Biomathematics Seminar: Hybrid models for liquid crystals and their applications
22 October 2013 14:00 in CM105
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. In both cases, we find six distinct states and compute bifurcation diagrams as a function of the anchoring strength. We introduce the concept of an optimal boundary condition that prescribes the optimal interpolation between defects at the vertices. We discover a novel two-dimensional biaxial order reconstruction pattern connecting the vertices, as 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 too 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.
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