Digital Commons Network^™

Quantifying Grain Size In Scanning Electron Microscopy Images, Katherine Hoffsetz

Discovery Day - Daytona Beach

This project explores advanced image analysis techniques to assess the microstructure of highly strained austenitic stainless steel. Utilizing Python imaging libraries such as scikit-image and OpenCV, we aim to extract precise measurements for grain size from scanning electron microscopy (SEM) images. These metrics will be examined against the computed grain sizes of the sample from electron backscatter diffraction measurements. By automating the extraction of grain size measurements from SEM images, this study contributes to steamlining the quality assurance/ quality control of industrially processed materials.

Earthquake-Resistant Design And Base Isolation Techniques, Christian George, Jacob Sweeten, Gabriela Cotto, Savion Stewart

Discovery Day - Daytona Beach

Earthquake-resistant design has become a critical feature in construction near active fault lines, where seismic activity is most frequent and potentially destructive. In recent years, technological advancements have significantly improved methods for protecting buildings from earthquake damage. Among these innovations, base isolation systems have appeared as one of the most effective solutions. By decoupling a building from ground motion, base isolators reduce the transmission of seismic forces, helping to prevent structural damage and support building stability during earthquakes. In addition to improving safety, base isolation systems can also reduce long-term costs associated with earthquake-related repairs and maintenance. Base-isolated structures are …

Analyzing Fungal Growth Dynamics Under Different Environmental Conditions Using A Lotka–Volterra Competition System, Maria Ordonez, Fabrio Araujo

Discovery Day - Daytona Beach

Fungi play a critical role in ecosystems as decomposers that recycle nutrients and maintain environmental balance. Their populations are influenced by multiple environmental factors such as temperature, humidity, nutrient availability, and interactions with other organisms. In this project, the Lotka–Volterra model is used to analyze how competing fungal species interact and how these interactions influence population dynamics over time. By modeling two fungal populations competing for the same limited resources, the equations illustrate how environmental conditions and competition coefficients determine whether one species dominates; both species coexist, or one species becomes extinct. The model provides insight into how changes in …

Asymptotic Enumeration Of K-Bounded Functions Using Toeplitz Matrices, Tiago Cavalcante Trindade, Pedro Martineli

Rose-Hulman Undergraduate Mathematics Journal

We introduce the concept of $(\alpha, \lambda)$-bounded functions, characterized by limited local variation, which is especially useful in discrete sets. Initially, we formally define these functions and investigate their fundamental properties, highlighting significant differences from continuous functions. The main result obtained is the asymptotic estimate of $a(n, k)$, representing the number of functions from $[n]$ to $[n]$ that are $k$-bounded with respect to the Manhattan distance. The proof of this result combines Toeplitz matrices with a well-known inequality from graph theory.

Synthetic Strategies For Bioactive Peptides: From Aggregation Inhibitors To The Total Synthesis Of Tunicyclin C, Stephanie Graciela Garcia Morin

Theses and Dissertations

In Alzheimer's disease (AD), a brain protein called "tau" abnormally clumps and forms neurofibrillary tangles (NFTs), causing damage to brain cells. Ac-PHF6-NH2 is a hexapeptide segment of tau protein that plays a dominant role in tau aggregation and is used as a model to design tau protein aggregation inhibitors. In this research we synthesized four dehydroamino acid (□AA) containing PHF6 analogues with △Abu (derived from L-threonine) and △Val (derived from □-OH-Valine) at position 2 or 3 via dehydrations or azlactone ring-openings as key reactions. We evaluated their proteolytic resistance, ability to inhibit aggregation of PHF6, and impact on the morphology …

Sustainability Challenges And Opportunities In A University Police Fleet: A Case Study Of Idling, Emissions, And Electrification Potential, Van Slusser

School of Political Science, Public Affairs, Legal and Security Studies Faculty Publications

This case study examines fleet sustainability challenges within the University of Texas Rio Grande Valley Police Department, a multicampus public safety agency operating aging gasoline vehicles central to daily patrol and administrative functions. Rising maintenance costs, increased vehicle downtime, and extensive idling created both operational strain and avoidable environmental impacts. Aging internal-combustion vehicles contributed to elevated emissions and fuel consumption, particularly under high-heat conditions and equipment demands typical of campus policing. Telematics monitoring indicated that approximately 48% of total engine-on time consisted of idling, highlighting a substantial source of avoidable fuel use and emissions. The study employed a qualitative case …

