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Small-amplitude, high-frequency (ultrasound) forcing of fluid/particle systems is being used in a number of applications associated with non-destructive fluid mixing and the movement/manipulation of particles in suspension. Of most importance in this context are the second-order, steady, effects arising from the nonlinear interaction of a leading-order oscillatory field with itself. In this thesis we consider some of these steady effects in both incompressible and compressible fluids. We first consider the axisymmetric steady streaming generated in an incompressible, viscous fluid contained between two (radially) infinite parallel plates, each oscillating in a direction normal to its own plane. In the limit of small-amplitude, high-frequency oscillations, we show that the steady-streaming flow in the fluid bulk is driven by thin streaming sublayers at the plates, at which the normal velocity is zero and the radial velocity varies linearly with distance from the axis of rotational symmetry. Effectively, in the bulk flow, the bounding plates appear as (no-slip) impermeable walls that stretch radially. This bulk-flow problem is extended to allow for the analogous steady flow of two immiscible, incompressible, viscous fluids, each undergoing a radial-stretching motion appropriate to high-frequency steady streaming. For a flat interface between the fluids, a self-similar solution reduces the Navier--Stokes equations to a nonlinear boundary-value problem, the solution of which exhibits an interesting structure in the limit of large Reynolds number. In this limit, solutions can be found using matched asymptotic expansions, but the location of the interface between the fluids can only be determined if terms that are exponentially small in the Reynolds number are included. It is shown that for fluids of almost-equal densities, exponentially-small differences can have a leading-order effect on the observed flow. The second part of the thesis is concerned with the (steady) acoustic radiation force on a rigid sphere submerged in a compressible, inviscid fluid, when the wavelength of the incident acoustic field is large compared to the radius of the sphere. In this limit, a matched asymptotic expansion method is used to derive an expression for the acoustic radiation force, on both fixed and free rigid spheres, due to a range of incident fields. For incident acoustic fields that are appropriate to planar and circular waveguides/channels, expressions are derived for the scattered field and the radiation force on a rigid sphere in the long-wavelength limit. Fixed and free spheres located both on and off the axis of symmetry of these incident fields are considered. This is an extension to the current literature, in which numerical methods are used to examine the scattering from spheres in an off-axis position, and problems are restricted to the consideration of fixed spheres only. It is shown that there are stable and unstable positions within the waveguide where any off-axis acoustic radiation force vanishes, leaving only an along-channel component. For free spheres, these positions are shown to be dependent on the relative particle density and it is suggested that this may allow for a mechanism to sort such small particles radially in a circular waveguide, if secondary scattering effects are neglected.

Le sujet de la thèse s’inscrit dans le cadre du développement de modèles pour la simulation du contrôle non-destructif (CND) par ultrasons. L'objectif à long terme est la mise au point, par une méthode de rayons, d’un outil complet de simulation des échos issus de la géométrie (surfaces d’entrée, de fond…) ou des structures internes des pièces inspectées. La thèse vise plus précisément à intégrer le phénomène de diffraction par les dièdres à un modèle existant dérivant de l’acoustique géométrique et qui prend uniquement en compte les réflexions sur les faces.Pour cela, la méthode dite des fonctions spectrales, développée initialement pour le cas d'un dièdre immergé, est développée et validée dans un premier temps dans le cas des ondes acoustiques pour des conditions aux limites de type Dirichlet ou Neumann. La méthode est ensuite étendue à la diffraction des ondes élastiques par des dièdres infinis à faces libres et d'angles quelconques, pour une incidence 2D puis pour une incidence 3D. Cette méthode est semi-analytique puisque les solutions recherchées s'écrivent sous la forme d'une somme d'une fonction singulière, qui est déterminée analytiquement à l'aide d'un algorithme récursif, et d'une fonction régulière, qui est approchée numériquement.Les codes correspondants sont validés par comparaison à une solution exacte dans le cas acoustique et par comparaison à d'autres codes (semi-analytiques et numériques) dans le cas élastique. Des validations expérimentales du modèle élastodynamique sont également proposées. / This thesis falls into the framework of model development for simulation of ultrasonic non-destructive testing (NDT). The long-term goal is to develop, using ray methods, a complete simulation tool of specimen echoes (input, back-wall surfaces...) or echoes of inner structures of inspected parts. The thesis aims more specifically to integrate the phenomenon of diffraction by wedges to an existing model derived from geometrical acoustics, which only accounts for reflections on the wedge faces.To this end, a method called the spectral functions method, which was initially developed for immersed wedges, is developed and validated as a first step in the case of acoustic waves with Dirichlet or Neumann boundary conditions. The method is then extended to elastic wave diffraction by infinite stress-free wedges of arbitrary angles, for 2D and 3D incidences. This method is semi-analytic since the unknown solutions are expressed as the sum of a singular function, determined analytically using a recursive algorithm, and a regular function which is approached numerically.The corresponding codes are validated by comparison to an exact solution in the acoustic case and by comparison to other codes (semi-analytic and numerical) in the elastic case. Experimental validations of the elastodynamic model are also proposed.

