Mathematical Modelling of Exotic Liquid Crystalline Phases

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Liquid crystals are an interesting state of matter with long-range orientational order but withoutpositional order. Consequently these materials can flow like liquids but at the same time, retain anelastic, solid-like response to deformations in their orientational order. The liquid crystal industryis expected to be worth more than 190 billions US dollars by 2023, and yet the technology behindit still relies largely on the nematic phase which was first studied by Leslie, Ericksen and deGennes et al. in the 1960's.The usual nematic phase in liquid crystals is formed by rod-shaped molecules. At hightemperature, the molecules' orientations are completely random [this is called the isotropic phase,see Fig. 1(a) left]. On the other hand at low temperature, the molecules tend to align along somespontaneously broken direction [this is called the nematic phase, see Fig. 1(a) right]. The followingyoutube video, by my student: https://www.youtube.com/watch?v=dzS7-ddZAzQ demonstrates asimple isotropic-nematic phase transition using just a gas lighter and a laptop screen