Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [120]-124).

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [129]-134).

Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Aug. 6, 2009). Vita. Includes bibliographical references.

The work is concerned with the band-limited signal extrapolation using truncated series of prolate spheroidal wave function. Our aim is to investigate the extent to which it is possible to extrapolate signal from its samples taken in a finite interval. It is often believed that this extrapolation method depends on computing definite integrals. We show an alternative approach by using the least squares method and we compare it with the methods of numerical integration. We also consider their performance in the presence of noise and the possibility of using these algorithms for real-time data processing. Finally all proposed algorithms are tested using real data from a microphone array, so that their performance can be compared.

Models of the spontaneous emission and absorption of photons coupled to the electronic states of quantum dots, molecules, N-V (single nitrogen vacancy) centers in diamond, that can be modeled as artificial few level atoms, are important to the development of quantum computers and quantum networks. A quantum source modeled after an effective few level system is strongly dependent on the type and coupling strength the allowed transitions. These selection rules are subject to the Wigner-Eckert theorem which specifies the possible transitions during the spontaneous creation of a photonic state and its subsequent emission. The model presented in this dissertation describes the spatio-temporal evolution of photonic states by means of a Dirac-like equation for the photonic wave function within the region of interaction of a quantum source. As part of this aim, we describe the possibility to shift from traditional electrodynamics and quantum electrodynamics, in terms of electric and magnetic fields, to one in terms of a photonic wave function and its operators. The mapping between these will also be presented herein. It is further shown that the results of this model can be experimentally verified. The suggested method of verification relies on the direct comparison of the calculated density matrix or Wigner function, associated with the quantum state of a photon, to ones that are experimentally reconstructed through optical homodyne tomography techniques. In this non-perturbative model we describe the spontaneous creation of photonic state in a non-Markovian limit which does not implement the Weisskopf-Wigner approximation. We further show that this limit is important for the description of how a single photonic mode is created from the possibly infinite set of photonic frequencies νk that can be excited in a dielectric-cavity from the vacuum state. We use discretized central-difference approximations to the space and time partial derivatives, similar to finite-difference time domain models, to compute these results. The results presented herein show that near field effects need considered when describing adjacent quantum sources that are separated by distances that are small with respect to the wavelength of iii their spontaneously created photonic states. Additionally, within the future scope of this model, we seek results in the Purcell and Rabi regimes to describe enhanced spontaneous emission events from these few-level systems, as embedded in dielectric cavities. A final goal of this dissertation is to create novel computational and theoretical models that describe single and multiple photon states via single photon creation and annihilation operators.

Many-body perturbation theory and coupled-cluster theory, combined with carefully constructed basis sets, can be used to accurately compute the properties of small molecules. We applied a series of methods and basis sets aimed at reaching the ab initio limit to determine the barrier to planarity for ethylene cation. For potential energy surfaces corresponding to bond dissociation, a single Slater determinant is no longer an appropriate reference, and the single-reference hierarchy breaks down. We computed full configuration interaction benchmark data for calibrating new and existing quantum chemical methods for the accurate description of potential energy surfaces. We used the data to calibrate single-reference configuration interaction, perturbation theory, and coupled-cluster theory and multi-reference configuration interaction and perturbation theory, using various types of molecular orbitals, for breaking single and multiple bonds on ground-state and excited-state surfaces. We developed a determinant-based method which generalizes the formulation of many-body wave functions and energy expectation values. We used the method to calibrate single-reference and multi-reference configuration interaction and coupled-cluster theories, using different types of molecular orbitals, for the symmetric dissociation of water. We extended the determinant-based method to work with general configuration lists, enabling us to study, for the first time, arbitrarily truncated coupled-cluster wave functions. We used this new capability to study the importance of configurations in configuration interaction and coupled-cluster wave functions at different regions of a potential energy surface.

An accurate and generalized global retrieval algorithm from satellite observations is a prerequisite to understand the radiative effect of atmospheric aerosols on the climate system. Current operational aerosol retrieval algorithms are limited by the inversion schemes and suffering from the non-uniqueness problem. In order to solve these issues, a new algorithm is developed for the retrieval of non-spherical dust aerosol over land using multi-angular radiance and polarized measurements of the POLDER (POLarization and Directionality of the Earth’s Reflectances) and wide spectral high-resolution measurements of the MODIS (MODerate resolution Imaging Spectro-radiometer). As the first step to account for the non-sphericity of irregularly shaped dust aerosols in the light scattering problem, the spheroidal model is introduced. To solve the basic electromagnetic wave scattering problem by a single spheroid, we developed an algorithm, by transforming the transcendental infinite-continued-fraction-formeigen equation into a symmetric tri-diagonal linear system, for the calculation of the spheroidal angle function, radial functions of the first and second kind, as well as the corresponding first order derivatives. A database is developed subsequently to calculate the bulk scattering properties of dust aerosols for each channel of the satellite instruments. For the purpose of simulation of satellite observations, a code is developed to solve the VRTE (Vector Radiative Transfer Equation) for the coupled atmosphere-surface system using the adding-doubling technique. An alternative fast algorithm, where all the solid angle integrals are converted to summations on an icosahedral grid, is also proposed to speed-up the code. To make the model applicable to various land and ocean surfaces, a surface BRDF (Bidirectional Reflectance Distribution Function) library is embedded into the code. Considering the complimentary features of the MODIS and the POLDER, the collocated measurements of these two satellites are used in the retrieval process. To reduce the time spent on the simulation of dust aerosol scattering properties, a single-scattering property database of tri-axial ellipsoid is incorporated. In addition, atmospheric molecule correction is considered using the LBLRTM (Line-By-Line Ra- diative Transfer Model). The Levenberg-Marquardt method was employed to retrieve all the interested dust aerosol parameters and surface parameters simultaneously. As an example, dust aerosol properties retrieved over the Sahara Desert are presented.

