The elasto-/hydro-dynamics of quasicrystals with 12- and 18-fold symmetries in some soft matters and mathematical solutions

The observation recently of 12-fold quasicrystals in polymers, nanoparticle mixture and 12-fold and 18-fold quasicrystals in colloidal solutions are important events for the study of quasicrystals. To describe the mechanical behaviour we propose a new solid-liquid phase quasicrystal model for some soft matters including polymers and colloids. The so-called new solid-liquid phase, is a new phase model of anisotropic fluid, but different from liquid crystal phase, here the structure presents quasiperiodic symmetry. Based on the model, the elasticity, fluidity and viscosity of the material have been studied, the relevant mathematical theory has also been proposed. Some mathematical solutions of the theory are discussed.