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The two-dimensional problem of potential flow around two circular cylinders is considered for given velocity at infinity, circulations around cylinders, and the radii and relative position of the cylinders. Exact analytical formulas for the complex potential and the complex conjugate velocities in terms of the Jacobi theta functions are derived. The circulations around the cylinders are uniquely determined using the Gol'dshtik's minimax principle: the circulations should be selected so that the maximum fluid velocity in the stream is minimal.

The propagation and destruction of nonlinear internal waves in the summer-autumn period at the hydrophysical test site of the Pacific Oceanological Institute, FEB RAS in the shelf zone of the Sea of Japan have been studied for a number of years. By continuous measurement of vertical temperature and velocity distribution at depths of 20-60 m using bottom stations and by a regular study of the distributions of the main hydrodynamic characteristics along selected paths, mechanisms have been determined for the generation and propagation of nonlinear packets of internal waves due to internal tide decay and other short-period sources of thermocline deformation have been detected that can be attributed to the propagation of benthic and surface vortex structures. High spatiotemporal resolution of the temperature field in the neighborhood of bottom stations made it possible to reveal the fine structure of wave perturbations of various types. Multilayer shallow-water models for wave-packet propagation have been developed and verified using the data of full-scale and laboratory experiments.

This paper presents a three-dimensional direct numerical simulation of the chaotic dynamics of the free surface of a dielectric liquid placed in an external tangential electric field. The physical model includes the effects of energy pumping (external force), energy dissipation (viscosity), and surface tension. As the external electric field strength increases, a transition from the turbulence of dispersive capillary waves (at zero field) to anisotropic electrohydrodynamic wave turbulence is observed. In the strong field limit, where the fluid motion becomes highly anisotropic, a cascade of small-scale capillary waves is formed that propagates perpendicular to the external field direction. In this regime of motion, a new turbulence spectrum occurs, which differs from the classical spectrum of capillary turbulence.

The possibility of changing the morphology of the silicon surface at certain parameters of the glow discharge is shown. It has been established that oxidation is the main process influencing the surface morphology during glow discharge plasma treatment. As a result of processing in the investigated range of parameters, various stages of the surface oxidation process are observed: the formation of a uniform oxide layer, the formation of nano- and microstructures of silicon oxide. It is shown that these processes lead to surface modification, which acquires stable hydrophilic and superhydrophilic properties.

Predicted numerical distributions of the vibrational temperature of molecular oxygen behind a reflected shock wave are compared with experimental measurements in a shock tube. The computations are performed with the use of five two-temperature models (those developed by Park and Kuznetsov, β-model, and models of Marrone and Treanor and by Macheret and Fridman), five dissociation constants, and three variants of the source term that describes the rate of change of the vibrational energy due to chemical reactions. The Landau-Teller model is used to calculate the rate of translational-vibrational energy transfer, and the time of vibrational relaxation is calculated by the Millikan-White formula with allowance for Park's high-temperature correction. The numerical and experimental results are found to be in reasonable agreement. The greatest difference between the numerical and experimental data is observed in the region of relaxation of the shock wave incident onto the wall.

To study the effect of laser surface remelting (LSR) on the organization and properties of a 304 stainless steel surface layer, the microscopic morphology, hardness, roughness, adhesion, and corrosion resistance of the remelted layer (RL) are examined by changing the laser scanning speed (LSS). The experimental results show that the LSR technique hardens the 304 stainless steel substrate surface with a substrate hardness of 185 HV, and the maximum hardness after remelting is 248.9 HV. With an increase in the LSS, the surface roughness gradually decreases, while the bonding force first increases and then decreases, with the maximum bonding force being 26.1 N. At the LSS of 20 mm/s, the phase distribution in the RL is more uniform. The maximum self-corrosion potential of the RL reaches -0.718V, and the self-corrosion current density is 3.872 A/cm². The surface properties of 304 stainless steel are improved by using LSR.

This paper presents the results of numerical analysis of the filtration equations for highly miscible liquids obtained by two-scale homogenization of the Navier-Stokes and Cahn-Hilliard equations for two-dimensional flows. It is shown that the permeability tensor is generally anisotropic. For one-dimensional flows, the miscibility dynamics is investigated, and it is shown that the displacement of one phase by injection of another phase can occur even in the absence of a pressure gradient in the sample.

Taking into account the degradation of the properties of materials, an analysis of the nonlinear processes of deformation and fracture in a preloaded three-dimensional body with a sharp concentrator in the zone of a dissimilar joint under impact was performed. A generalized mathematical model of nonlinear interrelated deformation and destruction of damaged polycrystalline media subjected to time-varying thermomechanical influences is presented. The strong nonlinearity of the model is due to large (finite) strains and the strain-rate dependent behavior of media with a variable microstructure. Taking into account the anisotropic hardening of media and the Bauschinger effect, the corresponding nonlinear boundary value problems are formulated and their solutions are obtained using efficient numerical methods. The viscosity of the medium and second-order gradients from the internal variables of the system were used as regulators of the correctness of the problem statement. Experimental data were used to test the model. Simulation results presented.

The strength of a rectangular plate with two opening-mode (mode I) edge cracks was studied using the Neuber-Novozhilov approach and a modified Leonov-Panasyuk-Dugdale model with nonzero prefracture zone. A coupled discrete-integral fracture criterion is used since the stress field in the vicinity of the crack tip has a singularity. At the tip of a real crack, the fracture criterion for ultimate strain is satisfied, and at the tip of the model crack, the criterion for normal stresses is satisfied. The constitutive equations for the analytical model are analyzed. Simple formulas for fracture load in quasi-brittle and quasi-ductile fracture are derived. Plate fracture curves are constructed for a plane stressed state.

Equations are obtained that describe the process of propagation of elastic waves in a collapsing solid. It is shown that the solution of the equation for the velocity potential of acoustic emission longitudinal waves can be represented as a superposition of the fields of an ensemble of radiating cavities - monopoles. The parameters of the ensemble of monopoles are selected in such a way that the structural characteristics of a medium with cavities differ slightly from those of a solid body.