标题： 电场弗雷德里克斯兹异常行为 显示英文标题

标题： Anomalous behavior of electric-field Fréedericksz transitions

摘要： 尼特液态晶体中的弗雷德里克斯转变被重新审视，重点在于磁场系统和电场系统之间的差异。在液晶介质中，磁场可以被视为均匀的；而一般的非均匀指向场也会导致局部电场的不均匀。尽管存在这些差异，普遍的观点认为，在相同几何结构下，电场弗雷德里克斯转变的局部不稳定阈值公式可以通过将磁场参数替换为相应的电场参数来获得。然而，在[Arakelyan, Karayan 和 Chilingaryan, 苏联物理文档, 29 (1984) 202-204]中显示，在六个经典的电场弗雷德里克斯转变中的两个中，局部不稳定阈值应严格大于由磁场类比预测的值。为什么会出现这种阈值的提高被仔细研究，并给出了一种简单的测试方法来确定何时可能发生这种情况。这种“异常行为”不仅限于经典的弗雷德里克斯转变，在某些层状系统（平面胆甾相、层列相A）和某些表现出周期性不稳定的向列相系统中也存在。 显示英文摘要

摘要： Fr\'eedericksz transitions in nematic liquid crystals are re-examined with a focus on differences between systems with magnetic fields and those with electric fields. A magnetic field can be treated as uniform in a liquid-crystal medium; while a nonuniform director field will in general cause nonuniformity of the local electric field as well. Despite these differences, the widely held view is that the formula for the threshold of local instability in an electric-field Fr\'eedericksz transition can be obtained from that for the magnetic-field transition in the same geometry by simply replacing the magnetic parameters by their electric counterparts. However, it was shown in [Arakelyan, Karayan, and Chilingaryan, Sov. Phys. Dokl., 29 (1984) 202-204] that in two of the six classical electric-field Fr\'eedericksz transitions, the local-instability threshold should be strictly greater than that predicted by this magnetic-field analogy. Why this elevation of the threshold occurs is carefully examined, and a simple test to determine when it can happen is given. This "anomalous behavior" is not restricted to classical Fr\'eedericksz transitions and is shown to be present in certain layered systems (planar cholesterics, smectic-A) and in certain nematic systems that exhibit periodic instabilities.