Solitons in plasma with a hall dispersion

A system of equations of perfect magnetohydrodynamics is considered with allowance for Hall currents. The study of one-dimensional steady solutions which are damped at infinity can be reduced to the investigation of a Hamiltonian dynamic system with right-hand sides that are not single valued. A qualitative investigation of the system is carried out, with the determination of the region of existence of the given solutions. The solutions have the form of solitary waves — solitons. An exact solution in quadratures is obtained, which describes the structure of the solitons. The existence of two solitons of the Alfvén type is indicated. The existence domain of the corresponding solutions is analyzed. In the limiting cases of magnetosonic and Alfvén solitons, the solutions are expressed in explicit form in elementary functions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–168, September–October, 1985.     

Propagation of instability in electron beam systems

The nature of the normal mode instability of a plasma interacting with an electron beam [1] is studied. Dispersion equations of this type also occur for a whole series of physical phenomena. The velocities at which the initially localized disturbance propagates in an infinite system are determined. It is shown that the system is globally unstable [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–132, July–August, 1977.In conclusion, the author thanks A. G. Kulikovskii and A. A. Barmin for valuable advice and their interest in the work.     

Numerical solution of the problem of the flow of a supersonic gas stream over the upper surface of a delta wing in the expansion region

A numerical method is described for the calculation of supersonic flow over the arbitrary upper surface of a delta wing in the expansion region. The shock wave must be attached everywhere to the leading edge of this wing from the side of the lower surface. The stream flowing over the wing is assumed to be nonviscous. A problem with initial conditions at some plane and with boundary conditions at the wing surface and the characteristic surface is set up for the nonlinear system of equations of gas dynamics. The difference system of equations, which approximates the original system of differential equations on a grid, has a second order of accuracy and is solved by the iteration system proposed in [1]. The initial conditions are determined by the method of establishment of self-similar flow. A number of examples are considered. Comparison is made with the solutions of other authors and with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 76–81, November–December, 1973.The author thanks A. S. II'ina who conducted the calculations and V. S. Tatarenchik for advice.     

Theory of slightly perturbed three-dimensional flows in nozzles

The theory of slightly perturbed flows in conical nozzles is used to determine the transverse force and moment generated in the presence of asymmetric perturbations. A system of ordinary differential equations is derived for finding the transverse force and moment. An approximate analytical solution of this system is constructed and its qualitative features are studied. A comparison is made with a numerical solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–154, January–February, 1977.     

Dynamic-model reduction for a multimass system with nonideal constraint in a seismic damper

A dynamic model for a multimass system with a seismic damper as a nonlinear inertial component is reduced via balancing. The seismic damper is subject to a nonideal constraint. As an example, the order of the system of differential equations is reduced by one for a dynamic three-mass system. A comparison of the processes in the original and reduced systems confirms that it is possible to use balancing to simplify such models Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 136–144, August 2008.     

The experimental analysis of non-linear waves in mechanical systems

Summary A system is described for experimentally analysing non-linear waves to a high degree of accuracy. The system has been used in conjunction with aWeissenberg rheogoniometer and some specimen results are presented on a complex soap-based grease, a synthetic dye based grease and a polymer solution.     

Overlapping grids and multigrid methods for three-dimensional unsteady flow calculations in IC engines

A new computational methodology with emphasis on using an overlapping grid technique and a multigrid method has been developed. The main feature of the present overlapping-grid system is of extended flexibility to deal with three-dimensional complex multicomponent geometries. The multigrid method is incorporated into this technique to accelerate the convergence of the numerical solution. The current scheme has been applied for computations of the laminar flows in the multicomponent configuration of internal combusion engines. The flow is governed by three-dimensional, time-dependent, incompressible Navier-Stokes equations with the continuity equation. A time-independent grid system is constructed for the moving boundary, i.e. the moving piston in the engine. This grid system is entirely different from others for the same problem in previous works. The performance of the present method has been validated by comparing the results with those from an equivalent, single-grid method and those from experiments. In addition, the flexibility and potential of the method has been demonstrated by calculating several cases which would be very difficult to be handled by other schemes.     

Vibrationally nonequilibrium flow of a compressible gas in an axisymmetric channel in the presence of glow discharge

A laminar subsonic flow of CO-He-N₂ mixture in an axisymmetric channel with glow discharge is investigated. The actual flow diagram is modeled on the basis of a system of narrow-channel equations. The results of the calculations are compared with the experimental data. The possibility of applying a one-dimensional system of equations is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 114–119, November–December, 1985.The authors wish to thank B. S. Aleksandrov for his help in the work.     

Vortex motions of liquid in a narrow channel

Quasi-linear integrodifferential equations that describe vortex flows of an ideal incomparessible liquid in a narrow curved channel in the Eulerian-Lagrangian coordinate system are considered. The necessary and sufficient conditions for hyperbolicity of the system of equations of motion are obtained for flows with a monotonic velocity depth profile. The propagation velocities of the characteristics and the characteristic form of the system are calculated. A particular solution is given in which the system of integrodifferential equations changes type with time. The solution of the Cauchy problem is given for linearized equations. An example of initial data for which the Cauchy problem is ill-posed is constructed. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 38–49, July–August, 1998.     

On the control problem for a compound wheeled vehicle

A compound transport vehicle with one steerable wheel is considered as a controlled mechanical system with nonholonomic constraints. A control system for this system is synthesized within the framework of the kinematic approximation. A procedure is proposed to synthesize a robust controller for the system. The efficiency of this procedure is demonstrated with an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 105–112, November 2007.     

Dynamic Processes in a Spheroidal Seismic-Damping Mechanism

A mathematical model of a variable-structure system of solids with rolling friction and unilateral sliding friction bonds is described. The model can be applied to seismic isolation mechanisms. Conditions for transition between the possible structures of the equations of state are formulated. The behavior of the system with kinematically defined motion of the base is analyzed as an example__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 119–127, January 2005.     

Shallow waves in a two-layer vortex fluid under a lid

A mathematical model of the vortex motion of an ideal two-layer fluid in a narrow straight channel is considered. The fluid motion in the Eulerian-Lagrangian coordinate system is described by quasilinear integrodifferential equations. Transformations of a set of the equations of motion which make it possible to apply the general method of studying integrodifferential equations of shallow-water theory, which is based on the generalization of the concepts of characteristics and the hyperbolicity for systems with operator functionals, are found. A characteristic equation is derived and analyzed. The necessary hyperbolicity conditions for a set of equations of motion of flows with a monotone-in-depth velocity profile are formulated. It is shown that the problem of sufficient hyperbolicity conditions is equivalent to the solution of a certain singular integral equation. In addition, the case of a strong jump in density (a heavy fluid in the lower layer and a quite lightweight fluid in the upper layer) is considered. A modeling that results in simplification of the system of equations of motion with its physical meaning preserved is carried out. For this system, the necessary and sufficient hyperbolicity conditions are given. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 68–80, May–June, 1999.     

Analysis of hydrodynamic behaviors of multiple net cages in combined wave–current flow

Numerical simulation is performed to analyze the hydrodynamic response of a net cage and submerged mooring grid system exposed to waves and current. A series of experiments are conducted to validate the numerical model of net cage and grid mooring system. The numerical results of this model correspond with those obtained from experimental observations. Then, the numerical simulation of a multi-cage and mooring system under the action of waves combined with current is conducted. The influence of waves and current directions and the length of grid lines on the cage responses are discussed. The twin mooring system and the orthogonal mooring system are compared. Results show that for the orthogonal mooring system, the maximum tension force on the anchor line of the four-cage system is less than four times of that of the single-cage system, when both waves and current travel along the x-axis. The minimum net cage volume holding coefficient of the single-cage system is smaller than that of the four-cage system. The amplitude of the mooring line tension force for the twin mooring system is larger than the orthogonal mooring system.     

