利用向列相液晶弹性理论, 研究了混合排列柱状薄层中的向列相液晶指向矢的分布。向列相液晶被限定在两个同心圆柱构成的薄层中, 在内外表面施加强锚定及弱锚定边界条件, 锚定易取向方向取径向和轴向（垂直柱轴及平行柱轴）的边界条件, 得到了四种混合排列柱状薄层模型RsZw、ZwRs、RwZs、ZsRw。基于Frank弹性自由能和Rapini-Papoular近似的表面能, 研究了不同锚定强度、不同内半径及不同弹性常数值的指向矢分布, 计算机模拟得出指向矢取向的曲线图。由于柱对称性、锚定强度、薄层厚度以及弹性各向异性共同竞争的影响, 这四种模型的指向矢分布有着很大的不同。

By using nematic liquid crystal elastic theory, we study the director distributions of nematic liquid crystal in hybrid arrangement cylindrical cells. Nematic liquid crystal is restricted in two concentric cylindrical layers, inside and outside surface application strong anchoring and weak anchoring boundary condition, anchor set to boundary conditions of the radial and axial direction(vertical and parallel axis), obtaining four models ZsRw, ZwRs, RsZw and RwZs. Based on the Frank elastic free energy and the Rapini Papoular approximation to the surface anchoring strength, we obtain the director distributions with antagonistic anchoring conditions, different radius and different elastic constants. We calculate and simulate the director orientation graph. Because of the influence of column symmetry, anchoring strength, layer thickness and elastic anisotropy, the director distributions of these four models are very different.