Nonlinear waves in an active-dissipative disperse medium

Nonlinear waves in a medium involving dissipation, dispersion, and enhancement described by the generalized Kuramoto-Sivashinsky equation are discussed. Analytical solutions of the equation are obtained in the form of solitary waves. For numerical modeling of the nonlinear waves a difference scheme is suggested. Interaction of nonlinear waves described by the Kuramoto-Sivashinsky model is considered. It is shown that for specified values of the problem parameters there is one solitary wave described by the initial model. The dependences of the velocity and amplitude of this wave on the problem parameters are determined. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 1, pp. 149–154, January–February, 1998.     

Long-wave transverse instability of interfacial gravity–capillary solitary waves in a two-layer potential flow in deep water

Interfacial gravity–capillary plane solitary waves, driven by the gravitational force in the presence of interfacial tension in a two-layer deep-water potential flow, bifurcate in the form of wavepackets with a non-zero carrier wavenumber at which the phase speed is minimized. A stability property for the interfacial gravity–capillary plane solitary waves is presented within the framework of the full Euler equations: according to a linear stability analysis based on the perturbation method, such waves are unstable under weak and long-wave disturbances in the transverse direction to the dominant wave propagation. An instability criterion is verified that the total mechanical energy of the solitary waves is a decreasing function of the solitary wavespeed, owing to the fact that the speed of the bifurcating solitary wavepackets is less than the minimum of the phase speed. This result is consistent with an earlier study on the transverse instability of the longitudinally stable interfacial gravity–capillary solitary waves from the Benjamin model equation for weakly nonlinear long interfacial elevations (Kim and Akylas, J Fluid Mech 557:237–256, 2006). The analysis is also applicable to other interfacial gravity–capillary solitary waves that may bifurcate below the minimum of the phase speed, regardless of any restrictions on fluid depths in two-layer potential flows.     

On propagation of linear waves in a cylindrical channel with a permeable wall

Problems on propagation of harmonic waves and of waves of finite duration in a cylindrical channel filled by a liquid or a gas and surrounded by a porous permeable space are considered. A wave equation describing the dynamics of small disturbances in a cylindrical channel with a permeable wall is obtained. Results of the analysis of wave evolution are presented for the cases of channel filling by a liquid and a gas. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 907–913, November–December, 1997.     

Solitons of a surface magnetostatic spin wave in a ferrite-insulator-metal structure

The nonlinear Schrodinger equation is analyzed in order to theoretically investigate nonlinear surface magnetostatic spin waves in a planar ferrite-insulator-metal structure. It is shown that for specific distances between the metal screen and the ferromagnetic film, pulses of surface magnetostatic spin waves may propagate as envelope solitons. Pis’ma Zh. Tekh. Fiz. 25, 48–54 (February 26, 1999)     

Thermo elastic waves with thermal relaxation in isotropic micropolar plate

In the present investigation, we have discussed about the features of waves in different modes of wave propagation in an infinitely long thermoelastic, isotropic micropolar plate, when the generalized theory of Lord–Shulman (L–S) is considered. A more general dispersion equation is obtained. The different analytic expressions in symmetric and anti-symmetric vibration for short as well as long waves are obtained in different regions of phase velocities. It is found that results agree with that of the existing results predicted by Sharma and Eringen in the context of various theories of classical as well as micropolar thermoelasticity.     

Interaction of relaxational waves with waves of a redistributing surfactant on a free surface of a liquid

Thermal capillary wave motion on a charged free surface of a liquid covered with a surfactant film gives rise to waves of redistributing charge (equalizing the electrical potential) and waves of the surfactant (equalizing the concentration of the surfactant). Numerical analysis of the dispersion equation shows that in some range of physical parameters the waves of charge interact with the waves of surfactant, forming two new branches of charge-concentration waves. Pis’ma Zh. Tekh. Fiz. 23, 25–31 (September 26, 1997)     

Generation of electromagnetic waves by electrons rotating in a radial electrostatic field in free space

