Generalized Hydrodynamics for Second 2D Soft-Matter Quasicrystals
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摘要: 提出了第一类与第二类二维准晶概念.在笔者已有工作(范天佑. 软物质准晶广义流体动力学方程组[J]. 应用数学和力学, 2016,37(4): 331-344.)的基础上,对可能的7次、9次和14次对称软物质第二类二维准晶广义流体动力学进行了全面讨论,建立了它们的终态控制方程组,为软物质准晶学科的发展提供了一个数学模型,为探讨有关物理问题的时间空间演化提供了可操作的实际可行的求解体系和分析工具,是对该工作的一个重要发展.Abstract: The concept on the first and second kinds of 2D quasicrystals was put forward, and through extension of ref.[1], the generalized hydrodynamics for possible soft-matter quasicrystals with 7-, 9- and 14-fold symmetries was suggested based on the Langevin equation and with the derivation method of the Poisson bracket. The derivation referred to the previous work of the author. The soft-matter quasicrystals observed so far were 2D ones. From this point of view, all the soft-matter quasicrystals both discovered and possibly discovered were considered in ref.[1] and the present work from the angle of symmetry and generalized hydrodynamics, where the equation of state as a key, was built by ref.[1]. Final governing equations (7), (9) and (11) were similar to those given in ref.[1], and the solution was also similar, so that the way of solution for the first kind of 2D soft-matter quasicrystals is beneficial to the second kind.
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