Physical Sciences and Mathematics Commons^™

Modeling Vibration Stiffness: An Analytical Extension Of Hertzian Theory For Angular Contact Bearings With A Thin Viscoelastic Coating, Davis R. Burton

Honors Theses

This thesis considers the novel angular contact rolling-element bearings proposed by NASA’s Glenn Research Center, which are coated with a thin solid lubricant that exhibits viscoelastic behavior. Current analytical models for the dynamic stiffness matrix of angular contact bearings, critical for vibration analysis, lack the ability to model the effects of a solid coating, as well as the time dependencies inherent in viscoelastic theory. The author first presents an overview of the stiffness matrix derivation, followed by a treatment of the underlying Hertzian contact theory. An analytical extension of this theory is proposed which accounts for a thin elastic layer …

The Mathematical And Historical Significance Of The Four Color Theorem, Brock Bivens

Honors Theses

Researching how the Four Color Theorem was proved, its implications on the mathematical community, and interviews with working mathematicians to develop my own personal opinions on the significance of the Four Color Theorem.

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.