This project will support graduate students, postdoctoral fellows and visiting scientists who are all working with faculty members at Carnegie-Mellon University on various problems in the nonlinear theory of continuum mechanics. The principal goal is to train the next generation of workers in the mathematical aspects of materials science by providing them access to the expertise and guidance of applied mathematicians and materials scientists who are at the forefront of the application of advanced analytical and numerical methods to problems involving phase transitions and microstructure. As an illustration of the research to be undertaken in this grant consider the problem of how to grow crystals as free as possible from defects. The solution of such a complicated problem requires the cooperation of mathematicians and materials scientists who are able to solve effectively mathematical models of crystal growth and then use those solutions to design better manufacturing processes. It is a truly synergistic relationship since the mathematicians need the physical expertise of the materials people and the materials scientists need the mathematicians to solve the models. Thus there is a real need to train young scientists in this cross-disciplinary field by allowing them to work with the best people in both applied mathematics and materials science.
