Inelastic behavior in steel special moment frames occurs through the development of plastic hinges at locations near the ends of the beam. The main objective of using a reduced beam connection is to force the formation of plastic hinges to be formed at the reduced beam section rather than at the ends of the beam which otherwise would lead to brittle failure of the beam-column connections. The beam has two reduced beam sections, each located at a certain distance from the face of the column, so that the plastic hinges are formed symmetrically at each of this section. When acted upon by lateral loads, the maximum moments occur at the ends of the beam. Therefore, the plastic hinges form at the reduced beam section. However, when a frame is subjected to a combination of gravity and lateral loads, the plastic hinge formation at one of the reduced beam section is not so clear and further analysis has to be done to study the effect. FEMA 350 indicates that the desired plastic hinge location is only valid for beams with gravity loads representing a small portion of the total flexural demand. If gravity demands significantly exceed 30% of the girder plastic capacity then further plastic analysis of the frame should be performed to determine the appropriate hinge locations. The scope of my thesis is mainly to study the combined effect of gravity and lateral loads on the formation of plastic hinges in steel moment frames with reduced beam section connections.

Reduced organic sulfur (ROS) compounds are environmentally ubiquitous and play an important role in sulfur cycling as well as in biogeochemical cycles of toxic metals, in particular mercury. Development of effective methods for analysis of ROS in environmental samples and investigations on the interactions of ROS with mercury are critical for understanding the role of ROS in mercury cycling, yet both of which are poorly studied. Covalent affinity chromatography-based methods were attempted for analysis of ROS in environmental water samples. A method was developed for analysis of environmental thiols, by preconcentration using affinity covalent chromatographic column or solid phase extraction, followed by releasing of thiols from the thiopropyl sepharose gel using TCEP and analysis using HPLC-UV or HPLC-FL. Under the optimized conditions, the detection limits of the method using HPLC-FL detection were 0.45 and 0.36 nM for Cys and GSH, respectively. Our results suggest that covalent affinity methods are efficient for thiol enrichment and interference elimination, demonstrating their promising applications in developing a sensitive, reliable, and useful technique for thiol analysis in environmental water samples. The dissolution of mercury sulfide (HgS) in the presence of ROS and dissolved organic matter (DOM) was investigated, by quantifying the effects of ROS on HgS dissolution and determining the speciation of the mercury released from ROS-induced HgS dissolution. It was observed that the presence of small ROS (e.g., Cys and GSH) and large molecule DOM, in particular at high concentrations, could significantly enhance the dissolution of HgS. The dissolved Hg during HgS dissolution determined using the conventional 0.22 µm cutoff method could include colloidal Hg (e.g., HgS colloids) and truly dissolved Hg (e.g., Hg-ROS complexes). A centrifugal filtration method (with 3 kDa MWCO) was employed to characterize the speciation and reactivity of the Hg released during ROS-enhanced HgS dissolution. The presence of small ROS could produce a considerable fraction (about 40% of total mercury in the solution) of truly dissolved mercury (< 3 kDa), probably due to the formation of Hg-Cys or Hg-GSH complexes. The truly dissolved Hg formed during GSH- or Cys-enhanced HgS dissolution was directly reducible (100% for GSH and 40% for Cys) by stannous chloride, demonstrating its potential role in Hg transformation and bioaccumulation.

This dissertation presents results about computations of Graev metrics on free groups and characterizes isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. In Chapter 2, computations of Graev metrics are performed on free groups. One of the related results answers an open question of Van Den Dries and Gao. In Chapter 3, isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces are characterized. The notion of generalized tree is defined and a correspondence between the isomorphism group of a generalized tree and the isometry group of a Heine-Borel Polish ultrametric space is established. The concept of a weak inverse limit is introduced to capture the characterization of isomorphism groups of generalized trees. In Chapter 4, partial results of isometry groups of uncountable compact ultrametric spaces are given. It turns out that every compact ultrametric space has a unique countable orbital decomposition. An orbital space consists of disjoint orbits. An orbit subspace of an orbital space is actually a compact homogeneous ultrametric subspace.

Data generated by complex, computational models can provide highly accurate predictions of hydrological and hydrodynamic data in multiple dimensions. Unfortunately, however, for large data sets, running these models is often timeconsuming and computationally expensive. Thus, finding a way to reduce the running time of these models, while still producing comparable results, is of notable interest. The Inference Engine is a proposed system for doing just this. It takes previously generated model data and uses them to predict additional data. Its performance, both accuracy and running time, has been compared to the performance of the actual models, in increasingly difficult data prediction tasks, and it is able, with sufficient accuracy, to quickly predict unknown model data.

