Bachelor of Science, Ashland University, 2017, Mathematics/Computer Science

The Riemann integral is often introduced to undergraduate calculus students, as its definition and related theorems are relatively straightforward to understand. However, the Riemann integral is limited in its power to integrate a wide variety of functions. This paper introduces an alternate definition of the integral, known as the generalized Riemann integral. This version of the integral was introduced around 1960 by Ralph Henstock and Jaroslav Kurzweil, and its definition and theorems are almost as simple as the traditional Riemann integral, yet its power to integrate functions far surpasses Riemann's integral. This paper includes an overview of the most important theorems and definitions related to the generalized Riemann integral and explains how it can be used to supplement, or even replace, the Riemann integral in undergraduate calculus and analysis courses.

Committee: Darren Wick Ph.D. (Advisor); Gordon Swain Ph.D. (Committee Member); Christopher Swanson Ph.D. (Committee Member) Subjects: Applied Mathematics; Education; Mathematics; Mathematics Education

Doctor of Philosophy, The Ohio State University, 2014, Electrical and Computer Engineering

This dissertation presents approaches to solve the multi-scale and wideband problems using surface integral equation methods based on the skeletonalization technique, which in essence identifies the numerically independent elements from a larger set of unknowns. In the low frequency or multi-scale scenario, overly dense mesh is generated in a global or local scale. The method is extended to composite material through the integral equation discontinuous Galerkkin method via enhanced enforcement of transmission conditions. Conventional multi-level fast multipole method(MLFMM) faces low frequency breakdown since a large number of basis functions are concentrated within the leaf level groups, whose size is typically larger than λ/4. The computational complexity rapidly approaches that of conventional MoM, which is O (N 2) for both CPU time and memory consumption for iterative solvers. In this dissertation a hierarchical multi-level fast multipole method (H-MLFMM) is proposed to accelerate the matrix-vector multiplication for low frequency and multi-scale problems. Two different types of basis functions are proposed to address these two different natures of physics corresponding to the electrical size of the elements. Moreover, the proposed H-MLFMM unifies the procedures to account for the couplings using these two distinct types of basis functions. O(N) complexity is observed for both memory and CPU time from a set of numerical examples with fixed mesh sizes. Numerical results are included to demonstrate that H-MLFMM is error controllable and robust for a wide range of applications. On the other hand, condition number of the system matrix deteriorates due to the overly dense mesh. This would greatly affect the convergence of iterative solvers, if convergence can ever be attained. Direct solver This thesis proposes an algorithm exploits the smoothness of the far field and computes a low rank decomposition of the off-diagonal coupling blocks of the matrices through a set (open full item for complete abstract)

Committee: Jin-Fa Lee (Advisor); Robert Lee (Committee Member); Fernando Teixeira (Committee Member) Subjects: Electromagnetics

Master of Science, University of Akron, 2007, Electrical Engineering

An integral state-variable feedback controller was developed to regulate flow in a rotodynamic magnetically suspended centrifugal pump (MSCP). The controller specification was to maintain blood flow within 15% of 4 L/min against an open-loop load disturbance resulting in changes in pressure difference of ± 50 mmHg about nominal 100 mmHg occurring at 100 mmHg/min. For controller and observer design purposes, the nonlinear system was represented by a state-space model linearized about a nominal operating point with an output disturbance. A proportional integral (PI) observer was developed to estimate the unmeasurable states and disturbance. Matlab® was used for model identification and design and simulation of the controller and observer, which were then implemented using Labview®. In simulation and on the physical system, the controller maintained acceptable blood flow against an extreme unknown load disturbance occuring at a rate of approximately 200 mmHg/min.

