Mathematical Sciences: Mathematical Problems from Materials Science

首席研究员将继续研究相干相变的变分模型、复合材料有效模的最优边界和非凸变分问题的松弛之间的联系。特别是，他将尝试通过体积能最小化来预测两相相干相混合物的微观结构，评估表面能在确定相干相混合物微观结构中的作用，并通过均匀小应变变形理论从线性结果中导出非线性几何结果。

The principal investigator will continue looking at the connection between variational models of coherent phase transitions, optimal bounds on the effective moduli of composites and the relaxation of nonconvex variational problems. In particular, he will attempt to predict the microstructure of two- phase coherent phase mixtures via bulk energy minimization, evaluate the role of surface energy in determining the microstructure of coherent phase mixtures, and derive nonlinear results geometrically from linear ones by means of a theory of deformations with uniformly small strain.