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This paper presents a universal method for constructing an agent-based model of complex systems for their further clear computer representation by means of object-oriented programming languages. The method specifies both steps of model developing from the mathematical description of the system to the determined architecture of the program simulating the system. The efficiency of the method is illustrated by the construction of the two simulation models for the complex systems of various origins: the interactive simulation of the stock exchange and space-time simulation of biological species competition.

We consider a model of stacked long Josephson junctions (LJJ), which consists of alternating superconducting and dielectric layers. The model takes into account the inductive and capacitive coupling between the neighbor junctions. The model is described by a system of nonlinear partial differential equations with respect to the phase differences and the voltage of LJJ, with appropriate initial and boundary conditions. The numerical solution of this system of equations is based on the use of standard three-point finite-difference formulae for discrete approximations in the space coordinate, and the applying the four-step Runge-Kutta method for solving the Cauchy problem obtained. Designed parallel algorithm is implemented by means of the MPI technology (Message Passing Interface). In the paper, the mathematical formulation of the problem is given, numerical scheme and a method of calculation of the current-voltage characteristics of the LJJ system are described. Two variants of parallel implementation are presented. The influence of inductive and capacitive coupling between junctions on the structure of the current-voltage characteristics is demonstrated. The results of methodical calculations with various parameters of length and number of Josephson junctions in the LJJ stack depending on the number of parallel computing nodes, are presented. The calculations have been performed on multiprocessor clusters HybriLIT and CICC of Multi-Functional Information and Computing Complex (Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna). The numerical results are discussed from the viewpoint of the effectiveness of presented approaches of the LJJ system numerical simulation in parallel. It has been shown that one of parallel algorithms provides the 9 times speedup of calculations.

We develop the software tool for integration of dynamics models, which are inhomogeneous over mathematical properties and/or over requirements to the time step. The family of algorithms for the parallel computation of heterogeneous models with different time steps is offered. Analytical estimates and direct measurements of the error of these algorithms are made with reference to weakly coupled ODE sets. The advantage of the algorithms in the time cost as compared to accurate methods is shown.

The generalization of Margolus’s block cellular automaton on a hexagonal grid is formulated. Statistical analysis of the results of probabilistic cellular automation for vast variety of this scheme solving the test task of diffusion is done. It is shown that the choice of the hexagon blocks is 25% more efficient than Y-blocks. It is shown that the algorithms have polynomial complexity, and the polynom degree lies within 0.6÷0.8 for parallel computer, and in the range 1.5÷1.7 for serial computer. The effects of embedded into automaton’s field defective cells on the rate of convergence are studied also.

The work submits new release of the FlowVision software designed for automation of engineering calculations in computational fluid dynamics: FlowVision 3.09.05. The FlowVision software is used for solving different industrial problems. Its popularity is based on the capability to solve complex non-tradition problems involving different physical processes. The paradigm of complete automation of labor-intensive and time-taking processes like grid generation makes FlowVision attractive for many engineers. FlowVision is completely developer-independent software. It includes an advanced graphical interface, the system for specifying a computational project as well as the system for flow visualization on planes, on curvilinear surfaces and in volume by means of different methods: plots, color contours, iso-lines, iso-surfaces, vector fields. Besides that, FlowVision provides tools for calculation of integral characteristics on surfaces and in volumetric regions.

The software is based on the finite-volume approach to approximation of the partial differential equations describing fluid motion and accompanying physical processes. It provides explicit and implicit methods for time integration of these equations. The software includes automated generator of unstructured grid with capability of its local dynamic adaptation. The solver involves two-level parallelism which allows calculations on computers with distributed and shared memory (coexisting in the same hardware). FlowVision incorporates a wide spectrum of physical models: different turbulence models, models for mass transfer accounting for chemical reactions and radioactive decay, several combustion models, a dispersed phase model, an electro-hydrodynamic model, an original VOF model for tracking moving interfaces. It should be noted that turbulence can be simulated within URANS, LES, and ILES approaches. FlowVision simulates fluid motion with velocities corresponding to all possible flow regimes: from incompressible to hypersonic. This is achieved by using an original all-speed velocity-pressure split algorithm for integration of the Navier-Stokes equations.

