Island Dynamics Model for Epitaxial Growth

    This work is intended to numerically simulate the growth of a thin film formed by molecular beam epitaxy with a modified island dynamics model. In particular, we extend the model to include the Ehrlich-Schwoebel barrier over step edges in order to investigate its influence on island morphology and roughening, which leads to the formation of mounds. Optimal control of the growth process is necessary for the creation of nanostructures like quantum dots, quantum dot arrays, and quantum posts.

Simulation of Porous Media Flows

    Porous media flows are important large scale geological flows where the behavior is determined by micro scale processes. Examples include carbon dioxide sequestration in aquifers, ground water hydrology, and enhanced oil recovery. We utilize a level set approach with the full Navier Stokes equations to simulate an immiscible multiphase flow (ex: oil penetrating into water in a porous bedrock).