An inverse problem for a system with a moving boundary

The problem of estimating the right-hand side of a nonlinear parabolic equation is considered. A finite-step algorithm based on the model positional control method and the finite element method is proposed. The algorithm is robust to informational noise and computational errors. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 23–33.     

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.     

Compressible gas flow inside a cylindrical channel with a source on the channel axis

The article solves the problem of compressible nonviscous gas flow inside a cylindrical channel in the presence of a source on the channel axis. The cases considered include a supersonic spherically symmetrical source and a hypersonic source modeling jet flow. The numerical solution is obtained by two methods: one method treats the flow singularities (shocks, etc.) in explicit form, while the other uses the “through calculation” procedure. The solution is applied to analyze the physical flow pattern and the distribution of gasdynamic parameters in the shock layer, in particular on the channel walls. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 169–180.     

Dependence of the dynamic strength of a glass-reinforced plastic on the mechanical and geometric parameters of its components

The dependence of the dynamic strength of a glass-reinforced plastic on the mechanical and geometric parameters of its components is investigated.Moscow Institute of Electronic Machine-Building; All-Union Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Oblast'. Translated from Mekhanika Polimerov, No. 2, pp. 366–370, March–April, 1974.     

Some features of viscous gas flow injected into a supersonic stream from the lateral surface of a cylinder

The article presents a procedure and results of numerical analysis of the structure of flow near an elongated cylinder with a spherically blunted nose that moves with a supersonic velocity with local injection of gas from its lateral surface. The analysis is based on the solution of the full Navier-Stokes equations for a compressible gas. Nonstationary fluctuations in the region of the condensation discontinuity are detected in the given range of Mach and Reynolds numbers. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 119–124.     

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.     

Insulated antenna in a layered medium

The article presents a generalization of the integral equation of an insulated linear antenna immersed in a cylindrically layered lossy dielectric medium. The insulation is provided by a lossless dielectric layer. The kernel of the integral equation is represented as a superposition of the fundamental solutions of the wave equation with equivalent propagation constants for the given media. A generalization to a plane-layered medium is proposed. The problem of a vertical radiator above a layered half-space is considered. Translated from Chislennye Metody v Matematicheskoi Fiziki, Published by Moscow University, Moscow, 1996, pp. 80–88.     

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.     

Development of integro-differential methods of parameter determination for a sum of exponential functions

We consider the problem of determination of decay decrements and amplitudes of exponential functions form observations with errors of the sum of these functions on a nonuniform grid. The integro-differential methods proposed by other authors lead to numerically unstable ill-posed problems, and make it impossible to estimate the errors in the results. New approaches are proposed that overcome these difficulties. The effectiveness of the proposed solutions is demonstrated. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University. Moscow, 1996, pp. 129–136.     

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.     

Changes in the supermolecular structure and physico-mechanical properties of a polycarbonate subjected to supplementary heat treatment

The possibility of modifying the supermolecular structure of polycarbonate by suitable supplementary heat treatment is demonstrated. An improvement in the physico-mechanical and service properties controlled by the supermolecular structure of the polycarbonate is noted.Departmental Plastics Laboratory, Ministry of the Machine-Tool and Tool Industry of the USSR, Moscow. Moscow Mendeleev Chemical Engineering Institute. State Scientific-Research Institute of Machine Science, Moscow. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 347–349, March–April, 1969.     

Percolation model of SHF breakdown in a dielectric

A percolation model of gas-discharge evolution is described in the cellular automaton paradigm, which makes it possible to overcome difficulties associated with the complex geometry of discharge structures. The two-dimensional case is considered, when the potential of the discharge region is zero and the potential on the outer boundary varies harmonically. Both linear and circular polarization of the external field is allowed. Typical fractal structures are derived, and their fractal dimension is calculated by two methods.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 10–16.     

Inverse coefficient problem for a nonlinear differential equation and an iterative solution method

The article considers the determination of the solution-dependent coefficient of a nonautonomous ordinary differetial equation with a parameter. Reduction of the inverse problem to a nonlinear operator equation is used to prove existence and uniqueness theorems and to propose an iterative solution method. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 5–17.     

Axisymmetric excitation of a dielectric torus: Numerical solution

The article considers the mathematical model of a lens antenna in the shape of a homogeneous dielectric torus excited by an axial magnetic dipole. The boundary-value problem for an elliptical differential equation is posed and reduced by the fundamental solution method to an integral equation of 2nd kind over the torus section. A numerical algorithm is proposed, and the numerical results are compared with experimental findings. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 109–115.     

Supersonic longitudinal flow past a cylinder in the presence of a second coaxial cylinder in the wake

The compressible-gas complete Navier-Stokes equations are applied for a numerical analysis of the flow structure between two coaxial cylinders of equal radius set in tandem in a supersonic flow. The results for Re_∞=10⁴, M_∞=3 ω=0.75, Tw=1.08, when the distance between the coaxial cylinders is equal to two blunt-nose radii, show that the flow between the cylinders is subsonic and quasiperiodic. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 199–203.     

The dynamic problem of a cylinder with a slowly changing internal boundary

The problem of a hollow, viscoelastic cylinder confined in a shell is considered, and it is shown that the internal diameter changes. The fluctuations arising on applying a variable, internal pressure are analyzed.Institute of Flectronic Engineering, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1059–1065, November–December, 1972.     

Application of the particle method to simulate one-dimensional bounded plasma with a distributed sources

We consider the behavior of a plasma bounded in the longitudinal direction by absorbing walls. The model contains charged particles (electrons and ions) moving in the direction of an external magnetic field with two velocity components: longitudinal and transverse. The charged particles are created in pairs by a distributed source. The working model is based on the electrostatic “particles in a cell” method augmented by Emmert's model for a volume source and a model of binary Coulomb particle collisions using the Monte Carlo method. Calculation results are reported for a model with electron-ion collisions and for a collisionless plasma model. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 100–109.     

Inverse problem of electromagnetic sounding of the shape of a conducting body

The inverse problem of electromagnetic sounding of the shape of a conducting body is considered in the framework of the two-dimensional model with E-polarization, assuming a cylindrical body of an arbitrary cross section embedded in a layered medium. The integral equations are obtained for the case of an ideally conducting body and a body of finite conductivity. The linearization method is applied to obtain an iterative method that finds a correction to the initial shape. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 96–103.     

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.     

Bending of a cantilevered glass-reinforced plastic cylindrical shell weakened by a circular opening

The stress concentration is investigated in the neighborhood of a circular opening in a cantilevered glass-reinforced plastic cylindrical shell with a concentrated load at the free end. The problem is solved by the Bubnov method using a Ural-2 computer. The theoretical results have been checked experimentally on glass-reinforced plastic shells.All-Union Correspondence Polytechnic Institute, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 152–157, January–February, 1970.