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The article is devoted to the construction and investigation of an averaged mathematical model of an aluminum-cobalt-molybdenum hydrocracking catalyst oxidative regeneration. The oxidative regeneration is an effective means of restoring the activity of the catalyst when its granules are coating with coke scurf.

The mathematical model of this process is a nonlinear system of ordinary differential equations, which includes kinetic equations for reagents’ concentrations and equations for changes in the temperature of the catalyst granule and the reaction mixture as a result of isothermal reactions and heat transfer between the gas and the catalyst layer. Due to the heterogeneity of the oxidative regeneration process, some of the equations differ from the standard kinetic ones and are based on empirical data. The article discusses the scheme of chemical interaction in the regeneration process, which the material balance equations are compiled on the basis of. It reflects the direct interaction of coke and oxygen, taking into account the degree of coverage of the coke granule with carbon-hydrogen and carbon-oxygen complexes, the release of carbon monoxide and carbon dioxide during combustion, as well as the release of oxygen and hydrogen inside the catalyst granule. The change of the radius and, consequently, the surface area of coke pellets is taken into account. The adequacy of the developed averaged model is confirmed by an analysis of the dynamics of the concentrations of substances and temperature.

The article presents a numerical experiment for a mathematical model of oxidative regeneration of an aluminum-cobalt-molybdenum hydrocracking catalyst. The experiment was carried out using the Kutta–Merson method. This method belongs to the methods of the Runge–Kutta family, but is designed to solve stiff systems of ordinary differential equations. The results of a computational experiment are visualized.

The paper presents the dynamics of the concentrations of substances involved in the oxidative regeneration process. A conclusion on the adequacy of the constructed mathematical model is drawn on the basis of the correspondence of the obtained results to physicochemical laws. The heating of the catalyst granule and the release of carbon monoxide with a change in the radius of the granule for various degrees of initial coking are analyzed. There are a description of the results.

In conclusion, the main results and examples of problems which can be solved using the developed mathematical model are noted.

The creation of a virtual laboratory stand that allows one to obtain reliable characteristics that can be proven as actual, taking into account errors and noises (which is the main distinguishing feature of a computational experiment from model studies) is one of the main problems of this work. It considers the following task: there is a rectangular waveguide in the single operating mode, on the wide wall of which a technological hole is cut, through which a sample for research is placed into the cavity of the transmission line. The recovery algorithm is as follows: the laboratory measures the network parameters (S₁₁ and/or S₂₁) in the transmission line with the sample. In the computer model of the laboratory stand, the sample geometry is reconstructed and an iterative process of optimization (or sweeping) of the electrophysical parameters is started, the mask of this process is the experimental data, and the stop criterion is the interpretive estimate of proximity (or residual). It is important to note that the developed computer model, along with its apparent simplicity, is initially ill-conditioned. To set up a computational experiment, the Comsol modeling environment is used. The results of the computational experiment with a good degree of accuracy coincided with the results of laboratory studies. Thus, experimental verification was carried out for several significant components, both the computer model in particular and the algorithm for restoring the target parameters in general. It is important to note that the computer model developed and described in this work may be effectively used for a computational experiment to restore the full dielectric parameters of a complex geometry target. Weak bianisotropy effects can also be detected, including chirality, gyrotropy, and material nonreciprocity. The resulting model is, by definition, incomplete, but its completeness is the highest of the considered options, while at the same time, the resulting model is well conditioned. Particular attention in this work is paid to the modeling of a coaxial-waveguide transition, it is shown that the use of a discrete-element approach is preferable to the direct modeling of the geometry of a microwave device.

A hybrid cluster implies the use of computational devices with radically different architectures. Usually, these are conventional CPU architecture (e.g. x86_64) and GPU architecture (e. g. NVIDIA CUDA). Creating and exploiting such a cluster requires some experience: in order to harness all computational power of the described system and get substantial speedup for computational tasks many factors should be taken into account. These factors consist of hardware characteristics (e.g. network infrastructure, a type of data storage, GPU architecture) as well as software stack (e.g. MPI implementation, GPGPU libraries). So, in order to run scientific applications GPU capabilities, software features, task size and other factors should be considered.

