The rapid advances in material sciences within the last 30 years opens the possibility of understanding general principles and relationships linking macroscopic properties to corresponding molecular and atomic processes. However, future progress is hampered by expensive and time-consuming experiments and by the enormous complexity of phenomena. Huge improvements in the ability to measure the properties of materials has led to much improved characterization of materials. This precision of measurement has not yet been matched by corresponding improvements in mathematical theory, which could guide the development and optimization of materials on topics such as phase transitions and microstructure, molecular theory of materials, disordered materials, etc.

New mathematical ideas may help in improving modeling of materials, in deriving innovative and efficient numerical methods, and in developing approximate models which are amenable to mathematical analysis. The goal of the year in "Mathematical Methods in Materials Science" is to bring together materials scientists and mathematicians to talk to each other, to transfer problems, ideas and methods from one community to another, so as to enhance further progress in the understanding of materials. We also hope that the program will have an impact upon the career path of the postdoctorates, thereby strengthening future links between mathematicians and materials scientists. The year program will focus on topics such as phase transitions, optimal materials, the passage from atomistic to continuum theory, disordered materials, materials for nonlinear optics, and polymers. The mathematical disciplines involved in the program will include partial differential equations, numerical analysis, homogenization and stochastic techniques, and geometric and topological methods for polymers.


Fall Quarter, September 5 - December 24, 1995:
Phase Transitions, Optimal Microstructures and Disordered Materials

Winter Quarter, January 2 - March 31, 1996:
Particulate Flows, Thin Films and Nonlinear Optical Materials

Spring Quarter, April 1 - June 30, 1996:
Numerical Methods and Topological/Geometric Properties in Polymers