Cette thèse examine deux façons de diminuer la complexité des problèmes de propagation d'ondes diffractées par un obstacle borné : la diminution des domaines de calcul à l'aide de milieux fictifs absorbants permettant l'adjonction de conditions aux limites exactes et la recherche d'une nouvelle approximation spatiale sous forme polynomiale donnant lieu à des schémas explicites où la stabilité est indépendante de l'ordre choisi. Dans un premier temps, on réduit le domaine de calcul autour de domaines non nécessairement convexes, mais propres aux problèmes de scattering (non trapping), à l'aide de la méthode des Perfectly Matched Layers (PML). Il faut alors considérer des domaines d'exhaustion difféomorphes à des convexes avec des hypothèses "presque" nécessaires. Pour les Equations de type Maxwell et Ondes, l'existence et l'unicité sont montrées dans tout l'espace et en domaine artificiellement borné, tant en fréquentiel qu'en temporel. La décroissance est analysée localement et asymptotiquement et des simulations numériques sont proposées. La deuxième partie de ce travail est une alternative à l'approximation de type Galerkin Discontinu, inspirée des résultats de régularité de J. Rauch, présentant l'avantage de conserver une condition CFL de type Volumes Finis indépendante de l'ordre d'approximation, aussi bien pour des maillages structurés que déstructurés. La convergence de cette méthode est démontrée via la consistance et la stabilité, grâce au théorème d'équivalence de Lax-Richtmyer pour des domaines structurés. En déstructuré, la consistance ne pouvant plus s'établir au moyen de la formulation de Taylor, la convergence n'est plus assurée, mais les premiers tests numériques bidimensionnels donnent d'excellents résultats.

<p>Two methods for evaluating and improving plane wave beamforming have beendeveloped. The methods estimate the shape of the wavefront and use theinformation in the beamforming. One of the methods uses estimates of the timedelays between the sensors to approximate the shape of the wavefront, and theother estimates the wavefront by matching the received wavefront to sphericalwavefronts of different radii. The methods are compared to a third more commonmethod of beamforming, which assumes that the impinging wave is planar. Themethods’ passive ranging abilities are also evaluated, and compared to a referencemethod based on triangulation.Both methods were evaluated with both real and simulated data. The simulateddata was obtained using Raylab, which is a simulation program based on ray-tracing. The real data was obtained through a field-test performed in the Balticsea using a towed array sonar and a stationary source emitted tones.The performance of the matched beamformers depends on the distance to the tar-get. At a distance of 600 m near broadside the power received by the beamformerincreases by 0.5-1 dB compared to the plane wave beamformer. At a distance of300 m near broadside the improvement is approximately 2 dB. In general, obtain-ing an accurate distance estimation proved to be difficult, and highly dependenton the noise present in the environment. A moving target at a distance of 600 mat broadside can be estimated with a maximum error of 150 m, when recursiveupdating of the covariance matrix with a updating constant of 0.25 is used. Whenrecursive updating is not used the margin of error increases to 400 m.</p>

Ocular fundus image can provide information on pathological changes caused by local ocular diseases and early signs of certain systemic diseases. Automated analysis and interpretation of fundus images has become a necessary and important diagnostic procedure in ophthalmology. Among the features in ocular fundus image are the optic disc, fovea (central vision area), lesions, and retinal vessels. These features are useful in revealing the states of diseases in the form of measurable abnormalities such as length of diameter, change in color, and degree of tortuosity in the vessels. In addition, retinal vessels can also serve as landmarks for image-guided laser treatment of choroidal neovascularization. Thus, reliable methods for blood vessel detection that preserve various vessel measurements are needed. In this paper, we will examine the pathological issues in the analysis of retinal vessels in digital fundus images and give a survey of current image processing methods for extracting vessels in retinal images with a view to categorize them and highlight their differences and similarities. We have also implemented two major approaches using matched filter and mathematical morphology respectively and compared their performances. Some prospective research directions are identified. / Singapore-MIT Alliance (SMA)

The focus of this study is the prediction of trajectories of solid particles injected into either a cylindrically- shaped solid rocket motor (SRM) or a bidirectional vortex chamber (BV). The Lagrangian particle trajectory is assumed to be governed by drag, virtual mass, Magnus, Saffman lift, and gravity forces in a Stokes flow regime. For the conditions in a solid rocket motor, it is determined that either the drag or gravity forces will dominate depending on whether the sidewall injection velocity is high (drag) or low (gravity). Using a one-way coupling paradigm in a solid rocket motor, the effects of particle size, sidewall injection velocity, and particle-to-gas density ratio are examined. The particle size and sidewall injection velocity are found to have a greater impact on particle trajectories than the density ratio. Similarly, for conditions associated with a bidirectional vortex engine, it is determined that the drag force dominates. Using a one-way particle tracking Lagrangian model, the effects of particle size, geometric inlet parameter, particle-to-gas density ratio, and initial particle velocity are examined. All but the initial particle velocity are found to have a significant impact on particle trajectories. The proposed models can assist in reducing slag retention and identifying fuel injection configurations that will ensure proper confinement of combusting droplets to the inner vortex in solid rocket motors and bidirectional vortex engines, respectively.

