Homogenization of a Ginzburg-Landau model for a nematic liquid crystal with inclusions. (English) Zbl 1162.35316
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.
Reviewer: Marco Biroli (Milano)
MSC:
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35J20 | Variational methods for second-order elliptic equations |
| 82D25 | Statistical mechanics of crystals |
| 76M50 | Homogenization applied to problems in fluid mechanics |
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