A Pressure Field in an Acoustic Medium Containing a Cylindrical Solid and a Sphere Oscillating in a Predetermined Manner

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered     

Whole field measurement of temperature in water using two-color laser induced fluorescence

 A technique is described that measures the instantaneous three-dimensional temperature distribution in water using two-color laser-induced fluorescence (LIF). Two fluorescent dyes, Rhodamine B and Rhodamine 110, are used as temperature indicators. A laser light sheet scanned across the entire measurement volume excites the fluorescent dye, and an optical system involving a color beam splitter gives the intensity distribution of the individual fluorescent dyes on two separate monochrome CCD cameras. The ratio of these fluorescence intensities at each point of the image is calibrated against the temperature to eliminate the effect of the fluctuation of illuminating light intensity. A stable thermally stratified layer was measured by this system to evaluate the total accuracy of the measurement system. The random error of the measurement was ±1.4 K with 95% confidence. Measurements of thermal convection over a heated horizontal surface show temperature iso-surfaces having typical structures such as plumes, ridges and thermals. Received: 1 October 1997/Accepted: 23 March 1998     

Stress distribution around a circular cylindrical cavity in a prestressed plate

A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and used to determine the stress state of a plate with a circular cylindrical cavity __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 28–39, January 2008.     

Multi-frequency oscillations in self-excited systems

A self-excited three-mass chain system is considered here. For a self-excitation of van der Pol type, the possibility of multi-frequency oscillations is investigated. Both analytical approximate solutions and numerical simulation are used. The averaging method is used to establish existence and stability of the normal modes, the two-frequency modes as well as the three-frequency oscillations solutions. We found at first that the single mode seems to prevail. However a three-frequency solution can be stabilised by adapting the system slightly. A generic bifurcation diagram is given where all the possible phase portraits are sketched. The flow turns out to be quite predictable. There is no “room” for chaos or strange attractors. This behaviour is not typical for systems of coupled oscillators but turns out to be partly related to the involved symmetries as well as the particular choice of the system parameters.     

A rigorous assessment of the benefits of miniaturization in the Kolsky bar system

A rigorous experimental and numerical assessment is made of the benefits and limits of miniaturization in the Kolsky bar system. The primary issues that arise in very high strain rate testing (stress equilibration, inertial effects, wave dispersion, friction, and controllability of deformations) are addressed through experiments coupled with explicit finite element analyses. A miniaturized Kolsky bar system that includes the input bar is developed, together with the use of the laser occlusive radius detector to obtain local measurements of specimen strain during the very high rate deformations. It is demonstrated that this miniaturized Kolsky bar system can be used to provide fully validated results, including the explicit determination of equilibration, over a very wide range of strain rates (1×10³ to 5×10⁴ s⁻¹). The desired high strain rate can be achieved even at low accumulated strains, and the total strain developed can be controlled very effectively. Specific conditions are developed for determining the range of utility of the technique for a given material. The technique is applied to the characterization of 6061-T651 aluminum, and the results are compared with the results obtained using a conventional Kolsky bar.     

Evaluation of autooscillation parameters in two-mass systems with dey friction

A system of two differential equations is used to describe the motion of a two-mass system subject to a constant force and viscous and dry friction. The relationship between dry friction and the relative sliding force is expressed in terms of an odd nonmonotonic function with a discontinuity of the second kind. The averaging method is used for analytical analysis. The initial system of differential equations is transformed into a system with rapidly rotating phase by introduction of special variables. Partical solutions of the first approximation equations are obtained, and their stability studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 32, No. 8, pp. 87–94, August, 1996.     

“Bunched” model of corona discharge in a gas-dynamical flow

In the present paper, a theoretical model of corona discharge is proposed for the case when electric charge transport is implemented by means of the motion of discrete charged bunches of finite dimensions. A system of equations and boundary conditions is formulated for the study of unsteady cyclic processes in a corona discharge. The electric field induced by the space charge of bunches and the presence of an external electric circuit are taken into account. A solution of the formulated system of equations for corona discharge with spherical geometry is obtained. The integrated (current-voltage) characteristics and the amplitude-frequency characteristics of the corona discharge are found. The proposed theory is generalized to the case of a corona discharge in a moving gas. The unsteady characteristics of corona discharge with spherical geometry for gas motion in a radial direction are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 153–160, January–February, 1986.The authors wish to express their gratitude to V. A. Likhter and V. I. Shul'gin for their useful discussions and valuable observations.