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The polypolar system of coordinates is formed by a family of a parametrized on a radius isofocal of kf-lemniscates. As well as the classical polar system of coordinates, it characterizes a point of a plane by a polypolar radius ρ and polypolar angle φ. For anyone connectedness a family isometric of curve ρ = const – lemniscates and family gradient of curves φ = const – are mutually orthogonal conjugate coordinate families. The singularities of polypolar coordination, its symmetry, and also curvilinear symmetries on multifocal lemniscates are considered.

A new grid and cloud services simulation for NICA accelerator complex data storage and processing system are described. This system is focused on improving the efficiency of the grid-cloud systems development by using work quality indicators of some real system to design and predict its evolution. For these purpose the simulation program are combined with real monitoring system of the grid-cloud service through a special database. An example of the program usage to simulate a sufficiently general cloud structure, which can be used for more common purposes, is given.

In the field of naval architecture the most competent recommendations in verification and validation of the numerical methods were developed within an international workshop on the numerical prediction of ship viscous flow which is held every five years in Gothenburg (Sweden) and Tokyo (Japan) alternately. In the workshop “Gothenburg–2000” three modern hull forms with reliable experimental data were introduced as test cases. The most general case among them is a containership KCS, a ship of moderate specific speed and fullness. The paper focuses on a numerical research of KCS hull flow, which was made according to the formal procedures of the workshop with the help of CEA FlowVision. Findings were compared with experimental data and computational data of other key CEA.

Comets and asteroids are recognized by the scientists and the governments of all countries in the world to be one of the most significant threats to the development and even the existence of our civilization. Preventing this threat includes studying the motion of large meteors through the atmosphere that is accompanied by various physical and chemical phenomena. Of particular interest to such studies are the meteors whose trajectories have been recorded and whose fragments have been found on Earth. Here, we study one of such cases. We develop a model for the motion and destruction of natural bodies in the Earth’s atmosphere, focusing on the Benešov bolid (EN070591), a bright meteor registered in 1991 in the Czech Republic by the European Observation System. Unique data, that includes the radiation spectra, is available for this bolid. We simulate the aeroballistics of the Benešov meteoroid and of its fragments, taking into account destruction due to thermal and mechanical processes. We compute the velocity of the meteoroid and its mass ablation using the equations of the classical theory of meteor motion, taking into account the variability of the mass ablation along the trajectory. The fragmentation of the meteoroid is considered using the model of sequential splitting and the statistical stress theory, that takes into account the dependency of the mechanical strength on the length scale. We compute air flows around a system of bodies (shards of the meteoroid) in the regime where mutual interplay between them is essential. To that end, we develop a method of simulating air flows based on a set of grids that allows us to consider fragments of various shapes, sizes, and masses, as well as arbitrary positions of the fragments relative to each other. Due to inaccuracies in the early simulations of the motion of this bolid, its fragments could not be located for about 23 years. Later and more accurate simulations have allowed researchers to locate four of its fragments rather far from the location expected earlier. Our simulations of the motion and destruction of the Benešov bolid show that its interaction with the atmosphere is affected by multiple factors, such as the mass and the mechanical strength of the bolid, the parameters of its motion, the mechanisms of destruction, and the interplay between its fragments.

Scheduling computational workflows represented by directed acyclic graphs (DAGs) is crucial in many areas of computer science, such as cloud/edge tasks with distributed workloads and data mining. The complexity of online DAG scheduling is compounded by the large number of computational nodes, data transfer delays, heterogeneity (by type and processing power) of executors, precedence constraints imposed by DAG, and the nonuniform arrival of tasks. This paper introduces the Multi-Agent Local Voting Protocol (MLVP), a novel approach focused on dynamic load balancing for DAG scheduling in heterogeneous computing environments, where executors are represented as agents. The MLVP employs a local voting protocol to achieve effective load distribution by formulating the problem as a differentiated consensus achievement. The algorithm calculates an aggregated DAG metric for each executor-node pair based on node dependencies, node availability, and executor performance. The balance of these metrics as a weighted sum is optimized using a genetic algorithm to assign tasks probabilistically, achieving efficient workload distribution via information sharing and reaching consensus among the executors across the system and thus improving makespan. The effectiveness of the MLVP is demonstrated through comparisons with the state-of-the-art DAG scheduling algorithm and popular heuristics such as DONF, FIFO, Min- Min, and Max-Min. Numerical simulations show that MLVP achieves makepsan improvements of up to 70% on specific graph topologies and an average makespan reduction of 23.99% over DONF (state-of-the-art DAG scheduling heuristic) across randomly generated diverse set of DAGs. Notably, the algorithm’s scalability is evidenced by enhanced performance with increasing numbers of executors and graph nodes.

The article presents updated technologies for solving two classes of linear resource allocation problems with dynamically changing characteristics of situational management systems and awareness of experts (and/or trained robots). The search for solutions is carried out in an interactive mode of computational experiment using updatable knowledge systems about problems considered as constructive objects (in accordance with the methodology of formalization of knowledge about programmable problems created in the theory of S-symbols). The technologies are focused on implementation in the form of Internet services. The first class includes resource allocation problems solved by the method of targeted solution movement. The second is the problems of allocating a single resource in hierarchical systems, taking into account the priorities of expense items, which can be solved (depending on the specified mandatory and orienting requirements for the solution) either by the interval method of allocation (with input data and result represented by numerical segments), or by the targeted solution movement method. The problem statements are determined by requirements for solutions and specifications of their applicability, which are set by an expert based on the results of the portraits of the target and achieved situations analysis. Unlike well-known methods for solving resource allocation problems as linear programming problems, the method of targeted solution movement is insensitive to small data changes and allows to find feasible solutions when the constraint system is incompatible. In single-resource allocation technologies, the segmented representation of data and results allows a more adequate (compared to a point representation) reflection of the state of system resource space and increases the practical applicability of solutions. The technologies discussed in the article are programmatically implemented and used to solve the problems of resource basement for decisions, budget design taking into account the priorities of expense items, etc. The technology of allocating a single resource is implemented in the form of an existing online cost planning service. The methodological consistency of the technologies is confirmed by the results of comparison with known technologies for solving the problems under consideration.

The work is dedicated to the use of the software package Turbulence Problem Solver (TPS) for numerical simulation of a wide range of laser problems. The capabilities of the package are demonstrated by the example of numerical simulation of the interaction of femtosecond laser pulses with thin metal bonds. The software package TPS developed by the authors is intended for numerical solution of hyperbolic systems of differential equations on multiprocessor computing systems with distributed memory. The package is a modern and expandable software product. The architecture of the package gives the researcher the opportunity to model different physical processes in a uniform way, using different numerical methods and program blocks containing specific initial conditions, boundary conditions and source terms for each problem. The package provides the the opportunity to expand the functionality of the package by adding new classes of problems, computational methods, initial and boundary conditions, as well as equations of state of matter. The numerical methods implemented in the software package were tested on test problems in one-dimensional, two-dimensional and three-dimensional geometry, which included Riemann's problems on the decay of an arbitrary discontinuity with different configurations of the exact solution.

Thin films on substrates are an important class of targets for nanomodification of surfaces in plasmonics or sensor applications. Many articles are devoted to this subject. Most of them, however, focus on the dynamics of the film itself, paying little attention to the substrate, considering it simply as an object that absorbs the first compression wave and does not affect the surface structures that arise as a result of irradiation. The paper describes in detail a computational experiment on the numerical simulation of the interaction of a single ultrashort laser pulse with a gold film deposited on a thick glass substrate. The uniform rectangular grid and the first-order Godunov numerical method were used. The presented results of calculations allowed to confirm the theory of the shock-wave mechanism of holes formation in the metal under femtosecond laser action for the case of a thin gold film with a thickness of about 50 nm on a thick glass substrate.

Traditional methods for solving the traveling salesman problem are not effective for high-dimensional problems due to their high computational complexity. One of the most effective ways to solve this problem is the decomposition approach, which includes three main stages: clustering vertices, solving subproblems within each cluster and then merging the obtained solutions into a final solution. This article focuses on the third stage — merging cycles of solving subproblems — since this stage is not always given sufficient attention, which leads to less accurate final solutions of the problem. The paper proposes a new modified Sigal algorithm for merging cycles. To evaluate its effectiveness, it is compared with two algorithms for merging cycles — the method of connecting midpoints of edges and an algorithm based on closeness of cluster centroids. The dependence of quality of solving subproblems on algorithms used for merging cycles is investigated. Sigal’s modified algorithm performs pairwise clustering and minimizes total distance. The centroid method focuses on connecting clusters based on closeness of centroids, and an algorithm using mid-points estimates the distance between mid-points of edges. Two types of clustering — k-means and affinity propagation — were also considered. Numerical experiments were performed using the TSPLIB dataset with different numbers of cities and topologies to test effectiveness of proposed algorithm. The study analyzes errors caused by the order in which clusters were merged, the quality of solving subtasks and number of clusters. Experiments show that the modified Sigal algorithm has the smallest median final distance and the most stable results compared to other methods. Results indicate that the quality of the final solution obtained using the modified Sigal algorithm is more stable depending on the sequence of merging clusters. Improving the quality of solving subproblems usually results in linear improvement of the final solution, but the pooling algorithm rarely affects the degree of this improvement.