Committee: Jose Alexis De Abreu-Garcia (Advisor) Subjects:

Master of Arts, The Ohio State University, 1939, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1961, Graduate School

Committee: Not Provided (Other) Subjects:

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

Committee: Not Provided (Other) Subjects:

Master of Arts, The Ohio State University, 1940, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 2008, Graduate School

Committee: Not Provided (Other) Subjects:

Doctor of Philosophy, The Ohio State University, 2024, Aerospace Engineering

Fluid-Structure Interactions (FSI) are a quintessential multi-disciplinary challenge, where the flowfield is influenced by the structure, and structural deformation is induced by the flow pressure. Computational and experimental research thrusts often seek to answer specific problems for specific configurations, offering observational answers to relatively complex problems. While there is a large body of work on FSI as a whole, the specific coupling mechanisms between the fluid and structural surface in the context of turbulent boundary layers (TBLs) in supersonic flows is an under-explored area of study. This dissertation details progress addressing this gap through cooperative consideration of high-fidelity simulations, classical semi-empirical models, analysis of the governing equations, and data-driven models. Large-Eddy Simulations (LES) of TBLs with static deformations are compared against classical semi-empirical models to characterize applicability to statically deformed surfaces for predicting loads transmitted from the boundary layer to the structure. Additionally, analysis of the governing equations, in conjunction with data-driven modeling, is used to extract a coherent link between structural deformation and the onset of local flow separations. Finally, a parametric study is carried out using Reynolds-Average Navier-Stokes (RANS) and Kriging surrogates to assess the impact of statically deformed surfaces on a downstream ramp. LES indicates that for a variety of deformations sized on the order of the incoming boundary layer, localized flow separation can develop. This leads to important flow modifications that are not readily captured with low-fidelity or semi-empirical models. Motivated by this, a first-order link between local flow separation and structural deformation parameters is established using the Momentum Integral Equation (MIE) combined with data-driven analysis. The curvature of the surface is identified as the dominant structural param (open full item for complete abstract)

Committee: Jack McNamara (Advisor); Datta Gaitonde (Advisor); Scott Peltier (Committee Member); Jen-Ping Chen (Committee Member); Lian Duan (Committee Member) Subjects: Aerospace Engineering

Doctor of Philosophy (Ph.D.), University of Dayton, 2023, Electrical Engineering

The recent pandemic of Corona-virus Disease 2019 (COVID-19) caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) showed an urgent need to rapidly and accurately identify the genetic material of SARS-CoV-2, an enveloped ribonucleic acid (RNA) virus, in upper respiratory specimens from people. Further, foodborne and waterborne diseases are not only spreading faster, but also appear to be emerging more rapidly than ever before and are able to circumvent conventional control measures. The Polymerase Chain Reaction (PCR) system is a well-known diagnostic tool for many applications in medical diagnostics, environmental monitoring, and food and water quality assessment. Here, we describe the design, development, and testing of a portable, low-cost, and real-time PCR system that can be used in emergency health crises and resource-poor situations. The described PCR system incorporates real-time reaction monitoring using fluorescence as an alternative to gel electrophoresis for reaction analysis, further decreasing the need of multiple reagents, reducing sample testing cost, and reducing sample analysis time. The bill of materials cost of the described system is approximately $340. The described PCR system utilizes a novel progressive selective proportional–integral–derivative controller that helps in reducing sample analysis time. In addition, the system employs a novel primer-based approach to quantify the initial target amplicon concentration, making it well-suited for food and water quality assessment. The developed PCR system performed DNA amplification at a level and speed comparable to larger and more expensive commercial table-top systems. The fluorescence detection sensitivity was also tested to be at the same level as commercially available multi-mode optical readers, thus making the PCR system an attractive solution for medical point-of-care and food and water quality assessment. In general, sensitive testing methods require genetic material (open full item for complete abstract)

Committee: Vamsy Chodavarapu P.E., Ph.D. (Committee Chair); Amy Neidhard-Doll P.E., Ph.D. (Committee Member); Guru Subramanyam Ph.D. (Committee Member); Yvonne Sun Ph.D. (Advisor) Subjects: Biomedical Engineering; Electrical Engineering

