Related papers: Power spectrum for fractal distributions
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…
We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
We introduce the basic techniques used for the analysis of three dimensional and two dimensional galaxy samples. We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each…
We propose a new method to analyze fluctuations in the strength function phenomena in highly excited nuclei. Extending the method of multifractal analysis to the cases where the strength fluctuations do not obey power scaling laws, we…
We derive the effective potential for composite fields in a class of (quasi-) planar models with long-range interactions. This class of models can be relevant for high temperature superconductors and graphite. The fractal structure of the…
Frequency power spectra due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes are considered. For pulses with constant duration, there is an exponential frequency spectrum which is independent of…
City size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from…
This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a…
We present a simple numerical model for investigating the general properties of fragmentation. By use of molecular dynamics simulations, we study the impact fragmentation of a solid disk of interacting particles with a wall. Regardless of…
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…
The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six…
The dissipation of acoustic wave propagation has long been found to obey an empirical power function of frequency, whose exponent parameter varies through different media. This note aims to unveil the inherent relationship between this…
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated…
We investigate numerically the power-law random matrix ensembles. Wavefunctions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
We discuss properties of Alfv\'enic fluctuations with large amplitude in plasmas characterised by low magnetic field compression. We note that in such systems power laws can not develop with arbitrarily steep slopes at large scales, i.e.…
We describe an attempt to reconstruct the initial conditions for the formation of cosmological large-scale structure. The power spectrum of the primordial fluctuations is affected by bias, nonlinear evolution and redshift-space distortions,…