Since completing my PhD in 2005, I have been fortunate to work with some amazingly gifted mathematicians and applied scientists on interesting problems from the following areas of research :

Kinetic Theory of Plasma Dynamics

My research in the area of plasma dynamics has been a combination of joint work with Jack Schaeffer (Carnegie Mellon) and Robert Glassey (Indiana), and some solitary investigation.  For the most part, the joint work involves the study of large time behavior of collisionless plasma, specifically solutions to the Vlasov-Poisson and Vlasov-Maxwell systems.  The more solitary research has focused largely on well-posedness for the Vlasov-Poisson system with steady spatial asymptotics, and infinite mass and energy.  This problem considers the behavior of electrons upon interaction with a fixed background of positive ions.  Recently, I’ve also become interested in well-posedness for Vlasov-Maxwell since very little is known for this model in the realm of classical solutions. Physically, these systems of partial differential equations model phenomena like the Solar Wind, a stream of charged particles continuously ejected from the sun which generally engulfs our solar system.

Projects supported by NSF and the
Center for Undergraduate Research
in Mathematics (CURM) at BYU

Multiscale Analysis of Bionanosystems

My research in the area of multi-scale analysis is a joint venture with the Center for Cell and Virus Theory within the Department of Chemistry at Indiana University.  Currently, we are in the midst of creating a dynamical software system which can be used to predict the influence of host media (such as vaccine or antiviral therapeutic molecules) on the structural stability of a virus.  The construction of such software is quite challenging, mainly due to the dependence of changes in macroscopic (i.e., nanoscale) viral structure upon behavior at the atomistic level, and hence the need to include large numbers (in the millions) of atoms in standard viral simulations.  Instead of a very costly and time consuming all-atom modeling approach, we develop methods for selecting and utilizing slowly-varying “Order Parameters'' (OPs) which can be used in lieu of standard independent variables, such as atomistic position and momentum, to capture nanoscale features and track structural changes in the virus.  By simulating the Langevin-type stochastic differential equations that stem from a natural multiscale analysis, these OPs can be co-evolved with the atomistic variables, resulting in no loss of accuracy but enormous gains in computational efficiency.

Projects supported by the NIH through
the Center for Physics-based Simulation
of Biological Structures (SimBioS)