L'instabilité du drapeau et la nage des poissons sont deux des problèmes d'interaction entièrement couplés fluide-structure. Ils peuvent être considérés comme l’ interaction entre la structure déformable (plaque) et un écoulement de grand nombre de Reynolds. Si la plaque est allongée (petit rapport d’aspect), la théorie du corps élancé (Lighthill 1960) applique pour calculer la force de pression exercée sur la plaque par le fluide. Alors que pour une plaque avec une très grande envergure (grand rapport d’aspect), la théorie bidimensionnelle de l’aile instationnaire (Wu 1961) est utilisée pour modéliser la dynamique de l'écoulement. Cependant, aucun de ces deux modèles donne la force de pression précise agissant sur une plaque avec un rapport d'aspect intermédiaire. Généralement, l'écoulement entourant peut être modélisé par l'équation de Laplace (en termes de potentiel de vitesse) avec une condition aux limites de Neumann. Par la méthode de Green, le problème se réduit à une équation intégrale de surface portante (mathématiquement appelée l’équation intégrale de Fredholm de première espèce avec un noyau singulier). Le saut de potentiel peut être trouvé en inversant l'équation de surface portante, et la distribution de saut de pression peut être par conséquent obtenue en appliquant l'équation de Bernoulli instationnaire.Dans cette thèse, l'équation de surface portante est résolue numériquement par la méthode de surface portante à fréquence fixée. La méthode numérique proposée est validée par les modèles théoriques (théorie du corps élancé et 2D théorie de l’aile instationnaire). L'équation de surface portante est également résolue analytiquement dans la limite du petit rapport d’aspect, par la méthode de raccordement de développement asymptotique (Matched Asymptotic Expansion) ou encore la technique asymptotique proposée. La méthode analytique proposée donne la force de pression plus précise sur une surface avec un rapport d’aspect intermédiaire (de 0 à 0.5), par rapport à la théorie du corps élancé. Cela en fait est un bon candidat pour l'optimisation et le contrôle. Le modèle de fluide analytique proposée est ensuite couplé avec l'équation d’Euler-Bernoulli de poutre pour étudier l’ instabilité du drapeau. Nous étudions l'influence du rapport d'aspect et le ratio de masse sur la vitesse d'écoulement critique. Les résultats montrent de très bons accords à ceux de Eloy et al. 2007. Le modèle de fluide d'analyse proposée est également appliqué au problème de la nage des poissons. Une nouvelle formule de la moyenne de poussée est proposée, et une analyse qualitative sur la morphologie du poisson est effectuée. De ces études, nous pouvons conclure que le modèle proposé fluide peut être considéré comme la théorie du corps élancé corrigée pour l'effet de rapport d'aspect. Ainsi, l'écoulement autour d'une surface de rapport d’aspect intermédiaire peut être inclus par ce modèle. / The flapping flag instability and fish swimming are two fully-coupled fluid-structure interaction problems. They can be considered as the interaction between a deformable structure (plate) and a high Reynolds number flow. If the plate is elongated (small aspect ratio), Slender-body theory (Lighthill 1960) applies to calculate the pressure force exerted on the plate by the surrounding flow. While for a plate with very large span (large aspect ratio), 2D unsteady airfoil theory (Wu 1961) is used to model the dynamics of the surrounding flow. However, none of these two models gives accurate pressure force acting on a plate with intermediate aspect ratio. Generally, the surrounding flow can be modeled by the Laplace equation (in terms of velocity potential) with a Neumann boundary condition. By means of Green representation theorem, the problem reduces to a lifting-surface integral equation (mathematically called Fredholm integral equation of first kind with a singular kernel). The potential jump can be found by inverting this lifting-surface equation, and the pressure jump distribution can be therefore obtained by applying unsteady Bernoulli equation. In this thesis, the lifting-surface equation is solved numerically through the fixed-frequency lifting-surface method. The proposed numerical method is validated by the theoretical models (Slender-body theory and 2D unsteady airfoil theory). The lifting-surface equation is also solved analytically in the limit of small aspect ratio, by the Matched Asymptotic Expansion method or alternatively the proposed asymptotic technique. The proposed analytical method gives more accurate pressure force on a surface with intermediate aspect ratio (ranging from 0 to 0.5), comparing to Slender-body theory. This makes it a good candidate for the optimization and control. The proposed analytical fluid model is then coupled with Euler-Bernoulli beam equation to study the flapping flag instability. We investigate the influence of plate aspect ratio and mass ratio on the critical flow velocity. The results show very good agreements to those of Eloy et al. 2007. The proposed analytical fluid model is also applied to the fish swimming problem. A new formula of mean thrust is proposed, and a qualitative analysis on the fish morphology is performed. From these studies, we can conclude that the proposed fluid model can viewed as Slender-body theory corrected for the aspect ratio effect. Thus, the flow surrounding a lifting-surface with intermediate aspect ratio can be included by this model

The problem of rough surface scattering and propagation over rough terrain in ducting environments has been receiving considerable attention in the literature. One popular method of modeling this problem is the parabolic wave equation (PWE) method. In this method, the Helmholtz wave equation is replaced by a PWE under the assumption of predominant forward propagation and scattering. The resulting PWE subjected to the appropriate boundary condition(s) is then solved, given an initial field distribution, using marching techniques such as the split-step Fourier algorithm. As is obvious from the assumption on which it is based, the accuracy of the PWE approximation deteriorates in situations involving appreciable scattering away from the near-forward direction, i.e. when the terrain under consideration is considerably rough. The backscattered field is neglected in all PWE-based models. An alternative and more rigorous method for modeling the problem under consideration is the boundary integral equation (BIE) method, which is formulated in two steps. The first step involves setting up an integral equation (the magnetic field integral equation, MFIE, or the electric field integral equation EFIE) governing currents induced on the rough surface by the incident field and solving for these currents numerically. The resulting currents are then used in the appropriate radiation integrals to calculate the field scattered by the surface everywhere in space. The BIE method accounts for all orders of multiple scattering on the rough surface and predicts the scattered field in all directions in space (including the backscattering direction) in an exact manner. In homogeneous media, the implementation of the BIE approach is straightforward since the kernel (Green's function or its normal derivative) which appears in the integral equation and the radiation integrals is well known. This is not the case, however, in inhomogeneous media (ducting environments) where the Green's function is not readily known. Due to this fact, there has been no attempt, up to our knowledge, at using the BIE (except under the parabolic approximation) to model the problem under consideration prior to the work presented in this thesis. In this thesis, a closed-form approximation of the Green's function for a two-dimensional ducting environment formed by the presence of a linear-square refractivity profile is derived using the asymptotic methods of stationary phase and steepest descents. This Green's function is then modified to more closely model the one associated with a physical ducting medium, in which the refractivity profile decreases up to a certain height, beyond which it becomes constant. This modified Green's function is then used in the BIE approach to study low grazing angle (LGA) propagation over rough surfaces in the aforementioned ducting environment. The numerical method used to solve the MFIE governing the surface currents is MOMI, which is a very robust and efficient method that does not require matrix storage or inversion. The proposed method is meant as a benchmark for people studying forward propagation over rough surfaces using the parabolic wave equation (PWE). Rough surface scattering results obtained via the PWE/split-step approach are compared to those obtained via the BIE/MOMI approach in ducting environments. These comparisons clearly show the shortcomings of the PWE/split-step approach. / Ph. D.

abstract: To establish reliable wireless communication links it is critical to devise schemes to mitigate the effects of the fading channel. In this regard, this dissertation analyzes two types of systems: point-to-point, and multiuser systems. For point-to-point systems with multiple antennas, switch and stay diversity combining offers a substantial complexity reduction for a modest loss in performance as compared to systems that implement selection diversity. For the first time, the design and performance of space-time coded multiple antenna systems that employ switch and stay combining at the receiver is considered. Novel switching algorithms are proposed and upper bounds on the pairwise error probability are derived for different assumptions on channel availability at the receiver. It is proved that full spatial diversity is achieved when the optimal switching threshold is used. Power distribution between training and data codewords is optimized to minimize the loss suffered due to channel estimation error. Further, code design criteria are developed for differential systems. Also, for the special case of two transmit antennas, new codes are designed for the differential scheme. These proposed codes are shown to perform significantly better than existing codes. For multiuser systems, unlike the models analyzed in literature, multiuser diversity is studied when the number of users in the system is random. The error rate is proved to be a completely monotone function of the number of users, while the throughput is shown to have a completely monotone derivative. Using this it is shown that randomization of the number of users always leads to deterioration of performance. Further, using Laplace transform ordering of random variables, a method for comparison of system performance for different user distributions is provided. For Poisson users, the error rates of the fixed and random number of users are shown to asymptotically approach each other for large average number of users. In contrast, for a finite average number of users and high SNR, it is found that randomization of the number of users deteriorates performance significantly. / Dissertation/Thesis / Ph.D. Electrical Engineering 2010