FlowVision enables solving multi-physic problems with use of different modeling tools. For instance, one can simulate multi-phase flows with use of the VOF method, flows past bodies moving across a stationary grid (within Euler approach), flows in rotary machines with use of the technology of sliding grid. Besides that, the software solves fluid-structure interaction problems using the technology of two-way coupling of FlowVision with finite-element codes. Two examples of solving challenging problems in the FlowVision software are demonstrated in the given article. The first one is splashdown of a spacecraft after deceleration by means of jet engines. This problem is characterized by presence of moving bodies and contact surface between the air and the water in the computational domain. The supersonic jets interact with the air-water interphase. The second problem is simulation of the work of a human heart with artificial and natural valves designed on the basis of tomographic investigations with use of a finite-element model of the heart. This problem is characterized by two-way coupling between the “liquid” computational domain and the finite-element model of the hart muscles.

At present modern quantum technologies can get a new twist of development, which will certainly give an opportunity to obtain solutions for numerous problems that previously could not be solved in the framework of “traditional” paradigms and computational models. All mankind stands at the threshold of the so-called “second quantum revolution”, and its short-term and long-term consequences will affect virtually all spheres of life of a global society. Such directions and branches of science and technology as materials science, nanotechnology, pharmacology and biochemistry in general, modeling of chaotic dynamic processes (nuclear explosions, turbulent flows, weather and long-term climatic phenomena), etc. will be directly developed, as well as the solution of any problems, which reduce to the multiplication of matrices of large dimensions (in particular, the modeling of quantum systems). However, along with extraordinary opportunities, quantum technologies carry with them certain risks and threats, in particular, the scrapping of all information systems based on modern achievements in cryptography, which will entail almost complete destruction of secrecy, the global financial crisis due to the destruction of the banking sector and compromise of all communication channels. Even in spite of the fact that methods of so-called “post-quantum” cryptography are already being developed today, some risks still need to be realized, since not all long-term consequences can be calculated. At the same time, one should be prepared to all of the above, including by training specialists working in the field of quantum technologies and understanding all their aspects, new opportunities, risks and threats. In this connection, this article briefly describes the current state of quantum technologies, namely, quantum sensorics, information transfer using quantum protocols, a universal quantum computer (hardware), and quantum computations based on quantum algorithms (software). For all of the above, forecasts are given for the development of the impact on various areas of human civilization.

The study of the physiological and pathophysiological processes in the cardiovascular system is one of the important contemporary issues, which is addressed in many works. In this work, several approaches to the mathematical modelling of the blood flow are considered. They are based on the spatial order reduction and/or use a steady-state approach. Attention is paid to the discussion of the assumptions and suggestions, which are limiting the scope of such models. Some typical mathematical formulations are considered together with the brief review of their numerical implementation. In the first part, we discuss the models, which are based on the full spatial order reduction and/or use a steady-state approach. One of the most popular approaches exploits the analogy between the flow of the viscous fluid in the elastic tubes and the current in the electrical circuit. Such models can be used as an individual tool. They also used for the formulation of the boundary conditions in the models using one dimensional (1D) and three dimensional (3D) spatial coordinates. The use of the dynamical compartment models allows describing haemodynamics over an extended period (by order of tens of cardiac cycles and more). Then, the steady-state models are considered. They may use either total spatial reduction or two dimensional (2D) spatial coordinates. This approach is used for simulation the blood flow in the region of microcirculation. In the second part, we discuss the models, which are based on the spatial order reduction to the 1D coordinate. The models of this type require relatively small computational power relative to the 3D models. Within the scope of this approach, it is also possible to include all large vessels of the organism. The 1D models allow simulation of the haemodynamic parameters in every vessel, which is included in the model network. The structure and the parameters of such a network can be set according to the literature data. It also exists methods of medical data segmentation. The 1D models may be derived from the 3D Navier – Stokes equations either by asymptotic analysis or by integrating them over a volume. The major assumptions are symmetric flow and constant shape of the velocity profile over a cross-section. These assumptions are somewhat restrictive and arguable. Some of the current works paying attention to the 1D model’s validation, to the comparing different 1D models and the comparing 1D models with clinical data. The obtained results reveal acceptable accuracy. It allows concluding, that the 1D approach can be used in medical applications. 1D models allow describing several dynamical processes, such as pulse wave propagation, Korotkov’s tones. Some physiological conditions may be included in the 1D models: gravity force, muscles contraction force, regulation and autoregulation.

