Studying the Complex Oscillations of a Star in the Field of a Galaxy

The oscillations of a star in the filed of a galaxy are studied. Initial energy conditions are established under which regular and complex oscillations occur. The latter are different from regular oscillations by the presence of saddle solutions in the trajectory. Unstable oscillations are due to only saddle solutions, with the trajectory tending to infinity     

Influence of the parameters of a cross-flow on the gain in a jet

A system of equations is proposed for calculating a turbulent axisymmetric jet in a cross-flow for gases with different physical properties. The mixing of carbon dioxide gas with excited nitrogen and helium in a gas-discharge laser has been investigated numerically. Vibrational relaxation of the mixed gases was taken into account. The calculated gain agrees satisfactorily with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–37, July–August, 1930.We thank A. P. Napartovich for helpful discussions and V. F. Gerasiaov for providing the experimental data.     

Calculation of the movement of a twisted flow of a gas suspension about the end of a semi-infinite cylinder

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 27–32, May–June, 1993.     

Computer solution of the problem of the depletion of a stratum with a gasified liquid in the case of the work of a round battery of boreholes

The article discusses the problem of the depletion of a round stratum with a gasified liquid, in the case of the work of a round battery of boreholes with constant end-face pressures. The nonlinear differential equations describing the filtration process are replaced by finite-difference equations, which are solved numerically using a computer program. The condition for the convergence of the finite-difference scheme used is given. The proposed algorithm is used to solve a concrete example. By making analogous calculations for different variants of a given number of boreholes, of the end-face pressures, of the radius of the battery, valuable information can be obtained with respect to their optimal values, the time of the start of secondary methods of exploitation, the volume of gas dissolved in the petroleum, as well as the output of petroleum, which is easily calculated from the known values of the pressure and the petroleum saturation at any given moment of time.     

Influence of the atmosphere on the magnitude of the hydrodynamic forces in the case of a disk in a flat encounter with the surface of a compressible liquid

If the velocities with which bodies enter liquids are small, and the bodies are not too blunt, the magnitudes of the hydrodynamic forces can be satisfactorily determined in the framework of the approximation of an incompressible liquid and depend on the density of the liquid, the velocity of entry, and the geometrical parameters (shape of the body, angles of entrance and attack). If the velocity is increased or the encounter with the surface becomes nearly flat, the compressibility of the liquid and the presence of an atmosphere begin to influence the hydrodynamic forces significantly. The influence of the compressibility on the magnitude of the impact loads has been investigated theoretically and experimentally [1–8]. The influence of the atmosphere in the case of an incompressible liquid has also been taken into account [9–11]. In the case of a flat encounter the two factors (compressibility of the liquid and presence of the atmosphere) simultaneously influence the development of the impact process. The present paper reports experimental results and computer calculations of the impact loads in the case of a flat encounter of a disk and the surface of a compressible liquid in atmospheres of helium, air, and freon.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 15–20, May–June, 1984.     

On the effect of a high-frequency magnetic field on the instability of a plasma

The action of a high-frequency magnetic field on low-frequency instabilities of a plasma is considered. The harmonics of the high-frequency field that appear under these conditions are taken into account. It is shown that their effect on the reduction of the growth rate of the instability is weak. However, in analyzing the oscillation spectrum consideration of these harmonics is necessary, since they have the same growth rate as does the suppressed instability. It is well known that in a plasma situated in a strong magnetic field H_0Z unstable oscillations develop, the most dangerous being electrostatic oscillations that propagate almost perpendicular to the magnetic field (k k_¦). These oscillations have the form of troughs extended almost along H_0Z. If it were possible by some method to create conditions under which particles of one species (either electrons or ions) would have time to traverse the distance between the humps of the troughs in a time considerably shorter than the period 2/ of the unstable oscillations, then the potential of the instability would be smoothed out (i.e., the instability would be suppressed). This may be achieved by exciting a high-frequency magnetic field H₁(t) = H₁ cos t( ) in the plasma, which is oriented perpendicular to the constant field H_0z. Then the crossing of the humps by the particles is achieved as a result of motion with thermal velocities along the resultant curved magnetic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 10–14, March–April, 1971.The author thank A. V. Gordeev for fruitful discussions.     

Motion of a sphere in a vibrating liquid in the presence of a wall

A solution is obtained for the problem of the motion of a sphere in an ideal liquid bounded from outside by a wall which performs specified vibrations far from the sphere. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090, Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 125–132, July–August. 1999.