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Rotor angle stability is the ability of the interconnected synchronous machines of a power system to remain in synchronism. This stability problem is concerned with the behavior of one or more synchronous machine after they have been perturbed. These perturbations can be small or large depending upon the type of disturbances considered. The work presented in this thesis is focused on the power system behavior when subjected to small disturbances. The ?small signal? disturbances are considered sufficiently small for the linearization of system equations to be permissible for the purpose of the analysis. The first step in the small signal stability studies is to obtain initial steady state conditions using load flow solutions. After establishing initial conditions, an unregulated mathematical model of the power system is formed. The mathematical model obtained is a set of nonlinear coupled first order differential equations. The method of small changes, called the perturbation method, is used to linearize these nonlinear differential equations. The equations are then written in a linear state space model form. The eigenvalues and the participation factors are obtained from the state matrix and the contribution of a particular machine in a particular mode or oscillations (or eigenvalue) can be examined for the small signal stability studies.

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La propagation des ondes ultrasonores à travers des cristaux phononiques CP à deux dimensions 2D constitués de diffuseurs solides dans des matrices solide et fluide est ici étudiée, ainsi que la caractérisation de ces milieux et leur application à l’imagerie acoustique. Les techniques expérimentales utilisées permettent une mesure complète des champs transmis à travers les cristaux. Les études sont menées dans des bandes fréquentielles autorisant les effets de réfraction négative indispensables à l’obtention d’une résolution inférieure à la limite de diffraction (super-résolution). De manière à compléter les analyses, différents outils théoriques sont exploités Décomposition en Ondes Planes et Eléments Finis, notamment.La première partie du document concerne la réalisation et la caractérisation de cristaux phononiques possédant des propriétés nécessaires à la réalisation de systèmes d’imagerie acoustique réfraction négative, contours équi-fréquences circulaires, accord d’indice, accord d’impédance. Cette première étude est menée sur un cristal à matrice solide, elle met en relief la possibilité de générer différents modes de Bloch au cours de la propagation. L’accord d’indice avec l’eau n’étant cependant pas obtenu, la seconde partie porte sur la réfraction négative et la focalisation des ondes à travers un CP à matrice fluide. Les propriétés du CP déterminées, le dernier chapitre s’attache à évaluer les performances des systèmes d’imagerie développés : dynamique et résolution. / This investigation deals with wave propagation in two dimensional phononic crystals (PC) made of solid scatterers embedded in solid or fluid matrices. After characterizing such composite materials, their application to acoustic imaging is brought to the forth. The ultrasonic techniques used in the experiments allow the complete measurement of the acoustic transmitted fields and the investigations concern frequency bandwidth able to exhibit negative refraction allowing Oie super-resolution effects. In order to complete the analysis, different theoretical tools are used: Plane Wave Expansion (PWE) and Finite Elements Method (FEM).The first part of this work deals with the realization and characterization of PC to be introduced into acoustic imaging devices (lenses) based on negative refraction. Special attention is given to characteristics such as circular equi-frequency contours, or index and impedance matching. However, during the acoustic wave propagation in a solid PC immersed in water, the presence of different Bloch modes contributing to the transmission of ultrasound is revealed and the index matching was not possible to obtain. Therefore the second part of the manuscript deals with negative refraction and waves focusing through a PC filled with a fluid. After determining the crystal properties, last chapter is devoted to the evaluation of the performances of acoustic imaging systems based on phononic lens.

