Related papers: Fractal properties of stellar systems and random f…
Chapter 13: SOC Systems in Astrophysics --- Content list: 13.1 Theory -- 13.1.1 The Sacle-Free Probability Theorem - 13.1.2 The Fractal-Diffusive Spatio-Temporal Relationship - 13.1.3 Size Distributions of Astrophysical Observables - 13.1.4…
The Universe that we know is populated by structures made up of aggregated matter that organizes into a variety of objects; these range from stars to larger objects, such as galaxies or star clusters, composed by stars, gas and dust in…
The analytical generalization of the classical dynamical friction formula (derived under the assumption that all the field particles have the same mass) to the case in which the masses of the field particles are distributed with a mass…
The effect of curvature on the results of fractal analyses of the galaxy distribution is investigated. We show that, if the universe satisfies the criteria of a wide class of parabolic homogeneous models, the observers measuring the fractal…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
This letter matches the shape of the star formation intensity distribution function to empirical laws such as the Schmidt law. The shape of the distribution at a redshift of one is reproduced from the empirical Schmidt law with a critical…
The diffusion of electronic wave packets in one-dimensional systems with on-site, binary disorder is numerically investigated within the framework of a single-band tight-binding model. Fractal properties are incorporated by assuming that…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
It is presented the general properties of N-dimensional multi-component or many-particle systems exhibiting self-similar hierarchical structure. Assuming there exists an optimal coarse-graining scale at which the quality and diversity of…
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W(F,d…
One of the most well known random fractals is the so-called Fractal percolation set. This is defined as follows: we divide the unique cube in $\mathbb{R}^d$ into $M^d$ congruent sub-cubes. For each of these cubes a certain retention…
We analyze the internal velocity dispersions of a sample of 172 nearby galaxy clusters (z < 0.15), each of which has at least 30 available galaxy redshifts, and spans a large richness range. Cluster membership selection is based on…
This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schr\"{o}dinger Equation and provides insights into its consequences. The study presents a General Solution for…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…
The conjecture that dark matter in galaxies is mostly cold fractal gas is developed in the more general context of the thermodynamics of the ideal isothermal gas subject to gravitational instability. This simple gas model already contains…
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…
This work examines a relativistic model for the observed inhomogeneities of the large scale structure where the hypothesis that this structure can be described as being a self-similar fractal system is advanced. The concept of hierarchical…