Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6929339 | Journal of Computational Physics | 2018 | 54 Pages |
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 Î-convergence of our discrete energy to the continuous energy.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Ricardo H. Nochetto, Shawn W. Walker, Wujun Zhang,