We investigate the truncated moment problem, especially the Carathéodory number, the set of atoms and determinacy.

Density functional theory (DFT) calculations (using Becke's exchange in conjunction with Lee-Yang-Parr's correlation functional (BLYP) and Becke's three-parameter hybrid DFT/HF method using Lee-Yang-Parr's correlation functional (B3LYP)) have been carried out to investigate the structure, dipole moment, and vibrational spectrum of azulene. Structural parameters obtained by both BLYP/6-31G* and B3LYP/6-31G* geometry optimization are in good agreement with available experimental data and show clearly the aromatic nature (bond equalization), a property the Hartree-Fock theory fails to describe correctly. The BLYP/6-31G* and B3LYP/6-31G* dipole moments are within experimental uncertainty and are in good agreement with results obtained from the much more expensive MP2 and MR-SDCI calculations. Most of the BLYP/6-31G* vibrational frequencies are in excellent agreement with available experimental assignments. On the basis of the calculated results, assignments of some missing frequencies in the experimental studies are proposed.

Designing photonic-plasmonic nanostructures with desirable electromagnetic properties is a central problem in modern photonics engineering. As limited by available materials, engineering geometry of optical materials at both element and array levels becomes the key to solve this problem. In this thesis, I present my work on the development of novel methods and design strategies for photonic-plasmonic structures and metamaterials, including novel Green’s matrix-based spectral methods for predicting the optical properties of large-scale nanostructures of arbitrary geometry. From engineering elements to arrays, I begin my thesis addressing toroidal electrodynamics as an emerging approach to enhance light absorption in designed nanodisks by geometrically creating anapole configurations using high-index dielectric materials. This work demonstrates enhanced absorption rates driven by multipolar decomposition of current distributions involving toroidal multipole moments for the first time. I also present my work on designing helical nano-antennas using the rigorous Surface Integral Equations method. The helical nano-antennas feature unprecedented beam-forming and polarization tunability controlled by their geometrical parameters, and can be understood from the array perspective. In these projects, optimization of optical performances are translated into systematic study of identifiable geometric parameters. However, while array-geometry engineering presents multiple advantages, including physical intuition, versatility in design, and ease of fabrication, there is currently no rigorous and efficient solution for designing complex resonances in large-scale systems from an available set of geometrical parameters. In order to achieve this important goal, I developed an efficient numerical code based on the Green’s matrix method for modeling scattering by arbitrary arrays of coupled electric and magnetic dipoles, and show its relevance to the design of light localization and scattering resonances in deterministic aperiodic geometries. I will show how universal properties driven by the aperiodic geometries of the scattering arrays can be obtained by studying the spectral statistics of the corresponding Green’s matrices and how this approach leads to novel metamaterials for the visible and near-infrared spectral ranges. Within the thesis, I also present my collaborative works as examples of direct and inverse designs of nanostructures for photonics applications, including plasmonic sensing, optical antennas, and radiation shaping.

This paper presents results of an experimental investigation to study the structural performance and deformability of a concrete bridge deck reinforced with corrosion resistant reinforcing (CRR) bars, i.e., bars that exhibit improved corrosion resistance when embedded in concrete as compared to traditional black steel. Flexural tests of one-way slabs were conducted to simulate negative transverse flexure over a bridge girder as assumed in the commonly employed strip design method. The bar types studied were Grade 60 (uncoated), epoxy-coated reinforcing (ECR, Grade 60), Enduramet 32 stainless steel, 2304 stainless steel, MMFX2, and glass fiber reinforced polymer (GFRP). The experimental program was designed to evaluate how a one-to-one replacement of the Grade 60 with CRR, a reduction of concrete top clear cover, and a reduction in bar quantities in the bridge deck top mat influences flexural performance at service and ultimate limit states. Moment-curvature predictions from the computer-based sectional analysis program Response 2000 were consistent with the tested results, demonstrating its viability for use with high strength and non-metallic bar without a defined yield plateau.    Deformability of the concrete slab-strip specimens was defined with ultimate-to-service level ratios of midspan deflection and curvature. The MMFX2 and Enduramet 32 one-to-one replacement specimens had deformability consistent with the Grade 60 controls, demonstrating that bridge deck slabs employing high strength reinforcement without a defined yield plateau can still provide sufficient ductility at an ultimate limit state. A reduction in bar quantity and cover provided acceptable levels of ductility for the 2304 specimens and MMFX2 reinforced slabs. / Master of Science

