I used the Newtonian gravity differential equations to numerically evolve three body orbits after first verifying the code base with some convergence analyses on Keplerian orbits. In particular I considered with an equal mass binary on a nearly circular orbit and a much smaller more distant planet on a nearly circular orbit about that. I demonstrated that energy transfer occurs between the inner binary and outer planet over one orbit of the outer planet, independent of the resolution of the integration. 

This is a known result, that I reproduced as part of a plan to do further explorations with the code. Ultimately, I decided that it was time to move toward something more likely to result in a job. I worked on this project extremely extremely part time between August 2018 and January 2021. 

This project was my masters work at Louisiana State University, June 2014-Oct 2017 (graduated Dec 2017). 

An extreme mass ratio inspiral (EMRI) between two black holes occurs when a stellar mass black hole orbits a super massive black hole and emits gravitational waves, causing the orbit to lose energy and spiral inward, and spiral inward. This happens because of the interaction of the particle (stellar-mass black hole) with it's own field as it orbits in the more impressive field of the super-massive blackhole.

I have simulated the scalar field approximation to this self-force, using a discontinuous Galerkin grid, in 3+1D, with a multiple moment decomposition, in C++, based on the SelfForce1D FORTRAN code from the Blackhole Perturbation Toolkit/Einstein Toolkit. 

In this project, I graduated prior to implementing the backreaction. I implemented the numerical evolution around a Schwarzschild black hole on a circular orbit by solving the scalar wave equation from the ground up in C++ based on the original FOTRAN code. From this, I was able to evolve and visualize the evolution of the self force for each mulitpole moment in response to the radially symmetric orbital motion, and the numerical transients in the simulation prior to achieving that stable computation of the orbit.

In my Computational Physics II class in 2016 at LSU, I completed a final project in parallelization using mpi4py. In this project, I simulated a 48x48 pixel image of a black hole using a map of the galaxy and using ray tracing by numerically solving the  general relativistic geodesic equation for the propogation of light, from the camera back to its source. 

From Aug 2008-Jan 2011, I was a member of the LIGO group at U of MN. In that group I worked on gravity gradient noise due to seismic waves and also writing and testing a new gravitational wave detection algorithm. I was responsible for the radon transform search, which used a modified form of radon transforms based on a weighted sum of SNRs, to search for line like patterns in a spectrogram (constant f dot). I implemented a search and tested parameter recovery for a specific test waveform of line like signals. The spectrogram is below. 

From July 2012- July 2013, I worked on a fractional calculus project at St Cloud State University. In this project I developed an algorithm based on shifting averages between registers or bins and tested it in C++. The goal of the algorithm was to account for the deep memory of a fractional integral or derivative, that may depend on an infinite number of prior integration time steps. 

My most significant accomplishment prior to that was to compute the first exoplanet statistics using a simulation of the galactic line of sight toward Carina and the galactic bulge based on the Hipparchus catalogue and on the OGLE-III transit magnitude cuts for planet candidates (2005-2006). 

I have also done a theoretical particle physics computation related to the muon anomalous magnetic moment and characterized the performance of Avalanching Photodiodes for the NOvA neutrino detector (2007-2008). 

As an undergraduate I determined the feasibility of using Einstein rings and galactic one dimensional velocity dispersions of the lensing galaxy to measure the cosmological constant and the matter density of the universe, given the observational scenario existing at the time in 2003-2004.