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A relaxed model and its homogenization for nematic liquid crystals in composite materials
Author(s) -
Shen Quan,
Calderer M. Carme
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.458
Subject(s) - liquid crystal , homogenization (climate) , mathematics , composite number , rendering (computer graphics) , energy functional , magnetic field , condensed matter physics , statistical physics , materials science , mathematical analysis , physics , computer science , algorithm , quantum mechanics , biodiversity , ecology , computer graphics (images) , biology
We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen–Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non‐linear. We employ two‐scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd.