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The axisymmetric contact problem of sliding of two solid parabolic indenters on a viscoelastic half-space with constant velocity is considered. Shear stresses modeling the adhesive component of the friction force act in the contact area. The model of the foundation material is described by an integral operator with an exponential kernel characterized by one relaxation time. The problem is solved by the boundary element method. The dependences of the contact characteristics on the sliding velocity, the normal load, and the distance between the centers of the indenters is analyzed. The results can be used to study the effect of the roughness elements modeled by two indenters on the contact characteristics and the deformation component of the friction force.

The influence of boundary conditions on the fracture of brittle geomaterial in the stress concentration zone under biaxial loading with account for the size effect is theoretically and experimentally studied. The calculation results are compared with the experimental data.

The linear plane problem of oscillations of an elliptic cylinder in an ideal incompressible fluid of finite depth in the presence of an ice cover of finite length is solved. The ice cover is modeled by an elastic plate of constant thickness. The hydrodynamic loads acting on the body are determined as functions of the oscillation frequency and the positions of the cylinder and plate.

The unsteady isothermal flow of a dense layer of a granular medium around an obstacle in a plane channel is modeled using the momentum transfer equations for an incompressible viscous liquid medium based on the slip of the medium at the walls. The validity of this approach is tested by comparing the calculated and experimental data for the flow of a highly concentrated granular medium with high flowability. The effect of periodic change in the flow rate of the granular medium over time in the inlet section of the plane channel on the unsteady distributions of the velocity and temperature fields is studied.

A method is proposed to determine the moduli of thin ferroelectric films subjected to forced deformation due to the mismatch between the crystal lattice sizes of the film and substrate materials and the difference of their thermal expansion coefficients. Models of single-crystal films of barium titanate are studied using the eighth-degree Landau thermodynamic potential. It is shown that in the considered range of forced strain of the barium titanate film, three main states exist: a tetragonal phase ($c$ phase) of 4mm symmetry with spontaneous polarization directed along the normal to the film plane; an orthorhombic phase ($aa$ phase) of 2 mm symmetry with polarization oriented along the diagonal plane of the film; monoclinic phase ($r$ phase) of $C_\rm m$ symmetry with the intermediate direction of polarization. All phases are separated by the lines of transitions of the second kind. Dependences of the elastic, electric and piezoelectric moduli on the magnitude of forced strain are plotted. It is shown that at the phase boundaries there is an anomalous change in the constants of the ferroelectric film and in the region of existence of the $r$ phase, some moduli reach extreme values.

This paper is devoted to methods of estimating the combustion regimes of gaseous fuel in vortex chambers of various designs in the presence of a bed of inert particles in the chamber, which rotate with the gas flow. A simple geometric criterion for determining the possibility of fuel combustion in the particle bed without the formation of a flame above the bed is proposed.

This work is an experimental and theoretical study of the dependence of normal flame velocity in polydisperse aerosuspensions of aluminum particles on the parameters of the particle size distribution function. It is shown that the velocity decreases with increasing dispersion of the distribution function as a result of reduction of the specific reaction surface.

The effect of sodium hydrogen carbonate and ammonium chloride on the combustion of iron aluminum thermite in air at atmospheric pressure is experimentally studied. The effect of salt additives on the average linear velocity of combustion, the relative yield of the metallic phase in the ingot, and the relative weight loss during thermite combustion are investigated. The concentration flammability limits of the mixtures under consideration are determined.

This paper presents a physicomathematical model for the combustion of N powder which takes into account chemical reactions in the condensed and gas phases. On the burning surface, boundary conditions (coupling conditions) are specified. Results of calculation of the burning rate of N powder at constant pressure are in good agreement with available experimental data. The extinction of combustion of N powder by a sharp pressure drop pressure is simulates. Calculations of the boundary values of the degree and rate of pressure drop at which extinction of N powder occurs are in good agreement with published data of measurements.

The shock wave motion of a mixture of a gas and fine solid particles is considered with allowance for the difference in velocities and the particle phase pressure, which is described by Anderson-type and other equations. Various forms of the equation of state for the particle phase are described. Graphical illustrations are given for the equation determining the composite type of this model with the particle phase pressure being neglected. Under certain assumptions, the complete model can be reduced to a hyperbolic system of equations. Types of shock waves formed in such a mixture are determined for this system of equations. The statements are illustrated by results of numerical simulations.