非线性波映照流方程的尖锐界面极限

Sharp Interface Limit of Nonlinear Wave Mapping Flow Equation

液晶的界面问题与普通流体的两相共存问题有着很大差异。本文基于Landau-de Gennes Q-张量理论,针对液晶无序相–向列相相变问题,使用匹配的渐近展开方法,在无序相和向列相区域进行外展开,在过渡的尖锐界面区域进行内展开,推导出不耦合流体从Landau-de Gennes流到尖锐界面模型的极限,得到指向矢n的演化遵循波映照热流,分离无序相和向列相的尖锐界面区域的演化由平均曲率流确定。

The interface problem of liquid crystal is very different from the two-phase coexistence problem of ordinary fluid. Based on Landau-de Gennes Q-tensor theory, aiming at the disordered nematic phase transition of liquid crystal, the matched asymptotic expansion method is used to expand outside the disordered phase and nematic phase region and inside the transitional sharp interface region, the limit of uncoupled fluid from Landau-de Gennes flow to sharp interface model is deduced, and it is obtained that the evolution of director n follows wave mapped heat flow, the evolution of the sharp interface region separating the disordered phase and the nematic phase is determined by the mean curvature flow.