Dans les applications, on rencontre fréquemment des structures minces de géométrie<br />complexe qui nécessitent l'utilisation de maillages surfaciques comportant des éléments<br />triangulaires. Il faut donc trouver des éléments finis triangulaires de coque qui<br />soient robustes vis-à-vis du verrouillage numérique, mais aussi au défaut de consistance.<br />Nous avons formulé un test numérique qui permet de détecter le verrouillage<br />membranaire, et également l'existence de modes parasites de membrane. L'élément<br />MITC6a (Bathe et Lee) apparaî t comme le meilleur élément à six noeuds, mais il<br />exhibe des modes parasites de membrane qui peuvent considérablement détériorer la<br />solution numérique. Nous proposons une technique de filtrage qui consiste à ajouter<br />un terme de stabilisation de cisaillement non réduit et nous avons défini l'élément<br />MITC6rs avec une interpolation plus riche pour le cisaillement. Après une évaluation<br />numérique détaillée, nous recommandons l'usage de l'élément MITC6a stabilisé.

Ce mémoire est dédié à l'étude de la stabilité des systèmes à retards via les méthodes temporelles de Lyapunov. Au-delà des formes usuelles de stabilité, nous étudions quatre autres propriétés : stabilité entrée-sortie, stabilité en temps fini, stabilité entrée-état et stabilité pratique. Après une large introduction, le second chapitre se focalise sur la stabilité entrée-sortie des systèmes linéaires à retards variables par une approche originale se basant sur des fonctionnelles de Lyapunov-Krasovskii. La forme descripteur est utilisée pour obtenir des conditions en termes d'inégalités matricielles. Dans le troisième chapitre, la stabilité en temps fini caractérise un équilibre asymptotiquement stable qui, de plus, est atteint en temps fini. Plusieurs résultats sont proposés concernant la stabilité et la stabilisation sur des systèmes non-linéaires et linéaires respectivement. Les premiers exemples de systèmes stables en temps fini sont donnés. Ensuite, la stabilité entrée-état est analysée dans le cadre des systèmes non linéaires soumis à des perturbations larges. Cette nouvelle notion est étendue au cas des systèmes retardés et plusieurs résultats sont proposés via des fonctionnelles de Krasovskii. Le dernier chapitre se consacre à l'étude de la stabilité pratique appliquée au problème de la réticence dans la commande par modes glissants. En présence de retards, cette technique de type “grands gains” peut provoquer une oscillation importante sur l'état du système — notamment lorsque la dynamique des actionneurs ne peut être négligée. Le phénomène de réticence est analysé formellement et de nombreuses simulations permettent de confirmer les avantages de la méthode proposée.

Le travail de thèse présenté dans ce manuscrit a consisté à explorer les possibilités d'associations d'émetteurs compatibles silicium efficaces à température ambiante avec des cavités à modes de galerie intégrées sur silicium.<br />La première partie de l'étude concerne le développement de matériau émetteur utilisant l'erbium. Différentes matrices sont utilisées afin d'aboutir à une émission efficace à 1,54 µm à température ambiante : silice, silicium sur isolant (SOI) et silice non-stoechiométrique (SRO : nanoclusters de silicium en matrice de silice). Les émetteurs retenus pour l'étude, le silicium sur isolant et l'erbium associé au SRO, sont ensuite intégrés à des cavités de type microdisque par des procédés de lithographie et gravure dérivés de ceux utilisés en microélectronique. Dans le cas des disques à base de silice, un recuit au laser CO2 permet de s'affranchir des rugosités résiduelles par fusion des bords du disque conduisant à la formation de tores.<br />Les structures obtenues sont ensuite étudiées au moyen d'un banc de photoluminescence spécifique développé au laboratoire tenant compte des caractéristiques de l'émission dans les modes de galerie et permettant leur évaluation fine. Le couplage de l'émission du silicium et du SRO dopé erbium à des modes de galerie possédant des facteurs de qualité de plusieurs milliers (jusqu'à Q ≈ 90000) est ainsi observé à température ambiante. Ces résultats, associés à la possibilité de coupler les cavités à des guides démontrée pour les disques SOI, ouvrent des perspectives particulièrement intéressantes du point de vue de la recherche appliquée (sources intégrées) comme de la recherche fondamentale (effets CQED sur les terres rares).

