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A finite-element model of liquid-crystal hydrodynamics based on the Qian and Sheng formulation has been developed. This formulation is a generalization of the Ericksen-Leslie theory to include variations in the order parameter, allowing for a proper description of disclinations. The present implementation is well suited to treat properly the various length scales necessary to model large regions yet resolve the rapid variations in the order parameter in proximity to disclinations.Index Terms-Finite elements, liquid-crystal (LC) modeling, variable order parameter.

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The anisotropic anchoring effect of a treated solid surface on a nematic liquid crystal is described in the Landau-de Gennes theory using a power expansion on the tensor-order parameter and two mutually orthogonal unit vectors. The expression has three degrees of freedom, allowing for independent assignment of polar and azimuthal anchoring strengths and a preferred value of the surface-order parameter. It is shown that in the limit for a uniaxial constant-order parameter, the expression simplifies to the anisotropic generalization of the Rapini-Papoular anchoring energy density proposed by Zhao et al. Experimentally measurable values with a physical meaning in the Oseen-Frank theory can be scaled and assigned to the scalar coefficients of the tensor-orderparameter expansion. Results of numerical experiments comparing the anchoring according to the study of Zhao et al. in the Oseen-Frank theory and the power expansion in the Landau-de Gennes theory are presented and shown to agree well. Index Terms-Anchoring, liquid crystal (LC).Eero Willman received the M.Eng. degree in electronic and electrical engineering from the Department of Electronic and Electrical Engineering, University College London, London, U.K., in 2003, where he is currently working toward the Ph.D. degree.His current research interests include computer modeling and development of modeling tools for the simulation of nematic-liquid-crystal devices.

Liquid crystals are attractive materials for use in millimeter-wave band communications devices due to their large birefringence and reconfigurability. However, characterizing these materials is challenging at these frequencies. This work describes the modeling tools that have been developed for the accurate analysis of the liquid crystal orientation and of the wave propagation through the inhomogeneous and anisotropic liquid crystal layer. It also shows how the modeling has been used in conjunction with experimental measurement to characterize liquid crystal materials over a wide frequency range.

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