distribution function

The conventional approach to constructing a three-dimensional distribution of the Earth's masses involves using Stokes constants incrementally up to a certain order. However, this study proposes an algorithm that simultaneously considers all of these constants, which could potentially provide a more efficient method. The basis for this is a system of equations obtained by differentiating the Lagrange function, which takes into account the minimum deviation of the three-dimensional mass distribution of the planet's subsoil from one-dimensional referential one.

Recently, the optimization issue relevance of reinforced concrete (RC) structures design solutions through the maximum use of their bearing capacity resource has increased significantly; in turn, solving this issue depends on a fundamental understanding of the reliability and durability concepts. Because any loads, impacts, or bearing capacity reserve parameters are random variables, there is a need to build stochastic models, which can become the “reliability design” concept base shortly.

We propose an approximation of pair correlations for solving the equations of the kinetic theory of long-wave (or large-scale) fluctuations in gaseous media.  The basic ones are the general nonlinear equations of the large-scale fluctuations theory at the kinetic stage of system evolution, derived from the first principles of statistical mechanics.  We show that based on the equations of the long-wave fluctuations kinetics in the case of weak interaction between particles, in the approximation of pair fluctuations it is possible to reproduce the main results of the quasi-linear theory of pl

A kinetic approach based on a modified chain of BBGKI equations for nonequilibrium particle distribution functions was used to describe the ion transfer processes in the ionic solution – porous medium system.  A generalized kinetic equation of the revised  Enskog–Vlasov–Landau theory for the nonequilibrium ion distribution function in the model of charged solid spheres is obtained, taking into account attractive short-range interactions for the ionic solution – porous medium system.

Based on a chain of BBGKI equations with a modified boundary condition that takes into account multiparticle correlations, kinetic equations in the approximate "pairs" collisions and in the polarization approximation, taking into account the interaction through the third particle, obtained.  The specifics of the model representation of the pair potential of particle interaction through short-range and long-range parts were taken into account.  In the case of the short-range potential in the form of the potential of solid spheres, the contribution of Enskog's revised theory to the complete i

The dissolving process of benzoic acid polydisperse mixture in the gas-liquid flow has been examined. On the basis of criterial dependence and the theory of local isotropic turbulence the mass-transfer coefficient was determined experimentally and theoretically and their values were compared. Theoretical calculation of polydisperse mixture dissolution was performed during periodic dissolution under variable driving force. Theoretical and experimental results were compared.