An exact solution that describes steady flow of viscous incompressible fluid with coupled convective and diffusion effects (coupled dissipative Soret and Dufour effects) has been found. To analyze shear fluid flow an over determined boundary value problem has been solved. The over-determination of the boundary value problem is caused by the advantage of number of equations in non-linear Oberbeck-Boussinesq system against number of unknown functions (two components of velocity vector, pressure, temperature and concentration of dissolved substance). Non-trivial exact solution of system consisting of Oberbeck-Boussinesq equations, incompressibility equation, heat conductivity equation and concentration equation has been built as Birich- Ostroumov class exact solution. Since the exact solution a priori satisfies the incompressibility equation the over-determined system is solvable. Existence of stagnation points is shown both in general flow and in secondary fluid motion without vorticity. Conditions of countercurrent appearance are found.

A nonlinear model describing the movement of a pipeline with fluid moving through it and allowing consideration of a number of applications that do not have solutions within the linear model is proposed. The problem of equilibrium of a pipe with fluid moving through it in the gravity field is solved. An exact solution for the simplified non-stationary model equation is constructed.

In 1974 an unusual phenomenon called Usherenko effect was observed in impact experiments [1,2]. Surprisingly large were impact produced craters whose depth varied between 100 and 10000 times the impactor’s size. For materials whose static strength is small or zero, e.g., sand or water, the depth of penetration is no larger than 100 times the size. When a macro-size body impacts on a barrier, it produces a crater whose depth is normally in a ratio of no larger than 6-10 to the body’s size regardless impact parameters. The papers [1,3] give overviews of models which were developed to explain the phenomenon. They all try to answer why material resistance to the penetration of micro-size impactors suddenly decreases. We suggest a model that uses the concept of particle entrainment by a shock produced by the impact of a bunch of particles on a barrier. The approach was proposed by V.A. Simonenko [4]. It is based on calculations by the finite-difference technique TWS [5,6]. Such an approach shows prospects for further development with account for new experimental results obtained after 1991. The goal of this paper is to demonstrate feasibility of applying this approach for justification of impactor’s acceleration in solid.

Some iterative methods for calculating self-balanced stresses under shrinkage of a ball inclusion enclosed in a spherical matrix of a physically nonlinear damageable material. The stability of this system was studied using methods of catastrophe theory. It has been established that the beginning of divergence of the proposed iterative processes coincides with the moment of transition of the system to an unstable position of equilibrium.

In this article, the results of experimental and numerical studies of the behavior of perturbed interface between air and helium are presented. The interface is initially accelerated by the incident shock wave coming from air to helium and then decelerated by a series of reflected shock waves. Two types of initial interface perturbations like "saw" and "step" are considered.

In doing research on the turbulent mixing (TM) of two gases different in density, it is of great interest to study experimentally the 3D density distribution pattern of chemically nonreactive gases in the TM zone. For this purpose, noncontact and, particularly, optical techniques to obtain experimental data may be attractive. This article discusses the possibility of using pulsed laser interferometry in this application. Based on this technique, the experiment should result in the mixture density distribution integrated along the light path. Requirements for high-quality interference patterns have been analyzed in application to typical experimental conditions, to show that they may be produced with specific restrictions set on the mixture constitution. Generally, the TM zone has no symmetry. Therefore, the problem of reconstructing 3D density distributions (TDD) of gases can be solved by sufficiently providing many TM zone integral projections (or aspects). It is technically difficult and expensive to achieve this large number of aspects ( N > 10). Therefore, it is essential that a reconstruction method be selected to allow the solution of the problem with the least possible number of aspects. Given that the experiment data are incomplete, the reconstruction methods that are based on the concept of maximum data entropy did well. Information a priori about the solution to be sought for an isobaric gas mixture is that its each constituent has invariable density. Thus, a functional data entropy can be defined that is similar to Fermi gas in statistical physics. An algorithm has been suggested for reconstruction as a modified maximum-bounded entropy procedure (Bashurin et al. 1995). This makes reasonable good reconstruction achievable even with as few aspects as N = 4. Experiments on the study of TM of a propane jet in air using a four-aspects laser interferometer were provided and reconstruction of propane concentration distribution was conducted. The results allow determination of the TM zone spectral characteristics.

In a number of experiments with high-velocity powder streams, ultra-deep penetration of individual microparticles into obstacles has been observed on impact of them with rigid barriers. Previous ideas about crater formation are not in a state to explain this penetration. A hypothesis is suggested and discussed for capture of microparticles by an SW front which has a finite width in real materials. From equilibrium conditions for all of the forces acting on a particle, a condition is obtained for this entrainment. A number of numerical experiments are provided which point to the competence of this hypothesis.

In underground explosions executed in the interests of ejection, downcomer funnel or bulging hillock formation, the soil properties influence not only the quantitative parameters substantially, but also the qualitative pattern of the explosion. Thus, under the same conditions of charge embedding and power, a downcomer funnel or bulging hillock can be formed depending on the properties of the rock. The majority of explosions are performed in hard rock. Hence, the model of the soil should be suitable to describe its fundamental properties. A model of rocky soil is presented in this paper, the scheme for a numerical computation of the problem is described, and results of certain computations are presented.

The article discusses the self-similar problem of the motion of a spherical piston in a medium with “dry” friction and the differential connection between the first invariant of the stress tensor and the second invariant of the tensor of the deformation rates. For the case of flow with a shock wave, the method of a stationary wave is used to obtain the required relationships at a strong discontinuity. It is disclosed that the velocity of the piston, as well as the relationship between the cultivation coefficients and the dry friction, are determined by the smoothness of the friction.

We study the self-similar problem concerning the motion of a spherical piston in a medium with “dry” friction. The piston moves with constant velocity in a nonideal medium.