Modeling Stellar Structure: Comparing Numerical Solutions Of The Lane-Emden Equation, Jasman Jasmanjot, Bailey Dale, Ryan Dickey

Discovery Day - Daytona Beach

The Lane-Emden equation is a differential equation that is often used in astrophysics to describe the distribution of the density inside a star, and by extension, its pressure distribution. Analytic solutions of the Lane-Emden equation can only be found at polytropic indices n = 0,1,5, matching certain physical conditions. For all other polytropic values, a numerical solution is needed. In this work, a comparison between two numerical schemes for solving the Lane-Emden equation is presented, namely the Euler method and the classical 4th order Runge-Kutta method. The accuracy of these models is first compared to the cases with known analytical …

Numerical Methods For Nonlinear Problems Using The Finite Element Method, Logan Price

Discovery Day - Daytona Beach

Numerical Methods for Nonlinear Problems Using the Finite Element Method is a computational mathematics capstone that builds and tests finite element method (FEM) workflows for nonlinear partial differential equations in FreeFEM++, with ParaView used for visualization. Two nonlinear model problems are used to demonstrate the approach. The first is a semilinear reaction-diffusion equation with a cubic nonlinearity. A manufactured solution is used so accuracy can be checked at a fixed final time, and refinement studies in both time step and mesh size are run while nonlinear iteration counts are tracked to show solver effort. The second problem is the steady …

Estimating The Effects Of Dark Matter Capture On The Sun Using Asteria And Analytic Stellar Scaling, Skylar G. Butler

Discovery Day - Daytona Beach

We investigate how the internal structure of the Sun would change if dark matter particles were present at densities predicted by Galactic halo models. Dark matter capture rates were computed using the Python code Asteria, which implements the multi-element capture formalism of Gould (1987) to determine the rate at which dark matter particles scatter and become gravitationally bound inside the Sun. Because Asteria calculates only the capture rate, we developed a post-processing Python-based analysis to estimate the resulting physical effects using analytic scaling relations from previous solar dark matter studies. These relations were used to compute the effective dark matter …

Low-Complexity Polynomial Ring Learning For Quantum Space Assets, Lola Torres

Discovery Day - Daytona Beach

Secure communication for space-based systems requires cryptographic methods that remain both reliable and efficient under strict computational constraints. This work investigates a low-complexity polynomial ring learning algorithm designed for quantum space assets, including satellite–ground communication systems. The project focuses on post-quantum cryptographic principles, where encryption and decryption rely heavily on repeated polynomial operations; this can be computationally expensive with constrained platforms. This is addressed with reformulating polynomial multiplication as a structured linear transformation on coefficient vectors. By representing these operations as matrices with a cyclic structure, the structure allows the use of the discrete Fourier transform (DFT); this will simplify …

Quantifying The Effect Of Metallicity On Stellar Properties And Evolutionary Timescales, Jacob Becker

Discovery Day - Daytona Beach

Stellar age estimations derived from asteroseismology depend on stellar models that are sensitive to metallicity (Z). Variations in this parameter could alter the agreement between gyrochronological and asteroseismic ages, as well as main sequence lifetimes and observational properties such as effective temperature and luminosity. We test how much typical metallicity differences (±0.2 dex) affect main-sequence models of solar-type stars. Using MESA, evolutionary tracks are created for 1 M☉ stars at three metallicities (Z = 0.009, 0.014, 0.022), and it is measured how these changes shift the positions of the zero-age main sequence and the corresponding main sequence lifetimes. This work …

Complex Continued Fractions And Inadmissible Sequences, Carolina A. Rizzi, Holly Vanlooy

Rose-Hulman Undergraduate Mathematics Journal

Serret's Theorem says that real numbers are related by a type of Möbius transformation if and only if the tails of their regular continued fraction expansions are the same. Serret’s Theorem does not hold for Hurwitz Continued Fractions in the complex plane due to a counterexample of Lakein. By applying transformations that convert inadmissible sequences into their admissible forms, we explain Lakein's counterexample from an algorithmic perspective. We provide additional counterexamples and prove that there exists an uncountably infinite family of counterexamples.

