Doctor of Philosophy, The Ohio State University, 2022, Mathematics

Motivated by definitions in mixed Hodge theory, we define the weight filtration and the monodromy weight filtration on the combinatorial intersection cohomology of a fan. These filtrations give a natural definition of some multivariable invariants of subdivisions of polytopes, lattice polytopes, and fans, namely, the mixed h-polynomial, the refined limit mixed h*-polynomial and the mixed cd-index. Previously, only the refined limit mixed h*-polynomial had a geometric interpretation, which came from filtrations on the cohomology of a schon hypersurface. In addition, using comodule techniques, we show that the mixed cd-index determines the mixed h-polynomial.

Committee: Eric Katz (Advisor); David Anderson (Committee Member); Maria Angelica Cueto (Committee Member) Subjects: Mathematics

Master of Science, University of Toledo, 2014, College of Engineering

The most stable isotope of radon is Radon-222, which is a decay product of radium-226 and an indirect decay product of uranium-238, a natural radioactive element. According to the United States Environmental Protection Agency (USEPA), radon is the primary cause of lung cancer among non-smokers. The USEPA classifies Ohio as a zone 1 state because the average radon screening level is more than 4 picocuries per liter. To perform preventive measures, knowing radon concentration levels in all the zip codes of a geographic area is necessary. However, it is impractical to collect the information from all the zip codes due to its inapproachability. Several interpolation techniques have been implemented by researchers to predict the radon concentrations in places where radon data is not available. Hence, to improve the prediction accuracy of radon concentrations, a new technique called Quantile Regression Forests (QRF) is proposed in this thesis. The conventional techniques like Kriging, Local Polynomial Interpolation (LPI), Global Polynomial Interpolation (GPI), and Radial Basis Function (RBF) estimate output using complex mathematics. Artificial Neural Networks (ANN) have been introduced to overcome this problem. Although ANNs show better prediction accuracy in comparison to more conventional techniques, many issues arise, including local minimization and over fitting. To overcome the inadequacies of existing methods, statistical learning techniques such as Support Vector Regression (SVR) and Random Forest Regression (RFR) were implemented. In this thesis, Quantile Regression Forest (QRF) is introduced and compared with SVR, RFR, and other interpolation techniques using available operational performance measures. The study shows that QRF has least validation error compared with other interpolation techniques.

Committee: Vijay Devabhaktuni (Committee Chair); Ashok Kumar (Committee Member); Mansoor Alam (Committee Member) Subjects: Applied Mathematics; Electrical Engineering; Mathematics

Master of Science in Engineering (MSEgr), Wright State University, 2011, Mechanical Engineering

A high/variable-order numerical simulation procedure for gas dynamics problems was developed to model steep grading physical phenomena. Higher order resolution was achieved using an orthogonal polynomial Gauss-Lobatto grid, adaptive polynomial refinement and artificial diffusion activated by a pressure switch. The method is designed to be computationally stable, accurate, and capable of resolving discontinuities and steep gradients without the use of one-sided reconstructions or reducing to low-order. Solutions to several benchmark gas-dynamics problems were produced including a shock-tube and a shock-entropy wave interaction. The scheme's 1st-order solution was validated in comparison to a 1st-order Roe scheme solution. Higher-order solutions were shown to approach reference values for each problem. Uniform polynomial refinement was shown to be capable of producing increasingly accurate solutions on a very coarse mesh. Adaptive polynomial refinement was employed to selectively refine the solution near steep gradient structures and results were nearly identical to those produced by uniform polynomial refinement. Future work will focus on improvements to the diffusion term, complete extensions to the full compressible Navier-Stokes equations, and multi-dimension formulations.

