Date of Award


Document Type



Santa Clara : Santa Clara University, 2019

Degree Name

Master of Science (MS)


Applied Mathematics

First Advisor

Betty Young

Second Advisor

Stephen Chiappari


The results presented in this applied mathematics Masters thesis are based on some of the research I performed while a Santa Cara University (SCU) student, working alongside experimental physicists Prof. Betty Young (SCU) and Dr. Arran Phipps, Prof. Kent Irwin and others at Stanford University. This thesis focuses on my analytical and numerical analyses, and mathematical modeling of experiments that use Superconducting Quantum Interference Devices (SQUIDs) to make precision measurements of modern physical phenomena. Using a variety of mathematical methods and analyses, I was able to understand and explain the origin of undesirable hysteresis observed in a key SQUID circuit and identify a theoretical criterion that can be used to avoid such instabilities. Next, I analyzed the Savitsky-Golay filter and produced a robust Matlab procedure that can be used to understand how filtering can be used to remove Gaussian noise from a Lorentzian distribution with minimum distortion. Lastly, I developed a simulation package for Dark Matter (DM) Radio, an innovative new physics experiment that uses a tunable superconducting lumped-element resonator to search for light-field dark matter. The package is capable of simulating an entire DM Radio experiment and provides powerful insight into how the experiment can be optimized. I present here an overview of the primary mathematical analysis methods used for all of this work, and show results obtained from some of the calculations and simulations I developed as part of this thesis.