Project G.L.E.N., Alexis Peshehonoff, Makaylei Huggins, Bernard Muich, William John, Nicholas Fazzolari, Kai Hong, Nicholas Krasznavolgyi, Caitlyn A. Gabrinowitz, Grace Forbes, Harris Meyer, Jakob Graudons, Georgii Dubrov, Aditya Bhattacharya, Augustine Balish, Zachary Ort, Stephen Syvertson, Sajid Berhane

Discovery Day - Daytona Beach

Project G.L.E.N., formally known as “Refining Enhanced Fujita Wind Estimates via Unmanned Collection of In-Situ Tornadic Data Measurements,” is an ongoing initiative aimed at advancing tornado research through the development and deployment of an unmanned tornado probe. Through the Gale Level Environmental Navigator (G.L.E.N.) probe, a remote-controlled unit equipped with specialized meteorological sensors and innovative design features, we aim to collect real-time, onsite data from within tornadoes. This approach allows for direct measurement of internal atmospheric conditions such as wind speeds, pressure fluctuations, temperature, humidity, and other storm dynamics while removing human risk from tornado interception, significantly enhancing the safety …

String-Of-Pearls Measurements Of Supersonic Plasma Jets Using Magnetospheric Multiscale Satellites, Amelia Koth

Discovery Day - Daytona Beach

High-energy supersonic plasma jets form when the solar wind, which is a flow of charged particles from the Sun, slows down as it encounters Earth’s magnetic shield. Occasionally, the solar wind remains at supersonic speeds as it enters this region. This forms plasma jets that propagate toward Earth; these jets can carry strong magnetic fields, drive magnetic reconnection, and potentially initiate substorms that lead to auroral activity.   Previously studied plasma jets occurred when the interplanetary magnetic field (IMF) points southward. In contrast, this study focuses on northward IMF conditions, which are less understood, yet still capable of producing supersonic jets. …

Extending The Essentially Entropic Lattice Boltzmann Method To Three-Dimensional Turbulent Flows, Michael Derderian

Discovery Day - Daytona Beach

The Entropic Lattice Boltzmann Method (EELBM) has demonstrated strong numerical stability and accuracy for two-dimensional simulations, particularly at higher resolutions where the entropic formulation introduces only minimal stabilizing turbulent viscosity and eventually converges to the Lattice Bhatnagar–Gross–Krook (LBGK) formulation. This built-in stabilization can be interpreted as an implicit large-eddy simulation (LES) model, allowing EELBM to capture complex turbulent behavior without requiring explicit subgrid-scale closures. While these advantages have been thoroughly validated in 2D, understanding how the entropic constraint regulates dissipation in three dimensions is essential for assessing EELBM’s suitability for practical, turbulence-dominated applications. This work focuses on the development and …

Age Reassignment Using Luminescence Dating For The Mammoth Site, Black Hills, South Dakota, Usa, Shannon A. Mahan, Jim I. Mead, P.R. Hanson, Emma T. Krolczyk, Christopher N. Jass

School of Natural Resources: Faculty Publications

The Mammoth Site (MS) at Hot Springs, South Dakota, provides a unique opportunity to reconstruct paleoenvironmental conditions on the Northern Great Plains of the United States. Previous radiocarbon analyses of mammoth bone apatite suggested the MS sinkhole was deposited ∼42–23 cal ka BP. However, two U-series ages and one thermoluminescence (TL) age ranged between 150 and 101 ka, suggesting the bones were considerably older. We analyzed six samples from the bone bed using infrared-stimulated luminescence (IRSL) on feldspars, because the quartz luminescence was saturated; the ages ranged from approximately 232 to 160 ka, showing better agreement with previous U-series and …

A Qualitative Analysis Of Human-Ai Interaction Through Animated Shapes, Kavya Dipen Shah, Angel Hinojosa, Caroline Deck

Discovery Day - Daytona Beach

As technology becomes more advanced, it is important to understand how people perceive the intentions and abilities of machines. This project, conducted in the InTeRACT Lab, explores how we attribute humanlike qualities to different types of agents, ranging from animals to robots. The study analyzes data from an experiment where participants watched animations of moving triangles. Although the videos were identical, participants were told the shapes represented either humans, robots, dogs, or inanimate objects. While previous math-based data showed that these labels changed how people felt, those structured scales didn't allow for a natural, unbiased explanation of what people actually …

Social Attributions Of Moving Shapes: Comparing Qualitative Analyses Of Humans Vs. Ai, Angel Hinojosa

