Related papers: Characterizing cluster morphology using vector-val…
The formation, inner properties, and spatial distribution of galaxy groups and clusters are closely related to the background cosmological model. We use numerical simulations of variants of the CDM model with different cosmological…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
In this paper we explore the mathematical properties of wavefunction coefficients in power-law FRW cosmologies, and establish their relation to cluster algebras. We focus on the particular contributions to the wavefunction coefficient…
The study of the morphology of 2D projected maps of galaxy clusters is a suitable approach to infer, from real data, the dynamical state of those systems. We recently developed a new method to recover the morphological features in galaxy…
We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular…
We investigate the internal structure of clusters of galaxies in high-resolution N-body simulations of 4 different cosmologies. There is a higher proportion of disordered clusters in critical-density than in low-density universes, although…
The phases of the Fourier modes appearing in a plane-wave expansion of cosmological density fields play a vital role in determining the morphology of gravitationally-developed clustering. We demonstrate this qualitatively and quantitatively…
A sample of hundreds of simulated galaxy clusters is used to study the statistical properties of galaxy cluster formation. Individual assembly histories are discussed, the degree of virialization is demonstrated and various commonly used…
We explore the use of the tangential component of weak lensing shear to characterize the ellipticity of clusters of galaxies. We introduce an ellipticity estimator, and quantify its properties for isolated clusters from LCDM N-body…
We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers ($\beta_{\rm k},k=1,...,D$), which…
We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on…
The massive dark matter halos that host groups and clusters of galaxies have observable properties that appear to be log-normally distributed about power-law mean scaling relations in halo mass. Coupling this assumption with either…
We review recent advancements in cosmology with galaxy clusters. Galaxy clusters are the most massive objects in the Universe. Consequently the cluster number density as a function of cluster mass, or cluster abundance, is sensitive to…
We investigate the supercluster shape properties of the all-sky observed (Abell/ACO) and simulated (Virgo data) cluster catalogues using an approach based on differential geometry. We reliably identify rich superclusters by applying…
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
Studies of galaxy clusters have proved crucial in helping to establish the standard model of cosmology, with a universe dominated by dark matter and dark energy. A theoretical basis that describes clusters as massive, multi-component,…
The precise determination of global properties of galaxy clusters, and their scaling relations, is a task of prime importance for the use of clusters as cosmological probes. We performed a detailed XMM-Newton study of 14 X-ray luminous…
We describe a new way to relate an acyclic, skew-symmetrizable cluster algebra to the representation theory of a finite dimensional hereditary algebra. This approach is designed to explain the c-vectors of the cluster algebra. We obtain a…