Field-theory models that admit alternative Lagrangian formulations. II

A large class of field-theory models that admit alternative Lagrangian formulations is described. It includes, in particular, all bi-Lagrangian field theories with hyperregular first-order Lagrangians.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 55–64, January, 1992.     

Influence of the nature of the modifying cation on the activity and selectivity of CO/SiO2 catalysis of hydrocarbon synthesis from CO and H2

The catalytic properties of Co/SiO₂ catalysis, modified with cations (L) of various chemical types, were investigated in the synthesis of higher hydrocarbons from synthesis gas. A number of changes ascertained in the specific catalytic activity and selectivity, depending on the nature of L, were interpreted on the basis of the previously substantiated mechanism of hydrogenation of CO on transition metals.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 3, pp. 197–201, May-June, 1992.     

Three-dimensional theory of the equation of ablation of bodies in a high-temperature gas stream

An integrodifferential ablation equation is obtained within the framework of a local-integral model with allowance for three-dimensional effects in the convective heat transfer law. Owing to the dependence of the latter on the azimuthal derivatives of the surface shape, determined by the divergence of the inviscid streamlines at the surface, this equation is third-order in the space variables, and if the asymmetry of the problem is small, acquires the features of the wave equation. An attempt is made to classify such equations, and in particular their characteristic properties, and the regions of influence and dependence of the solutions, etc., are investigated. These results can be useful both for further analytic research and in developing numerical methods of solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–151, January–February, 1987.     

On the possible separation of the phase enriched with Nb in superconducting intermetallic Nb<Subscript>3</Subscript>Sn irradiated with fast protons

The results of the study of magnetization and dynamic magnetic susceptibility are correlated with changes in the microstructure of superconducting intermetallic Nb₃Sn plates irradiated at the Kurchatov Institute cyclotron with fast protons with an energy of 12.8 MeV to a fluence of 1 · 10¹⁸ cm^?2. The dependence of the superconducting transition temperature on the total irradiation dose is determined. For one of the samples, the dynamic magnetic susceptibility exhibits several steps corresponding to superconducting transitions at different temperatures. It is assumed that a Nb-enriched phase is separated in the region of maximum radiation damages. A microstructural analysis shows the appearance of randomly oriented Nb-enriched regions from 0.1 to 0.5 μm in size.     

Luminescent sensor materials based on rare-earth element complexes for detecting cations,anions, and small molecules

Russian Chemical Bulletin - Various strategies for producing lanthanide-containing luminescent sensors, which were used mainly in the studies of 2015–2021, are considered. The review is...     

Basic Relationships of the Autowave Model of a Plastic Flow

Russian Physics Journal - Macroscopic laws of the development of plastic flow localization autowaves in metals, alloys, alkali halide crystals, and rocks are investigated. It is shown that the...     

Model of a viscous nonequilibrium shock layer with a thin shock wave

It is shown that the concept of a viscous shock layer with boundary conditions specified in a thin shock wave is unsuitable for analyzing the flow of a chemically reacting gas, even in the case of high Reynolds numbers; it may produce a finite error when determining the parameters of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1973.     

Method of effective length for the boundary layer on a thin filament drawn out of a half-space

Heat transfer from a thin filament pulled from a half-space is considered. On the basis of the self-similar solution, obtained in the study, and using the method of effective length, the friction and heat transfer coefficients on the surface of a thin filament of varying radius and with distributed surface temperature and velocity are determined. The results obtained with this approximate method agree well with the results of a numerical solution of the boundary layer equations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–28, January–February, 1994.     

Boundary layer development in a gas flow with stagnation enthalpy varying across the streamlines

We consider a laminar boundary layer for which the stagnation enthalpy specified in the initial section is variable with height. Such problems arise, for example, for bodies located in the wake behind another body, for hypersonic flow past slender blunted bodies (as a result of the large transverse entropy gradients in the highentropy layer), for stepwise variation of the temperature of a surface on which there is an already developed boundary layer, for sudden expansion of the boundary layer as a result of its flow past a corner of the surface, etc.Strictly, we should in such cases solve the boundary layer equations (if the longitudinal gradients are much smaller than the transverse) with the specified initial distribution of the quantities. However, from the physical point of view, the distributed region may be broken down into two regions, the near-wall boundary layer and an outer region which is a gas flow with constant velocity and the specified initial temperature profile, whose calculation yields the edge conditions for the boundary layer. The boundary between the regions is determined from the condition of adequately smooth matching of the solutions. This approach is much preferable to the first, since it permits avoiding (within the framework of boundary layer theory) the difficulties associated with the presence of a possible singularity at the initial point of the surface due to the discontinuity of the boundary conditions at this point, and also permits using conventional boundary layer theory if the effect of the viscosity in the outer region is not significant. However, this partition requires additional justifications of the possibility of independent determination of the solution in the outer region and the determination of the edge of the boundary layer, considered as the region of influence of the wetted surface. The boundary layer in a nonuniform flow has been considered in several works for a linear initial velocity or temperature profile [1–3].It should be noted that the linear initial enthalpy or velocity profiles for constant gas properties do not undergo changes under the influence of viscosity or thermal conductivity. Thus the fundamental characteristic features noted above which are associated with the presence of the two regions and their interaction in essence cannot be investigated using these examples.In this study we obtain and analyze the exact solutions of the equations of the compressible boundary layer for a power-law variation of the initial stagnation enthalpy profile as a function of the stream function for a constant initial velocity. Here it is shown that the influence of the boundary conditions at the wall are actually localized in the near-wall boundary layer, which is similar in dimensions to the conventional velocity or thermal boundary layers. In the region which is external with relation to this layer, in accordance with the physical picture described above, the solution coincides with the solution of the Cauchy problem for the heat conduction equation, which describes the development of the initial temperature profile in an infinite steady-state flow with constant velocity.It is shown that for the sufficiently smooth initial profiles which are of interest in practice the outer flow undergoes practically no changes until we reach the inner boundary layer, and it may be calculated using the perfect gas laws.