Prof. Dr. Ricardo Nochetto (University of Maryland): Nematic liquid crystals with variable degree of orientation
Monday, 30.01.2017 16:15 im Raum M4
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 equations for
the minimizer contain a degenerate elliptic equation for the director
field, which allows for line and plane defects to have finite energy.
We present a structure preserving discretization of the liquid crystal
energy with piecewise linear finite elements that can handle the
degenerate elliptic part without regularization, and show that it is
consistent and stable. We prove Gamma-convergence of discrete global
minimizers to continuous ones as the mesh size goes to zero. We develop
a quasi-gradient flow scheme for computing discrete equilibrium
solutions and prove it has a strictly monotone energy decreasing
property. We present simulations in two and three dimensions to
illustrate the method's ability to handle non-trivial defects as well as
colloidal and electric field effects. This is joint work with S. Walker
and W. Zhang.
Angelegt am Monday, 09.01.2017 15:00 von Carolin Gietz
Geändert am Thursday, 12.01.2017 17:42 von Mario Ohlberger
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