Physical Sciences and Mathematics Commons^™

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon

Mechanical Engineering

This report aims to allow our sponsor, to review our design process of the Hitch Cart Landing Gear Prototype. In the design overview section of this report, we discuss the primary design modifications we made to the wheel mechanism of the existing hitch cart prototype, including the addition of the ACME screws and the folding brackets. This allows our sponsor to see the intended improvements made to the past prototype and understand the primary goal of our project. Then, in the implementation section, we cover the entire manufacturing process to allow our sponsor to understand what manufacturing steps must be …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations & Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

Interpreting Shift Encoders As State Space Models For Stationary Time Series, Patrick Donkoh

Electronic Theses and Dissertations

Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can …

Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace

Electronic Theses, Projects, and Dissertations

Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …

Modeling Vibration Stiffness: An Analytical Extension Of Hertzian Theory For Angular Contact Bearings With A Thin Viscoelastic Coating, Davis R. Burton

Honors Theses

This thesis considers the novel angular contact rolling-element bearings proposed by NASA’s Glenn Research Center, which are coated with a thin solid lubricant that exhibits viscoelastic behavior. Current analytical models for the dynamic stiffness matrix of angular contact bearings, critical for vibration analysis, lack the ability to model the effects of a solid coating, as well as the time dependencies inherent in viscoelastic theory. The author first presents an overview of the stiffness matrix derivation, followed by a treatment of the underlying Hertzian contact theory. An analytical extension of this theory is proposed which accounts for a thin elastic layer …

Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad

Dissertations

The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …

Exploration Of Characteristic Curve In Fox Float 3 Shock Dampers To Expedite Shock Damp Tuning., Joshua R. Moore

Honors College Theses

The shock absorber is an integral part of a vehicle suspension system and has a strong influence on its performance, especially in the case of motorsports. It is important to study the force versus velocity relationship, commonly known as the characteristic curve of the shock absorber both during compression and rebound. Vendor-supplied characteristics often reflect the behavior of the shock absorber in a particular setting. However, during the installation, the settings inside the shock absorber are adjusted to increase the human comfort level and performance of the vehicle. This may change the characteristic curve of the shock. The available data …

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

Honors Program Theses and Research Projects

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks

LSU Doctoral Dissertations

This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …

New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman

Dissertations, Theses, and Capstone Projects

Univariate polynomial root-finding is a venerated subjects of Mathematics and Computational Mathematics studied for four millenia. In 1924 Herman Weyl published a seminal root-finder and called it an algorithmic proof of the Fundamental Theorem of Algebra. Steve Smale in 1981 and Arnold Schonhage in 1982 proposed to classify such algorithmic proofs in terms of their computational complexity. This prompted extensive research in 1980s and 1990s, culminated in a divide-and-conquer polynomial root-finder by Victor Pan at ACM STOC 1995, which used a near optimal number of bit-operations. The algorithm approximates all roots of a polynomial p almost as fast as one …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

A New Proper Orthogonal Decomposition Method With Second Difference Quotients For The Wave Equation, Andrew Calvin Janes

Masters Theses

"Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In \cite {Sarahs}, a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this thesis, we extend the new DQ POD approach from \cite {Sarahs} to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and …

Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, Nouf Alrubea Almutiben

Theses and Dissertations

We consider the symmetry algebra of the geodesic equations of the canonical
connection on a Lie groups. We mainly consider the solvable indecomposable four,
five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that
have an abelian and not abelian complement. In this particular case, we have only
one algebra in dimension four namely; A4,12 , and three algebras in dimension five
namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in
Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an
abelian complement, and there are eight algebras that …

Data Driven And Machine Learning Based Modeling And Predictive Control Of Combustion At Reactivity Controlled Compression Ignition Engines, Behrouz Khoshbakht Irdmousa

Dissertations, Master's Theses and Master's Reports

Reactivity Controlled Compression Ignition (RCCI) engines operates has capacity to provide higher thermal efficiency, lower particular matter (PM), and lower oxides of nitrogen (NOx) emissions compared to conventional diesel combustion (CDC) operation. Achieving these benefits is difficult since real-time optimal control of RCCI engines is challenging during transient operation. To overcome these challenges, data-driven machine learning based control-oriented models are developed in this study. These models are developed based on Linear Parameter-Varying (LPV) modeling approach and input-output based Kernelized Canonical Correlation Analysis (KCCA) approach. The developed dynamic models are used to predict combustion timing (CA50), indicated mean effective pressure (IMEP), …

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

Electronic Theses and Dissertations

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

Electronic Theses and Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

Adaptation Reshapes The Distribution Of Fitness Effects, Diego Tenoch Morales Lopez

Electronic Thesis and Dissertation Repository

The process of adaptation has been of interest since the XIX century, when Darwin first proposed the idea of natural selection. Since then, there has been a myriad of theoretical and empirical works that have expanded the field. From the many evolutionary insights these works have produced, a foundational idea is that spontaneous mutations in the genome of organisms can produce changes to their reproductive success that might confer an advantage for the mutant organisms with respect to their peers. Therefore, mutations drive adaptive evolution by virtue of their heritable effects on fitness. Empirical measures of the distribution of these …

Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin

Electronic Theses and Dissertations

This thesis explores the utilization of game theory and nonsmooth functions to enhance the accuracy of epidemiological simulations. Traditional sensitivity analysis encounters difficulties when dealing with nondifferentiable points in nonsmooth functions. However, by incorporating recent advancements in nonsmooth analysis, sensitivity analysis techniques have been adapted to accommodate these complex functions. In pursuit of more accurate simulations, evolutionary game theory, primarily the replicator equation, is introduced, modeling individuals’ decision making processes when observing others’ choices. The SEIR model is explored in depth, and additional complexities are incorporated, leading to the creation of an expanded SEIR model, the Be-SEIMR model.

