High-precision quantum simulation of small atomic and excitonic systems (Summer 2015 - Present)

This work is performed under the supervision of Prof. Kálmán Varga, and in
collaboration with several members of his research group at Vanderbilt
University. See Prof. Varga's website
for more information.

We perform high-precision calculations using the Stochastic Variational Method (SVM)
in the explicitly-correlated Gaussian (ECG) basis to compute the energy spectra and
stationary-state wavefunctions of quantum-mechanical few-body systems.
These widely applicable techniques allow us to rigorously analyze few-body
systems in a variety of problem domains across the physics and
physical chemistry literature.

Our most recent application of SVM-ECG calculations has focused on the
characterization of electron-hole interactions in 2D semiconductor materials.

Automatic derivation of high-order numerical methods for systems of ordinary differential equations (Fall 2013 - Spring 2014)

This work was performed under the supervision of Dr. Samuel N. Jator of
Austin Peay State University.

We used symbolic algebra techniques to automatically derive linear multistep
methods (LMMs) to solve systems of ordinary differential equations (ODEs).
We also developed a suite of tools to characterize and compare these LMMs

analytically, by computing their order of accuracy and region of
(absolute) stability, and

numerically, by automatically applying them to a suite of test problems
to measure their performance of real-world examples.

Specific methods with a combination of good analytical and numerical
characteristics were identified and published.