Related papers: Power spectrum for fractal distributions
Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack…
Fluctuations in the boundary region of the Alcator C-Mod tokamak have been analyzed using gas puff imaging data from a set of Ohmically heated plasma density scan experiments. It is found that the relative fluctuation amplitudes are modest…
We discuss the estimation of galaxy correlation properties in several volume limited samples, in different sky regions, obtained from the Fourth Data Release of the Sloan Digital Sky Survey. The small scale properties are characterized…
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
The power spectrum of mass density fluctuations is evaluated from the Mark III and the SFI catalogs of peculiar velocities by a maximum likelihood analysis, using parametric models for the power spectrum and for the errors. The applications…
A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model…
Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
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…
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
Atmospheric flows exhibit selfsimilar fractal spacetime fluctuations manifested as the fractal geometry to global cloud cover pattern and inverse power law form for power spectra of meteorological parameters such as windspeed, temperature,…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
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…
We show that hyperscaling and finite-size scaling imply that the probability distribution of the order parameter in finite size critical systems exhibit data collapse. We consider the examples of equilibrium critical systems, and a…
The model of the universe is considered in which background of the universe is not defined by the matter but is a priori specified as a homogenous and isotropic flat space. The scale factor of the universe follows the linear law. The scale…
Some years ago we proposed a new approach for the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical physics. This led to the surprising result that galaxy correlations are fractal and not…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…