The vibrational entropy calculated by applying the harmonic oscillator approximation to all vibrational degrees of freedom is inherently inaccurate. One major reason is because low frequency modes such as internal rotations are not properly described by this approximation. Various techniques were developed in the past to overcome this problem. The hindered rotor potential can be approximated by a series of cosine functions, and the relevant coe cients can be determined by tting to a calculated potential energy surface. However, such a method is di cult and time consuming. Therefore, in this dissertation we propose and describe two less tedious approaches to determine entropy of internal rotational modes. The rst approximation is to express the barrier height in terms of the harmonic oscillator frequency, the local periodicity, and the reduced moment of inertia of the rotation and to approximate the torsional potential by a single cosine function. Thus, the 1D Schr odinger equation for internal rotations can be solved without nding the torsional potential, transition states, or barrier heights. We propose a further simpli cation to this approach, achieved through a simple mathematical formula, that interpolates the hindered rotor entropy between the free rotor and harmonic oscillator limits. We also propose a procedure to automatically determine the axis of rotation for any hindered rotor. The proposed methods were applied to determine the torsional entropy of n- alkanes from ethane to hexane. The entropies calculated from the proposed methods give good agreement with the experimental and accurately calculated values and have a signi cantly better accuracy than the harmonic oscillator approximation. Furthermore, we performed approximate and full hindered rotor treatments to nd the corrected vibrational entropy of bis(chromiumtricarbonyl) dibenzo[a,e]cyclooctatetraene (DBCOT). The eighth chapter of this dissertation is an independent molecular dynamics (MD) project to study how ethanol interacts with human and mouse Toll-Like- Receptor3 (TLR3) monomers and a TLR3-dsRNA complex. No major structural changes were observed during the ethanol docking and subsequent MD simulations, but the MD simulations revealed a reduction in the proportion of alpha helix present during a 1000 ns MD simulation on the h-TLR3 monomer in 0.5 percent ethanol.

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The purpose of this study was to compare joint moments during the active peak vertical ground reaction force (PVGRF) when running in three conditions. Twenty-five subjects, sixteen male and nine female, were measured using 3-dimensional motion analysis while running barefoot, in Vibram FiveFingers® (VF®) minimalist running shoes and in traditional running shoes at a 7-minute-mile pace (3.84 m/s). Joint moment differences were calculated and compared using a mixed model analysis of variance. Results showed the VF® was effective at mimicking both the kinetic and kinematic attributes of barefoot running. The only significant difference found when comparing barefoot and VF® running was in the ankle angle (p < .005). All other variables in the lower extremity were the same for the two conditions. Though the subjects in our study had no previous experience with VF® (or barefoot) running they were able to closely mimic barefoot running upon initial running trials. Joint moments at the ankle were higher for barefoot and VF® running (p < .001) when compared with shod running. This may potentially lead to a greater risk of injury at the ankle joint when running barefoot or in VF®. The hip joint moments were only different when comparing the barefoot condition to the shod condition (p=.002), with the barefoot condition higher than shod running. The knee joint moment was smaller during the VF® and barefoot conditions when compared with shod running (p < .001) and may lead to a decrease in injury rates at the knee. Though a reduction in moments of the lower extremity may lead to a decrease of injury at the corresponding joint, it is important to consider the adaptations that take place as a result of varying stresses. According to Wolff's law, bone and surrounding tissue will adapt to the loads it is placed under. Taking this into consideration, it is important to remember that lower moments may lead to weaker bones and surrounding tissues and without compensation for these reduced loads, injury rates may remain the same over time.

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In recent earthquakes, structures have not performed as well as expected resulting in a need for better means of retrofitting and improvements in seismic design. Fiber Reinforced Polymers (FRP), as a material with potential to increase strength and ductility of columns in conjunction with capacity design methodology, has promise for seismic design. By investigating the displacement, ductility, and flexural strength properties of FRP confined reinforced concrete circular cross sections, this study analyzes the seismic applications of FRP confinement. The study is performed by incorporating an FRP confined concrete stress-strain model into a developed Moment-Curvature and PM Interaction software. This software conducts a comparison between traditional steel and FRP confined sections while performing parameter studies on the 28-day unconfined concrete compressive strength, longitudinal reinforcing ratio, cross section diameter, FRP confinement jacket thickness-cross section diameter ratio, and FRP confinement system design variables. These studies validate FRP’s performance for seismic applications resulting in several design recommendations to increase displacement capacity, ductility, and flexural strength and, thus, seismic performance.