Scalar and vector perturbations in a universe with nonlinear perfect fluid

We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.

Redistribution and realization of energy at different scale-hierarchical levels of coalrock massif

The research of redistribution and realization of energy at different scale-hierarchical levels at the Donbas coalrock massif based on the parameters of faultings and gas-dynamic phenomena has been conducted. It is proved that the energy transfer, incoming by impulses in post-inversion time of the geological development in Donbas, occurs throughout the whole structure of coal, due to the formation of energy connection between individual elements of the molecular structure. This process is accompanied by transition of free energy into a bound state with increase in ordering of the molecular structure and aromaticity of the coal substance (local increase in the degree of catagenetic transformations). The conditions of energy accumulation and realization depend on the peculiarities of molecular processes occurring in dislocations of different types. Less energy is accumulated in tensile zones than in compression zones, which is confirmed by the intensity of coal and gas outbursts. It has been established that the energy entering the multifractal geological environment in Donbas from external sources is also redistributed fractionally by the system, causing the formation of multiscale discrete inhomogeneities, which provides the massif with specific properties and ability to self-organization. A fractal model of the structure of the coalrock massif is proposed.

Cosmic screening of the gravitational interaction

We study a universe filled with cold dark matter in the form of discrete inhomogeneities (e.g. galaxies) and dark energy in the form of a continuous perfect fluid. We develop a first-order scalar perturbation theory in the weak gravity limit around a spatially flat Friedmann universe. Our approach works at all cosmic scales and incorporates linear and nonlinear effects with respect to energy density fluctuations. The gravitational potential can be split into individual contributions from each matter source. Each potential is characterized by a Yukawa interaction with the same range, which is of the order of 3700 Mpc at the present time. The derived equations can form the theoretical basis for numerical simulations for a wide class of modern cosmological models.

Dynamic Properties of Composite Materials Using a T-Matrix to Describe Microstructure

ABSTRACTA dispersion equation is obtained for plane wave propagation in a discrete random medium. The effect of multiple scattering between the discrete inhomogeneities, statistical correlation in the position of the scatterers, details of the geometry, size and properties of the inhomogeneity via the T-matrix are considered. The resulting effective wavenumber for the average or composite medium depends on the above parameters and the frequency. The complex effective wavenumber in turn can be related to the effective properties of the composite material. The formalism is extremely well suited for numerical computation and can thus yield results suited for engineering applications. The other advantage is that the generality of the T-matrix description makes it convenient for describing acoustic, electromagnetic and elastodynamic problems.