Grant: Discovery Grants Program - Individual

In this research program I will be focussing on two classes of problems that are driven by industry but require the application of innovative mathematics. I will be concerned with: (A). The simulation of manufacturing techniques used to produce certain classes of semiconductors. Semiconductors surround us and for specialized electronic devices, any improvements in their manufacturing technique will have a direct impact on our daily lives. Such specialized materials are very costly to produce so the development of mathematical models and mathematical simulations are very cost effective tools that can be used to advance the state of the art in this industrial sector. In particular, for this research program, I will attempt to identify optimal growing conditions for semiconductor crystals that evolve with the growing crystal. The primary crystal under concern is InSb which distinguishes itself from the already extensive crystal growth research in that to produce a crystal free of defects, the crystal must be i) grown with a nontrivial lateral shape and ii) be allowed to produce facets. (B). Problems from the oil recovery and environmental engineering fields. I hope to develop methodologies that will increase our understanding of the underlying processes. Here my research will address the modelling and simulation of processes that include multiple phases (solid, liquid, gas) and more than one material. I will be particularly concerned with the mechanisms that limit instabilities in steam/bitumen flow in the fluid coking process, and in the environmental field I want to develop multiscale models to help predict the retention and propagation of pollutants within the soil.