Quantum chemical methods to predict experimental chiroptical properties by solving the time-dependent Schrödinger equation are useful in the assignment of absolute configurations. Chiroptical properties, being very sensitive to the electronic structure of the system, require highly-accurate methods on the one hand and on the other, need to be able to be computed with limited computational resources. The calculation of the optical rotation in the solution phase is complicated by solvent effects. In order to capture those solvent effects, we present a study that uses conformational averaging and time-dependent density functional theory calculations that incorporate solvent molecules explicitly in the quantum mechanical region. While considering several controllable parameters along which the system's optical rotation varies, we find that the sampling of the dynamical trajectory and the density functional chosen have the largest impact on the value of the rotation. In order to eliminate the arbitrariness of the choice of density functional, we would prefer to use coupled cluster theory, a robust and systematically improvable method. However, the high-order polynomial scaling of coupled cluster theory makes it intractable for numerous large calculations, including the conformational averaging required for optical rotation calculations in solution. We therefore attempt to reduce the scaling of a linear response coupled cluster singles and doubles (LR-CCSD) calculation via a perturbed pair natural orbital (PNO++) local correlation approach which uses an orbital space created using a perturbed density matrix. We find that by creating a "combined PNO++" space, incorporating a set of orbitals from the unperturbed pair natural orbital (PNO) space into the PNO++ space, we can obtain well-behaved convergence behavior for both CCSD correlation energies and linear response properties, including dynamic polarizabilities and optical rotations, for the small systems considered. The PNO++ and combined PNO++ methods require aggressive truncation to keep the computational cost low, due to an expensive two-electron integral transformation at the beginning of the calculation. We apply the methods to larger systems than previously studied and refine them for more aggressive truncation by exploring an alternative form of the perturbed density and a perturbation-including weak pair approximation. / Doctor of Philosophy / Theoretical chemistry attempts to provide connections between the structure of molecules and their observable properties. One such family of observables are chiroptical properties, or the effect of the medium on the light which passes through it. These properties include the scattering, absorption and change in polarization of light. Light being classically an electromagnetic field, chiroptical properties can be derived by treating molecules quantum mechanically and the light classically. The prediction of chiroptical properties on computers using the principles of quantum mechanics is still a growing field, being very sensitive to the method used, and requiring considerations of factors such as conformations and anharmonic corrections. Matching experimental properties is an important step in the creation of a reliable method of predicting properties of systems in order to provide more information than can be obtained through experimental observation. This work begins by addressing the problem of matching experimentally obtained quantities. Our results show that current time-intensive methods still fall short in the matching of experimental data. Thus, we then move on to approximating a more robust but computationally expensive method in order to be able to use a more accurate method on a larger scale than is currently possible. On obtaining positive results for small test systems, we test the new method on larger systems, and explore possible improvements to its accuracy and efficiency.

Phosphorus chemistry controls key aspects of eutrophication, microbial nutrition, corrosion and other environmental processes. It is commonly assumed that phosphorus occurs exclusively as phosphate (+5) in nature. In fact, although phosphate is undoubtedly dominant in many systems, phosphorus compounds with lower oxidation states (reduced phosphorus) can also be present in the environment and could be of practical importance in many circumstances. Most reduced phosphorus compounds are likely to originate in steel-making or thermal phosphorus plants. It was determined that reduced phosphorus would not be detected in routine environmental analyses even if they were present. A new method was developed to detect these compounds, and in a preliminary survey reduced phosphorus was proven to be present in water that contacts corroding iron pipes, steel slag samples, phosphorus plant wastewater, phosphite fertilizers, and in sewage treatment plant effluent. However, no evidence could be obtained for massive bio-reduction of phosphates that has been proposed by some researchers. Given that phosphorus is often a limiting nutrient, and phosphorus compounds sometimes inhibit and sometimes catalyze practically important reactions (e.g. iron corrosion), future work should examine reduced phosphorus occurrence and chemistry in greater detail. / Ph. D.

The demand for consumer credit is an area of economics that is of great interest to those in the lending community. While much research has been performed on this topic in the financial industry, the findings have been very closely guarded for competitive reasons. In this study, reduced form equations were derived to form the basis of a 2SLS regression model. This model was used to estimate the demand for consumer credit in the United States over the period 1973 - 2002. Six independent variables were included in the analysis: monetary base, unemployment rate, consumer confidence index, disposable personal income, federal funds interest rate and the price/barrel of oil. The model results concluded that only two of these variables significantly affect the demand for consumer credit &#8211; disposable personal income (DPI_t) and the unemployment rate (uet). The error terms were compared against those derived from two alternative models using the same data sets &#8211; a trend model and an autoregressive model &#8211; AR(1). The root mean square error (RMSE) for the reduced form model was significantly lower then that of the trend model, but slightly higher then the AR(1) model. The objectives of this study are to: (1) produce an accurate model that defines the drivers behind the demand for consumer credit, while (2) producing results consistent with econometric theory. Based on this set of objectives, the reduced form model is the superior of the three models included in this study. / Master of Arts

