We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field and its degree of orientation, where the pair minimizes a sum of Frank-like energies and a double well potential. In particular, the Euler-Lagrange equati...
Creator:
Nochetto, Ricardo (University of Maryland)
Created:
2018-03-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The inverse photolithography problem is a key step in the production of integrated circuits. I propose a regularization and computation strategy for this optimization problem, whose key feature is a regularization procedure for a suitable thresholding operation. The validity of the method is shown by a convergence analysis and by numerical exper...
Creator:
Rondi, Luca (Università di Trieste)
Created:
2016-12-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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-sta...
Creator:
Walker, Shawn (Louisiana State University)
Created:
2018-02-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 w...
Creator:
Walker, Shawn (Louisiana State University)
Created:
2018-01-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
