Doctor of Philosophy, University of Akron, 2014, Chemistry

This dissertation addresses the effect of large amplitude vibrations (LAV or LAVs) on the other small amplitude vibrations (SAVs) for investigating the vibrational dynamics on the molecular systems ranging from G6 to G12 symmetry, including methanol, methylamine, nitromethane, 2-methylmalonaldehyde (2-MMA) and 5-methyltropolone (5-MT). The study of the high-resolution infrared spectrum of methylamine (CH3NH2) in the nu11 asymmetric CH stretch region (2965-3005 cm-1) under sub-Doppler slit-jet conditions reveals that the torsion-inversion tunneling patterns are heavily impacted by perturbations and hence different both from the ground state and from the theoretical predictions. Two torsion-inversion tunneling models are reported for studying the high-barrier tunneling behavior in the methyl CH stretch vibrationally excited states of the molecules with G12 symmetry. These models predict the inverted tunneling pattern of the four tunneling states (A, B, E1 and E2 symmetries) in the asymmetric CH stretch excited states relative to the ground state. The trends in the patterns relative to tunneling rates and coupling parameters are presented and comparisons are made to the available experimental data. Additionally, a remarkable result that follows from the approximate adiabatic separation of the fast and slow vibrations in methanol is the existence of vibrational conical intersections (CIs) where the surfaces representing the two asymmetric CH stretches meet like the points of two cones touching point-to-point. The CIs occur in the slow coordinates space consisting of the torsion and the COH bend. Finally, the analysis of the high-resolution synchrotron based Fourier transform infrared (FTIR) spectrum for NO2 in-plane rock, nu7 , band of nitromethane reveals that the rotational energy pattern in the lowest torsional state ( m' = 0) of the upper vibrational state is similar relative to the vibrational ground state.

Committee: David S. Perry Dr. (Advisor); Mesfin Tsige Dr. (Committee Member); David A. Modarelli Dr. (Committee Member); Alper Buldum Dr. (Committee Member); Christopher J. Ziegler Dr. (Committee Member) Subjects: Chemistry

Doctor of Philosophy (PhD), Ohio University, 2011, Mathematics (Arts and Sciences)

An R module M is herein called torsion if each element has nonzero annihilator, and faithful if the annihilator of M is zero. The central theme of this dissertation is exploration of which rings admit modules that are simultaneously faithful and torsion, termed FT modules. If a ring R admits an FT right module, it is called right faithful torsion or a right FT ring, and similarly for the left-hand side. The ring is said to have FT rank equal to κ if κ is a nonzero cardinal and is the least cardinality of a generating set for an FT module over R. By convention, rings which are not FT have FT rank 0. After a survey of the requisite definitions from abstract algebra, several observations are made and lemmas are proven. It is shown that a ring with infinite right FT rank must have a properly descending chain of nonzero ideals of the same length as its FT rank. Using families of ideals with the finite intersection property, we construct torsion modules which are faithful when the family has intersection zero. Using this, it is possible to show that infinite FT ranks can only be regular cardinals. We determine the propagation of FT rank in standard ring constructions such as direct products, matrix rings, and the maximal right ring of quotients. To paraphrase the results: a product is FT if it has an FT factor, infinite products are always FT, matrix rings are often FT, and the FT property travels down from the maximal right ring of quotients. The next portion of the dissertation gives an account of all that is known about several classes of rings and whether they are FT or not. The two prominent examples of rings that are not right FT are 1) quasi-Frobenius rings R such that R/rad(R) is a finite product of division rings, and 2) any ring R with an essential minimal right ideal. We show that finite products of simple rings are FT exactly when they are not finite products of division rings, with possible ranks 0 and 1. Domains are FT exactly when they are not division ri (open full item for complete abstract)

Committee: Sergio Lopez-Permouth PhD (Advisor); Phillip Ehrlich PhD (Committee Member); Dinh Huynh PhD (Committee Member); William Kaufman PhD (Committee Member); Gregory Oman PhD (Committee Member) Subjects: Mathematics

Master of Science, The Ohio State University, 2005, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1950, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1967, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1963, Graduate School

Committee: Not Provided (Other) Subjects:

Doctor of Philosophy, The Ohio State University, 2018, Mathematics

During the mid-twentieth century, Paul Erdos and Alfred Renyi developed their now-standard random graph model. Beyond being practical in graph theory to nonconstructively prove the existence of graphs with certain interesting properties, the Erdos–Renyi model is also a model for generating random (one-dimensional) topological spaces. Within the last fifteen years, this model has been generalized to the higher-dimensional simplicial complex model of Nati Linial and Roy Meshulam. As in the case of the probabilistic method more generally, there are (at least) two reasons why one might apply random methods in topology: to understand what a "typical" topological space looks like and to give nonconstructive proofs of the existence of topological spaces with certain properties. Here we consider both of these applications of randomness in topology in considering the properties of torsion in homology of simplicial complexes. For the former, we discuss experimental results that strongly suggest torsion in homology of random Linial–Meshulam complexes is distributed according to Cohen–Lenstra heuristics. For the latter, we use the probabilistic method to give an upper bound on the number of vertices required to construct d-dimensional simplicial complexes with prescribed torsion in homology. This upper bound is optimal in the sense that it is a constant multiple of a known lower bound.

Committee: Matthew Kahle (Advisor); Elliot Paquette (Committee Member); Jean-Francois Lafont (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2018, Mathematics

This work deals with various phenomena relating to complex geometry. We are particularly interested in non-Kahler Hermitian manifolds, and most of the work here was done to try to understand the geometry of these spaces by understanding the torsion. Chapter 1 introduces some background material as well as various equations and inequalities on Hermitian manifolds. We are focused primarily on the inequalities that are useful for the analysis that we do later in the thesis. In particular, we focus on k-Gauduchon complex structures, which were initially defined by Fu, Wang, and Wu. Chapter 2 discusses the spectral geometry of Hermitian manifolds. In particular, we estimate the real eigenvalues of the complex Laplacian from below. In doing so, we prove a theorem on non-self-adjoint drift Laplace operators with bounded drift. This result is of independent interest, apart from its application to complex geometry. The work in this section is largely based on the Li-Yau estimate as well as an ansatz due to Hamel, Nadirashvili and Russ. Chapter 3 considers orthogonal complex structures to a given Riemannian metric. Much of the work in this section is conjectural in nature, but we believe that this is a promising approach to studying Hermitian geometry. We do prove several concrete results as well. In particular, we show how the moduli space of k-Gauduchon orthogonal complex structures is pre-compact.

Committee: Fangyang Zheng (Advisor); Bo Guan (Committee Member); King-Yeung Lam (Committee Member); Jean-Francois Lafont (Committee Member); Mario Miranda (Committee Member) Subjects: Mathematics

Doctor of Philosophy (Ph.D.), University of Dayton, 2017, Mechanical Engineering

Modern plasticity models contain numerous parameters that no longer correlate directly to measurements, leading to a lack of uniqueness during parameter identification. This problem is exacerbated when using only uniaxial test data to populate a three-dimensional model. Parameter identification typically is performed after all experiments are completed, and experiments using different loading conditions are seldom conducted for validation. Experimental techniques and computational methods for parameter identification are sufficiently advanced to permit real-time integration of these processes. This work develops a methodology for integrating multiaxial experimentation with constitutive parameter calibration and validation. The integrated strategy provides a closed-loop autonomous experimental approach to parameter identification. A continuous identification process guides the experiment to improve correlation across the entire axial-torsional test domain. Upon completion of the interactive test, constitutive parameters are available immediately for use in finite element simulations of more complex geometries. The autonomous methodology is demonstrated through both analytical and physical experiments on Ti-6Al-4V. The proposed approach defines a framework for parameter identification based on complete coverage of the stress and strain spaces of interest, thereby providing greater model fidelity for simulations involving multiaxial stress states and cyclic loading.

Committee: Robert Brockman (Advisor); Steven Donaldson (Committee Member); Thomas Whitney (Committee Member); Andrew Rosenberger (Committee Member); Reji John (Committee Member) Subjects: Engineering; Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 1983, Graduate School

Committee: Not Provided (Other) Subjects: Education

Doctor of Philosophy, The Ohio State University, 1969, Graduate School

Committee: Not Provided (Other) Subjects: Engineering

Doctor of Philosophy, The Ohio State University, 1968, Graduate School

Committee: Not Provided (Other) Subjects: Engineering

Doctor of Philosophy, The Ohio State University, 1964, Graduate School

Committee: Not Provided (Other) Subjects: Engineering

Doctor of Philosophy, The Ohio State University, 1961, Graduate School

Committee: Not Provided (Other) Subjects: Engineering

MS, University of Cincinnati, 2016, Engineering and Applied Science: Mechanical Engineering

