论文标题
稳定性与赔率：染色性液晶的情况
Stability Against the Odds: the Case of Chromonic Liquid Crystals
论文作者
论文摘要
如最近的许多实验所揭示的染色性液体晶体的基态与普通的列液晶晶体完全不同：它是扭曲而不是均匀的。坦率的经典弹性理论要求一个埃里克森（Ericksen）的不平等现象被侵犯了这种状态的共同解释。由于总的来说，这种违规行为使弗兰克的弹性自由能功能无限，因此出现了问题，即扭曲的基态是否可以在本地稳定。我们肯定地回答了这个问题。在得出这一结论时，在刚性容器边界的实验中施加的特定边界条件和我们在此得出的一般公式在弗兰克弹性自由能的第二个变化中扮演的特定边界条件发挥了中心作用。
The ground state of chromonic liquid crystals, as revealed by a number of recent experiments, is quite different from that of ordinary nematic liquid crystals: it is twisted instead of uniform. The common explanation provided for this state within the classical elastic theory of Frank demands that one Ericksen's inequality is violated. Since in general such a violation makes Frank's elastic free-energy functional unbounded below, the question arises as to whether the twisted ground state can be locally stable. We answer this question in the affirmative. In reaching this conclusion, a central role is played by the specific boundary conditions imposed in the experiments on the boundary of rigid containers and by a general formula that we derive here for the second variation of Frank's elastic free energy.
