Topology and bistability in liquid crystal devices.

We study nematic liquid crystal configurations in a prototype bistable device\char22{}the post aligned bistable nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field $\mathbf{n}$, in a model version of the PABN cell. First, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry.