Equations of dynamics of a mixture composed of a gas and hollow selective‐permeable microspheres

Based on the laws of conservation of mass, momentum, and energy, equations of dynamics of multiphase systems, which are gas mixtures with hollow microspheres with selectively permeable shells, are obtained under the assumption of quasisteadiness of the process offilling the microspheres by the gas. Acoustic characteristics of the system composed of a uniform gas and hollow permeable microspheres are studied using a simplified (onevelocity and onetemperature) model. The frequency dependences of velocity and damping coefficient of sound are determined with regard for gas density (pressure) relaxation inside the microspheres.     

Flow of a Viscoplastic Fluid on a Rotating Disk

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Biological control of a predator–prey system through provision of a super predator

In this paper, we make a systematic analysis of the dynamics of a predator–prey system with type-II functional response, in which the predator growth rate is affected by the presence of a super predator. The main aim of this research is to study the consequences of the presence of a super predator on the system dynamics. The existence and stability of the different possible equilibrium points are studied, and we conclude that the maximum consumption rate of a super predator plays a key role in determining the eventual state of the ecosystem. A detailed bifurcation analysis is carried out through numerical simulations, and we observe that theoretically it is possible to control the dynamics of the system by manipulating the consumption rate of the super predator.     

Stability of Filtration of a Gas—Liquid Mixture

The stability of steady regimes of filtration of a gas—liquid mixture at pressure lower than the saturation pressure is studied for the case of a nonmonotonic dependence of the relative phase permeability of the liquid on the gas saturation. It is shown that periodic self–oscillations can appear, and their evolution leads to deterministic chaos due to the appearance and destruction of quasiperiodic motions.     

Oscillations of a?beam with a?time-varying mass

This paper analyzes dynamical behavior of a simply supported Euler?CBernoulli beam with a time-varying mass on its surface. Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal resonances. The asymptotical solutions for the beam displacement has been found by combining the classical Galerkin method with the averaging method for equations in Banach spaces. The resonance conditions have been derived. It has been proposed a method for finding a number of possible resonances.Effect of the beam parameters on its dynamical behavior is investigated as well.     

Interaction of an unsteady two‐phase jet with a layer of a disperse medium

Discharge of a twophase jet from a cylindrical channel into a bounded layer of a disperse medium is numerically simulated using the equations of the mechanics of heterogeneous media with allowance for the differences in velocity, temperature, and phase stresses. The effect of separation of the gas phase from the disperse phase in the layer is revealed and verified experimentally. A comparison with a similar process of gas discharge at equal initial pressures shows that in the interaction with the disperse layer, the twophase flow has a longer momentum and direction.     

Nonlinear analysis of a structure loaded by a stochastic excitation

For a non-linear system excited by a stochastic load which is expressed as a time series,a recursive method based on the Z-transform is presented.To identify the obtained response time series,a discrete wavelet transform (DWT) technique is proposed.     

On a Turbulent Mixing Layer Created Downstream of a “Λ” Notch Simulating One Wavelength of a Chevron Nozzle

Measurements were carried out in a turbulent mixing layer formed downstream of a splitter plate, that had a Λ-shaped trailing edge. The results revealed that the center of the mixing layer shifts toward the high-speed flow while its sides bend toward the low speed stream at larger distances from the splitter plate. This suggests the existence of a counter rotating streamwise eddies that dominate the flow and substantially increase its level of turbulence relative to the classical plane mixing layer. The change in the orientation of the vorticity, emanating from a chevron nozzle, decreases the susceptibility of the flow to spanwise uniform periodic excitation relative to a classical plane mixing layer.     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Experimental Investigation of Stability of a Hypersonic Boundary Layer on a Cone–Flare Model

Stability of a hypersonic flow in the regions of laminar separation of the boundary layer on a cone–flare model is experimentally studied for a Mach number M = 5.92. Development of natural disturbances and artificial wave packets in the boundary layer and separation region is examined. It is shown that highfrequency disturbances are predominantly amplified in the separation region; the most unstable waves are those propagating with an angle close to 60° to the freestream direction. It is found that separation and reattachment lines are generators of twodimensional disturbances.     

Deformation of a Droplet of an Organic Water—Coal Fuel in a Gas Flow

This paper describes an experimental study of deformation of a droplet of an organic water—coal fuel in a gas flow. The experimental data obtained are used to develop a technique that serves as a basis for a numerical study of integral characteristics of deformation of the droplets of organic water—coal fuel 4.5 mm in diameter with a gas flow velocity of 2 m/s and a temperature of 298 K. The characteristic changes of the area of longitudinal and transverse sections of the droplets of the organic water—coal fuel during their gravitational deposition in time are revealed. It is shown that the theoretical and experimental data satisfactorily agree.     

Stressed state near a wedge‐shaped twin with a disbalance of densities of twinning dislocations

The influence of disbalance of densities of twinning dislocations at the boundaries on the stressed state inside a wedgeshaped twin, near its top, and in external regions adjoining the twinning boundary is studied using a dislocation model.     

