标题： 针轮图案和粉末衍射 显示英文标题

标题： Pinwheel patterns and powder diffraction

摘要： 尽管锯齿形图案及其高维推广表现出连续的圆或球对称性，但它们是完全有序的。 同样的对称性在相应的衍射图像中出现。 有趣的是，它们也来自于无定形系统，以及在通过粉末衍射研究时的常规晶体。 我们提出了调查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。 我们专注于可通过锯齿形铺砌的替代规则访问的特性，该规则基于两种不同的原型瓷砖。 由于明显的相似性，我们将我们的结果与正方形晶格的粉末衍射的玩具模型进行比较。 显示英文摘要

摘要： Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they also arise from amorphous systems, and also from regular crystals when investigated by powder diffraction. 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. We concentrate on properties that are accessible via an alternative substitution rule for the pinwheel tiling, based on two different prototiles. Due to striking similarities, we compare our results with the toy model for the powder diffraction of the square lattice.