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The central objective of this dissertation is developing new methods for calculating higher-order nonlinear optical responses of atoms, molecules, and ions, and discussing the relevant physical mechanisms that give rise to harmonic generation, Kerr effect, and higher-order Kerr effect. The applications of nonlinear optical properties in development of predictive models for femtosecond laser filamentation dynamics, photoemission spectroscopy, imaging, and design of new molecular systems have motivated the theoretical investigations in advancing methods for calculating nonlinear optical properties and finding the optimum conditions for controlling the nonlinearities. The time-dependent nonlinear refractive index coefficient 4 n is investigated for argon and generalized for all noble gas atoms helium, neon, krypton, and xenon in the wavelengths ranging from 250 nm to 2000 nm, using ab initio methods. The secondorder polynomial fitting of DC-Kerr, electric-field-induced second-harmonic generation (ESHG), and static second-order hyperpolarizability have been performed, using an auxiliary electric field approach to obtain the corresponding fourth-order optical properties. An expression on the basis of static, DC-Kerr, DFWM fourth-order hyperpolarizability is derived, which allows the calculations of the DSWM coefficients with considerably reduced error. The results of the calculations suggest that filament stabilization is most likely to be induced by the generation of free electrons. Applications of these calculations resolve the HOKE controversy and are important for the development of predictive models for femtosecond laser filamentation dynamics. In a series of proof-of-concept studies, the approach was employed for calculating dynamic linear and nonlinear hyperpolarizability of the radical cations. In this regard, the polarizability and second-order hyperpolarizability of nitrogen radical cation were investigated, using density functional theory (DFT) and multi-configurational self-consistent field (MCSCF) methods. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient for nitrogen radical cation, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The calculations of second-order optical properties for nitrogen radical cation as a function of bond length have been investigated to study the effect of internuclear bond distance on optical process. The variation of nonlinear responses versus bond length shows the potential application in finding optimum conditions for higher values of nonlinear coefficients. Furthermore, the computation of dynamic second-order hyperpolarizabilities for multiply ionized noble gases have been studied in the wavelength ranging from 100 nm to the red of the first multi-photon resonance all the way toward the static regime, using the MCSCF method. The results indicate that the second-order hyperpolarizability coefficients decrease when the electrons are removed from the systems. As the atoms reach higher ionization states, the second-order hyperpolarizability responses as a function of wavelength, become less dispersive. The second-order hyperpolarizability coefficients for each ionized species have also been investigated in terms of quantum state symmetries; the results suggest that the sign of the optical responses for each ionized atom depends on the spin of the quantum states defined for the ionized species. The calculations are of value for predictive models of high-harmonic generation in multiply ionized plasma at X-ray photon energies. This research also focuses on investigating possible mechanisms for photodissociation of polyatomic molecules (acetophenone and the substituted derivatives) ionized through strong field infrared laser pulses. In this regard, quantum mechanical methods are combined with pump-probe spectroscopy to understand and control the dissociation dynamics in strong field regime. The applications of quantum mechanical models in interpreting time-resolved wavepacket dynamics and achieving coherent control has stimulated the interest to explore the PESs and investigate the role of conical intersections in wavepacket dynamics in strong field regime. The electronic ground and excited states for acetophenone radical cation and the substituted derivatives have been investigated to probe the resonance features observed in measurements at 1370 nm with laser intensity of 1013 W cm-2. The ten lowest lying ionic potential energy surfaces (PESs) of the acetophenone radical cation were explored, and the three-state conical intersection was mapped onto the PES, using MCSCF model to propose a photo-dissociation mechanism for acetophenone undergoing tunnel ionization and elucidate the potential dissociation pathways for formation of benzoyl fragment ion, as well as phenyl, acylium, and butadienyl small fragment ions. Similar calculations are presented for propiophenone radical cation which support the existence of a one-photon transition from the ground ionic to a bright dissociative D2 state, where motion of the acetyl group from a planar to nonplanar structure within the pulse duration enables the otherwise forbidden transition. The wavepacket dynamics in acetophenone molecular ion is modeled using the classical wavepacket trajectory calculations, to propose the mechanism wherein the 790 nm probe pulse excites a wavepacket on the ground surface D0 to the excited D2 surface at a delay of 325 fs. The innovations of this research are used to design control strategies for selective bond-breaking in acetophenone radical cation, as well as design control schemes for other molecules. / Chemistry

Granular materials, such as sand, are systems consisting of huge numbers of particles that interact with each other through inter-particle contacts. Different from continuum materials, a granular material displays distinctive features due to the discrete nature of the microstructure, characterized by a spatial arrangement of inter-particle connection as well as a force-chain network. With a consideration of the contact force, the overall contact network is divided into a strong sub-network and a weak sub-network that carry contacts with normal contact forces larger and lower than the average normal contact force, respectively. Thus, the fabric anisotropy for different contact networks, are employed to characterize the microstructure of the granular material. In this research, the behavior of granular materials subjected to quasi-static shear was extensively investigated in terms of the fabric evolution including the magnitude and direction of anisotropy for different contact networks. Both statistical and micromechanical approaches were adopted to obtain the macroscopic properties, such as the fabric tensor, Cauchy stress tensor and the second-order work, in terms of the micro-scale variables. The discrete element method (DEM) was employed to simulate laboratory tests along fixed loading paths; for example, 2D tests along proportional strain paths, 2D simple shear tests and 3D tests along radial stress paths on the π-plane. Results demonstrated that the induced fabric anisotropy for the overall contact network can be related to the deviatoric stress ratio for both two-dimensional and three-dimensional conditions. The relation was found to be not unique, depending on the loading paths as well as the stress state. Nevertheless, a unique linear fabric-stress relation was presented between the stress tensor and fabric tensor for the strong sub-network. Specifically, the obliquity of this linear relation was found to be a function of the mean stress. This description held true for initially isotropic specimens subjected to proportional and non-proportional loading paths. On the other hand, for the initially anisotropic specimen, this correspondence only worked at the critical stress state. According to Nicot and Darve (2006), the macro second-order work cannot be interpreted as a summation of the local second-order work from the contact plane. The second-order work induced by the fabric evolution and the volumetric change must also be taken into account. The second-order work induced by the fabric evolution cannot be neglected in 2D analysis along proportional strain paths. Moreover, the vanishing of the second-order work is related to the fabric anisotropy in contact sub-networks that the decrease of fabric anisotropy for the weak sub-network or the degradation of weak sub-network was observed to be an indicator of deformation instability even though the strong sub-network dominants the shear resistance. The degradation of strong sub-network was a necessary but not a sufficient condition of instability. The direction of the fabric anisotropy for the strong sub-network was observed to be coaxial with the orientation of the principal stress. The principal direction of fabric anisotropy for the weak sub-network was always perpendicular to that of the strong sub-network, regardless of whether the principal stress rotated or not. For the overall contact network, however, the direction of the fabric anisotropy was not necessarily in line with the major principal stress direction, even for an initial isotropic granular assembly. Therefore, the finding by Radjaï et al.(1998) that the direction of the fabric anisotropy for the weak sub-network is perpendicular to that for the overall contact network only held true for the loadings in which the critical stress could be approached no matter if the principal stress orientation rotated or not. Under this circumstance, the fabric anisotropy for the overall contact network could be interpreted as a function of sub-networks’ anisotropy weighted by the ratio of contact number in each sub-network over the total number of contacts. At critical state, both the strong sub-network and the overall contact network developed high fabric anisotropy with the weak sub-network being mostly isotropic. When plotted on the π-plane, both the fabric anisotropy for the strong sub-network and the fabric anisotropy for the overall contact network depended on the stress paths but were independent of the mean stress level. The response surface of the former could be expressed as a Lade’s surface. The response envelope of the latter was an inverted Lade’s surface. / Dissertation / Doctor of Philosophy (PhD) / In civil engineering, granular materials are ubiquitous, such as sand, gravel, rock, and concrete. Due to the discrete nature of microstructure, this type of material usually displays exceedingly complicated behaviours under shear, for example, dilatancy, non-coaxiality, critical state, instability, and anisotropy. These mechanical responses are notoriously difficult to model and most existing models are phenomenological and lack a clear physical meaning. To provide a clear physical meaning for the constitutive model of granular material, the current study explored the evolution of the microstructure within the granular material subjected to quasi-static shear and the micromechanical origins of those macroscopic behaviours such as critical state, non-coaxiality, and instability. Both micromechanical analysis and discrete element method were applied. Results showed that the evolution of the whole microstructure depended on the loading condition. However, the evolution of the microstructure joined by the ‘strong contacts’ was independent of the loading path. At critical state, the microstructure was highly anisotropic, not unique and depended on the stress paths. The rearrangement of the microstructure helped to maintain the stability of a granular material. The instability of the granular material was triggered by the failure of the microstructure joined by the ‘weak contacts’.

In this thesis, we study problems related to the reconstruction (up to bi-interpretability) of first-order theories from various functorial invariants: automorphism groups, endomorphism monoids, (categories of) countable models, and (ultra)categories of models. / Thesis / Master of Science (MSc)

