Mathematical Sciences: Mathematical Problems in Electromagnetism and Elasticity

这个项目涉及数学建模， 电磁和弹性材料。 这些材料 其特征在于平衡构型表现出多个 阶段。 实例包括弹性铁磁体和刚性铁磁体。 超导体 基本的建模工具将使用 空间非局部能量项惩罚振荡， 经典态和杨测度态的方差。 也 包括的是存在的结果，为短时间动态的 满足广义强椭圆性假设的材料 关于电磁和弹性性质以及 理想弹性体的平衡解 抗磁性（弹性超导体） 这些研究将有助于更好地了解 弹性和电磁材料的力学性能 和复合材料，并将产生影响的发展， 合成具有最佳性能的材料。

This project involves mathematical modeling of electromagnetic and elastic materials. These materials are characterized by equilibrium configurations exhibiting multiple phases. Examples include elastic ferromagnets and rigid superconductors. The basic modeling tools will be the use of spatially nonlocal energy terms to penalize oscillations in classical states and the variance of Young-measure states. Also included are existence results for short time dynamics of materials satisfying a generalized strong ellipticity hypothesis on electromagnetic and elastic properties and existence of equilibrium solutions for elastic bodies with perfect diamagnetism (elastic superconductors.) These studies will lead to a better understanding of the mechanical properties of elastic and electromagnetic materials and composites and will have an impact on the development and synthesis of materials with optimal properties.