Committee: George Huang PhD (Advisor); George Huang PhD (Committee Member); Joseph Shang PhD (Committee Member); Miguel Visbal PhD (Committee Member) Subjects: Fluid Dynamics; Mechanical Engineering

Doctor of Philosophy, University of Toledo, 2006, Physics

The main effort of the present dissertation is to establish a framework for construction of the numerical solution of the system of partial differential equations for the coefficients in the N-term expansion of the solution of the Boltzmann equation in Legendre polynomials, also known as the PN approximation of the Boltzmann equation. The key feature of the discussed solution is the presence of multiple waves moving in opposite directions in both velocity and spatial domains, which requires transformation of the expansion coefficients to characteristic variables and a directional treatment (up/down winding) of their velocity and spatial derivatives. After the presence of oppositely directed waves in the general solution is recognized, the boundary conditions at the origin of velocity space are formulated in terms of the arriving and reflected waves, and the meaning of the characteristic variables is determined, then the construction proceeds employing the standard technique of operator splitting. Special effort is made to insure numerically exact particle conservation in treatment of the advection and scattering processes. The constructed numerical routine has been successfully coupled with a solver for the Poisson equation in a self-consistent model of plasma discharge in argon for a two parallel-plate bare electrode geometry. The results of this numerical experiment were presented at the workshop on "Nonlocal, Collisionless Electron Transport in Plasmas" held at Plasma Physics Laboratory of Princeton University on August 2-4, 2005.

Committee: Constantine Theodosiou (Advisor) Subjects: Physics, Fluid and Plasma

Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering

Turbo codes are a class of high performance error correcting codes (ECC) and an interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions of interleavers are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and Takeshita have shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. Recently, quadratic permutation polynomial (QPP) based interleavers have been proposed into 3rd Generation Partnership Project Long Term Evolution (3GPP LTE) draft for their excellent error performance, simple implementation and algebraic properties which admit parallel processing and regularity. In some applications, such as deep space communications, a simple implementation of deinterleaver is also of importance. In this dissertation, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial (deinterleaver) for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. We also consider the inverses of QPPs which do not admit quadratic inverses. It is shown that most 3GPP LTE interleavers admit quadratic inverses. However, it is shown that even when the 3GPP LTE interleavers do not admit quadratic inverses, the degrees of the inverse polynomials are less than or equal to 4, which allows a simple implementation of the deinterleavers. An explanation is argued for the observation. The minimum distance and its multiplicity (or the first a few terms of the weight distribution) of error correcting codes are used to estimate the error performance at high signal-to-noise ratio (SNR). We consider efficient algorithms that find an upper bound (UB) on the minimum distance of turbo codes designed with QPP interleavers. Permutation polynomials have been extensively studied, but simple coefficient tests for permutati (open full item for complete abstract)

Committee: Hesham El Gamal (Advisor) Subjects:

Master of Science, University of Akron, 2012, Applied Mathematics

Many numerical methods are the result of replacing a function by its interpolating polynomial; quadrature formulas are one such method. In this research a special class of quadrature formulas are used that incorporate equally spaced points and zeros of Chebyshev polynomials simultaneously. Some properties of these quadrature formulas are investigated, and they will be used to develop single step methods for solving ordinary differential equations. Examples are presented to compare the approximated solutions with exact solutions.

Committee: Ali Hajjafar Dr. (Advisor); John Heminger Dr. (Other) Subjects: Applied Mathematics

Master of Science (M.S.), University of Dayton, 2024, Aerospace Engineering

Traditional conceptual-level aerodynamic analysis is limited to empirical and/or inviscid models due to considerations of computational cost and complexity. There is a distinct desire to incorporate higher-fidelity analysis into the conceptual-design process as early as possible. This work seeks to enable the use of high-fidelity data by developing and applying multi-fidelity surrogate models that can efficiently predict the underlying response of a system with high accuracy. To that end, a novel form of the multi-fidelity polynomial chaos expansion (PCE) method is introduced, extending the surrogate modeling technique to accept three distinct fidelities of input. The PCE implementation is evaluated for a series of analytical test functions, showing excellent accuracy in creating multi-fidelity surrogate models. Aerodynamic analysis of a generic hypersonic vehicle (GHV) is performed using three codes of increasing fidelity: CBAERO (panel code), Cart3D (Euler), and FUN3D (RANS). The multi-fidelity PCE technique is used to model the aerodynamic responses of the GHV over a broad, five-dimensional input domain defined by Mach number, dynamic pressure, angle of attack, and left and right control surface settings. Mono-, bi-, and tri-fidelity PCE surrogates are generated and evaluated against a high-fidelity “truth” database to assess the global error of the surrogates focusing on the prediction of lift, drag, and pitching moment coefficients. Both monofidelity and multi-fidelity surrogates show excellent predictive capabilities. Multi-fidelity PCE models show significant promise, generating aerodynamic databases anchored to RANS fidelity at a fraction of the cost of direct evaluation.

