Hybrid modelling of a planar liquid crystal device
By: Apala Majumdar
From: University of Bath
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2013-11-20]
This talk focuses on the development, analysis and numerical implementation of mathematical models for a planar bistable nematic device reported in a paper by Tsakonas, Davidson, Brown and Mottram. We model this device within a continuum Landau-de Gennes framework and investigate the cases of strong and weak anchoring separately. We model the device in two dimensions and three dimensions separately. In two dimensions, we recover the experimentally observed diagonal and rotated solutions and compute bifurcation diagrams for the stable equilibria as a function of the anchoring strength. In three dimensions, we recover the diagonal and rotated equilibria for micron-scale wells. As the well size is progressively decreased, we discover a novel two-dimensional biaxial order reconstruction pattern connecting the vertices when the device width becomes comparable to the biaxial correlation length. We develop a parallel lattice-based Landau-de Gennes interaction potential, by analogy with the Lebwohl-Lasher lattice-based model and study multistability within this discrete framework by means of Monte Carlo methods. The different numerical approaches are compared and we conclude with a brief discussion on a multiscale modelling approach wherein a lattice-based interaction potential is coupled to a conventional continuum model. This is joint work with Samo Kralj, Chong Luo and Radek Erban.