Mathematical Sciences: Calculus of Variations, Material Microstructure, and Stochastic Evolution Problems

三个不同但松散相关的研究项目是 （a）研究拉夫连季耶夫现象， 等周约束问题及其与 非线性弹性中的空穴效应，（B）研究 具有层状微结构的材料和具有负性的材料 毛细作用，和（c）随机双曲方程和 液晶中随机控制 每个部分 代表了数学工具的进一步发展 在研究人员以前的工作中开发的，以及 引入新的研究课题。 这三个项目的动机都来自于连续体中的问题 力学 其目的是了解一个 各种各样的新材料，并发展数学， 将有助于解释，预测和控制他们的机械 行为

Three distinct but loosely related research projects are planned: (a) A study of the Lavrentiev phenomenon for isoperimetrically constrained problems and its relationship with cavitation effects in nonlinear elasticity, (b) A study of materials with layered microstructure and materials with negative capillarity, and (c) Stochastic hyperbolic equations and stochastic control in nematic liquid crystals. Each part represents a further development of the mathematical tools developed in the investigator's previous work, as well as the introduction of new research topics. The three projects are motivated by problems from continuum mechanics. The objective is to understand the physics of an assortment of novel materials and to develop mathematics which will help to explain, predict, and control their mechanical behavior.