Digital Commons Network^™

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 …

Optimization Of Engine, Jordan Reed, Dev Shah

Discovery Day - Daytona Beach

A matrix-based framework for modeling and optimizing fluid and gas in feed systems to pressurize for propulsion applications using advanced linear algebra techniques will be used in this project. The governing equations are derived from conservation of mass, momentum, and energy and are formulated in state space form. This enables the system to be expressed as a set of coupled linear differential equations. These equations are assembled into structured system matrices that show the interactions between pressure, flow rate, and component dynamics. This representation allows for numerical implementation and scalability to complex systems with multiple components. System behavior is analyzed …

Laser-Based Optical Communications For Spacecraft Information Transfer, Ibrahim Arnous

Discovery Day - Daytona Beach

This course-based, in-progress project explores optical communications as a spacecraft subsystem and examines how light-based systems can be used to transmit information in space. As modern missions demand faster and more efficient data transfer, optical communications have emerged as an important area of interest alongside traditional communication methods. The purpose of this project is to study the role of optical communication in spacecraft design, with attention to its principles, advantages, limitations, and broader relevance to future missions. Using a comparative and research-based approach, the project investigates how these systems function, what engineering challenges they introduce, and why they are becoming …

Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Bianca Gerity, Arineh Shahbazi

Discovery Day - Daytona Beach

A seiche oscillation is a standing wave that oscillates in an enclosed body of water, like a lake or pool. Seiches are caused by strong winds, earthquakes, and rapid atmospheric changes. Seiches are an excellent real-world example of damped harmonic motion. The physics of these unique vibrations can actually be modeled using a second-order differential equation for damped oscillators of the general form mx''+cx'+kx=0, where m represents the mass of the vibrating water column, c represents the energy dissipation due to friction and viscosity, and k represents the force governed by gravity and the basin's geometry. The objective of this …

Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della

Discovery Day - Daytona Beach

Combustion instability in liquid rocket engines is driven by coupling acoustic pressure oscillations and unsteady heat release. To achieve specific desired outcomes, small perturbations can be made to either decay or grow, depending on system dynamics and artificial parameters. Using a linearized eigenvalue framework, where eigenvalues determine growth/decay rates and frequencies, and eigenvectors describe spatial mode shapes and couplings between pressure, velocity, and heat release, a mathematical model can be derived to describe said behavior for a cross-section of the rocket engine. The Rayleigh criterion is used to identify conditions under which energy is added to oscillations, while flame transfer …

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 …

Navier Stokes Pressure Drop Derivation, Brayden Benedetti, Gedaliah Dimbert, Jaden Turobiner

Discovery Day - Daytona Beach

Accurate prediction of pressure losses in propellant and fluid feed systems is essential for reliable design and operation of aerospace and industrial flow networks. This project presents a systematic derivation of a practical pressure drop calculator for a feed system using isopropyl alcohol, beginning from the fundamental conservation laws and culminating in an engineering-level computational model. Starting with the differential form of the Navier–Stokes equations for incompressible flow, the governing equations are simplified through a series of physically justified assumptions, including steady-state flow, negligible body forces, and fully developed internal flow within circular piping. The resulting momentum balance is reduced …

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 …

School-Centered Tobacco Retailer Exposure And Neighborhood Opportunity Across Urban And Rural Tennessee, Sima Namin Dr, Jacob Black, Jennifer Ferris, Robert E. Heidel Dr

Journal of Appalachian Health

Introduction: Tobacco retailer availability contributes to youth tobacco use, and retailers are concentrated in socioeconomically disadvantaged communities. However, few studies have examined how school-centered retailer exposure intersects with neighborhood opportunity in a predominantly rural Appalachian state.

Purpose: The purpose of this study is to assess the association between neighborhood opportunity and school-centered tobacco retailer exposure across Tennessee (TN), including differences by rurality and Appalachian status.

Methods: We constructed a tract-level, school-centered youth tobacco exposure index for TN using tobacco retailer locations and public and private K-12 school data. The index incorporated retailer proximity, density, and distance-decay accessibility measures. Child Opportunity …

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 …

Mechanical Vibrations And Damping, Axon Deadrick, Will Standish, Tanay Agarwal

Discovery Day - Daytona Beach

Mechanical vibrations occur in many engineering systems and can be described using second-order differential equations. In this project, the motion of vibrating systems is studied using the mass–spring model. The focus is on three types of oscillations: free vibrations, dampened vibrations, and forced oscillations. Free vibration describes how a system moves when it is displaced and then released without any external force. Damped vibration includes effects such as friction or resistance that cause the motion to gradually decrease over time. Forced oscillations occur when an external force acts on the system and continuously drives the motion. This project also examines …