The perfectly matched layer (PML) is a novel technique to simulate the absorption of waves in unbounded domains. The underlying equations are often a system of second order hyperbolic partial differential equations. In the numerical treatment, second order systems are often rewritten and solved as first order systems. There are several benefits with solving the equations in second order formulation, though. However, while the theory and numerical methods for first order hyperbolic systems are well developed, numerical techniques to solve second order hyperbolic systems are less complete. We construct a strongly well-posed PML for second order systems in two space dimensions, focusing on the equations of linear elasto-dynamics. In the continuous setting, the stability of both first order and second order formulations are linearly equivalent. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability at most resolutions. In the second order setting growth occurs only if growing modes are well resolved. We determine the number of grid points that can be used in the PML to ensure a discretely stable PML, for several anisotropic elastic materials. We study the stability of the PML for problems where physical boundaries are important. First, we consider the PML in a waveguide governed by the scalar wave equation. To ensure the accuracy and the stability of the discrete PML, we derived a set of equivalent boundary conditions. Second, we consider the PML for second order symmetric hyperbolic systems on a half-plane. For a class of stable boundary conditions, we derive transformed boundary conditions and prove the stability of the corresponding half-plane problem. Third, we extend the stability analysis to rectangular elastic waveguides, and demonstrate the stability of the discrete PML. Building on high order summation-by-parts operators, we derive high order accurate and strictly stable finite difference approximations for second order time-dependent hyperbolic systems on bounded domains. Natural and mixed boundary conditions are imposed weakly using the simultaneous approximation term method. Dirichlet boundary conditions are imposed strongly by injection. By constructing continuous strict energy estimates and analogous discrete strict energy estimates, we prove strict stability.

The Nicoya Peninsula of Costa Rica is unusually close to the Middle America Trench (MAT), such that interface locking along the megathrust is observable under land. Here, rapid convergence between the downgoing Cocos and the over-riding Caribbean plates at ~85mm/yr allows for observable high strain rates, frequent large earthquakes and ongoing micro-seismicity. By taking advantage of this ideal location, a network of 20 on-land broadband seismometers was established in cooperation between UC Santa Cruz, Georgia Tech, and OVSICORI, with most stations operating since 2008. To evaluate what seismicity tells us about the ongoing state of coupling along the interface, we must consistently evaluate the location and magnitude of ongoing micro- seismicity. Because of large levels of anthropogenic, biologic, and coastal noise, automatic detection of earthquakes remains problematic in this region. Thus, we resorted to detailed manual investigation of earthquake phases. So far, we have detected nearly 7,000 earthquakes below or near Nicoya between February and August 2009. From these events we evaluate the fine-scale frequency-magnitude distribution (FMD) along the subduction megathrust. The results from this b-value mapping‟ are compared with an earlier study of the seismicity 9 years prior. In addition, we evaluate them relative to the latest geodetically derived locking. Preliminary comparisons of spatial and temporal variations of the b-values will be reported here. Because ongoing manual detection of earthquakes is extremely laborious and some events might be easily neglected, we are implementing a match-filter detection algorithm to search for new events from the continuous seismic data. This new approach has been previously successful in identifying aftershocks of the 2004 Parkfield earthquake. To do so, we use the waveforms of 858 analyst-detected events as templates to search for similarly repeating events during the same periods that have been manually detected. Preliminary results on the effectiveness of this technique are reported. The overall goal of this research is to evaluate the evolution of stress along the megathrust that may indicate the location and magnitude of potentially large future earthquakes. To do so, I make the comparison between the FMD and the interface locking. Only positive correlations are observed in the Nicoya region. The result is different from the one derived from the seismic data set that was recorded 9 years before our data. Therefore, to substantiate the causes for the different relationships between the b-value and the coupling degree, we need additional data with more reliable magnitudes.

The purpose of this master thesis was to investigate how effiecient the extractionof radiofrequency quality metrics from digital video broadcast (DVB) streamscan become using software defined radio. Software defined radio (SDR) is a fairlynew technology that offers you the possibility of very flexible receivers and transmitters where it is possible to upgrade the modulation and demodulation overtime. Agama is interested in SDR for use in the Agama Analyzer, a widely deployedmonitoring probe running on top of standard services. Using SDR, Agama coulduse that in all deployments, such as DVB by cable/terrestrial/satellite (DVBC/T/S), which would simplify logistics. This thesis is an implementation of a SDR to be able to receive DVB-C. TheSDR must perform a number of adaptive algorithms in order to prevent the received symbols from being significantly different from the transmitted ones. Themain parts of the SDR include timing recovery, carrier recovery and equalization.Timing recovery performs synchronization between the transmitted and receivedsymbols and the carrier recovery performs synchronization between the carrierwave of the transmitter and the local oscillator in the receiver. The thesis discusses various methods to perform the different types of synchronizations andequalizations in order to find the most suitable methods.

