My current project is to model the major components missing from my previous potential development effort: The electrostatic and induction interactions may be very small to negligible in methane, but most interesting systems will need an accurate model of these energy components if we want to simulate them with a similar standard of accuracy as we used for the methane potential. Keep an eye out on the arXiv for our first (publishable) results.
The long-term goal of my PhD research was to create a potential for molecular simulations of alkanes in order to make accurate predictions of their viscosities. This requires an extremely accurate treatment of all components of the potential – intramolecular, repulsion, and dispersion. One can achieve this accuracy at an acceptable cost by machine learning from quantum mechanical calculations (e.g. from DFT), which we do in our group with Gaussian processes (Gaussian Approximation Potentials, or GAP).
My research showed that this goal can be achieved by creating a new set of machine learning potentials for liquid methane with GAP, showing in the process that many effects must be modelled properly in order to get the right answer for the right reasons: Many-body effects, quantum nuclear effects, and an accurate description of the short-range repulsive regime are all either ignored or averaged into the most common potentials for liquid simulation. The machine learning approach, in contrast, enables all of these effects to be modelled explicitly, and shows — in contrast to the traditional liquid potentials — a systematic improvement of its predictions as the underlying model accuracy (measured against gold-standard quantum chemistry) is improved. The methodology developed as part of this work should be applicable to longer alkanes, where the intramolecular potential becomes more important, and could be extended to more complicated molecules with significant electrostatic interactions. These results are presented in an article that was recently published in JCTC.
“Stochastic Simulation of Genetic Regulatory Networks with Delayed Reactions” (archived here). In this project with Prof. Jorge Viñals at the University of Minnesota, I implemented a stochastic simulation algorithm for chemical networks with delayed reactions (code) to simulate a simple model of a biological clock across a stochastic (Hopf) bifurcation.
LANL summer project
Report LA-UR-13-26449 “Eigenfunction decomposition of reactor perturbations and transitions using MCNP Monte Carlo”. Part of a summer research program, another student and I, under the mentorship of Forrest Brown at LANL, tested a new feature in the MCNP 6 code for Monte Carlo simulation of nuclear reactors. We tested algorithms for computing eigenvectors of the fission matrix and, from those, transition coefficients between normal and perturbed states of the reactor.
My first research project in scientific computing, under the supervision of Brian Vankoten and Prof. Mitchell Luskin at the mathematics deparUniversity of Minnesota. Here I studied how several algorithms for optimization and dynamics (tasks fundamental to atomistic simulation) work by implementing them in MATLAB and testing them on a Lennard-Jones model system. It was already possible, even with such a simple system in two dimensions, to observe effects such as crystallization and grain boundaries. Report here.