Synthesized field method in inverse problems of magnetotelluric sounding

A new method is proposed and investigated for solving the inverse three-dimensional problem of magnetotelluric sounding. The method uses the tangential electric field on the Earth's surface, which is synthesized from the known impedance.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 115–121.     

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.     

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.     

Fredholm equations of the first kind

A method is described for solving the Fredholm integral equation of the 1st kind by passage to the moment L-problem. The problem is reduced to a linear programming problem. A bound of the method for a particular normed space is derived. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 34–38.     

High-frequency projection method for plane problems of wave diffraction on dielectric bodies

A version of the Galerkin incomplete projection method is described for plane problems of wave diffraction on dielectric bodies of arbitrary shape. The proposed method generalizes the Sommerfeld method, which constructs diffraction series rapidly converging at high frequencies for circular and spherical bodies. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 58–67.     

Dynamic mechanical properties of multicomponent polymeric compositions

The mechanical relaxation processes in rubber-polymer compositions have been investigated by the forced nonresonance vibration method. A method of evaluating black-filled polymer mixtures with advantages over microscopic methods is proposed.Scientific-Research Institute of the Tire Industry, Moscow. V. I. Lenin Moscow State Pedagogical Institute, Laboratory of Problems in Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 138–141, January–February, 1970.     

Galerkin method for the linear-radiator integral equation

The article examines the general Galerkin method scheme for the singular integral equation in the problem of radiation from a finite-thickness linear radiator. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 150–158.     

Using completely implicit methods to solve the direct problem of nozzle theory

An iterative method from the class of completely implicit methods (CIM) is proposed for solving the equation of the velocity potential of elliptical-hyperbolic type. The advantage of the proposed method compared to other CIM schemes is demonstrated in application to mixed perfect gas flows in a nozzle of a given shape. Accuracy issues, rate of convergence, and various techniques of ensuring stability in the hyperbolic region are discussed. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 39–51.     

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.     

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.     

High-frequency asymptotic method for investigating the problem of excitation of a thin dielectric coating of an ideally conducting cylinder (H-polarization)

An incomplete Galerkin projection method is constructed and proved as a generalization of the Sommerfeld method for the problem of plane diffraction of the field of a point source on an ideally conducting circular cylinder coated by a thin homogeneous dielectric layer with an arbitrary boundary, in the H-polarization case. An explicit asymptotic solution is obtained in the form of a generalized Watson series. Specific eesonance phenomena are investigated for a boundary layer with corner points. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 132–149.     

Analysis of the iterative method of solution of integral diffraction equations

The article investigates the convergence of an iterative method of solution of the integral equation for the diffraction problem of an electromagnetic field in a nonabsorbing medium. The convergence region of the iterative process is determined for the diffraction of a plane wave on a dielectric cylinder in a homogeneous space.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 112–114.     

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.     

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.     

High-frequency approximation of the green's function for the Helmholtz equation in an axial nonhomogeneous medium

A method is proposed for constructing the field of a point source in an axial two-dimensionally nonhomogeneous medium. The problem is reduced to an integral equation of the 2nd kind. If the frequency ω of the point source is sufficiently high, the equation can be solved by the method of successive approximations. The Neumann series converges in the usual sense for ω>>1 and it is an asymptotic series for ω→∞. The Neumann series also converges in the case of weak dependence of the medium on the coordinate φ. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 104–108.     

Applied aspects of the theory of continuation of solutions of wave-scattering boundary-value problems

The article compares two approaches to continuation of solutions of external boundary-value problems for the Helmholtz equation outside the original region in the solution space — analytical continuation and the generalized image method. The comparison focuses on naturalness and ease of use of the mathematical model for the construction of numerical algorithms. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 68–79.     

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.     

Method of successive approximations in the nonlinear theory of viscoelasticity

A method of successive approximations, a generalization of the Il'yushin method of elastic solutions, is proposed for solving problems of the nonlinear theory of elasticity in which the stress-strain relation is given in the form of a time operator Frechet-differentiable in a neighborhood of zero. The nonlinear relaxation kernels are found from the given nonlinear creep kernels for the principal quadratic theory of elasticity. These relations make it possible to formulate the boundary value problem for this theory. By way of illustration the problem of the pressure exerted on a space by a sphere is examined within the framework of the developed theory. The question of the convergence of the method is discussed in relation to the quadratic theory of visco-elasticity.Presented at the Third All-Union Conference on Theoretical and Applied Mechanics, Moscow (January, 1968).Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 236–242, March–April, 1969.     

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.     

Sudden buckling of the outer layer of a noncentrally compressed triple-layer rod

The stability of the outer nonmetallic layer of a triple-layer rod with foam core was studied both experimentally and theoretically by the energy balance method. The buckling of the outer layer occurs by a sudden transition to a nonadjacent equilibrium form and this process should be seen in regard to a set of deformational factors.Moscow State University for Ecology and Environmental Studies, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 525–530, July–August, 1996.