My current research interests center upon modeling, analysis and simulation of crystal growth on both atomistic and continuum length-scales. This research can be broken down into three principal areas described below:
This is the study of the phase transformation of liquid into solid. Frequently the solidification process involves fluid flow as well as solidification. Solidification problems are examples of free-boundary problems, where the mathematical model must specify both bulk fields and interfacial quantities, including the location of the solid-liquid interface. The phenomenon of interest in solidification are interfacial instability and the growth of dendrites (snowflake like structures).
When the instabilities during solidification are highly pronounced, there are a large number of dendrites that form a "mushy layer''. The mushy layer is often modeled as a homogenized porous medium with solid-fraction dependent permeability. Convection in mushy zones leads to interesting flow phenomena and bifurcation structure.
When crystal growth occurs at very slow rates (usually from a vapor growth or molecular beam process) the instabilities that occur during solidification of liquids are avoided. This results in the production of materials with uniform crystal structures. Since this process is slow, it produces only small amounts of material which are typically used to coat another material with a thin film. Thin film growth is studied using a variety of simulation and modeling techniques, depending on the length scale of interest. These include continuum approaches, Monte-Carlo models, molecular dynamics and fundamental models relying on quantum mechanics. Presently, much of my research involves kinetic Monte-Carlo (KMC) simulation.