Analytical Solutions of the Equation Describing Internal Gravity Waves Generated by a Moving Nonlocal Source of Perturbations

Computational Mathematics and Mathematical Physics - The problem of constructing analytical solutions describing internal gravity wave fields generated by a nonlocal source of perturbations moving...     

Analytical Solutions of the Internal Gravity Wave Equation in a Stratified Medium with Shear Flows

Computational Mathematics and Mathematical Physics - The problem of constructing internal gravity wave fields generated by an oscillating localized point source of disturbances in a stratified...     

Interaction of 1-acylamino-2,2-dichloroethenyl(triphenyl)phosphonium chlorides with alkanolamines

Abstract

It is shown that the interaction of 1-acylamino-2,2-dichloroethenyl(triphenyl)-phosphonium chlorides with alkanolamines having a primary amino group results in the formation of 4-oxazolylphosphonium salts containing hydroxyalkylamine substituents at position 5 of the oxazole cycle. Under similar conditions the reaction of N-substituted alkanolamines with 1-acylamino-2,2-dichloroethenyl-(triphenyl)phosphonium chlorides leads to the formation of 1,3-oxazolidin-2-ylidene derivatives, in which the triphenylphosphonium group is located in the side chain. The structure of the new synthesized compounds has been reliably proven by elemental analysis, IR, ¹Н, ¹³С, ³¹Р NMR spectroscopy, mass spectrometry and single crystal X-ray diffraction.     

Early Stage of Structural Changes and Molecular Dynamics of Cytochrome C in an Aqueous Solution Caused by the Addition of Methanol

Crystallography Reports - Molecular dynamics simulations of horse heart cytochrome C were performed in an aqueous solution and in a 50 : 50 water–methanol mixture. Three independent 100-ns...     

Three-dimensional instability of an elliptic Kirchhoff vortex

The instability of a Kirchhoff vortex [1–3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4–6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4–9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1988.     

Example of parametric resonance in a rotating flow

Parametric resonance is one of the common types of instability of mechanical systems [1]. A standard example of the equations describing parametric oscillations is the Mathieu equation and its generalizations. In hydrodynamics these oscillations have been closely studied in connection with the problem of the vertical oscillations of a vessel containing an incompressible fluid in a uniform gravity field [1–5]. In this paper a new example of a flow whose stability problem reduces to the Mathieu equation is given. This is a flow of special type in a rotating cylindrical channel. The direction of the angular velocity is perpendicular to the channel axis, and its magnitude varies periodically with time. Flows with this geometry are of potential interest in technical applications [6, 7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–177, March–April, 1987.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Mathematical modeling of mechanical properties of metals and alloys at large strains

We discuss problems in mathematical modeling of the mechanical behavior of metals and alloys at large strains. Attention is mainly paid to the analysis of the stress-strain state of specimens and structural fragments made of highly plastic materials with the effect of stability loss under tensile stresses taken into account. We discuss the methods for determining the true property diagram at strains exceeding the ultimate uniform strain. We process experimental data and determine the true property diagrams for AMg6, AMg6M, and 1201 aluminum alloys and BrKh08 alloy. To calculate the load-carrying capacity of structural members, one often uses the conventional ultimate strength σ _b accepted in regulations as a material characteristic. But it follows from the method for experimentally determining this characteristic that it depends on the properties of the specimen viewed as a structure. As a result, a formal use of fracture criteria recommended in regulations leads to a discrepancy between design and experimental values of fracture loads. Nowadays, the finite element method is widely used in practical strength analysis. This method permits one to study the elastoplastic strained state of geometrically complicated structures in detail, take into account physical nonlinearity at large strains, determine damage boundaries, and improve experimental methodology. The wide capabilities of this method allow one to use test results more completely.     

Slow motions of a solid in a continuously stratified fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 55–60, March–April, 1991.     

Jet flow around a plate near a wall

Chaplygin's method [1] has been extended by Fal'kovich [2] to the case of several characteristic velocities; it has here been used to solve the two-dimensional unsymmetrical problem of subsonic gas jet flow around a plate near a solid wall. The Zhukovskii-Roshko scheme [3,4] has been used with a stagnant zone ahead of the plate. Formulas are derived for the current function, normal-pressure coefficient, and geometrical elements of the flow. The result is extended to the case of an incompressible fluid by passing to the limit.