Related papers: Power spectrum for fractal distributions
The properties of the galaxy distribution at large scales are usually studied using statistics which are assumed to be self-averaging inside a given sample. We present a new analysis able to quantitatively map galaxy large scale structures…
While galaxy cluster catalogs were compiled many decades ago, other structural elements of cosmic web are detected at definite level only in the newest works. For example, extragalactic filaments were described by velocity field and SDSS…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
We explore the deep ultraviolet (that is, short-distance) limit of the power spectrum (PS) and of the correlation function of a cold dark matter dominated Universe. While for large scales the PS can be written as a double series expansion,…
The position of the degree scale feature in the CMB spectrum is determined within the framework of the fractal universe with a power index of 2.
In the cold dark matter (CDM) picture of structure formation, galaxy mass distributions are predicted to have a considerable amount of structure on small scales. Strong gravitational lensing has proven to be a useful tool for studying this…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
To test the primordial power spectra predicted by a double inflationary model with a break of amplitude $\Delta=3$ at a scale of $2\pi/k\approx 10 \hm$ and CDM as dominant matter content, we perform PM simulations with 128$^3$ particles on…
We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) $\Gamma(r)$ is a power law up to the sample effective depth ($\sim 30 h^{-1}Mpc$), showing the…
We present a brief introduction to the statistical properties of systems with large fluctuations. We point out that for such systems the relevant statistical quantities are scaling exponents and the nature of fluctuations is completely…
The power spectrum (PS) of {\it mass} density fluctuations, independent of ``biasing", is estimated from the Mark3 Catalog of Peculiar Velocities of galaxies using Bayesian statistics. A parametric model is assumed for the PS, and the free…
Using the apparatus of correlation Gamma-function (``conditional density''), we have analyzed spatial clustering of objects from several different samples of galaxies, clusters and superclusters. On small scales the distribution of objects…
A novel fractal analysis of the cosmic web structure is carried out, employing the Sloan Digital Sky Survey, data release 7. We consider the large-scale stellar mass distribution, unlike other analyses, and determine its multifractal…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
The nearest neighbor distribution (Chandrasekhar 1943) is generalized to fractal stellar systems.For such systems an asymptotic distribution of the magnitude of large random forces and a formula for the effective mean interparticle spacing…
We estimate the mass density fluctuations power spectrum (PS) on large scales by applying a maximum likelihood technique to the peculiarvelocity data of the recently completed redshift-distance survey of early-type galaxies (ENEAR). The…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…