Homogenization of a Ginzburg-Landau model for a nematic liquid crystal with inclusions (Q1775757)

The authors consider a nonlinear homogenization problem relative to a Ginzburg-Landau functional with a (positive or negative) surface energy term, which describes a nematic liquid crystal with inclusions. The inclusions are separated by distances of the same order \(\epsilon\) of their size and Have periodic or non-periodic distribution. The authors show that the corresponding homogenized problem is described by an anisotropic Ginzburg-Landau functional. Computational formulas for the effective material characteristic of an effective medium are obtained. The authors prove also that a cross-term corresponding to interactions between the bulk and the surface energy terms does not appear at the leading order in the homogenized problem.