Abstract

We study dynamic processes in liquid crystals using a simplified mathematical model in which a liquid crystal is considered as a finely dispersed continuous medium with rotating particles that has elastic resistance to volume deformation and viscoelastic resistance to the relative rotation of particles. The oscillatory regime of rotational motion described by the Klein–Gordon equation for tangential stress is studied. Moment interactions of particles due to the inhomogeneity of the rotation field are taken into account. The dispersion properties described by a subsystem of two equations for tangential stress and angular velocity are investigated. These equations are used to numerically analyze the rotation field in a liquid crystal under the action of tangential stress caused by the thermal expansion of a metal plate at the boundary. We consider the problem of perturbation of an extended layer of a 5CB liquid crystal by an electric field generated by charges on capacitor plates located periodically along the layer. Singularities of the electric potential at the ends of the capacitor plates are selected explicitly. Some results of computations simulating the Fréedericksz effect in the liquid crystal layer are presented.

中文翻译：

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弱摄动作用下液晶的动力学模型

摘要

我们使用简化的数学模型研究液晶中的动力学过程，在该数学模型中，液晶被视为具有旋转粒子的细分散连续介质，该粒子具有对体积变形的弹性抵抗力和对粒子相对旋转的粘弹性抵抗力。研究了由切向应力的Klein-Gordon方程描述的旋转运动的振荡状态。考虑了由于旋转场的不均匀性引起的颗粒间的矩相互作用。研究了由两个方程的切向应力和角速度子系统描述的色散特性。这些方程式用于数值分析在边界处金属板的热膨胀引起的切向应力作用下液晶中的旋转场。我们考虑由电场引起的5CB液晶扩展层扰动问题，该电场是由沿该层周期性放置的电容器板上的电荷产生的。明确选择电容器板末端的电势奇异性。提出了一些模拟液晶层中Fréedericksz效应的计算结果。