A Stress Analysis of Some Fundamental Specimens of Soft-Matter Quasicrystals with Eightfold Symmetry Based on Generalized Dynamics

This paper reports a stress analysis of some fundamental samples made of soft-matter quasicrystals with 8-fold symmetry based on the generalized dynamics. The most distinction from the hydrodynamics for solid quasicrystals is that the structure of soft matter belongs to a complex liquid, which is an intermediate phase between solid and liquid and behaves natures of both solid and liquid. In addition, the soft-matter quasicrystals possess high symmetry, and the symmetry breaking is of fundamental importance. So the Landau symmetry breaking theory and elementary excitation principle are therefore the paradigm of the study of soft-matter quasicrystals. Soft-matter quasicrystals belong to the complex fluid, in which the fluid phonon elementary excitation is introduced apart from the phonon and phason elementary excitations. With this model and the equation of state, the equations of motion for possible soft-matter quasicrystals of 8-fold symmetry are derived. The initial boundary value problems for the xy plane field are solved by applying the finite difference method, in which the z-direction represents the 8-fold symmetry axis. A complete hydrodynamics analysis is given to quantitatively explore the phonon, phason, and fluid fields as well as their interactions in the physical time-space domain. The analysis shows the governing equations are exact to the prediction of the dynamics of soft-matter quasicrystals. The computational results reveal the gigantic differences of physical properties between solid and soft-matter quasicrystals.