A theoretical analysis is made of mechanisms for the generation of electromagnetic waves by electrons rotating in a radial electrostatic field formed by a positively charged filament in free space. A dispersion equation is obtained to describe the interaction between the waves and nonrelativistic electrons. It is shown that electromagnetic fields can be generated by means of Čerenkov resonance. The frequencies and growth rates of the emitted waves are determined and their dependence on the parameters of the problem is investigated. Pis’ma Zh. Tekh. Fiz. 25, 1–4 (November 12, 1999)     

Investigation on the Nonlinear Excitation in an Array of Spin Valve Pillars During the propagation of Electromagnetic Wave

We have investigated the nonlinear excitations in an array of spin valve pillars during the propagation of an electromagnetic wave. The flowing electrons exhibit spins transportation effect due to the torque experienced by the spin magnetization. From the Hamiltonian which models the spin interaction in a spin valve array, we have studied the effect of perturbation using multiple scale expansion and Reduction Perturbation method. The Landau–Lifshitz–Gilbert equation of magnetization, which models the evolution of magnetization of the ferromagnetic layer, is studied along with Maxwell’s equation for the electromagnetic waves. It is found that the system of equations reduce to the celebrated modified KdV equation. The solution of the spin excitations are localized solitons. The physically interesting solitons can be harnessed to the increase in density of memory devices.     

On the problem of instability of the boundary of two media of finite thickness

A dispersion determinant nonlinear as far as the combination of frequency and relative velocity is concerned has been derived in the problem on propagation of waves at the boundary of liquid layers of finite thickness. The structure and physical meaning of the equation obtained have been discussed. The limiting cases have been considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 127–133, November–December, 2007.     

Stability of hydraulic fall and sub-critical cnoidal waves in water flows over a bump

A forced Korteweg–de Vries (fKdV) equation can be used to model the surface wave of a two-dimensional water flow over a bump when the upstream Froude number is near one. The fKdV model typically has four types of solutions: sub-critical cnoidal waves, sub-critical hydraulic fall, transcritical upstream soliton radiation, and supercritical multiple solitary waves. This paper provides a numerical demonstration of the stability of the hydraulic falls and cnoidal waves solutions.     

Features of combined instability of a charged interface between moving media

In solving the problem on the propagation of small-amplitude waves on a charged horizontal interface between two liquids, in the dispersion determinant derived, a term that is nonlinear with respect to the wave frequency combination and the velocity ratio between the upper and lower liquids has been obtained. The structure and the physical meaning of the equation obtained have been discussed. The notion of effective surface tension has been introduced. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 5, pp. 64–69, September–October, 2007.     

Shock waves in an elastic pipeline

The formation of shock waves from the solitary Gaussian and hyperbolic waves in an elastic pipeline has been investigated. It is shown that the parameters of these waves — the path length and the time of formation — differ insignificantly from the analogous parameters of the shock waves formed from the sine waves. The evolution of the discontinuity surface in these shock waves has been considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 489–495, May–June, 2008.     

Effect of inertia on the Marangoni instability of two-layer channel flow, Part II: normal-mode analysis

The effect of inertia on the Yih–Marangoni instability of the interface between two liquid layers in the presence of an insoluble surfactant is assessed for shear-driven channel flow by a normal-mode linear stability analysis. The Orr–Sommerfeld equation describing the growth of small perturbations is solved numerically subject to interfacial conditions that allow for the Marangoni traction. For general Reynolds numbers and arbitrary wave numbers, the surfactant is found to either provoke instability or significantly lower the rate of decay of infinitesimal perturbations, while inertial effects act to widen the range of unstable wave numbers. The nonlinear evolution of growing interfacial waves consisting of a special pair of normal modes yielding an initially flat interface is analysed numerically by a finite-difference method. The results of the simulations are consistent with the predictions of the linear theory and reveal that the interfacial waves steepen and eventually overturn under the influence of the shear flow.     

