Epitaxy
I have helped developed computational methods for the study of epitaxial surface growth. The methods are based on kinetic Monte Carlo, and my focus has been to create models that improve computational efficiency.
HomoEpitaxy
Homoepitaxy involves the deposition of atoms onto like atoms. There is no lattice mismatch, and so strain can be ignored. For many realistic situations, the rate limiting step is surface diffusion. We derived a method that allows atoms to take longer steps when far from a step edge. This was part of my dissertation, and also published in Phys. Rev. B 72, 205421 (2005). A pdf version is here.
HeteroEpitaxy
Heteroepitaxy involves the deposition several species of atoms onto a substrate. Lattice mismatch implies that strain plays an important role the the growth dynamics. I have contributed to the construction of a code that will solve the strain field and compute the elastic energy of a heterogeneous lattice of atoms. This work is not yet published.
Fractal growth
Diffusion-limited aggregation (DLA) is a process by which particles aggregate onto a cluster by diffusion. The process forms fractal clusters of great complexity. I investigated whether or not the average of many DLA clusters is equivalent to growth by the average diffusion field. This was part of my dissertation, and is published in Phys. Rev. E 68, 020401. A pdf version is here.
Front propagation
There is some interest in comparing a discrete formulation of front propagation with continuum theory. In principle the approach to the continuum limit is very slow. To investigate this computationally, requires simulations involving very large densities. I am developing a multiscale model which can accurately and efficiently compute large density systems.
Cathode flicker
When current is passed through a plasma from a cathode to an anode, the steady state flux can be computed. What if the velocity that the elections are emitted at fluctuates? Can the current be increased? This is a new project I am working on.