<p> Quantum Monte Carlo techniques stochastically evaluate integrals to solve the many-body Schr&ouml;dinger equation. QMC algorithms scale favorably in the number of particles simulated and enjoy applicability to a wide range of quantum systems. Advances in the core algorithms of the method and their implementations paired with the steady development of computational assets have carried the applicability of QMC beyond analytically treatable systems, such as the Homogeneous Electron Gas, and have extended QMC&rsquo;s domain to treat atoms, molecules, and solids containing as many as several hundred electrons.</p><p> FN-DMC projects out the ground state of a wave function subject to constraints imposed by our ansatz to the problem. The constraints imposed by the fixed-node Approximation are poorly understood. One key step in developing any scientific theory or method is to qualify where the theory is inaccurate and to quantify how erroneous it is under these circumstances.</p><p> I investigate the fixed-node errors as they evolve over changing charge density, system size, and effective core potentials. I begin by studying a simple system for which the nodes of the trial wave function can be solved almost exactly. By comparing two trial wave functions, a single determinant wave function flawed in a known way and a nearly exact wave function, I show that the fixed-node error increases when the charge density is increased. Next, I investigate a sequence of Lithium systems increasing in size from a single atom, to small molecules, up to the bulk metal form. Over these systems, FN-DMC calculations consistently recover 95% or more of the correlation energy of the system. Given this accuracy, I make a prediction for the binding energy of Li₄ molecule. Last, I turn to analyzing the fixed-node error in first and second row atoms and their molecules. With the appropriate pseudo-potentials, these systems are iso-electronic, show similar geometries and states. One would expect with identical number of particles involved in the calculation, errors in the respective total energies of the two iso-electronic species would be quite similar. I observe, instead, that the first row atoms and their molecules have errors larger by twice or more in size. I identify a cause for this difference in iso-electronic species. The fixed-node errors in all of these cases are calculated by careful comparison to experimental results, showing that FN-DMC to be a robust tool for understanding quantum systems and also a method for new investigations into the nature of many-body effects.</p>

<p> The compressible Rayleigh-Taylor instability (RTI) occurs when a fluid of low molar mass supports a fluid of higher molar mass against a gravity-like body force or in the presence of an accelerating front. Intrinsic to the problem are highly stratified background states, acoustic waves, and a wide range of physical scales. The objective of this thesis is to develop a specialized computational framework that addresses these challenges and to apply the advanced methodologies for direct numerical simulations of compressible RTI. Simulations are performed using the Parallel Adaptive Wavelet Collocation Method (PAWCM). Due to the physics-based adaptivity and direct error control of the method, PAWCM is ideal for resolving the wide range of scales present in RTI growth. Characteristics-based non-reflecting boundary conditions are developed for highly stratified systems to be used in conjunction with PAWCM. This combination allows for extremely long domains, which is necessary for observing the late time growth of compressible RTI. Initial conditions that minimize acoustic disturbances are also developed. The initialization is consistent with linear stability theory, where the background state consists of two diffusively mixed stratified fluids of differing molar masses. The compressibility effects on the departure from the linear growth, the onset of strong non-linear interactions, and the late-time behavior of the fluid structures are investigated. It is discovered that, for the thermal equilibrium case, the background stratification acts to suppress the instability growth when the molar mass difference is small. A reversal in this monotonic behavior is observed for large molar mass differences, where stratification enhances the bubble growth. Stratification also affects the vortex creation and the associated induced velocities. The enhancement and suppression of the RTI growth has important consequences for a detailed understanding of supernovae flame front acceleration and fuel capsule designs for inertial confinement fusion.</p>

<p> Accurate, cross-scanner assessment of in-vivo air density used to quantitatively assess amount and distribution of emphysema in COPD subjects has remained elusive. Hounsfield units (HU) within tracheal air can be considerably more positive than -1000 HU. With the advent of new dual-source scanners which employ dedicated scatter correction techniques, it is of interest to evaluate how the quantitative measures of lung density compare between dual-source and single-source scan modes. This study has sought to characterize in-vivo and phantom-based air metrics using dual-energy computed tomography technology where the nature of the technology has required adjustments to scatter correction. </p><p> Anesthetized ovine (N=6), swine (N=13: more human-like rib cage shape), lung phantom and a thoracic phantom were studied using a dual-source MDCT scanner (Siemens Definition Flash. Multiple dual-source dual-energy (DSDE) and single-source (SS) scans taken at different energy levels and scan settings were acquired for direct quantitative comparison. Density histograms were evaluated for the lung, tracheal, water and blood segments. Image data were obtained at 80, 100, 120, and 140 kVp in the SS mode (B35f kernel) and at 80, 100, 140, and 140-Sn (tin filtered) kVp in the DSDE mode (B35f and D30f kernels), in addition to variations in dose, rotation time, and pitch. To minimize the effect of cross-scatter, the phantom scans in the DSDE mode was obtained by reducing the tube current of one of the tubes to its minimum (near zero) value.</p><p> When using image data obtained in the DSDE mode, the median HU values in the tracheal regions of all animals and the phantom were consistently closer to -1000 HU regardless of reconstruction kernel (chapters 3 and 4). Similarly, HU values of water and blood were consistently closer to their nominal values of 0 HU and 55 HU respectively. When using image data obtained in the SS mode the air CT numbers demonstrated a consistent positive shift of up to 35 HU with respect to the nominal -1000 HU value. In vivo data demonstrated considerable variability in tracheal, influenced by local anatomy with SS mode scanning while tracheal air was more consistent with DSDE imaging. Scatter effects in the lung parenchyma differed from adjacent tracheal measures.</p><p> In summary, data suggest that enhanced scatter correction serves to provide more accurate CT lung density measures sought to quantitatively assess the presence and distribution of emphysema in COPD subjects. Data further suggest that CT images, acquired without adequate scatter correction, cannot be corrected by linear algorithms given the variability in tracheal air HU values and the independent scatter effects on lung parenchyma.</p>