Committee: Markus Rumpfkeil (Advisor); Jose Camberos (Committee Member); Timothy Eymann (Committee Member) Subjects: Aerospace Engineering

PHD, Kent State University, 0, College of Arts and Sciences / Department of Mathematical Sciences

Let R be a ring, σ be an automorphism of R, and D be a σ-derivation of R. We will show that if R is an algebra over a field of characteristic 0 and D is q-skew, then J(R[x; σ, D]) = I ∩ R + I_0 where I = {r ∈ R : rx ∈ J(R[x; σ, D])} and I_0 = {\sum_{i≥1} r_ix^i : r_i ∈ I}. We will prove that J(R[x; σ, D]) ∩ R is nil if σ is locally torsion and one of the following conditions is given: (1) R is a PI-ring and D is q-skew, (2) R is an algebra over a field of characteristic p > 0 and D is a locally nilpotent derivation such that σD = Dσ. This answers partially an open question by Greenfeld, Smoktunowicz and Ziembowski. In addition, we will discuss differential polynomial rings. Let R be an algebra over a field of characteristic 0 and let d be a nilpotent derivation of R. We will show that the Jacobson radical of a differential polynomial ring R[x; d] is of the form I[x; d], where I is a nil ideal of R. This partially answers an open question posed by Smoktunowicz. We also study iterated differential polynomial rings over locally nilpotent rings and show that a large class of such rings are Behrens radical. In particular, that extends recent results of Chebotar, Chen, Hagan and Wang.

Committee: Mikhail Chebotar (Advisor); Artem Zvavitch (Committee Member); Feodor Dragan (Committee Member); Joanne Caniglia (Committee Member); Evgenia Soprunova (Committee Member) Subjects: Mathematics

Doctor of Philosophy in Engineering, Cleveland State University, 2022, Washkewicz College of Engineering

In engineering fields, computational models provide a tool that can simulate a real world response and enhance our understanding of physical phenomenas. However, such models are often computationally expensive with multiple sources of uncertainty related to the model's input/assumptions. For example, the literature indicates that ligament's material properties and its insertion site locations have a significant effect on the performance of knee joint models, which makes addressing uncertainty related to them a crucial step to make the computational model more representative of reality. However, previous sensitivity studies were limited due to the computational expense of the models. The high computational expense of sensitivity analysis can be addressed by performing the analysis with a reduced number of model runs or by creating an inexpensive surrogate model. Both approaches are addressed in this work by the use of Polynomial chaos expansion (PCE)-based surrogate models and design of experiments (DoE). Therefore, the objectives of this dissertation were: 1- provide guidelines for the use of PCE-based models and investigate their efficiency in case of non-linear problems. 2- utilize PCE and DoE-based tools to introduce efficient sensitivity analysis approaches to the field of knee mechanics. To achieve these objectives, a frame structure was used for the first aim, and a rigid body computational model for two knee specimens was used for the second aim. Our results showed that, for PCE-based surrogate models, once the recommended number of samples is used, increasing the PCE order produced more accurate surrogate models. This conclusion was reflected in the R2 values realized for three highly non-linear functions ( 0.9998, 0.9996 and 0.9125, respectively). Our results also showed that the use of PCE and DoE-based sensitivity analyses resulted in practically identical results with significant savings in the computational cost of sensitivity an (open full item for complete abstract)

Committee: Jason Halloran (Advisor); Lutful Khan (Committee Member); Daniel Munther (Committee Member); Josiah Sam Owusu-Danquah (Committee Member); Stephen Duffy (Committee Member) Subjects: Biomechanics; Biomedical Engineering; Biomedical Research; Civil Engineering

