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Thesis (Ph.D.)--Boston University / This thesis presents methods for interpolating transfer functions of damped vibrating systems. Primary applications lie in the design and control of damped structures. The interpolations reduce the number of frequencies at which the transfer function must be computed or measured. The transfer functions are assumed to have impulse responses that are real-valued and causal, so a method is developed for constructing interpolations that implicitly satisfy these conditions. The method is applied to a particular choice of basis function that corresponds to a Fourier series in the time domain. Numerical results indicate that satisfaction of the causality condition increases the accuracy of the interpolation. A detailed investigation is made into interpolations for viscously damped systems, whose transfer functions are linear combinations of basis functions derived from the complex-valued eigenpairs of the system. Since the estimation of all eigenpairs is computationally expensive, a method is developed to estimate only those eigenpairs that significantly contribute to the transfer function in the specified frequency band. The method uses eigenvalues of the corresponding undamped system, which are much easier to compute, as starting guesses in an iterative algorithm. One advantage of the method is the assurance that it finds all eigenvalues in a specified region of the complex plane.

Angular differential imaging provides a novel way of probing high contrast regions of our universe. Until now, its applications have been primarily localized to searching for exoplanets around nearby stars. This work presents a suite of applications of angular differential imaging from the theoretical underpinning of data reduction, to its use characterizing substellar objects, to a new application looking for the host galaxies of damped Lyman α systems which are usually lost in the glare of ultra-bright quasars along the line of sight. The search for exoplanets utilizes angular differential imaging and relies on complex algorithms to remove residual speckles and artifacts in the images. One such algorithm, the Template Locally Optimized Combination of Images (TLOCI), uses a least-squares method to maximize the signal-to-noise ratio and can be used with variable parameters, such as an input spectral template, matrix inversion method, aggressivity and unsharp mask size. Given the large volume of image sequences that need to be processed in any exoplanet survey, it is important to find a small set of parameters that can maximize detections for any conditions. Rigorous testing of these parameters were done with on-sky images and simulated inserted planets to find the optimal combination of parameters. Overall, a standard matrix inversion, along with two to three input templates, a modest aggressivity of 0.7 and the smallest unsharp mask was found to be the best choice to balance optimal detection. Beyond optimizations, TLOCI has been used in conjunction with angular differential imaging to characterize substellar objects in our local solar neighbourhood. In particular, the star HD 984 was imaged as a part of the Gemini Planet Imager Exoplanet Survey. Although previously known to have a substellar companion, new imaging presented here in the H and J bands help further characterize this object. Comparisons with a library of brown dwarf spectral types found a best match to HD 984 B of a type M7±2. Orbital fitting suggests an 18 AU (70 year) orbit, with a 68% confidence interval between 12 and 27 AU. Object magnitude was used to find the luminosity, mass and temperature using DUSTY models. Although angular differential imaging has proven its value in high contrast imaging, it has largely remained in the field of substellar object detection, despite other high contrast regimes in which it could be applied. One potential application is outside the local solar neighbourhood with studies of damped Lyman α systems, which have struggled to identify host galaxies thought to be caused by systems seen in the spectra of bright quasars. Work herein presents the first application of angular differential imaging to finding the host galaxies to damped Lyman α systems. Using ADI we identified three potential systems within 30kpc of the sightline of the quasar and demonstrate the potential for future imaging of galaxies at close separations. In summary, this thesis presents a comprehensive look at multiple aspects of high contrast angular differential imaging. It explores optimizations with a data reduction algorithm, implementations characterizing substellar objects, and new applications imaging galaxies. / Graduate

