Semester

Spring

Date of Graduation

2020

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Zachariah B Etienne

Committee Co-Chair

Adam Halasz

Committee Member

Sean T McWilliams

Committee Member

Harvey Diamond

Committee Member

Casian Pantea

Abstract

In this dissertation we apply techniques of numerical analysis to current questions related to understanding gravity. The first question is that of sources of gravitational waves: how can we accurately determine the intrinsic physical parameters of a binary system whose late inspiral and merger was detected by the Laser Interferometer Gravitational-Wave Observatory. In particular, state-of-the-art algorithms for producing theoretical waveforms are as many as three orders of magnitude too slow for timely analysis. We show that direct software optimization produces a two order of magnitude speedup. We also describe documentation efforts undertaken so that the software may be rewritten to enhance both performance and physical realism.

The second question is that of measuring Newton's gravitational constant G. In particular, the results of experiments measuring G have differed by as many as ten standard deviations. Measuring the oscillation frequency of a magnetically-levitated microsphere shows promise for sharpening the value of G, and the system for this measurement was found to accurately measure low-frequency accelerations. As such, this system forms a prototype for a room-temperature, low-mass accelerometer. At the center of the accelerometer and G measurements lies a new image analysis technique we developed for determining the position of the microsphere to 1.6 nm.

Embargo Reason

Publication Pending

Available for download on Thursday, April 29, 2021

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