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Liquid crystal defects, a critical overview

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The Mathematics of Liquid Crystals

Defects in liquid crystals present an extremely vast set of situations, depending on the nature of the order parameter, elasticity properties, boundary conditions. One distinguishes : defects characteristic of liquid crystalline media with one or two discrete repeat distances (smectic and columnar phases) which can be investigated by pure geometric methods ; defects characteristic of a director order parameter, which employ the Volterra process (for one dimensional defects) and topological methods, those latter providing scope for defects of various dimensionalities ; finally continuous defects whose consideration is essential for a description of defect physical properties. These topics will be confronted with an historical point of view and possible future developments.

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

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