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 …

Steam Distillation Of Jasmine, Mikayla Hulvey, Meliah Martin

Discovery Day - Daytona Beach

This experiment aimed to isolate various components, including benzyl acetate, linalool, indole, and farnesene, from jasmine buds. The functional groups include an ester in benzyl acetate, an alcohol in linalool, an amine in indole, and alkenes in farnesene. Jasmine buds were combined with distilled water and steam distilled using a standard distillation apparatus. The distillate, containing hydrosol and trace amounts of essential oil, was then collected for extraction using methyl tert-butyl (MTBE) for a liquid-liquid extraction. The organic layer was then separated, washed using brine, dried over anhydrous sodium sulfate, and then transferred for later analysis. The essential oil obtained …

A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie

Discovery Day - Daytona Beach

A Differential Equation Approach to Heat Flow in a Thin Rod examines how differential equations can be used to model and understand heat conduction in a fundamental physical system. Heat transfer in solids is a key concept in physics and engineering, particularly in systems where temperature changes over time. A thin rod provides a useful one-dimensional model for studying how heat moves through a material and how temperature varies along the rod as time passes. The primary objective is to develop a mathematical description of this process using differential equations. The analysis begins with physical principles such as conservation of …

Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore

Discovery Day - Daytona Beach

This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional …

Mechanical Vibrations And Damping – Structural Analysis, Kelsey Hunsicker, Sarah Kraus, Sophia Muller Martinelli De Souza

Discovery Day - Daytona Beach

Mechanical Vibrations are crucial in understanding and structural analysis of engineering systems such as bridges and airplane wings. If not considered, these vibrations can lead to structural fatigue or failure. By using differential equations, structural vibrations will be examined. Researching the different kinds of vibrations and damping will help to find the vibration behavior of the system. For example, a mass-spring damper system will use second-order linear differential equations. The systems model can be shown to be underdamped, overdamped, or critically damped. These will compare the amplitudes and oscillation differences between the systems by using computational code. Analyzing these differences …

Numerical Investigation Of The Nonlinear Simple Pendulum And The Dependence Of Oscillation Period On Initial Angle, Kelly Wold, Aidan Hart, Patrick Gilliam

Discovery Day - Daytona Beach

Numerical Investigation of the Nonlinear Simple Pendulum and the Dependence of Oscillation Period on Initial Angle examines how the oscillation period of a simple pendulum varies with initial angular displacement and evaluates the accuracy of numerical methods in capturing this behavior. In classical treatments, the small-angle approximation simplifies the governing differential equation and predicts a constant period independent of amplitude; however, this assumption breaks down for larger angles, where the system exhibits nonlinear dynamics. The objective of this project is to model the full nonlinear equation of motion and quantify how the period depends on initial conditions. To achieve this, …

Engineering Path Trajectories With Gravitational Fields, Eliane Dean, Aidan Hart, Isabel Noot, Nathan Browning, Valeria Villazon Fito

Discovery Day - Daytona Beach

This project explores how vector calculus concepts play a role in aerospace engineering though spacecraft trajectory design. In particular, the notion of vector fields is used to model the gravitational force, whose work done is expressed through line integrals. By taking the curl of the gravitational field and showing it is zero, the field is recognised as conservative, implying that the work done by gravity is path independent. This property is conceptually linked to gravitational potential energy and the principle of energy conservation. The results are then applied to spacecraft motion, where engineers use energy-base methods to determine efficient trajectories …

Visualizing The Invisible: Simulating Electromagnetic Field In 3d Space With Matlab, Aashman Gupta, Eliane Dean, Riley Esperanca, Hailey Grabinski, Jacob Summerhays, Ameya Sute

Discovery Day - Daytona Beach

Electromagnetic field behaviours in free space are defined by Maxwell’s Equations, which couple the temporal and spatial variations of electric and magnetic fields through partial derivatives. These derivatives quantify the rate of change of each field’s vector component with respect to position and time in a 3D lattice, forming the basis for numerical field analysis. This research will develop a mathematical and computational framework using multivariable calculus to model, simulate, and visualize electromagnetic wave propagation in free space using MATLAB. Gradient, divergence, and curl operations are implemented to compute local field variations and energy transfer. The resulting data are used …

