Voronoi镶嵌和宇宙网络：宇宙中的空间模式和聚类
Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe
摘要：
宇宙物质的空间分布在几兆秒差距到一百多兆秒差距的尺度上，呈现出一种突出而普遍的泡沫状模式。Voronoi网格是一种灵活的数学模型，用于描述这种网状的空间模式。它们可能是低密度膨胀的空洞区域决定了兆秒差距宇宙的空间组织，而物质则聚集在空洞之间的高密度非连续性和壁状空隙中的演化的自然渐近结果。我们描述了正在进行的调查的各种方面的宇宙学相关的空间分布和统计的框架内的Voronoi镶嵌的结果。特别诱人的是发现一个深刻的缩放的集群强度和集群程度的棋盘形节点的分布，暗示的集群属性的星系团。细胞模式可能是一个内在的“几何偏差”聚类的来源。
英文摘要：
The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial patterns. They would be the natural asymptotic result of an evolution in which low-density expanding void regions dictate the spatial organization of the Megaparsec Universe, while matter assembles in high-density filamentary and wall-like interstices between the voids. We describe the results of ongoing investigations of a variety of aspects of cosmologically relevant spatial distributions and statistics within the framework of Voronoi tessellations. Particularly enticing is the finding of a profound scaling of both clustering strength and clustering extent for the distribution of tessellation nodes, suggestive for the clustering properties of galaxy clusters. Cellular patterns may be the source of an intrinsic ``geometrically biased'' clustering.
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