La Théorie Variationnelle des Rayons Complexes (TVRC) est une méthode ondulatoire adaptée à la résolution de problèmes de vibrations dans le domaine des moyennes fréquences. Elle utilise une formulation faible du problème qui permet d'utiliser n'importe quelles fonctions de forme qui vérifient l'équation d'équilibre à l'intérieur du sous domaine. Ainsi la solution peut être approximée par une répartition intégrale d'ondes planes, cette approche est particulièrement efficace en moyenne fréquence et conduit a un très bon taux de convergence de la méthode. Dans les travaux précédents, l'amplitude des ondes planes était discrétisée par une fonction constante par morceaux. Dans cette thèse, une nouvelle forme de discrétisation est proposée, basée sur les séries de Fourier. L'extension aux problèmes tridimensionnels est directe grâce à l'utilisation des harmoniques sphériques. Cette nouvelle approche permet d'améliorer l'efficacité et la robustesse de la méthode grâce notamment à un schéma d'intégration semi-analytique. Cette nouvelle version de la TVRC est alors capable de traiter des problèmes d'une complexité industrielle, et de résoudre des problèmes à des fréquences relativement élevées. / The Variational Theory of Complex Rays (VTCR) is a wave-based computational approach dedicated to the resolution of medium-frequency problems. It uses a variational formulation of the problem which enables one to use any type of shape function within the substructures provided that it verifies the governing equation. Thus, the solution can be approximated using plane waves, which is very interesting in the medium-frequency vibration domain and also leads to a strong convergence of the method. In the previous works, this was shown in the case of acoustic problems in which the amplitudes of the plane waves were calculated as wavebands. In this thesis, we propose a new approximation of these amplitudes based on Fourier series. The extension to 3D problems is straightforward thanks to the use of spherical harmonics. We show that this approach increases the robustness of the method as it handles problems of industrial complexity, makes it more efficient numerically thanks to analytical integration and extends its applicability to somewhat higher frequencies.

In the exploration of chemical systems through quantum mechanics, accurate treatment of the electron wavefunction, and the related electron density, is fundamental to extracting information concerning properties of a system. This work examines challenges in achieving accurate chemical information through manipulation of the one-electron basis set.

As CMOS technology scaling is fast approaching its fundamental limits, several new nano-electronic devices have been proposed as possible alternatives to MOSFETs. Research on emerging devices mainly focusses on improving the intrinsic characteristics of these single devices keeping the overall integration approach fairly conventional. However, due to high logic complexity and wiring requirements, the overall system-level power, performance and area do not scale proportional to that of individual devices. Thereby, we propose a fundamental shift in mindset, to make the devices themselves more functional than simple switches. Our goal in this thesis is to develop a new nanoscale fabric paradigm that enables realization of arbitrary logic functions (with high fan-in/fan-out) more efficiently. We leverage on non-equilibrium spin wave physical phenomenon and wave interference to realize these elementary functions called Spin Wave Functions (SPWFs). In the proposed fabric, computation is based on the principle of wave superposition. Information is encoded both in the phase and amplitude of spin waves; thereby providing an opportunity for compressed data representation. Moreover, spin wave propagation does not involve any physical movement of charge particles. This provides a fundamental advantage over conventional charge based electronics and opens new horizons for novel nano-scale architectures. We show several variants of the SPWFs based on topology, signal weights, control inputs and wave frequencies. SPWF based designs of arithmetic circuits like adders and parallel counters are presented. Our efforts towards developing new architectures using SPWFs places strong emphasis on integrated fabric-circuit exploration methodology. With different topologies and circuit styles we have explored how capabilities at individual fabric components level can affect design and vice versa. Our estimates on benefits vs. 45nm CMOS implementation show that, for a 1-bit adder, up to 40x reduction in area and 228x reduction in power is possible. For the 2-bit adder, results show that up to 33x area reduction and 222x reduction in power may be possible. Building large scale SPWF-based systems, requires mechanisms for synchronization and data streaming. In this thesis, we present data streaming approaches based on Asynchronous SPWFs (A-SPWFs). As an example, a 32-bit Carry Completion Sensing Adder (CCSA) is shown based on the A-SPWF approach with preliminary power, performance and area evaluations.