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The effect of external fields in the theory of liquid crystals. (English) Zbl 1250.82048

Summary: We consider the response of the external field to the theory of liquid crystals. We treat the Landau-de Gennes functional with the Dirichlet boundary condition for the director field which may be non-constant. We show that there exist two families of critical points such that one carries out the superheating fields of superconductors, and the other one carries out strong stability. We also show that under some conditions, strong field does not bring the pure nematic state which is different response from superconductors.

MSC:

82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
35A15 Variational methods applied to PDEs
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
82B27 Critical phenomena in equilibrium statistical mechanics
82D55 Statistical mechanics of superconductors
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References:

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