Two methods for evaluating and improving plane wave beamforming have beendeveloped. The methods estimate the shape of the wavefront and use theinformation in the beamforming. One of the methods uses estimates of the timedelays between the sensors to approximate the shape of the wavefront, and theother estimates the wavefront by matching the received wavefront to sphericalwavefronts of different radii. The methods are compared to a third more commonmethod of beamforming, which assumes that the impinging wave is planar. Themethods’ passive ranging abilities are also evaluated, and compared to a referencemethod based on triangulation.Both methods were evaluated with both real and simulated data. The simulateddata was obtained using Raylab, which is a simulation program based on ray-tracing. The real data was obtained through a field-test performed in the Balticsea using a towed array sonar and a stationary source emitted tones.The performance of the matched beamformers depends on the distance to the tar-get. At a distance of 600 m near broadside the power received by the beamformerincreases by 0.5-1 dB compared to the plane wave beamformer. At a distance of300 m near broadside the improvement is approximately 2 dB. In general, obtain-ing an accurate distance estimation proved to be difficult, and highly dependenton the noise present in the environment. A moving target at a distance of 600 mat broadside can be estimated with a maximum error of 150 m, when recursiveupdating of the covariance matrix with a updating constant of 0.25 is used. Whenrecursive updating is not used the margin of error increases to 400 m.

This dissertation consists of three projects in matched case-control studies. In the first project, we employ a general bias preventive approach developed by Firth (1993) to handle the bias of an estimator of the log-odds ratio parameter in conditional logistic regression by solving a modified score equation. The resultant estimator not only reduces bias but also can prevent producing infinite value. Furthermore, we propose a method to calculate the standard error of the resultant estimator. A closed form expression for the estimator of the log-odds ratio parameter is derived in the case of a dichotomous exposure variable. Finite sample properties of the estimator are investigated via a simulation study. Finally, we apply the method to analyze a matched case-control data from a low-birth-weight study. In the second project of this dissertation, we propose a score typed test for checking adequacy of a functional form of a covariate of interest in matched case-control studies by using penalized regression splines to approximate an unknown function. The asymptotic distribution of the test statistics under the null model is a linear combination of several chi-square random variables. We also derive the asymptotic distribution of the test statistic when the alternative model holds. Through a simulation study we assess and compare the finite sample properties of the proposed test with that of Arbogast and Lin (2004). To illustrate the usefulness of the method, we apply the proposed test to a matched case-control data constructed from the breast cancer data of the SEER study. Usually a logistic model is needed to associate the risk of the disease with the covariates of interests. However, this logistic model may not be appropriate in some instances. In the last project , we adopt idea to matched case-control studies and derive an information matrix based test for testing overall model adequacy and investigate the properties against the cumulative residual based test in Arbogast and Lin (2004) via a simulation study. The proposed method is less time consuming and has comparative power for small parameters. It is suitable to explore the overall model fitting.

The Finite Element Method (FEM) is a powerful numerical method to solve wave propagation problems for open-region electromagnetic radiation/scattering problems involving objects with arbitrary geometry and constitutive parameters. In high-frequency applications, the FEM requires an electrically large computational domain, implying a large number of unknowns, such that the numerical solution of the problem is not feasible even on state-of-the-art computers. An appealing way to solve a large FEM problem is to employ a Domain Decomposition Method (DDM) that allows the decomposition of a large problem into several coupled subproblems which can be solved independently, thus reducing considerably the memory storage requirements. In this thesis, two new domain decomposition algorithms (FB-DDM and ILF-DDM) are implemented for the finite element solution of electromagnetic radiation/scattering problems. For this purpose, a nodal FEM code (FEMS2D) employing triangular elements and a vector FEM code (FEMS3D) employing tetrahedral edge elements have been developed for 2D and 3D problems, respectively. The unbounded domain of the radiation/scattering problem, as well as the boundaries of the subdomains in the DDMs, are truncated by the Perfectly Matched Layer (PML) absorber. The PML is implemented using two new approaches: Locally-conformal PML and Multi-center PML. These approaches are based on a locally-defined complex coordinate transformation which makes possible to handle challenging PML geometries, especially with curvature discontinuities. In order to implement these PML methods, we also introduce the concept of complex space FEM using elements with complex nodal coordinates. The performances of the DDMs and the PML methods are investigated numerically in several applications.