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The development of a high-temperature gas-cooled reactor (HTGR) constituting a part of nuclear power-and-process station and intended for large-scale hydrogen production is now in progress in the Russian Federation. One of the key objectives in development of the high-temperature gas-cooled reactor is the computational justification of the accepted design.

The article gives the procedure for the computational analysis of thermal and physical characteristics of the high-temperature gas-cooled reactor. The procedure is based on the use of the state-of-the-art codes for personal computer (PC).

The objective of thermal and physical analysis of the reactor as a whole and of the core in particular was achieved in three stages. The idea of the first stage is to justify the neutron physical characteristics of the block-type core during burn-up with the use of the MCU-HTR code based on the Monte Carlo method. The second and the third stages are intended to study the coolant flow and the temperature condition of the reactor and the core in 3D with the required degree of detailing using the FlowVision and the ANSYS codes.

For the purpose of carrying out the analytical studies the computational models of the reactor flow path and the fuel assembly column were developed.

As per the results of the computational modeling the design of the support columns and the neutron physical characteristics of the fuel assembly were optimized. This results in the reduction of the total hydraulic resistance of the reactor and decrease of the maximum temperature of the fuel elements.

The dependency of the maximum fuel temperature on the value of the power peaking factors determined by the arrangement of the absorber rods and of the compacts of burnable absorber in the fuel assembly is demonstrated.

The work is devoted to the description of the author’s formal statements of the clustering problem for a given number of clusters, algorithms for their solution, as well as the results of using this toolkit in medicine.

The solution of the formulated problems by exact algorithms of implementations of even relatively low dimensions before proving optimality is impossible in a finite time due to their belonging to the NP class.

In this regard, we have proposed a hybrid algorithm that combines the advantages of precise methods based on clustering in paired distances at the initial stage with the speed of methods for solving simplified problems of splitting by cluster centers at the final stage. In the development of this direction, a sequential hybrid clustering algorithm using random search in the paradigm of swarm intelligence has been developed. The article describes it and presents the results of calculations of applied clustering problems.

To determine the effectiveness of the developed tools for optimal clustering of multidimensional objects according to a variety of heterogeneous indicators, a number of computational experiments were performed using data sets including socio-demographic, clinical anamnestic, electroencephalographic and psychometric data on the cognitive status of patients of the cardiology clinic. An experimental proof of the effectiveness of using local search algorithms in the paradigm of swarm intelligence within the framework of a hybrid algorithm for solving optimal clustering problems has been obtained.

The results of the calculations indicate the actual resolution of the main problem of using the discrete optimization apparatus — limiting the available dimensions of task implementations. We have shown that this problem is eliminated while maintaining an acceptable proximity of the clustering results to the optimal ones. The applied significance of the obtained clustering results is also due to the fact that the developed optimal clustering toolkit is supplemented by an assessment of the stability of the formed clusters, which allows for known factors (the presence of stenosis or older age) to additionally identify those patients whose cognitive resources are insufficient to overcome the influence of surgical anesthesia, as a result of which there is a unidirectional effect of postoperative deterioration of complex visual-motor reaction, attention and memory. This effect indicates the possibility of differentiating the classification of patients using the proposed tools.

The article is dedicated to mathematic modeling of natural water desalination process by method of thermal distillation. The article gives the equations which allow describing the processes of film flowing and boiling of water, steam condensation and vacuum maintenance. The article presents the algorithm of calculation, implemented in MatLab computer mathematic system and Excel electronic tables, and the initial data required for the calculation. The model has been checked for adequacy. The calculation of ten-effect distillation system is given. The results of work can be used in design and optimization of process conditions for distillation systems.

This paper presents the analysis of dependences between frame basic cell geometry parameters and function via finite element analysis. The simplified models of frame cell with varied strut width, thickness and quantity in a circle was researched to evaluate radial forces, maximum stress and strain, permanent residual strain and pinching load forces. The outcomes of this study might help in the development of new artificial heart valves and during the analysis of existing in-clinical TAVI prostheses.

