PATTERN FORMATION AND SYMMETRY OF FIELDS IN ELECTROHYDRODYNAMICSS IN LIQUID CRYSTALS

研究了向列取向取向垂直于电极的向列取向液晶的电流体动力学不稳定性。在同向取向EHD中，系统不仅具有连续的旋转对称性，而且具有连续的平移对称性。这种对称性在对流开始时导致了额外的新的戈德斯通模式，并极大地改变了分岔特性以及观察到的模式。本研究得到的结果如下：(1)由于连续旋转对称而增加Goldstone模态的系统，从非对流状态直接过渡到时空混沌。2)初始分岔发生超临界。宏观随机运动的相关时间随着与起始点的偏差成反比而变长，即出现临界慢化现象。根据这种行为，将时空混沌命名为软模态湍流（SMT）。(3)由于磁场诱导出首选轴，抑制了Goldstone模式的产生，因此可以通过施加磁场来控制附加Goldstone模式的稳定性。因此，在叠加强磁场下，可以观察到周期模式。4)发现了现有理论无法预测的新型之字形模式。(5)从这些研究结果可以清楚地看出，导致SMT的驱动力是由共滚方向与波矢量之间的非平行取向引起的。根据磁场强度的不同，时空混沌有两种类型。通过观察横摇方向的空间功率谱和分布函数，明确了两者之间的过渡。卷存在于所有方向或只存在于磁场感应的首选方向。前一种称为SMT，后一种称为缺陷湍流。因此，过度的对称性会导致混沌，而从空间均匀状态直接过渡到混沌的内在机制是由于与光谱的Goldstone模耦合而导致短波模式的不稳定。在此基础上，EHD理论有望得到新的发展。少

The electrohydrodynamic instability (EHD) in nematic liquid crystals is investgated using homeotropically aligned systems where the nematic director orients perpendicular to the electrodes. In homeotropically aligned EHD the system has a continuously rotational symmetry as well as a translational one. This symmetry leads to additional new Goldstone modes at onset of convections and dramatically changes the bifurcation properties as well as observed patterns. The obtained results in the present study are as follows.1) In the system with additional Goldstone modes due to continuous rotational symmetry, a direct transition from nonconvective states to spatiotemporal chaos is observed.2) The bifuration at onset occurs supercritically. The correlation time of macroscopic randam motions becomes longer inversely proportional to the deviation from the onset, that is, a critical slowing down phenomenon is observed. From this behavior the spatiotemporal chaos has been named the soft mode turbule … More nce (SMT) .3) The stability of additional Goldstone modes can be controlled by application of magnetic field since magnetic fields induce the prefered axis and suppress the generation of the Goldstone modes. Therefore under superimposing strong magnetic fields periodic patterns are observed.4) New type of zig-zag patterns are found out which are not predicted in currently available thcories.5) It is clarified from these findings that driving forccs which result in SMT are induced by non-parallel orientation between the director and the wavevector of covective rolls.6) Depending on the strength of magnetic fields there are two types of spatiotemporal chaos. The transition between them is clearly defined by looking the spatial power spectra of patterns and distribution functions of roll orientations.7) The rolls exist either in all directions or only in the prefered directions induced by magnetic fields. Then the formet one is called SMT and the latter the defect turbulence.Thus excess of symmetry can result in chaos and the intrinsic mechanism for direct transition to chaos from a spatially uniform state is destabilization of short-wavelength modes due to coupling with Goldstone modes of the spectrum. Based on these results, new theory will be expected in EHD. Less