A descriptive case study examined the gender differences concerning computer technology (IT) by a convenience sample (N = 180, 76%) of 11 th and 12 th graders at an elite public high school, recently named the "second best high school in America" (Newsweek, 2000), in suburban Northern Virginia. The purpose of the study was to examine the apparent discrepancy in male and female differences in computer use, interests, and attitudes. The research design included a student questionnaire combining the Computer Attitude Rating Scale (CARS, Heinssen, Glass, & Knight, 1987) and the Attitudes toward Computer Technology (ACT, Delcourt & Kinzie, 1993) with demographic and academic data (GPA, PSAT, and SAT I), and the Strong Interest Inventory (Strong, 1994). Chi-square tests of association for categorical data and t tests for independence of means for metric data were used to analyze the data, which resulted in several statistically significant relationships (p = < .05) and meaningful effect sizes (> .70). The results were higher mean scores for the Strong Realistic General Occupational Theme (males) and Artistic Theme (females); the Athletic and Mechanical Basic Interest Scales (males) and Music/Drama, Art, Culinary Arts, and Social Service Scales (females), and Risk-Taking Personal Style Scales (males) and Working Style with People (females). Females also had higher GPAs, levels of computer anxiety, resistance to technology, and avoidance of careers and study in computer fields. Females chose Pre-Medicine majors to help others and males chose Computer Science majors to gain financial rewards. The implications for practice and research included: female technology internships, 9th grade mechanical and technical training, computer anxiety group counseling, cooperative learning and hands on instruction, female-friendly computer and computer science classes, equal access to computers at all grade levels, student-parent information programs concerning the many opportunities and high paying jobs available in computer technology, female orientated computer games, and more non-linear computer programs and activities that encourage females to "have fun" with computers and not view them as machines. A longitudinal study of the current sample and research at other grade levels and locations were recommended. / Ph. D.

The design earthquake selection problem is fundamentally probabilistic. Disaggregation of a probabilistic model of the seismic hazard offers a rational and objective approach that can identify the most likely earthquake scenario(s) contributing to hazard. An ensemble of time series can be selected on the basis of the modal earthquakes derived from the disaggregation. This gives a useful time-domain realization of the seismic hazard, to the extent that a single motion parameter captures the important time-domain characteristics. A possible limitation to this approach arises because most currently available motion prediction models for peak ground motion or oscillator response are essentially independent of duration, and modal events derived using the peak motions for the analysis may not represent the optimal characterization of the hazard. The elastic input energy spectrum is an alternative to the elastic response spectrum for these types of analyses. The input energy combines the elements of amplitude and duration into a single parameter description of the ground motion that can be readily incorporated into standard probabilistic seismic hazard analysis methodology. This use of the elastic input energy spectrum is examined. Regression analysis is performed using strong motion data from Western North America and consistent data processing procedures for both the absolute input energy equivalent velocity, (Vea), and the elastic pseudo-relative velocity response (PSV) in the frequency range 0.5 to 10 Hz. The results show that the two parameters can be successfully fit with identical functional forms. The dependence of Vea and PSV upon (NEHRP) site classification is virtually identical. The variance of Vea is uniformly less than that of PSV, indicating that Vea can be predicted with slightly less uncertainty as a function of magnitude, distance and site classification. The effects of site class are important at frequencies less than a few Hertz. The regression modeling does not resolve significant effects due to site class at frequencies greater than approximately 5 Hz. Disaggregation of general seismic hazard models using Vea indicates that the modal magnitudes for the higher frequency oscillators tend to be larger, and vary less with oscillator frequency, than those derived using PSV. Insofar as the elastic input energy may be a better parameter for quantifying the damage potential of ground motion, its use in probabilistic seismic hazard analysis could provide an improved means for selecting earthquake scenarios and establishing design earthquakes for many types of engineering analyses. / Ph. D.

Crash tests of strong-post w-beam guardrail have focused entirely on the performance of new guardrail. The risk posed by minor damage modes, e.g. small deflections and missing posts, has never been evaluated. Using finite element models validated by real world crash tests, this study assessed the safety risk of crashes into guardrail with minor damage. The minor damage modes under consideration for this study were rail and post deflection, missing posts, rail flattening, and post/rail separation. Each of these damage modes was evaluated according to the testing protocols laid out in National Cooperative Highway Research Program (NCHRP) Report 350, test level 3. A number of minor damage modes were found to pose significant risks to vehicle occupants and should be repaired as soon as possible. In order of priority of repair, these modes are missing posts, rail and post deflection over 6â , and rail flattening over 50%. Damage modes of less concern were rail and post deflections less than 6â , rail only deflection up to 6â , flattening less than 50%, and separation of the posts from rails. These recommendations were on the conservative side because preventing occupant injury was the highest priority of guardrail performance. Guardrails with rail and post deflection posed a risk of vehicle vaulting due to lowered rail height and failure of the posts to separate from the rails. This risk would be even greater for guardrails embedded in soft soils, which allow for greater deflection. Guardrails with missing posts frequently resulted in snagging of the vehicle tire on the downstream posts, as well as large increases in the tension carried by the rails during impact. Flattened rails posed a risk of vehicle rollover as they provided a ramp-like surface which caused the side of the vehicle to move upward, greatly increasing the change of override. Flattening also occurs frequently with other damage modes. Pre-existing separation of posts from the rails was found to have very little effect on the crash outcome. Separation of the posts from the rails was desirable as it prevented failure modes that were observed for the rail and post deflection simulations while maintaining the post contributions to lateral strength of the guardrail. / Master of Science