论文标题
在常规和随机的二维十字架上
On regular and random two-dimensional packing of crosses
论文作者
论文摘要
通常，包装问题，即使是常规几何形状的物体，通常都是非平凡的。对于少数特殊的形状，已知晶体以及随机的不规则的二维（2D）包装的特征。 2D十字的包装尚不属于解决问题的类别。我们在具有不同长宽比（臂宽度与长度）的杂交的实验中证明，实际上通过随机包装来实现堆积分数，我们将它们与最密集的常规填料结构进行了比较。我们确定将随机放置杂交集合的局部相关性压实在平面中，直到它们堵塞为止。在2至3个交叉长度上发现了短距离定向顺序。同样，邻居空间分布的相关性延伸了2至3个十字。显然，在空间相关函数中，十字的几何形状与峰之间没有简单的关系。但是，方向相关性的某些特征在直觉上很明显。
Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packings are known. The packing of 2D crosses does not yet belong to the category of solved problems. We demonstrate in experiments with crosses of different aspect ratios (arm width to length) which packing fractions are actually achieved by random packing, and we compare them to densest regular packing structures. We determine local correlations of the orientations and positions after ensembles of randomly placed crosses were compacted in the plane until they jam. Short-range orientational order is found over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions of neighbors extend over 2 to 3 crosses. Apparently, there is no simple relation between the geometries of the crosses and peaks in the spatial correlation functions. Some features of the orientational correlations, however, are intuitively evident.
