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The paper studies the local variation of
the concentration of a neutral dilute
solution during its radial flow around a
spherical cavity in the approximations
of an adsorption layer and the Langmuir
adsorption kinetics. The authors used
the boundary-layer method and the method
of asymptotic series expansion of the
solution in a small parameter, which is
the ratio of the time of establishing an
adsorption equilibrium to the time of
establishing a steady diffusion layer
around the cavity. The equations
obtained for a zeroth approximation were
studied analytically and numerically. In
the case of high-frequency oscillations
of the cavity in the solution, a
solution of the problem was found that
corresponds to the process of
"straightened" adsorption or "pumping"
an admixture into the adsorption layer.

Stability of periodic solutions of a
non-self-similar nonlinear problem is
studied. The problem describes the
thermal state of an axial fluid flow
with continuously distributed sources of
heat. The flow experiences the action of
external low-amplitude perturbations
changing in time in accordance with
known periodic laws. The spectral
problem is solved by the method of
parametrix, and the critical conditions
of the thermal explosion are determined
in the linear approximation. Stability
of the periodic solution at the critical
point is evaluated using the known
theorem of factorization, which takes
into account the effect of nonlinear
terms of the heat-balance equation. The
calculation results show that the
periodic solution is stable if the total
action of external periodic
perturbations at the critical point is
directed to reduction of the fluid-flow
temperature.

A model governing a steady flow of a
viscoplastic material between coaxial
cylinders is proposed. Nonlinear
velocity sensitivity typical of
superplastic materials is taken into
account. An algorithm of calculating the
characteristics of the material is
developed. The algorithm is based on the
experimental data on moments and angular
velocities of the rotating coaxial
cylinders. The stability of the
algorithm to errors in the initial data
is estimated.

An isotropic linear-elastic
(viscoelastic) plane containing various
physically nonlinear elliptic inclusions
is considered. It is assumed that the
distances between the centers of the
inclusions are much greater than their
dimensions. The problem is to determine
the orientation of the inclusions and
the loads applied at infinity which
ensure a specified value of the
principal shear stress in each
inclusion. Necessary and sufficient
conditions of existence of the solution
of the problem are formulated for a
plane strain of an incompressible
inhomogeneous medium.

Direct and inverse problems of forming of long-length profiles with double curvature and a given angle of twisting under conditions of creep are considered. A finite-difference scheme for the numerical solution is proposed. Examples of solving problems with different types of external actions for a profile with a rectangular cross section are given. Experimental and numerical data are compared for twisting of beams with square and circular cross sections in the regime of creep at temperatures of 725 and 740°C for St. 45 steel.

This paper considers a model of a
plastically compressible porous medium
with a cylindrical-type yield condition
and its associated constitutive
relations, which ensure independent
mechanisms of shear and compaction of
the porous material. This allows one to
use the well-known theorems of plastic
theory to analyze plastically
compressible media and obtain analytical
solutions for a number of boundary-value
problems, including those taking into
account conditions on strong-
discontinuity surfaces. Results from
full-scale studies of the structural
periodicity of noncompact materials
using wavelet analysis were employed to
choose a physical model for a porous
body and determine the properties and
dimensions of a representative volume.
The problem of extrusion of a porous
material through a conical matrix was
solved.

Fracture of a composite medium with a
brittle matrix is studied. The brittle
or plastic material of the reinforcing
elements is highly deformable. For
normal-rupture macrocracks, necessary
criteria of brittle strength and
sufficient criteria of quasibrittle
strength are proposed. Simple analytical
dependences of the macrocrack length on
the loading parameter, structural,
rigidity, and strength parameters of the
medium, and damage parameters of the
material of the components are obtained.
The critical loads for these criteria
may differ substantially even if the
reinforcement coefficient is small and
the material of reinforcing elements is
highly deformable. If the necessary
criterion is satisfied, crack extension
occurs and microcracks are formed in the
bonds of the structure located ahead of
the macrocrack tip. The number of
damaged bonds depends on the macrocrack
opening and characteristics of
postcritical deformation of the damaged
bonds.

Sufficient conditions of technical
stability of nonlinear dynamic states of
extended elastic flying systems in
controlled longitudinal vertical flight
are obtained. In these flying systems,
the effect of variation of their cross-
sectional area, transverse strains, and
oscillations is taken into account. The
formulated criteria of technical
stability depend on the basic parameters
of the process controlled, namely, on
the increment of the transverse load due
to the curvature of the axis of the
system and aerodynamic forces during
vertical flight.

The problem of interpretation of hot-
wire measurements of acoustic fields in
compressible flows is considered.
Relations between mass-flow and total-
temperature fluctuations registered by a
hot-wire anemometer and pressure and
velocity fluctuations are found. The
relations obtained are applicable in the
general case for measurement of
resultant acoustic fluctuations at some
point of the flow, which are generated
by arbitrary distributed sources of
sound with prior-unknown properties.

Combustion of fog consisting of a hydrogen