<p> Optical microscopy is one of the oldest and most important imaging techniques; however, its far-field resolution is diffraction-limited. In this dissertation, we proposed and developed a novel method of optical microscopy with super-resolution by using high-index dielectric microspheres immersed in liquid and placed on the surface of the structures under study. We used barium titanate glass microspheres with diameters of D~2-220 &mu;m and refractive indices <i> n</i>&sim;1.9-2.1 to discern minimal feature sizes &sim;&lambda;/4 (down to &sim;&lambda;/7) of various photonic and plasmonic nanostructures, where &lambda; is the illumination wavelength. We studied the magnification, field of view, and resolving power, in detail, as a function of sphere sizes.</p><p> We studied optical coupling, transport, focusing, and polarization properties of linear arrays of dielectric spheres. We showed that in arrays of spheres with refractive index n=<rad><rcd>3</rcd></rad>, a special type of rays with transverse magnetic (TM) polarization incident on the spheres under the Brewster&#129;'s angle form periodically focused modes with radial polarization and <i> 2D</i> period, where <i> D</i> is the diameter of the spheres. We showed that the formation of periodically focused modes in arrays of dielectric spheres gives a physical explanation for beam focusing and extraordinarily small attenuation of light in such chains. We showed that the light propagation in such arrays is strongly polarization-dependent, indicating that such arrays can be used as filters of beams with radial polarization. The effect of forming progressively smaller focused beams was experimentally observed in chains of sapphire spheres in agreement with the theory.</p><p> We studied optical coupling,transport, focusing, and polarization properties of linear arrays of dielectric spheres. We showed that in arrays of spheres with refractive index n=&#129;&atilde;3, a special type of rays with transverse magnetic (TM) polarization incident on the spheres under the Brewster&#129;'s angle form periodically focused modes with radial polarization and 2D period, where D is the diameter of the spheres. We showed that the formation of periodically focused modes in arrays of dielectric spheres gives a physical explanation for beam focusing and extraordinarily small attenuation of light in such chains. We showed that the light propagation in such arrays is strongly polarization-dependent, indicating that such arrays can be used as filters of beams with radial polarization. The effect of forming progressively smaller focused beams was experimentally observed in chains of sapphire spheres in agreement with the theory.</p>

<p> Using the Hampton University (HU) Mie and Raman lidar, tropospheric temperature profiles were inferred from lidar measurements of anti-Stokes rotational Raman (RR) backscattered laser light from atmospheric nitrogen and oxygen molecules. The molecules were excited by 354.7 nanometer (nm) laser light emitted by the HU lidar. Averaged over 60-minute intervals, RR backscattered signals were detected in narrow 353.35 nm and 354.20 nm spectral bands with full-widths-at-half-maxima (FWHM) of 0.3 nm. During the special April 19-30, 2012, Ground-Based Remote Atmospheric Sounding Program (GRASP) campaign, the lidar temperature calibration coefficients were empirically derived using linear least squares and second order polynomial analyses of the lidar backscattered RR signals and of reference temperature profiles, obtained from radiosondes. The GRASP radiosondes were launched within 400 meters of the HU lidar site. Lidar derived temperature profiles were obtained at altitudes from the surface to over 18 kilometers (km) at night, and up to 5 km during the day. Using coefficients generated from least squares analyses, nighttime profiles were found to agree with profiles from reference radiosonde measurements within 3 K, at altitudes between 4 km and 9 km. Coefficients generated from the second order analyses yielded profiles which agreed with the reference profiles within 1 K uncertainty level in the 4 km to 10 km altitude region. Using profiles from GRASP radiosondes, the spatial and temporal homogeneities of the atmosphere, over HU, were estimated at the 1.5 K level within a 10 km radius of HU, and for observational periods approaching 3 hours. Theoretical calibration coefficients were derived from the optical and physical properties of the HU RR lidar and from the spectroscopic properties of atmospheric molecular nitrogen and oxygen. The theoretical coefficients along with lidar measurements of sky background radiances were used to evaluate the temporal stability of the empirically derived temperature profiles from the RR lidar measurements. The evaluations revealed systematic drifts in the coefficients. Frequent reference radiosonde temperature profiles should be used to correct for the drifts in the coefficients. </p><p> For the first time, the cause of the coefficient drifts has been identified as the differences in the aging of the spectral responses of the HU lidar detector pairs. For the first time, the use of lidar sky background measurements was demonstrated as a useful technique to correct for the coefficient drift. This research should advance the derivations of lidar temperature calibration coefficients which can be used for long observational periods of temperature fields without the need for frequent lidar calibrations using radiosondes. </p>

