Solutions for hydrodynamics of 5-and 10-fold symmetry quasicrystals

doi:10.1007/s10483-016-2133-9

Abstract

Abstract:

This study carries out a complete analysis of time-space solution of hydrodynamics of pentagonal/decagonal quasicrystals. The behaviors of wave propagation for phonons and diffusion for phasons and coupling between phonon-phason fields are explored explicitly. Comprehensive discussion on physical time-space variations of all hydrodynamic field variables of the alloy quasicrystals is given. The computational specimen is simple, convenient in testing computational results, and provides a possibility that is easy to test experimentally. The quantitative results of mass density, viscosity velocities, phonon displacements, phason displacements, phonon stresses, phason stresses, viscosity stresses, and their time-space variations help us understand the motion of solid quasicrystals in a hydrodynamic condition (long-wavelength and low-frequency). The analysis presented in this paper can be used for octagonal and dodecagonal quasicrystals and is easily extended to other two-dimensional quasicrystals and three-dimensional icosahedral quasicrystals. Some problems explored by the computational results are also discussed.

Key words: mathematical solution, finite difference method, quasicrystal, hydrodynamics

2010 MSC Number:

74C20

Hui CHENG, Tianyou FAN, Hao WEI. Solutions for hydrodynamics of 5-and 10-fold symmetry quasicrystals. Applied Mathematics and Mechanics (English Edition), 2016, 37(10): 1393-1404.

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