Related papers: Scaling Laws in the Cosmic Structure and Renormali…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
The process of formation of fractal structure in one-dimensional self-gravitating system is examined numerically. It is clarified that structures created in small spatial scale grow up to larger scale through clustering of clusters, and…
A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…
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…
Unless there is evidence for fractal scaling with a single exponent over distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be questioned. The…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large scale structures in the Universe is that they occupy a relatively…
We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description…
The surface density of the star formation rate in different galaxies, as well as in different parts of a single galaxy, scales nonlinearly with the surface density of the total gas. This observationally established relation is known as the…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
Over the past three decades the established view of a nearly homogeneuous, featureless Universe on scales larger than a few Megaparsec has been completely overhauled. In particular through the advent of ever larger galaxy redshift surveys…
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…
The geometrically different plan forms of near wall plume structure in turbulent natural convection, visualised by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and…