Nonlinear surface waves with allowance for the saturation effect

It is shown that for a medium with the dielectric function given by the expression ε=ε ₁+(ε ₂−ε ₁)tanh(E ²/E _s ² ), where ε ₁ and ε ₂ are constants and E _s is the saturation field, there is a threshold value of the power density at which a nonlinear surface wave can be excited. T. G. Shevchenko Pridnestrov State-Corporate University Pis’ma Zh. Tekh. Fiz. 23, 36–39 (December 12, 1997)     

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.     

Propagation of elastic waves in a micropolar sphere

The problem of harmonic wave propagation in a solid micropolar sphere is solved by considering the two scalar and two vector equations governing the motion. Stress free boundary conditions are applied and a characteristic equation is obtained. The characteristic determinant can be resolved into the product of two independent determinants. Two classes of motion are observed which have been analysed in detail.     

Dispersion of surface waves at a dielectric-high temperature superconductor interface with allowance for energy dissipation

The dispersion characteristics of surface waves at a dielectric-high temperature superconductor (HTSC) interface have been studied with allowance for energy dissipation. Conditions of the existence of surface waves and the corresponding dispersion relations are determined at temperatures below the HTSC critical temperature. The frequency dependences of the penetration depth in each medium and the free path of surface polaritons are described. In the frequency range studied, these quantities can vary within several orders of magnitude.     

Fragmentation of a sphere initiated by hypervelocity impact with a thin sheet

Selected results of tests in which 9.53-mm-diameter, 2017-T4 aluminum spheres impacted 0.25-mm- to 4.80-mm-thick, 6061-T6 aluminum sheets are presented. Impact velocities for these tests ranged from 1.98 km/s to 7.38 km/s. Flash x-rays were used to view the debris clouds produced by the impacts. As impact velocity was increased, failure of the aluminum sphere progressed through the following stages of fracture and fragmentation: (1) formation of a spall failure at its rear surface, (2) development of a detached shell of spall fragments, and (3) complete disintegration of the sphere. The threshold impact velocity for development of the spall failure in the sphere was observed to be a function of the bumper-thickness-to-projectile-diameter ratio (t/D), and to increase as the t/D ratio decreased. When the debris cloud was fully developed, the disintegrated projectile formed its dominant feature--an internal structure, composed of a front, center, and rear element, located at the front of the debris cloud. The front element was small and consisted of finely-divided projectile and bumper material. The bulk of the fragmented projectile was contained in the center element, a disc-like structure made up of a large central fragment surrounded by numerous smaller fragments. A shell of fragments, spalled from the rear of the sphere, formed the rear element. Radiographs of the debris clouds were analyzed to determine the size and size distribution of certain fragments within the cloud. The size of the large fragment was shown to be dependent on impact velocity and t/D ratio. The smaller fragments in the center element were several times larger than the fragments in the shell of spall fragments forming the rear element. Detailed analyses of fragments in the shell of spall fragments were made. The analyses indicated their median Martin's statistical diameter exhibited an orderly dependence on impact velocity and t/D ratio.     

Investigation of gasdynamic processes by the method of traveling waves with allowance for volumetric sources and sinks

Using the method of traveling waves, we investigate the effect of volumetric sources and sinks of mass and energy on the motion of gas. We assume that the strengths of the sources are power functions of the temperature and density. The solution of the corresponding system of ordinary differential equations is constructed analytically: the sought functions are represented in explicit or implicit form. It is shown that the presence of sources or sinks leads to substantially new properties of the solutions of the equations of gas dynamics. Depending on the initial parameters of the problem, the solution may exist both at any instant of time t > 0 and only in a finite interval of t. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 1, pp. 139–148, January–February, 1998.     

Energy transfer in a dielectric medium with allowance for the relaxation polarization

Energy relations of the macroscopic electrodynamics of a dielectric medium are considered with allowance for the relaxation polarization. An expression for the dielectric loss power flux density is obtained in the case of an arbitrary time-dependent electric field. An energy characteristic of the efficiency of insulators for capacitive energy storages is proposed.     

Scattering of electromagnetic waves by a coated not perfectly conducting sphere

We consider the low-frequency scattering problem of a plane electromagnetic wave by a sphere, which is covered by a penetrable concentric spherical shell. The medium, occupying the shell, is lossless while on the surface of the core an impedance boundary condition is satisfied. The impedance boundary condition was introduced by Leontovich (Investigations of Radiowave Propagation. Part II, Academy of Science, Moscow, 1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first orders while in the far field we derive the leading non-vanishing terms for the scattering amplitude and the scattering cross-section. Spherical coated obstacles are very important in applications. Small particles in biological suspensions, cells, some human organs, atmospheric particles and granules within composite materials are only a few examples of applied interest in science and technology.     