Machine learning is emerging as a powerful tool to data science and is being applied in almost all subjects. In many applications, the number of features is com- parable to the number of samples, and both grow large. This setting is usually named the high-dimensional regime. In this regime, new challenges arise when it comes to the application of machine learning. In this work, we conduct a high-dimensional performance analysis of some popular classification and regression techniques. In a first part, discriminant analysis classifiers are considered. A major challenge towards the use of these classifiers in practice is that they depend on the inverse of covariance matrices that need to be estimated from training data. Several estimators for the inverse of the covariance matrices can be used. The most common ones are estimators based on the regularization approach. In this thesis, we propose new estimators that are shown to yield better performance. The main principle of our proposed approach is the design of an optimized inverse covariance matrix estimator based on the assumption that the covariance matrix is a low-rank perturbation of a scaled identity matrix. We show that not only the proposed classifiers are easier to implement but also, outperform the classical regularization-based discriminant analysis classifiers. In a second part, we carry out a high-dimensional statistical analysis of linear support vector regression. Under some plausible assumptions on the statistical dis- tribution of the data, we characterize the feasibility condition for the hard support vector regression and, when feasible, derive an asymptotic approximation for its risk. Similarly, we study the test risk for the soft support vector regression as a function of its parameters. The analysis is then extended to the case of kernel support vector regression under generalized linear models assumption. Based on our analysis, we illustrate that adding more samples may be harmful to the test performance of these regression algorithms, while it is always beneficial when the parameters are optimally selected. Our results pave the way to understand the effect of the underlying hyper- parameters and provide insights on how to optimally choose the kernel function.

In this dissertation we consider the problem of cooperative sensing for secondary user access to primary user spectrum in cognitive radio systems. Using a fusion center or an access point, the cooperative users decide on the availability of spectrum for their use. Both Neyman-Pearson and Bayes criterion are considered for performance assessment. Our work on the asymptotic performance of counting rules with a very large number of sensors in decentralized detection problem shows that majority logic fusion rule has the same order of performance when compared to the best fusion rule based on the binary decisions received from the observing sensors in a network. In cognitive radio context, very large number of sensors may not be realistic and hence we would like to examine the performance of majority logic and counting rules involving a finite and small number of sensors. Uniformly most powerful test for decentralized detection for testing parameter θ when the observation is a sample from uniform (0,θ) distribution is investigated and it is shown that OR rule has the best performance among all counting rules in error free channel. The numerical study for reporting channel as a binary symmetric channel (BSC) with probability of bit error is also investigated and the results show that 2-out-of-5 or 2-out-of-10 has better performance among other k-out-of-n rules, whenever OR rule is not able to provide a probability of false alarm at the sensor, that lies over (0,1) at a given probability of bit error.

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<p> Steady state response of a single degree of freedom system with impact damper, with the main emphasis of two impacts (symmetric or unsymmetric)/cycle motion, and its asymptotic stability criterion are derived analytically. Stability regions are determined for wide range of parameters of the impact damper by using digital computer. </p> <p> Experimental study is also made to verify the assumptions taken in the analytical solution and to obtain general response of the system for wide range of parameters of the impact damper. </p> <p> As a result, it is found that unsymmetric two impacts per cycle motion exists and is stable for a wide range of parameters of the impact damper. </p> <p> Also, it is found that three and four impacts/cycle motions exist and are stable. </p> <p> Stability boundaries are found to be a complicated function of the impact damper parameters. </p> / Thesis / Master of Engineering (MEngr)

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