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―Synaesthetic perception as a mode of being: Crossings of the sensuous and the poetic‖ seeks to disclose the harmonious interrelationship between synaesthetic modes of being, wildness, the poetic, and education. Merleau-Ponty (1962) and, more recently, David Abram (1997) have both proposed that synaesthetic perception, characterized by the overlapping and intertwining of the senses, is common to our direct, preconceptual experience in the life-world. Although we often disregard and discount synaesthetic capacities because they are non-linguistic and non-rational, they are an essential and rich characteristic of being human. The inquiry suggests that greater sensorial awareness that comes from awakening a trust in our sensuous embodied selves is promoted by being in the presence of the poetics of everyday circumambient wildness and in engagements with certain poetic writings which are grounded in the natural realm. Synaesthetic perception, a non-linguistic mode of knowing, must be accorded greater respect; it must be acknowledged and encouraged in all areas of education. Nature poetry, which is rooted in the texture of our ordinary sensuous experience amid wild others, can be an ally of education in this endeavour. The study proposes that it is through an awakening of the wisdom of the senses that we might recognize and value the importance of cultivating an ecopoetic rootedness in and reciprocity with the earth. The practice of a synaesthetic mode of being might bring about a positive transformative power, one that inspires a resistance to the encroachment of technocratic, dehumanizing controls on many aspects of our lives, and urges us to create a more wholesome, habitable earthhome for both human and nonhuman. This is a poetizing inquiry, an increasingly accepted form of qualitative arts-based inquiry, that is written in verse, and presented in a poetic dialogic format. This methodology, which is congruent with the central position of the poetic in the study, is informed by the writer‘s background in poetry and literature. Each of the four chapter-long stanzas takes up one of the main themes: synaesthetic perception as a mode of being, the pulse of childhood knowing, a poetic sense of dwelling, and the intertwining of the senses and the poetic. A distinctive feature of the dissertation is that each stanza is fashioned as a polyvocal performative dialogue: an intertwining of poems, poetic fragments and the voices of others with the researcher‘s own verse-voice. The inquiry is offered as an experimental work in process. The reader is invited to engage in the dialogues by bringing her/his own sensuous experiences in the wild and knowledge of poetry to the piece, thus becoming a co-creator of the inquiry. / Graduate

L’objectif de ce travail est d’établir des résultats de rigidité spectrale pour des familles C1 d’opérateurs (pseudo-)différentiels elliptiques auto-adjoints Pt, t ϵ [0, ẟ] sur une variété lisse compacte M sans bord de dimension n ≥ 2. Dans les deux premiers chapitres, on étudie des hamiltoniens proches d’un hamiltonien intégrable qui est non dégénéré au sens de Kolmogorov (Système KAM). On y construit une forme normale de Birkhoff au voisinage de chaque tore KAM ayant une fréquence diophantienne. Dans les chapitres 3 et 4 on établit une forme normale de Birkfoff quantique afin de construire des familles C1 de quasi-modes. Ces dernières permettent de relier les propriétés spectrales de Pt aux propriétés dynamiques des tores KAM. Les deux derniers chapitres proposent des applications en lien avec la transformée de Radon ainsi qu’une étude sur les surfaces de rotation. / The aim of this work is to obtain spectral rigidity results for C1 families of elliptic self-adjoint (pseudo-)differential operators Pt, t ϵ [0, ẟ], on a smooth closed manifold M of dimension n ≥ 2. In the first two chapters, we investigate Hamiltonians close to a given integrable Hamiltonian which is non-degenerate in the sense of Kolmogorov (KAM system). This allows us to obtain a Birkhoff normal form in a neighborhood of any KAM tori with a Diophantine frequency. In the third and fourth chapters, we construct a quantum Birkhoff normal form and obtain C1 families of quasimodes. Using the quasi-modes, we establish a connection between the spectral properties of Pt and the dynamical properties of the KAM tori. The last two chapters provide applications of these results to the Radon transform and the surfaces of revolution.

Future NASA plans to launch large space strucutres solicit the need for effective vibration control schemes which can solve the unique problems associated with unwanted residual vibration in flexible spacecraft. In this work, a unique method of input command shaping called impulse shaping is examined. A theoretical background is presented along with some insight into the methdos of calculating multiple mode sequences. The Middeck Active Control Experiment (MACE) is then described as the testbed for hardware experiments. These results are shown and some of the difficulties of dealing with nonlinearities are discussed. The paper is concluded with some conclusions about calculating and implementing impulse shaping in complex nonlinear systems.