Master of Science, The Ohio State University, 2023, Mechanical Engineering

This project's purpose was to develop and validate the methodologies that can be used as a baseline for turbulence characterization of the in– cylinder engine flow. In – cylinder flow is a complex combination of swirl and tumble, but since it is dominated by tumble, the flow initialization used in this project was of pure tumble in nature. In the end, the results yielded the effect of factors such as grid size, turbulence model, simulation time step, CFL number and analysis techniques on determining time constants for decay equations and integral length scale. Results from the grid convergence study concluded that for specific case in this project 0.5mm grid is the most appropriate grid for flow modelling. In addition to that, it was observed that a 0.5mm mesh can resolve 80 – 90% of the essential scales that were present in the domain during the decay period of the simulation cycle. Study of the turbulence model gave an insight on the robust modelling capabilities of the Realizable K – Epsilon turbulence model to calculate the Turbulent Kinetic Energy growth and decay in the flow domain. Consequently, the gap of scale resolving inability of RANS turbulence models such as Realizable K – Epsilon was filled by WALE sub grid LES model. The detail eddy representation of LES model aided in choosing this turbulence model for determination of Integral Length Scale. Finally, multiple geometries of the stationary cylinder with pent – roof head is analyzed to investigate the relation of TKE decay time constant with piston position. A decreasing trend in the time constant with the piston position is observed for multiple geometries which can be used to extrapolate the time constants for piston position that have not been simulated explicitly. Some benefits of this research are the development of the base methodologies that can not only be used in turbulence flow characterization for stationary in – cylinder flow but for motored and firing conditions as well.

Committee: Zhenyu Wang (Committee Member); Clarissa Belloni (Committee Member) Subjects: Mechanical Engineering

Master of Arts (MA), Bowling Green State University, 1964, Mathematics

Committee: David M. Krabill (Advisor) Subjects: Mathematics

Master of Arts (MA), Bowling Green State University, 1949, Mathematics

Committee: David M. Krabill (Advisor) Subjects: Mathematics

Master of Science in Engineering, University of Akron, 2022, Civil Engineering

Stress Intensity Factor (SIF) is a parameter that characterizes the stresses and displacements near a crack tip and is widely used as a measure of how acute the defect caused by the crack(/s) in the material is. Any prediction of crack growth or any choice of a limiting value for the maximum crack dimensions or stress, is contingent upon an accurate determination of the Stress Intensity Factors. This thesis incorporates a detailed description of the analytical derivations of Stress Intensity Factors for an infinite, isotropic, cracked plate, subjected to a tensile far-field state of stress following the method of Singular Integral Equations, based upon the work of W.K. Binienda et al. (1992a). The calculations of local stresses and displacements for the crack problem are done by formulating the problem as a superposition of two auxiliary problems; the one without any crack, being under tension, and the other as a mixed boundary value problem defined for normal compressive tractions within the crack domain and for displacements outside the crack domain. Emphasis is placed on Binienda's (1992a) realization that, at this stage, invoking the stress and displacement boundary conditions into the dual integral equations for the displacement components (u and v), result in a form that is not solvable for the unknown constants C1 through C4. To overcome this difficulty, a form of “auxiliary functions” f1(x) and f2(x) is adopted which was used by Binienda (1992a) following Erdogan (1978) and other researchers. Unknown constants C1 through C4 are expressed and solved in terms of auxiliary functions f1(x) and f2(x) using the continuity conditions that the normal stress in the vertical direction, and the shear stress, for the upper as well as lower halves of the plate, are equal. This is followed by formulation of total stresses for the jth crack defined as the local stresses for the jth crack plus the contribution of the remaining cracks. These are obtained by coordinate and (open full item for complete abstract)

Committee: Wieslaw Binienda (Advisor); Ping Yi (Committee Member); Anil Patnaik (Committee Member) Subjects: Civil Engineering; Mechanical Engineering; Mechanics

PHD, Kent State University, 2022, College of Education, Health and Human Services / School of Teaching, Learning and Curriculum Studies

