完全连接的N维骨架：探索宇宙网的演化
The fully connected N-dimensional skeleton: probing the evolution of the cosmic web
摘要：
本文提出了一种计算密度场临界子集全谱系的方法。它是基于分水岭技术，并使用概率传播计划，以提高质量的分割，绕过离散的采样。它可以应用于任意尺寸和几何形状的空间。对于一个$d$维空间，这种递归的空间分割产生了一系列$n$维子空间的$d-1$，这些子空间完全表征了密度场的拓扑.层次结构的最后一个一维流形是场的主要临界线的全连通网络：骨架。它对应于连接最大值和鞍点的线的子集，并提供了构成宇宙网络的细丝的定义，作为一个精确的物理对象，这使得计算其任何属性成为可能，例如其长度，曲率，连通性等。当骨架提取应用于宇宙学N体模拟的初始条件和他们现在的非线性对应，它表明，宇宙网络的时间演化，作为跟踪的骨架，以及占Zel'dovich近似。将这个骨架与经历泽尔多维奇映射的初始骨架进行比较，表明在宇宙网的形成过程中有两种效应在竞争：一方面，通过初始条件的骨架的简单变形捕获的较大细丝的一般膨胀，另一方面，更多的较小细丝的收缩，融合和消失。其他应用的N维骨架和它的峰值补丁层次进行了讨论。
英文摘要：
A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the discreteness of the sampling. It can be applied within spaces of arbitrary dimensions and geometry. This recursive segmentation of space yields, for a $d$-dimensional space, a $d-1$ succession of $n$-dimensional subspaces that fully characterize the topology of the density field. The final 1D manifold of the hierarchy is the fully connected network of the primary critical lines of the field : the skeleton. It corresponds to the subset of lines linking maxima to saddle points, and provides a definition of the filaments that compose the cosmic web as a precise physical object, which makes it possible to compute any of its properties such as its length, curvature, connectivity etc... When the skeleton extraction is applied to initial conditions of cosmological N-body simulations and their present day non linear counterparts, it is shown that the time evolution of the cosmic web, as traced by the skeleton, is well accounted for by the Zel'dovich approximation. Comparing this skeleton to the initial skeleton undergoing the Zel'dovich mapping shows that two effects are competing during the formation of the cosmic web: a general dilation of the larger filaments that is captured by a simple deformation of the skeleton of the initial conditions on the one hand, and the shrinking, fusion and disappearance of the more numerous smaller filaments on the other hand. Other applications of the N dimensional skeleton and its peak patch hierarchy are discussed.
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。
