Related papers: Minkowski Functionals of Abell/ACO Clusters
(abridged) We estimate the cluster-galaxy cross-correlation function (Xi_cg), from the APM galaxy and galaxy cluster surveys, both in real space from the inversion of projected statistics and in redshift space using the galaxy and cluster…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
As deeper galaxy catalogues are soon to come, it becomes even more importantto measure large-scale fluctuations in the catalogues with robust statistics that cover all moments of the galaxy distribution.In this paper we reinforce a direct…
The Algebraic Cluster Model(ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable…
The probability distribution $\mu_{cl}$ of a general cluster point process in a Riemannian manifold $X$ (with independent random clusters attached to points of a configuration with distribution $\mu$) is studied via the projection of an…
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…
In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…
We investigate the statistical properties of the APM-Stromlo redshift survey by using the concepts and methods of modern Statistical Physics. We find that galaxy distribution in this survey exhibits scale invariant properties with fractal…
Using a suite of $N$-body simulations we study the angular clustering of galaxies, halos, and dark matter in $\mathrm{\Lambda \text{CDM}}$ and Modified Gravity (MG) scenarios. We consider two general categories of such MG models, one is the…
The dynamic behavior of cluster algorithms is analyzed in the classical mean field limit. Rigorous analytical results below $T_c$ establish that the dynamic exponent has the value $z_{sw}=1$ for the Swendsen-Wang algorithm and $z_{uw}=0$…
Minkowski's question mark function is the distribution function of a singular continuous measure: we study this measure from the point of view of logarithmic potential theory and orthogonal polynomials. We conjecture that it is regular, in…
We present the composite luminosity function (hereafter LF) of galaxies for 80 Abell clusters studied in our survey of the Northern Hemisphere, using DPOSS data in the framework of the CRoNaRio collaboration. Our determination of the LF has…
Deep imaging data from the Keck II telescope are employed to study the globular cluster (GC) populations in the cores of six rich Abell clusters. The sample includes A754, A1644, A2124, A2147, A2151, and A2152, and spans the redshift range…
The spatial distribution of galaxy clusters is a valuable probe for inferring fundamental cosmological parameters. We measured the clustering properties of dark matter haloes from the \textsc{Pinocchio} simulations, in the redshift range…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution…
We consider mean-field models for data--clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of…
We present a new determination of the mass function of galaxy clusters, based on optical virial mass estimates for a large sample of 152 nearby (z\le0.15) Abell-ACO clusters, as provided by Girardi et al. (1998). This sample includes both…
We discuss how different theoretical predictions for the variance $\sigma^2$ of the distribution of radio sources can be matched to measurements from the FIRST survey at different flux limits. The predictions are given by the integration of…
The Minkowski product of unit quaternion sets is introduced and analyzed, motivated by the desire to characterize the overall variation of compounded spatial rotations that result from individual rotations subject to known uncertainties in…