Dust‐ion‐acoustic precursor of a shock wave

The effect of charged dust particles on the structure of the plasma precursor of a strong shock wave is studied. The conditions of formation of a weak discontinuity front are obtained. It is shown that resonant modes can occur in which the concentration of dust particles in the neighborhood of the front increases. In the case of positively charged particles of dust, the formation of a localized compaction region in the form of a soliton bunch is possible and the dependence of the amplitude of the soliton on shockwave velocity is nonmonotonic. In the case of negatively charged particles of dust, a rarefaction wave is formed. The indicated phenomena can substantially affect the concentration of the neutral component in a slightly ionized plasma.     

On a Volume‐Constrained Variational Problem

. Existence of minimizers for a volume-constrained energy $ E(u) := \int_{\Omega} W(\nabla u)\, dx Existence of minimizers for a volume-constrained energy E(u) : = ò_W W(?u) dx E(u) := \int_{\Omega} W(\nabla u)\, dx where L^N({u = z_i}) = a_i, i = 1, ?, P, {\cal L}^N(\{u = z_i\}) = \alpha_i, i = 1, \ldots, P, is proved for the case in which z_iz_i are extremal points of a compact, convex set in \Bbb R^d\Bbb R^d and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1d=1, P=2P=2, W(x)=|x|²W(\xi)=|\xi|^2, and the &-limit as the sum of the measures of the 2 phases tends to \L(W)\L(\Omega) is identified. Minimizers are fully characterized when N=1N=1, and candidates for solutions are studied for the circle and the square in the plane.     

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.     

On the Propagation of Long‐Wave Perturbations in a Two‐Layer Free‐Boundary Rotational Fluid

A mathematical model for the propagation of longwave perturbations in a freeboundary shear flow of an ideal stratified twolayer fluid is considered. The characteristic equation defining the velocity of perturbation propagation in the fluid is obtained and studied. The necessary hyperbolicity conditions for the equations of motion are formulated for flows with a monotonic velocity profile over depth, and the characteristic form of the system is calculated. It is shown that the problem of deriving the sufficient hyperbolicity conditions is equivalent to solving a system of singular integral equations. The limiting cases of weak and strong stratification are studied. For these models, the necessary and sufficient hyperbolicity conditions are formulated, and the equations of motion are reduced to the Riemann integral invariants conserved along the characteristics.     

Re‐Entering of Bodies with a Positive Lift‐to‐Drag Ratio into the Earth's Atmosphere

The problem of gliding descent of a smooth blunted body with a positive lifttodrag ratio in the Earth's atmosphere is solved within the framework of the parabolized viscous shock layer model.     

Increasing pressure difference via a gas‐dynamic window for electron‐beam extraction

The functioning of a gasdynamic window designed as an evacuation chamber with orifices 1 mm in diameter for electronbeam extraction from vacuum (10 Pa) into the atmosphere is analyzed. An increase pressure difference is attained due to the ejecting effect arising when the gas flows over an element of the gasdynamic window with pressure taps in the wall. A method for calculating the area of the pressure taps is presented.     

Relaxation of a Low‐Intensity Atomic Beam in a Quiescent Gas

Relaxation of a lowintensity atomic beam in a gas at rest is examined by means of numerical modeling with the method of test particles. Temperaturefield features in the mixing region are considered. A relation between the relaxation length and the initial velocity and mass of injected particles is obtained. Conditions are found under which the relaxation length is minimal.     

Viscosity of a Dilute Suspension in a High‐Frequency Electromagnetic Field

The action of a highfrequency electromagnetic field on a dilute suspension of spherical particles with a constant dipole moment is studied using statistical mechanics. An expression for effective viscosity is obtained. It is shown that the shear viscosity of the dilute suspension depends on the frequency, magnitude, and direction of the highfrequency electromagnetic field. Depending on the frequency of the highfrequency electromagnetic field, the rotation of the suspension particles is decelerated or accelerated, with the viscosity increasing or decreasing, respectively. It is shown that the acceleration of the suspension particles by a highfrequency electromagnetic field and, hence, the decrease in shear viscosity has a resonant nature.     

Description of a Flow of a Gas‐Condensate Mixture in an Axisymmetric Capillary Tube by the Density‐Functional Method

An isothermal flow of a twophase multicomponent mixture through a smalldiameter capillary tube is examined by the densityfunctional method. For low ratios of the characteristic radius of the capillary to its length, a general form of the dominating term in the asymptotic solution is found. An improved version of the law of mixture transfer is obtained. The form of possible corrections to the Darcy law for the filtration rates of the phases is discussed.     

Two‐fluid hydrodynamic model of a bubble flow

A computational model for an unsteady onedimensional gas–liquid flow taking into account gravity is proposed. The model includes the Zuber–Findlay relation and solutions of the Cauchy problem close to the solutions of drift models. It is shown that the effect of attached mass has a significant influence on the acoustic characteristics of the system of equations.     

