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

TL;DR

This paper develops three-dimensional governing equations for the generalized dynamics of 18-fold symmetry soft-matter quasicrystals, incorporating phonons and phason excitations, with implications for thermodynamics.

Contribution

It introduces a novel three-dimensional formulation of the dynamics equations for 18-fold symmetry quasicrystals using group representation theory.

Findings

Derivation of equations including first and second phason excitations

Inclusion of an equation of state for thermodynamic analysis

Provides a comprehensive theoretical framework for quasicrystal dynamics

Abstract

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.