Shape factor of a specimen in relation to the connection between brittle strength and time

On the basis of the thermal fluctuation theory of brittle fracture of solids an equation is derived for the strength of specimens of various cross-section profile as a function of temperature and time. The theoretical calculations of the shape factor were carried out on a computer.V. I. Lenin Moscow State Pedagogical Institute, Laboratory for Problems in the Physics of Polymers. Translated from Mekhanika Polimerov, No. 1, pp. 157–159, January–February, 1972.     

Calculation of the residual stresses in wound glass-reinforced plastics

The effect of the winding and polymerization conditions on the residual stress distribution in wound glass-reinforced plastic cylinders is subjected to a numerical analysis. The calculations are based on the method proposed in [1]. The computer data are examined and the theoretical and experimental results compared.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1026–1030, November–December, 1970.     

Bifurcation analysis of the mathematical model of the NO+CO/Pt(100) reaction

The article presents a detailed bifurcation analysis of steady and periodic states for a new mathematical model of the NO+CO/Pt(100) reaction. Various bifurcation diagrams are constructed in the planes of partial reagent pressures and surface temperature. Regions with oscillations and multiple steady solutions are investigated. Isolated branches of steady and periodic states are identified. An “explosive” bifurcation of the periodic solution leading to chaotic alternation of small-and large-amplitude oscillations is detected and analyzed for the first time. A good quantitative fit is demonstrated between modeling results and experimental data. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 52–78.     

Mathematical and informational issues of radiological element analysis

The article examines the mathematical model of recorded data and issues of sample element analysis by radionuclide methods. The proposed element-analysis technology is software-implemented in an intelligent interactive-graphical environment, which provides opportunities for active interaction with data banks and inclusion of expert support. This environment makes it possible to apply complex data-processing schemes coded in a special-purpose language and to adapt processing models and procedures to the specific features of data streams and to properties of the technological process or experiment. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 79–86.     

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.     

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.     

Anisotropic ring stretched by rigid half-disks

A theoretical basis is provided for the experimental method of determining the elastic and strength properties of materials by stretching ring specimens with a pair of rigid half-disks. The equilibrium equations of the plane problem for an anisotropic ring with mixed boundary conditions are solved by means of an expansion in Fourier series with respect to the circumferential coordinate. Numerical results obtained on a computer are analyzed. The dependence of the circumferential stress concentration coefficient on various parameters is investigated.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1113–1116, November–December, 1970.     

Way of Measuring Data Transfer Delays among Graphics Processing Units at Different Nodes of a Computer Cluster

Moscow University Computational Mathematics and Cybernetics - The basics of load tests for a computer cluster with a large number of GPUs (graphics processing units) distributed over the...     

Hereditary theory of creep and low-cycle fatigue of polymeric materials

The results of an investigation of the creep of polymethyl methacrylate under alternating loading and recovery are presented. The experiments ended in the failure of the specimen. The creep data obtained are described on the basis of the nonlinear Boltzmann-Persoz theory and Bryzgalin's theory of hereditary recovery. Korabel'nikov's result, according to which for alternating loading and recovery the total time under load up to failure is less than the static life of the polymer, is confirmed.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow; Scientific-Research Institute of Mechanics, Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 615–621, July–August, 1970.     

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.     

On fixed points of algebraic actions on ℂ n

It is shown that the action regarded for a rather long time by experts as a possible example disproving the conjecture on the existence of fixed points for reductive algebraic group actions on affine spaces is not an action on an affine variety, and therefore provides no example of this kind. Moreover, it is shown that the actions naturally related to the original one provide no examples of this kind as well. Supported by CRDF grant RM1-206 and INTAS grant INTAS-OPEN-97-1570. Moscow Independent University. Moscow Institute of Electronics and Mathematics. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 34, No. 1, pp. 41–50, January–March, 2000 Translated by V. L. Popov     

A method for approximate construction of the basic component in the class of functions of bounded variation

The article considers the construction of a stable approximation of the basic component in an experimental spectrum. Conditions of independence and nondegeneracy are introduced for the local resonance nonhomogeneities and the basic component, which is treated as a continuous smooth function whose local variation is substantially less than the variation of the local nonhomogeneities. The problem of approximating the basic component is shown to have a unique solution under these conditions. A stable algorithm is developed for the construction of the basic component. The algorithm is applied to construct the basic component from typical spectrometric data, and the results are compared with other known basic-component fitting methods. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 137–146.     

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.     