In the paper we study sequences of random functions which are defined by some interpolation procedures for a given random function. We investigate the problem in what sense and under which conditions the sequences converge to the prescribed random function. Sufficient conditions for convergence of moment characteristics, of finite dimensional distributions and for weak convergence of distributions in spaces of continuous functions are given. The treatment of such questions is stimulated by an investigation of Monte Carlo simulation procedures for certain classes of random functions. In an appendix basic facts concerning weak convergence of probability measures in metric spaces are summarized.

This thesis is about detection of cracks in single-crystalline silicon wafers by using a vibration method in the form of an impact test. The goal to detect cracks from vibration measurements introduced by striking the silicon wafer with an impact hammer. Such a method would reduce costs in the production of solar cells. It is an inexpensive, relatively simple method which if commercialized could be used as an efficient in-line production quality test. A hammer is used as the actuator and a microphone as the response sensor. A signal analyzer is used to collect the data and to compute frequency response. Parameters of interest are audible natural frequencies, peak magnitudes, damping ratio and coherence. The data reveals that there are differences in frequency between the cracked silicon wafers and the non-cracked silicon wafers. The resonant peaks in the defective wafers were not as sharp (i.e., lightly damped) and occurred at lower frequencies (i.e., lower stiffness) with a lower magnitude and a higher damping ratio. These differences could be used to detect damaged product in a solar cell production line.

It is essential to understand natural fracture systems embedded in shale-gas reservoirs and the stress fields that influence how induced fractures form in targeted shale units. Multicomponent seismic technology and elastic seismic stratigraphy allow geologic formations to be better images through analysis of different S-wave modes as well as the P-wave mode. Significant amounts of energy produced by P-wave sources radiate through the Earth as downgoing SV-wave energy. A vertical-force source is an effective source for direct SV radiation and provides a pure shear-wave mode (SV-SV) that should reveal crucial information about geologic surfaces located in anisotropic media. SV-SV shear wave modes should carry important information about petrophysical characteristics of hydrocarbon systems that cannot be obtained using other elastic-wave modes. Regardless of the difficulties of extracting good-quality SV-SV signal, direct shear waves as well as direct P and converted S energy should be accounted for in 3C seismic studies. Acquisition of full-azimuth seismic data and sampling data at small intervals over long offsets are required for detailed anisotropy analysis. If 3C3D data can be acquired with improved signal-to-noise ratio, more uniform illumination of targets, increased lateral resolution, more accurate amplitude attributes, and better multiple attenuation, such data will have strong interest by the industry. The objectives of this research are: (1) determine the feasibility of extracting direct SV-SV common-mid-point sections from 3-C seismic surveys, (2) improve the exploration for stratigraphic traps by developing systematic relationship between petrophysical properties and combinations of P and S wave modes, (3) create compelling examples illustrating how hydrocarbon-bearing reservoirs in low-permeable rocks (particularly anisotropic shale formations) can be better characterized using different S-wave modes (P-SV, SV-SV) in addition to the conventional P-P modes, and (4) analyze P and S radiation patterns produced by a variety of seismic sources. The research done in this study has contributed to understanding the physics involved in direct-S radiation from vertical-force source stations. A U.S. Patent issued to the Board of Regents of the University of Texas System now protects the intellectual property the Exploration Geophysics Laboratory has developed related to S-wave generation by vertical-force sources. The University’s Office of Technology Commercialization is actively engaged in commercializing this new S-wave reflection seismic technology on behalf of the Board of Regents. / text

Using innovative materials or devices in techniques for strengthening or repair of RC concrete members may provide interesting alternatives for structural engineers. Laboratory tests were conducted on full scale reinforced concrete columns and a masonry wall that suffered severe damage. Carbon Fiber Reinforced Polymer - CFRP sheets and anchors were used to improve shear capacity or ductility elements. CFRP jacket were installed on column hinge regions while diagonal ties (tension braces) were used on the masonry wall. Mechanical splices were used in columns where concrete crushed and bars buckled by replacing the buckled bars and providing continuity to the longitudinal reinforcement. It was found that performance of the retrofitted members was comparable to that using conventional techniques and the performance was generally better than certain “fast” retrofit procedures reported in the literature. The choice of technique depends on the degree of damage, the cost of replacement, and performance required. Having the results of cyclic load tests of rehabilitated concrete members, envelope or backbone curves were obtained following the ASCE41-07 and proposed ASCE41-13 procedures. The backbone curves were used to develop behavioral models that can be used in the analysis and design of those types of concrete members and retrofit procedures. The inclusion of the behavioral models into current Performance Based Seismic Design procedures for strengthening of existing or repaired damaged buildings is proposed. / text

