Thesis (Ph. D.)--Washington State University, December 2006. / Includes bibliographical references (p. 136-144).

Thesis (Ph. D.)--Drexel University, 2006. / Includes abstract and vita. Includes bibliographical references (leaves 68-70).

Made available in DSpace on 2014-06-11T19:25:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-02Bitstream added on 2014-06-13T20:13:59Z : No. of bitstreams: 1 araujo_ran_me_guara.pdf: 540167 bytes, checksum: 19447329cebde1ebf3fd733fca4193d8 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Universidade Estadual Paulista (UNESP) / Neste trabalho é feito o estudo do fenômeno da captura gravitacional temporária e do conceito de esfera de influência, considerando o papel da velocidade relativa. Este estudo foi feito através de simulações numéricas do problema circular restrito de três corpos e através do monitoramento da energia do problema de dois corpos. No caso da captura gravitacional temporária nós acompanhamos a variação de energia do problema de dois corpos (partícula-corpo secundário), de uma partícula que sofre um encontro próximo com um corpo massivo (um planeta, por exemplo). A evolução dessa energia mostra se a partícula foi capturada, ou não, para algumas condições iniciais específicas. Este procedimento resultou na obtenção de funções matemáticas que permitem o cálculo do chamado raio de captura em função da velocidade relativa. No estudo numérico da esfera de influencia, a variação da energia do problema de dois corpos no tempo também foi acompanhada, mas desta vez nós acompanhamos a energia do problema partícula-corpo central, para uma partícula que sofre um encontro próximo com o corpo secundário. A evolução desta energia mostra se a partícula foi afetada significativamente, ou não, pela influência gravitacional do corpo secundário, para condições iniciais específicas. Este procedimento resulta na obtenção de funções matemáticas que permitem o cálculo do raio da esfera de influência em função da velocidade relativa. Finalmente, a manobra de swing-by foi aplicada no estudo do caso dos asteróides Vesta e Magnya com o objetivo de explicar sua distante localização orbital em relação aos demais membros da família do asteróide Vesta. Este estudo mostrou que uma mudança na órbita do Magnya não seria proporcionada apenas pelo swing-by, e que ele deveria sofrer a ação de outros mecanismos para causar tal mudança. / This work studies the phenomenom of the temporary gravitational capture and the concept of sphere of influence, taking into account the relative velocity. It has been done through numerical simulations of the restricted three-body problem, and through the analysis of the two-body energy. In the case of the temporary gravitational capture we followed the temporal variation of the two-body energy (particle-secondary body) of a particle that suffers a close enconter with a massive body (a planet, for instance). The evolution of such energy shows if the particle was captured or not, for some specific initial conditions. This procedure results in mathematical functions to calculate the so called capture radius as a function of the relative velocity. In the numerical study of the sphere of influence, we also followed the temporal variation of the two-body energy but, at this time, we followed the energy particle-central body of a particle that suffers a close encounter with a massive body (called secondary body). The evolution of such energy shows if the particle was significantly affected by the gravitational influence of the secondary body or not, for some specific initial conditions. This procedure results in mathematical functions to calculate the sphere of influence as a function of the relative velocity. Finally, the swing-by maneuver was applied in the study of the case of the asteroids Vesta and Magnya, in order to explain its distant orbital localization relative to the localization of the others members of the Vesta’s family. This study showed that a change in the orbit of Magnya would not be proporcioned only by the swing-by, and that the asteroid Magnya should suffer the action of others mechanisms to cause it.

In this thesis, we present a series of methods, applications, and results on the subject of modern gravitational-wave astrophysics. This ranges from the detection of gravitational-wave phenomena to the analysis of detector data to applications of the measurements to astrophysics. We first introduce the theory, detection, and sources of gravitational waves. We review the characterization of gravitational-wave detector data, and we present a method to identify detector artifacts in gravitational-wave data using only auxiliary detector data. We then introduce two methods in gravitational-wave data analysis: first, we offer a method for searching detector data for unmodeled gravitational-wave events. Second, we present a method for the rapid estimation and communication of the inclination angle of compact binary mergers. Finally, we explore three astrophysical applications of some the methods introduced: first, we show the effect of prior knowledge of inclination on the localization of binary black-hole mergers and its applications. Second, we explore the follow-up potential of the Cherenkov Telescope Array to gravitational-wave sources at high energies. Last, we show that publicly available gravitational-wave event information is capable of estimating the chirp masses of gravitational-wave sources, thereby identifying promising mergers for electromagnetic follow-up.

