广义Fibonacci镶嵌的超带隙和周期近似
Super band gaps and periodic approximants of generalised Fibonacci tilings
摘要：
我们目前的数学理论理解广义斐波那契平铺形成的异质材料的透射光谱。我们的结果，第一，超带隙，这是光谱间隙存在的任何周期近似的准晶材料。这个理论，其次，建立了这些周期近似的准确性，在这个意义上，他们忠实地再现了主要的频谱间隙。我们根据相关的传输矩阵的迹线上的生长条件来描述超带隙。我们的理论包括一个大家庭的广义斐波那契镶嵌，包括贵金属平均和金属平均模式。我们证明了我们的基本结果，通过分析三种不同的一维波现象：压缩波在离散的质量弹簧系统，轴向波在结构杆和弯曲波在多支撑梁。在所有这三种情况下，该理论给出了准确的预测的超级带隙，可以忽略不计的计算成本和显着更高的精度比以前的估计。
英文摘要：
We present mathematical theory for understanding the transmission spectra of heterogeneous materials formed by generalised Fibonacci tilings. Our results, firstly, characterise super band gaps, which are spectral gaps that exist for any periodic approximant of the quasicrystalline material. This theory, secondly, establishes the veracity of these periodic approximants, in the sense that they faithfully reproduce the main spectral gaps. We characterise super band gaps in terms of a growth condition on the traces of the associated transfer matrices. Our theory includes a large family of generalised Fibonacci tilings, including both precious mean and metal mean patterns. We demonstrate our fundamental results through the analysis of three different one-dimensional wave phenomena: compressional waves in a discrete mass-spring system, axial waves in structured rods and flexural waves in multi-supported beams. In all three cases, the theory is shown to give accurate predictions of the super band gaps, with negligible computational cost and with significantly greater precision than previous estimates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
