Numerical analysis of the eigenfrequency spectrum of shells of revolution

M. V. Lomonosov Moscow State University, Institute of Mathematical Modeling of Russian Academy of Sciences, Moscow. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 19–24.     

Majorizing difference schemes for parabolic equations on unstructured grids

Moscow Physico-Technical Institute. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 105–113.     

Stabilization of uncertain systems on rings

M. V. Lomonosov Moscow State University. Translated from Matematicheskoe Modelirovanie. Published by Moscow University, Moscow, 1993, pp. 279–295.     

Equilibrium conditions for multilayered anisotropic viscoelastic plates in a complex state of stress

Systems of linear differential-difference equations describing the complex state of stress of multilayered viscoelastic and elastic plates are obtained.Moscow Institute of Electronic Machine Building; All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 281–288, March–April, 1973.     

A difference spline scheme for navier-stokes equations in natural variables

A difference scheme is proposed for solving Navier-Stokes equations in “veiocity-pressure” variables. It is constructed using one-dimensional discrete parabolic splines. The monotonizing properties of the scheme are investigated with prototype problems. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 33–38.     

Contrast structures: Theory and applications

M. V. Lomonosov Moscow State University. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 63–67.     

Modeling and numerical analysis of mass transport and migration of radioactive heat sources in the context of thermal evolution of the Earth

Mass transport models are described for the processes of density differentiation, convection, and fractional crystallization, including simultaneous occurrence of these processes, in the context of thermal and structural evolution of the Earth. Results of numerical analysis are reported.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 122–141.     

Calculation of radial supersonic gas flow past sharp-nosed cones

The paper presents the results of numerical analysis of supersonic source flow of a gas past sharp-nosed cones. Axisymmetric and three-dimensional flows are considered. The flow geometry and the distributions of the gas-dynamic parameters in the shock layer are analyzed; their asymptotic properties are established. The numerical solutions are compared with solutions for uniform gas flow past a cone.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 32–47.     

Finite abelian group methods in iterative algorithms for solving boundary-value problems with a boundary surface of complex structure

We consider external boundary-value problems for the Laplace equation on surfaces of complex structure. Various iterative computational schemes are constructed for numerical solution of the corresponding integral equations using set-theoretical group methods. Simulation results of electron-optical images are reported. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 16–27.     

Continuous regularized proximal minimization method

A continuous regularization method based on the proximal method is proposed for minimization problems with an inexact objective function. Sufficient convergence conditions are given, and the regularizing operator is constructed. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 5–25.     

Investigation of the fiber packing density in a unidirectional composite

Recommendations are made for designing a unidirectional composite with an optimal arrangement of the fibers. The effect of the fiber diameter distribution law on the packing density is investigated.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow. Moscow Institute of Electronic Machine-Building. Translated from Mekhanika Polimerov, No. 3, pp. 538–541, May–June, 1976.     

Simulation of oscillation modes in a supersonic unrated jet impinging on a cavity

The flow of a supersonic underexpanded jet past a cavity is analyzed numerically. Through difference schemes approximate to first, second, and third order are used. The focus is on oscillation modes and their effect on back-flow. Deceased. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 181–188.     

A method for calculating the current distribution in an unsymmetric oscillator with several excitation points

A method is proposed for calculating the current distribution in an unsymmetric oscillator with several excitation points joined by a common distribution line. The radiator and the distribution line are represented by multipoles, which are described by scattering matrices. The elements of the radiator scattering matrix are calculated by the integral equation method. The calculation results are compared with experimental findings.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 71–76.     

Compression of an orthotropic prism

The formulation and mathematically correct solution of a three-dimensional boundary value problem are given. A numerical calculation is presented for a prism of Canadian spruce and the displacement and stress fields are determined.Presented at a scientific seminar on polymer mechanics held in the Mechanics-Mathematics Department of Moscow State University, February 7, 1968.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 810–815, September–October, 1968.     

The probability function of a generalized poisson distribution and special polynomials

The probability function of a generalized Poisson distribution is written in terms of modified Hermite polynomials of 2nd kind in many variables. Their relationship is established with special polynomials previously derived for this purpose. The properties of the polynomials and the probability function are studied. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 160–169.     

Continuous regularized variable-metric proximal minimization method

The article considers the variable-metric continuous proximal method for the convex programming problem. The convergence of the method is proved. The regularized version of the method is proposed for the case where the objective function and the feasible set are defined inexactly. A regularizing operator is constructed. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 39–47.     

Scattering of a plane wave on a wavy surface

Numerical methods are proposed for solving problems of diffraction of a plane electromagnetic wave on a nonhomogeneous interface of two media. Strictly periodic cylindrical surfaces are considered, as well as surfaces that are nonplanar on a finite section. Algorithms are developed for computing the characteristics of the reflected field in the far zone. Numerical results are reported for various electrodynamic models, and their limits of applicability are investigated.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 86–111.     

Development and analysis of a mathematical model of the Earth's upper atmosphere

Tomsk State University. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 122–138.     

Effect of loading on the roughness set in run-in metal - rubber surfaces

A study has been made on the effect of loading on the roughness set of a metal surface run-in with rubber containing an SKN-18 + SKN-26 nitrile rubber blend in conditions of friction without lubrication. The experimental results are compared with those calculated.State Scientific-Research Institute of Mechanical Engineering, Moscow. Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 737–740, July–August, 1972.     

Inverse sounding problem using stabilization of the magnetic field of a loop

We consider the inverse sounding problem for a stratified medium using the variable magnetic field of a loop. A uniqueness theorem and a theorem ensuring stable determination of the integral conductivity of the medium are proved. An algorithm is proposed for the solution of the inverse problem based on a transformation from the time domain to the frequency domain. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 87–95.