Discovery Day - Daytona Beach

As technology becomes more intelligent, the relationship between humans and machines is rapidly shifting. Whether a machine is perceived as a capable partner or a source of wariness often depends on the intentions and abilities, we attribute to it. My research in the InTeRACT Lab seeks to empirically assess these perceptions by comparing how we view different nonhuman agents, ranging from animals to robots.   This study analyzes qualitative data from a task where participants viewed animations of moving triangles. While the videos remained the same, participants were told the shapes represented either humans, robots, dogs, or inanimate shapes. Previous quantitative …

Investigating The Spatial Scales Of Ionospheric Irregularities Using Wavelet Analysis, Nash Mcleod

Discovery Day - Daytona Beach

Investigating the Spatial Scales of Ionospheric Irregularities Using Wavelet Analysis:   Ionospheric radio wave scintillation arises from plasma density irregularities in Earth’s ionosphere. Consequently, rapid fluctuations occur in the phase and amplitude of Global Navigation Satellite System (GNSS) signals and can impact communication and navigation systems. These irregularities span from a wide range of spatial and temporal scales and evolve dynamically under the influence of magnetosphere-ionosphere (MI) processes. We investigate phase and amplitude scintillation events using Continuous Wavelet Transform (CWT) to study the spatial evolution of ionospheric irregularities. These irregularities are thought to be formed via different plasma mechanisms such as …

Bounded Thunderstorm Tracking Of Lightning Events With Muon Detection, Skylar Wardlaw, Ainsley Helgerson, Maria Kaminska, Logan Velvet, Georgii Dubrov, Jackson Stewart, Aaron Jung, Nathaniel O’Hara, Amelia Koth, Nash Mcleod, Emaleth Wyckoff

Discovery Day - Daytona Beach

The muon is a high-energy particle that can be produced by cosmic rays and trigger upper-atmospheric particle cascades and energetic processes. It has been hypothesized that such cascades are at the onset of lightning. As such, muons serve as a valuable probe for investigating the underlying mechanisms of its initiation, whose full governing dynamics remain vastly unknown despite extensive research. Traditional approaches to lightning research involve simulations and observations of the discharge itself, but the role of high-energy particle interactions has yet to be fully constrained. The CosmicWatch Muon Detector design enables the detection of atmospheric muons through scintillation events, …

Effect Of Anode Size On The Properties Of Constricted Hollow Anode Pulsed Plasma Source, Nirav Patel, Garret Seckinger

Discovery Day - Daytona Beach

With the advent of ion thrusters, burns requiring large velocity changes can be performed with a fraction of the propellant required by traditional chemical rocket engines. However, current ion thrusters produce thrust in the order of millinewtons and thus cannot be viable for launching vehicles or burns requiring velocity changes in a small amount of time. Furthermore, current ion thrusters experience grid and component erosion, where the two grids at the termination of the nozzle slowly erode due to particle impact, and the hot electrodes degrade due to high thermal load. This limits the life of ion engines, which require …

Polymer Degradation And Their Environmental Impact, Addison Orr, Vanessa Gilbert

Discovery Day - Daytona Beach

Synthetic polymer material usage has increased significantly within the last several decades due to their durability, resistance to mechanical wear, low density, and inexpensiveness. Despite these advantages, most synthetic polymers are not biodegradable and instead undergo slow degradation processes. The processes are multifaceted, involving physical, chemical, and biological mechanisms influenced by material properties and environmental conditions, such as soil, light, temperature, and moisture levels. As a result, the polymers break into microplastics and contaminate air, water, and soil, posing risks to human health and surrounding ecosystems. Additionally, polymer degradation can release harmful substances that disrupt food chains and can lead …

Production And Analysis Of Lavender Essential Oil: Extraction, Composition, And Applications, Mary Zoeller

Discovery Day - Daytona Beach

Steam distillation was performed to extract essential oil from lavender and analyze its chemical composition. Lavender is known to contain several compounds such as linalool, terpinen-4-ol, and linalyl acetate, which contribute to its characteristic aroma and biological activity. The purpose of this experiment was to isolate these compounds without decomposition and identify them using gas chromatography–mass spectrometry (GC-MS). Approximately 14.851 g of lavender was heated with water to generate steam, which carried the volatile compounds into a condenser where the vapor was cooled and collected. The distillate was transferred to a separatory funnel to isolate the organic layer from the …

Bridging Discrete And Continuous Systems: Fibonacci Sequences And Exponential Growth From Odes, Martyna Wojcik