One of the central problems limiting the application of accurate {em ab initio} methods to large molecular systems is their high computational costs, i.e., their computing and storage requirements exhibit polynomial scaling with the size of the system. For example, the coupled cluster singles and doubles method with the perturbative inclusion of triples: the CCSD(T) model, which is considered to be the ``gold standard'' of quantum chemistry scales as 𝑂(N⁷) in its canonical formulation, where $N$ is a measure of the system size. However, the steep scaling associated with these methods is unphysical since the property of dynamic electron correlation or dispersion (for insulators) is local in nature and decays as R⁻⁶ power of distance. Different reduced-scaling techniques which attempt to exploit this inherent sparsity in the wavefunction have been used in conjunction with the coupled cluster theory to calculate ground-state properties of molecular systems with hundreds of heavy atoms in reasonable computational time. However, efforts towards extension of these methods for describing response properties like polarizabilities, optical rotations, etc., which are related to the derivative of the wavefunction with respect to external electric or/and magnetic fields, have been fairly limited and conventional reduced-scaling algorithms have been shown to yield large and often erratic deviations from the full canonical results. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different chiral drug candidates. In this work, we identify the reasons behind the unsatisfactory performance of the pair natural orbital (PNO) based reduced-scaling approach for calculating linear response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}) that can provide the necessary accuracy at significantly lower computational costs. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. {em J. Phys. Chem. A}, 2017, 121(3), pp 708 716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}). The essence of these modified schemes (FVNO++ and PNO++) lie in finding suitable field perturbed one-electron densities to construct ``perturbation aware" virtual spaces which, by construction, are much more compact for describing response properties, making them ideal for applications on large molecular systems. / Ph. D.

Through the exploitation of data-sparsity ---a catch all term for savings gained from a variety of approximations--- it is possible to reduce the computational cost of accurate electronic structure calculations to linear. Meaning, that the total time to solution for the calculation grows at the same rate as the number of particles that are correlated. Multiple techniques for exploiting data-sparsity are discussed, with a focus on those that can be systematically improved by tightening numerical parameters such that as the parameter approaches zero the approximation becomes exact. These techniques are first applied to Hartree-Fock theory and then we attempt to design a linear scaling massively parallel electron correlation strategy based on second order perturbation theory. / Ph. D.

This thesis explores the field of legged robots with reduced degree-of-freedom (DOF) leg mechanisms. Multi-legged robots have drawn interest among researchers due to their high level of adaptability on unstructured terrains. However, conventional legged robots require multiple degrees of freedom and each additional degree of freedom increases the overall weight and complexity of the system. Additionally, the complexity of the control algorithms must be increased to provide mobility, stabilization, and maneuvering. Normally, robotic legs are designed with at least three degrees of freedom resulting in complex articulated mechanisms, which limits the applicability of such robots in real-world applications. However, reduced DOF leg mechanisms come with reduced tasking capabilities, such as maintaining constant body height and velocity during locomotion. To address some of the challenges, this thesis proposes a novel bipedal robot with reduced DOF leg mechanisms. The proposed leg mechanism utilizes the Reuleaux triangle to generate the foot trajectory to achieve a constant body height during locomotion while maintaining a constant velocity. By using a differential drive, the robot is also capable of steering. In addition to the analytical results of the trajectory profile of each leg, the thesis provides a trajectory function of the Reuelaux triangle cam with respect to time such that the robot can maintain a constant velocity and constant body height during walking. An experimental prototype of the bipedal robot was integrated and experiments were conducted to evaluate the walking capability of the robot. Ongoing future work of the proposed design is also outlined in the thesis. / Master of Science / Bipedal robots are a type of legged robots that use two legs to move. Legs require multiple degrees of freedom to provide propulsion, stabilization, and maneuvering. Additional degrees of freedom of the leg result in a heavier robot, more complex control method, and more energy consumption. However, reduced degree of freedom legs result in a tradeoff between certain tasking capabilities for easier controls and lower energy consumption. As an attempt to overcome these challenges, this thesis presents a robot design with a reduced degree of freedom leg mechanism. The design of the mechanism is described in detail with its preliminary analysis. In addition, this thesis presents experimental validation with the robot which validates that the robot is capable of moving with constant body height at constant velocity while being of capable of steering. The thesis concludes with a discussion of the future work.