Physical Sciences and Mathematics Commons^™

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 …

Self-Quenching Of Carbon Monoxide In The Presence Of Noble Gases, Madeline V. Hinkle

Honors Theses

Precise rate coefficients for the vibrational relaxation pathways of CO(v)-CO in the presence of Ar and Kr have been determined through the work of this thesis. This work was motivated by the need to find a more cost-effective alternative to using xenon as a bath gas, which has increased significantly in price in the past few years. Similar experiments within this lab at Bucknell have been conducted in the past using argon, which can be used in the same manner as xenon but comes at a much lower price, but the experiments yielded inferior results compared to those using xenon. …

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.

Centers Of N-Degree Poncelet Circles, Georgia Corbett

Honors Theses

Given a circle inscribed in a polygon inscribed in the unit circle, if one connects all the vertices with line segments we get a family of circles called a package of Poncelet circles, due to its connection to a theorem of Poncelet. We are interested in where the centers of the Poncelet circles can be. Specifically, we have shown that if one of the circles in the Poncelet package is centered at 0, then all of the circles must be centered at 0 as well. This was proven by Spitkovsky and Wegert in 2021 using elliptic integrals but we …

Evaluating Field Evidence Of Fine-Grained Sediment Abrasion In Gravel-Bedded Rivers: A Case Study Of The Lillooet And Suiattle Rivers In The Cascade Volcanic Arc (British Columbia, Canada, And Washington, Usa), Devin T. Johnson

Honors Theses

Steep, gravel-bedded rivers are important sites for studying gravel abrasion, where material transported as bed load experiences size reduction and rounding due to grain-to-grain collisions. Studying fine sediment (diameter) abrasion and grain shape changes in fluvial systems is more challenging due to difficulties in quantifying sediment shape at this scale, but it is assumed that fine particles traveling in suspension do not experience abrasion. Improvements in particle characterization technology now allow for the accurate, rapid quantification of particle shape for sediments as fine as 0.8 μm through dynamic image analysis. Here we use the Camsizer X2 (CX2) to test the …

Computationally Modeling The Human-Structure Interaction Response Of An Occupied Cantilevered Structure, Brennan Smith

Honors Theses

There is a limited understanding of the impact that passive human occupants have on a dynamic structural system, referred to as Human-Structure Interaction (HSI). Cantilevers are naturally prone to excessive vibrations due to their long unsupported spans, and cantilevered structures such as those commonly found in the seating area of a stadium facility or concert hall are designed to support a high density of occupancy.

This study determined that HSI in cantilevered structures can be modeled using a simple two-degree-of-freedom system. The results of the model were validated by data that was collected on a small-scale laboratory structure intentionally designed …