G. W. Young and S. I. Hariharan
Modeling and Scaling of Material Processing Systems, DMS-9972185

The proposed projects concern the development and application of mathematical methods for the formulation, analysis and solution of material processing system models.  Specifically, the aims are to examine time-dependant sharp-interface solidification models, phase-to-field models, and chemical vapor disposition (CVD) models.  The general goals of the projects are to examine simple model problems to determine the process sensitivity to the operating conditions, describe the scientific phenomena of heat, mass, and momentum transport within the system, and to elucidate the coupled dynamics of the transport mechanisms.  Specifically, investigations will include investigation of time varying evolution of solidifying fronts and concentration profiles in a two-dimensional configuration, a multi-parameter asymptotic expansion approach for investigation of phase-field models, and reactor and development of an evolution equation for the gas/solid interface of the deposited film.

The proposed investigations deal with verification of mathematical models that are pertinent to industrial material processing.  Solidification is a common phenomena in an industrial material processing.  It describes the state change from liquid to solid.  Experimentally, it has been observed that the solidification process yields solidified surfaces which are dendritic in nature.  Computer simulations also show these structures.  Correctness of these simulations still lacks verification.  The first two parts of the proposed work will address this issue.  The third part of this work concerns thin film formation as related to designing high performance materials.  Once such process for making this film is called Chemical Vapor Disposition (CVD).  CVD devices are generally referred to as reactors.  Mathematical models for these are often complex.  To analyze these models, computer simulations are used.  We propose to investigate simplifying these models, so that a complex computer code can be verified against the simpler models for correctness.