Population Dynamics And Bifurcations In Predator-Prey Systems With Allee Effect, Yanni Zeng

Electronic Thesis and Dissertation Repository

This thesis investigates a series of nonlinear predator-prey systems incorporating the Allee effect using differential equations. The main goal is to determine how the Allee effect affects population dynamics. The stability and bifurcations of the systems are studied with a hierarchical parametric analysis, providing insights into the behavioral changes of the population within the systems. In particular, we focus on the study of the number and distribution of limit cycles (oscillating solutions) and the existence of multiple stable states, which cause complex dynamical behaviors. Moreover, including the prey refuge, we examine how our method benefits the low-density animals and affects …

High-Performance Computing In Covariant Loop Quantum Gravity, Pietropaolo Frisoni

Electronic Thesis and Dissertation Repository

This Ph.D. thesis presents a compilation of the scientific papers I published over the last three years during my Ph.D. in loop quantum gravity (LQG). First, we comprehensively introduce spinfoam calculations with a practical pedagogical paper. We highlight LQG's unique features and mathematical formalism and emphasize the computational complexities associated with its calculations. The subsequent articles delve into specific aspects of employing high-performance computing (HPC) in LQG research. We discuss the results obtained by applying numerical methods to studying spinfoams' infrared divergences, or ``bubbles''. This research direction is crucial to define the continuum limit of LQG properly. We investigate the …

Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye

Electronic Theses and Dissertations

Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …

Mathematical Evaluation Of Ulnar Nerve Somatosensory Evoked Potentials (Sseps), Maribel Carmen Gomez

Theses and Dissertations

As the number of individuals suffering with low back and neck pain rises, we find people undergoing spinal procedures more often. In means, of safeguarding the patient and their neurological structures during the procedure intraoperative neuro-physiological monitoring (I.O.M) has been more widely used amongst surgeons orthopedic and neuro alike. During these procedures, a modality widely used for both low back and neck surgery is somatosensory evoked potentials (SSEPs). The aim of neuro-technicians is to obtain a baseline waveform that can be considered present and reliable. When obtaining SSEPs the technician can encounter obstacles with ’noisy’ wave-forms due to …

Parameter Estimation For Patient Enrollment In Clinical Trials, Junyan Liu

Undergraduate Honors Theses

In this paper, we study the Poisson-gamma model for recruitment time in clinical trials. We proved several properties of this model that match our intuitions from a reliability perspective, did simulations on this model, and used different optimization methods to estimate the parameters. Although the behaviors of the optimization methods were unfavorable and unstable, we identified certain conditions and provided potential explanations for this phenomenon and further insights into the Poisson-gamma model.

An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson

Electronic Theses, Projects, and Dissertations

The field of differential geometry is brimming with compelling objects, among which are warped products. These objects hold a prominent place in differential geometry and have been widely studied, as is evident in the literature. Warped products are topologically the same as the Cartesian product of two manifolds, but with distances in one of the factors in skewed. Our goal is to introduce warped product manifolds and to compute their curvature at any point. We follow recent literature and present a previously known result that classifies all flat warped products to find that there are flat examples of warped products …

Generative Adversarial Game With Tailored Quantum Feature Maps For Enhanced Classification, Anais Sandra Nguemto Guiawa

Doctoral Dissertations

In the burgeoning field of quantum machine learning, the fusion of quantum computing and machine learning methodologies has sparked immense interest, particularly with the emergence of noisy intermediate-scale quantum (NISQ) devices. These devices hold the promise of achieving quantum advantage, but they grapple with limitations like constrained qubit counts, limited connectivity, operational noise, and a restricted set of operations. These challenges necessitate a strategic and deliberate approach to crafting effective quantum machine learning algorithms.

This dissertation revolves around an exploration of these challenges, presenting innovative strategies that tailor quantum algorithms and processes to seamlessly integrate with commercial quantum platforms. A …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect., Isaac Johnson

Electronic Theses and Dissertations

A protection zone model represents a patchy environment with positive growth over the protection zone and strong Allee effect growth outside the protection zone. Generally, these models are considered through the corresponding eigenvalue problem, but that has certain limitations. In this thesis, a general protection zone model is considered. This model makes no assumption on the direction of the traveling wave solution over the Strong Allee effect patch. We use phase portrait analysis of this protection zone model to draw conclusions about the existence of equilibrium solutions. We establish the existence of three types of equilibrium solutions and the necessary …

Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright

Theses and Dissertations

Microorganisms often swim within complex fluid environments composed of multiple materials with very different properties. Biological locomotion, including swimming speed, is significantly impacted by the physical composition and rheology of the surrounding fluid environment, as well as the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary greatly. Through computational simulations, we first investigate the classical Taylor’s swimming sheet problem near interfaces within multi-fluid environments using a two-fluid immersed boundary method. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …