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Erratum: Reexamination of the Helfrich-Hurault effect in smectic-A liquid crystals (Physical Review E (2005) 72 (041708))
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Periodic splay-twist Fréedericksz transition for nematics confined between two concentric cylinders
No full textcrystals confined between two infinite concentric cylinders. The calculation of Lonberg and Meyer Phys. Rev. Lett. 55, 718 1985 , for nematics sandwiched between two infinite planes, is extended to annular domains.
The phase transition is triggered by an applied voltage between the outer and the inner delimiting walls. The critical threshold behavior is analyzed via the linearized Euler-Lagrange equations related to the Frank's free
energy. It is found that, the threshold depends on both the ratio between the twist and the splay elastic constants, and the sample radii ratio. Results for planar samples are recovered in the thin cell limit. With
respect to the planar geometry, our analysis predicts that for annular geometries the periodic Fréedericksz
transition is also allowed for elastic anisotropies K2 / K1 > 0.303
Cooling a spherical nematic shell
Full text linkWithin the framework of Landau-de Gennes theory for nematic liquid crystals, we study the temperature-induced isotropic-nematic phase transition on a spherical shell under the assumption of degenerate tangential anchoring. Below a critical temperature, a thin layer of nematic coating a microscopic spherical particle exhibits nonuniform textures due to the geometrical frustration. We find the exact value of the critical threshold for the temperature and determine exactly the nematic textures at the transition by means of a weakly nonlinear analysis. The critical temperature is affected by the extrinsic curvature of the sphere, and the nematic alignment is consistent with the Poincaré-Hopf index theorem and experimental observations. The stability analysis of the bifurcate textures at the isotropic-nematic transition highlights that only the tetrahedral configuration is stable
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