Digital Commons Network^™

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

On Distortion Of Surface Groups In Right-Angled Artin Groups, Lucas Bridges

Mathematical Sciences Undergraduate Honors Theses

Surfaces have long been a topic of interest for scholars inside and outside of mathe- matics. In a topological sense, surfaces are spaces which appear flat on a local scale. Surfaces in this sense have a restricted set of properties, including the behavior of loops around a surface, codified in the fundamental group.

All but 3 surface groups have been shown to embed into a class of groups called right-angled Artin groups. The method through which these embeddings are created places large restrictions on all homomorphisms from surface groups to right-angled Artin groups.

One such restriction on these homomorphisms is …

Atmospheric Deposition Trends Are Primarily Decreasing In Arkansas And Tennessee, Anna Mccarty

Crop, Soil and Environmental Sciences Undergraduate Honors Theses

Atmospheric deposition has likely changed with the influence of increasing global temperatures and subsequent changes in precipitation across the United States and globally. The objective of this project was to analyze atmospheric deposition across northern Arkansas and Tennessee. The three specific objectives were to: i) evaluate trends in atmospheric deposition of various element/compounds, ii) assess the relationship between atmospheric deposition and rainfall, and iii) evaluate if rainfall-adjusted atmospheric deposition is changing over time. Six sites were analyzed from 1980 to 2022, including AR16, AR27, TN00, TN04, TN11, and TN14, which span over northern Arkansas and across Tennessee. The Mann-Kendall Test …

An Exploration Of Procedural Methods In Game Level Design, Hector Salinas

Computer Science and Computer Engineering Undergraduate Honors Theses

Video games offer players immersive experiences within intricately crafted worlds, and the integration of procedural methods in game level designs extends this potential by introducing dynamic, algorithmically generated content that could stand on par with handcrafted environments. This research highlights the potential to provide players with engaging experiences through procedural level generation, while potentially reducing development time for game developers.

Through a focused exploration on two-dimensional cave generation techniques, this paper aims to provide efficient solutions tailored to this specific environment. This exploration encompasses several procedural generation methods, including Midpoint Displacement, Random Walk, Cellular Automata, Perlin Worms, and Binary Space …

The Quantitative Analysis And Visualization Of Nfl Passing Routes, Sandeep Chitturi

Computer Science and Computer Engineering Undergraduate Honors Theses

The strategic planning of offensive passing plays in the NFL incorporates numerous variables, including defensive coverages, player positioning, historical data, etc. This project develops an application using an analytical framework and an interactive model to simulate and visualize an NFL offense's passing strategy under varying conditions. Using R-programming and data management, the model dynamically represents potential passing routes in response to different defensive schemes. The system architecture integrates data from historical NFL league years to generate quantified route scores through designed mathematical equations. This allows for the prediction of potential passing routes for offensive skill players in response to the …

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough

Mechanical Engineering Undergraduate Honors Theses

Mechanical Exfoliation of Graphene is an often-overlooked portion of the fabrication of quantum devices, and to create more devices quickly, optimizing this process to generate better flakes is critical. In addition, it would be valuable to simulate test pulls quickly, to gain insight on flake quality of various materials and exfoliation conditions. Physical pulls of graphene at various temperatures, pull forces, and pull repetitions were analyzed and compared to the results of ANSYS simulations, solved for similar results. Using ANSYS’ ability to predict trends in exfoliations, flake thickness and coverage using stress and deflection analyses were investigated. Generally, both strongly …

Examining The Relationship Between Manning's Roughness Coefficient And Stage, Henry Holtkamp

Biological and Agricultural Engineering Undergraduate Honors Theses

This paper uses LOESS regression to predict Manning's roughness coefficient to calculate flows in natural stream channels. Manning's roughness coefficient can introduce variability into Manning's equation, potentially destabilizing results. Utilizing LOESS to find n based on backcalculated n from collected discharge vs. stage information is the best way to acquire accurate Manning's roughness coefficient values at a variety of flows. Book values tend to drastically overestimate which can have wide-ranging implications for water allocation, flood management, maintaining environmental flows, and maintaining water quality.

