论文标题
通货膨胀与投影集中的基于上的系统：窗口在平均和衍射中的作用
Inflation versus projection sets in aperiodic systems: The role of the window in averaging and diffraction
论文作者
论文摘要
基于剪切和项目方法的瓷砖是用于描述Aperiodic固体的关键模型系统。通常，晶体学的兴趣量涉及在大斑块上平均，并且仅在无限体积的极限中得到很好的定义。特别是，自相关和衍射度量就是这种情况。对于切割和项目系统，可以方便地将平均传输到内部空间，这意味着处理相应的窗口。我们以斐波那契平铺的平均炮击数量的示例来说明这一点，并查看此示例的衍射标准方法。此外，我们讨论了通货膨胀对称切割和项目结构的最新发展，这些发展是基于重生合作共生的内部对应物。最后，我们简要审查了最近越来越受欢迎的超均匀性的概念及其对大约结构的应用。
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the infinite-volume limit. In particular, this is the case for autocorrelation and diffraction measures. For cut and project systems, the averaging can conveniently be transferred to internal space, which means dealing with the corresponding windows. We illustrate this by the example of averaged shelling numbers for the Fibonacci tiling and review the standard approach to the diffraction for this example. Further, we discuss recent developments for inflation-symmetric cut and project structures, which are based on an internal counterpart of the renormalisation cocycle. Finally, we briefly review the notion of hyperuniformity, which has recently gained popularity, and its application to aperiodic structures.
