Dynamics of Filaments and Cellular Patterns in Fluid ; Its Universality and Mechanisms

流体中细丝和细胞模式的动力学；

基本信息

批准号：
06302024
负责人：
S Kai
金额：
$ 3.01万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

Cellular patterns and filaments, which appear in dissipative systems far from equilibrium such as convective systems, chemical reaction systems and turbulence, have been studied on their universality as well as their individual formation mechanisms. Standing upon the above viewpoints, the investigations have been experimentally and theoretically done after classified into three subjects due to differences of their dynamics and dimensionality ; (1) surface and line defect systems such as an interface between two phases, filaments and vortices, (2) chemical reaction diffusion systems accompanied by hydrodynamic phenomena and (3) bulk celullar convections and turbulence. The results obtained are as follows. (1) In bulk convective phenomena such as the Rayleich-Benard convection and the electroconvection in liquid crystals, common (universal) aspects related to the pattern selection and the Busse diagram were obtained. Simultaneously the different behavior was also observed which was due to symmetrical differences of the systems. Therefore it was clarified that the symmetry of considered dynamics and the symmetrical arguments were vert important and universal to understand pattern formation. We obtained the universal spatio-temporal scaling at the phase slip process for one-and two-dimensional systems. It is therefore expected to be unversal even for the phase slip in a three dimensional system, for example vortices. Then the dynamics of a vortex is described through the scaling. (2) Common statistical properties and expressions were obtained through the relation between the curveture of filaments and the responsible background-field. (3) Though the universality among them was qualitatively understood, quantitative understandings have not been obtained yet. They are still left as future problems.

细胞模式和丝状结构出现在对流系统、化学反应系统和湍流等远离平衡的耗散系统中，人们对其普遍性及其各自的形成机制进行了研究。基于以上观点，根据动力学和维度的差异，将研究分为三个主题，分别从实验和理论上进行了研究； (1) 表面和线缺陷系统，例如两相、细丝和涡流之间的界面，(2) 伴随流体动力学现象的化学反应扩散系统，以及 (3) 整体细胞对流和湍流。得到的结果如下。 (1)在液晶中的瑞利希-贝纳德对流和电对流等体对流现象中，获得了与模式选择和布斯图相关的共同（普遍）方面。同时，还观察到由于系统的对称差异而导致的不同行为。因此，澄清了所考虑的动力学的对称性和对称参数对于理解模式的形成非常重要和普遍。我们获得了一维和二维系统相滑过程中的通用时空标度。因此，即使对于三维系统（例如涡流）中的相滑移，它也是通用的。然后通过缩放来描述涡旋的动力学。 (2)通过细丝的曲率与背景场的关系，得到了常用的统计特性和表达式。 (3)虽然对它们之间的普遍性有了定性的认识，但尚未获得定量的认识。它们仍然是未来的问题。