The stiffness, particularly torsion stiffness, of a frame, body or chassis is of paramount concern to the automotive structural engineer. An accurate measurement of torsion stiffness has several useful applications, among which are the characterization of construction quality, model calibration and suspension tuning. Static techniques for measuring torsion stiffness are perhaps as old as the automotive industry itself, and each manufacturer has its own version of the classical static torsion stiffness test. It is also common for a manufacturer to quote a new model's torsion stiffness in industry publications, the values of which continually increase with improving material and construction technologies. In recent years, dynamic methods have emerged which approach the problem of measuring torsion stiffness using experimental frequency response function (FRF) and modal analysis techniques. The primary purpose of this thesis is to further determine the utility of one such dynamic method, namely, the enhanced Rotational Compliance Function (eRCF), in terms of its accuracy in relation to an implementation of the classical static torsion stiffness test. To this end, two automotive frames made by the University of Cincinnati Formula SAE® (UC-FSAE) Team are the test structures. When compared to typical commercial automotive structures, which contain embedded frames and surface shear panels, these steel triangulated frames are considered simple structures. In order to produce quality static values, the UC-FSAE static torsion stiffness measurement apparatus is to be updated and improved.

Committee: Randall Allemang Ph.D. (Committee Chair); David L. Brown Ph.D. (Committee Member); Allyn Phillips Ph.D. (Committee Member) Subjects: Mechanical Engineering; Mechanics

Doctor of Philosophy, The Ohio State University, 2015, Chemical Physics

Astrochemistry studies chemical reactions that occur in the interstellar medium. Most astrochemical studies focus on the detection of interstellar molecules via rovibrational spectroscopy or the interpretation of their abundance using reaction dynamics. This thesis is divided into two parts, and in each of them we address one of the two aspects from the perspective of theoretical chemistry. In the first part we propose the synthetic route for propene (CH3-CH=CH2), which has a surprisingly high abundance as the most saturated organic molecule in the extremely cold and thin gas-phase medium. Based on the reaction rates obtained from experiments and ab initio calculations for all three reactions in this route, we simulate the time-evolution for the abundance of propene and find that our synthetic route is able to reproduce part of the observed propene abundance. In the second part we discuss the spectroscopy and the dynamics of H5+, aiming to decipher its role as the intermediate of the astrochemically important proton transfer reaction, H3+ + H2 -> H5+ -> H2 + H3+. The large amplitude motions (LAM's) in H5+ allow the protons to permute between H3+ and H2 and result in products that have different nuclear spins and rovibrational states from the reactants. These LAM's introduce challenges to the theoretical studies of H5+ because the conventional harmonic oscillator and rigid rotor approximation is no longer valid. Diffusion Monte Carlo and its extensions are used to capture the couplings between LAM's and other rovibrational modes in H5+. Specifically, we focus on three LAM's: the proton transfer vibration, the H2-H2 torsion, and the internal rotation of H3+ about its C3 symmetry axis. For selected states of H5+, we evaluate energies and wave functions as well as the reaction paths for the above-mentioned proton transfer process. In the spectroscopic studies, we find that the proton transfer vibration has a significant mixing with the dissociation vibration, (open full item for complete abstract)

Committee: Anne McCoy (Advisor); Terry Miller (Committee Member); John Wilkins (Committee Member) Subjects: Physical Chemistry

Master of Science in Biological Sciences, Youngstown State University, 2014, Department of Biological Sciences and Chemistry

Understanding of the interplay between bone loading patterns and bone material properties in mammals has been based primarily on evidence from upright eutherians, which show limb bones that are loaded predominantly in anteroposterior (AP) bending with minimal torsion. However, loading patterns from the femora of marsupial opossums using crouched limb posture, show appreciable torsion while the bone experiences mediolateral (ML) bending. These data indicated greater locomotor loading diversity than was previously recognized, and suggested the possibility that ancestral loading patterns found in sprawling reptiles might have been retained among basal mammals. To further test this hypothesis, in vivo locomotor strains were recorded from the femur of the nine-banded armadillo (Dasypus novemcinctus). Orientations of principal strains and magnitudes of shear strains indicate that their femora are exposed to a limited amount of torsion, while loading is dominated by ML bending that places the medial aspect of the femur in compression and the lateral aspect in tension. This orientation of bending is similar to that found in opossums, but planar strain analyses indicate much more of the armadillo femur experiences tension during bending, potentially due to the actions of large muscles attached to the robust third trochanter (T3). Comparisons of peak locomotor loads to evaluations of femoral mechanical properties lead to estimates of limb bone safety factors between 2.3--5.0 in bending, similar to other eutherians, but lower than opossums and most sprawling taxa. Thus, femoral loading patterns in armadillos show a mixture of similarities to both opossums (ML bending) and eutherians (limited torsion and low safety factors), along with unique features (high axial tension) that likely relate to their distinctive hindlimb anatomy.

