Pattern Formation in Liquid Crystals --Symmetry of Fields and Nonequilibrium Macroscopic Fluctuation--

在目前的研究中，我们_制备的电对流细胞的最初两个不同的对称性使用的容器的表面处理。一种称为垂面排列，另一种称为平面排列。两者都表现出非平衡宏观波动（时空混沌）超过一定阈值的施加电压。在垂面排列中，系统具有连续的旋转对称性，由于这种对称性，首先得到了软模湍流（SMT），并表明了以下事实。（1）对流场和取向场之间存在着与对称性有关的强相互作用。一种是普通轧辊，另一种是斜轧辊。当外加电压的频率改变时，它们之间出现过渡。它可以看作是一种类似于有序-无序的过渡。（2）相关长度满足关系式： ...更多信息 是的。这里ε是由SMT的阈值标准化的施加电压。(3)In在一维垂面系统中，软模湍流的阈值比二维系统中的阈值更高。这可能是由于有限的尺寸效应。（4）由涨落的时间相关性得到的软模湍流动力学与系统维数的关系表明，动力学与系统维数无关，在平面排列中，系统初始破缺了连续旋转对称性。在这种情况下，观察到的缺陷晶格图案从冻结的宏观波动作为周期性的缺陷对齐。（1）缺陷晶格是由反常的辊不稳定性和斜变不稳定性两种模式叠加而成。（2）晶格结构在空间中超过某一阈值时部分坍缩。塌陷面积随外加电压的增大而增大。这是一种典型的时空混沌，又称时空混沌（STI）。通过进一步增加施加的电压，整个区域变成湍流。（3）通过在与晶格自发振荡相同的频率下叠加所施加的电压中的调制，在塌陷区域中再现晶格结构。因此，STI可以通过小的周期扰动控制，即混沌控制可以在大的空间自由度的系统中实现。少

In the current study, we_prepare electroconvective cells of initially two different symmetries using the surface treatment of the container. One is called the homeotropic alignment and the other the planar one. Both show nonequilibrium macroscopic fluctuations (spatiotemporal chaos) beyond certain thresholds of applied voltages. Below we describe typical properties of pattern dynamics observed in both systems depending on the symmetries.In the homeotropic alignment the system has continuously rotational symmetry, due to this symmetry the soft-mode turbulence (SMT) is obtained at first, and shows the following facts.(1)There observe strong interactions between convective and orientational fields related to the symmetries. One is normal rolls, and the other is oblique rolls. The transition between them appears when the frequency of applied voltages is changed. It may be regarded as the transition something similar to order-disorder one.(2)The correlation length ξ satisfies the relation ξ … More ∝ ε^<-1/2>. Here ε is an applied voltage normalized by the threshold for SMT.(3)In the one dimensional homeotropic system, the threshold of the soft-mode turbulence is shifted to higher value than that in two dimensional systems. It may be due to a finite size effect.(4)According to the relation between the dynamics of the soft-mode turbulence and the dimensionality of the system obtained from the temporal correlation of the fluctuations, dynamics is independent of the dimensionality of system.In the planar alignment, the system has initially broken the continuously rotational symmetry. In this case the defect lattice pattern is observed resulting from frozen macroscopic fluctuations as a periodic defect alignment.(1)The defect lattice forms due to superposition of two modes by abnormal rolls instability and skewed-varicose one.(2)The lattice structure partially collapses in space beyond a some threshold. The collapse area increases with the applied voltage. This is a typical spatiotemporal chaos, especially called spatiotemporal intermittency (STI). By further increase of applied voltages, the whole area becomes turbulence.(3)The lattice structure is reproduced in the collapse area by superimposing the modulation in the applied voltage at the same frequency as the lattice spontaneous oscillation. Thus STI can be controlled by small periodic perturbations, that is, the chaos control can be realized in systems with large spatial degrees of freedom. Less