It is proposed to consider the channeling effect in the so-called accompanying reference system moving with the velocity equal to the longitudinal component of the channeled particle velocity. In such a system, particle motion is finite and similar to the vibrational motion in a one-dimensional potential (plane channeling) or two-dimensional finite motion in the central field (axial channeling). For relativistic electrons, such motion can be considered both in quantum and classical approximations. In classical consideration, such important characteristics of motion and electromagnetic radiation as the intensity of the resulting electromagnetic radiation, its spectral characteristics, and characteristic times of electron energy loss can be calculated quite simply. Using the results of the classical approach, it is possible to estimate the characteristic life times of quantum channeled states and the probability of transitions between them, which can be done only numerically in the pure quantum approach. In this paper, the method of simplified analytical consideration is applied to calculate the spectral characteristics and radiation intensity, which accompanies the axial channeling GeV electrons. It is shown that this mechanism can lead to the conversion of a significant part of the energy of the electron beam passing through the oriented single crystal target about 1 cm thick into high-energy gamma-ray photons when.

   The problem of an increase in the thermodynamic potentials of an ensemble of nanoparticles compared to a microcrystal because of the surface tension effect has been formulated and solved. The results have been applied to nanostructures composed of indium and gold with different size distributions including even, linear, exponential, and normal. The largest increase for indium (9.44 · 10^–29 J per particle at 300 K) and gold (1.19 · 10^–28 J) occurs with the linearly decreasing distribution function and with one of configurations of the normal distribution, respectively. Physically, the results appear to be reasonable because ultrasmall nanoparticles, which has a particular meaning for the effect, dominate in both cases. The surface tension effect in gold is more pronounced than in indium. The presence of ultrasmall nanoparticles in an ensemble has the vacancy-related effect that reduces thermodynamic potentials of the system to dominate over the surface tension effect, which determine the stability of the system. The vacancy-related effect drops sharply with a decrease in the number of ultrasmall nanoparticles and, under certain conditions, can become smaller than the surface tension effect. An overall increase in the thermodynamic potentials can potentially result in the loss of the system stability.

   The widespread use and improvement of laser technologies in the economies of the most developed countries is a global trend in world development. The use of laser technologies is crucial for increasing labor productivity and competitiveness of the national economy, expanding the possibilities of its integration into the world economic system. The possibility of using laser technologies for the processing of technogenic mineral raw materials is considered. The ability of laser radiation to create high heat flux densities in a locally limited area of the surface, sufficient to heat, melt, or evaporate almost any material, is the basis for laser processing of materials. An LS-06 technological cw ytterbium fiber laser with a wavelength of 1060 nm serves as a powerful source of a directed energy flux during laser processing. The effect of continuous laser radiation on mineral objects containing gold, which cannot be extracted by gravitational methods, has been studied. As the studied objects, natural mineralogical samples with an aluminosilicate matrix from a placer deposit were selected. All mineralogical samples contained metal particles, including gold in the form of impurities. As a result of laser processing of gold-bearing mineralogical samples, the formation of fused objects - conglomerates was established. Scanning electron microscopy revealed that after laser energy exposure, the samples were superficially micro-inhomogeneous silicate cakes, on the surface of which agglomerated crystal structures of gold were formed, ranging in size from 300 nm to 30 μm. It has been established in the work that the optimal radiation power of this laser source is in the range from 90 to 180 W.

   One of the results of mass screening of pregnant women in the Moscow region has been reported. The screening purpose is to detect prognostic signs of preeclampsia, which is a severe pregnancy complication. In the screening process for each patient, the placental concentrations of angiogenic PLGF protein and anti-angiogenic SFLT-1 protein in blood serum have been measured. According to the medical literature, these proteins can serve as signs (markers) of possible preeclampsia development. Statistical processing of screening data has been carried out using tools of our logical symptom method. In a sample containing 564 patients without preeclampsia, the dependence of the concentration of each of the markers on the gestational period has been obtained. A mathematical model of the relationship between the concentrations of markers during pregnancy is constructed. The model demonstrates that the concentration of the SFLT-1 marker in the first half of pregnancy in patients without preeclampsia monotonously “follows” an increase in the concentration of the PLGF marker. The former concentration continues to monotonically increase in the second half of pregnancy, when the latter concentration decreases. In patients with preeclampsia, the behavior of the concentration of the SFLT-1 marker inhibitor is catastrophically changed: in the second half of the pregnancy, its concentration increases sharply and remains high until the end of pregnancy. Thus, the effectiveness of these markers is confirmed as signs of preeclampsia in the late periods of pregnancy.

