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首页> 外文期刊>International journal of non-linear mechanics >Curvature-induced ordering in cylindrical nematic shells
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Curvature-induced ordering in cylindrical nematic shells

机译：圆柱向列壳中的曲率诱导有序

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摘要

In this paper we study theoretically the equilibrium configurations of two-dimensional nematic liquid crystals on a cylindrical surface. Configurations are described through a tensor-order parameter that provides information about the tangential optical axis and the dispersion of the molecules around it. Equilibrium equations are obtained by the surface Landau-de Gennes energy recently proposed in Napoli and Vergori [Physical Review E 061701 (2012)]. We show that, whenever free boundary conditions are applied, the extrinsic curvature induces the alignment of the optical axis along the cylinder axis. On the contrary, when strong planar anchoring is imposed on the boundaries, the curvature triggers a sort of Freedricksz-like transition in the alignment. We provide the asymptotic solution of the non-linear problem with strong planar anchoring boundary conditions for elongated cylindrical shells.
机译：在本文中，我们从理论上研究了二维向列液晶在圆柱表面上的平衡构型。通过张量级参数来描述配置，该参数提供有关切向光轴及其周围分子的色散的信息。平衡方程是通过最近在那不勒斯和韦格里[Physical Review E 061701（2012）]中提出的Landau-de Gennes表面能获得的。我们表明，每当应用自由边界条件时，外部曲率都会引起光轴沿着圆柱轴对齐。相反，当在边界上施加强力的平面锚固时，曲率会在路线中触发某种类似于Freedricksz的过渡。我们为细长圆柱壳提供了具有强平面锚固边界条件的非线性问题的渐近解。

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