A relativistic electron in the axial channeling regime in a single crystal moves along a helical trajectory around some regular chain of positive ions, forming an axial channel. In the accompanying reference frame moving along the channel axis at a velocity equal to the longitudinal component of the electron velocity, the channeling motion is finite and can be considered as an implementation of the two-dimensional relativistic atom model with controlled parameters. The depth and shape of the effective potential of the ionic chain depends on the chemical composition of the crystal, its crystallographic structure, and orientation, as well as on the relativistic energy of the particle moving in the channel. The motion in the axial channeling regime even in the bent crystal and its axial channels remains stable if the bending angle is not too large. The maximum possible bending angle is estimated using calculated adiabatic invariants of motion. It is demonstrated that the channeling motion regime can be stable only if the bending angle does not exceed the Lindhard critical channeling angle. Thus, the possibility of deflecting beams of accelerated charged particles by bent crystals is limited to just small angles of deflection.

A method for parametric determination of the incident thermal specific load on the mirror elements of space systems has been proposed. This problem is solved as a problem of finding an extremum between the theoretical and experimental temperature fields in the places where temperature sensors are installed. First, it is necessary to solve the “direct” problem of heat exchange for the test object and set the basic functions describing the shape of the incident thermal flow. The heat exchange process is accompanied by a one-dimensional radiant-conductive heat transfer inside the material. Consequently, in addition to solving the heat equation, it is necessary to solve the equation of radiation transfer inside the mirror element. As boundary conditions, the equality of heat flows is applied: the resulting heat flow on the one hand and zero heat flows to the lower base of the mirror on the other hand since all surfaces except one are thermally insulated for modeling one-dimensional heating. Next, the standard deviation between the experimental and theoretical temperature fields is compiled and the resulting functional is minimized. Regularization is used to overcome the inaccuracy due to the inaccuracy of the source data. The iterative regularization method where the regularizing parameter is the iteration number is chosen for the regularization procedure. The conjugate gradient method, as the most accurate method of the first order of convergence is chosen as the optimization algorithm. The results obtained can be used to evaluate the boundary conditions of products for a wide temperature range.

An algorithm for constructing the first integrals of one class of nonlinear ordinary differential equations of the second order is proposed. Special approaches such as the simplest equation method are usually used to find analytical solutions of these equations. The proposed algorithm makes it possible to find general solutions of nonlinear differential equations in some cases. The algorithm is illustrated in application to the complex Ginzburg–Landau equation. The solution of this equation is sought using traveling wave variables. It is shown that the proposed algorithm allows one to reduce a rather complex nonlinear ordinary differential equation of the second order to a first order differential equation, the general solution of which can be represented as a quadrature. With some restrictions on the arbitrary constants, the solution of the Ginzburg–Landau equation can be presented in the form of an analytical expression.

The non-autonomous nonlinear system of two first order differential equations with arbitrary parameter and the autonomous system of two nonlinear differential equations with quadratic nonlinearity of derivation of unknown functions, containing arbitrary parameters a, α, β, and γ and nonzero parameters b and c satisfying the conditions (b² – c²)(b² – 4c²)(4b² – c²)  = 0 are studied. The conditions on the parameters of the mentioned systems have been determined under which their general solutions have no moving special critical points, i.e., have the Painlevé property (the systems are Painlevé systems). It is proved that the non-autonomous system for any value of the parameter l is a Painlevé type system and is equivalent in one of its components to the second order differential equation obtained by N.A. Kudryashov. The solution of this equation is expressed in terms of the solution of the second Painlevé equation. Direct and inverse Bäcklund transformations have been constructed for this equation. Each component of the autonomous system is equivalent to two second order nonlinear differential equations. It is examined whether these equations have the Painlevé property depending on parameter values. It is proved that the autonomous system with the parameters b² = c²  ≠ 0 is a Painlevé type system: it is equivalent to second-order differential equations, which are either integrated in elliptic functions or admit linearization. In the other two cases, it has this property if a = 0.

A magnetic gas dynamics system of equations including the magnetic viscosity is considered. To study this system, systems of partial differential equations is reduced to systems of ordinary differential equations using two approaches. In the first approach, the independent variable $\psi$ of systems of ordinary differential equations  is such that the equation ψ(x, y, z, t) = const defines the level surface of the solutions of the original system (components of the velocity vector and components of the magnetic field strength). In the second approach, irrotational motions of plasma are considered, in which the components of the velocity are derivatives of some function Q = Q(x, y, z, t). In this case, the equation ψ(x, y, z, t) = const defines the level surface of the function Q = Q(x, y, z, t) and the components of the magnetic field vector. Some exact solutions of the considered system of partial differential equations are found. It is shown that functional arbitrariness is preserved in each of the considered approaches when determining level surfaces. The available functional arbitrariness is used in the problem of location of streamlines of the potential plasma flow and magnetic field lines on a certain surface. An algorithm for obtaining such a surface is described.

The system of Maxwell’s equations is considered after the transition from the Cartesian to cylindrical coordinate system. Instead of the first two traditional components of magnetic and electric field strength, radial and circumferential components of these vectors are introduced. The resulting system of partial differential equations does not explicitly include the dependence on the polar angle. In the case where the desired functions depend only on time and the radial coordinates, specific solutions of the system of Maxwell’s equations are constructed using the separation of variables.