   The generalized Duffing equation obtained using traveling wave variables in the equation describing the propagation of pulses in an optical fiber has been considered. An ordinary second-order differential equation is represented as a dynamical system. For the generalized Duffing equation without the external force, equilibrium points are found and their stability is investigated. The results of the study are presented in the table, where the type of stability for each of the five equilibrium points is indicated depending on the parameters of the equation. The parameters at which the system has homoclinic and heteroclinic orbits are found. Using the Melnikov method, it has been found that homoclinic chaos is always implemented in the studied system for some values of the parameters. Damping is used to control chaotic dynamics in the system. Constraints on the parameters at which chaos is implemented are obtained for the damped system. Bifurcation diagrams of the system are plotted in the absence and presence of the controller. According to the Bennetin algorithm, the largest Lyapunov exponent of a dynamical system is calculated as a function of the amplitude of the driving force. The results obtained by numerical analysis are in agreement with those obtained theoretically by the Melnikov method.

   A nonlinear partial differential equation describing the propagation of highly dispersed pulses in optical fibers is studied. Taking into account the Ablowitz–Ramani–Segur hypothesis, the reduction of the original partial differential equation to an ordinary differential equation is considered. Using the traveling wave variables, the ordinary differential equation is obtained in which the imaginary and real parts are separated from each other. Equating them to zero gives a system of ordinary differential equations. The integrability of this system is investigated using the Painlevé test. It is shown that the system of ordinary differential equations does not pass the Painlevé test, since there is only one integer Fuchs index. At the third step of the Painlevé test, the conditions for the compatibility of the system are found. Taking into account these conditions, the sixth-order ordinary differential equation is obtained. Exact solutions for the ordinary differential equation are constructed using the simplest equation method. The constructed solutions are expressed in terms of elliptic sine and exponential functions, and have the form of periodic and solitary waves, respectively.

   The temperature distribution, gas flow pattern and velocity in the reaction zone of a furnace for the carbothermal synthesis of uranium and plutonium nitrides have been numerically analyzed. The heater temperature, flow rate and temperature of the gas supplied to the furnace retort are the input data for the analysis. The analysis is performed using a CFD model of the furnace developed and validated for the isothermal holding and transient modes of the furnace. The CFD model takes into account two specific features of the carbothermal synthesis reaction of uranium and plutonium nitrides such as a change in the thermophysical properties of the charge in the process of transformation of UO₂ and PuO₂ into (U, Pu)N, and heat release during the exothermic reaction. The furnace has a fairly wide range of process parameters, which make it possible to ensure the temperature of the entire volume of the charge within the range of (1650 ± 50)°С for the carbothermal synthesis of uranium and plutonium nitrides. It has been shown that the maximum temperature unevenness in the charge volume does not exceed 65°C. The analysis of the gas flow pattern inside the retort shows that the delivery of nitrogen and nitrogen-hydrogen mixture to the reaction zone of the entire volume of the charge, as well as the removal of gaseous reaction products from the retort, is ensured. Since the gas flow rate and the temperature do not significantly affect the charge temperature inside the retort, these parameters should be selected taking into account the optimal behavior of the chemical carbothermal reaction for the synthesis of uranium and plutonium nitrides. The results of the numerical analysis illustrate the capabilities of CFD modeling of thermophysical processes inside the retort furnace at the equipment development stage and at the stages of selection and justification of the furnace operation modes.

   The efficiency of uranium mining by the in-situ leaching method depends on the opening scheme choice at the design stage of a production unit. An information system for the design and optimization of opening schemes for technological units of an underground leaching field is presented. Opening schemes are built on the basis of geological and mathematical models of deposits, including the distribution of effective capacity and productivity. The system allows the construction of in-line, cellular, and adaptive opening schemes, in accordance with the specified parameters. The construction can be performed in manual or automatic modes. For the created opening schemes, the geotechnological parameters of the operational units, the predicted geotechnological and financial and economic indicators of mining for a given degree of uranium extraction are calculated. The unit parameters are calculated on the basis of the spatial distributions of physical quantities. Adequate mathematical models are used to calculate predictive geotechnological and financial and economic indicators. The constructed opening schemes can be optimized in the manual or automatic mode based on the use of the gradient descent method. During optimization, the block can be rotated, moved, or resized. During optimization, various objective functions, as well as their linear combination, can be used. The system also allows customizing and generating the report documentation. The system consists of five modules that interact with the project base, geological, and technological databases. Interaction with the databases is carried out through SQL queries. The use of the system will allow automating the process of selecting the most effective opening schemes, improving the quality of report documents, and increasing the accuracy of forecasting.