The impact of a rigid sphere with an elastic layer of finite thickness

Summary The problem of the impact of a rigid sphere with an elastic isotropic layer is considered in the initial stage of dynamic interaction. The initial stage is characterized by the fact that the velocity of the displacement of the intersection points of the sphere with the upper boundary of the layer is larger than the velocity of longitudinal waves, hence the free surface normal to the contact domain with the body is undisturbed. The method of successive approximations as well as the ray method, according to which the solution behind the fronts of incident and reflected waves is constructed in terms of power series (ray expansions), are used as methods of solution. In the problem under consideration, we used one-term ray expansions whereby the main characteristics of the shock interaction have been obtained, and the possibility of localized damage of the material of the layer at the points lying along the central ray has been examined.     

Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness

The propagation behavior of transverse surface waves (Love waves) in a piezoelectric half space of polarized ceramics carrying a functionally graded material layer is studied from the three-dimensional equations of linear piezoelectricity. The Wentzel–Kramers–Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations of analytical solutions in the functionally graded layer. The dispersion relations of Love wave in the structure are obtained for both electrically open and shorted cases. Firstly, these solutions are used to study effect of the gradient coefficients on the dispersive relations and phase velocities of Love wave propagation. Then influence of the gradient coefficients on the electromechanical coupling factor is discussed in detail. The results reported are meaningful for the design of surface acoustic wave (SAW) devices with high performance.     

Numerical study of asteroid impact on the earth’s surface with allowance for gravitation and radiation energy transfer

The study presents a procedure for numerical modeling and results of gasdynamic calculations of asteroid impact on the surface in a two-dimensional axisymmetric formulation for impact velocities of ∼ 50 km/sec and asteroid dimensions of ∼ 1 km. The effect of gravity and radiation energy transfer are taken into account. Radiation transfer is calculated using the equations of radiation diffusion in the multigroup approximation with respect to the photon energy (10 spectral groups). The equations of radiation diffusion are solved by the method of alternating directions.     

Heat transfer in a fluidized bed with allowance for the filtration component

A two-phase model of surface-to-pseudoturbulent dispersed bed heat transfer is applied for calculating temperature fields in a fluidized bed. Calculation results are compared with experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 3, pp. 360–364, September, 1982.     

Transverse surface waves in a piezoelectric material carrying a gradient metal layer of finite thickness

The existence and propagation behavior of transverse surface waves in a layered structure concerning a piezoelectric substrate and a gradient metal layer are theoretically investigated in this paper. The Wentzel-Kramers-Brillouin (WKB) method is applied to obtain the analytical solutions in the gradient metal layer. The dispersion equation for transverse surface waves in such structure is obtained in a quite simple mathematical form, where the material gradient of the metal layer assumes arbitrary functions. Effects of material gradient on three types of dispersion behavior are discussed in detail based on a proper classification. Numerical results show that the material gradient in the metal layer evidently affects the fundamental mode shape of the transverse surface waves but has negligible effects on the higher order modes.     

Oblique impact of frictionless spheres: on the limitations of hard sphere models for granular dynamics

When granular systems are modeled by hard spheres, particle?Cparticle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the particles are the same before and after such an event. We show that depending on the material and system parameters, this assumption may fail. For the case of viscoelastic particles we present a universal condition which allows to assess whether hard-sphere modeling and, thus, event-driven Molecular Dynamics simulations are justified.     

Criterion for the onset of ostwald ripening stage with allowance for the particle number fluctuations in a nucleus

A theory of condensation is proposed for an open system in which the growth rate varies with the number of particles and the total particle concentration (supersaturation flux) varies with the time as described by power laws with arbitrary exponents (indices). It is established that the distribution of nuclei with respect to their sizes z, which is formed at the nucleation stage, is subject to fluctuational blurring. The dependence of the distribution width on the average size z is related in a nontrivial manner to the values of the growth and flux indices. Conditions for the onset of the Ostwald ripening (OR) stage in the system are analyzed with allowance for fluctuations in the number of particles. It is shown that the Kukushkin-Osipov criterion remains valid, since the transition curve occurs in a region where the distribution width grows slower than z. At the same time, the form of the initial condition and the character of evolution of the distribution at the OR stage significantly vary under the action of fluctuations.     

Crater formation in a plastic target under hypervelocity impact

The analytical models of crater formation in a semi-infinite target under hypervelocity impact have been analyzed. It has been shown by numerical calculations that to approximately calculate the crater size for a narrow range of impact velocities, the model of an ideal plastic body can be used. A new analytical model of crater formation in a plastic target, which describes the experimental data in a wide range of impact conditions, is suggested. The crater formes are analyzed.     

Two-dimensional convective diffusion of a radioactive impurity with allowance for sorption in a porous medium

A mathematical model of the two-dimensional convective diffusion of radionuclide transfer in a porous medium has been considered. A fundamental solution in the form of Green's function has been obtained for this model. The analytical expressions of the impurity-concentration distribution for stationary conditions and for a few kinds of boundary conditions have been given. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 417–420, May–June, 2008.