Digital Commons Network^™

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 …

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 …

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).

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 …

Fieldwork Educators' Perspectives On Occupational Therapy Students Addressing Sexuality And Intimacy: Expectations, Supports, And Barriers, Elizabeth Deluca-Berg

Student Dissertations

Sexuality and intimacy are recognized as meaningful occupations within occupational therapy practice; however, they remain inconsistently addressed in clinical care. Previous research has identified limited educational preparation as a contributing factor to occupational therapists' discomfort and lack of confidence in addressing these occupations. Although classroom instruction provides foundational knowledge, Level II fieldwork serves as the primary setting in which students apply knowledge within authentic clinical environments. Despite the central role of FW educators in facilitating students' professional development, little research has explored how they prepare OT students to address sexuality and intimacy during fieldwork. The purpose of this basic qualitative …

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.

Mystical Revelation And Knowledge Of God: Reclaiming Spirituality In Theology Through The Mystics, Elizabeth A. Merski

Electronic Theses and Dissertations

Since the scholastic era, the pursuit of God has occurred preeminently through reason, leading to an imbalanced theology of God that persists to the present day in the form of intellect-centered theology. As a resolution, this work proposes that the mobilization of private, mystical revelation as a source of legitimized theological knowledge of God has the potential to close the existent epistemological gap between reason/belief and theology/spirituality, demonstrating the integral unity between authentic knowledge of God and the receiver’s personal acceptance of God in faith. After examining the required methodological components for the discipline of theology and identifying criteria for …

Phenotypic And Biochemical Responses Of High-Yield Tomato Varieties To Salinity And Drought Stress, Shahida Ferdousee, Myung Hwangbo, Md Sakil Arman, Muhammad Abul Kalam Azad, Ajit Ghosh, Jongsun Kim

School of Earth, Environmental, & Marine Sciences Faculty Publications

Abiotic stresses can influence plant growth and productivity by causing physiological, biochemical, molecular, and morphological changes. Salinity and drought are increasing in frequency and intensity because of climate change. Therefore, this study assessed four high-yield tomato cultivars under 150 mM NaCl and 260 mM mannitol treatments to characterize physiological (i.e., chlorophyll level, root/shoot length, and relative water content) and biochemical responses (i.e., GLY I/II and DLDH enzyme activities, proline, and hydrogen peroxide). Results indicated that the four BARI tomato varieties showed genotype- and treatment-specific physiological and biochemical responses rather than a single uniform tolerance pattern. BARI tomato 2 maintained relatively …

Beyond The Pencil: Creating Early Writers, Pamela L. Gernaat

Masters Projects

“Schools in many countries are faced with the challenge of developing student writing proficiency. Identifying and implementing effective writing instruction for young, beginning writers play important roles in improving student writing performance. Providing effective writing instruction to beginning writers can promote writing development and minimize the number of children who encounter challenges in learning to write” (Finlayson & McCrudden, 2022, p. 1). Despite the amount of research that has been done on the importance of early writing instruction, many lower elementary students struggle with the ability to write and cannot keep up with the cognitive demands of written instruction. Many …

A Graphical Approach To Isospectral Unfoldings, Dallin Seyfried

Theses and Dissertations

Isospectral reductions are mathematical techniques used to shrink a matrix, or a graph, into a smaller, dimensionally reduced form while preserving its spectrum. Simple graphs that share isospectral reductions also share quantum walk properties. As such we further develop the inverse process, isospectral unfoldings, to find graphs that share isospectral reductions. We first prove many conditions relating to isospectral reductions and unfoldings. Afterwards, we define two new unfolding processes: general unfolding which unfolds the graph one vertex at a time, and equitable partition unfolding which excels at larger graph unfolding. In particular, through equitable partition unfolding, we discover many graphs …

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 …

Measuring The Tokenization Premium: A Cost Audit For Underserved Language Communities, Avijit Roy, Proma Roy, Hrishitva Patel

Publications and Research

Large language models are increasingly deployed as general-purpose educational and technical assistance systems, but their basic infrastructure does not treat languages equally. One underexamined source of disparity is tokenization: semantically equivalent content can require substantially different token counts across languages, affecting API cost, latency, and usable context length before a model is even invoked. We introduce the Tokenization Equity Audit (TEA), a reproducible benchmark for measuring tokenization premiums in technical tutoring content. TEA evaluates three widely used tokenizers, GPT-4o’s o200k base, Qwen2.5-7B, and Mistral-7B, on a 120-item Python debugging corpus translated from English into Bengali, Hindi, Arabic, Tamil, and Yoruba. …

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 …

Effective Visibility In The Infrared Bands, Peter L. Dean-Erlander, Steven T. Fiorino, Ronald G. Driggers