The solution of the insufficiently studied leader–follower problem has been studied within a reinforcement learning neural network model. The reinforcement learning algorithm chosen for training the neural network model is the proximal policy optimization algorithm. In order to implement the training, an emulator of the environment for the leader–follower problem has been developed. The emulator allows one to set up an environment with a different number of obstacles and routes of different lengths and complexity, as well as to configure the desired behavior of the follower agent following the leader. The developed emulator is performant enough for the feasibility of training the reinforcement learning leader–follower models, the adjustment of which requires a large number of training iterations for routes and obstacles of various complexity in the environment. The presented results include the choice of features characterizing the current observable environment of the agent for the reinforcement learning model. A model trained according to the reinforcement learning principles on a set of features of ray-type range sensors can significantly improve the accuracy of solving the problem, reaching 77% of the successful execution of routes, making mistakes mostly when the leader moves in the opposite direction.

A neural network interface for converting complex Russian-language text commands for robotic devices into the RDF-format is presented. The interface involves neural network models to recover missing verbs, split compound commands into single ones, and parse single commands. In order to train these models, training and testing samples have been formed: a data set for learning to divide compound commands into single commands and to analyze single commands has been created with the help of a specially-developed text command generator, using which 55000 simple commands and 16000 composite commands have been generated using special templates; for the task of recovering missing verbs, the corpus from the Dialog-21 conference is used, containing 16000 sentences, of which 5000 have missing verbs; the test set is assembled using crowdsourcing technology and contains 1300 examples. The methods used for text analysis are based on language models and neural networks with Transformer architecture. The accuracy of using a resourceintensive language model (MultilingualBERT) and the resource-efficient distilled version RuBERT-tiny of RuBERT has been evaluated. The results of the dependence of the command parsing accuracy on the presence of punctuation marks and capital letters in the text are presented.

The study of thermoluminescence and photoluminescence spectra allows us to propose a thermoluminescence mechanism for MgB₄O₇:Dy,Na, which is similar to that previously known for MgB₄O₇:Tm. Here, the release of holes from the hole trapping center gives rise to the main working peak of thermoluminescence. The fading of dose information in MgB₄O₇:Dy,Na thermoluminescent detectors (TLD-580N) exposed to light (365, 395, and 470 nm) is also studied. The thermoluminescence peaks diminish without any pronounced optically stimulated luminescence. According to the proposed model, light releases electrons, which recombine with holes in hole traps, after which thermoluminescence becomes impossible.

The clinical application of medical proton and ion accelerators requires more accurate and reliable devices for diagnostics of radiation parameters. For the radiotherapy procedures by high-energy beams of heavy charged particles, high-precision monitoring systems are needed to determine the intensity, position, and spatial distribution of the therapeutic beam in real time with minimum particle flux disturbance. Existing measuring systems do not meet all the necessary requirements. In this connection, it becomes relevant to develop a detecting device for recording the spatial and energy characteristics of proton and ion beams. In this work, the detecting device is developed to measure the transverse distribution of the intensity of hadron beams. The developed detector should allow the implementation of the multi-angle scanning method, which was proposed in our previous works and was successfully tested on X-ray and electron beams. As a result, a scheme of the developed detector has been proposed and the corresponding detecting device has been assembled. The device working medium is a thin scintillation fiber suitable for detecting high-energy hadron beams. The developed detector has been tested on proton and carbon ion beams. The horizontal profiles of the proton and ion beams for different energies measured using the developed and film detectors have been compared. As a result, it has been shown that the developed detector is suitable for measuring the transverse intensity distribution of high-energy proton and ion beams.

The application of radiation therapy in combination with other methods for cancer treatment allows achieving good therapeutic results. It is necessary to form the optimal dose distribution in the target volume for the effective implementation of radiation therapy procedures. Boluses are special devices made of tissue-equivalent materials and placed on the skin surface. Their applications allow changing the dose distribution in the irradiated volume in accordance with the clinical task. This is relevant to the photon irradiation of tumors located close to the skin surface. The use of standard materials such as wax, gelatin, and various gels to fabricate boluses is limited because of the change in the shape and size of such samples during operation. In this work, the possibility of using 3D-printing techniques to fabricate boluses for gamma therapy is explored. For this purpose, a numerical model has been developed involving the real parameters of the gamma radiation medical source and the plastic properties. The calculated and experimental percentage depth dose distributions in plastic, dose values behind plastic samples of different heights, which simulate the simple bolus, and dose distribution behind a printed plastic sample, which simulates a bolus with a complex geometry, have been obtained. The numerical simulation data and experimental results are in good agreement. The work results indicate that the developed numerical model is suitable for calculating the geometric parameters of plastic boluses made by 3D-printing. It has been shown that ABS plastic boluses are applicable for the formation of medical gamma beams.

IBR-2M pulsed reactor has the most intense neutron flux around world ~10¹⁶ n/cm²·sec at the moderator surface in the peak. It is expected that, IBR-2M reactor will get out of service between 2030–2032. The decision was taken to construct a new pulsed reactor to replace IBR-2M reactor and complement the research capabilities of the high-flux research nuclear reactor PIK in Russian federation. At the moment, serious work is underway in FLNP JINR at Dubna to design the NEPTUNE reactor. The NEPTUNE reactor is the first reactor in the world to use Np-237 as a nuclear fuel, and it is expected that the neutron flux at the moderator surface (at the peak and average neutron flux) will be the highest in the world. This work aims to optimize the thermal (water) moderator for a new pulsed research reactor NEPTUNE in order to maximize the thermal and epi-thermal neutron flux and to adjust the neutron spectrum. As a result, four possible dimensions were proposed to conduct different experiments. And it was suggested to make a chamber which volume and thickness of water can be changed to adjust the neutron spectrum.