“Russian killer” no. 2: A challenging geometric theorem with human and machine proofs

In February 1998 Sergey Markelov [71 from the Moscow Center for Continuous Mathjematics Education sent a set of five geometric theorems to Dongming Wang for testing the capability of his GEOTHER package [8], with the aim of presenting a challenge to computer provers to prove really hard theorems. These theorems have been     

Hybrid synthesis of the optimal discrete nonlinear filter

It has been known for many years that an optimal discrete nonlinear filter may be synthesized for systems whose plant dynamics, sensor characteristics and signal statistics are known by applying Bayes' Rule to sequentially update the conditional probability density function from the latest data. However, it was not until 1969 that a digital computer algorithm implementing the theory for a one-state variable one-step predictor appeared in the literature. This delay and the continuing scarcity of multidimensional nonlinear filters result from the overwhelming computational task which leads to unrealistic data processing times. For many nonlinear filtering problems analog and digital computers (a hybrid computation) combine to yield a higher data rate than can be obtained by con¬ventional digital methods. This paper describes an implementation of the theory by means of a hybrid computer algorithm for the optimal nonlinear one-step predictor.

The hybrid computer algorithm presented reduces the overall solution time per prediction because:

1) Many large computations of identical form are executed on the analog computer in parallel.

2) The discrete running variable in the digital algorithm may be replaced with a continuous analog computer variable in one or more dimensions leading to increased computational speed and finer resolution of the exponential transformation.

3) The modern analog computer is well suited to generate functions such as the expo¬nential at high speed with modest equipment.

4) The arithmetic, storage, and control functions performed rapidly by the digital computer are utilized without introducing extensive auxiliary calculations.

To illustrate pertinent aspects of the algorithm developed, the scalar cubed sensor problem previously described by Bucy is treated extensively. The hybrid algorithm is described. Problems associated with partitioning of equations between analog and digital computers, machine representations of variables, setting of initial conditions and floating of grid base are discussed. The effects of analog component bandwidths, digital-to-analog and analog-to-digital conversion times, analog computer mode switching times and digital computer I/O data rates on overall processing time are examined. The effect of limited analog computer dynamic range on accuracy is discussed. Results from a simulation of this optimal predictor using MOBSSL, a continuous system simulation language, are given. Timing estimates are presented and compared against similar estimates for the all digital algorithm.

For example, given a four-state variable optimal 1-step predictor utilizing 7 discrete points in each dimension, the hybrid algorithm can be used to generate predictions accurate to 2 decimal places once every 10 seconds. An analog computer complement of 250 integra¬tors and multipliers and a high-speed 3rd generation digital computer such as the CDC 6600 or IBM 360/85 are required. This compares with a lower bound of about 3 seconds per all digital prediction which would require 49 CDC 6600's operating in parallel. Analytical and simulation work quantifying errors in one state variable filters is presented. Finally, the use of an interactive graphic system for real time display and for filter evaluation is described.     

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.     

Long-time asymptotics for a classical particle interacting with a scalar wave field

We consider the Harniltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to a confining external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. We prove that solutions of finite energy converge, in suitable local energy seminorms, to the set of stationary solutions in the long time limit t f oo. The rate of relaxation to a stable stationary solution is determined by spatial decay of initial data. 'Supported partly by French-Russian A.M.Liapunov Center of Moscow State University, by research grants of RFBR (9601-00527) and of Volkswagen-Stiftung.     

Exact solution to the behavior of the electron plasma in a metal layer in an alternating electric field

Exact expressions are obtained for the first time for the response of the conduction electrons in a metal layer to an external alternating electric field. Case's well-known method of separation of the variables is modified, and the methods of singular integral equations and boundary-value problems of complex analysis are used. The solutions can be used to determined the screened field and also the absorption in a metal layer in a wide range of frequencies.N. K. Krupskaya Moscow Region Pedagogical Institute; Moscow Institute of Chemical Mechanical Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 2, pp. 179–189, February, 1992.     

Relation between the shear and longitudinal viscosity coefficients for concentrated polymer solutions

A relation between the shear and longitudinal viscosity coefficients is obtained on the basis of the theory of flow of polymeric systems in the single relaxation time approximation. A comparison of the shear and longitudinal viscosity coefficients for polymer melts and solutions shows that the relation obtained is valid over a broad stress region.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Scientific-Research Institute of Synthetic Fibers, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 124–131, January–February, 1973.     

Model studies of stress-intensity factors near cracks interacting with fibers

The problem of determining the stress-intensity factors near cracks interacting with fibers is solved for the first time using data from optical-polarization measurements. Simplified models of composites are investigated — plates reinforced with single short fibers with cracks assigned on one of the ends of the fibers and tensioned in the direction of the fibers. The plates (dies) were fabricated from a photosensitive material, and the fibers were modeled by bars of steel, glass, and polymer. The stress-intensity factors were determined from Eq. (5) using data derived from optical-polarization measurements at several points by the nonlinear method of least squares. We investigated the influence exerted by several physical and geometric parameters on the stress-intensity factors. It was established that the stress-intensity factor K₁ near the end of a crack interacting with a fiber is higher than the factor K⁰ ₁ near a crack of corresponding length in the unreinforced plate. The ratio K₁/K⁰ ₁ depends on the mechanical properties of the fiber and die materials and the geometric dimensions of the crack and fiber. Despite the fact that these results were obtained using simplified models of composites, they are of interest for evaluation of the failure and serviceability of real composites.Scientific-Research Institute of Mechanics, M. V. Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 493–501.