The purpose of this investigation was to explore the effects of stereotype threat on women's construction of gender and mathematical identities, and to examine how these various cognitive negotiations may affect their mathematical reasoning on challenging definite integral applications. This was a qualitative study that primarily utilized the episodic narrative interview method. A sample of 20 Calculus II students were given a calculus assessment and a survey regarding the importance of gender and mathematics to their identities. Results of the surveys were used to identify a purposeful sample of four participants to be interviewed. Analysis of the interview transcripts revealed four themes that offer some insight into women's experiences at the intersection of gender, mathematics, and stereotype threat. The findings include evidence that both gender identification and domain identification (the strength with which one identifies with mathematics) influence the effects of stereotype threat. More specifically, women, whose gender is more central to their identity and who care the most about their identities as mathematicians appear to be more vulnerable to the effects of stereotype threat. Findings also support earlier claims that gendered discourse in mathematics harms women's construction of mathematical identities.

Committee: Karl Kosko (Committee Chair) Subjects: Mathematics; Mathematics Education; Pedagogy

BA, Oberlin College, 2022, Religion

This paper explores the roots of Hindu Nationalist religiopolitical rhetoric. The argument centers around Ram Madhav's 2021 book The Hindutva Paradigm: Integral Humanism and the Quest for a Non-Western Worldview. In addition, it examines texts from the websites of various organizations in the Sangh Parivar, a term used for a collection of groups that are aligned in their conservative, Hindu Nationalist agenda. A rhetorical analysis of Hindu Nationalists' language reveals how the Sangh Parivar attempts to distinguish its worldview from so-called western social structures in order to establish the ancient legitimacy of Brahminical Hinduism. Further, this paper frames contemporary Hindu Nationalist rhetoric within the context of historical British colonial efforts to reify Brahminical Hinduism and consolidate Hindu identity in contrast to a Muslim ethnoreligious “other” for Britain's political benefit. This framing reveals how Hindu Nationalist rhetoric parallels and builds on colonial political tactics, illuminating the fallacy of Hindu Nationalists' anticolonial narrative.

Committee: Emilia Bachrach (Advisor); Corey Ladd Barnes (Advisor) Subjects: Political Science; Religion; Religious History; Rhetoric; Sociology; South Asian Studies

Doctor of Philosophy (Ph.D.), University of Dayton, 2022, Theology

This dissertation is about the problem of history in modern theology. It describes early Christian conceptions of history and truth and sketches a genealogy of the impact of modern historical consciousness on Christianity. By focusing on Third Republic France, and then the work of the bible scholar Alfred Loisy, this dissertation seeks to situate the Modernist Crisis, where the conflict between history and theology erupted most violently. In so doing, the way in which conceptions of doctrine are embedded within histories, contexts, and politics is revealed. To flesh out this same point, in its later chapters, this dissertation shifts its attention to Catholic engagement with the right-wing and fascist movements of the twentieth- century. To this end, the career of Jacques Maritain (d. 1973) proves particularly important. His move from reactionary politics in his youth toward the articulation of a “New Christendom” reveals the extent to which theology and politics co-constitute each other. More than that, this dissertation looks at Maritain's role in the religious freedom debates of the Second Vatican Council. The final thesis of the dissertation is that the thinking Maritain utilizes in articulating his New Christendom - what he calls “prise de conscience” or “awareness” - offers a contribution to the ongoing conversations about continuity and discontinuity that mark Catholic reflection on the problems of history and doctrine.

Committee: William Portier (Advisor); Jana Bennett (Committee Member); Thomas Guarino (Committee Member); Vincent Miller (Committee Member); Dennis Doyle (Committee Member) Subjects: History; Philosophy; Political Science; Religion; Religious History; Theology

