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## An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects

### Abstract

We develop a fast and accurate approximation of the normally stiff equations which minimize the Landau–de Gennes free energy of a nematic liquid crystal. The resulting equations are suitable for all configurations in which defects are not present, making them ideal for device simulation. Specifically they offer an increase in computational efficiency by a factor of 100 while maintaining an error of order $(10^{-4})$ when compared to the full stiff equations. As this approximation is based on a $\mathcal{Q}$-tensor formalism, the sign reversal symmetry of the liquid crystal is respected. In this paper we derive these equations for a simple two-dimensional case, where the director is restricted to a plane, and also for the full three-dimensional case. An approximation of the error in the perturbation scheme is derived in terms of the first order correction, and a comparison to the full stiff equations is give

Topics: QA, QC
Year: 2010
OAI identifier: oai:eprints.soton.ac.uk:164053
Provided by: e-Prints Soton

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