This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density γ and the integral differential density γ∗ of the dust distribution in the Einstein-de Sitter...

Power-law relationships appear to characterize many patterns observed in ecology, from the level of individuals to the level of ecosystems (Calder 1984, Gaston and Blackburn 2000). These power laws often hold over scale ranges sufficiently large to justify the search for a unifying theoretical framework explaining the relationship between these patterns. A promising avenue for discovering such ...

Original scientific paper Rock burst is a common serious geological hazard in underground engineering, which seriously affects the progress of projects. The mechanism of rock burst can be explained by the distribution law of rock fragments and its fractal characteristics. A simulation experiment of rock burst was conducted with the granite samples under a biaxial loading machine system to analy...

Study of a mature petroleum play in the Western Canada Sedimentary Basin (WCSB) indicates that the spatial distribution of petroleum accumulations exhibits a self-affinity characteristic. This characteristic motivated the examination of a fractal model for a quantitative description of petroleum resource spatial distribution. The proposed approach transforms the spatial information with respect...

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here one such mixed model, the quenched-trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble- and time-averaged mean-square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergo...

Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the large scale correlations in the galaxy spatial distribution. There are, in fact, no longer doubts since two decades of the existence of very large scale structu...

Three-dimensional fractal models on grids of ∼ 200 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 intensity levels and the mass and size distribution functions of the clipped peaks and their subpeaks are determined. These distribution functions are analogous...

A long standing approximation in EM logging for fractures has been to assume that a fracture is an extended thin sheet, perhaps a half-plane. This approximation can be useful and is theoretically and numerically convenient. However, examination of core, FMS logs, and outcrop reveals that fracture zones can be geometrically self-similar over dimensional scales of less than millimeters to kilomet...

We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, an...

Properties of Tolman-Bondi (TB) model produced by two set of initial conditions, 1) fractal density and simultaneous bang time and 2) fractal density and linear Hubble law, are studied. It is shown for the first set that for some physical resonable values of parameters of the model, the central density and the cosmological density parameter Ω0, an area of compatibility of initial conditions has...