All issues

Numerical simulation of moving sportsman external flow is presented. The unique method is developed for obtaining integral aerodynamic characteristics, which were the function of the flow regime (i.e. angle of attack, flow speed) and body position. Individual anthropometric characteristics and moving boundaries of sportsman (or sports equipment) during the race are taken into consideration.

Numerical simulation is realized using FlowVision CFD. The software is based on the finite volume method, high-performance numerical methods and reliable mathematical models of physical processes. A Cartesian computational grid is used by FlowVision, the grid generation is a completely automated process. Local grid adaptation is used for solving high-pressure gradient and object complex shape. Flow simulation process performed by solutions systems of equations describing movement of fluid and/or gas in the computational domain, including: mass, moment and energy conservation equations; state equations; turbulence model equations. FlowVision permits flow simulation near moving bodies by means of computational domain transformation according to the athlete shape changes in the motion. Ski jumper aerodynamic characteristics are studied during all phases: take-off performance in motion, in-run and flight. Projected investigation defined simulation method, which includes: inverted statement of sportsman external flow development (velocity of the motion is equal to air flow velocity, object is immobile); changes boundary of the body technology defining; multiple calculations with the national team member data projecting. The research results are identification of the main factors affected to jumping performance: aerodynamic forces, rotating moments etc. Developed method was tested with active sportsmen. Ski jumpers used this method during preparations for Sochi Olympic Games 2014. A comparison of the predicted characteristics and experimental data shows a good agreement. Method versatility is underlined by performing swimmer and skater flow simulation. Designed technology is applicable for sorts of natural and technical objects.

Radiopharmaceuticals with iodine radioisotopes are now widely used in imaging and non-imaging methods of nuclear medicine. When evaluating the results of radionuclide studies of the structural and functional state of organs and tissues, parallel modeling of the kinetics of radiopharmaceuticals in the body plays an important role. The complexity of such modeling lies in two opposite aspects. On the one hand, excessive simplification of the anatomical and physiological characteristics of the organism when splitting it to the compartments that may result in the loss or distortion of important clinical diagnosis information, on the other – excessive, taking into account all possible interdependencies of the functioning of the organs and systems that, on the contrary, will lead to excess amount of absolutely useless for clinical interpretation of the data or the mathematical model becomes even more intractable. Our work develops a unified approach to the construction of mathematical models of the kinetics of radiopharmaceuticals with iodine isotopes in the human body during diagnostic and therapeutic procedures of nuclear medicine. Based on this approach, three- and four-compartment pharmacokinetic models were developed and corresponding calculation programs were created in the C⁺⁺ programming language for processing and evaluating the results of radionuclide diagnostics and therapy. Various methods for identifying model parameters based on quantitative data from radionuclide studies of the functional state of vital organs are proposed. The results of pharmacokinetic modeling for radionuclide diagnostics of the liver, kidney, and thyroid using iodine-containing radiopharmaceuticals are presented and analyzed. Using clinical and diagnostic data, individual pharmacokinetic parameters of transport of different radiopharmaceuticals in the body (transport constants, half-life periods, maximum activity in the organ and the time of its achievement) were determined. It is shown that the pharmacokinetic characteristics for each patient are strictly individual and cannot be described by averaged kinetic parameters. Within the framework of three pharmacokinetic models, “Activity–time” relationships were obtained and analyzed for different organs and tissues, including for tissues in which the activity of a radiopharmaceutical is impossible or difficult to measure by clinical methods. Also discussed are the features and the results of simulation and dosimetric planning of radioiodine therapy of the thyroid gland. It is shown that the values of absorbed radiation doses are very sensitive to the kinetic parameters of the compartment model. Therefore, special attention should be paid to obtaining accurate quantitative data from ultrasound and thyroid radiometry and identifying simulation parameters based on them. The work is based on the principles and methods of pharmacokinetics. For the numerical solution of systems of differential equations of the pharmacokinetic models we used Runge–Kutta methods and Rosenbrock method. The Hooke–Jeeves method was used to find the minimum of a function of several variables when identifying modeling parameters.

