Effective surface energies in nematic liquid crystals as homogenized rugosity effects

Abstract

We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques of Gamma convergence and demonstrate that the effect of fine-scale surface oscillations may be replaced by an effective homogenized surface energy on a simpler domain. The homogenization limit is then quantitatively studied in a simplified setting, obtaining convergence rates.