Continuum Physics and Systems of Conservation Laws

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This award will support the continuation and expansion of the research and scientific training in applied mathematics at the Center for Nonlinear Analysis in the Department of Mathematical Sciences, Carnegie Mellon University. Research will focus on the mathematical description and prediction of a range of phenomena that occur in material science applications. The study of mathematical models for novel man-made materials such as shape memory alloys, ferroelectric, magnetic and magnetostrictive materials, composites, liquid crystals, and thin films, will play a central role in the program. Phase transitions, defectiveness and defect propagation, grain boundaries and their evolution, the prediction of macroscopic behavior and its interplay with microstructural features, superconductivity, elasto-plastic systems, hyperbolic conservation laws, stability, metastability, and other topics will be addressed. The study of these questions will advance the frontiers of nonlinear analysis and scientific computation.The goal of this work is to identify and develop new applications of the mathematical sciences. The main focus will be on nonlinear behavior of materials and concomitant issues in analysis and computation. Large scale computing will play a central role in all of our work. The Center will promote close collaboration between mathematicians and scientists from other fields. Main activities will be centered around intense, short workshops on selected topics at the forefront of interdisciplinary research, a postdoctoral training program where emphasis will be placed on research opportunities available at the interface between the mathematical and physical sciences, and a visitors program. The visitors program and the workshops will be coordinated around research themes selected on an annual basis. Some of our resources will be devoted to a secondary research thrust in mathematical finance.