The article describes the state of the art computer simulation in the field of metal forming processes, the main problem points of traditional methods were identified. The method, that allows to predict the deformation distribution in the volume of deformable metal with taking into account of microstructure behavioral characteristics in deformation load conditions, was described. The method for optimizing computational resources of multiscale models by using statistical similar representative volume elements (SSRVE) was presented. The modeling methods were tested on the process of single pass drawing of round rod from steel grade 20. In a comparative analysis of macro and micro levels models differences in quantitative terms of the stress-strain state and their local distribution have been identified. Microlevel model also allowed to detect the compressive stresses and strains, which were absent at the macro level model. Applying the SSRVE concept repeatedly lowered the calculation time of the model while maintaining the overall accuracy.

The well-known “Sea battle” game is in the focus of the current job. The main goal of the article is to provide modified version of “Sea battle” game and to find optimal players’ strategies in the new rules. Changes were applied to attacking strategies (new option to attack hitting four cells in one shot was added) as well as to the size of the field (sizes of 10 × 10, 20 × 20, 30 × 30 were used) and to the rules of disposal algorithms during the game (new possibility to move the ship off the attacking zone). The game was solved with the use of game theory capabilities: payoff matrices were found for each version of altered rules, for which optimal pure and mixed strategies were discovered. For solving payoff matrices iterative method was used. The simulation was in applying five attacking algorithms and six disposal ones with parameters variation due to the game of players with each other. Attacking algorithms were varied in 100 sets of parameters, disposal algorithms — in 150 sets. Major result is that using such algorithms the modified “Sea battle” game can be solved — that implies the possibility of finding stable pure and mixed strategies of behaviour, which guarantee the sides gaining optimal results in game theory terms. Moreover, influence of modifying the rules of “Sea battle” game is estimated. Comparison with prior authors’ results on this topic was made. Based on matching the payoff matrices with the statistical analysis, completed earlier, it was found out that standard “Sea battle” game could be represented as a special case of game modifications, observed in this article. The job is important not only because of its applications in war area, but in civil areas as well. Use of article’s results could save resources in exploration, provide an advantage in war conflicts, defend devices under devastating impact.

In the present paper, we discuss the possibility of a simplified three-dimensional unsteady simulation of plasma-assisted combustion of gaseous fuel in a supersonic airflow. Simulation was performed by using FlowVision CFD software. Analysis of experimental geometry show that it has essentially 3D nature that conditioned by the discrete fuel injection into the flow as well as by the presence of the localized plasma filaments. Study proposes a variant of modeling geometry simplification based on symmetry of the aerodynamic duct and periodicity of the spatial inhomogeneities. Testing of modified FlowVision $k–\varepsilon$ turbulence model named «KEFV» was performed for supersonic flow conditions. Based on that detailed grid without wall functions was used the field of heat and near fuel injection area and surfaces remote from the key area was modeled with using of wall functions, that allowed us to significantly reduce the number of cells of the computational grid. Two steps significantly simplified a complex problem of the hydrocarbon fuel ignition by means of plasma generation. First, plasma formations were simulated by volumetric heat sources and secondly, fuel combustion is reduced to one brutto reaction. Calibration and parametric optimization of the fuel injection into the supersonic flow for IADT-50 JIHT RAS wind tunnel is made by means of simulation using FlowVision CFD software. Study demonstrates a rather good agreement between the experimental schlieren photo of the flow with fuel injection and synthetical one. Modeling of the flow with fuel injection and plasma generation for the facility T131 TSAGI combustion chamber geometry demonstrates a combustion mode for the set of experimental parameters. Study emphasizes the importance of the computational mesh adaptation and spatial resolution increasing for the volumetric heat sources that model electric discharge area. A reasonable qualitative agreement between experimental pressure distribution and modeling one confirms the possibility of limited application of such simplified modeling for the combustion in high-speed flow.

А new cloud center of parallel computing is to be created in the Laboratory of Information Technologies (LIT) of the Joint Institute for Nuclear Research JINR) what is expected to improve significantly the efficiency of numerical calculations and expedite the receipt of new physically meaningful results due to the more rational use of computing resources. To optimize a scheme of parallel computations at a cloud environment it is necessary to test this scheme for various combinations of equipment parameters (processor speed and numbers, throughput оf а communication network etc). As a test problem, the parallel MPI algorithm for calculations of the long Josephson junctions (LDJ) is chosen. Problems of evaluating the impact of abovementioned factors of computing mean on the computing speed of the test problem are solved by simulation with the simulation program SyMSim developed in LIT.

The simulation of the LDJ calculations in the cloud environment enable users without a series of test to find the optimal number of CPUs with a certain type of network run the calculations in a real computer environment. This can save significant computational time in countable resources. The main parameters of the model were obtained from the results of the computational experiment conducted on a special cloud-based testbed. Computational experiments showed that the pure computation time decreases in inverse proportion to the number of processors, but depends significantly on network bandwidth. Comparison of results obtained empirically with the results of simulation showed that the simulation model correctly simulates the parallel calculations performed using the MPI-technology. Besides it confirms our recommendation: for fast calculations of this type it is needed to increase both, — the number of CPUs and the network throughput at the same time. The simulation results allow also to invent an empirical analytical formula expressing the dependence of calculation time by the number of processors for a fixed system configuration. The obtained formula can be applied to other similar studies, but requires additional tests to determine the values of variables.

Seasonal migrations and herd instinct are traditionally recognized as wild reindeer (Rangifer tarandus L.) species-specific behavioral signs. These animals are forced to overcome water obstacles during the migrations. Behaviour peculiarities are considered as the result of the selection process, which has chosen among the sets of strategies, as the only evolutionarily stable one, determining the reproduction and biological survival of wild reindeer as a species. Natural processes in the Taimyr population wild reindeer are currently occurring against the background of an increase in the influence of negative factors due to the escalation of the industrial development of the Arctic. That is why the need to identify the ethological features of these animals completely arose. This paper presents the results of applying the classical methods of the theory of optimal control and differential games to the wild reindeer study of the migration patterns in overcoming water barriers, including major rivers. Based on these animals’ ethological features and behavior forms, the herd is presented as a controlled dynamic system, which presents also two classes of individuals: the leader and the rest of the herd, for which their models, describing the trajectories of their movement, are constructed. The models are based on hypotheses, which are the mathematical formalization of some animal behavior patterns. This approach made it possible to find the trajectory of the important one using the methods of the optimal control theory, and in constructing the trajectories of other individuals, apply the principle of control with a guide. Approbation of the obtained results, which can be used in the formation of a common “platform” for the adaptive behavior models systematic construction and as a reserve for the cognitive evolution models fundamental development, is numerically carried out using a model example with observational data on the Werchnyaya Taimyra River.

The paper presents a mathematical model that describes the process of obtaining biogas from livestock waste. This model describes the processes occurring in a biogas plant for mesophilic and thermophilic media, as well as for continuous and periodic modes of substrate inflow. The values of the coefficients of this model found earlier for the periodic mode, obtained by solving the problem of model identification from experimental data using a genetic algorithm, are given.

For the model of methanogenesis, an optimal control problem is formulated in the form of a Lagrange problem, whose criterial functionality is the output of biogas over a certain period of time. The controlling parameter of the task is the rate of substrate entry into the biogas plant. An algorithm for solving this problem is proposed, based on the numerical implementation of the Pontryagin maximum principle. In this case, a hybrid genetic algorithm with an additional search in the vicinity of the best solution using the method of conjugate gradients was used as an optimization method. This numerical method for solving an optimal control problem is universal and applicable to a wide class of mathematical models.

In the course of the study, various modes of submission of the substrate to the digesters, temperature environments and types of raw materials were analyzed. It is shown that the rate of biogas production in the continuous feed mode is 1.4–1.9 times higher in the mesophilic medium (1.9–3.2 in the thermophilic medium) than in the periodic mode over the period of complete fermentation, which is associated with a higher feed rate of the substrate and a greater concentration of nutrients in the substrate. However, the yield of biogas during the period of complete fermentation with a periodic mode is twice as high as the output over the period of a complete change of the substrate in the methane tank at a continuous mode, which means incomplete processing of the substrate in the second case. The rate of biogas formation for a thermophilic medium in continuous mode and the optimal rate of supply of raw materials is three times higher than for a mesophilic medium. Comparison of biogas output for various types of raw materials shows that the highest biogas output is observed for waste poultry farms, the least — for cattle farms waste, which is associated with the nutrient content in a unit of substrate of each type.