Volume 59, Nº 3 (2018)

A numerical investigation of the properties of two different ion-acoustic solitons has been performed by using analytical solutions of the Schamel equation. A new type of the analytical solution of the Schamel equation that describes soliton propagation with a negative phase velocity has been found for the first time. This new type of the solution has been applied to investigate the physical properties of two different plasmas and to understand the effect of nonextensivity and the effect of trapped electrons on ion-acoustic waves in a superthermal plasma. It is shown that the soliton amplitude and width depend on the nonextensivity parameter, superthermality of the electron distribution, and characteristic trapping parameter.

Rotation bifurcation in a steady axisymmetric thermocapillary flow of an incompressible fluid filling a semi-infinite space bounded by the free surface with a nonuniform distribution of temperature is studied. The fluid flow is calculated on the basis of Navier–Stokes equations under the assumption of small diffusion coefficients. It is shown that the bifurcation triggers rotational motion in a thin Marangoni boundary layer in the case of local cooling of the free boundary near the axis of symmetry and in the presence of an external flow; there is no rotation outside this layer. In the case of local heating of the free boundary, rotation is not observed.

The problem of injection of a hydrate-forming gas (methane) into a snow layer whose pores are initially saturated with the same gas is solved. Self-similar solutions describing the temperature and pressure fields and the snow, hydrate, and gas distributions in the layer are constructed. It is shown that, depending on the initial thermobaric state of the snow–methane system and the rate of gas injection, three characteristic zones can be distinguished in the filtration region: a near zone, in which snow is completely converted into hydrate and, consequently, the hydrate layer is saturated with gas; an intermediate zone, in which gas, snow, and hydrate are in phase equilibrium; far zone filled with gas and snow. It is shown that the length of the heated zone decreases with increasing initial snow content in the layer and with decreasing injected gas pressure. It is also shown that the length of the region of hydrate formation increases with increasing permeability. It is noted that the heating of the intermediate zone occurs more rapidly.

The effects of the camber ratio on the hydrodynamic and structural behaviors of a NACA-based ducted marine propeller in the wake flow behind an underwater axisymmetric body are numerically studied by computational fluid dynamics methods, in particular, the finite element method. The results are presented in terms of the efficiency, deflection, pressure coefficient, and natural frequencies. It is shown that the wake flow strongly affects the performance of the selected propulsion system. It is shown that the distributions of the camber ratio over the blades of the propeller nonlinearly changes its resistance against cavitation occurrence and deflection, and also changes its hydrodynamic performance and vibrational behavior.

A mathematical model of blood circulation in human lower limbs is proposed. The model is based on the laws of motion (filtration) of a viscous fluid in a heterogeneous medium consisting of two or more interpenetrating continua. It is assumed that the blood system consists of a distribution network of comparatively large vessels (arterioles) connected to small capillaries and a similarly structured collection network of small capillaries united into larger veins. A system of parabolic differential equations is derived, for which a problem with no initial data is posed. A periodic (in time) solution of the system corresponding to harmonic oscillations defined by the cardiac rhythm is found. Analytical solutions for particular cases of problems following from the general model of blood circulation are obtained. Numerical calculations are performed, and a numerical solution is found for a one-dimensional problem with parameters similar to those corresponding to real conditions of blood circulation with allowance for the cross-sectional area of the muscular tissue of the lower limb.

Analytical frequency dependences of the absorption coefficient, wavenumber, and phase velocity were constructed for filtration-wave fields in a highly permeable interlayer bounded from above and from below by layers having high permeability in the vertical direction. It is shown that as the frequency decreases, the phase velocity of the wave decreases to values below this velocity in the porous medium and low-frequency deceleration occurs.

Within the framework of the anisotropic theory of elasticity, a three-dimensional contact problem of interaction of two massive transversely isotropic bodies, whose dimensions substantially exceed the size of the contact region, is investigated. In this case, the isotropy planes of contacting elastic bodies are mutually perpendicular. Exact and numerical solutions of the problem are determined. Calculations for various transversely isotropic materials are carried out.

A percolation model of nanocomposite reinforcement is under study. It is shown that the degree of reinforcement of polyurethane–carbon nanotube nanocomposites depends on the structure of nanofillers, which are annular formations. This structure is most accurately characterized by its fractal dimension. It is established that the creation of a structure with negative percolation indices allows for a significant increase in the degree of reinforcement of considered nanocomposites at low nanofiller concentrations.

A technique for identification of hereditary properties under conditions of short-time creep of Plexiglas is developed. The technique is based on experimental determination of shifting of the center of decaying flexural vibrations of vertically aligned test samples after their preliminary maintaining in a static bent state. Mathematically, the technique is based on using the finite element method and integral equations of the theory of hereditary viscoelasticity with the Koltunov–Rzhanitsyn hereditary kernel. An object function is constructed for identification of rheological parameters of this kernel. The minimum of this function is found by the direct search method, which does not require the function gradient to be known. The hereditary kernel of Plexiglas averaged on the basis of data for several test samples is obtained as a function of time.

The problem of steady radial vibrations of a thin electroelastic hollow disk in the presence of a preliminary inhomogeneous plane stress–strain state is solved. Vibrations are induced by applying a potential difference across the electrodes placed on the end surfaces of the disk. Equations of the vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lam´e problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining a pre-stress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial data specified with an error is analyzed.

Laser welding of the 1420 alloy of the Al–Mg–Li system is experimentally studied for the purpose of its optimization. Various modes of heat treatment of fixed joints obtained by means of laser welding are considered. Heat treatment modes that allow significant enhancement of the welded joint density as compared to the as-received alloy are chosen. The ultimate relative elongation of samples after ageing is found to decrease by a factor of 3.