Doctor of Philosophy, The Ohio State University, 2022, Mechanical Engineering

A modified version of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm is presented for the construction of higher order Lagrangian and NURBS-enhanced (NE) finite element meshes. CISAMR non-iteratively transforms a structured grid into a conforming mesh with an upper bound of three on aspect ratios of resulting elements. In this thesis, we introduce new algorithmic aspects for generating higher-order Lagrangian and NE meshes using CISAMR. For each type of element, a comprehensive study is then provided on the performance of first, second, and third-order meshes for solving linear elastic problems with smooth and oscillatory curvilinear edges. In these examples, local gradient recovery error, computational cost, and implementation complexity are used as performance metrics. Outcomes of this numerical study are used as a case study to elucidate some of the common sources of bias in interpreting or presenting results. In particular we show how bias, whether purposeful or not, could lead to misleading conclusions regarding the performance of a numerical technique that could even contradict the actual situation. In the next part, we expand the CISAMR algorithm for modeling complex two-dimensional (2D) crack growth problems involving contact/friction along the crack surface and interaction between multiple cracks. The CISAMR algorithm transforms a structured mesh into a high-quality conforming mesh non-iteratively, which is an attractive feature for modeling the evolution of the crack geometry with minimal changes to the underlying mesh structure. To model such problems, the mesh structure is first adaptively refined and updated near the crack tip to form a spider-web pattern of elements for the accurate approximation of the energy release rate and thereby predicting the new crack path. In each step of the crack advance simulation, a small subset of elements in the vicinity of the crack tip detected by employing a tree data structure a (open full item for complete abstract)

Committee: Soheil Soghrati Dr (Advisor); David Talbot Dr (Committee Member); Rebecca Dupaix Dr (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy (PhD), Ohio University, 2022, Civil Engineering (Engineering and Technology)

Semi-integral abutment bridges are integral abutment bridges with a flexible interface at the abutment to reduce the force transferred to the foundation. Wingwalls in abutment and semi-integral abutment bridges are designed as retaining walls to avoid the sliding of the backfill soil behind the bridge abutments and roadways. Using turn-back wingwalls that are parallel to the bridge diaphragm can provide support for the parapets and minimize the total longitudinal pressure on the abutments. These walls are subjected to axial forces and bending moments due to the thermal movements. These forces can affect the orientation and the connection details of the wingwalls, which could cause cracks in the wingwalls. Despite several studies on integral abutment bridges, there are no studies that combined the behavior of the drilled shafts, footings, abutment walls, and the turnback wingwalls of semi-integral abutment bridges. The long-term performance of a semi-integral abutment bridge with turn-back wingwalls supported on drilled shafts in Ohio was investigated in this doctorate study by instrumenting five drilled shafts, footing, the forward abutment wall, and one of the wingwalls during construction. Strain and temperature were collected in 2017, 2018, and 2019. It was found that the seasonal and daily temperature changes have a significant effect on the changes in the strain in the substructure. The behavior of the abutment wall significantly affects the behavior of the wingwall, footing, and drilled shafts. It was also noticed that the behavior of the abutment was irreversible, and the top of the abutment wall and the top of the drilled shaft induced higher strain than the bottom. Cracks were noticed at the front face of the abutment wall and wingwall, and these cracks tended to close as the air temperature decreased and open as the air temperature increased. The extremely cold weather conditions induced tensile strain higher than the allowable stra (open full item for complete abstract)

Committee: Issam Khoury (Advisor); Eric Steinberg (Committee Member); Jay Wilhelm (Committee Member); Sergio Lopez-Permouth (Committee Member); Shad Sargand (Committee Member); Teruhisa Masada (Committee Member) Subjects: Civil Engineering

PhD, University of Cincinnati, 2021, Arts and Sciences: Mathematical Sciences

The fifth order KdV equations model the plasma waves and other dispersive phenomena when the contribution of the third order KdV-type dispersion is small. In recent years, the well-posedness of the fifth order KdV equations, that is existence, uniqueness of the solution, and continuous dependence of the solution on datum(initial value or boundary values), has been intensively studied by mathematicians using the methods already developed for the KdV equation on the real line, periodic domain, half-line, and bounded domain.

Committee: Bingyu Zhang Ph.D. (Committee Chair); Donald French Ph.D. (Committee Member); Michael Goldberg Ph.D. (Committee Member); Andrew Lorent Ph.D. (Committee Member) Subjects: Mathematics