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The present paper considers the ultimate
(under heating conditions) kinematic
characteristics of composite solid
bodies accelerated by unsteady magnetic-
field pressure. The accelerated sheet
comprises two layers: a layer of a
composite material consisting of a
mixture of two materials with different
electrothermal properties and a
homogeneous material layer. The
electrical properties of the composite
layer with the coordinate are varied
along the coordinate by changing the
volume concentration of its constituent
materials. For an exponential magnetic
field rise, an analytical solution is
obtained for the problem of determining
the optimum distribution of the volume
concentration of the composite
constituents for which there is a
maximum increase in the ultimate
velocity of the sheet. Numerical
simulation showed that the distribution
of the volume concentration obtained
from analytical relations is also nearly
optimal for pulse shapes of the
accelerating magnetic field different
from exponential ones. The possibility
of considerably increasing the ultimate
velocity through the use of composite
layers compared to the ultimate
velocities for the homogeneous materials
constituting the composite is shown
analytically and numerically.

The breakdown channel pressure is
estimated for the initial stage of
breakdown of a KCl crystal using
experimental data on the fracture of KCl
crystals upon anode pulsed discharges,
the known strength of this crystal, and
solutions of the corresponding static
boundary-value problem of the
anisotropic theory of elasticity.

This paper considers the generation of a
longitudinal magnetic field between
rigid conducting layers of different
electrical conductivity which are in
shear motion at constant velocity across
the flux lines of the initial field. The
amplification limits for the generated
field due to the finite thickness of the
conducting layers are established. The
evolution of the magnetic field under
various conditions of generation was
described using the models of two layers
of finite thickness, a semi-infinite
layer and a layer of finite thickness,
and two semi-infinite layers.

This paper analyzes some physical effects that occur on the electrode surface in plasma-armature rail launchers when the linear current density is higher than critical value. It is shown that under typical experimental conditions, Rayleigh–Taylor and Kelvin–Helmholtz instabilities and magnetohydrodynamic instabilities, which arise from the interaction of the current with the self-magnetic field, can develop over times much smaller than the launcher operation time and can be responsible for the entry of the electrode material into the discharge. Flash radiography of the electrode surface confirmed the presence of inhomogeneities and ejection of the material from the surface. Under certain conditions, the emergence of conducting metal jets from the electrode surface was detected.

The problem of interaction of shock
waves of various types (completely
dispersed, frozen-dispersed, dispersed-
frozen, and frozen shock waves with a
two-front configuration) with a
motionless combined discontinuity in a
mixture of two condensed materials is
considered. The mathematical description
is based on the equations of mechanics
of heterogeneous media in a one-
dimensional isothermal approximation
with allowance for differences in
velocities and pressures of the
components. In the equilibrium
approximation in terms of velocities and
pressures of the components, the wave
configuration and flow parameters are
determined in all equilibrium states
behind the incident, transient, and
reflected shock waves.

The paper gives an exact solution of the
steady system of equations for stable
three-component diffusion in the entire
range of concentrations for a long
capillary under a controlled capillary
pressure differential. The solution
allows one to calculate the
distributions of component
concentrations and mixture density along
the capillary. It is shown that if the
diffusion coefficients are markedly
different, an extremum of mixture
density can arise inside the capillary.
In particular, if the density of the
mixture in the upper flask is higher
than that in the lower flask and the
stratification of the system is
generally stable, a region with a
reverse density gradient that is
unstable against gravity convection can
appear inside the capillary. A
comparison with experimental results
shows that the resistance to gravity
convection is disturbed when an extremum
of mixture density arises in the channel
during steady diffusion.

A partially invariant solution of the
Euler equations is considered, where the
vertical component of velocity is a
function of the vertical coordinate and
time, whereas the remaining components
of velocity and pressure are independent
of the polar angle in a cylindrical
coordinate system. Using the
classification of equations obtained by
analysis of an overdetermined system, we
consider two hyperbolic systems: the
first one describes the motion of a
cylindrical layer of an ideal
incompressible liquid under a punch, and
the second system allows obtaining
solutions in a half-cylinder with
singularities at the axis of symmetry. A
class of new exact solutions is
obtained, which describe vortex motion
of an ideal incompressible liquid,
including the motion with singularities
(sources of vortices) located along the
axis of symmetry.

Axially symmetrical waves on the surface
of a ferromagnetic viscous-fluid 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 time-
dependent magnetic field. The film
thickness was assumed to be small
compared to the radius of the conductor.
In the long-wave 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.

The regions of parametric resonance were
determined for a sphere immersed in water
and suspended from a string with varying
tension.

A solution is derived for the two-
dimensional unsteady problem of the
behavior of an elastic beam of finite
dimensions floating on the free surface
of water under external loading. It is
assumed that the fluid is ideal and
incompressible and its depth is well
below the beam length. The simultaneous
motion of the beam and the fluid is
considered within the framework of
linear theory, and the fluid flow is
assumed to be potential. The behavior of
the beam under various loadings with and
without allowance for the inertia of the
load is studied.