The single scattering properties of atmospheric particles are fundamental to radiative simulations and remote sensing applications. In this study, an efficient technique, namely, the pseudo-spectral time-domain (PSTD) method which was first developed to study acoustic wave propagation, is applied to the scattering of light by nonspherical particles with small and moderate size. Five different methods are used to discretize Maxwell’s equations in the time domain. The perfectly matched layer (PML) absorbing boundary condition is employed in the present simulation for eliminating spurious wave propagations caused by the spectral method. A 3-D PSTD code has been developed on the basis of the five aforementioned discretization methods. These methods provide essentially the same solutions in both absorptive and nonabsorptive cases. In this study, the applicability of the PSTD method is investigated in comparison with the Mie theory and the T-matrix method. The effects of size parameter and refractive index on simulation accuracy are discussed. It is shown that the PSTD method is quite accurate when it is applied to the scattering of light by spherical and nonspherical particles, if the spatial resolution is properly selected. Accurate solutions can also be obtained from the PSTD method for size parameter of 80 or refractive index of 2.0+j0. Six ice crystal habits are defined for the PSTD computational code. The PSTD results are compared with the results acquired from the finite difference time domain (FDTD) method at size parameter 20. The PSTD method is about 8-10 times more efficient than the conventional FDTD method with similar accuracy. In this study, the PSTD is also applied to the computation of the phase functions of ice crystals with a size parameter of 50. Furthermore, the PSTD, the FDTD, and T-matrix methods are applied to the study of the optical properties of horizontally oriented ice crystals. Three numerical schemes for averaging horizontal orientations are developed in this study. The feasibility of using equivalent circular cylinders as surrogates of hexagonal prisms is discussed. The horizontally oriented hexagonal plates and the equivalent circular cylinders have similar optical properties when the size parameter is in the region about from 10 to 40. Otherwise, the results of the two geometries are substantially different.

The finite-difference time-domain (FDTD) method is one of the most popular numerical electromagnetic analysis tools. This method has been applied to a wide variety of problems such as antennas, electronic packaging, waveguides, etc. However, it is not suitable for large scale structures. The enormous memory requirement prohibits the use of FDTD to a large electrical size. Recently, the pseudospectral time-domain (PSTD) method has been introduced for solution of Maxwell¡¦s equation. This method adopts the Fourier transform algorithm to perform the spatial derivatives. According to Nyquist sampling theorem, it requires only 2 cells per wavelength, so that it is possible to efficiently model larger scale problems. This thesis describes a combination of PSTD and FDTD method applied in different directions. The FDTD be applied to directions along fine structures and the PSTD be applied in direction along large structures.

Atmospheric particles, i.e. ice crystals, dust particles, and black carbon, show significant complexities like irregular geometries, inhomogeneity, small-scale surface structures, and play a significant role in the atmosphere by scattering and absorbing the incident solar radiation and terrestrial thermal emission. Knowledge of aerosol scattering properties is a fundamental but challenging aspect of radiative transfer studies and remote sensing applications. This dissertation tries to improve our understanding on the scattering properties of atmospheric particles by investigating both the scattering algorithms and the representation of the realistic particles. One part of this dissertation discusses in details the pseudo-spectral time domain algorithm (PSTD) for calculating scattering properties, its advantages and the elimination of the Gibbs phenomenon. The applicability of the parallelized PSTD implementation is investigated for both spherical and nonspherical particles over a wide range of sizes and refractive indices, and the PSTD is applied for spherical particles with size parameters up to 200, and randomly oriented non-spherical ones with size parameters up to 100. The relative strengths of the PSTD are also shown by a systematic comparison with the discrete dipole approximation (DDA). The PSTD outperforms the DDA for particles with refractive indices larger than 1.4, and ones with smaller refractive indices by large sizes (e.g. size parameters larger than 60 for a refractive index of 1.2). The results suggest significant potential of the PSTD for the numerical investigation of the light scattering and corresponding atmospheric applications. The other part of this dissertation investigates the effects of particle complexities on the light scattering properties of the atmospheric particles, and three aspects corresponding to the irregular geometry, inhomogeneity and surface roughness are studied. To cover the entire particle size range from the Rayleigh to the geometric- optics regimes, the PSTD (for relatively small particles) is combined with the im- proved geometric-optics method (IGOM) that is only applicable for large particles. The Koch-fractal geometry is introduced to model the light scattering properties of aerosol, and performs an excellent job of reproducing the experimental measurements of various mineral dust particles. For the inhomogeneous particles, the applicability of the effective medium approximations (EMA) is tested, and the EMA can be used to approximate the scattering properties of inhomogeneous particles only when the particles are uniformly internal mixtures. Furthermore, an irregular rough model is developed to study the effects of the small-scale surface roughness on the light scattering properties. In conclusion, the dissertation finds that the complexities of atmospheric particles have to be fully considered to obtain their scattering properties accurately.

The pseudo-spectral time domain (PSTD) and discrete dipole approximation (DDA) are two of the most popular methods to model the single-scattering properties of ice crystals and aerosols. Both methods solve for Maxwell’s equations. The PSTD method uses a Fourier pseudo-spectral method and a finite-difference method to compute the spatial and temporal derivatives of electromagnetic fields. The DDA method uses an electromagnetic integral equation in the frequency domain to calculate the single-scattering properties. We used a spherical model for this study because the analytical solution was given by the Lorenz-Mie theory. Previous studies have found that at refractive indices between 1.2 and 1.5, PSTD computed the single-scattering properties of spherical particles faster for large size parameters, while DDA was more computationally efficient at small size parameters; however, these previous studies did not consider absorptive cases. The purpose of this study was to expand the range of refractive indices to include absorptive cases and to determine which method was more efficient for computing the single-scattering properties of atmospheric particles within set criteria. The PSTD and DDA methods were systematically assessed in this study for 31 different realistic complex refractive indices. Similar to the previous studies, it was found that PSTD was more efficient than DDA for particles with large size parameters. The results in this study were consistent with the previous studies for non-absorptive to moderately absorptive particles. However, for strongly absorptive cases, DDA was more efficient than PSTD at all size parameters for the absorptive particles. It was also determined that the efficiencies of the two methods were dependent on both the real and imaginary parts of the complex refractive index. The significance of this study was to improve our understanding of the capabilities of the PSTD and DDA methods for computing single-scattering properties.

Childhood exposure to familial violence increases risk for adult pathology, namely posttraumatic stress disorder (PTSD) and depression. Primary PTSD symptoms of hyperarousal and avoidance are implicated in overgeneral memory (OGM) theory in prior research. Individuals with trauma history tend to report OGMs, or non-specific autobiographical memories, perhaps to avoid unpleasant arousal elicited by recalling specific events. OGM, PTSD, depression, and arousal were assessed in adults with and without familial violence history. Arousal was measured via galvanic skin response (GSR) during an autobiographical memory task (AMT), requiring memory recall in response to emotionally-valenced cue words. Familial violence history was linked to higher incidence of PTSD symptoms. Childhood psychological violence was predictive of adult PTSD. Rates of depression, OGM, and arousal did not significantly vary by violence history. Significant gender differences were found relating to type of violence exposure and adult functioning. Research limitations, clinical implications, and future research suggestions are discussed.