Physical Sciences and Mathematics Commons^™

Knot Theory In Virtual Reality, Donald Lee Price

Masters Theses & Specialist Projects

Throughout the study of Knot Theory, there have been several programmatic solutions to common problems or questions. These solutions have included software to draw knots, software to identify knots, or online databases to look up pre-computed data about knots. We introduce a novel prototype of software used to study knots and links by using Virtual Reality. This software can allow researchers to draw links in 3D, run physics simulations on them, and identify them. This technique has not yet been rigorously explored and we believe it will be of great interest to Knot Theory researchers. The computer code is written …

Diving Into Reliable Numerical Observability And Stabilization Of The One-Dimensional Wave Equation, Emma Moore

Mahurin Honors College Capstone Experience/Thesis Projects

In this project, a one-dimensional wave equation, which is a partial differential equation (PDE) describing vibrations on a string, is considered. It is known that the PDE model is exactly observable and exponentially stabilizable. The main goal of this project is to construct a numerical approximation technique, so-called the direct filtering technique, to prove that the Finite Difference and Finite Element space-discretized 1-D wave equations (i) with homogeneous Dirichlet boundary conditions are uniformly observable, (ii) with controlled boundary conditions are uniformly exponentially stable, as the approximation parameters tend to zero. It is crucial to develop reliable numerical approximation techniques for …

Regression Analysis: Graduation Rate In Kentucky Public High Schools, Rebecca Price

Mahurin Honors College Capstone Experience/Thesis Projects

Kentucky’s Public High School graduation rates vary widely across the rural and urban regions in the state. In addition to their graduation rates, each of these schools have their own unique demographics, funding, teacher-student ratio, etc. that define said school’s identity. This research aims to analyze the aforementioned variables, as well as other variables listed on each school state report card, in order to create a model to predict any school’s graduation rate.

In order to create this model, data was taken on all public high schools in Kentucky from the Kentucky Department of Education’s School Report Card. Data were …

An Analysis Of A Hybrid Steel Bridge, Andrew Iglehart

Mahurin Honors College Capstone Experience/Thesis Projects

The American Institute of Steel Construction hosts a competition for graduating college seniors each year. The competition is designing and fabricating a scaled steel bridge within certain parameters. Each year the parameters change to allow different seniors to face similar challenges without copying the previous year’s work. Before the outbreak of COVID-19, a bridge was fabricated as per the rules in the 2020, and the same bridge was used for the 2021 competition. With a bridge already fabricated and being used for the competition, a question arose about analyzing the bridge.

This thesis encompasses the entire analysis of the steel …