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The lattice Boltzmann method is employed to simulate heat transfer in the flow past three arrangements of elliptical and circular cylinders under an isothermal boundary condition. The lattice Boltzmann equations and the Bhatnagar-Gross-Krook model are used to simulate two-dimensional forced convection at 30 ≤ Re ≤ 100 and Pr = 0.71. Pressure distributions, isotherms, and streamlines are obtained. Vortex shedding maps are observed in detail for several cases. The present results are in good agreement with available experimental and numerical data.

An analytical solution of the problem of electrochemical machining of metals by a curvilinear cathode tool with allowance for a discontinuous function that describes the dependence of the current efficiency on the current density is obtained. According to the hydrodynamic itnerpretation, the original problem reduces to the problem of the theory of ideal fluid flows with a free surface. It is demonstrated that the use of the proposed dependence of the current efficiency on the current density ensures the existence of three domains on an unknown treated surface; these domains have different laws of the distribution of the charge fraction spent on metal dissolution. Results calculated for various particular cases are presented.

This paper presents a synergetic model that can be used to describe the boundary friction of two atomically smooth solid surfaces separated by an ultrathin lubricant layer. The model is constructed using the Lorenz equations, which are parameterized by shear stresses, shear strains, and the lubricant temperature. Given the spatial heterogeneity of these parameters, it is shown that a structure with two types of domains is formed during friction on the contact plane. Time dependences of the fractal dimensions of the domain distributions over the contact plane are calculated, and it is shown that there exists a time when the fractal dimensions take minimum values. During the evolution, the system tends to a homogeneous state in which the entire contact area is subjected to constant shear stresses which determine the relative velocity of motion of the friction blocks.

Dependences of the drag and lift force coefficients of a magnetized sphere in a hypersonic rarefied plasma flow on the angle between the plasma flow velocity and the intrinsic magnetic induction vector of the body are obtained in a wide range of the ratio of the magnetic pressure to the plasma flow pressure. It is shown that by changing the orientation of the magnetic field vector of the body and the incoming flow velocity, it is possible to control the dynamic interaction in the plasma--body system, namely, to decelerate and accelerate the magnetized sphere in the rarefied hypersonic plasma flow.

A physicochemical model of generation of nonequilibrium molecular radiation in the vacuum ultraviolet (VUV) spectral range behind the shock wave in air for shock wave velocities of 4.5 to 9.5 km/s is developed. Experimental results obtained in a shock tube in investigations of photoionization of air ahead of the shock wave front are used for verification of the numerical model of VUV radiation in the wavelength range from 85 to 105 nm. Model calculations show that nonequilibrium VUV radiation arises in a very thin high-temperature layer behind the shock wave front and is affected by the presence of electrons.

The problem of the impact of an elongated solid body with a flat bottom on a thin layer of an ideal incompressible liquid is considered in the case where the horizontal component of the body velocity is substantially greater than its vertical component. The initial stage of the impact is studied in which the a priori unknown contact area between the body and the liquid is rapidly expanding. The loads on the body are determined by the plane section method. The method of matched asymptotic expansions is used to determine the position and size of the contact spot in each section. The coupled problem is solved: the liquid flow due to the motion of the body and the body motion itself are determined simultaneously. A system of integrodifferential equations was obtained and used for numerical investigation of the body motion under the action of hydrodynamic loads, and the hydrodynamic pressure distribution over the contact spot was determined.

A boundary layer flow of a non-Newtonian fluid in the presence of nanoparticles is examined. The flow is caused by a vertical stretching sheet. Convergence of the solution obtained is checked. The values of velocity, temperature, skin friction, and Nusselt number in the boundary layer are obtained.

The flow in a channel with a backward-facing step and a rib mounted upstream of the step and generating flow disturbances is studied experimentally by the method of particle image velocimetry. It is demonstrated that mounting of a single rib leads to deformation of the profiles of the mean streamwise velocities and turbulent fluctuations. The effect of the position and height of a single rib on the recirculation region behind the backward-facing step is analyzed. Reduction of the recirculation region size behind the step in the case of flow reattachment upstream of the step is validated.

This paper presents a new accurate solution of the Navier -Stokes equations in the Boussinesq approximation that describes the thermocapillary advective flow in a slowly rotating horizontal layer of incompressible liquid with free boundaries. Such a flow emerges in the case of linear temperature distribution over horizontal coordinates or in the case of heat flux distribution on the layer boundaries. The influence of the Taylor, Marangoni, Grashof, and Biot numbers on the flow and temperature velocity profiles is studied.

The relevance of the research of the problems and peculiarities of modern economic education taking into account information technologies is due to significance of the results in the applications. Such an analysis is doubly important for Russia, and naturally affects the educational system as a whole and economical education in particular. In the last decades there has been formed a single information and communication space, which allows using mondialist methods to manage the economy in real time. Modern economy presupposes an appropriate level of education, takes into account the adaptation of national economies to the new conditions. The fundamental role is played by computerization of production technology, characteristic of post-industrial economy, which leads to the intellectualization of labor, greatly enhancing the creative potential in it. Modern economies are increasingly moving closer to the process of education, allowing developing a universal method of introduction of new informational means of communication. The idea of creating a world educational space uniting the existing national education systems is becoming increasingly popular. Economic education aims at the formation of the new man, thus it accumulates inseparable dialectical unity of conservation and development of the best educational traditions in a broad economic range. Currently there is actualized the need for the formation of new methods, leveling the above negative consequences. In accordance with the economic laws there is established the structure and functioning of economy of a particular country. Modern education must include the moral and spiritual elements. The concepts of sustainable development of Russia can be successfully implemented by relying on originality, which corresponds to a new educational paradigm, which is based on tradition and focused on the future. Future economic education should help meet the urgent needs of the modern man, the restoration of social justice, improve the health of the nation, and so on. It is these directions of state policies that should be emphasized, although the results of the strategic plan will emerge in years, but they will have the key importance for the restoration of the power and greatness of the country.