Exploring Decentralized Computing Using Solid And Ipfs For Social Media Applications, Pranav Balasubramanian Natarajan

Computer Science and Computer Engineering Undergraduate Honors Theses

As traditional centralized social media platforms face growing concerns over data privacy, censorship, and lack of user control, there has been an increasing interest in decentralized alternatives. This thesis explores the design and implementation of a decentralized social media application by integrating two key technologies: Solid and the InterPlanetary File System (IPFS). Solid, led by Sir Tim Berners-Lee, enables users to store and manage their personal data in decentralized "Pods," giving them ownership over their digital identities. IPFS, a peer-to-peer hypermedia protocol, facilitates decentralized file storage and sharing, ensuring content availability and resilience against censorship. By leveraging these technologies, the …

Rice Biomass Response To Various Phosphorus Fertilizers In A Phosphorus-Deficient Soil Under Simulated Furrow-Irrigation, Jonathan B. Brye

Crop, Soil and Environmental Sciences Undergraduate Honors Theses

Wastewater-recovered phosphorus (P), in the form of the mineral struvite (MgNH4PO4⋅6H2O), may provide a sustainable alternative to rapidly decreasing rock phosphate reserves. Struvite can be generated via chemical and/or electrochemical precipitation methods, potentially reducing the amount of P runoff to aquatic ecosystems. The objective of this greenhouse tub study was to evaluate the effects of chemically- and electrochemically precipitated struvite (CPST and ECST, respectively) on above- and belowground plant response in a hybrid rice cultivar (Gemini 214, RiceTec) grown using furrow-irrigation compared to other common fertilizer-P sources [i.e., triple super phosphate (TSP) and diammonium phosphate (DAP)] in a P-deficient silt …

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough

Physics Undergraduate Honors Theses

Mechanical Exfoliation

Modeling Sex-Specific Changes In Myocardial Fibrosis, Grace Martin

Chemical Engineering Undergraduate Honors Theses

Heart disease the leading cause of death for both men and women in the United States. Cardiac fibrosis, or accumulation of extracellular matrix proteins in the heart, can occur after a heart attack and increase the risk for further complications. Current treatments for heart disease do not include extracellular matrix regulators, partly due to the complicated signaling network responsible for the production of these proteins. By using a computational model of the signaling network in cardia fibroblasts, the relationship between particular molecules and downstream extracellular matrix production can be examined.

Biological sex is an important factor for cardiac health and …

Survival Of Methanogens Desiccated On Mars Soil Simulants: Implications For Life On Mars, Lanee Knight

Biological Sciences Undergraduate Honors Theses

Because of Mars’s chemical features, it can be studied in the search for life and is a significant figure in the study of astrobiology (McKay, 2010). Dr. Kral’s laboratory studies methanogens, microorganisms in the domain Archaea, as possible life forms on Mars. Since some methanogens can withstand harsh environmental conditions and emit methane as a waste product, the growth of these microorganisms can be used as an indicator of potential life in the Mars subsurface (Kral et al., 1998). In this research, four methanogens, Methanothermobacter wolfeii, Methanobacterium formicicum, Methanosarcina barkeri, and Methanococcus maripaludi were desiccated in the …

Using Empathy To Shift Climate Change Attitudes., Carson Haller

Crop, Soil and Environmental Sciences Undergraduate Honors Theses

It has shifted from a hunch to an existential threat, it is a harbinger of disaster and bankruptcy, backed by science, and yet a considerable portion of Americans still believe that climate change is a hoax. It is becoming increasingly imperative to convince this portion to join the fight. It has been found that empathy is an effective method of persuasion, prompting the question of whether empathy could be used shift climate change attitudes. The hypothesis of this study was that if a person feels empathy for somebody harmed by the effects of climate change, they will be more willing …

Encapsulated 2d Materials And The Potential For 1d Electrical Contacts, Sarah Wittenburg

Physics Undergraduate Honors Theses

The utilization of two-dimensional materials and heterostructures, particularly graphene and hexagonal boron nitride, have garnered significant attention in the realm of nanoelectronics due to their unique properties and versatile functionalities. This study focuses on the synthesis and fabrication processes of monolayer graphene encapsulated between layers of hBN, aiming to explore the potential of these heterostructures for various electronic applications. The encapsulation of graphene within hBN layers not only enhances device performance but also shields graphene from environmental contaminants, ensuring long-term stability. Experimental techniques, including mechanical exfoliation and stamp-assisted transfer, are employed to construct three-layer stacks comprising hBN-graphene-hBN. The fabrication process …

