Possible soft-matter quasicrystals of 5- and 10-fold symmetries and hydrodynamics

The dynamics and wave propagation of possible soft-matter quasicrystals with 5- and 10-fold symmetries are studied. Apart from elementary excitations - phonons and phasons, the fluid phonon is introduced in the study for the hydrodynamics of the matter, which was originated from the Landau school. The essential difference of soft-matter quasicrystals with solid quasicrystals lies in the existence of fluid phonon and the interaction between fluid phonon, phonons and phasons. By extending the hydrodynamics theory of solid quasicrystals proposed by Lubensky et al. the hydrodynamics theory of soft-matter quasicrystals is suggested, and we give a numerical implementation through finite difference method. The results in this paper explore some dynamic and wave propagating behaviour of soft-matter quasicrystals with 5- and 10-fold symmetries.