Three-dimensional equations of generalized dynamics of 18-fold symmetry soft-matter quasicrystals

This letter presents a three-dimensional form of governing equations of generalized dynamics of 18-fold symmetry soft-matter quasicrystals, according to the dynamics basis there are first and second phason elementary excitations apart from phonons and fluid phonon. In the derivation, the group representation theory is a key point. The complete form of the theory includes an equation of state. The governing equations present some important meaning in the study on thermodynamics of the matter which is also introduced.