Optical whispering-gallery mode (WGM) cavities, which exhibit extraordinary spatial and temporal confinement of light, are one of the leading transducers for examining molecular recognition at low particle counts. With the advent of hybrid photonic-plasmonic and increasingly sophisticated forms of these resonators, the importance of supporting numerical methods has correspondingly become evident. In response, we adopt a full-vector finite difference approximation in order to solve for WGM's in terms of their field distributions, resonant wavelengths, and quality factors in the context of naturally discontinuous permittivity structure. A segmented Taylor series and alignment/rotation operator are utilized at such singularities in conjunction with arbitrarily spaced grid points. Simulations for microtoroids, with and without dielectric nanobeads, and plasmonic microdisks are demonstrated for short computation times and shown to be in agreement with data in the literature. Constricted surface plasmon polariton (SPP) WGM's are also featured within this document. The module of this thesis is devised as a keystone for composite WGM models that may guide experiments in the field. / Graduate

Modern mobile devices incorporate several transmit and receive antennas in highly constrained volumes. As miniaturized antennas impinge upon fundamental physical limits on efficiency, new design approaches are required to support ever-smaller devices with more varied and robust communication performance. We take an unconventional design approach in which an arbitrary metallic structure and its components can be modified to act as efficient radiators. Using eigenmode analysis and the theory of characteristic modes (TCM), we develop algorithms that allow for effective integration of antennas with mechanical structures and enable structure reuse, helping meet stringent space and weight constraints without sacrificing electromagnetic performance. We derive TCM-based objectives for effective exploration of the design space in the electromagnetic (EM) domain. The procedure includes a feed placement technique that identifies viable excitation points on the structure without running full EM analysis. In addition to computational advantages, this provides a point of comparison among a variety of antenna shapes. Empirical evaluation shows that the estimates of radiated power from TCM can effectively guide optimization toward structures with improved radiating properties. Automated feed placement increases the proportion of good-quality designs among the explored candidates by consistently selecting the most promising feed positions. The ability of the TCM-based algorithm to direct the search is further validated on two real-world applications: integration of a GPS antenna with the frame of a mobile phone and integration of an S-band antenna with the frame of a small spacecraft. To the best of our knowledge, this is the first work that applies TCM to automated optimization of antennas. We investigate how to leverage domain-specific methods and solution representations in the coupled optimization of antennas. We develop a novel multiobjective optimization framework based on local search in each domain. In this procedure, the local optima in each objective are obtained and modified to create a new population of candidate designs. On a number of benchmark problems, the proposed technique is competitive with leading multi-objective algorithms: while it finds a less uniform distribution along the Pareto front, it shows better performance in locating solutions at the boundaries of the tradeoff curve. The local search algorithm is successfully applied to topology optimization of an antenna for a CubeSat, a small low-cost satellite platform.

The expectation that light waves are the only way to gather information about the distant universe dominated scientific thought, without serious alternative, until Einstein’s 1916 proposal that gravitational waves are generated by the dynamics of massive objects. Now, after nearly a century of speculation, theoretical development, observational support, and finally, tremendous experimental preparation, there are good reasons to believe that we will soon directly detect gravitational waves. One of the most important of these good reasons is the fact that matched filtering enables us to dig gravitational wave signals out of noisy data, if we have prior information about the signal’s morphology. Thus, at the interface of Numerical Relativity simulation, and data analysis for experiment, there is a central effort to model likely gravitational wave signals. In this context, I present my contributions to the modeling of Gravitational Ringdown (Kerr Quasinormal Modes). Specifically by ap- propriately interfacing black hole perturbation theory with Numerical Relativity, I present the first robust models for Quasinormal Mode excitation. I present the first systematic de- scription of Quasinormal Mode overtones in simulated binary black hole mergers. I present the first systematic description of nonlinear Quasinormal Mode excitation in simulated bi- nary black hole mergers. Lastly, it is suggested that by analyzing the phase of black hole Quasinormal Modes, we may learn information about the black hole’s motion with respect to the line of sight. Moreover, I present ongoing work at the intersection of gravitational wave modeling and machine learning. This work shows promise for the automated and near optimal placement of Numerical Relativity simulations concurrent with the near optimal linear modeling of gravitational output.