Symplectic approach for plane elasticity problems of two-dimensional octagonal quasicrystals
Symplectic approach for plane elasticity problems of two-dimensional octagonal quasicrystals
复制标题
二维八角准晶平面弹性问题的辛法
DOI：
10.1016/j.amc.2021.126043
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发表时间：
2021
影响因子：
4
通讯作者：
Alatancang Chen
中科院分区：
文献类型：
--
作者：
Yanfen Qiao;Guolin Hou;Alatancang Chen
本文采用辛方法（SA）来分析二维（2D）八角准晶体（QC）的平面弹性问题。首先将点群 8mm 八角形量子点的平衡方程转化为哈密顿对偶方程。然后应用变量分离的方法推导出相应的哈密顿算子矩阵的辛特征值问题。基于特征值分析和辛特征向量展开，建立了具有选定边界条件的点群8mm八角QC的精确解析解。通过有限积分变换方法 (FITM) 给出并验证了声子和相子位移的数值结果，这对于其他数值方法的验证很有用。此外，受SA的启发，简化了劳厄15级八角QCs的平面弹性平衡方程，这是一个悬而未决的问题。这里提出的方法是合理和系统的，具有清晰的逐步推导程序，因此它具有解决其他量子力学平面弹性问题的潜力。本文获得的结果可以作为未来研究的基准。
The symplectic approach (SA) is used in this paper to analyze the plane elasticity problems of two-dimensional (2D) octagonal quasicrystals (QCs). The equilibrium equations for point group 8mm octagonal QCs are first transferred into Hamiltonian dual equations. Then the symplectic eigenvalue problem of the corresponding Hamiltonian operator matrix is derived by applying the method of separation of variables. Based on the eigenvalue analysis and expansion of symplectic eigenvectors, the exact analytic solutions for point group 8mm octagonal QCs with selected boundary conditions are established. Numerical results for the phonon and phason displacements are presented and validated by the finite integral transform method (FITM), which are useful for validation of other numerical methods. In addition, inspired by the SA, the equilibrium equations of plane elasticity of octagonal QCs with Laue class 15 are simplified, which is an open problem. The approach presented here is rational and systematic with clear step-by-step derivation procedure, thus it has potential for plane elasticity problems of other QCs. The results obtained in this paper can serve as benchmarks for future researches.
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