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 …

Modelling Quadcopter Thrust And Torque Using Lu-Decomposition, Diya Patil

Discovery Day - Daytona Beach

3 & 4 motor systems have been in the world of aviation in many different forms as the field grows and evolves. To understand the complexities of an Unmanned Aerial Vehicle (UAV) and its stability, assessing the amount of thrust put into each motor can help generate the torque produced despite factors such as multidirectional movement. While a UAV does this multiple times a second, producing a simplified version of this calculation can aid in simpler models simulating UAV movement. Due to the popularity of the quadcopter drone, a simple algorithm depicting thrust through each spinning motor can aid in …

Bridging The Gap: Cybersecurity And Occupational Safety Frameworks In Ai Data Centers, Athena Leader

Discovery Day - Daytona Beach

Bridging the Gap: Cybersecurity and Occupational Safety Frameworks in AI Data Centers   As artificial intelligence infrastructure expands, AI data centers represent a critical and underexamined convergence of cybersecurity and occupational safety risk. Existing frameworks such as NIST, OSHA, and ISO standards were largely developed in isolation, leaving significant gaps in how organizations manage risks that are simultaneously digital and physical in nature. This study investigates the gaps and overlaps between cybersecurity and occupational safety frameworks as they apply specifically to AI data center environments. Drawing on a targeted literature review of established regulatory and standards-based frameworks, this research identifies where …

Exploring The Motivations Of Undergraduate Sport Management Students, Kyle J. Brannigan, Tyler J. Hajek

The COSMA Journal

This study explored the motivations of undergraduate sport management in four university programs. Convergent mixed-methods research through the theoretical framework of Self-Determination Theory was incorporated with an adapted questionnaire of the Academic Motivation Scale and semi-structured interviews through Thematic Analysis. Ninety-six surveys with nine interviews were deemed usable across four regionally focused, vocationally minded, and accessible universities. Overall, students reported higher levels of extrinsic motivation than intrinsic motivation. The findings suggested intrinsic motivation to know and extrinsic motivation through regulation for identification scored highest with the participants. No significant differences were found between classes and ethnicities. However, male students experienced …

Simulations Of Phugoid Motion Of Jal 123, Dereth J J. Drake Scheuermann

Georgia Journal of Science

Airplanes rely on a balance between the four forces of flight: lift, weight, thrust, and drag. If these forces are balanced, the airplane will remain stable. However, if structurally or systematically compromised, the motion can rapidly become unstable. In the aviation industry, mistakes in repairs and aircraft design can lead to accidents causing the loss of life in some cases. In this article, we will be analyzing what happened 70 Japan Airlines flight 123 and how the flight’s motion deteriorated due to a defective repair. More specifically, we will discuss the aerodynamic effects of phugoid motion and how it developed …

Underclosed Posets, Richard Ngo

McNair Summer Research Program

Underclosed complexes are a recent generalization of interval graphs to higher dimensions. Motivated by underclosed complexes, we define and study underclosed posets. Order ideals of these posets correspond to pure underclosed complexes. We classify which principal order ideals are rank-symmetric (and in fact are self-dual).

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 …

Behavioral Effects Of Novel Treatments For Pain Management Using Combinatorial Methods, Rohit Rajeev Nambiar

Theses and Dissertations

Pain, despite being an uncomfortable feeling to experience, is a necessary protective mechanism for the body1. Understanding that pain results from several different mechanisms within the body is important to discovering the optimal way to treat and manage a person’s pain. Modern medicine has seen numerous advancements in treating or managing acute and chronic pain, particularly with opioid drugs. However, these treatments come with potential side effects, including opioid use disorder (OUD) and fatal overdose. Finding new treatment methods, or improving existing methods, is crucial for patients with pain. This thesis explores two projects looking to develop safer analgesia using …

Teaching Writing With Confidence: A Professional Learning Series To Build Special Education Teachers' Knowledge And Self-Efficacy For Explicit Writing Instruction, Lindsay E. Bowen

Masters Projects

Writing is an essential skill used to communicate ideas effectively, assess understanding, and demonstrate critical thinking across educational and workplace settings. Yet, research demonstrates that a majority of special education teacher preparation programs do not offer standalone courses in writing instruction methods, leaving many special education teachers to enter the profession with limited knowledge of effective writing instruction for students with high-incidence disabilities. This project explores current research on effective sentence-level writing instruction for students with high-incidence disabilities, as well as a research-based approach for applying these practices in a systematic yet adaptable manner to meet the needs of individual …

Butte Priority Soils Operable Unit (Bpsou) 2026 Monthly Progress Report. Consent Decree For The Butte Priority Soils Operable Unit. Civil Action No. Cv 89-039-Bu-Seh, Josh Bryson

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.