em cosmologia quântica holográfica e no estudo de condensados de tachyon. Finalmente, calculamos a função de três pontos para o modelo de Wess-Zumino-Witten no nível de Kac-Moody k > 2 e o caso particular 0 < k < 2, este último tem uma interpretação em cenários dependentes do tempo para a teoria das cordas. Aqui nós vamos encontrar uma relação análoga ao que temos para a função de correlação do space-like e time-like na Teoria de Campo de Liouville.