Related papers: Analysis of Large Scale Structure using Percolatio…
The X-ray morphologies of clusters of galaxies display significant variations, reflecting their dynamical histories and the nonlinear dependence of X-ray emissivity on the density of the intracluster gas. Qualitative and quantitative…
The traditional method of morphological classification, by visual inspection of images of uniform quality and by reference to standards for each type, is critically examined. The rate of agreement among traditional morphologists on the…
We study the influence of the various parameters of scenarios of large-scale structure formation on properties of galaxy clusters, and investigate which cluster properties are most sensitive to these parameters. We present a set of large…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters. The early Universe, however, was almost smooth, with only slight 'ripples' seen in the cosmic microwave background radiation. Models of the…
Since the appearance of the classical paper of Lifshitz almost half a century ago, linear stability analysis of cosmological models is textbook knowledge. Until recently, however, little was known about the behavior of higher than linear…
Molecular clouds show complex structures reflecting their non-linear dynamics. Many studies investigating the bridge between their morphology and physical properties have shown the value of non-Gaussian higher-order statistics in capturing…
Modern redshift surveys such as the 2 degree field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS) reveal the fully 3 dimensional distribution of a million or so galaxies over a large cosmological volume. Visually…
The discovery of the large-scale structure has transformed our view of galaxy formation and evolution. Filaments of the cosmic web provide key environments that channel the growth of structures. Guided by predictions from cosmological…
Measurements of the peculiar velocities of large samples of galaxies enable new tests of the standard cosmological model, including determination of the growth rate of cosmic structure that encodes gravitational physics. With the size of…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
Using Shapefinders, which are ratios of Minkowski functionals, we study the morphology of neutral hydrogen (HI) density fields, simulated using semi-numerical technique (inside-out), at various stages of reionization. Accompanying the…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Within the framework of hierarchical clustering scenarios, we investigate the consequences for the properties of virialized halos of the constraints provided by numerical simulations on the first few correlation functions. Thus, we show…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
We present a morphological study of the two richest superclusters from the 2dF Galaxy Redshift Survey (SCL126, the Sloan Great Wall, and SCL9, the Sculptor supercluster). We use Minkowski functionals, shapefinders, and galaxy group…