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.     

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.     

Dispersion of Dynamically Passive Impurities in Non‐One‐Dimensional Liquid Flow

Equations that describe dispersion of a substance in a nononedimensional incompressible liquid flow through a plane channel are derived. The model under consideration extends the traditional Taylor model to the case where sources of the substance are present in the flow and relaxation transfer processes are taken into account. Additional conditions for the dispersion equations are obtained. The relation between the proposed model and the Taylor model is analyzed. Based on the equations obtained, the mass transfer between circulation regions in the flow is calculated and a system of cellularmodel equations for stagnant cavities is constructed.     

High‐Velocity Penetration of Plane Shaped‐Charge Jets into Nonlinear Media

This paper reports results of metallographic analysis of metal samples cut from targets penetrated by plane shapedcharge jets. It is shown that the plastic deformation due to penetration has a turbulent nature and, in some cases, it occurs in metals with fractal structure formed after passage of the shock wave running ahead of the jet. A penetration model is proposed that takes into account the nonlinear behavior of the target material and the fractality of its structure.     

Electrical Characteristics of Three‐Component Dielectric Composites with Close‐Packed Inclusions

The electric field and effective permittivity are calculated for a twodimensional threecomponent dielectric material reinforced by cylindrical fibers. A composite material with a square close packing of inclusions is considered. The field in the periodic system is investigated using the exact solution of the model problem of interaction of two dissimilar cylindrical inclusions in an external homogeneous electric field. A diagram of the relative effective permittivity is constructed.     

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.     

Calculation of Transport‐Equation Eigenvalues

The eigenvalue problem for the transport equation with variable coefficients in an arbitrary domain with a smooth boundary is considered. A saturationfree numerical algorithm is constructed. Examples of numerical calculations are given, which prove the effectiveness of the proposed procedure.     

Exact solutions and mathematical properties of boundary‐value problems for dynamic‐diffusion boundary layers

The paper studies boundaryvalue problems for dynamicdiffusion boundary layers occurring near a vertical wall at high Schmidt numbers and for dynamic boundary layers whose inner edge is adjacent to the dynamicdiffusion layers. Exact solutions for boundary layers at small and large times are derived. The wellposedness of the boundaryvalue problem for a steady dynamicdiffusion layer is studied.     

Heat‐and mass‐transfer characteristics in a spatial subsonic flow around a blunt body

A study was performed of methods for controlling thermal regimes in a spatial supersonic flow around a blunt body with the simultaneous use of gas injection from the surface of the porous bluntness and heat flow in the shell material. The effect of the nonisothermicity of the shell wall on the heat and masstransfer characteristics in the boundary layer was taken into account by solution of the problem in a conjugate formulation. It is shown that heat conducting materials can be used to advantage to reduce the maximum temperatures in the screen zone.     

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.     

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.     

Protective properties of hot‐air screens

An analytical and numerical study of protective properties of hotair screens is performed for a plane wave with a triangular profile. The reduction of the shockwave pressure behind the screen is only observed at temperatures higher a certain critical value; at lower temperatures, the pressure is higher than that in a shock wave traveling in an isothermal gas. With allowance for real properties of air, an analytical relation between the critical temperature of the hot screen and the incidentwave intensity is obtained.     

Effect of free‐stream turbulence on the boundary‐layer structure with diffusion combustion of ethanol

The effect of turbulization of a subsonic air flow on the boundarylayer structure was experimentally studied during evaporation and combustion of ethanol behind an obstacle 3–6 mm high. It is shown that turbulization increases the thermal boundarylayer thickness by a factor of 2, where as the dynamic boundarylayer thickness changes weakly. For 1–18% turbulence at the entrance, the change in the momentum thickness along the channel is close to the change in the momentum thickness for a laminar isothermal boundary layer without injection. Local regions of elevated turbulence with a high intensity of heat and mass transfer arise in the case of combustion behind the obstacle at a distance of 40–50 obstacle heights.     

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.     

Complicated structures of galilean‐invariant conservation laws

This paper continues previous investigation of Galileaninvariant equations of mathematical physics, which was begun with the use of the Clebsch–Gordan coefficients from the theory of products of the represented group SO(3). Complex systems of conservation laws and thermodynamic identities are constructed. Concrete examples are given.     

Self‐similar solutions of unsteady boundary layers

Selfsimilar solutions are considered for the unsteady dynamicdiffusion boundary layer that forms near a vertical wall at high Schmidt numbers and for the dynamic boundary layer adjacent to the dynamicdiffusion layer at the inner edge. It is shown that a countercurrent flow zone forms in the flow region of the dynamic boundary layer.     

Supersonic Three‐Dimensional Flow Around Two Bodies

A supersonic threedimensional flow around two bodies located one behind the other is experimentally studied. The flow structure between the bodies is analyzed. Zones of the maximum force loads on the surface of the rear body are determined.     

Modification of the kolsky method for studying properties of low‐density materials under high‐velocity cyclic strain

A modification of the Kolsky method with the use of the split Hopkinson bar is proposed, which allows testing lowdensity materials under cyclic loads of an identical sign. Cyclic dynamic testing of specimens is based on the essential difference of acoustic impedances of the material of the specimen tested from the material of pressure bars. The choice of the supportbar length several times greater than the loadingbar length allows registration of strain pulses in several cycles. Results are presented for the proposed modification of the Kolsky method used for tests in compression of foam plastic of two densities under three loading cycles.     

Divergence‐Measure Fields and Hyperbolic Conservation Laws

. We analyze a class of vector fields, called divergence‐measure fields. We establish the Gauss‐Green formula, the normal traces over subsets of Lipschitz boundaries, and the product rule for this class of fields. Then we apply this theory to analyze entropy solutions of initial‐boundary‐value problems for hyperbolic conservation laws and to study the ways in which the solutions assume their initial and boundary data. The examples of conservation laws include multidimensional scalar equations, the system of nonlinear elasticity, and a class of systems with affine characteristic hypersurfaces. The analysis in also extends to . (Accepted July 16, 1998)