The propagation of a beam of shear waves along the generatrix of a nonlinear viscoelastic cylindrical shell of the Sanders–Koiter model is simulated by asymptotic integration methods. It is assumed that the shell is made of a material characterized by a cubic dependence between stress and strain intensities, the dimensionless parameters of wall thinness and physical nonlinearity are quantities of the same order of smallness, and the ratio of viscoelastic constants is a dimensionless parameter of a higher order of smallness. A variation of the multiscale expansion method is used, which makes it possible to determine the wave propagation velocity from the linear approximation equations and, in the first essentially nonlinear approximation, to obtain a resolving nonlinear quasi-hyperbolic equation for the leading term of the expansion of the shear component of the displacement. The derived equation is a cubic nonlinear modification of the dispersionless Kadomtsev–Petviashvili–Burgers equation, being a special case of the modified Khokhlov–Zabolotskaya–Kuznetsov equation. The solution of the derived equation is sought in the form of one harmonic with a slowly changing complex amplitude, since in deformable media with cubic nonlinearity the effect of wave self-action significantly prevails over the effect of higher harmonic generation. As a result, the Ginzburg-Landau equation is obtained for the complex amplitude, for which an exact physically consistent solution is constructed.

For NPPs with RBMK reactors, a physical problem of choosing a time shift between power unit shutdowns is formulated and solved in order to maximize the use of the fuel energy resource of reactors being decommissioned. The mathematical model used to solve the optimization problem is based on a point model of the fuel assembly distribution dynamics by energy production (fuel assembly spectrum), which allows predicting the change in the fuel assembly spectrum over time in an operating reactor depending on the tactics of loading burnt-out fuel assemblies from a shut-down reactor. It is shown that optimal planning of the shift between power unit shutdowns allows saving hundreds of "fresh fuel assemblies" depending on the selected fuel afterburning strategy. The paper examines a scenario in which one of the reactors is shut down and the second one continues to operate for a limited time. The possibility of loading fuel from the first reactor to the second one is studied in order to minimize the total consumption of fresh fuel assemblies. The proposed approach takes into account both physical and technological limitations. The results of numerical modeling are presented, demonstrating the efficiency of the proposed fuel redistribution algorithm. The obtained data can be used in planning the decommissioning of power units in order to increase fuel efficiency and reduce the costs of purchasing fresh fuel assemblies.

This work presents a numerical study of the stress-strain state of the human maxilla under masticatory load with different dental implantation options. The finite element method was used to obtain the results. The geometric model is constructed using real сomputed tomography scans of a patient with dental implants. It is shown that as the number of implants increases, in the range from 4 to 8, the magnitude of mechanical stress on the bone monotonically decreases. This finding allows us to state that the option with the largest number of implants is the safest in terms of operation. It has been shown that increasing the size of the implant reduces the amount of mechanical stress on both bones and implants. The influence of different angles of posterior implant placement is demonstrated. The conclusions obtained in the article are independent of the mechanical properties of the bone set in the model, under the approximation of an isotropic and homogeneous jaw material in an elastic formulation.

We study the linear inverse problem of determining the unknown, time-dependent right-hand side (source function) in a one-dimensional parabolic equation with a weakly degenerate principal part defined in divergence form. The additional observation condition is specified in integral form. Sufficient conditions are established under which a solution to the inverse problem under consideration exists and is unique. No restrictions are imposed on the value of T or the size of the domain, i.e. the proven theorems are of a global nature. The solution is understood in the generalized sense according to Sobolev; in particular, the unknown source function is sought in the space L2(0, T). The equation’s coefficients may depend on both the time and spatial variables. Degeneracy of the equation is also permitted in both the time and spatial variables. Proofs of the existence and uniqueness theorems for the solution of the inverse problem are based on the study of the unique solvability of the corresponding direct problem, which is also new and of independent interest. When studying the unique solvability of the inverse problem, it is reduced to studying the solvability of a certain operator equation, using general theorems of functional analysis

The studies of the past temperatures  at the Earth surface is important problem for prediction of the climate changes.  The systematic instrumental temperature measurements took place no more than two centuries. Thus, indirect estimations of the past temperatures present main information on the past climate. It is considered that the measured temperatures in the boreholes can be used to reconstruct the past surface temperatures at the Earth. The inverse problem on the past surface temperature reconstruction based on the measured borehole temperature in glaciers and rocks is studied.   In common case the solution of this problem is not unique and stable. There were many such reconstructions, however, the properties of such solutions have not been derived. We find out that the solution of this problem is not unique and stable. Unfortunately, various previous reconstructions do not take into account these properties. We prove in this paper that the uniqueness and stability properties take place for the inverse problems that assume solution in the form of the finite segments of the Fourier series.

