Related papers: Power spectrum for fractal distributions
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
Stability and diversity are two key properties that living entities share with spin glasses, where they are manifested through the breaking of the phase space into many valleys or local minima connected by saddle points. The topology of the…
This comment is in response to the paper by L. Guzzo recently appeared in ``New Astronomy'' related to our work. The subject of the discussion concerns the correlation properties of galaxy distribution in the available 3-d samples. There is…
We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We study the cosmological power spectra (PS) of the differential and integral galaxy volume number densities $\gamma_i$ and $\gamma_i^{*}$, constructed with the cosmological distances $d_i$ $(i=A,G,L,Z)$, where $d_A$ is the angular diameter…
We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…
The fractal structure with a power index of 2 is considered within the framework of the universe with the linear law of evolution. The fractal structure arises due to the linear evolution of the scale of mass. Potential fluctuations connect…
Nonlinear dissipative systems in the state of self-organized criticality release energy sporadically in avalanches of all sizes, such as in earthquakes, auroral substorms, solar and stellar flares, soft gamma-ray repeaters, and pulsar…
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…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
Three-dimensional fractal models on grids of 200**3 pixels are generated from the inverse Fourier transform of noise with a power law cutoff, exponentiated to give a log normal distribution of density. The fractals are clipped at various…
The `plate tectonics' is an observed fact and most models of earthquake incorporate that through the frictional dynamics (stick-slip) of two surfaces where one surface moves over the other. These models are more or less successful to…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
I review some results of estimation of the power spectrum of density fluctuations from galaxy redshift surveys and discuss advances that may be possible with the Sloan Digital Sky Survey. I then examine the realities of power spectrum…
The primordial matter power spectrum quantifies fluctuations in the distribution of dark matter immediately following inflation. Over cosmic time, over-dense regions of the primordial density field grow and collapse into dark matter halos,…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
Using a set of 28 high resolution, high signal to noise ratio (S/N) QSO Ly-alpha absorption spectra, we investigate the non-Gaussian features of the transmitted flux fluctuations, and their effect upon the power spectrum of this field. We…