Dans cette thèse, nous nous intéressons à deux approximations hyperboliques des équations de Navier-Stokes incompressibles en dimensions 2 et 3 d'espace. Dans un premier temps, on considère une perturbation hyperbolique de l'équation de la chaleur, introduite par Cattaneo en 1949, pour remédier au paradoxe de la propagation instantanée de cette équation. En 2004, Brenier, Natalini et Puel remarquent que la même perturbation, qui consiste à rajouter ε∂tt à l'équation, intervient en relaxant les équations d'Euler. En dimension 2, les auteurs montrent que, pour des sonnées régulières et sous certaines hypothèses de petitesse, la solution globale de la perturbation converge vers l'unique solution globale de (NS). En 2007, Paicu et Raugel améliorent les résultats de [BNP] en étendant la théorie à la dimension 3 et en prenant des données beaucoup moins régulières. Nous avons obtenu des résultats de convergence, avec données de régularité quasi-critique, qui complètent et prolongent ceux de [BNP] et [PR]. La seconde approximation que l'on considère est un nouveau modèle hyperbolique à vitesse de propagation finie. Ce modèle est obtenu en pénalisant la contrainte d'incompressibilité dans la perturbation de Cattaneo. Nous démontrons que les résultats d'existence globale et de convergence du précédent modèle sont encore vérifiés pour celui-ci. / In this work, we are interested in two hyperbolic approximations of the 2D and 3D Navier-Stokes equations. The first model we consider comes from Cattaneo's hyperbolic perturbation of the heat equation to obtain a finite speed of propagation equation. Brenier, Natalini and Puel studied the same perturbation as a relaxed version of the 2D Euler equations and proved that the solution to this relaxation converges towards the solution to (NS) with smooth data, provided some smallness assumptions. Later, Paicu and Raugel improved their results, extending the theory to the 3D setting and requiring significantly less regular data. Following [BNP] and [PR], we prove global existence and convergence results with quasi-critical regularity assumptions on the initial data. In the second part, we introduce a new hyperbolic model with finite speed of propagation, obtained by penalizing the incompressibility constraint in Cattaneo's perturbation. We prove that the same global existence and convergence results hold for this model as well as for the first one.

When a ferromagnet is heated, it loses its magnetism. Stars and planets have magnetic fields, as does the Earth. But it is known that the center of the Earth is very hot. Therefore, to sustain the large magnetic field of a planet, we cannot look to simple ferromagnetism like that of a bar magnet, but we have to look at the movement of electric charges within the Earth’s molten core to generate magnetic field. This magnetic field sustainment against ohmic dissipation by turbulent flow is referred to as the turbulent dynamo effect. Theoretical research into the mechanisms that create the dynamo has been actively pursued for several decades, culminating recently in massive computer simulations of the Earth’s core. Most of these studies have employed the equations of magnetohydrodynamics (MHD), a nonlinear theory of electrically conducting fluids. The EDQNM (Eddy-Damped Quasi-Normal Markovian) closure is a statistical model designed so that the turbulence equations derived from Navier-Stokes dynamics can be closed and satisfy the realizability condition of positivity of the kinetic energy spectrum. In case of MHD turbulence, realizability requires more work. We have proved in an earlier work that equations analogous to those expected of the EDQNM closure for MHD without mean fields satisfy the appropriate realizability conditions (Turner and Pratt 1999). In this work, we discuss requirements needed to make the MHD equations realizable with mean fields, extending those of neutral fluid turbulence by Turner [1]. Finally, we discuss direct numerical simulations and the correspondence of the statistical theories with simulation results.

Strong damped Lyman alpha absorption (DLA) lines seen spectra of distant quasar are believed to arise when the sight line to the quasar goes trough the disc of a galaxy or a proto galaxy. Most of the neutral matter in the universe is contained in these clouds of neutral hydrogen that cause the absorption lines. Hence these DLAs are reservoirs for the formation of stars and galaxies throughout the universe. Despite intensive efforts over more than two decades only few galaxies responsible for the DLAs have been found. The problem is that the galaxies that harbour the neutral clouds are not necessarily bright, and selecting galaxies based on absorption lines could well select different types of galaxies than found in large surveys. If we are to understand how galaxies form out of neutral gas clouds it is essential to locate the galaxies in which DLAs reside. <br><br> This thesis explores the use of integral field spectroscopy (IFS) to observe quasars known to have strong absorption lines in their spectra. IFS allows us to obtain a spectrum at many spatial points close to the quasar, thus providing images and spectroscopy simultaneously. From the imaging part, we can directly identify objects, and from the spectroscopy we can calculate the distances to the objects. When the distance of the object found in emission matches the distance to the object that cause the DLA line, we have identified the absorbing galaxy. <br><br> Using this technique, we have showed that we can successfully recover a few DLA galaxies known previously from the literature. In a survey aimed to increase the number of DLA galaxies we have identified eight new candidate DLA galaxies. The projected distances from the candidates to the quasar sight lines indicate that the DLA galaxies have sizes similar to local disc galaxies. Hence our results suggest that large discs may be present when the universe was just 2 billion years old. We furthermore find no differences between the sizes of the very distant DLA galaxies and those that are not so distant. The large sizes imply that their neutral hydrogen masses are also similar to those in local galaxies, but we argue that the DLA galaxies are not necessarily as luminous as the present day disc galaxies. <br><br> Taking advantage of the three-dimensional view provided by the IFS data, the second part of this thesis investigates extended emission line regions arising in the quasar neighborhood. We find that extended emission line nebulae are common around quasars, and explore the effects that may be the cause. Some quasars are known to be powerful radio emitters while others are not detected at radio wavelengths. We find that significantly larger and brighter emission line nebulae are found around the quasars which have the brightest radio emission, and in particular those that have large radio jets. The existence of the nebulae can be interpreted as an interaction of the radio jet with the surrounding medium, but we can not rule out a scenario where there are density or temperature differences in the surrounding environment. Only for the brightest object, where additional velocity information can be derived from the IFS data, can we argue for an interaction. <br><br> In conclusion the use of IFS to search for faint emission lines, both from point sources and extended nebulae provides exciting new results within the scientific areas studied here. / Man glaubt, daß starke gedämpfte Lyman alpha Absorptionslinien (damped Lyman alpha lines, DLA lines) in den Spektren entfernter Quasare entstehen, wenn die Sichtlinie zu dem Quasar durch eine Galaxie oder eine Proto-Galaxie geht. Die meiste neutrale Materie des Universums ist in diesen Wolken aus neutralem Wasserstoff enthalten, die die Absorptionslinien verursachen. Daher sind diese DLAs Reservoire für die Bildung von Sternen und Galaxien im gesamten Universum. Trotz intensiver Anstrengungen seit mehr als zwei Jahrzehnten konnten nur wenige Galaxien gefunden werden, die für DLAs verantwortlich sind. Das Problem ist, daß die Galaxien, die die neutralen Wolken beherbergen, nicht notwendigerweise hell sind, und Galaxien basierend auf Absorptionslinien zu selektieren, könnte leicht andere Typen von Galaxien selektieren, als diejenigen, die in großen Durchmusterungen gefunden werden. Wenn wir verstehen wollen wie Galaxien aus neutralen Gaswolken entstehen, ist es entscheidend, die Galaxien ausfindig zu machen, in denen DLAs liegen. <br><br> Diese Doktorarbeit erforscht die Nutzung der Ganzfeldspektroskopie (integral field spectroscopy, IFS), um Quasare zu beobachten, die bekanntermaßen starke Absorptionslinien in ihren Spektren haben. IFS erlaubt uns, ein Spektrum an vielen räumlichen Punkten nahe des Quasars zu erhalten, somit Bilder und Spekroskopie gleichzeitig zu liefern. Aus den Bildern können wir direkt Objekte identifizieren und aus der Spektroskopie können wir die Entfernungen zu den Objekten