Artificial neural network models have been developed that provide the magnetospheric parameters Dst, polar cap potential and the midnight equatorward boundary of diffuse aurora. Layered feedforward neural networks have successfully learned the relationship between the solar wind and the magnetospheric parameters using supervised back-propagation training. All models have achieved a higher prediction accuracy than the existing empirical or statistical models. These models are applied to the prediction of the parameters, which will then be used by the Rice Magnetospheric Specification and Forecast Model (MSFM). The neural network models are able to forecast the magnetospheric parameters 30 to 60 minutes ahead using the information from a solar wind monitor spacecraft. With the forecast values, the MSFM will be able to forecast particle fluxes in the inner magnetosphere. The MSFM is applied to the April 1988 magnetic storm for the forecast capability test. The neural network modeling, the comparison of the prediction accuracy with other methods and the result of the MSFM forecast capability test are presented.

The exponentially decaying semi-stationary states of an assembly of identical classical radiators can have decay rates and resonant frequencies significantly different from that of an isolated radiator. These coherent effects on classical radiators emitting classical waves apply also to the particle processes in quantum limits, leading to the superradiant and subradiant modes with widths(decay rates) greatly enhanced or suppressed and resonant energies significantly shifted. The purpose of this thesis is to investigate these coherent effects on slow neutron-heavy nuclei interaction. A simple field model is introduced to show the coherent effects on the decay rates and resonant energies of two identical decaying states and on the neutron widths and resonant energies of neutron-two nuclei scattering. The latter case is also obtained by multiple scattering theory and is extended to a more general case of neutron-N nuclei scattering. The coherent effects on neutron width near Bragg angle in a crystal are also investigated.

Spin-lattice, T$\sb1$, and spin-spin, T$\sb2$, relaxation times of the alkanes from n-pentane to n-hexadecane were measured at 25$\sp\circ$C. The T$\sb1$ values agree well with those of previous investigators. The values of T$\sb1$ and T$\sb2$ were equal for each alkane studied. Empirical correlations were found between T$\sb1$ and two parameters: the acentric factor and the rotational coupling coefficient. The product $\eta$T$\sb1$ was constant for all the alkanes except n-pentane. The spin-lattice relaxation time was dedimensionalized and a three parameter corresponding states correlation was developed following the treatment of Tham and Gubbins (42) for transport coefficients. Excellent correspondence was found for the saturated alkanes over the temperature range 22 to 90$\sp\circ$C and for benzene from 12 to 63$\sp\circ$C. Spin-lattice relaxation times of mixtures of n-hexane and n-hexadecane were measured at 25$\sp\circ$C. The decay of magnetization could not be described by a single exponential curve. The results were analyzed using three methods. (Abstract shortened with permission of author.)

We have used the density functional ab initio method to study the reactivity of small clusters (ammonia reacting with GaAs clusters), and the effects of electric field on adatom-surface interactions (H and Al adsorbed on Si(111) surface). In the case of NH$\sb3$ reactivity at various sites of a Ga$\rm\sb5As\sb5$ cluster, a strong correlation is found between the adsorbate-cluster binding energy and charge transfer. Ionizing the bare cluster to a cationic charge state enables multiple chemisorption of ammonia, which is much less favored on a neutral cluster and can be prohibited on a negatively charged cluster. In the case H and Al adsorbed on a Si(111) surface, the influence of an external electric field, such as that present in a scanning tunnelling microscope (STM), on the chemisorption bond is investigated. The changes in charge distributions, vibrational frequencies and adsorbate desorption barriers are calculated as a function of the strength and direction of the electric field. We find that the characteristics of the chemisorption bond can, to a large extent, be controlled through the externally applied field.

High power femtosecond VUV/XUV pulses covering new spectral regions have been generated through nonlinear interaction of a femtosecond KrF laser with xenon and argon. Conversion efficiencies as high as 10$\sp{-3}$ have been observed. A six-wave mixing process and several four-wave mixing processes under intense light field have been experimentally studied. The temporal duration of the femtosecond VUV pulse has been experimentally measured for the first time based on the defocusing caused by a femtosecond laser produced plasma.