Institute of Mathematical Machines and Systems Problems

The article is devoted to the study of international approaches to assessing the reliability of cluster computing systems and their combination with modern domestic methodologies. Cluster systems are widely used in fundamental and applied research, numerical modeling of complex physical processes, climate forecasting, analysis of large volumes of data, the aerospace and automotive industries, energy, cloud computing, and other areas. Therefore, assessing the relia-bility of cluster computing systems is critically important for ensuring their continuous opera-tion and resistance to failures under conditions of intensive load. A comprehensive assessment of the reliability of cluster systems consists of the following stages: analysis of system structure components, calculation of reliability metrics, modeling of failure scenarios, analysis of com-bined failure probabilities, and assessment of redundancy. It has been determined that, in gen-eral, cluster systems have a so-called «k» with «n» structure, therefore, reliability metrics are calculated according to the corresponding domestic methodologies. In the general case, failures of cluster computing systems are non-monotonic in nature. Consequently, to calculate the prob-ability of a failure-free operation, modern domestic methodologies based on the DN-distribution of failures can be used. Assessment of the reliability of cluster computing systems is a multi-level approach that combines analytical, experimental, and model research methods. Such a comprehensive approach allows the identification of potential bottlenecks in the system architecture, identify critical components, and assess the risks of failures. This enables timely implementation of effective mechanisms for fault tolerance, redundancy, and automatic recov-ery.

This chapter first reviews existing parallel and distributed processing models and technologies for comparison with the chosen Spatial Grasp Technology (SGT) for this book which is based on distributed and parallel processing, management, and control too. It then describes the general features of SGT and its basic Spatial Grasp Language (SGL) with its top summary, main components, and control states. It explains how SGL scenarios evolve and provides details of the networked language implementation, as well as components of the distributed SGL interpreter.

<strong class="journal-contentHeaderColor">Abstract.</strong> A gravitational sinking of the particulate organic matter (POM) is a key mechanism of vertical transport of carbon in the deep ocean and its subsequent sequestration. The size spectrum of these particles is formed in the euphotic layer by the primary production and various mechanisms including food web consumption. The mass of particles, as they descend, changed under aggregation, fragmentation, bacterial decomposition which depends on the water temperature and oxygen concentration, particle sinking velocity, age of the organic particles, ballasting and other factors. In this paper, we developed simple Eulerian-Lagrangian approach to solve equations for sinking particulate matter when the influence of the size and age of particles, temperature and oxygen concentration on their dynamics and degradation processes were taken into account. The model considers feedback between degradation rate and particle sinking velocity. We rely on the known parameterizations, but our Eulerian-Lagrangian approach to solving the problem differs, allowing the algorithm to be incorporated into biogeochemical global ocean models with relative ease. Two novel analytical solutions of a system of the one-dimensional Eulerian equation for POM concentration and Lagrangian equations for particle mass and position were obtained for constant and age-dependent degradation rates. At a constant rate of particle sinking, they correspond to exponential and power-law profiles of the POM concentration. It was found that feedback between degradation rate and sinking velocity results to a significant change in POM and POM flux vertical profiles. The calculations are compared with the available measurement data for POM and POM flux for the latitude band of 20&ndash;30&deg; N in the Atlantic and Pacific Oceans and 50&ndash;60&deg; S in the Southern Ocean. The dependence of the degradation rate on temperature significantly affected the profiles of POM concentration enhancing the degradation of sinking particles in the ocean&rsquo;s upper layer and suppressing it in the deep layer of the ocean. The influence of oxygen concentration in all cases considered was insignificant compared to the distribution of temperature with depth.

The Arctic Ocean and the North Pacific are the main reservoirs of anthropogenic radionuclides introduced in the past 80 years. The Lagrangian particle tracking approach was applied to the Arctic oceans to study the pathways of 137Cs contamination from point sources representing the locations of solid radioactive waste in the bays of the Novaya Zemlya archipelago and in the Kara Sea. The model includes radioactive decay and the interaction of dissolved radionuclides with suspended and bottom sediments. Lagrangian model uses accurate approach for simulating the absorption-desorption processes and novel algorithm for the bottom boundary conditions. As input for the model, the 3D hydrodynamic fields from NEMO model simulation with 10 km horizontal resolution and 121 vertical layers were used. 3D velocity fields along with vertical velocity and vertical turbulent mixing coefficient were used from NEMO simulation for 38 years from 1980 to 2018. Suspended sediment concentration fields were reconstructed using the 1D SEDTRANS05 sediment transport model in each grid node.A set of potential scenarios of radioactive release were considered to analyse the most probable pathways of contamination. In each simulation, 1M of particles was used and individual trajectories were stored. The maps of visitation probability were built to show pathways of radioactivity contamination in the Arctic Ocean from the selected sources.

We compared circulations under the Filchner-Ronne Ice Shelf (FRIS) and the Ross Ice Shelf (RIS) using output from the Whole Antarctica Ocean Model driven by repeated year atmospheric forcing and processed by the particle-tracking Parcels model. Three Lagrangian characteristics were calculated: the visitation frequency, the mean age, and the representative particle trajectory. In both FRIS and RIS, the High Salinity Shelf Water (HSSW) entered through depressions off the western coast of ice shelves. We found that HSSW transformed into the Ice Shelf Water that departed both ice shelves at central ice front locations (approximately 58-57°W in Ronne Ice Shelf and 175°W in RIS). The outflow through the Ronne Ice Front we identified has not attracted attention until now, although it has been observed. Almost half of the particles departed FRIS through the Ronne Ice Front, whereas about 20% stayed under FRIS. The rest of the particles flow out through the Filchner Trough. In contrast, only 2% of the particles stayed under RIS. The mean age of water leaving FRIS through the Ronne Ice Front and the water leaving RIS was 7–8 years, whereas the water leaving FRIS through the Filchner Trough was about 10 years.

The paper proposes a method for strategic planning of cybersecurity measures for critical infrastructure objects, developed on the basis of a formalized SWOT model that integrates qualitative analysis of strengths, weaknesses, opportunities, and threats with quantitative assessment of risks, costs, and the effectiveness of protective actions. Unlike the classical descriptive SWOT analysis, which lacks analytical consistency, the proposed approach involves constructing a mathematical model of strategic planning in which each factor is represented by a weighted set, and the relationships between internal and external factors are defined through a strategic influence matrix. An integrated risk coefficient is introduced, taking into account the probability of threat realization, the level of its impact on critical functions, and the residual vulnerability of the system. This enables a transition from qualitative expert assessment to an optimization problem of maximizing cybersecurity effectiveness under resource constraints. The mathematical model implements multicriteria optimization, where the objective function describes the difference between the expected efficiency of measures and the weighted cost of their implementation while maintaining the permissible level of residual risk. To select a rational set of actions, methods of fuzzy normalization of evaluations and Pareto optimization are applied, ensuring adaptive planning in a dynamic threat environment. Based on the model, an architecture of a cybersecurity situational center is developed, implementing functions of monitoring, protection level assessment, risk forecasting, and decision support at the strategic level. Modeling results demonstrated that the use of the formalized SWOT approach increases coherence between tactical and strategic decisions, reduces residual risk by 25–30%, and enhances the resilience of critical infrastructure operations. The proposed method can be integrated into decision-support systems of cybersecurity situational centers and serve as an analytical core of national cybersecurity platforms to strengthen the resilience and continuity of critical infrastructure.

Purpose of work is development of design method of robust combined electromagnetic silence including active and solid passive parts for improvement of silence effectiveness of Magnetic Field (MF) generated by Overhead Power Lines (OPL) inside old residential buildings and for reducing sensitivity to system parameters changes based on 3D modeling and geometric inverse magneto quasi-static problem solution. Combined silence includes double-circuit active and U-shaped solid passive part and MF level reducing efficiency increased. Combined silence design reduced to Geometric Inverse Magneto quasi–Static Problem (GIMGSP) solution based on Minimax Vector Optimization Problem (MMVOP) solution with Vector Objective Function (VOF) calculated based on 3D Maxwell equations solutions in quasi-stationary approximation by COMSOL Multiphysics ® software package used. MMVOP solution calculated based on Multiswarm Particle Optimization Algorithm (MSPOA) from Pareto-optimal solutions taking into account binary preference relations. Active silence system two compensation winding’s spatial location coordinates as well as windings currents magnitudes and phases calculated during combined silence design. U-shaped solid passive silence parameters also calculated. Modeling and experimental studies of designed combined system effectiveness MF silence generated by OPL inside old residential buildings carried out based on 3D modeling presented. Initial MF level possibility reduced to sanitary standards level shown.

The article is devoted to solving the problem of determining the resilience of critical infrastructure systems to malicious actions of adversaries. Different modeling methods and their integration are considered. Using the example of a system of systems, including energy and transport networks, the application of methods of agent, network, economic modeling and the method of system dynamics are considered, which are combined into a single structure of analysis for the development of algorithms for general decision-making support for the protection of critical infrastructure systems.

This work aims to conduct theoretical and experimental studies on the energy and force parameters of the separation process, as well as the geometric accuracy of the separated tubular workpiece using the "eccentric twisting" method. A mathematical model of a device with a "crank-circular" mechanism for cutting pipes by "eccentric twisting" has been developed. The technological process of cutting pipes by "eccentric twisting" was simulated using the DEFORM-3D software package. The results of experimental studies are in good agreement with the theoretical data calculated using the proposed mathematical model and the specialized program DEFORM-3D. The maximum differences between the cutting torque values obtained theoretically and experimentally do not exceed 6%. For the industrial implementation of research results, a design of an installation with a wedge-hinged drive with a concave wedge in combination with a "crank-circular" mechanism for separating pipes by the "eccentric torsion" scheme is proposed.