Committee: Michael Butcher PhD (Advisor); Mark Womble PhD (Committee Member); Thomas Diggins PhD (Committee Member) Subjects: Biomechanics

MS, University of Cincinnati, 2010, Engineering : Mechanical Engineering

Designing an automotive chassis is not an intuitive process. It, at times, can be very difficult depending on the geometry of the structure. Research was conducted at the University of Cincinnati to alleviate the burden of this task. Software tools were developed to help speed the design process. A new technique of measuring the torsional stiffness of a Formula SAE chassis design was created. Finally, a recommended process is presented to perform the design and validation of a Formula SAE chassis. As engineers we turn to different tools that we have access to in order to understand and iterate a design. In the area of space frames, design tools can be limited. To get an understanding of a chassis design, engineers turn to Finite Element Analysis (FEA) to gain a better understanding of these types of structures. Ultimately, manual iterations are not enough to completely optimize a structure to a desired goal. Software tools need to be developed in order to have a deep understanding of how the structure performs at each iteration. Two tools, a sensitivity and optimization tool, were written and the outcome of each is discussed. Until 2007, the UC Formula SAE team has validated only the current year's frame design and not the entire chassis design. In the world of Formula One racing it is essential to have knowledge not only of frame stiffness but also hub to hub chassis stiffness.Various ways to test chassis stiffness were investigated and designed. A static test was developed and performed. A finite element model and its correlation to this static test is discussed.

Committee: Randall Allemang PhD (Committee Chair); Allyn Phillips PhD (Committee Member); David Thompson PhD (Committee Member) Subjects: Automotive Materials

Master of Science in Mechanical Engineering, University of Toledo, 2011, College of Engineering

The objectives of this study were to investigate the fatigue behavior of three high hardness steels, where each of the three steels had a hardness of 60 HRC (653 HB). Solid specimens of three different materials were tested under normal environmental laboratory conditions. Axial monotonic and fatigue properties were obtained through the use of a uniaxial testing machine. A large portion of the axial fatigue testing was performed under fully-reversed loading conditions, but a portion of the testing was conducted to evaluate the effects of introducing a mean stress. Fully-reversed pure torsion fatigue data were also generated using an axial-torsion test machine. The focus of the testing was directed toward longer life tests with several shorter life tests to obtain the stress-life curves in both the low and high cycle regimes. Significant scatter in the experimental data in some instances necessitated a statistical investigation. The fully-reversed axial testing produced both surface and subsurface specimen failures for all three steels, while the pure torsion testing resulted in surface failure on the maximum principal plane. The axial stress-life curves were predicted by using material hardness, and the predictions were found to be reasonable when compared with the experimental curves for two of the three steels. With the maximum principal stress, maximum principal strain, von-Mises, and Tresca criteria, the hardness predicted stress-life curves were converted into shear stress-life predictions. As a result, the maximum principal strain criterion was found to provide the best prediction. The same criteria were then used to correlate the axial and torsion fully-reversed data for each material, and the maximum principal strain criterion was found to provide the best predictions. The area0.5 parameter for the axial fatigue limit prediction provided estimated fatigue limits for subsurface inclusion failures. This parameter was found to predict fatigue limits that w (open full item for complete abstract)

Committee: Dr. Ali Fatemi PhD (Committee Chair); Dr. Efstratios Nikolaidis PhD (Committee Member); Dr. Yong Gan PhD (Committee Member) Subjects: Engineering

Master of Science, University of Toledo, 2007, Civil Engineering

Located in Northwestern Ohio, the Veterans' Glass City Skyway (VGCS) will carry I-280 over the Maumee River. Composed of 8,800-feet of precast, post-tensioned segmental box girders, the VGCS will feature a 1,225-feet cable stay span with a single plane of stays and was designed by FIGG Bridge Engineers, Inc. ODOT contracted the University Research Team (URT) composed of faculty and students from the University of Toledo and the University of Cincinnati to instrument the VGCS for health monitoring throughout construction. This research will address two important issues associated with the Maumee River Crossing project. First, in order to accurately predict live load response for a structure such as this, it is important to perform testing to determine elastic bridge response. In the case of the VGCS, the URT was presented with several opportunities to perform live load testing during the construction process. Data was recorded as the segment hauler used to transport segments traveled over the bridge. Additionally, prior to installation of the last two segments required for completion of the main span, the instrumentation was set to record data as the hydraulic truck cranes used for installation were repositioned from the tip of cantilever span to the opposing side of the final gap. This research will investigate the elastic bridge response during the aforementioned construction loads. Second, while performing a check of the proposed construction erection sequence, concerns arose from finite element modeling that there was a potential for the localized zones of high stress in the bottom slab caused by transverse bending. The URT installed gages in the bottom slab of two segments to monitor this behavior and resolve discrepancies in the finite element analyses. This research presents data collected from these segments at key construction stages.

Committee: Douglas Nims (Advisor) Subjects: Engineering, Civil