  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.