Self‐Equilibrated Stress Fields in a Continuous Medium

It is proved that the solutions of the static equations of a continuous medium constructed in terms of a stress function are selfequilibrated. From a mathematical point of view, these functions can be treated as the connectivity coefficients of the intrinsic geometry of the medium. It is shown that from a physical point of view, the existence of selfequilibrated stress fields is due to a nonuniform entropy distribution in the medium. As an example, for a circle in polar coordinates and a cylindrical sample, a selfequilibrated stress field and an elastic field compensating for its surface component are constructed and it is shown how to write the equation for the intrinsic geometrical characteristics.     

Stability and Self‐Oscillations of a Rotor Containing a Conducting Liquid in a Magnetic Field

This paper considers the problem of the stability in the small of the steadystate spinning of a rotor with a cylindrical cavity partly filled with a viscous, incompressible, conducting liquid in a magnetic field. The responses of the buttend boundary layers and the resultant force exerted by the liquid on the rotor performing circular precession of small radius are determined. The plane of the viscoelastic restraint parameters of the rotor axis was Dpartitioned into regions with different degrees of instability is constructed. Steadystate spinning near the boundary of the region of stability in the space of parameters is studied assuming nonlinear responses of the supports. It is shown that passage through the boundary of the region of stability leads to bifurcation of the steadystate spinning regime, resulting in periodic motion of the type of circular precession. The origin ofperiodic motion from steadystate spinning can be subcritical or supercritical.     

Sudden Blocking of a Supercritical Open‐Channel Flow

This paper reports results of experiments in which a steadystate nonuniform supercritical openchannel flow was suddenly blocked by a rapidly falling gate at a downstream distance of about one hundred critical depths. This results in a hydraulic jump propagating upstream. Experimental data on the shape, height, and propagation speed of its leading front are given. It is shown that the parameters of the jump differ significantly from the values found using a quasistationary approach.     

Wave regimes on a ferromagnetic viscous‐fluid film flowing down a vertical cylinder

Axially symmetrical waves on the surface of a ferromagnetic viscousfluid film flowing down a cylindrical conductor with alternating current are considered. In this case, in addition to the gravitational force, the film is affected by a spatially nonuniform timedependent magnetic field. The film thickness was assumed to be small compared to the radius of the conductor. In the longwave approximation, a model equation for the deviation of the film thickness from its undisturbed value is obtained. Some numerical solutions of this equations are reported.     

Magnetic Dipole Moment from a One‐Kiloton Underground Nuclear Explosion in a Cavity

This paper reports the results of numerical modeling of the magnetic dipole moment produced by displacement of the Earth's magnetic field in a onekiloton underground nuclear explosion in a cavity. It is shown that with increase in cavity size, the magnetic dipole moment increases, reaching 10⁷ A · m², which is approximately 200 times the magnetic dipole moment from a camouflet explosion. A factor of 100 decrease in the initial air density in cavities with radii of 10 and 20 m results in a reversal of the direction of the magnetic dipole moment vector.     

The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic‐to‐Orthorhombic Phase Transformation

. We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic‐to‐orthorhombic transformation of type ${\mathcal P}^{(432)} \to {\mathcal P}^{(222)'}We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic-to-orthorhombic transformation of type P⁽⁴³²⁾ ? P^(222)￠{\mathcal P}^{(432)} \to {\mathcal P}^{(222)'}. The free energy density modeling such a crystal is minimized on six energy wells that are pairwise rank-one connected. We consider the energy minimization problem with Dirichlet boundary data compatible with an arbitrary but fixed simple laminate. We first show that for all but a few isolated values of transformation strains, this problem has a unique Young measure solution solely characterized by the boundary data that represents the simply laminated microstructure. We then present a theory of stability for such a microstructure, and apply it to the conforming finite element approximation to obtain the corresponding error estimates for the finite element energy minimizers.     

Disruption of Shaped‐Charge Jets by a Pulsed Current

This paper gives results from experimental studies of the effect of electricpulse parameters on the development of current instability and disruption of shapedcharge jets. A simple physical model for the development of current instability and the decrease in the cavern depth in the target is proposed. Notations are introduced and analytical expressions are obtained for the critical current (critical linear current density) and the ideal shape of the current pulse required for the disruption of shapedcharge jets. It is shown that the estimate of the final cavern depths in steel target for the proposed model is in fairly good agreement with both experimental values of cavern depths in targets and with the results of numerical calculations using quasitwodimensional unsteady models of MHD instability and volume disruption.     

Interaction of Large‐Scale and Small‐Scale Oscillations During Separation of a Laminar Boundary Layer

The mutual influence of shortwave oscillations (instability waves of the separated boundary layer) and longwave disturbances at the frequency of shedding of periodic largescale vortices is experimentally studied in flow separation behind a step. The possibility of controlling the process of vortex formation by exciting amplifying disturbances in the shear layer is demonstrated.