Faculty Publications

Visibility is an atmospheric metric for the comparison of terrestrial imaging conditions and locations. A limitation of visibility is that it is defined for the visible spectrum only, and there is no simple infrared equivalent. This study compares three reflective infrared wavebands: near-IR (NIR), shortwave IR (SWIR), and extended shortwave IR (eSWIR), to the visible band across a global set of cities to develop three rule-of-thumb functions for IR effective visibility. To accomplish this, a radiometric sensor model is combined with the Laser Environmental Effects Definition and Reference (LEEDR) software package to calculate the visibility of a black-and-white contrast target …

The Mathematics Of Calendar Patterns: Day-Of-Week Phenomena, Number Patterns, And Recreational Investigations, Vijender Nallapu, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Calendars are among the most familiar mathematical structures encountered in everyday life. Beyond their practical use in organizing dates and measuring time, calendars contain a rich collection of numerical patterns, symmetries, and arithmetic relationships. Many of these patterns can be explored using only elementary mathematics, making calendars an attractive subject for recreational investigation and mathematical enrichment.

In this article we examine several mathematical properties arising from the structure of monthly calendars. We investigate arithmetic patterns associated with rows, columns, and rectangular blocks of dates, establish properties of calendar squares, and explore connections with modular arithmetic through day-of-week calculations. We also …

Gwtc-4.0: Constraints On The Cosmic Expansion Rate And Modified Gravitational-Wave Propagation, A. G. Abac, I. Abouelfettouh, Teviet Creighton, Mario C. Diaz, Raul Alberto Espinosa Perez, J. Lawrence, Francisco Llamas Villarreal, Soma Mukherjee, Volker Quetschke, Miriam Ramos Arevalo, Wenhui Wang

Physics & Astronomy Faculty Publications

We analyze data from 142 of the 218 gravitational-wave (GW) sources in the fourth LIGO-Virgo-KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-4.0) to estimate the Hubble constant H0 jointly with the population properties of merging compact binaries. We measure the luminosity distance and redshifted masses of GW sources directly; in contrast, we infer GW source redshifts statistically through (i) location of features in the compact object mass spectrum and merger rate evolution, and (ii) identifying potential host galaxies in the GW localization volume. Probing the relationship between source luminosity distances and redshifts obtained in this way yields constraints on cosmological parameters. …

Functionality Risk Assessment And Risk-Based Management For Critical Infrastructure Systems, Anteneh Zewdu Deriba

Dissertations and Theses

Critical infrastructure systems such as transportation networks serve as the lifelines of modern society, supporting economic activity and ensuring access to critical services. Their disruption under extreme events can produce consequences extending far beyond physical damage to individual assets. In transportation networks for instance, failures of critical assets such as bridges and tunnels can reduce accessibility of communities, limit freight capabilities for commerce, and increase travel distance and travel time of road users. These consequences associated with the system functionality loss are tied not only to the physical vulnerability and failure of individual assets, but also to the system configuration …

Vedic Mathematics And Mental Computation: Fast Multiplication Techniques, Algebraic Foundations, And Historical Perspectives, Rakesh Bhatia, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Mental computation has fascinated mathematicians, educators, and students for centuries. Various computational techniques allow arithmetic calculations to be performed rapidly without the use of calculators or computers. Among these methods, several popular techniques are associated with what is commonly known as Vedic Mathematics. In this article, we examine a collection of fast multiplication techniques, including multiplication near powers of ten, multiplication by eleven, squaring numbers ending in five, and the vertical-and-crosswise method. For each technique, we provide elementary mathematical explanations based on algebraic identities and place-value representations.

Hidden Symmetries Of The Classical 3×3 Magic Square, Vijender Nallapu, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The classical 3×3 magic square is one of the most famous objects in recreational mathematics. Its defining feature is that every row, every column, and the two main diagonals have the same sum. However, beyond this well-known property, the square contains several hidden symmetries involving rotations, reflections, complementary pairs, parity, and balance around the central entry. In this article, we present an elementary exploration of these symmetries and show how the classical magic square provides a beautiful introduction to mathematical structure and pattern recognition.

Curious Patterns And Identities Involving Consecutive Integers, Carlo Cattani, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Consecutive integers exhibit numerous surprising patterns and elegant identities. In this article, we investigate several classical properties involving products, sums, divisibility, perfect squares, cubes, pronic numbers, triangular numbers, sums of squares, and Pythagorean triples. Using only elementary algebra, symmetry arguments, and mathematical induction, we establish a collection of identities that reveal rich connections among these classical topics. The exposition is intended for students, teachers, and recreational mathematicians, illustrating how simple observations about consecutive integers can lead to beautiful mathematical patterns and deeper insights into elementary number theory.