The model of the process of using machinery and equipment is considered, which takes into account the probabilistic nature of the process of their operation and sale. It takes into account the possibility of random hidden failures, after which the condition of the machine deteriorates abruptly, as well as the randomly arising need for premature (before the end of its service life) sale of the machine, which requires, generally speaking, random time. The model is focused on assessing the market value and service life of machines in accordance with International Valuation Standards. Strictly speaking, the market value of a used machine depends on its technical condition, but in practice, appraisers only take into account its age, since generally accepted measures of the technical condition of machines do not yet exist. As a result, the market value of a used machine is assumed to be equal to the average market value of similar machines of the corresponding age. For these purposes, appraisers use coefficients that reflect the influence of the age of machines on their market value. Such coefficients are not always justified and do not take into account either the degradation of the machine or the probabilistic nature of the process of its use. The proposed model is based on the anticipation of benefits principle. In it, we characterize the state of the machine by the intensity of the benefits it brings. The machine is subjected to a complex Poisson failure process, and after failure its condition abruptly worsens and may even reach its limit. Situations also arise that preclude further use of the machine by its owner. In such situations, the owner puts the machine up for sale before the end of its service life (prematurely), and the sale requires a random timing. The model allows us to take into account the influence of such situations and construct an analytical relationship linking the market value of a machine with its condition, and calculate the average coefficients of change in the market value of machines with age. At the same time, it is also possible to take into account the influence of inflation and the scrap cost of the machine. We have found that the rate of prematurely sales has a significant impact on the cost of new and used machines. The model also allows us to take into account the influence of inflation and the scrap value of the machine. We have found that the rate of premature sales has a significant impact on the service life and market value of new and used machines. At the same time, the dependence of the market value of machines on age is largely determined by the coefficient of variation of the service life of the machines. The results obtained allow us to obtain more reasonable estimates of the market value of machines, including for the purposes of the system of national accounts.

In this paper, we illustrates the ways to improve abilities of the computing environments by using virtualization, single system image (SSI) and hypervisor technologies’ collaboration for goal to improve computational abilities. Recently cloud computing as a new service concept has become popular to provide various services to user such as multi-media sharing, online office software, game and online storage. The cloud computing is bringing together multiple computers and servers in a single environment designed to address certain types of tasks, such as scientific problems or complex calculations. By using virtualization technologies, cloud computing environment is able to virtualize and share resources among different applications with the objective for better server utilization, better load balancing and effectiveness.

Modern power transportation systems are the complex engineering systems. Such systems include both point facilities (power producers, consumers, transformer substations, etc.) and the distributed elements (f.e. power lines). Such structures are presented in the form of the graphs with different types of nodes under creating the mathematical models. It is necessary to solve the system of partial differential equations of the hyperbolic type to study the dynamic effects in such systems.

An approach similar to one already applied in modeling similar problems earlier used in the work. New variant of the splitting method was used proposed by the authors. Unlike most known works, the splitting is not carried out according to physical processes (energy transport without dissipation, separately dissipative processes). We used splitting to the transport equations with the drain and the exchange between Reimann’s invariants. This splitting makes possible to construct the hybrid schemes for Riemann invariants with a high order of approximation and minimal dissipation error. An example of constructing such a hybrid differential scheme is described for a single-phase power line. The difference scheme proposed is based on the analysis of the properties of the schemes in the space of insufficient coefficients.

Examples of the model problem numerical solutions using the proposed splitting and the difference scheme are given. The results of the numerical calculations shows that the difference scheme allows to reproduce the arising regions of large gradients. It is shown that the difference schemes also allow detecting resonances in such the systems.

Soil as a complex multifunctional open system is one of the most difficult object for modeling. In spite of serious achievements in the soil system modeling, existed models do not reflect all aspects and processes of soil organic matter mineralization and humification. The problems and “hot spots” in the modeling of the dynamics of soil organic matter and biophylous elements were identified on a base of creation and wide implementation of ROMUL and EFIMOD models. The following aspects are discussed: further theoretical background; improving the structure of models; preparation and uncertainty of the initial data; inclusion of all soil biota (microorganisms, micro- and meso-fauna) as factors of humification; impact of soil mineralogy on C and N dynamics; hydro-thermal regime and organic matter distribution in whole soil profile; vertical and horizontal migration of soil organic matter. An effective feedback from modellers to experimentalists is necessary to solve the listed problems.

The possibility of numerical 3D simulation of thrombi formation is considered.

The developed up to now detailed mathematical models describing formation of thrombi and clots include a great number of equations. Being implemented in a CFD code, the detailed mathematical models require essential computer resources for simulation of the thrombi growth in a blood flow. A reasonable alternative way is using reduced mathematical models. Two models based on the reduced mathematical model for the thrombin generation are described in the given paper.

The first model describes growth of a thrombus in a great vessel (artery). The artery flows are essentially unsteady. They are characterized by pulse waves. The blood velocity here is high compared to that in the vein tree. The reduced model for the thrombin generation and the thrombus growth in an artery is relatively simple. The processes accompanying the thrombin generation in arteries are well described by the zero-order approximation.

A vein flow is characterized lower velocity value, lower gradients, and lower shear stresses. In order to simulate the thrombin generation in veins, a more complex system of equations has to be solved. The model must allow for all the non-linear terms in the right-hand sides of the equations.

The simulation is carried out in the industrial software FlowVision.

The performed numerical investigations have shown the suitability of the reduced models for simulation of thrombin generation and thrombus growth. The calculations demonstrate formation of the recirculation zone behind a thrombus. The concentration of thrombin and the mass fraction of activated platelets are maximum here. Formation of such a zone causes slow growth of the thrombus downstream. At the upwind part of the thrombus, the concentration of activated platelets is low, and the upstream thrombus growth is negligible.

When the blood flow variation during a hart cycle is taken into account, the thrombus growth proceeds substantially slower compared to the results obtained under the assumption of constant (averaged over a hard cycle) conditions. Thrombin and activated platelets produced during diastole are quickly carried away by the blood flow during systole. Account of non-Newtonian rheology of blood noticeably affects the results.

This article discusses the contribution of computing resources monitoring system to the work of a distributed computing system. Method of evaluation of this contribution and performance monitoring system based on measures of certainty the state-controlled system is proposed. The application of this methodology in the design and development of local monitoring of the Central Information and Computing Complex, Joint Institute for Nuclear Research is listed.

This is a brief review of the subjects, and an impression of some talks, which were given at the Schools on modelling complex biological systems. Those Schools reflected a logical progress in this way of thinking in our country and provided a place for collective “brain-storming” inspired by prominent scientists of the last century, such as A. A. Lyapunov, N. V. Timofeeff-Ressovsky, A. M. Molchanov. At the Schools, general issues of methodology of mathematical modeling in biology and ecology were raised in the form of heated debates, the fundamental principles for how the structure of matter is organized and how complex biological systems function and evolve were discussed. The Schools served as an important sample of interdisciplinary actions by the scientists of distinct perceptions of the World, or distinct approaches and modes to reach the boundaries of the Unknown, rather than of different specializations. What was bringing together the mathematicians and biologists attending the Schools was the common understanding that the alliance should be fruitful. Reported in the issues of School proceedings, the presentations, discussions, and reflections have not yet lost their relevance so far and might serve as certain guidance for the new generation of scientists.

Many properties of ordinary differential equations systems solutions are determined by the properties of the equations in variations. An ODE system, which includes both the original nonlinear system and the equations in variations, will be called an extended system further. When studying the properties of the Cauchy problem for the systems of ordinary differential equations, the transition to extended systems allows one to study many subtle properties of solutions. For example, the transition to the extended system allows one to increase the order of approximation for numerical methods, gives the approaches to constructing a sensitivity function without using numerical differentiation procedures, allows to use methods of increased convergence order for the inverse problem solution. Authors used the Broyden method belonging to the class of quasi-Newtonian methods. The Rosenbroke method with complex coefficients was used to solve the stiff systems of the ordinary differential equations. In our case, it is equivalent to the second order approximation method for the extended system.

As an example of the proposed approach, several related mathematical models of the blood coagulation process were considered. Based on the analysis of the numerical calculations results, the conclusion was drawn that it is necessary to include a description of the factor XI positive feedback loop in the model equations system. Estimates of some reaction constants based on the numerical inverse problem solution were given.

Effect of factor V release on platelet activation was considered. The modification of the mathematical model allowed to achieve quantitative correspondence in the dynamics of the thrombin production with experimental data for an artificial system. Based on the sensitivity analysis, the hypothesis tested that there is no influence of the lipid membrane composition (the number of sites for various factors of the clotting system, except for thrombin sites) on the dynamics of the process.