This report discusses opportunities and problems of hybrid computations. Some statistics from tests programs and applications runs will be demonstrated. The main focus of interest is open source applications (e. g. OpenFOAM) that support GPGPU (with some parts rewritten to use GPGPU directly or by replacing libraries).

There are several approaches to organize heterogeneous computations for different GPU architectures out of which CUDA library and OpenCL framework are compared. CUDA library is becoming quite typical for hybrid systems with NVIDIA cards, but OpenCL offers portability opportunities which can be a determinant factor when choosing framework for development. We also put emphasis on multi-GPU systems that are often used to build hybrid clusters. Calculations were performed on a hybrid cluster of SPbU computing center.

The article covered results of three-dimensional modeling of ecologic situation of shallow water on the example of the Azov Sea with using schemes of increased order of accuracy on multiprocessor computer system of Southern Federal University. Discrete analogs of convective and diffusive transfer operators of the fourth order of accuracy in the case of partial occupancy of cells were constructed and studied. The developed scheme of the high (fourth) order of accuracy were used for solving problems of aquatic ecology and modeling spatial distribution of polluting nutrients, which caused growth of phytoplankton, many species of which are toxic and harmful. The use of schemes of the high order of accuracy are improved the quality of input data and decreased the error in solutions of model tasks of aquatic ecology. Numerical experiments were conducted for the problem of transportation of substances on the basis of the schemes of the second and fourth orders of accuracy. They’re showed that the accuracy was increased in 48.7 times for diffusion-convection problem. The mathematical algorithm was proposed and numerically implemented, which designed to restore the bottom topography of shallow water on the basis of hydrographic data (water depth at individual points or contour level). The map of bottom relief of the Azov Sea was generated with using this algorithm. It’s used to build fields of currents calculated on the basis of hydrodynamic model. The fields of water flow currents were used as input data of the aquatic ecology models. The library of double-layered iterative methods was developed for solving of nine-diagonal difference equations. It occurs in discretization of model tasks of challenges of pollutants concentration, plankton and fish on multiprocessor computer system. It improved the precision of the calculated data and gave the possibility to obtain operational forecasts of changes in ecologic situation of shallow water in short time intervals.

Study of work of heating equipment is an actual issue because it allows determining optimal regimes to reach highest efficiency. At that it is very helpful to use computer simulation to predict how different heating modes influence the effectiveness of the heating process and wear of heating equipment. Computer simulation provides results whose accuracy is proven by many studies and requires costs and time less than real experiments. In terms of present research, computer simulation of heating of air tuyere of blast furnace was realized with the help of FEM software. Background studies revealed possibility to simulate it as a flat, axisymmetric problem and DEFORM-2D software was used for simulation. Geometry, necessary for simulation, was designed with the help of SolidWorks, saved in .dxf format. Then it was exported to DEFORM-2D pre-processor and positioned. Preliminary and boundary conditions were set up. Several modes of operating regimes were under analysis. In order to demonstrate influence of eah of the modes and for better visualization point tracking option of the DEFORM-2D post-processor was applied. Influence of thermal insulation box plugged into blow channel, with and without air gap, and thermal coating on air tuyere’s temperature field was investigated. Simulation data demonstrated significant effect of thermal insulation box on air tuyere’s temperature field. Designed model allowed to simulate tuyere’s burnout as a result of interaction with liquid iron. Conducted researches have demonstrated DEFORM-2D effectiveness while using it for simulation of heat transfer and heating processes. DEFORM-2D is about to be used in further studies dedicated to more complex process connected with temperature field of blast furnace’s air tuyere.

One of problems in developing the gas condensate fields lies on the fact that the condensed hydrocarbons in the gas-bearing layer can get stuck in the pores of the formation and hence cannot be extracted. In this regard, research is underway to increase the recoverability of hydrocarbons in such fields. This research includes a wide range of studies on mathematical simulations of the passage of gas condensate mixtures through a porous medium under various conditions.