The article presents a technique for analyzing the lighting characteristics of light-emitting diodes (hereinafter referred to as LEDs), which are represented by a wide range of materials of the AIIIBV group, with or without quantum wells, based on heterostructures or using a single-crystal material. This technique is intended for analyzing and rejecting LEDs, determining their individual proportionality coefficients, which allow for a targeted study of degradation processes in LEDs caused by various destructive effects. It is shown that characteristic regions of the operating current flow are distinguished on the L-I characteristic: the region of low currents LC, the region of the ohmic resistance of the LED - R region, the region of high currents HC, which are characterized by their own proportionality coefficients and have their own physical meaning. Physical and mathematical relationships are determined that describe the change in the output radiation power with an increase in the forward current for LEDs made of the listed materials. The application of this technique with a quantitative assessment of radiation power losses for a selected LED type in the LC and HC regions is shown. The dependence of the LED radiation power losses in the HC region on the operating current is shown. The presented method for assessing the lighting characteristics of LEDs is relevant in the case of exposure to special factors (ionizing radiation, long-term operation, electric fields, etc.), where losses in radiation power will be caused by the induced introduction of non-radiative recombination centers. 

The paper deals with the modeling of atomic structure of an interface between metallic iron and its oxide Fe₃O₄ (magnetite). Such boundaries arise, for example, during the formation of an oxide layer on the surfaces of pipes made of ferritic-martensitic steels used for protection against high-temperature corrosion in aggressive oxygen-containing environments, in particular, in liquid lead and lead-bismuth eutectics, which are considered as coolants in advanced fast neutron reactors. Theoretically possible versions of coherent surface conjugation of the crystal lattices of iron and magnetite are considered and the specific surface energies of corresponding interfaces are estimated using various interatomic interaction potentials and first-principles calculations. This made it possible to identify. The obtained results made it possible to identify the atomic structure of the interface between iron and magnetite, select configurations with the minimum energy for each potential used, and determine the most suitable interatomic interaction potential for further studies of the effects of irradiation on the iron-magnetite interface.

The method of polyenergetic implantation of helium ions into single-crystal silicon was investigated in order to form buried layers of high porosity, promising for creating structures of the "silicon-on-insulator" type. The creation of buried porous layers by implantation of helium ions and subsequent high-temperature annealing is very promising for further obtaining silicon-on-nothing and silicon-on-insulator structures. However, the porosity of the buried layers is limited by the blistering and flecking phenomena, which cause mechanical damage to the surface silicon at high implantation doses. The purpose of this work is to increase the helium ion implantation dose and, accordingly, increase the porosity of the buried layer after high-temperature annealing without deteriorating the quality of the surface silicon layer. We present a method consisting in creating an extended concentration profile with a concentration of 4∙10²¹ He⁺/cm³ with sequential implantation with energies of 70 and 35 keV. High-temperature annealing at 150°C/30 min leads to the formation of huge pores with a diameter of approximately 130 nm near the initial concentration maximum for the energy of 70 keV. It is concluded that the polyenergetic implantation method allows a significant increase in the implanted dose without the occurrence of surface defects, and the regulation of the annealing temperature opens up possibilities for controlling the distribution and size of pores in the buried layer.

The objective of the work presented in this publication was to study the parameters of a cooling system for argon filling the internal volume of an inert chamber. This objective was achieved by sequentially solving the following problems: numerical simulation of the cooling unit operation in an air environment; experimental determination of the cooling capacity of the cooling unit in an air environment and verification of the numerical simulation results; numerical simulation of the cooling unit operation in argon. The practical significance of the study is determined by the possibility of using the obtained results to optimize the design and operation of inert chamber cooling systems in technological processes with high thermal loads. The proposed operating parameters of the equipment ensure the required temperature, stability of the inert environment with minimal energy consumption and maximum heat removal efficiency. The main results of the study showed that optimal operation of the system is achieved at certain ratios of argon circulation rate, ethylene glycol temperature and fan speed. Critical values ​​of the parameters at which the cooling efficiency decreases were established. Based on the results of the work, data were obtained that can be used in the design of cooling systems for gaseous media of inert chambers.