PhD, University of Cincinnati, 2022, Arts and Sciences: Mathematical Sciences

In this digital age, well tested public-key cryptography is vital for the continuing function of society. An example of one of the uses of cryptography is signature schemes which allow us to digitally sign a document. However, quantum computers utilizing Shor's algorithm threaten the security of all the cryptosystem currently in use. What is needed is post-quantum cryptography: classical cryptographic algorithms able to resist quantum attacks. In 2016, NIST put out a call for proposals for post-quantum cryptosystems for standardization. We are currently in the third round of the “competition,” with many different types of schemes being proposed. In 2017, Ward Beullens et al. submitted the Lifted Unbalanced Oil and Vinegar signature scheme to the NIST competition, which is a modification to the Unbalanced Oil and Vinegar Scheme by Patarin. The main modification is called lifting, which is to take a polynomial over a small finite field and view it as a map over some extension field. LUOV made it into the second round of the competition, but two attacks by Ding et al. showed a flaw in the modifications of LUOV. The first attack was the Subfield Differential Attack (SDA) which prompted a change of parameters by the authors of LUOV. The second was the Nested Subset Differential Attack (NSDA), which broke half of the parameters put forward by the authors of LUOV again. Due to the strengths of these attacks and the possibility stronger ones of a similar nature exist, LUOV did not go into the third round. This dissertation shows that such a stronger attack, which will be called NSDA+, is possible. All three of the attacks SDA, NSDA, and NSDA+ are straightforward but powerful in application against the lifting modification. First in chapter 1, we will discuss what is a public key cryptosystem by looking at the original definition of Diffie and Hellman. Then we will talk of the NIST Post-Quantum Standardizat (open full item for complete abstract)

Committee: Jintai Ding Ph.D. (Committee Member); Seungki Kim Ph.D. (Committee Member); Robert Buckingham Ph.D. (Committee Member) Subjects: Mathematics

PHD, Kent State University, 2021, College of Arts and Sciences / Department of Mathematical Sciences

A popular problem to study is whether an element in a given ring or algebra may be written as a commutator, or sum of commutators. We will answer this question for nilpotent matrices over a variety of rings. Inspired by the L'vov-Kaplansky conjecture, we will examine the possible images of polynomials evaluated on matrices over an algebraically closed skew field.

Committee: Mikhail Chebotar (Advisor); Jenya Soprunova (Committee Member); Feodor Dragan (Committee Member); Brett Ellman (Committee Member); Donald White (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2021, Mathematics

This thesis contains two parts. In the first part, we discuss certain class of KP solitons in connections with singular projective curves, which are labeled by certain types of numerical semigroups. In particular, we show that some class of the (singular and complex) KP solitons of the $l$-th generalized KdV hierarchy with $l\ge 2$ is related to the rational space curves associated with the numerical semigroup $\langle l,lm+1,\ldots, lm+k\rangle$ where $m\ge 1$ and $1\le k\le l-1$. We also calculate the Schur polynomial expansions of the $\tau$-functions for those KP solitons. Moreover, we construct smooth curves by deforming the singular curves associated with the soliton solutions, then we check that quasi-periodic solutions of $l$-th generalized KdV hierarchy indeed degenerate to soliton solutions we begin with when we degenerate the underlying algebraic curve and the line bundle over it properly. For these KP solitons, we also construct the space curves from commutative rings of differential operators in the sense of the well-known Burchnall-Chaundy theory. This part is mainly based on a published paper \cite{Kodama-Xie2021KP}. In the second part, we discuss solutions of the full Kostant-Toda (f-KT) lattice and their connections with the flag varieties. Firstly, we carry out Kowalevski-Painlev\'e analysis for f-KT equation. In particular, we associate each solution of the indicial equations with a Weyl group element, provide explicit formulas for eigenvalues of Kowalevski matrix and at last parameterize all the Laurent series solutions by $\mathcal{G} \slash \mathcal{B} \times \mathbb{C}^n$ where $\mathcal{G} \slash \mathcal{B}$ is the flag variety and $\mathbb{C}^n$ represents the spectral parameters. Secondly, we use iso-spectral deformation theory to study f-KT in the Hessenberg form, and give explicit form of the wave functions and entries in the Lax matrix expressed by $\tau$-functions with which we study $\ell$-banded Kostant-Toda hierarchy. W (open full item for complete abstract)

Committee: Yuji Kodama (Advisor); David Anderson (Committee Member); Herb Clemens (Committee Member); James Cogdell (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2021, Mathematics

