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This paper gives an introduction to
formalization of Galilean-invariant and
thermodynamically consistent equations
of mathematical physics in which
unknowns are transformed in rotations by
irreducible representations of integer
weights. This formalization is based on
the theory of representations of the
group SO(3).

This paper presents a study of the
effect of a magnetic field and variable
viscosity on steady two-dimensional
laminar Darcy forced convection flow
over a flat plate with variable wall
temperature in a porous medium in the
presence of blowing (suction). The fluid
viscosity is assumed to vary as an
inverse linear function of temperature.
The derived fundamental equations on the
assumption of small magnetic Reynolds
number are solved numerically by using
the finite difference method. The
effects of variable viscosity, magnetic
and suction (or injection) parameters on
the velocity and temperature profiles as
well as on the skin-friction and heat-
transfer coefficients were studied. It
is shown that the magnetic field
increases the wall skin-friction while
the heat-transfer rate decreases.

The high velocity oblique collision of
samples of beryllium (beryllium and
stainless steel)was studied
experimentally. The disturbance
amplitudes of beryllium, magnesium,
aluminum, copper, and steel were
compared. It is established that for the
same Mach numbers, the disturbance
amplitude for beryllium is maximal. The
low plasticity and high brittleness of
beryllium determine the nature of
formation of a welded joint. Fusion and
mixing of the metals occur in a very
narrow zone, which practically cannot be
seen in microsections. Under oblique
collision of beryllium and steel, a
solid solution layer of elevated
hardness is attached to the interface.

A wide class of solutions of Euler
equations with quadratic pressure are
described. In Lagrangian coordinates,
these solutions linearize exactly
momentum equations and are characterized
by special initial data: the Jacobian
matrix of the initial velocity field has
constant algebraic invariants. The
equations are integrated using the
method of separation of the time and
Lagrangian coordinates. Time evolution
is defined by elliptic functions. The
solutions have a pole<!dash!>type
singularity at a finite time. A
representation for the velocity vortex
is given.

The paper studies the dynamics of a thin
curved vortex in a potential flow of an
ideal incompressible fluid. The flow is
specified by a number of geometrical
restrictions and does not satisfy the
Biot-Savart law. The form of the derived
equation of the vortex dynamics
coincides with the form of the well-
known equation of local induction for
self-induced vortex motion. The
parameters of the new equation are
simultaneously flow parameters, and in
this sense, they do not show uncertainty
typical of classical equations. The
coefficient of the new equation can take
any specified values not necessarily
much greater than unity, as required
according to the concept of local
induction)and generally is a function of
a natural filament parameter.

A paradox of the blunt edge of an
airfoil in an unsteady ideal flow is
established, which states that the
solution of the nonlinear problem of
unsteady flow around a blunt-edged
airfoil subject to strict boundary
conditions at this edge is physically
meaningless. The paradox is a
consequence of the adopted model of the
unsteady fluid flow near the blunt edge,
which assumes inflection of streamlines.
It is established that the solution of
the problem by local replacement of the
blunt edge by a sharp edge using the
hypothesis on the smoothness of
streamlines near the trailing edge is
physically meaningful.

Simulation was performed of the behavior of a vapor bubble in a liquid under laser irradiation in laboratory experiments. A mathematical model was developed to analyze the effect of heat conduction, diffusion, and mass transfer on the bubble dynamics under compression and expansion. It is found that at the stage of collapse, intense condensation occurs on the bubble wall, which results in a significant (more than 15- fold)decrease in bubble mass and an increase in pressure (to 10⁵ atm)and temperature (to 10⁴ K) Results of numerical calculations of the radius of the first rebound and the amplitude of the divergent shock wave in water are compared with experimental data. It is shown that small (about 1%)additives of an incondensable gas lead to a considerable decrease in mass transfer on the bubble wall.

The complex approach developed
previously for the numerical solution of
problems of optimization and designing
of airfoils is applied to solve the
problem of increasing the lift-to-drag
ratio of subsonic airfoils used.

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