Related papers: Power spectrum for fractal distributions
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
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…
The statistical analysis and the spherical wavelet analysis of the SDSS DR7 quasars distribution and of the WMAP CMB anisotropy are performed. They revealed the qualitative agreement between the angular power spectrum of CMB and the angular…
Fluctuations in the large-scale structure of the Universe contain significant information about cosmological physics, but are modulated in survey datasets by various observational effects. Building on existing literature, we provide a…
A crucial issue in cosmology is the determination of the fluctuation power spectrum.The standard picture of the matter clustering, the Cold Dark Matter model (and its variant), assumes that,on scales smaller than a certain ``flattening…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
Galaxy structures are certainly fractal up to a certain crossover scale \lambda_0. A clear determination of such a scale is still missing. Usually, the conceptual and practical implications of this property are neglected and the structures…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…
The power spectrum (PS) of mass density fluctuations, in the range $0.05 \leq k \leq 0.2 \ihmpc$, is derived from the Mark III catalog of peculiar velocities of galaxies, independent of ``biasing". It is computed from the density field as…
As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
We argue that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of surface fractal is shown to be a sum of the amplitudes of…
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…
We examine the power spectrum of clusters in the Press-Schechter (PS) theory and in N-body simulations to see how the power spectrum of clusters is related to the power spectrum of matter density fluctuations in the Universe. An analytic…
We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various…