Related papers: Fractal large-scale structure from a stochastic sc…
Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale…
A standard paradigm is now available for the recent evolution (z < 10) of structure on galactic and larger scales. Most of the matter is assumed to be dark and dissipationless and to cluster hierarchically from gaussian initial conditions.…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…
This article presents a statistical-mechanical treatment of a relationship (the force equation) between the gravitational potential for two particles and the correlation functions in a relaxed distribution of particles with different…
This article reviews the prevailing paradigm for how galaxies and larger structures formed in the universe: gravitational instability. Basic observational facts are summarized to motivate the standard cosmological framework underlying most…
Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D,…
Recent observational results indicate that the functional shape of the spatially-resolved star formation-molecular gas density relation depends on the spatial scale considered. These results may indicate a fundamental role of sampling…
We discuss how luminosity and space distribution of galaxies are naturally linked in view of their multifractal properties. In particular we show that the mass (luminosity) function corresponding to a multifractal distribution in a given…
Empirical star formation laws from the last 20 years are reviewed with a comparison to simulations. The current form in main galaxy disks has a linear relationship between the star formation rate per unit area and the molecular cloud mass…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations…
In a large scale view of the universe, galaxies are the basic unit of structure. A typical bright galaxy may contain 100 billion stars and span tens of thousands of light years, but the empty expanses between the galaxies are much larger…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
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…
The flocculent structure of star formation in 7 galaxies has a Fourier transform power spectrum for azimuthal intensity scans with a power law slope that increases systematically from -1 at large scales to -1.7 at small scales. This is the…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Recent studies have shown that massive galaxies in the distant universe are surprisingly compact, with typical sizes about a factor of three smaller than equally massive galaxies in the nearby universe. It has been suggested that these…