Nemato-Dynamics of Two-Dimensional Defect Structure

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Abstract A two-dimensional liquid crystal with a planar director field and perforated by a set of disclinations is studied for a given flow structure. The set of equations of motion governing the evolution of the director field and fluid flow is set up. This problem is mapped onto the collective state consisting of a set of disclinations and vortices moving in a potential flow. An effective Lagrangian for the disclinations and being equivalent to that used for 2 + 1-dimensional electrodynamics is tentatively proposed. Some aspects of the theory relative to the process of alignment of a liquid crystal under flow, and containing an intrinsic defect structure, are qualitatively discussed.

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