Related papers: Are galaxy distributions scale invariant? A perspe…
Starting with a simple two scalar field system coupled to a modified measure that is independent of the metric, we, first, find a Born-Infeld dynamics sector of the theory for a scalar field and second, show that the initial scale…
We have analyzed the behavior of the correlation length, $r_0$, as a function of the sample depth by extracting from the CfA2 redshift survey volume--limited samples out to increasing distances. For a fractal distribution, the value of…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
We extend a previous analysis [PRL {\bf 80}, 4693 (1998)] of breakdown of dynamical scale invariance in the coarsening of two-dimensional DLAs (diffusion-limited aggregates) as described by the Cahn-Hilliard equation. Existence of a second…
Central place systems have been demonstrated to possess self-similar patterns in both the theoretical and empirical perspectives. A central place fractal can be treated as a monofractal with a single scaling process. However, in the real…
Galaxy velocities in clusters, rotation curves of galaxies, and "vertical" oscillations in the Milky Way currently show too high velocities with respect to the masses thought to be involved. While these velocity excesses are currently…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
A model is presented for the origin of the large scale structure of the universe and their Mass-Radius scaling law; a fractal power law, $M \propto R^D$, with dimension $D=2$, most significantly. The physics is conventional, orthodox, but…
Using a sample of 133 991 galaxies distributed in the sky region $100^{\circ} <\alpha<270^{\circ}$ and $7^{\circ}<\delta<65^{\circ}$, extracted from the SDSS NASA/AMES Value Added Galaxy Catalog (AMES-VAGC), we estimate the fractal…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
We investigate the behaviour of galaxy clustering on large scales using the PSCz catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…
We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We…
In two dimensions, it is well known that the scale invariance can be considered as conformal invariance. However, there is no solid proof of this equivalence in four or higher dimensions. We address this issue in the context of 4d…
In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a model of 2d gravity modified by the $R^2$ term…