宇宙网的几何学：来自Delaunay网格的Minkowski泛函
Geometry of the Cosmic Web: Minkowski Functionals from the Delaunay Tessellation
摘要：
我们提出了一种新的方法来计算Minkowski泛函直接从点分布的Delaunay曲面提取的等密度曲面。这是一个重要的一步相比，以前的宇宙学研究时，等密度面是建立在一个统一的立方网格，因此具有统一的空间分辨率的领域。在宇宙学中，密度场是一个特别有趣的概念，它是从星系位置的高度不均匀分布中得到的。因此，空间均匀网格所带来的约束严重限制了对超星系团和星系空洞等大尺度天体的几何和形状的研究。我们的技术有可能消除这些限制中的大部分。一些简单的几何模型和应用程序的密度场的N体模拟的方法进行了测试。
英文摘要：
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological studies when the isodensity surface was built in the field on a uniform cubic grid and therefore having a uniform spatial resolution. The density field representing a particular interest in cosmology is the density of galaxies which is obtained from the highly nonuniform distribution of the galaxy positions. Therefore, the constraints caused by the spatially uniform grid put severe limitations on the studies of the geometry and shapes of the large-scale objects: superclusters and voids of galaxies. Our technique potentially is able to eliminate most of these limitations. The method is tested with some simple geometric models and an application to the density field from an N-body simulation is shown.
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