Do Heat Waves Drive Natural Selection In Damselflies?, Adam Baranyk

Biological Sciences Undergraduate Honors Theses

Climate change has led to changes in both mean temperatures and temperature extremes over the recent years. These changes have had differential effects on animals throughout the world. Ectotherms depend on their external environment for thermal regulation, making them especially susceptible to temperature extremes. It is not yet clear whether there is a relationship between physical traits in ectotherms, and survivorship throughout a heat wave. That is, whether or not temperature extremes driven survival selection. In this study, a heat wave was simulated artificially using thermally regulated mesocosms at different temperatures (18°C, 22° C, 26° C, 30° C) with a …

An In-Network Approach For Pmu Missing Data Recovery With Data Plane Programmability, Jack Norris

Computer Science and Computer Engineering Undergraduate Honors Theses

Phasor measurement unit (PMU) systems often experience unavoidable missing and erroneous measurements, which undermine power system observability and operational effectiveness. Traditional solutions for recovering missing PMU data employ a centralized approach at the control center, resulting in lengthy recovery times due to data transmission and aggregation. In this work, we leverage P4-based programmable networks to expedite missing data recovery. Our approach utilizes the data plane programmability offered by P4 to present an in-network solution for PMU data recovery. We establish a data-plane pipeline on P4 switches, featuring a customized PMU protocol parser, a missing data detection module, and an auto-regressive …

A Comprehensive Investigation Of The Influence Of Geometric Structure On The Shape Memory Performance Of Nafion, Jade Thomas

Physics Undergraduate Honors Theses

While perfluorosulfonic acid (PFSA) membranes have primarily been used in fuel cells due to their chemical, thermal, and mechanical stability, one PFSA, Nafion, boasts two unique characteristics: a broad glass transition (~55 °C to 130 °C) and a temperature-persistent electrostatic network. The combination of these two characteristics endows Nafion with exceptional shape memory properties – the ability of a material to morph and transform into pre-programmed shapes when exposed to an external stimulus – with enhanced permanent shape memorization, and a potentially near-infinite number of temporary shape memorization. This study focused on expanding the base of knowledge surrounding Nafion’s shape …

A Comprehensive Investigation Of The Influence Of Geometric Structure On The Shape Memory Performance Of Nafion, Jade Thomas

Mechanical Engineering Undergraduate Honors Theses

While perfluorosulfonic acid (PFSA) membranes have primarily been used in fuel cells due to their chemical, thermal, and mechanical stability, one PFSA, Nafion, boasts two unique characteristics: a broad glass transition (~55 °C to 130 °C) and a temperature-persistent electrostatic network. The combination of these two characteristics endows Nafion with exceptional shape memory properties – the ability of a material to morph and transform into pre-programmed shapes when exposed to an external stimulus – with enhanced permanent shape memorization, and a potentially near-infinite number of temporary shape memorization. This study focused on expanding the base of knowledge surrounding Nafion’s shape …

Comparing North American Professional Sports League Season Formats Using Monte Carlo Simulation, Lathan Gregg

Industrial Engineering Undergraduate Honors Theses

Each NFL, NBA, and MLB season consists of a regular season, in which teams play a set number of scheduled games and a playoff, in which qualifying teams compete for a championship. At the conclusion of each season, teams are ranked based on their performance throughout the season. This study aims to investigate the ability of each league's season format to accurately rank teams using Monte Carlo simulation. Matches between two teams are simulated by using the team’s assigned strength ranks to calculate a winning probability for each team. The winning probabilities are simulated with different skill values, dictating how …

Sequential Optimization For Stressor-Informed Test Planning Through Integration Of Experimental And Simulated Data, Jacob Brecheisen

Data Science Undergraduate Honors Theses

This technical report details an innovative approach in reliability engineering aimed at maximizing system durability through a synergistic use of physical experimentation and computer-based modeling. Our methodology explores the efficient design and analysis of computer experiments and physical tests to facilitate accelerated reliability growth, while leveraging a sequential integration of data from these two distinct sources: costly physical experiments, characterized by random errors, and inexpensive computer simulations, marked by inherent systematic errors. The key innovation lies in the adoption of a closed-loop design and analysis method. This method begins by identifying a viable subset of important environmental stressors—such as temperature, …