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Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic…
An approach to cosmological modelling is presented that incorporates the inhomogeneous structure of the Cosmic Web, specifically focusing on the interplay between cosmic voids and density walls. We extend the standard homogeneous and…
Three-dimensional fractal models on grids of 200**3 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…
An analytical expression is presented that allows gas-to-dust elemental depletions to be estimated in interstellar environments of different types, including Damped Ly alpha systems, by scaling an arbitrary depletion pattern chosen as a…
We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how…
The kinematics of molecular gas are crucial for setting the stage for star formation. One key question related to the kinematic properties of gas is how they depend on the spatial scale. We aim to describe the CO spectra, velocity…
While galaxy cluster catalogs were compiled many decades ago, other structural elements of cosmic web are detected at definite level only in the newest works. For example, extragalactic filaments were described by velocity field and SDSS…
Many recent models consider the structure of individual interstellar medium (ISM) clouds as a way to explain observations of large parts of galaxies. To compare such models to observations, one must understand how to translate between…
Fundamental thermodynamical concepts and a solid-state point defect elastic model are used to formulate a diffusivity-density scaling function for viscous liquids. It is proved in a straightforward manner that the scaling exponent…
We present a new statistical analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey (data release 7). A set of volume-limited samples shows that the stellar mass of galaxies is concentrated in a range of…
Understanding the distribution and properties of molecular clouds is crucial for tracing the structure and evolution of the interstellar medium and the large-scale morphology of the Milky Way. Here we present an all-sky catalog of 3,345…
The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the…
A self-similar formalism for the study of the gravitational collapse of molecular gas provides an important theoretical framework from which to explore the dynamics of star formation. Motivated by the presence of elongated and filamentary…
We examine how well the physical properties of clumps in turbulent molecular clouds can be determined by measurements of observed clump structures. We compare simulated observations of three-dimensional numerical models of isothermal,…
We study the effect of a weakly driven atomic cloud's polarization distribution on its photon scattering lineshape. In doing this, we find three distinct polarization regimes. First, for dilute clouds, the polarization magnitude is…
It has been recently shown that molecular clouds do not exhibit a unique shape for the column density probability distribution function (Npdf). Instead, clouds without star formation seem to possess a lognormal distribution, while clouds…
It is considered the model of the homogeneous and isotropic universe. The scale of length is defined via the laboratory scale of time by the motion of photon. This leads to the appearance of the inertial forces. The properties of the space…
We introduce a formalism to describe 2D-Potentials for 2D-matter (or charge) distributions with arbitrary elliptical symmetry including varying eccentricity and twisting of the iso-density curves. We use this approach to describe elliptical…
Although there are a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are very few observational studies investigating the relationship between the density variance ($\sigma^2$) and the sonic…
Recently Stanchev et al. (2015) proposed a technique to derive density scaling relations in a star-forming region from analysis of the probability distribution function of column density. We address the possible dependence of the outcome on…