• Electron transport in materials
• Low temperature plasma used in materials processing
• Feature evolution
• Spray forming
• Multiphase flows with phase transitions
• Numerical algorithms

Our focus in studying electron transport in materials is quantum mechanical effects. For this purpose, we use formulations based on the Non Equilibrium Green's Function (NEGF). We have used this formulation to study transport in one-dimension and are currently extending the method to two-dimensions. We have also used the method to study transport in nanotubes. Another topic of interest is to use the density matrix to study similar problems.

Plasma reactors are used in semiconductor device manufacturing. We have developed codes to simulate low temperature plasma found in Inductively Coupled Plasma (ICP) reactors, Electron Cyclotron Reactors (ECR), and Capacitively Coupled Plasma (CCP) reactors. Our approach uses the Moments of the Boltzmann Transport Equations or the Drift-Diffusion Equations.

Feature evolution involves modeling etching and deposition processes on the surface of a semiconductor wafer. Feature evolution requires knowledge of plasma conditions in the reactor. We have developed a level-set method to evolve features due to etching of surfaces.

Spray forming is a process in which a molten metal stream is atomized by gas jets and the droplets deposited on a substrate. Potential advantages of the process are in controlling alloy and grain structure. Modeling challenges are the atomization of the metal stream, droplet transport, solidification during droplet flight, and growth of the deposit.

Cavitation and bubble formation are important topics in underwater applications. Interest here is in modeling cavity and bubble formation as a phase transition.

Iterative methods are used in most of the computational modeling problems of interest to us. My interest is to make these and other numerical techinques we use for our problems work.

Topics that I expect will play more important roles in my research in the near future are Computational Astrobiology and Revolutionary Computing.