Homogeneous dynamics is the study of dynamics of various flows on homogeneous spaces. It has far-reaching impacts on other mathematical fields. Many applications of homogeneous dynamics is achieved via equidistribution of certain trajectories on homogeneous spaces. This work is comprised of two main parts. In the first part, we investigate Birkhoff genericity on certain submanifold of $X=SL_d(\bR)\ltimes (\bR^d)^k/ SL_d(\bZ)\ltimes (\bZ^d)^k$, where $d\geq 2$ and $k\geq 1$ are fixed integers. The submanifold we consider is parameterized by unstable horospherical subgroup $U$ of a diagonal flow $a_t$ in $SL_d(\bR)$. Under the assumption that the intersection of the submanifold with affine rational subspaces has Lebesgue measure zero, we show that the trajectory of $a_t$ along Lebesgue almost every point on the submanifold gets equidistributed on $X$. This generalizes the previous work of Fr\k{a}czek, Shi and Ulcigrai. Following the scheme developed by Dettmann, Marklof and Str\"{o}mbergsson, we then deduce an application of our results to universal hitting time statistics for integrable flows. In the second part, we study the limit distribution of $k$-dimensional polynomial trajectories on homogeneous spaces, where $k\geq 2$ is a fixed integer. When the averaging is taken on certain expanding boxes on $\bR^k$ and assume certain conditions on polynomial trajectories, we generalize Shah's limit distribution theorem of polynomial trajectories to higher dimensional case.

Committee: Nimish Shah (Advisor); James Cogdell (Committee Member); Daniel Thompson (Committee Member) Subjects: Mathematics

Doctor of Philosophy (PhD), Ohio University, 2021, Mathematics (Arts and Sciences)

The present work constitutes some contributions to the taxonomy of various classes of non-commutative rings. These include the classes of reversible, reflexive, semicommutative, 2-primal, NI, abelian, Dedekind finite, Armendariz, and McCoy rings. In addition, two new families of rings are introduced, namely right real McCoy and polynomial semicommutative. The first contribution concerns the hierarchy and interconnections of reflexive, abelian, and semicommutative rings in the setting of finite rings. It is shown that a minimal reflexive abelian non-semicommutative ring has order 256 and that the group algebra F_2D_8 is an example of such a ring. This answers an open question posed by Professor Steve Szabo in his paper on a taxonomy of finite 2-primal rings. The second set of contributions includes characterizations of reflexive, 2-primal, weakly 2-primal and NI rings in the setting of Morita context rings. The results on Morita context rings which are reflexive are shown to generalize known characterizations of prime and semiprime Morita context rings. Similarly, the results on 2-primal, weakly 2-primal and NI Morita context rings presented here generalize various known results for upper triangular matrix rings. Specifically, a characterization of NI Morita context rings is shown to be equivalent to the (most) famous conjecture in Ring Theory: Kothe's conjecture. The third collection of contributions addresses a study of right real McCoy rings and polynomial semicommutative rings; both classes of rings being introduced in this dissertation. The correlations between these types of rings is described, and a series of examples of finite polynomial semicommutative rings is given. In addition, equivalent conditions to the McCoy condition and some of its variations are addressed. Finally, the last contribution establishes that the rings of column finite matrices, and row and column finite matrices over a reflexive ring are reflexive non-Dedekind finite. This result, alon (open full item for complete abstract)

Committee: Sergio López-Permouth Dr. (Advisor); Winfried Just Dr. (Committee Member); Gulisashvilli Archil Dr. (Committee Member); Jeffrey Dill Dr. (Committee Member) Subjects: Mathematics

MS, University of Cincinnati, 2020, Engineering and Applied Science: Mechanical Engineering

Experimental modal analysis (EMA), which is an integral part of vibration analysis deals with finding the dynamic characteristics of a system namely the natural frequencies, damping and modal scaling. This information is crucial to the design of any structure as they would help predict the system response in its operating conditions. EMA is usually performed on an input output data model that is acquired from a structure. There are several methods which operate in the time and frequency domain to evaluate the modal parameters from a meaningful set of experimental data. The traditional polynomial based approaches use least squares methods to arrive at a good estimate of the numerator and the denominator matrix polynomials that can represent the frequency response functions. The modal parameters are then obtained from this mathematical fit of the experimental data. Another approach to this problem is the use of state space models used in controls domain. An nth order linear differential equation can be represented in the state space form with the defining system matrices A, B, C and D. The problem statement here is to fit the experimental data into its defining state space matrices of a suitable order since they would contain all the modal information in them. Numerical simulations for subspace identification (N4SID), developed by Van Overschee and de Moore, is one algorithm that can be used to build a state space model from measured input output data. This thesis work attempts to compare the above mentioned traditional polynomial based approaches to modal analysis with a state space based system identification approach using N4SID. Through these comparisons, the similarities in the description of a transfer function by these two methods are described. It also would serve as a starting point for its reader to compare more state space approaches with the traditional Unified Matrix Polynomial Approach (UMPA).

Committee: Randall Allemang Ph.D. (Committee Chair); Michael Mains M.S. (Committee Member); Allyn Phillips Ph.D. (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2020, Business: Business Administration

As ultra-high dimensional longitudinal data is becoming ever more apparent in fields such as public health, information systems, and bioinformatics, developing flexible methods with a sparse set of important variables is of high interest. In this setting, the dimension of the covariates can potentially grow exponentially with respect to the number of clusters. This dissertation research considers a flexible semiparametric approach, namely, partially linear single-index models, for ultra-high dimensional longitudinal data. Most importantly, we allow not only the partially linear covariates, but also the single-index covariates within the unknown flexible function estimated nonparametrically to be ultra-high dimensional. Using penalized generalized estimating equations, this approach can capture correlation within subjects, can perform simultaneous variable selection and estimation with a smoothly clipped absolute deviation penalty, and can capture nonlinearity and potentially some interactions among predictors. We establish asymptotic theory for the estimators including the oracle property in ultra-high dimension for both the partially linear and nonparametric components. An efficient algorithm is presented to handle the computational challenges, and we show the effectiveness of our method and algorithm via a simulation study and yeast cell cycle gene expression data. In addition, we develop an alternative solution methodology via the penalized quadratic inference function with partially linear single-index models for ultra-high dimensional longitudinal data. This methodology can improve the estimation efficiency when the working correlation structure is misspecified. Performance is demonstrated via a simulation study and analysis of a genomic dataset.

Committee: Peng Wang Ph.D. (Committee Chair); Yan Yu Ph.D. (Committee Chair); Lenisa Chang Ph.D. (Committee Member) Subjects: Business Administration

Master of Science, University of Toledo, 2009, Civil Engineering

Prediction of future pavement conditions is one of the important functions of pavement management systems. They are helpful in determining the rate of roadway network deterioration both at the network-level and project-level management, which forms a major part of engineering decision making and reporting. Network-level management focuses on determination and allocation of funds to maintain the pavement network above a specified operational standard and does not give importance to how the individual pavement sections deteriorate. Therefore, a survival time analysis is determined to predict the remaining service life. At the project-level, engineers make decisions on which pavement to repair, when and how to repair. Therefore, it requires more condition accuracy than network-level. The two adjustment methods proposed by Shahin (1994) and Cook and Kazakov (1987) are often used to obtain more condition prediction at the project-level. Both the Shahin and the Cook and Kazakov models take into account a family average curve in predicting deterioration of individual pavement sections. This prediction is done through the latest available condition-age point of an individual pavement section and does not consider all available data points. This study considers the most commonly used pavement condition prediction models viz. linear regression, polynomial constrained least squares, S-shape and power curve. The prediction accuracy of these four models is compared. Further the prediction accuracy of each of the four models is compared with their respective the Shahin's and the Cook's models to determine whether is it possible to further improve the prediction accuracy error for each of the four models.

Committee: Eddie Y. Chou PhD (Committee Chair); George J. Murnen PhD (Committee Member); Andrew G. Heydinger PhD (Committee Member) Subjects: Civil Engineering; Engineering; Transportation

Doctor of Philosophy in Engineering, Cleveland State University, 2019, Washkewicz College of Engineering

