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Modelling a planar bistable device on different scales

Tuesday 19th March 2013 - 09:50 to 10:40
INI Seminar Room 1
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 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. We also use the off-lattice based Gay Berne model to study the structure of the stable states. The different numerical approaches are compared and we discuss their relative strengths a nd shortcomings. We conclude by a brief discussion on a multiscale modelling approach wherein we can couple a lattice-based interaction potential to a conventional continuum model. This is joint work with Chong Luo and Radek Erban.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons