Ericksen model

Wednesday, February 28, 2018 - 3:30pm - 4:20pm
Shawn Walker (Louisiana State University)
We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent elastic constants that depends on two order parameters $\mathbf{n}$ (director) and $s$ (variable degree of orientation). We will also discuss the modeling of weak anchoring conditions (both homeotropic and planar), and fully coupled electro-statics with flexo-electric and order-electric effects.
Tuesday, January 16, 2018 - 2:00pm - 2:50pm
Shawn Walker (Louisiana State University)
We present a phase field model for nematic liquid crystal droplets with anisotropic surface tension. Our model couples the Cahn-Hilliard equation to Ericksen's one constant model for liquid crystals with variable degree of orientation. We present a special discretization of the liquid crystal energy that can handle the degenerate elliptic part without regularization. In addition, our discretization uses a mass lumping technique in order to handle the unit length constraint. Discrete minimizers are computed via a discrete gradient flow.
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