This article is an attempt to study the process of Rayleigh–Benard convective instability by the methods used for mathematical modeling of critical phenomena as nonequilibrium phase transitions in their initial stages of spinodal decomposition. We show that it is possible to extend the formalism adopted in the Cahn–Hillard theory of nonequilibrium phase transitions and perfected on problems of highgradient crystallization to other types of problems, in particular, those pertaining to the Rayleigh–Benard convective instability. For the initial stage of instability, a model is constructed that represents it as a nonequilibrium phase transition due to diffusive stratification. It is shown that the Gibbs free energy of deviation from the homogeneous state (with respect to the instability under consideration) is an analogue of the Ginsburg–Landau potential. Numerical experiments, by means of boundary temperature control, have been conducted with regard to self-excitation of the homogeneous state. Numerical analysis shows that convective flows may appear and proceed from regular forms (the so-called regular structures) to nonregular flows through a chaotization of the process. External factors, such as temperature growth, may lead to chaos via period doubling bifurcations.

For the laminar–turbulent transition, a model of reconstructing the initial stage of an instability treated as a nonequilibrium phase transition is developed. Its mechanism is based on diffusion stratification. It is shown that the Gibbs free energy of the deviation from the homogeneous state (with respect to the instability under consideration) is an analogue of the Ginzburg–Landau potentials. Numerical experiments concerning the self-excitation of a homogeneous state by applying a boundary control condition in the form of an increasing velocity were performed. Under an external influence (an increase in the velocity as input), the system exhibits a transition to chaos through period-doubling bifurcations similar to the Feigenbaum period-doubling cascade.

The initial stage of instability in the failure of a structural material treated as a nonequilibrium phase transition is reconstructed. Its mechanism is based on spinodal decomposition (diffusion separation).

The initial phase of instability in the structure of a solid in the form of a fracture process of the structure material as a nonequilibrium phase transition which depends on the spinodal decomposition (diffusion separation into two pases with different degradation factor) is reconstructed.

The initial phase of instability in the structure of a solid in the form of a fracture process of the structure material as a nonequilibrium phase transition which depends on the spinodal decomposition (diffusion separation into two pases with different degradation factor) is reconstructed.

The occurrence of convective currents and their development from regular forms with the subsequent transition to irregular turbulent currents draw attention to the fact that they are responsible for the efficiency of many technological processes of heat and mass transfer. Such technological processes are basic in the chemical, petrochemical, power, metallurgical and other industries. Convective flows arise in liquids and gases in the gravitational field in the presence of spatial inhomogeneity of the density created by the inhomogeneity of the temperature and the concentration of components arising during, for example, chemical reactions or other causes. With increasing temperature difference, the resting liquid loses its stability, which then leads to the appearance of a convective flow (Rayleigh-Benard instability). A further increase in the temperature difference leads to an instability of the primary convective flow, and the hydrodynamic crisis leads to a heat transfer crisis. The paper reconstructs the early stage of the Rayleigh-Benard convective instability considered as a nonequilibrium phase transition with the spinodal decomposition (diffusion separation) mechanism.

The initial stage of the Rayleigh–Bénard convective instability regarded as a nonequilibrium phase transition is reconstructed. Its mechanism is based on spinodal decomposition (diffusion separation).

The kinetics of external friction is compared with the molecular–mechanical theory of friction. It is shown that research on the topochemical kinetics of adhesive binding is still in its early stages. Calculation methods that incorporate experimental data must be developed.

Приводится реконструкция начальной стадии конвективной неустойчивости Рэлея-Бенара как неравновесного фазового перехода, механизмом которого является спинодальный распад (диффузионное расслоение).

The paper reconstructs the early stage of the Rayleigh-Benard convective instability considered as a nonequilibrium phase transition with the spinodal decomposition (diffusion separation) mechanism.

The initial stage of laminar-turbulent transition reconstruction, the mechanism of which is the spinodal fission (or diffusive bundle), is considered.

We construct a nonstandard regularization for a multicomponent Euler system and obtain analogs of the Hugoniót condition and the Lax stability condition. We investigate the local accessibility problem for phase space points and construct dual bifurcations of one-front solutions of the truncated Euler system into two-front solutions.

The initial stage of the laminar–turbulent transition is reconstructed. Its mechanism is based on spinodal decomposition (diffusion separation).

In the paper we study the reproducing of the initial phase of the inner turbulence (without regard for the boundary effects). The atypical regularization of multiple-component Euler system is made by the viscosity and diffuse layering introduction. The analogue of Hugoniot condition and the analogue of Lax stability condition are constructed for it. The problem of local accessibility of the phase space points is investigated. The bifurcations of one-front solutions of the abridged Euler system to the two-front solutions are obtained. The supersonic behaviour of bifurcations appearance is shown. The reconstruction of the initial phase of the inner turbulence (without regard for the boundary effects) is made including the mathematical description of the birth of two-speed flow (the Riemann-Hugoniot catastrophe) and alternation.