The paper contains the analysis of the domestic publications issued in 2013–2017 years and devoted to cellular automata. The most of them concern on mathematical modeling. Scientometric schedules for 1990–2017 years have proved relevance of subject. The review allows to allocate the main personalities and the scientific directions/schools in modern Russian science, to reveal their originality or secondness in comparison with world science. Due to the authors choice of national publications basis instead of world, the paper claims the completeness and the fact is that about 200 items from the checked 526 references have an importance for science.

In the Annex to the review provides preliminary information about CA — the Game of Life, a theorem about gardens of Eden, elementary CAs (together with the diagram of de Brujin), block Margolus’s CAs, alternating CAs. Attention is paid to three important for modeling semantic traditions of von Neumann, Zuse and Zetlin, as well as to the relationship with the concepts of neural networks and Petri nets. It is allocated conditional 10 works, which should be familiar to any specialist in CA. Some important works of the 1990s and later are listed in the Introduction.

Then the crowd of publications is divided into categories: the modification of the CA and other network models (29 %), Mathematical properties of the CA and the connection with mathematics (5 %), Hardware implementation (3 %), Software implementation (5 %), Data Processing, recognition and Cryptography (8 %), Mechanics, physics and chemistry (20 %), Biology, ecology and medicine (15 %), Economics, urban studies and sociology (15 %). In parentheses the share of subjects in the array are indicated. There is an increase in publications on CA in the humanitarian sphere, as well as the emergence of hybrid approaches, leading away from the classic CA definition.

In various applications arise problems modeled by nonlinear partial differential equations on graphs (networks, trees). In order to study such problems and various extreme situations arose in the problems of designing and optimizing networks developed the computational model based on solving the corresponding boundary problems for partial differential equations of hyperbolic type on graphs (networks, trees). As applications, three different problems were chosen solved in the framework of the general approach of network computational models. The first was modeling of traffic flow. In solving this problem, a macroscopic approach was used in which the transport flow is described by a nonlinear system of second-order hyperbolic equations. The results of numerical simulations showed that the model developed as part of the proposed approach well reproduces the real situation various sections of the Moscow transport network on significant time intervals and can also be used to select the most optimal traffic management strategy in the city. The second was modeling of data flows in computer networks. In this problem data flows of various connections in packet data network were simulated as some continuous medium flows. Conceptual and mathematical network models are proposed. The numerical simulation was carried out in comparison with the NS-2 network simulation system. The results showed that in comparison with the NS-2 packet model the developed streaming model demonstrates significant savings in computing resources while ensuring a good level of similarity and allows us to simulate the behavior of complex globally distributed IP networks. The third was simulation of the distribution of gas impurities in ventilation networks. It was developed the computational mathematical model for the propagation of finely dispersed or gas impurities in ventilation networks using the gas dynamics equations by numerical linking of regions of different sizes. The calculations shown that the model with good accuracy allows to determine the distribution of gas-dynamic parameters in the pipeline network and solve the problems of dynamic ventilation management.