Transitions and Defects in Ordered Materials

Luskin, James and Kinderlehrer will do research in mathematics and computations with reference to microstructures in crystals, dynamics of phase transitions, molecular forces and surface energy magnetostriction, and liquid crystal fluid flow. The growing alliance of nonlinear theory and analysis with scientific computation, since the early 1980's, has led to significant advances in our understanding of modern materials like shape-memory alloys, ferroelectrics, and highly magnetostrictive alloys. Chief among these are new ways of understanding defects and microstructure with emphasis on how they arise and deform. A consequence is the ability to predict detailed behavior at the microscopic level as will as macroscopic properties. This may provide a strategy for designing materials or devices to optimize desired electromechanical effects.