Vol 73, No 6 (2018)

The problem of the asymptotic stability of a stationary solution with an internal transition layer of a one-dimensional reaction–diffusion equation is considered. What makes this problem peculiar is that it has a discontinuity (of the first kind) of the reactive term (source) at an internal point of the segment on which the problem is stated, making the solutions have large gradients in the narrow transition layer near the interface. The existence, local uniqueness, and asymptotic stability conditions are obtained for the solution with such an internal transition layer. The proof uses the asymptotic method of differential inequalities. The obtained existence and stability conditions of the solution should be taken into account when constructing adequate models that describe phenomena in media with discontinuous characteristics. One can use the results of this work to develop efficient methods for solving differential equations with discontinuous coefficients numerically.

We propose a model of an infinite waveguide of constant rectangular cross section with losses in the walls which are described by the Schukin–Leontovich boundary conditions. The waveguide is analyzed using the non-complete Galerkin method. We use the standard basis for waveguide with ideally conducting walls supplemented with functions providing precise fulfillment of the boundary conditions. The eigen modes of the waveguide in the THz range are calculated and dispersion characteristics are obtained.

A model for the description of the distribution of magnetization across the thickness of a ferromagnetic semiconductor film is considered. Applying a constant electric field perpendicular to the film surface makes it possible to change the Curie temperature. The obtained formulas determine the dependence that this distribution has on the values of the physical parameters of the film.

The dynamics of the electron beam in a C-band linear accelerator, a bremsstrahlung source with a boundary energy switched between 2.5 MeV and 6 MeV, which is intended for stereotactic and three-dimensional conformal radiotherapy in static and rotational modes, was calculated.

In this paper, we investigated a system, is composed of a natural tungsten and bismuth cylindrical targets. The target has been optimized to produce the maximum of neutrons yield with a diameter of 20 cm and varying height from 10 to 80 cm. The target is bombarded with a high-intensity accelerator by a 0.1 to 3 GeV proton beam. The protons are assumed uniformly distributed across the beam of diameter 2 cm. In this work, we have used Monte Carlo method by using MCNP-6 code to simulate spallation neutron yield, neutron spectrum and distribution of the spallation neutrons coming out of the target in the target region. According to the results approving using several simulations for two targets tungsten and bismuth, the difference of spallation neutron yield increases by 8.92% using a bismuth target and for some beam energy 3 GeV.

A laser optoacoustic method for determining the volume concentration of a polymer binding and carbon filler in carbon fiber reinforced plastic (CFRP) composites has been proposed and realized. Composite samples fabricated by the vacuum infusion method were studied. The volume concentrations of epoxy resin were measured for a set of CFRP samples. We have shown that there are regions with an excess and a deficiency of the epoxy resin. The method could be used for testing of both reference samples and real composite structures.

This paper introduces an estimate for the strength of the correlation of layer thickness errors in the process of coating deposition with broadband optical monitoring. It is shown that a strong effect of self-compensation of deposition errors is observed in the case of a strong correlation of layer thickness errors. An estimate for the strength of this effect is introduced. Theoretical conclusions are confirmed by comparison with practical deposition results that demonstrate the presence of a strong self-compensation effect.

Simple analytical relationships between the geometry of aperiodic thin-layer structures and the phase component of the reflection coefficient were deduced and investigated. The effective optical thickness of an aperiodic structure was introduced as a new parameter and then was analytically defined. The two-layer thin-layer model was proposed to describe wave properties of aperiodic thin layer structures with a weak spatial heterogeneity of the refractive index. This model significantly simplifies the relations that are used to analyze wave properties of this class of multilayer structures. The validity of the analytical results was proved by corresponding numerical calculations.

Bound and free water are present in a wide variety of solids, that is single crystals, polymers, and biopolymers, as well as in media with a hydrogen bond network, as in water (2.7 ± 0.1 Å in length). Some objects behave in the same way as two-component systems (open systems) under external influences and demonstrate an abnormal change in properties at the same temperature as water. This paper presents the results of studies of the temperature behavior of the permittivity, conductivity, and conductivity relaxation time of some hydrophilic polymers, crystallohydrates, and ferroelectrics. The analysis of the results showed that temperature anomalies of the selected properties are observed in the vicinity of 20, 35, 65–75, and near 100°C, which are “special” temperatures for water: in the vicinity of 20, 35, 50°C the destruction of clusters of H₂O molecules occurs, while at higher temperatures there is a transition of structural water into free water. It is possible that the discrete nature of the diffuse temperature peaks of the properties is due to the presence of discrete energy levels of protons in the matrix–water system, which during stepwise heating (slow kinetics) leads to a rearrangement or destruction of the OH–O hydrogen bond network, as well as the overfilling of the proton levels in the two-minimum potential, the release of deep traps, and changes in the set of current carriers, their mobility, and the trajectories of transport in bulk.

Samples of Fe–B alloys have been prepared by quenching a melt using a rotating copper disk and then were certified by XRD analysis. Some of the alloys were found to possess an amorphous structure. Fe–B amorphous ribbons exhibit a sequence of gyromagnetic effects that replace each other as the temperature of the sample changes. These features were interpreted using magnetometry.

We have studied the effect of spherical SiO₂ nanoparticles with sizes of 20, 50, and 80 nm embedded in a PEDOT : PSS buffer layer on the performance of organic solar cells (OSCs) based on star-shaped oligomers. The current–voltage characteristics and absorption spectra of samples have been measured and analyzed; the morphology of the buffer layer surface with embedded nanoparticles has been studied. It has been shown that an increase in the OSC performance occurs in the case of embedded nanoparticles with a diameter of 20 and 50 nm and weakly depends on the concentration of the nanoparticles in the layer.

The objective of this study is to evaluate mathematically an empirical law governs the skin dose with photon beam energy and irradiation field size based on experiment data of dose distributions. The dose distributions were expressed on percentage depth dose (PDD). The measurements of PDDs were done as a function of irradiation field size with an uncertainty of 2% as recommended by IAEA protocols.

The skin dose corresponds to PDD at depth of 0 mm for photon beam energy of 6 and 18 MV. For these both photon beam energies, the skin dose increased linearly with irradiation field size and the skin dose rate decreased in power law as a function of irradiation field size with mathematical error under to 10%. This law allows us to predict the skin dose with irradiation field size for high radiotherapy quality and high protection of organ at risks.

In this paper the task of the operative monitoring of radiation conditions in the near-Earth space is considered as a part of a project Universat-SOCRAT of the system of small satellites, which is being developed at Moscow State University. The scientific approach to the realization of this task is determined. The choice of the satellite orbits and spatial orientation and the configuration of energetic charged particle detectors is validated taking into account other tasks performed by the projected satellite system.

The features of the dynamics of weak tsunami waves caused by the deep-focus Okhotsk Sea earthquake on May 24, 2013, are studied with numerical modeling. It is found that the vast area of coseismic deformations along with the shallow depth of the Sea of Okhotsk and high latitudes were favorable for effects of the Earth’s rotation in the dynamics of the 2013 Okhotsk Sea tsunami. The comparison of calculations with and without the Coriolis force showed that the Earth’s rotation significantly affects the wave field, changing the wave forms and the distribution of the maximum amplitudes.