Effect of the interrelationship of thermal and mechanical fields on the propagation of wave motions in cubically anisotropic thermoelastic materials

A characteristic equation for a system of equations of motion of a cubically anisotropic medium with allowance for the relaxation time of thermal disturbances has been obtained, and expressions for the velocities of propagation of modified elastic and thermal waves have been found. The surfaces of inverse velocities have been constructed and the influence of the effect of interrelationship of thermal and mechanical fields on the change in the phase velocities of propagation of a quasilongitudinal elastic wave and a thermal wave in different planes of a cubically anisotropic material has been analyzed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 384–388, March–April, 2008.     

Numerical determination of modal dispersion and AE signal characterization in waveguides through LBIE/BEM and time–frequency analysis

In the present paper a meshless local boundary integral equation (LBIE) method is employed for the numerical determination of dispersion curves in plate like waveguides. Next, the LBIE method is properly combined with the boundary element method (BEM) for the characterization of acoustic emission signals derived from nucleating surface-breaking and body cracks in plate-like waveguides being in contact with a fluid. The time history of the propagating guided waves is computed by means of either the LBIE method or the hybrid LBIE/BEM scheme and the representation of mode dispersion is accomplished through the Reassigned Smoothed Pseudo Wigner–Ville time–frequency analysis. The effectiveness of the method is demonstrated through representative numerical examples.     

Modulation of capillary oscillations of a charged drop of low-viscosity liquid by its elastic oscillations

A second-order linear differential equation describing the temporal evolution of the amplitudes of capillary waves in a drop of low-viscosity liquid with elastic properties is given with a complex coefficient multiplying the first derivative. It is shown that the capillary oscillations of the drop are modulated by its oscillations associated with the relaxation of the viscosity of the liquid. Pis’ma Zh. Tekh. Fiz. 24, 83–87 (April 12, 1998)     

Deformations and overlap of instability zones in the Mathieu-Hill equation

A numerical analysis of the Mathieu-Hill equation describing the time evolution of the amplitudes of capillary waves at the interface between two liquids, the upper moving relative to the denser lower liquid at a time-dependent velocity, is used to show that for certain values of the characteristic physical parameters, the zones of unstable amplitude growth become deformed and overlap to form a single, singly connected instability zone. Pis’ma Zh. Tekh. Fiz. 25, 13–18 (October 26, 1999)     

Temperature shock waves in a moving medium with allowance for the relaxation of the heat flux

The solution of the gasdynamic equation with allowance for the heat transfer in the relaxation of the heat flux is analyzed. The relations expressing the laws of conservation on the front of strong discontinuity of the quantities sought, including the discontinuity of the temperature and the heat-flux density, are discussed. The possibility of existence of two shock waves with fixed initial data is shown using the self-similar solution of the problem on gas motion ahead of the piston. The occurrence of two strong discontinuities is due to the presence of different velocities of propagation of gasdynamic and thermal disturbances — the velocity of sound and the finite rate of heat transfer at a nonzero time of relaxation of the heat flux. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 57–68, July–August, 2006.     

Strain–life curves of steels and methods for determining the curve parameters. Part 1. Conventional methods

The available publications give much consideration to strain–life curves which are usually described by the Basquin–Manson–Coffin equation. The parameters of this equation are related to those of the Ramberg–Osgood equation that represents the cyclic stress–strain diagram. Many different methods have been put forward for the assessment of parameters of these equations on the basis of static strength and plasticity characteristics. Most of the methods rely on a fairly small body of experimental evidence. Using the experimental data on static and cyclic strength and plasticity characteristics of about 200 various steels from the well-known publications, a statistical analysis of parameters of Basquin–Manson–Coffin and Ramberg–Osgood equations has been performed by each of the assessment methods, revealing their advantages and disadvantages.     

Interfacial capillary–gravity waves due to a fundamental singularity in a system of two semi-infinite fluids

The interfacial capillary–gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three- dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier–Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity.