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arXiv · 1708.00925

The Ericksen Model of Liquid Crystals with Colloidal and Electric Effects

Ricardo H. Nochetto·Shawn W. Walker·Wujun Zhang
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Abstract

We present a robust discretization of the Ericksen model of liquid crystals with variable degree of orientation coupled with colloidal effects and electric fields. The total energy consists of the Ericksen energy, a weak anchoring (or penalized Dirichlet) energy to model colloids, and an electrical energy for a given electric field. We describe our special discretization of the total energy along with a method to compute minimizers via a discrete quasi-gradient flow algorithm which has a strictly monotone energy decreasing property. Numerical experiments are given in two and three dimensions to illustrate that the method is able to capture non-trivial defect patterns, such as the Saturn ring defect. We conclude with a rigorous proof of the Gamma-convergence of our discrete energy to the continuous energy.

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Ricardo H. Nochetto, Shawn W. Walker, Wujun Zhang. 2017-08-02. The Ericksen Model of Liquid Crystals with Colloidal and Electric Effects. https://doi.org/10.1016/j.jcp.2017.09.035

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