berechnen. Wenn die Entfernung zum gefundenen Objekt mit der Entfernung zu einer DLA-Linie übereinstimmt, dann haben wir die absorbierende Galaxie gefunden. <br><br> Diese Methode anwendend, können wir zeigen, daß wir erfolgreich einige wenige schon aus der Literatur bekannte DLA-Galaxien wiederentdecken können. In einer auf Erhöhung der Zahl von DLA-Galaxien abzielenden Duchmusterung haben wir acht neue DLA-Galaxienkandidaten identifiziert. Die projizierten Entfernungen von den Kandidaten zu den Quasarsichtlinien lassen erkennen, daß die DLA-Galaxien ähnliche Größen haben, wie nahe Scheibengalaxien. Daher lassen unsere Resultate darauf schließen, daß es große Scheibengalaxien gegeben haben könnte, als das Universum gerade zwei Milliarden Jahre alt war. Außerdem finden wir keine Unterschiede zwischen den Größen der sehr weit entfernten DLA-Galaxien und jenen, die nicht so weit entfernt sind. Die Größen implizieren, daß ihre Massen gebunden in neutralem Wasserstoff auch ähnlich sind zu jenen in lokalen Galaxien, aber wir vertreten die Ansicht, daß DLA-Galaxien nicht notwendigerweise so leuchtkräftig sind wie heutige Scheibengalaxien. <br><br> Den dreidimensionalen Blick ermöglicht durch die IFS-Daten ausnutzend, untersucht der zweite Teil dieser Doktorarbeit ausgedehnte Emissionslinienregionen, die in der Nachbarschaft der Quasare entstehen. Wir finden heraus, daß ausgedehnte Emissionsliniennebel um Quasare häufig sind und erforschen die ihnen zugrundeliegenden Effekte. Einige Quasare sind bekannte starke Radioquellen, während andere nicht im Radiobereich entdeckt werden. Wir zeigen, daß bedeutend größere und hellere Emissionsliniennebel um Quasare gefunden werden, welche die stärkste Radioemission, insbesondere große Radiojets, aufweisen. Die Existenz der Nebel kann interpretiert werden als eine Wechselwirkung der Radiojets mit dem umgebenden Medium, aber wir können nicht ausschließen, daß es Dichte- oder Temperaturunterschiede in der Umgebung gibt. Nur für die hellsten Objekte, für die zusätzliche Geschwindigkeitsinformation aus den IFS-Daten abgeleitet werden kann, vertreten wir die Ansicht der Wechselwirkung. <br><br> Die Nutzung der IFS bei der Suche nach schwachen Emissionslinien von Punktquellen wie auch ausgedehnten Nebeln bietet spannende neue Ergebnisse in den hier studierten wissenschaftlichen Gebieten.

Nesse trabalho apresentamos o estudo do artigo [25] que analisa a existência de atratores globais para uma classe de equações da onda amortecida da forma \'épsilon u IND. tt\' + \'alpha\' (x) u IND. t\' + \'BETA\' (x)u - \'\\SIGMA SOBRE i, j\' \'\\PARTIAL ind. I\' (\'a IND. i j\' (x) \'PARTIAL IND. j u\') = f(x, u) , x PERTENCE A ÔMEGA\'\', t \'PERTENCE A\' [0,\'infinito\'), u (x, t) = 0, x \'PERTENCE A\' \'\\PARTIAL ÔMEGA\', t \'PERTENCE A\' [0, \'infinito\') definidas em um domínio arbitrário \'ÔMEGA\' / In this work we describe the results of the paper [25]. In [25] the authors prove existence of global attractors for the following semilinear damped wave equation \'\\épsilon u IND. t\'t + \'alpha\'(x)u IND. t\' + \'beta\' (x)u - \'\\SIGMA SOBRE i, j \'\\PARTIAL IND. i\' (\'a IND. i j\' (x) \'\\PARTIAL IND. j u\') = f (x, u), x \'IT BELONGS\' \'ÔMEGA\', t \'IT BELONGS\' [0, \'INFINITY\'), u(x,t), x \'IT BELONGS\' \'\\PARTIAL ÔMEGA\', t \'IT BELONGS\' [), \'INFINITY\'0 on an arbitrary domain \'OMEGA\'

The identification of the physical parameters (mass, stiffness, and damping) of structural, mechanical, and biomechanical systems is a major challenge in many applications, especially when dealing with old systems and biological systems with heavy damping and where environmental noises are presented. This work presents a novel methodology called eigenvector phase correction (EVPHC) to solve for the physical parameters of structural and biomechanical systems even with the existence of a significant amount of noise. The method was first tested on structural/mechanical systems and showed superior results when compared with an iterative method from the literature. EVPHC was then developed and used to identify the physical parameters of supine humans under vertical whole-body vibration. Modal parameters of fifteen human subjects, in the supine position, were first identified in this work using experimentation under vertical whole-body vibration. EVPHC was then used to solve an inverse modal problem for the identification of the stiffness and damping parameters at the cervical and lumbar areas of supine humans. The results showed that the resulting physical parameters were realistically close to those presented in the literature. The proposed human model was able to predict the time histories of the acceleration at the head, chest, pelvis, and legs very closely to those of the experimental measured values. A scaling methodology is also presented in this work, where an average human model was scaled to an individual subject using the body mass properties.

