High-flux research reactor SM was constructed in 1961. This is a vessel-type high-flux reactor with a trap and pressurized water cooling. The reactor design allows achieving high flux of thermal neutrons in the moderating trap located in the core centre with the hard neutron spectrum, the core volume being as small as possible.  The priority applications of the SM reactor are energy efficiency, power optimization and nuclear power engineering. The critical technologies that promote these applications are physics and engineering of high-flux research reactors, research reactors operation practice and nuclear fuel cycle, safe management of radioactive waste and spent nuclear fuel. The SM experimental cells and channels are used to irradiate samples of reactor materials under the specified conditions, to investigate into the properties of different materials under irradiation, to produce a wide range of radionuclides and make research into nuclear physics. To justify the safe and reliable operation of new fuels, the amount of irradiation-induced fission gas release out of the containment should be measured. The paper presents RIAR’s methodological approach to obtaining data on the activity and nuclide composition of fission gas when sampling from the sealed region with fuel rods during irradiation.

The comparative ab initio study of intermolecular interactions in methane-methane, neon-neon, and methane-neon dimers was carried out using the coupled cluster method taking into account single and double excitations and the non-iterative correction for triple excitations (CCSD(T)) with Dunning’s basis sets complemented with bond functions, as well as explicitly correlated coupled cluster method (F12-CCSD(T)). It was shown that in the case of the methane dimer, the pair density spherical mean constructed by the coupled cluster method has a minimum point only if set of bond functions centered on its minimum region is used. This result explains the inclusion of intermolecular electron correlation for wave function basis sets complemented by bond functions. Analyzing sections of the potential energy surface (PES) dimers made it possible to calibrate the set of bond functions, as well as to clarify the interaction energy in the neon dimer.

Multidimensional nonlinear Schrödinger equations of the general form are investigated, in which the potential and dispersion are specified by one or two arbitrary functions. The equations under consideration naturally generalize a number of related nonlinear partial differential equations that occur in various areas of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. Multidimensional and one-dimensional non-symmetry reductions are described, which lead the studied nonlinear Schrödinger equations to simpler equations of lower dimension or ordinary differential equations (or systems of ordinary differential equations). Special attention is paid to finding solutions with radial symmetry. Using methods of generalized separation of variables, new exact solutions of two-dimensional and n-dimensional nonlinear Schrödinger equations of the general form, which are expressed in quadratures or elementary functions, are found.

Shock-wave loading is the most commonly used way to study the dynamic properties of the materials since this permits the investigation into compressibility, phase transformations, and some other phenomena that take place in the high-pressure and high-temperature region. Explosive loading devices and light-gas guns are usually used as the shock-wave loading systems. The paper presents numerical evaluations of aluminum membrane opening (destruction) pressure in the high-pressure chamber of the pneumatic light-gas gun. The calculation results are compared with the experimental data. The simulations and experiments were aimed to evaluate the destruction pressure for a batch of membranes having different geometry, i.e. thickness and height of the unnotched part, because the data on the membrane load limits helps predict the pressure in the high-pressure chamber and the flyer acceleration. Besides, the effect of some factors on the membrane opening pressure is considered such as mechanical properties of the membrane material, the number of notches, i.e. stress concentrators on the membrane surface, the shape of notches, etc. The simulations demonstrated that the main factor affecting the spread in the membrane opening pressures is the material properties. To reduce this spread, one should control the material properties and choose the materials with more stable mechanical properties. The conclusions were validated by comparing the membrane testing data with the simulated results.At constant notch depth, the increase in membrane thickness reduces the membrane opening pressure due to higher stress concentration in the radial notches, as evidenced by the experimental data.

