Related papers: Gravitational force distribution in fractal struct…
The large scale gravitational potential distribution and its influence on the large-scale matter clustering is considered on the basis of six simulations. It is found that the mean separation between zero levels of the potential along…
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…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an…
The large-scale structure in the Universe is believed to arise out of small random density perturbations generated in the very early Universe, that are amplified by gravity. Large and usually intricate N-body simulations are typically…
We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson…
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…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
We analyse the spatial inhomogeneities ('spatial clustering') in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be…
We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
The gas clouds of the interstellar medium have a fractal structure, the origin of which has generally been thought to lie in turbulence. The energy of turbulence could come from galactic rotation at large-scale, then cascade down to be…
We show that the characteristic sizes of astrophysical and cosmological structures, where gravity is the only overall relevant interaction assembling the system, have a phenomenological relation to the microscopic scales whose order of…
This paper continues previous work on a novel alternative model of gravity, based on the theory of fractional-dimension spaces applied to Newton's law of gravitation. In particular, our Newtonian Fractional-Dimension Gravity is now applied…
Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite $N$ fluctuations and perturbations induced by the…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…