风车图案和粉末衍射
Pinwheel patterns and powder diffraction
摘要：
风车图案及其高维概化显示连续的圆形或球形对称性，尽管是完美有序的。同样的对称性也出现在相应的衍射图像中。有趣的是，它们也来自无定形系统，并且当通过粉末衍射研究时也来自规则晶体。我们目前的第一个步骤和结果对一个一般的框架，调查这样的系统，重点是统计特性，有助于理解和比较的衍射图像。我们专注于属性，可通过一个替代的替代规则的风车瓷砖，基于两个不同的prototile。由于惊人的相似性，我们比较我们的结果与玩具模型的粉末衍射的正方形晶格。
英文摘要：
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.
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。