The problem of finding the roots of high-degree polynomials is complex and generally unsolvable. However, in a number of special cases, the roots can be found. The article proposes an original approach to finding the roots of a partial fifth-degree polynomial containing a parameter as a free term. An attempt to find the roots of a parametric fifth-degree polynomial by representing this polynomial as a product of third- and second-degree polynomials, with the subsequent compilation of a system of equations for finding the coefficients of third- and second-degree polynomials, leads to very cumbersome equations, the complexity of solving which is very high. Therefore, an approach is proposed, the idea of which is that the roots are first found for fixed values of the parameter. Then, by setting a small increment to the parameter value, an analysis is carried out for changes in the values of the roots of the polynomial. This becomes possible due to the fact that the parameter is a free term of the polynomial and its increment leads to a shift in the polynomial graph along the vertical axis. This approach allows finding approximate values of roots without using iterative numerical methods.

During the decommissioning of nuclear power units with RBMK reactors, in addition to the energy resource of unburned fuel, there remains an unutilized operational resource (service life) of instruments, equipment elements, and other components in the shutdown units. Under certain conditions, this resource can be used in operating power units. An example of this is the remaining service life of coolant flow meters. The problem arises of optimizing the utilization of this resource. This study presents a mathematical model for predicting changes in the service life of flow meters, considering the probability of their failure and technological constraints on maximum operating hours. Various strategies for using the flow meter resource are examined in accordance with the planned sequential decommissioning of power units. Numerical studies allow the selection of the optimal strategy. It is shown that the savings effect from reusing flow meters depends on the assigned maximum operational time and can range from 40% to 100%.

As the level of automation of nuclear reactors developed, gradually automatic regulators changed from the level of maintaining individual parameters to group and then to functional-group control. Control algorithms of modern nuclear power plants use functional-group control, which allows to send commands of the common unit level instead of direct commands. Nowadays, design and construction of a new nuclear power plant with lead coolant is underway. To work out the normal operation algorithms and safety algorithms, a simulation system was created that allows installing the developed models of the nuclear power plant (process control object), models of equipment, process equipment on it and combining them in a single interaction environment. This article considers the possibility of using and implementing the control algorithm of a new nuclear power plant with lead coolant, which complements the standard algorithms of the control and protection system for neutron and technological parameters. For this purpose, a pre-prepared model of the reactor plant and models of the CPS equipment were installed on the simulation stand. The models of the control object and the CPS were supplemented with an exchange interface and an algorithm that allows controlling the operating modes of the process equipment at the pre-start and start-up stages of the RP. The result was a developed algorithm that eliminates the direct impact of the RP operator on technological operations during normal operation with the possibility of switching to manual mode when conditions appear that prohibit further operations

The article discusses the principles of building an information support system for decommissioned reactors, using the example of a nuclear power plant with an RBMK-1000 reactor. The article describes approaches to building the structure of algorithms for such a system, and discusses security functions that are important for their implementation, to be taken into account when building an information support system. The authors studied the neutron and technological parameters that allow monitoring and emergency protection of the reactor until the fuel is completely discharged from the reactor core, which has been shut down for decommissioning. Special attention in the article is paid to the fact that the information support system must comply with all the norms and rules applicable to systems operating at power units. The data obtained make it possible to develop a uniform approach, in the form of an information support system, which allows monitoring and protecting the reactor using fewer equipment compared to standard systems operating at power units that are operated in the power generation mode.

Today the processes that take place in society, science, high-tech production, and industry can be characterized as complex systems. In order to solve complex problems, new employeees with systemic thinking are needed. One of the key issues of modern pedagogy is the search for tools for the development of systems thinking. At the same time, the key point of teaching systems thinking should be the formation of such thinking, when goal-setting, responsibility for the result and for the consequences of certain decisions would be naturally formed in the process of learning. In schools and universities, separate courses, project-based forms of learning, etc., can be used as such tools aimed at the development of students' systems thinking, desire for knowledge, responsibility for decision-making. The article describes an experimental interactive course on solving case-oriented problems developed and implemented in MEPhI. The course was developed for high school students of the high school lyceum-preduniversitarium of MEPhI. The peculiarity of the course is its interactive character; the teacher acts as a moderator, interacting both with students and organising their interaction among themselves. This methodological approach not only forms systemic thinking as such, but also develops the skill of independent search, promotes involvement in the learning process, and increases motivation for learning.