In the present work, within the classical approach based on the Darcy law and the law of continuity of flows, we formulate an initial-boundary value problem for a system of nonlinear differential equations that describes a depletion of a multicomponent gas-condensate mixture in porous reservoir. A computational scheme is developed on the basis of the finite-difference approximation and the fourth order Runge .Kutta method. The scheme can be used for simulations both in the spatially one-dimensional case, corresponding to the conditions of the laboratory experiment, and in the two-dimensional case, when it comes to modeling a flat gas-bearing formation with circular symmetry.

The computer implementation is based on the combination of C++ and Maple tools, using the MPI parallel programming technique to speed up the calculations. The calculations were performed on the HybriLIT cluster of the Multifunctional Information and Computing Complex of the Laboratory of Information Technologies of the Joint Institute for Nuclear Research.

Numerical results are compared with the experimental data on the pressure dependence of output of a ninecomponent hydrocarbon mixture obtained at a laboratory facility (VNIIGAZ, Ukhta). The calculations were performed for two types of porous filler in the laboratory model of the formation: terrigenous filler at 25 .„R and carbonate one at 60 .„R. It is shown that the approach developed ensures an agreement of the numerical results with experimental data. By fitting of numerical results to experimental data on the depletion of the laboratory reservoir, we obtained the values of the parameters that determine the inter-phase transition coefficient for the simulated system. Using the same parameters, a computer simulation of the depletion of a thin gas-bearing layer in the circular symmetry approximation was carried out.

The numerical methods developed by the author recently for calculating the molecular system based on the direct solution of the Schrodinger equation by the Monte Carlo method have shown a huge uncertainty in the choice of solutions. On the one hand, it turned out to be possible to build many new solutions; on the other hand, the problem of their connection with reality has become sharply aggravated. In ab initio quantum mechanical calculations, the problem of choosing solutions is not so acute after the transition to the classical format of describing a molecular system in terms of potential energy, the method of molecular dynamics, etc. In this paper, we investigate the problem of choosing solutions in the classical format of describing a molecular system without taking into account quantum mechanical prerequisites. As it turned out, the problem of choosing solutions in the classical format of describing a molecular system is reduced to a specific marking of the configuration space in the form of a set of stationary points and reconstruction of the corresponding potential energy function. In this formulation, the solution of the choice problem is reduced to two possible physical and mathematical problems: to find all its stationary points for a given potential energy function (the direct problem of the choice problem), to reconstruct the potential energy function for a given set of stationary points (the inverse problem of the choice problem). In this paper, using a computational experiment, the direct problem of the choice problem is discussed using the example of a description of a monoatomic cluster. The number and shape of the locally equilibrium (saddle) configurations of the binary potential are numerically estimated. An appropriate measure is introduced to distinguish configurations in space. The format of constructing the entire chain of multiparticle contributions to the potential energy function is proposed: binary, threeparticle, etc., multiparticle potential of maximum partiality. An infinite number of locally equilibrium (saddle) configurations for the maximum multiparticle potential is discussed and illustrated. A method of variation of the number of stationary points by combining multiparticle contributions to the potential energy function is proposed. The results of the work listed above are aimed at reducing the huge arbitrariness of the choice of the form of potential that is currently taking place. Reducing the arbitrariness of choice is expressed in the fact that the available knowledge about the set of a very specific set of stationary points is consistent with the corresponding form of the potential energy function.

Analysis of regional economic indicators plays a crucial role in management and development planning, with Gross Regional Product (GRP) serving as one of the key indicators of economic activity. The application of artificial intelligence, including neural network technologies, enables significant improvements in the accuracy and reliability of forecasts of economic processes. This study compares three neural network algorithm models for predicting the GRP of a typical region of the Russian Federation — the Udmurt Republic — based on time series data from 2000 to 2023. The selected models include a neural network with the Bat Algorithm (BA-LSTM), a neural network model based on backpropagation error optimized with a Genetic Algorithm (GA-BPNN), and a neural network model of Elman optimized using the Particle Swarm Optimization algorithm (PSO-Elman). The research involved stages of neural network modeling such as data preprocessing, training model, and comparative analysis based on accuracy and forecast quality metrics. This approach allows for evaluating the advantages and limitations of each model in the context of GRP forecasting, as well as identifying the most promising directions for further research. The utilization of modern neural network methods opens new opportunities for automating regional economic analysis and improving the quality of forecast assessments, which is especially relevant when data are limited and for rapid decision-making. The study uses factors such as the amount of production capital, the average annual number of labor resources, the share of high-tech and knowledge-intensive industries in GRP, and an inflation indicator as input data for predicting GRP. The high accuracy of the predictions achieved by including these factors in the neural network models confirms the strong correlation between these factors and GRP. The results demonstrate the exceptional accuracy of the BA-LSTM neural network model on validation data: the coefficient of determination was 0.82, and the mean absolute percentage error was 4.19%. The high performance and reliability of this model confirm its capacity to predict effectively the dynamics of the GRP. During the forecast period up to 2030, the Udmurt Republic is expected to experience an annual increase in Gross Regional Product (GRP) of +4.6% in current prices or +2.5% in comparable 2023 prices. By 2030, the GRP is projected to reach 1264.5 billion rubles.

One of the important direction of cloud technologies development nowadays is a creation of methods for integration of various cloud infrastructures. An actuality of such direction in academic field is caused by a frequent lack of own computing resources and a necessity to attract additional ones. This article is dedicated to existing approaches to cloud infrastructures integration with each other: federations and so called ‘cloud bursting’. A ‘federation’ in terms of OpenNebula cloud platform is built on a ‘one master zone and several slave ones’ schema. A term ‘zone’ means a separate cloud infrastructure in the federation. All zones in such kind of integration have a common database of users and the whole federation is managed via master zone only. Such approach is most suitable for a case when cloud infrastructures of geographically distributed branches of a single organization need to be integrated. But due to its high centralization it's not appropriate when one needs to join cloud infrastructures of different organizations. Moreover it's not acceptable at all in case of clouds based on different software platforms. A model of federative integration implemented in EGI Federated Cloud allows to connect clouds based on different software platforms but it requires a deployment of sufficient amount of additional services which are specific for EGI Federated Cloud only. It makes such approach is one-purpose and uncommon one. A ‘cloud bursting’ model has no limitations listed above but in case of OpenNebula platform what the Laboratory of Information Technologies of Joint Institute for Nuclear Research (LIT JINR) cloud infrastructure is based on such model was implemented for an integration with a certain set of commercial cloud resources providers. Taking into account an article authors’ experience in joining clouds of organizations they represent as well as with EGI Federation Cloud a ‘cloud bursting’ driver was developed by LIT JINR cloud team for OpenNebula-based clouds integration with each other as well as with OpenStack-based ones. The driver's architecture, technologies and protocols it relies on and an experience of its usage are described in the article.

This paper is devoted to some variants of improving the convergence rate guarantees of the gradient-type algorithms for relatively smooth and relatively Lipschitz-continuous problems in the case of additional information about some analogues of the strong convexity of the objective function. We consider two classes of problems, namely, convex problems with a relative functional growth condition, and problems (generally, non-convex) with an analogue of the Polyak – Lojasiewicz gradient dominance condition with respect to Bregman divergence. For the first type of problems, we propose two restart schemes for the gradient type methods and justify theoretical estimates of the convergence of two algorithms with adaptively chosen parameters corresponding to the relative smoothness or Lipschitz property of the objective function. The first of these algorithms is simpler in terms of the stopping criterion from the iteration, but for this algorithm, the near-optimal computational guarantees are justified only on the class of relatively Lipschitz-continuous problems. The restart procedure of another algorithm, in its turn, allowed us to obtain more universal theoretical results. We proved a near-optimal estimate of the complexity on the class of convex relatively Lipschitz continuous problems with a functional growth condition. We also obtained linear convergence rate guarantees on the class of relatively smooth problems with a functional growth condition. For a class of problems with an analogue of the gradient dominance condition with respect to the Bregman divergence, estimates of the quality of the output solution were obtained using adaptively selected parameters. We also present the results of some computational experiments illustrating the performance of the methods for the second approach at the conclusion of the paper. As examples, we considered a linear inverse Poisson problem (minimizing the Kullback – Leibler divergence), its regularized version which allows guaranteeing a relative strong convexity of the objective function, as well as an example of a relatively smooth and relatively strongly convex problem. In particular, calculations show that a relatively strongly convex function may not satisfy the relative variant of the gradient dominance condition.