Human-machine interaction has become an important area of research as progress is made in the fields of rehabilitation robotics, powered prostheses, and advanced exercise machines. Adding to the advances in this area, a novel controller for a powered transfemoral prosthesis is introduced that requires limited tuning and explicitly considers energy regeneration. Results from a trial conducted with an individual with an amputation show self-powering operation for the prosthesis while concurrently attaining basic gait fidelity across varied walking speeds. Experience in prosthesis development revealed that, though every effort is made to ensure the safety of the human subject, limited testing of such devices prior to human trials can be completed in the current research environment. Two complementary alternatives are developed to fill that gap. First, the feasibility of implementing impulse-momentum sliding mode control on a robot that can physically replace a human with a transfemoral amputation to emulate weight-bearing for initial prototype walking tests is established. Second, a more general human simulation approach is proposed that can be used in any of the aforementioned human-machine interaction fields. Seeking this general human simulation method, a unique pair of solutions for simulating a Hill muscle-actuated linkage system is formulated. These include using the Lyapunov-based backstepping control method to generate a closed-loop tracking simulation and, motivated by limitations observed in backstepping, an optimal control solver based on differential flatness and sum of squares polynomials in support of receding horizon controlled (e.g. model predictive control) or open-loop simulations. The backstepping framework provides insight into muscle redundancy resolution. The optimal control framework uses this insight to produce a computationally efficient approach to musculoskeletal system modeling. A simulation of a human arm is evaluated in both structur (open full item for complete abstract)

Committee: Hanz Richter Ph.D. (Advisor); Antonie van den Bogert Ph.D. (Committee Member); Eric Schearer Ph.D. (Committee Member); Sailai Shao Ph.D. (Committee Member); Daniel Simon Ph.D. (Committee Member) Subjects: Biomechanics; Biomedical Engineering; Engineering; Mechanical Engineering; Robotics; Robots

Doctor of Philosophy, The Ohio State University, 2019, Materials Science and Engineering

The design framework for complex materials property and processing models within the Integrated Computational Material Engineering (ICME) is often hindered by the expensive computational cost. The ultimate goal of ICME is to develop data-driven, materials-based tools for the concurrent optimization of material systems while, improving the deployment of innovative materials in real-world products. Reduced-order, fast-acting tools are essential for both bottom-up property prediction and top-down model calibrations employed for modern material design applications. Additionally, reduced-order modeling requires formal uncertainty quantification (UQ) from the processing stages all the way down to the manufacturing and component design. The goal of this thesis is to introduce a machine learning-based, reduced-order crystal plasticity model for face-centered cubic (FCC) polycrystalline materials. This implementation was founded upon Open Citrination, an open-sourced materials informatics platform. Case studies for both the bottom-up property prediction and top-down optimization of model parameters are demonstrated within this work. The proposed reduced-order model is used to correctly approximate the plastic stress-strain curves and the texture evolution under a range of deformation conditions and strain rates specific to a material. The inverted pathway is applied to quickly calibrate the optimal crystal plasticity hardening parameters given the macroscale stress-strain responses and evolutionary texture under certain processing conditions. A visco-plastic self-consistent (VPSC) method is used to create the training and validation datasets. The description of the material texture is given through a dimension reduction technique which was implemented by principal component analysis (PCA). The microstructures of engineering materials typically involve an intricate hierarchical crystallography, morphology, and composition. Therefore, an accurate, virtual representation (open full item for complete abstract)

Committee: Stephen Niezgoda (Advisor); Yunzhi Wang (Committee Member); Michael Groeber (Committee Member); Maryam Ghazisaeidi (Committee Member) Subjects: Materials Science

MS, University of Cincinnati, 2019, Engineering and Applied Science: Civil Engineering

About 38% of total energy consumption in the US can be attributed to residential usage, 48% of which is consumed by Heating, Ventilation and Air Conditioning (HVAC) systems. Inefficient operation of energy systems in residential sector motivates many researchers to develop an easy and affective method to educate consumers and reduce inefficient usage. A detailed energy bill is proven to motivate users to reduce energy consumption by 6-20% . Further, a system or device level energy consumption data can be used to propose energy saving practices. Information of HVAC usage alone can trigger a big saving, as about half of total consumption is HVAC. However, existing methods to disaggregate usage rely on sensors or meters at the either device or central power-level, which hinders the utilization for home owners. Alternatively, information about monthly electric utility is normally accessible for households, which may be utilized to attain HVAC energy use through data mining techniques. In this study, machine learning is used to construct a regression model to accurately estimate HVAC energy used based on monthly electricity used (from utility bill), home profiles, and monthly weather data. The main dataset used for training and testing the model is from the Pecan Street home energy use dataset.

Committee: Julian Wang Ph.D. (Committee Chair); Hazem Elzarka Ph.D. (Committee Member); Jiaqi Ma Ph.D. (Committee Member) Subjects: Civil Engineering