参数化准周期性：广义Poisson求和及其在修正Fibonacci天线阵中的应用
Parameterizing Quasiperiodicity: Generalized Poisson Summation and Its Application to Modified-Fibonacci Antenna Arrays
摘要：
最近发现的“准晶体”，其X射线衍射图案揭示了某些不符合空间周期性的特殊功能，激发了研究“非周期秩序”的波动动力学含义。在天线阵列的辐射特性的上下文中，波的相互作用与准周期顺序的一个有启发性的新的（规范）的例子说明在这里为一维（1-D）阵列配置的基础上的“修改的斐波那契”序列，利用两个尺度的推广的标准泊松求和公式的周期性阵列。这使得一个“准Floquet”的辐射场的分析参数化，它提供了一些指导性的见解与准周期性的顺序相关的基本波机制，突出与周期性的情况下的相似性和差异。例子显示准周期无限和空间截断阵列，简要讨论计算问题和潜在的应用。
英文摘要：
The fairly recent discovery of "quasicrystals", whose X-ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of "aperiodic order". Within the context of the radiation properties of antenna arrays, an instructive novel (canonical) example of wave interactions with quasiperiodic order is illustrated here for one-dimensional (1-D) array configurations based on the "modified-Fibonacci" sequence, with utilization of a two-scale generalization of the standard Poisson summation formula for periodic arrays. This allows for a "quasi-Floquet" analytic parameterization of the radiated field, which provides instructive insights into some of the basic wave mechanisms associated with quasiperiodic order, highlighting similarities and differences with the periodic case. Examples are shown for quasiperiodic infinite and spatially-truncated arrays, with brief discussion of computational issues and potential applications.
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