Discovery Day - Daytona Beach

Bridging Discrete and Continuous Systems: Fibonacci Sequences and Exponential Growth from Ordinary Differential Equations       It has been observed that nature often exhibits specific patterns of growth and structure in biological systems and spiral formations. The Fibonacci sequence, defined as a discrete recursive sequence where each term is generated as the sum of the two preceding terms, “has been applied extensively to understand some natural phenomena” (Pakdemirli, 2023). In contrast, exponential growth describes a continuous process in which the rate of change of a quantity is proportional to its current value. Such behavior is modeled using differential equations that “produce solutions …

Application Of Navier Stokes In Cfd, Hayden Kerkhoff, Gavin Palmer, Garret Seckinger

Discovery Day - Daytona Beach

This project investigates the use of 2-Dimensional Computational Fluid Dynamics (CFD) to analyze aerodynamic behavior, then compare data with the numerical solution of the Navier–Stokes equations run by MATLAB. By leveraging open‑source and possible industry CFD platforms—including OpenFOAM and commercial solvers such as ANSYS Fluent and Inventor Professional—the study evaluates how computational methods simulate, optimize, and predict key aerodynamic quantities such as lift, drag, stall angle, and Reynolds number.   The project focuses on modeling an airflow over specific parameters, such as different angles of attacks and ISA Atmospheric Conditions. Parametric variations in density, angle of attack, chord length, and temperature …

Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti

Discovery Day - Daytona Beach

The Trajectory of a badminton Shuttlecock can vary significantly when compared to a classic projectile motion, primarily due to aerodynamic drag. This project aims to model the flight of the shuttlecock using Newton's second law for gravitational and drag related forces, resulting in a nonlinear system of a first order differential equation. The given parameters include the shuttlecock mass, cross-sectional area, air density, as well as the drag coefficient, determining the overall magnitude of the drag force. The resulting initial value problem is solved numerically using a multitude of Runge_Kutta methods to compare the accuracy and stability across different computational …

Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise

Discovery Day - Daytona Beach

The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known …

Simulating Pacemakers And Heartbeat Recovery Through Mathematical Modeling, Thomas Estrada, Jayla Edwards

Discovery Day - Daytona Beach

Title: Simulating Pacemakers and Heartbeat Recovery Through Mathematical Modeling   This study utilizes the Fitzhugh-Nagumo model to simulate cardiac electrical activity and the regulatory role of pacemakers through ordinary differential equations (ODEs). By defining the rate of change for membrane voltage, 𝑑𝑣/dt, and a recovery variable, 𝑑𝑤/dt, the model captures the heart's excitability and resting states. Central to the analysis is the stimulus current parameter, which represents the "kick" provided by a pacemaker to correct flatline conditions or weak heartbeats. Using Euler’s method for numerical integration, the research compares unstable cardiac rhythms against corrected periodic oscillations. Additionally, the project implements vector …

Understanding The Long-Term Patterns Of Change Of A Tidal Marsh In Mission Bay, San Diego, California, Carrie A. Shuster, Theresa Sinicrope Talley Ph.D., Drew Talley Ph.D., Zhi-Yong Yin Ph.D., Kellie Uyeda Ph.D.

Theses

Coastal marshes are among California’s most productive ecosystems and the most impacted, having been extensively modified by dredging, filling, and urban development. This thesis investigates over a century of change for a marsh in Northern Mission Bay, San Diego, California using ecological and spatial analyses.

Chapter 1 provides an overview of the environmental history and current land use of the Northern Mission Bay marsh, tracing changes from pre-contact Indigenous stewardship through colonial and modern urban development. It also introduces a restoration plant palette derived from historical and contemporary species occurrences, ecological functions, and documented cultural uses. By integrating ethnobotanical knowledge …

A Modeling Scenario For Cooling A Hot Vehicle In Florida, Jared Bunn, Bernadette Mullins, Elizabeth Hale, Jaeyoun Oh

CODEE Journal

This paper presents a group project assigned in a Calculus 2 course that has students work to develop, analyze, and draw conclusions about a modeling scenario for cooling a hot car. Using a modeling-first approach, instructors supported the students in class throughout the beginning of the project, enabling the groups to complete the remainder of the project on their own. Students used parameter estimation to tune their models to provided data: one for windows being up, and one for windows being down. This project provides an example of how modeling can be introduced early in a calculus course, rather than …