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Free Boundary-Value Problems for Liquid Crystals

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Free Boundary Problems and Related Topics

We discuss modelling strategies for free boundary-value problems arising in liquid crystal applications. We have recently modelled stable liquid crystal patterns in shallow cuboid-shaped nematic wells and have computed phase diagrams as a function of geometrical aspect ratio and anchoring strength on well boundaries. Recent work by Telo da Gama group (CFTC, Lisbon) shows that our computed patterns are also relevant to wedge-shaped nematic-filled wells at the isotropic-nematic transition temperature. At the isotropic-nematic transition temperature, the isotropic and nematic phases are separated by a free boundary, depending on the geometry and the surface effects at play. We discuss modelling approaches to this free-boundary problem and the role of such free boundaries in applications. This is joint work with Chong Luo, Samo Kralj and Samo Kralj.

This talk is part of the Isaac Newton Institute Seminar Series series.

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