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

液晶中的图案形成--场的对称性和非平衡宏观涨落--

基本信息

批准号：
14340123
负责人：
KAI Shoichi
金额：
$ 10.69万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

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

在当前的研究中，我们利用容器的表面处理制备了最初两种不同对称性的电对流电池。一种称为垂直排列，另一种称为平面排列。两者都显示出超出施加电压的特定阈值的非平衡宏观波动（时空混沌）。下面我们根据对称性描述在两个系统中观察到的模式动力学的典型特性。在垂直排列中，系统具有连续旋转对称性，由于这种对称性，首先获得软模式湍流（SMT），并显示以下事实。（1）观察到与对称性相关的对流场和定向场之间的强相互作用。一种是普通滚动，另一种是斜滚动。当施加电压的频率改变时，它们之间的转变就会出现。可以将其视为类似于有序-无序过渡的东西。 (2)相关长度Ψ满足关系式Ψ … More ∝ ε^<-1/2>。这里ε是通过SMT阈值归一化的外加电压。(3)在一维垂直系统中，软模湍流的阈值比二维系统中的阈值移动到更高的值。这可能是由于有限尺寸效应造成的。(4)根据涨落时间相关性得到的软模湍流动力学与系统维数之间的关系，动力学与系统维数无关。在平面排列中，系统初步打破了连续旋转对称性。在这种情况下，观察到的缺陷晶格图案是由冻结的宏观波动产生的，作为周期性缺陷排列。(1)缺陷晶格是由于异常滚动不稳定性和倾斜曲张模态的两种模式的叠加而形成的。(2)晶格结构在超过某个阈值的空间中部分塌陷。塌陷面积随着施加的电压而增加。这是一种典型的时空混沌，特别称为时空间歇性（STI）。通过进一步增加施加电压，整个区域变成湍流。(3)通过以与晶格自发振荡相同的频率在施加电压中叠加调制，在塌陷区域再现晶格结构。因此STI可以通过小的周期性扰动来控制，即可以在大空间自由度的系统中实现混沌控制。较少的