标题： 径向形式的泊松求和公式及其在粉末衍射和旋转图案中的应用 显示英文标题

标题： A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns

摘要： 从无定形系统中会产生具有连续旋转对称性的衍射图像，但当用粉末衍射研究规则晶体时也会产生这样的图像。 在理论方面，飞轮图案及其高维推广也显示出这种对称性，尽管它们是完全有序的。 我们提出了迈向研究此类系统的通用框架的第一步和结果，重点在于有助于理解和比较衍射图像的统计特性。 一种用于飞轮镶嵌的替代替换规则，使用两种不同的原型瓷砖，允许推导出这个仍有些神秘的例子的若干组合和谱特性。 这些结果与正方形晶格及其粉末衍射的特性进行了比较。 显示英文摘要

摘要： Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction.