The Ericksen Model of Liquid Crystals with Colloidal and Electric Effects
This work provides a rigorous numerical framework for simulating liquid crystal colloids under electric fields, which is important for applications in display technology and soft matter physics.
The authors developed a robust discretization for the Ericksen model of liquid crystals with colloidal and electric effects, and proved Gamma-convergence of the discrete energy to the continuous energy. Numerical experiments in 2D and 3D demonstrated the method's ability to capture non-trivial defect patterns like the Saturn ring defect.
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.