Transitions and Defects in Ordered Materials

Luskin， James和Kinderlehrer将在晶体的微观结构，相变动力学，分子力和表面能磁致伸缩以及液晶流体流动方面进行数学和计算方面的研究。自20世纪80年代初以来，非线性理论和分析与科学计算的日益结合，使我们对形状记忆合金、铁电体和高磁致伸缩合金等现代材料的理解取得了重大进展。其中主要的是理解缺陷和微观结构的新方法，重点是它们是如何产生和变形的。其结果是能够预测微观层面上的详细行为和宏观性质。这可能为设计材料或器件以优化期望的机电效果提供策略。

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.