Nonstationary interaction of supersonic inviscid gas flows

We consider the flow of supersonic homogeneous gas past a supersonic spherical source. This problem provides a gas-dynamic model of the interaction of interstellar wind with solar wind, and is thus also of independent interest. It is solved using an explicit through divergence scheme of third-order approximation. The analysis focuses on formation and stability of the structure of discontinuity surfaces and convergence to the stationary solution. The results are compared qualitatively and quantitatively with solutions obtained by other methods. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 125–128.     

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.     

System of equations describing the flow of viscous liquid and gas in a wide range of reynolds numbers

A mathematical model is proposed for describing stationary and various self-exciting nonstationary (including turbulent) flows of viscous liquid and gas. The model does not assume that the stressed state at the points of the medium is described by a symmetric stress tensor. The model thus allows for internal moments of elementary viscous liquid and gas volumes relative to their centers of mass and for unsymmetric strains.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 17–26.     

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.     

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.     

Investigation of surface destruction of construction materials under intense periodic heat transfer

The study simulates the surface destruction of structural steel elements in power installations as a result of interaction with periodic high-temperature chemically active flows. The system of equations of thermoelasticity with two spatial observations is used. The existence of high tangential and axial compressive stresses is established in a thin layer near the metal-gas interface. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 115–118.     

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.     

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.     

Investigation of stress intensity factors near interacting cracks in linear viscoelastic plates

Stress intensity factors as a function of time near interacting cracks during creep in plates made of linear viscoelastic materials are investigated. The interaction of collinear as well as parallel cracks disposed on different levels perpendicular to the tensile stress was studied. It was found that during interaction of collinear cracks, the stress intensity factor K₁(t) grew in creep and varied mainly due to the change in the distance between the tips of interacting cracks. There was practically no increase in the length of the crack. During interaction of parallel cracks, the value of K₁(t) decreased slightly in time, which was also due to an increase in the distance between the tips of the cracks in creep.Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 643–650, September–October, 1998.     

Theoretical strength of polymers in a completely oriented state

A solution is presented of the problem on the theoretical strength of a completely oriented polymer by accounting for the intermolecular interaction and finiteness in the length of polymer chains.V. I. Lenin Moscow State Pedagogical Institute, Research Laboratory of the Physics of Polymers. Translated from Mekhanika Polimerov, No. 3, pp. 458–464, May–June, 1970.     

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.     

Initial stage of laser-induced crack development in polymethyl methacrylate

It is shown that the successive stages of development of the damage caused by a laser beam are the same in technically pure polymethyl methacrylate and the same material containing artificially introduced absorbing particles. The formation of the characteristic flat cracks from gas bubbles in the specimen is observed. The mechanism of fracture development in polymethyl methacrylate is further refined.Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 551–552, May–June, 1971.     

Origin of laser damage in transparent dielectrics of the plexiglas type

A gasification mechanism is proposed. This mechanism is based on multiphoton photodegradation of the polymer molecules and the resulting formation of free radicals which trigger a chain reaction and the subsequent formation of gas molecules. The kinetics of this process, in which an important part is played by the microstructure of the material, are examined.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 232–238, March–April, 1973.     

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.     

Gibbs random fields invariant under infinite-particle Hamiltonian dinamics

The Liouville operator for an infinite-particle Hamiltonian dynamics corresponding to interaction potentialU is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interactionU.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 3, pp. 424–459, March, 1992.     

The theory of orientational drawing of linear amorphous polymers

On the basis of modern ideas on the structure of linear, amorphous polymers a model of a molecular, three-dimensional network with temporary cross-links and van der Waals interaction between the chains is presented. Using this model as a starting point, a differential equation for the deformation of a linear, amorphous polymer in the viscoelastic state is derived. The differential equation for the orientation of a linear, amorphous polymer, which describes the evolution of distribution functions for statistical segments, is obtained. Previously obtained results follow from this theory as special cases.V. I. Lenin State Pedagogic Institute, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1021–1028, November–December, 1974.     

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.     

Nicolai Nicolaevich Luzin and the Moscow school of the theory of functions

Shortly before the revolution of 1917, four papers written by participants in N. N. Luzin's analysis seminar at Moscow University appeared in the Comptes Rendus of the Paris Academy of Sciences. The publication of these papers--written by A. Ya. Khinchin, D. E. Menshov, P. S. Aleksandrov and M. Ya. Suslin--and Luzin's monograph, The Integral and Trigono-metric Series 1915, marked the emergence of Moscow University as a center of research in the theory of functions of a real variable. This paper describes Luzin's early mathematical education at Moscow University and the three year period he spent abroad (mainly in Paris) where he wrote a series of papers whose results form the core of his influential and widely praised monograph. Finally, we will show how Luzin's ideas formed the basis for the early investigations of a series of young Moscow mathematicians.     

A study of glass reinforced polyethylene

The effect of dressing a fiber on the wetting of it by a polyethylene melt is studied. The interconnection between the value of the adhesive strength and the residual stresses at the boundary between the glass fiber and polymer is analyzed. The role of the residual stresses during use of the glass-reinforced material and the part played by the chemical interaction between the polyethylene and the fiber in the water-resistant composition obtained in this way is analyzed.D. I. Mendeleev Moscow Chemicotechnical Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1048–1052, November–December, 1972.     

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.