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Order tensors of equilibrium phases

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If you have a question about this talk, please contact Mustapha Amrani.

The Mathematics of Liquid Crystals

Order in fluids is described by means of tensorial measures which have in general a statistical derivation, as appropriate moments of a molecular distribution function. Their very definition places order tensors at the crossroad between microscopic and macroscopic approaches, in that land of middle where “mesoscopic” theories flourish. We shall give specific examples of how different order tensors can describe the equilibrium phases of different ordered fluids. Both uniaxial and biaxial nematic liquid crystals will be covered, as well as smectic liquid crystals, thus showing how both orientational and spatial orderings can be represented in one and the same setting. Our presentation will not be limited to phases in bulk; ordering at interfaces will also be considered along with the ways it can be affected by the surface curvature. Similarly, ordering of fluids on two-dimensional curved manifolds will be described, and an “augmented” theory will be presente d for nematic shells, which to the in-plane orientational order adds information on the escape of molecules along the shell’s normal.

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

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