Applied mathematics of pattern formation in material sciences

我们对材料科学中各种宏观和微观图形的形成进行了理论分析和数值方法的发展。特别是，我们用数值和解析的方法研究了(1)嵌段共聚熔体中间相的结构转变；(2)带电胶体粒子的有序化动力学；(3)晶界动力学；(4)反应性相分离体系的磁区动力学；(5)细菌菌落的形成。其中一些工作是与实验者合作完成的。

We have carried out theoretical analysis and development of numerical method for studying various macroscopic and microscopic pattern formation in material sciences. In particular, we have investigated both numerically and analytically(1) structural transitions of mesophases in block copolymer melts(2) ordering dynamics of charged colloidal particles(3) dynamics of grain boundaries(4) domains dynamics of reactive phase separating systems and(5) formation of bacteria colony with chemotacsis.Some of these works have been performed in collaboration with experimentalists.Together with these studies, we have also developed fundamental theories of interface/grain boundary dynamics by means of singular perturbation and reduction method.