SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 304-334, January 2021.
Systems involving nematic liquid crystals subjected to magnetic fields or electric fields are modeled using the Oseen--Frank macroscopic continuum theory, and general criteria are developed to assess the local stability of equilibrium solutions. The criteria take into account the inhomogeneity of the electric field and the mutual influence of the electric field and the liquid-crystal director field on each other. The criteria show that formulas for the instability thresholds of electric-field Fréedericksz transitions cannot in all cases be obtained from those for the analogous magnetic-field transitions by simply replacing the magnetic parameters by the corresponding electric parameters, contrary to claims in standard references. A simple analytical test is provided to determine when an electric-field-induced instability can differ qualitatively from the analogous magnetic-field-induced instability. For the systems we study, it is found that taking into account the full coupling between the electric field and the director field can either elevate or leave unchanged an instability threshold (never lower it), compared to the threshold predicted by the magnetic-field analogy. The physical mechanism that underlies the effect of elevating an instability threshold is the increase in free energy associated with a first-order change in the ground-state electric field caused by a perturbation of the ground-state director field. Examples are given that involve classical Fréedericksz transitions and also periodic instabilities. The inclusion of flexoelectric terms in the theory is studied, and it is found that these terms are not capable of altering the instability thresholds of any of the classical Fréedericksz transitions.

中文翻译：

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向列型液晶中的电场诱导的不稳定性

SIAM应用数学杂志，第81卷，第2期，第304-334页，2021年1月。
使用Oseen-Frank宏观连续理论对涉及向列液晶的磁场或电场的系统进行建模，并开发了通用准则来评估平衡溶液的局部稳定性。该标准考虑了电场的不均匀性以及电场和液晶指向矢场彼此之间的相互影响。该标准表明，与标准参考文献中的权利要求相反，仅通过用相应的电参数代替磁参数，就不能从类似的磁场跃迁的那些方程中，在所有情况下都可以得到电场Fréedericksz跃迁的不稳定性阈值的公式。提供了一个简单的分析测试来确定电场诱发的不稳定性何时可以与类似的磁场诱发的不稳定性发生定性变化。对于我们研究的系统，发现与电场模拟所预测的阈值相比，考虑到电场与指向矢场之间的完全耦合可以提高或保持不变性阈值（永远不会降低）。 。引起不稳定性阈值升高的基础的物理机制是与由基态指向矢场的扰动引起的基态电场的一阶变化相关的自由能的增加。给出了涉及经典Fréedericksz过渡以及周期不稳定性的示例。