This work is concerned with how to extract information encoded in small scales of non-Gaussian fields, with the purpose of learning about cosmology using weak gravitational lensing. We do so by comparing different methods on simulated data sets. The topic is relevant, for upcoming galaxy surveys will map the late evolution of the matter density field, which is non-Gaussian, with an unprecedented level of detail, and any improvement on the analysis techniques will increase the experiments' scientific return. First, we investigate some non-Gaussian observables used in the weak lensing community. We analyze to what extent they are sensitive to the background expansion of the universe, and to what extent to the evolution of the structures responsible for the lensing. We then focus our attention on one such statistic, lensing peaks, and assess the performance of a simple halo-based model that has been proposed to forecast their abundance. We find some shortcomings of that semi-analytic approach, and proceed to review some minimal requirements for numerical simulations used to forecast non-Gaussian statistics, to reduce their computational cost while fulfilling the accuracy and precision required by future experiments. Second, we propose a novel measurement, that of the temperature dipole induced on the cosmic microwave background induced by the rotation of ionized gas around galaxies, as an additional observation to help constrain the distribution of baryonic matter on the smallest scales probed by WL experiments. The uncertainty in this distribution is a major theoretical systematic for future surveys. Third, we show how deep neural networks can be used to map pixel-level data into the cosmological parameters of interest, by-passing the previous compression step of measuring pre-designed statistics. We provide the first (simulation-based) credible contours based on neural networks applied to weak lensing data, and discuss how to interpret these models.

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A network of laser interferometer gravitational waves detectors spread across the globe is currently running and steadily improving. After complex data analysis from the output signal of the present detectors, astrophysical results begin to emerge with upper limits on gravitational wave sources. So far, however no direct detection has been announced. To increase the sensitivity of current detectors, a second generation of interferometers is planned which will make gravitational wave astronomy a reality within one decade. The advanced generation of interferometers will represent a substantial upgrade from current detectors. Especially, very high optical power will circulate in the arm cavities in order to reduce by one order of magnitude the shot noise limited sensitivity in high frequency. However, the theoretical shot noise limit will only be achieved after implementation of complex thermal lensing compensation schemes. Thermal lensing is direct consequence of the residual optical absorption inside the substrate and coating of the test masses and could have tragic consequences for the functionality of the interferometer. The Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) in collaboration with LIGO will run a series of high optical power tests to understand the characteristics and effects of thermal lensing. During these tests, techniques to compensate thermal lensing will be experimented. This thesis mainly focused on the first high optical power test in Gingin, Australia. The first test will consist of a Fabry Perot cavity with the sapphire substrate of the input mirror inside the cavity. Due to the high optical circulating power a strong convergent thermal lens will appear in the input mirror substrate. Because of the presence of the thermal lens inside the cavity, the size of the cavity waist will be reduced and the cavity circulating power will decrease. Simulations using higher order mode expansion and FFT propagation code were completed to estimate ways to compensate strong thermal lensing for the Gingin first test. The term `strong thermal lensing? is used because the thermal lens focal length is comparable to the design focal length of the optical components. The expected performance of a fused silica compensation plate is presented and advantages and limits of this method are discussed. Experimental results on small scale actuators which can potentially compensate thermal lensing are detailed. The knowledge gained from these experiments was valuable to design the real scale compensation plate which was used in the first Gingin test. This test was carried at the end of 2005. The thermal lens due to 1 kW of optical power circulating in the sapphire substrate was successfully compensated using a fused silica plate. Yet, thermal lensing compensation may only be required for room temperature advanced interferometer. Indeed, we showed that cooling the interferometer mirror to cryogenic temperature can eliminate the thermal lensing problem and also substantially decrease the mirror thermal noise.

The difficulties associated with the quantization of the gravitational field suggests a modification of space-time is needed. For example at suffici~ly small length scales the geometry of space-time might better discussed in terms of a noncommutative algebra. In this thesis we discuss a particular example of a noncommutative algebra, namely the symplectic Schonberg algebra, which we treat as a geometric algebra. Thus our investigation has some features in common with recent work that explores how geometry can be formulated in terms of noncommutative structures. The symplectic Schonberg algebra is a geometric algebra associated with the covariant and the contravariant vectors of a general affine space. The "embedding" of this space in a noncommutative algebra leads us to a structure which we regard as a noncommutative affine geometry. The theory in question takes us naturally to stochastic elements without the usual ad-hoc assumptions concerning measurements in physical ensembles that are made in the usual interpretation of quantum mechanics. The probabilistic nature of space is obtained purely from the structure of this algebra. As a consequence, geometric objects like points, lines and etc acquire a kind of fuzzy character. This allowed us to construct the space of physical states within the algebra in terms of its minimum left-ideals as was proposed by Hiley and Frescura [1J. The elements of these ideals replace the ordinary point in the Cartesian geometry. The study of the main inner-automorphisms of the algebra gives rise to the representation of the symplectic group of linear classical canonical transformations. We show that this group acts on the minimum left-ideal of the algebra and in this case manifests itself as the metaplectic group, i.e the double covering of the symplectic group. Thus we are lead to the theory of symplectic spinors as minimum left-ideals in exactly the same way as the orthogonal spinors can be formulated in terms of minimum left-ideals in the Clifford algebra .. The theory of the automorphisms of the symplectic Schonberg algebra allows us to give a geometrical meaning to integral transforms such as: the Fourier transform, the real and complex Gauss Weierstrass transform, the Bargmann (3) transform and the Bilateral Laplace transform. We construct a technique for obtaining a realization of these algebraic transformations in terms of integral kernels. This gives immediately the Feynmann propagators of conventional non-relativistic quantum mechanics for Hamiltonians quadratic in momentum and position. This then links our approach to those used in quantum mechanics and optics. The link between the theory of this noncommutative geometric algebra and the theory of vector bundles is also discussed.

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