A novel method by which to calculate the near edge X-rayabsorption fine structure region of the X-ray absorption spectrum has been derived and implemented. By means of damped coupled cluster theory at coupled cluster levels CCS, CC2, CCSD and CCSDR(3), the spectra of neon and methane have been investigated. Using methods incorprating double excitations, the important relaxation effects maybe taken into account by simultaneous excitation of the core electron and relaxation of other electrons. An asymmetric Lanczos-chain driven approach has been utilized as a means to partially resolve the excitation space given by the coupled cluster Jacobian. The K-edge of the systems have been considered, and relativistic effects are estimated with use of the Douglas--Kroll scalar relativistic Hamiltonian. Comparisons have been made to results obtained with the four-component static-exchange approach and ionization potentials obtained by the {Delta}SCF-method. The appropriate basis sets by which to describe the core and excited states have been been determined.  The addition of core-polarizing functions and diffuse or Rydberg functions is important for this description. Scalar relativistic effects accounts for an increase in excitation energies due to the contraction of the 1s-orbital, and this increase is seen to be 0.88 eV for neon. The coupled cluster hierachy shows a trend of convergence towards the experimental spectrum, with an 1s -&gt; 3p excitation energy for neon of an accuracy of 0.40 eV at a relativistic CCSDR(3) level of theory. Results obtained at the damped coupled cluster and STEX levels of theory, respectively, are seen to be in agreement, with a mere relative energy shift.

Nesse trabalho apresentamos o estudo do artigo [25] que analisa a existência de atratores globais para uma classe de equações da onda amortecida da forma \'épsilon u IND. tt\' + \'alpha\' (x) u IND. t\' + \'BETA\' (x)u - \'\\SIGMA SOBRE i, j\' \'\\PARTIAL ind. I\' (\'a IND. i j\' (x) \'PARTIAL IND. j u\') = f(x, u) , x PERTENCE A ÔMEGA\'\', t \'PERTENCE A\' [0,\'infinito\'), u (x, t) = 0, x \'PERTENCE A\' \'\\PARTIAL ÔMEGA\', t \'PERTENCE A\' [0, \'infinito\') definidas em um domínio arbitrário \'ÔMEGA\' / In this work we describe the results of the paper [25]. In [25] the authors prove existence of global attractors for the following semilinear damped wave equation \'\\épsilon u IND. t\'t + \'alpha\'(x)u IND. t\' + \'beta\' (x)u - \'\\SIGMA SOBRE i, j \'\\PARTIAL IND. i\' (\'a IND. i j\' (x) \'\\PARTIAL IND. j u\') = f (x, u), x \'IT BELONGS\' \'ÔMEGA\', t \'IT BELONGS\' [0, \'INFINITY\'), u(x,t), x \'IT BELONGS\' \'\\PARTIAL ÔMEGA\', t \'IT BELONGS\' [), \'INFINITY\'0 on an arbitrary domain \'OMEGA\'