摘要
建立了软物质准晶广义流体动力学方程组,其基础为广义Langevin方程,推导方法为Poisson括号,它参考了固体准晶的广义流体动力学方程组,但是两者存在原则的不同.固体准晶的广义流体动力学方程组考虑了固体粘性与声子弹性和相位子弹性的相互作用,没有状态方程问题;软物质准晶广义流体动力学方程组考虑的是软物质流体声子与声子弹性和相位子弹性的相互作用,按物理学术语多出了一种元激发,而且必须考虑状态方程问题,这是一个新课题,又增加了难点.实际应用的结果发现,软物质准晶广义流体动力学方程组大大激活了广义流体动力学的效能,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,求解的结果令人满意.
The equation systems of generalized hydrodynamics for soft-matter quasicrystals were established based on the Langevin equation,with the derivation method of Poisson bracket. The derivation was done with reference to the work on solid quasicrystals,for which there were only 2 kinds of elementary excitations： phonons and phasons. However,the generalized hydrodynamics for soft-matter quasicrystals was essentially different from that for solid ones. In the generalized hydrodynamics for solid quasicrystals the effects of solid viscosity and the interaction among viscosity,phonons and phasons were considered,without the need of state equations. Nevertheless,the fluid phonon and the interaction among fluid phonons,phonons and phasons in soft-matter quasicrystals were to be considered,where 3 kinds of elementary excitations,i. e. phonons,phasons and fluid phonons meant state equations were indispensable. This difficult problem was solved with the present method. The results showthe correctness and efficiency of the theoretical analysis.
出处
《应用数学和力学》
CSCD
北大核心
2016年第4期331-344,共14页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11272053)~~
关键词
软物质
准晶
广义流体动力学
状态方程
soft-matter
quasicrystal
generalized hydrodynamics
state equation