   The process of countercurrent pulsation extraction in a column-type apparatus with nozzles has been mathematically simulated. The operating parameters of the extraction process in the liquid-liquid system have been analyzed. A set of factors that have a significant impact on both individual stages of the extraction process and the structure of the process as a whole have been considered. A diffusion model, which contains two critical parameters, the coefficient of volumetric mass transfer and the coefficient of longitudinal diffusion, has been used to describe the process of mass transfer in the liquid–liquid system. Because of the lack of reliable data on the quantitative values of these parameters for the considered design of the extractor, and the impossibility of determining them experimentally, an attempt has been made to obtain the necessary data by means of numerical studies. Using the integral characteristics of the extraction process, averaged over the entire volume of the column, and criterion dependences characterizing the hydrodynamic, thermal, and mass transfer conditions of extraction, regression dependences have been obtained for the operating parameters of the extraction process in the form of functions of the input control factors. Taking into account the information received, a recursive computational scheme has been organized to determine the main output parameters of the extraction process. The results of calculations based on the created mathematical model can be used in practical work to optimize the operating modes of existing devices of this type.

   The influence of change in the ³He concentration in the beryllium core masonry on the reactivity margin during various campaigns has been described using the MIR reactor as an example. An algorithm is presented for the on-line calculation of  ³He concentrations in beryllium blocks of the core masonry, taking into account the actual distribution of the energy release over the cells of the working channels with fuel assemblies, the operating time at power, and the time of shutdowns between campaigns for refueling the reactor. The analysis of the actual performance of the reactor in the campaigns, which are close in terms of the duration of operation at power and in the loading of the loop channels but differing in times of the reactor stopping between the campaigns, is carried out. Through the study and analysis of experimental data on the operation of the reactor in campaigns of various durations, their characteristic properties have been revealed. The effect of the accumulated helium on the reactivity parameters of the reactor has been estimated. The nature of changes in the reactivity margin when operating at power, depending on the duration of the stay has been predicted using this estimate. In addition, the negative impact of poisoning nuclei on the state of beryllium blocks in a series of short-term campaigns, a feature of which is the excess of the preparation time for the campaign over the duration of the campaign itself, has been described. It has been shown that  ³He accumulates from campaign to campaign in a series of short-term campaigns, which inevitably leads to a decrease in the reactivity margin. During long-term operation at power, it has been found that this absorbing nuclide acts as a burnable absorber of neutrons, reducing the rate of loss of the reactivity margin.

   The current status of the technology for vitrification of high-level waste at the Radiochemical Plant of the Mayak Production Association has been described. Conceptual and technical solutions related to development of the technology for vitrification of different types of liquid HLW at the Mayak Production Association in the short and long terms have been considered. Problems of the Radiochemical Plant and their possible solutions, as well as main technical differences of the promising removable small-size melter from facilities used at the Mayak Production Association earlier, have been described. The maximum water evaporation capacity of the melter and its production capacity have been determined in terms of initial solution containing fluxing additives (sodium carbonate and borax) at simultaneous feeding of dry glass frit into the melter. The optimal conditions have been identified for molten glass discharge and for stopping the glass flow discharge for the second melter prototype. The performance of the system for dosing dry reacting agents and glass frit has been tested. The study includes two experiments on sedimentation and discharge of spherical metal powder simulating the disperse phase of noble metals, which are contained in HLW resulted from SNF reprocessing. A series of three discharge procedures characterized by a stepwise increase in the viscosity and temperature of glass melting by means of feeding the glass frit without fluxing solution have been performed. The thermophysical characteristics of the brickwork and studied electric parameters of the melter operation have been obtained. Process monitoring and control systems have been developed. The viscosity and chemical stability of the applied glass composition have been determined.