Pattern Formation in Nonequilibrium Dissipative Systems-Dynamics of Dissipative Structures in Liquid Crystals

本研究项目的目的是了解系统对称性对非平衡耗散系统中图案形成的作用，例如可吸收液体晶体中的电流体动力学不稳定性（EHD）。在EHD系统中，存在两种不同的排列;平面排列和垂面排列。关于平面系统中的斑图形成，已经获得了各种新的结果。与此相反的是，垂面体系中的EHD研究很少，至今没有得到有趣的结果，也没有新的物理现象。在本研究中，我们特别注意系统的对称性。在EHD模式的形成强烈依赖于系统的初始对称性，即无论是平面或垂面排列。然而，所谓的人字形图案出现独立于初始配置，即系统的初始对称性。因此，我们首先研究了这种模式的形成机制。然后发现人字形图案是类 ...更多信息 将其分为人字形A和人字形B四种不同的类型，这两种类型又进一步分为具有周期缺陷取向（DMC）和无缺陷人字形（DFC）的模式。DMC的形成是由于缺陷形成和指向矢变形之间的竞争不稳定性，类似于图灵不稳定性。人字形A和B的DFC机制尚不清楚。然而，很明显，人字形图案的形成与边界锚定无关，边界锚定总是导致图案形成中没有对称性依赖。SMT是一个独特的湍流在弱非线性制度连续连接到一个统一的定态通过一个单一的超临界分岔，因此，预计将得到准确的理解。这是由于连续旋转对称性导致的附加Goldstone模式，其可以通过施加磁场来抑制。在外加电场强度、频率和磁场强度参数之间的平面上得到了相图。两个不同的STC的已被发现依赖于系统的对称性。因此，排列（对称性）的微小变化导致图案形成的巨大差异。形成动力学必须分为两类：独立于对称性的普遍动力学和依赖于对称性的个体动力学。少

The aim of this research project is to understand a role of system symmetries on pattern formations in nonequilibrium dissipative systems such as electrohydrodynamic instability (EHD) in nematic liquid crysals. In the EHD system, there are two different alignments ; planar and homeotropic ones. Regarding pattern formations in planar systems various new results have been obtained. Contrary to this, the study of EHD in homeotropic systems was very few, and no interesting results and no new physics were obtained so far. In the present study, we especially pay our attention to symmetries of the systems. Pattern formations in EHD strongly depend on the initial synmmetries of the systems, that is either on planar or homeotropic alignments. However the so-called chevron patterns appear independently of initial align-ments, i.e. initial symmetry of the system. Therefore we investigate at first the formation mechanism of this type of patterns. Then it is found that the chevron patterns are clas … More sified into four different types, chevron A and B, both of which are further classified into the patterns with periodic defect orientation(DMC) and defect free chevrons (DFC). DMC forms due to competitive instability between defect formation and director defomation similar to Turing instability. The mechanism of DFC in chevron A and B are unknown yet. It becomes however clear that the chevron patterns are fomed independently of boundary anchoring which always leads to no symmetry dependence in the pattern formation.Regarding EHD in a homeotropic alignment with a continuously rotational symmetry, a spatio-temporal chaos called the softmode turbulence (SMT) appears. SMT is a unique turbulence in a weakly nonlinear regime continuously connecting to a uniform stationary state via a single supercritical bifuraction and therefore expected to be understood precisely. This results from the additional Goldstone mode due to the continuously rotational symmetry, which can be suppressed by application of magnetic fields. The phase diagram has been obtained on a plane among the parameters of applied electric field intensity, its frequency and magnetic field strength. Two different STC's have been found out which depend on the symmetry of the system. Thus the small change of alignments (symmetries) leads to the big difference of pattern formations. The formation dynamics must be classified into two categories ; universal dynamics independent of symmetries and individual dynamics dependent on symmetries. Less