A stable algorithm for separating the basic component of an experimental spectrum

The problem of separation of the basic component of an experimental spectrum is considered. An algorithm is described that constructs a stable approximation to the solution by introducing constraints on the measure of variation of the basic component. Applications of the algorithm for the construction of the basic component of a quasi-experimental spectrum are considered.Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach Matematicheskoi Fiziki, pp. 76–81, 1993.     

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.     

Application of a genetic algorithm to compute the control of a complex dynamic system

A genetic algorithm is applied to compute the control of a complex dynamic system. Methods are proposed to modify the genetic algorithm so as to adapt it to variation of the objective function. Comparison with dynamic programming results is carried out. The study was supported by the Russian Foundation of Basic Research (grant No. 9607-89110) and Ministry of Science (grants 0201.03.002 and 0201.03.003). Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 82–96, 1998.     

Two-dimensional filtration problem for solutions in a nonhomogeneous porous medium

We present a mathematical model of underground leaching by solutions filtering through a porous medium. The model describes the motion of solutions from injection to extraction boreholes, as well as dissolution and secondary deposition in reduced-pH regions. A numerical algorithm has been developed for solving the problem on a plane in the general case of a homogeneous medium that contains regions with various nonhomogeneities. The algorithm combines triangulation of the region with the finite element method. The model also allows slow variation over time of some of the process parameters, such as porosity and the filtration coefficient. Numerical results are reported for various cases. The model qualitatively describes the main regularities of underground leaching and can be used to study and understand the detailed dynamics of these processes. The model also fills gaps in geological prospecting data, and extraction curves constructed for different wells can be applied to determine the approximate location of a particular nonhomogeneity. Mathematical modeling can help to optimize mineral extraction by underground leaching. Translated from Prikladnaya Matematika i Informatika, No. 29, pp. 29–55, 2008.     

An algorithm for the constrained extremum problem

An algorithm is proposed to find the constrained minimum of a function. The algorithm uses differential equations that incorporate the problem constraints as singular manifolds. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 48–51.     

The construction of extensible polynomial lattice rules with small weighted star discrepancy

In this paper we introduce a construction algorithm for extensible polynomial lattice rules and we prove that the construction algorithm yields generating vectors of polynomials which are optimal for a range of moduli chosen in advance. The construction algorithm uses a sieve where the generating vectors are extended by one coefficient in each component at each step and where one keeps a certain number of good ones and discards the rest. We also show that the construction can be done component by component.

     

Separate reconstruction of solution components with singularities of various types for linear operator equations of the first kind

A linear operator equation of the first kind is investigated. The solution of this equation contains singularities of various types; namely, along with a smooth background, the solution has sharp bends and jump discontinuities. For the construction of a stable approximated solution, a modified Tikhonov method with a stabilizer in the form of the sum of three functionals is proposed. Each of the functionals accounts for the specific character of the corresponding component of the solution. Convergence theorems are formulated, a general discrete approximation scheme of the regularizing algorithm is justified, and results of numerical experiments are discussed.     

Singular approximation for the calculation of the elastic properties of reinforced systems

A method has been developed, based on the random field theory, for the calculation of the elastic properties of reinforced media. The solution is obtained in the form of an operator series, each term of which is based on the formal component of the second derivative of Green's tensor of incompatibility equations. The zero (singular) approximation of such a series takes into account the local part of interactions between the inhomogeneity grains. The singular approximation was used to calculate the elasticity moduli of unidirectionl reinforced materials.Moscow Institute of Electronics. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 502–506, May–June, 1973.     

Breaking of two-dimensional relativistic electron oscillations under small deviations from axial symmetry

A numerical asymptotic model for the breaking of two-dimensional plane relativistic electron oscillations under a small deviation from axial symmetry is developed. The asymptotic theory makes use of the construction of time-uniformly applicable solutions to weakly nonlinear equations. A special finite-difference algorithm on staggered grids is used for numerical simulation. The numerical solutions of axially symmetric one-dimensional relativistic problems yield two-sided estimates for the breaking time. Some of the computations were performed on the “Chebyshev” supercomputer (Moscow State University).     

Mathematical modeling of vertical electrical sounding of quasilayered media

The direct solution of the vertical electrical sounding problem is considered for three-dimensional quasilayered media. An efficient fast algorithm is obtained for computing the apparent resistivity curves in the two-dimensional case. A PC implementation of the algorithm is proposed. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 123–131.     

Selection of the optimal structure of chopped-strand composites

A mechanical model of the interaction between the reinforcing elements and the polymer matrix is proposed for glass-reinforced plastics with a random distribution of the reinforcing elements. On the basis of this model, a theoretical relation is obtained for the variation of the strength utilization factor with increase in the fiber length-to-diameter ratio, with allowance for the glass-to-resin ratio and the elastic characteristics of the components. The theoretical calculations are found to be in satisfactory agreement with the experimental data.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Region. Moscow Bauman Higher Technical College. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 288–297, March–April, 1969.     

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.     

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.     

Fractial parameterization of the structure of filled polymers

It is suggested to consider the structure of a filled polymer as a set of two or more multifractals. It is shown experimentally that the basic factor determining the fractal dimension of distribution of a disperse filler in the polymer is the size distribution of filler particles.Moscow State Open University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp 269–290, 1999.     

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.     

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.     

The dynamics of slender bodies in dense media under conditions of the local interaction model

Using a model of local interactions an asymptotic theory is constructed for the plane motion of a slender sharpened body of revolution when it is fully immersed in a dense medium and there is no flow separation at the lateral surface. Assuming that at the initial instant of time the dynamic component of the normal stress is much greater than the tensile strength, the domain of variation of the governing, parameters corresponding to asymptotically stable types of motion is found for translational motion of a body at zero angle of attack.     

Fast and accurate interpolation of large scattered data sets on the sphere

In this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented. The solution method is local and involves a modified spherical Shepard’s interpolant, which uses zonal basis functions as local approximants. The associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere. Specifically, this technique is mainly based on the partition of the sphere in a suitable number of spherical zones, the construction of spherical caps as local neighbourhoods for each node, and finally the employment of a spherical zone searching procedure. Computational cost and storage requirements of the spherical algorithm are analyzed. Moreover, several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm.     

An interactive method for parametric identification of the mathematical model of a parachute system using computer graphics

A simple mathematical model of the motion of a parachute system in space is described and an interactive algorithm for parametric identification of the model is proposed. The algorithm selects the model parameters that minimize the deviation of the calculated dependences from experimental observations on the computer graphic monitor.Moscow. Translated from Dinamicheskie Sistemy, No. 10, pp. 106–111, 1992.     

An inverse problem of atmospheric radar sounding

The paper considers the problem of determining the velocities of targets in the atmosphere given a set of Doppler spectra produced by continuous Doppler systems. The problem of determining the velocities of particles moving in a closed trajectory (a circle) is examined. A uniqueness theorem is proved for the reconstruction of velocities from two spectra. An algorithm is proposed for determining the sought function, and a numerical experiment is conducted to establish its efficiency.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 162–167.