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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

在目前的研究中，我们利用容器的表面处理来制备最初两种不同对称性的电对流池。一种称为同向排列，另一种称为平面排列。两者都表现出超过施加电压的特定阈值的非平衡宏观波动(时空混沌)。根据对称性的不同，我们描述了这两个系统中观察到的典型的花样动力学性质。在同向异性排列中，系统具有连续的旋转对称性，由于这种对称性，首先获得了软模湍流(SMT)，并表现出以下事实：(1)观察到与对称性相关的对流场和方向场之间的强烈相互作用。一种是普通轧辊，另一种是斜轧辊。当施加电压的频率改变时，它们之间的转变就会出现。它可以看作是类似于有序-无序的转变。(2)关联长度ξ满足关系ξ…更多∝ε^&lt；-1/2&gt；。这里，ε是由SMT阈值归一化的外加电压。(3)在一维同向同性系统中，软模湍流的阈值比二维系统的阈值移动得更高。(4)根据涨落的时间关联得到的软模湍流动力学与系统的维度之间的关系，动力学与系统的维度无关，在平面排列中，系统已经初步打破了连续转动对称性。在这种情况下，由冻结的宏观涨落引起的缺陷晶格图案被观察到为周期性的缺陷排列。(1)缺陷晶格是由于异常滚子不稳定性和歪曲曲折不稳定性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坍塌。崩塌面积随着外加电压的增加而增大。这是一种典型的时空混沌，特别是时空间歇性(STI)。随着外加电压的进一步增加，整个区域变得湍流。(3)通过在外加电压中叠加与晶格自发振荡相同频率的调制，在塌陷区再现了晶格结构。因此，STI可以通过小的周期扰动来控制，即可以在具有大空间自由度的系统中实现混沌控制。较少