Physicists solve problems and communicate their work using many external representations, such as equations, words, diagrams, graphs, sketches, pictures, and more. To learn physics, then, students must learn to use external representations. In this dissertation, I present three manuscripts. Each manuscript discusses how upper-division Paradigms in Physics students use multiple...
In 2013, Lemke Oliver created a list of all eta-quotients which are theta functions. Then in 2016, Folsom, Garthwaite, Kang, Swisher, and Treneer utilized this list of ``eta-theta'' functions along with Zwegers's construction of mock theta functions to create a set of mock modular forms which are also quantum modular...
Mathematical sophistication increases rapidly as students transition from lower- to upper-division physics courses. Complex algebra is one of the mathematical tools that is not introduced or used in lower-division physics courses but is pervasive throughout upper-division courses. In this dissertation, I study middle-division physics students' developing fluency with complex number...
Single-scattering tomography describes a model of photon transfer through a object in which photons are assumed to scatter at most once. The Broken Ray transform arises from this model, and was first investigated by Lucia Florescu, Vadim A. Markel, and John C. Schotland, [2], in 2010, followed by an inversion,...
In this dissertation, a group of vehicle dynamics simulation tools is developed with two primary goals: to accurately represent vehicle behavior and to provide insight that improves the understanding of vehicle performance. Three tools are developed that focus on tire modeling, vehicle modeling and lap time simulation.
Tire modeling is...
This thesis will cover work that I have completed relating to the field of terahertz (THz) science. My work has consisted of generating tunable, narrowband THz pulses in a table-top optical setup and using both narrow- and broadband THz pulses to study various material systems. Broadband THz pulses were used...
The extent to which thermoacoustic data determines the acoustic properties of an object was studied. In the case of one dimensional thermoacoustic imaging it was shown that constant acoustic profiles are uniquely specified from measurements. For a radial thermoacoustic problem we have shown that if the acoustic source is radial...
In source-detector radiation transport simulations, pulse height distributions are a useful metric in assessing the effectiveness of nuclear instrumentation. In the area of spectroscopy, pulse height distributions are used to identify an unknown source. It is widely believed that pulse height distributions cannot be created using deterministic methods. This quantity...
Gallium arsenide shows excellent promise for terahertz generation using mid infrared.
This is for two reasons. First, the indices of refraction for the terahertz (nTHz=3.61 at 1 THz) and mid infrared (nopt=3.431 at 2 μm) are close allowing a long interaction length.
Second, the linear absorption is low at terahertz...
The microscopic, momentum space, optical potential description of spin 1/2 x 1/2 scattering is extended to include the coupling of the singlet-triplet spin channels and
the exact handling of the Coulomb force. Computing performance in constructing
the optical potential and in solving the coupled-channels Lippmann-Schwinger equations
is enhanced by parallelization...