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Creators/Authors contains: "Hicks, Andrew L"

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  1. ; (, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)
    This paper discusses modeling and numerical issues in the simulation of the Landau--de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully-implicit, (weighted) $L^2$ gradient flow for computing energy minimizers of the LdG model, and note a time-step restriction for the flow to be energy decreasing. Furthermore, we give a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers, particularly when simulating cholesteric LCs that exhibit ``twist.'' Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical shells, with our finite element method. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction. 
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