九次对称软物质准晶的流体动力学分析

The Analysis of Dynamics of Soft-matter Quasicrystals with 9-fold Symmetry

本文建议并研究了9次对称软物质准晶的流体动力学模型。9次对称软物质准晶属于第二类软物质准晶,与第一类软物质准晶不同,除具有声子场、第二相位子场、流体声子场,还增加了第四个元激发——第一相位子场元激发。模型中,推导了可能的9次软物质准晶的运动方程组,采用有限差分法求解了二维9次对称软物质准晶的初边值定解问题,其中,全面分析了其流体动力学特征。从物理时空变化角度探索了声子场,第一、第二相位子场,流体声子场以及其相互作用。不同于14次软物质准晶,9次软物质准晶的声子和相位子不耦合,从而也证明了声子、相位子是否耦合对软物质准晶的力学特性有重大的影响。

In this paper, the hydrodynamic model for soft-matter quasicrystals is suggested and investigated in this paper.The 9-fold symmetry soft-matter quasicrystals belong to the second kind of soft-matter quasicrystals, which are different from the first ones, because they have another fourth elementary excitation---the first phason field,except from the phonon field, the second phason field and the fluid phonon field. In this model, the equations of motion for possible 9-fold soft-matter quasicrystals are derived, and the two-dimensional initial-boundary value problem of the soft matter quasicrystals is solved by finite difference method, in which a complete hydrodynamics analysis is given. The phonon, the first and second phason, the fluid phonon fields and their interactions in physical time-spatial domain are quantitatively explored. Apart from the 14-fold,there are on phonon-phason coupling in the 9-fold symmetry soft-matter quasicrystals. It is proved that whether the coupling between the phonon and phason has a great influence on the mechanics of soft-matter quasicrystals.