Phonon–phason dynamics and hydrodynamics of fivefold and tenfold symmetry quasicrystals

In view of the same model of fivefold and tenfold symmetry quasicrystals, with the same boundary and the same initial conditions, we have obtained a lot of results by phonon–phason dynamics and hydrodynamics and have performed a detailed comparative analysis. The quantitative results on mass density, viscosity velocities, phonon displacements, phason displacements, phonon stresses, phason stresses, and viscosity stresses and their time–space variations help us to understand the motion of solid quasicrystals. The analysis for octagonal and dodecagonal quasicrystals can be easily extended to other two-dimensional quasicrystals and three-dimensional icosahedral quasicrystals. These results reveal that the phonon field is dominated; moreover, the coupling between phonon and phason fields is important for the studied dynamic process, and these two elementary excitations are the main figures in the dynamic process. In contrast, the effects of the compressibility and viscosity are very weak, and they make almost no contribution to the dynamic process. For this dynamic process, the hydrodynamics and phonon–phason dynamics are equivalent, and the hydrodynamics can be simplified by phonon–phason dynamics for solid quasicrystals.