Superposition of finite-amplitude waves propagating in a principal plane of a deformed Mooney–Rivlin material

Here we consider finite-amplitude wave motions in Mooney–Rivlin elastic materials which are first subjected to a static homogeneous deformation (prestrain). We assume that the time-dependent displacement superimposed on the prestrain is along a principal axis of the prestrain and depends on two spatial variables in the principal plane orthogonal to this axis. Thus all waves considered here are linearly polarized along this axis. After retrieving known results for a single homogeneous plane wave propagating in a principal plane, a superposition of an arbitrary number of sinusoidal homogeneous plane waves is shown to be a solution of the equations of motion. Also, inhomogeneous plane wave solutions with complex wave vector in a principal plane and complex frequency are obtained. Moreover, appropriate superpositions of such inhomogeneous waves are also shown to be solutions. In each case, expressions are obtained for the energy density and energy flux associated with the wave motion.     

Existence of a Global Smooth Solution¶for a Degenerate Goursat Problem¶of Gas Dynamics

The Goursat problem of a mixed type equation , P≥ 0, is considered. At the ends of its supports we have P=0, which means it is degenerate hyperbolic. We prove the global existence of a smooth solution to the degenerate Goursat problem up to a boundary where P=0. This problem comes from the expansion of a wedge of gas with constant velocity into vacuum, in two-dimensional pressure-gradient equations in gas dynamics, where P is the pressure and P=0 means vacuum. Accepted June 16, 2000?Published online December 6, 2000     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Paradox of a particle’s trajectory moving on a string

This paper deals with the paradoxical properties of the solution of string vibration under a moving mass. The solutions published to date are not simple enough and cannot be applied to investigations in the entire range of mass speeds, including the overcritical range. We propose a formulation of the problem that allows us to reduce the problem to a second-order matrix differential equation. Its solution is characteristic of all features of the critical, subcritical, and overcritical motion. Results exhibit discontinuity of the mass trajectory at the end support point, which has not been previously reported in the literature. The closed solution in the case of a massless string is analyzed and the discontinuity is proved. Numerical results obtained for an inertial string demonstrate similar features. Small vibrations are analyzed, which is why the effect discussed in the paper is of purely mathematical interest. However, the phenomenon results in complexity in discrete solutions.     

Global dynamics and integrity of a two-dof model of?a?parametrically excited cylindrical shell

In this paper the global dynamics and topological integrity of the basins of attraction of a parametrically excited cylindrical shell are investigated through a two-degree-of-freedom reduced order model. This model, as shown in previous authors?? works, is capable of describing qualitatively the complex nonlinear static and dynamic buckling behavior of the shell. The discretized model is obtained by employing Donnell shallow shell theory and the Galerkin method. The shell is subjected to an axial static pre-loading and then to a harmonic axial load. When the static load is between the buckling load and the minimum post-critical load, a three potential well is obtained. Under these circumstances the shell may exhibit pre- and post-buckling solutions confined to each of the potential wells as well as large cross-well motions. The aim of the paper is to analyze in a systematic way the bifurcation sequences arising from each of the three stable static solutions, obtaining in this way the parametric instability and escape boundaries. The global dynamics of the system is analyzed through the evolution of the various basins of attraction in the four-dimensional phase space. The concepts of safe basin and integrity measures quantifying its magnitude are used to obtain the erosion profile of the various solutions. A detailed parametric analysis shows how the basins of the various solutions interfere with each other and how this influences the integrity measures. Special attention is dedicated to the topological integrity of the various solutions confined to the pre-buckling well. This allows one to evaluate the safety and dynamic integrity of the mechanical system. Two characteristic cases, one associated with a sub-critical parametric bifurcation and another with a super-critical parametric bifurcation, are considered in the analysis.     

Paradox of “Self-Outflow” of a Free Liquid Jet

The effect of accumulation of reversible strains on the pressure head is analyzed theoretically for elastic and viscoelastic liquid flow from convergent channels. It is shown that, depending on the rheological features of the liquids, the pressure head can both increase and decrease as compared with the pressure determined by the Bernoulli formula. In particular, a situation in which a liquid flows out without any pressure head applied (paradox of self-outflow) is possible within the framework of the model. Transition to different viscoelastic liquid flow regimes as a function of the constitutive parameters is considered with reference to a channel with a sharp bottleneck (abrupt decrease in the cross-section).     

Resonance Waves in a Model of a Two‐Layered Liquid

With allowance for surface interaction between phases, the behavior of longwave perturbations at the interface between two layers of dissimilar liquids, which form resonance triplets described by a pseudodifferential equation, is studied.     

Effect of Dynamic Prehistory on Aerodynamics of a Laminar Separated Flow in a Channel Behind a Rectangular Backward‐Facing Step

The effect of dynamic prehistory of the flow and the channelexpansion ratio on aerodynamics of a steady separated laminar flow behind a rectangular backwardfacing step located in a planeparallel channel is numerically studied. It is shown that the boundary layer upstream of the flow separation exerts a strong effect on flow characteristics behind the step. A decrease in the boundarylayer thickness in the cross section of the step leads to a decrease in the separationregion length, and an increase in the channelexpansion ratio with a fixed initial boundarylayer thickness and Reynolds number leads to an increase in the separationregion length.